Technical Aerodynamics [Third Edition]

Table of contents :
COVER
TITLE
COPYRIGHT
PREFACE TO THIRD EDITION
PREFACE TO SECOND EDITION
PREFACE TO FIRST EDITION
CONTENTS
CHAPTER 1. INTRODUCTION
1:1. TYPES OF AIRCRAFT
1:2. TYPES OF AIRPLANES
1:3. TYPES OF HELICOPTERS
1:4. TYPES OF MISSILES
1:5. PERFORMANCE OF AIRCRAFT
1:6. CONTROL OF AIRCRAFT
1:7. CONSTRUCTION OF PRINCIPAL PARTS OF AIRCRAFT
REVIEW QUESTIONS AND PROBLEMS
CHAPTER 2. FLUID STATICS AND NON-FLOW THERMODYNAMICS
2:1. PROPERTIES OF LIQUIDS AND GASES: DENSITY, VISCOSITY, CONDUCTIVITY, AND COMPRESSIBILITY
2:2. STATICS OF LIQUIDS: MANOMETERS , BAROMETERS
2:3. STATICS OF GASES: PERFECT GAS LAWS
2:4. SPEED OF SOUND IN AIR
2:5. MOIST AIR
2:6. VARIATION OF AIR WITH ALTITUDE: STANDARD AIR
2:7. PRESSURE AND DENSITY ALTITUDES: USE OF AIR CHART
PROBLEMS
CHAPTER 3. FLUID DYNAMICS AND THERMODYNAMICS OF FLOW
3:1. REALMS OF FLUID FLOW
3:2. STEADY-FLOW CONTINUITY EQUATION
3:3. STEADY-FLOW ENERGY EQUATION
3:4. STEADY-FLOW MOMENTUM EQUATION
3:5. APPLICATION OF STEADY-FLOW EQUATIONS
CHAPTER 4. FRICTIONLESS INCOMPRESSIBLE FLOW
4:1. BERNOULLI EQUATION: FLOW IN PIPES AND DUCTS AND BETWEEN STREAMLINES
4:2. MOMENTUM EQUATION: FORCES EXERTED BY JETS
4:3. TWO-DIMENSIONAL FLOW PATTERNS IN PERFECT FLUIDS
4:4. BODY PRESSURE DISTRIBUTION: PITOT TUBES
PROBLEMS
CHAPTER 5. FRICTIONLESS COMPRESSIBLE FLOW
5:1. RANGES OF COMPRESSIBLE FLOW: SUBSONIC, TRANSONIC, SUPERSONIC
5:2. ONE -DIMENSIONAL SUBSONIC COMPRESSIBLE FLOW
5:3. NORMAL SHOCK WAVES
5:4. TWO-DIMENSIONAL AND AXI -SYMMETRIC SUPERSONIC FLOW
PROBLEMS
CHAPTER 6. INCOMPRESSIBLE BOUNDARY- LAYER FLOW
6:1. BOUNDARY-LAYER FLOW
6:2. LAMINAR INCOMPRESSIBLE BOUNDARY LAYER
6:3. TURBULENT INCOMPRESSIBLE BOUNDARY LAYER
6:4. TRANSITION OF INCOMPRESSIBLE BOUNDARY LAYERS
6:5. SKIN FRICTION IN PIPES AND DUCTS
6:6. SEPARATION OF INCOMPRESSIBLE BOUNDARY LAYERS
6:7. INCOMPRESSIBLE BOUNDARY-LAYER FLOW AROUND A CYLINDER
6:8. INCOMPRESSIBLE BOUNDARY-LAYER FLOW AROUND A SPHERE
PROBLEMS
CHAPTER 7. COMPRESSIBLE AND HEAT- CONDUCTING BOUNDARY-LAYER FLOW
7:1. BOUNDARY-LAYER TEMPERATURE NEAR A SURFACE: RECOVERY FACTOR .
7:2. HEAT TRANSFER AND SKIN FRICTION
7:3. LAMINAR COMPRESSIBLE BOUNDARY LAYER
7:4. TURBULENT COMPRESSIBLE BOUNDARY LAYER
7:5. TRANSITION OF COMPRESSIBLE BOUNDARY LAYERS FROM LAMINAR TO TURBULENT
7:6. COMPRESSIBLE FLOW AROUND SPHERES AND CYLINDERS
PROBLEMS
CHAPTER 8. AERODYNAMIC TEST FACILITIES
8:1. FLIGHT TESTS
8:2. MOVING MODEL TESTS
8:3. WIND TUNNEL TYPES
8:4. TRANSONIC AND SUPERSONIC WIND TUNNELS
8:5. WIND TUNNEL BALANCES FOR FORCE TESTS
8:6. OTHER WIND TUNNEL TEST EQUIPMENT
CHAPTER 9. AIRFOILS AND ASPECT RATIO EFFECTS AT LOW SPEEDS
9:1. FORCES ON AIRFOILS; AIRFOIL COEFFICIENTS
9:2. STRAIGHT-LINE PLOTTING OF LOW SPEED AIRFOIL TEST DATA
9:3. MOMENTUM THEORY OF AIRFOILS
9:4. CIRCULATION THEORY OF AIRFOILS
9:5. ASPECT-RATIO CORRECTIONS
9:6. GROUND EFFECT; TUNNEL -WALL CORRECTIONS
9:7. EFFECTS OF CHORDWISE SLOT IN WINGS; INTERACTION OF TWO AIRPLANES FLYING SIDE BY SIDE
CHAPTER 10. AIRFOIL COMPRESSIBILITY EFFECTS
10:1. TWO-DIMENSIONAL AIRFOILS: SUBSONIC COMPRESSIBILITY EFFECTS
10:2. FINITE WINGS: SUBSONIC COMPRESSIBILITY EFFECTS
10:3. TRANSONIC COMPRESSIBILITY EFFECTS
10:4. SUPERSONIC WING CHARACTERISTICS
PROBLEMS
CHAPTER 11. AIRFOIL VISCOSITY EFFECTS
11:1. LOW-SPEED SCALE EFFECTS, WING SECTIONS
11:2. COMBINED HIGH SPEED AND SCALE EFFECTS, WING SECTIONS
11:3. SCALE EFFECTS ON FINITE WINGS
11:4. SPANWISE LOAD DISTRIBUTION
11:5. FLIGHT BOUNDARIES
PROBLEMS
CHAPTER 12. HIGH-LIFT DEVICES
12:1. NEED FOR HIGH-LIFT DEVICES
12:2. TRAILING EDGE FLAPS
12:3. LEADING EDGE SLATS AND SLOTS
12:4. BOUNDARY -LAYER CONTROL
PROBLEMS
CHAPTER 13. AIRFOIL SELECTION
13:1. SYSTEMATIC INVESTIGATIONS AND NUMBERING SYSTEMS
13:2. THE NACA 4-DIGIT GEOMETRIC SYSTEM
13:3. THE NACA 5 -DIGIT GEOMETRIC SYSTEM
13:4. THE NACA 1-SERIES AIRFOILS
13:5. THE NACA 6 -SERIES AIRFOILS
13:6. OTHER NACA SERIES
13:7. EFFECTS OF AIRFOIL GEOMETRY ON LOW-SPEED AERODYNAMIC CHARACTERISTICS
13:8. APPROXIMATE EQUIVALENCE OF MISCELLANEOUS AND NACA SERIES AIRFOILS
13:9. AERODYNAMIC AND STRUCTURAL COMPROMISES
13:10. AIRFOIL SELECTION CRITERIA FOR SUBSONIC AIRPLANES
13:11. AIRFOIL SELECTION CRITERIA FOR SUPERSONIC MISSILES
PROBLEMS
CHAPTER 14. DRAG ESTIMATES AND POWER CALCULATIONS
14:1. METHODS OF ESTIMATING DRAG
14:2. DRAG OF INFINITE CYLINDERS, INCLUDING WINGS
14:3. STREAMLINE BODIES: SUBSONIC
14:4. MISSILE BODIES: SUPERSONIC
14:5. NACELLE-WING COMBINATIONS
14:6. FUSELAGES ; COCKPIT ENCLOSURES
14:7. EXPOSED LANDING GEARS AND OTHER PROTUBERANCES
14:8. DRAG ESTIMATE FOR COMPLETE AIRPLANE
14:9. THRUST AND POWER REQUIRED FOR AIRPLANES IN LEVEL FLIGHT
14:10. GENERAL CHARTS OF THRUST AND POWER REQUIRED FOR LOW-SPEED AIRPLANES
14:11. DRAG ESTIMATES FOR SUPERSONIC VEHICLES
PROBLEMS
CHAPTER 15. AERONAUTICAL POWER PLANTS
15:1. POWER PLANT TYPES
15:2. PISTON ENGINES
15:3. SEA -LEVEL SUPERCHARGERS
15:4. SUPERCHARGED ENGINES
15:5. TURBOPROPS
15:6. TURBOJETS
15:7. RAMJETS
15:8. ROCKETS
15:9. NUCLEAR PROPULSION
PROBLEMS
CHAPTER 16. AIRPLANE PROPELLERS
16:1. PROPELLER CONSTRUCTION AND GEOMETRY
16:2. MOMENTUM THEORY OF PROPELLERS
16:3. SIMPLE BLADE -ELEMENT THEORY OF PROPELLERS
16:4. PROPELLER COEFFICIENTS AND PLOTTING OF DATA
16:5. PROPELLER PROBLEM TYPES AND METHODS OF SOLUTION
16:6. CORRECTION FACTORS FOR PROPELLER CHARACTERISTICS
16:7. STATIC THRUST:SLOW VENICLES AND VERTICAL TAKE-OFF AIRPLANES
16:8. DETAIL-DESIGN CONSIDERATIONS
PROBLEMS
CHAPTER 17. HELICOPTER PERFORMANCE
17:1. DEVELOPMENT OF THE HELICOPTER
17:2. LIMITATIONS OF HELICOPTER THEORY
17:3. HOVERING PERFORMANCE ANALYSIS
17:4. SPEED LIMITATIONS
17:5. POWER REQUIRED FOR LEVEL FLIGHT
17:6. HIGH SPEED AND MAXIMUM CLIMB CHARTS
17:7. AUTOROTATIVE DESCENT OF HELICOPTERS
PROBLEMS
CHAPTER 18. AIRPLANE PERFORMANCE
18:1. SPEED AND CLIMB OF PROPELLER -DRIVEN AIRPLANES
18:2. CEILINGS OF PROPELLER-DRIVEN AIRPLANES
18:3. PERFORMANCE OF PROPELLER- DRIVEN AIRPLANES
18:4. PERFORMANCE OF TURBOJET PROPELLED AIRPLANES
18:5. CRUISING RANGE AND ENDURANCE
18:6. TAKE -OFF CALCULATIONS
18:7. LANDING DISTANCE CALCULATIONS
18:8. GLIDINGAND DIVING
18:9. LEVEL AND GLIDING TURNS
PROBLEMS
CHAPTER 19. CONVERTIPLANES
19:1. TYPES OF CONVERTIPLANES
19:2. ROTATABLE -PROPELLER-AXIS AIRPLANES
19:3. UNLOADED ROTOR HELICOPTERS
19:4. OUTLOOK FOR CONVERTI PLANES .
PROBLEMS
CHAPTER 20. MISSILE PERFORMANCE
20:1. OUTLOOK FOR MISSILES
20:2. PERFORMANCE OF SUPERSONIC AIRCRAFT.
CHAPTER 21. STABILITY AND CONTROL
21:1. STABILITY AND CONTROL CONCEPTS
21:2. AXES , ANGLES , AND COEFFICIENTS
21:3. STATIC LONGITUDINAL STABILITY
21:4. STATIC DIRECTIONAL STABILITY
21:5. LATERAL STABILITY
21:6. CONTROL SURFACE CHARACTERISTICS
21:7. CONTROL AT HIGH SPEED
PROBLEMS
APPENDIX 1. NOTATION, ABBREVIATIONS, AND CONVERSION FACTORS
APPENDIX 2. PROPERTIES OF SOME LIQUIDS AND GASES
APPENDIX 3. PROPERTIES OF AIR
APPENDIX 4. COMPRESSIBLE FLOW CHARTS
APPENDIX 5. WING AND TAIL SURFACE DATA
APPENDIX 6. PARASITE DRAG DATA
APPENDIX 7. POWER PLANT AND PROPELLER DATA
APPENDIX 8. AIRCRAFT DATA
ANSWERS TO PROBLEMS
INDEX

Citation preview

UCS

University of

Michigan Libraries 1817 ARTES SCIENTIA

VERITAS

I 1

1

I

TECHNICAL AERODYNAMICS Third Edition

KARL

D.

WOOD , M.E. ,

Ph.D.

Professor and Head , Department of Aeronautical Engineering University of Colorado

PUBLISHED

BY THE AUTHOR

BY ULRICH'S BOOK STORE , ANN ARBOR, MICHIGAN

DISTRIBUTED

East Engin . Library

TL

TECHNICAL AERODYNAMICS

570

Third Edition

.W88

1955 First

and

Second editions

( consisting

of

16,000 copies )

about

1947 , by the McGraw-Hill Book Company Third edition copyright 1955 by the author .

copyright 1935 ,

All rights thereof

reserved .

, may

This book

not be reproduced

,

in

or

,

Inc.

parts

any form

without permission of the publisher .

The author also serves as Editor of the Prentice -Hall Aeronautical Engineering Series of textbooks , which includes " Fluid Mechanics , " by R. C. Binder ; " Thermodynamics , " by Franklin P. Durham ; " Aircraft Jet Powerplants , " by Franklin P. Durham ; " High Speed Aerodynamics , " by H. W. Sibert ; " Elementary Applied Aerodynamics , " by P. E. Hemke ; and These books " Fundamentals of Aircraft Structures , " by M. V. Barton . are referred to frequently in this text , and the format of this text has been intentionally made as similar to Binder's " Fluid Mechanics " as is possible in a lithoprinted book . This edition is published by the author without objection from Prentice - Hall , Inc. , but they are in no way responsible for details . The author is solely responsible and would appreciate having mistakes or errors called to his attention .

Typewritten by Mrs. Erma R. Tucker - Corona Model 88 typewriter with carbon ribbon , elite and " Secretariat Elite " type , and twenty special Greek symbols quickly replaceable on on Smith

keys number 42 and 43 .

Lithoprinted

ratio

with photographic reduction

4 : 3 by Cushing - Malloy , Inc. Ann Arbor , Michigan

in

of

the

87-15154

PREFACE TO THIRD EDITION

this edition , like that of the two preceding editions , is to provide a course of study for the engineering student ( or a re fresher course for the practicing engineer ) which will help fit him to The object of

the

make

performance ,

in

current importance With

stability

design calculations of the aircraft manufacturing industry .

an objective ,

such

and

aerodynamic

successive

editions

should

reflect the

manpower , distribution of engineering this basis , this third edition reduces the attention paid to light airplanes and seaplanes and increases the attention paid to jet propelled airplanes , jet propelled missiles , and helicopters and

present , and expected near future

activities

.

helicopter

-airplane

On

is almost completely out of propeller the is not , particularly

The biplane

combinations .

picture ,

development

the current but the turbine driven propeller . In the speed spectrum , the techniques of breaking through what was formerly called the " sonic barrier " of " Mach Number

sile

= 1" have been

designers are

now

well established struggling

and

supersonic airplane and

mis

to see how far they can penetrate into

the " thermal barrier " which begins to be formidable at a

Mach

Number

of

about 3 .

With the above increased scope of technical the last edition permissible

ritory

,

is

The development

) .

effort since

principles involved and basic also increased ( in spite of omissions now

the scope of fundamental

data necessary

aerodynamic

aerodynamic

in virgin

engineer continues to work

ter

try to design on the basis of insufficient information , and thus continues to direct the research laboratories , now calling espec and to

ially for

more

in the in the field

information

transonic

field

of mixed subsonic and

in which both the compressibility of air are major factors , and for which no simple scientific analyses are available . It is appropriate here to abstract the definitions of " scientific " and " technical " sometimes attributed to Kettering of General Motors , who supersonic flows and

the viscosity

is

don't understand

it . "

layers

,

and

reported to have said ,

stands

of hot boundary

it

; when

"When

we say a

we say

it is

iii

thing

is

' scientific ' we mean we

' technical ' we mean

nobody

under

PREFACE TO THIRD EDITION

In calling

author accepts Kettering's implication of incomplete understanding as part of the nor the book

" Technical

Aerodynamics , "

the

of the development engineer , but hopes that the areas of approximation reasonable will be properly differentiated from those of mal handicaps

reasonably exact knowledge

the text .

in the design field by " Airplane Design , " 10th Edition ( 1954 ) , distributed by the University Bookstore of Boulder , Colorado ; the 11th edition , scheduled for 1956 , is to be distributed by Ulrich's Book Store of Ann Arbor , Michigan . This text

is

in

supplemented

K. Boulder , Colorado June , 1955 .

iv

D.

WOOD

PREFACE TO SECOND EDITION

Twelve years ago the

of the

cause

this edition

years ,

by the

Not

field

is

45 lessons ,

this

book

The student

is

assumed

instruction in

and mathematics ,

Design , " 8th

in

He may

one

understanding of

This edition Colorado , who

is

dedicated

in

covered

to the

asked the questions and

-- especially

,

have taken courses

to Mrs.

Louise

Cornell ,

Purdue

and

the author help them find the

the preliminary H.

the

1.

students at

made

in fluid

necessarily

these subjects needed for Chapter

col

physics

before under

to the University of Colorado V - 12 students

fered with the author through thanks are due

of

in

background

good

these courses are not

the fundamentals

this text are

two such courses .

course in calculus

profitably also

and thermodynamics , though

prerequisite , since

for

four sixteen - week terms of

to have completed at least

college

;

first edi

Whereas the

intended to supply material

including

distri

Edition ,

three - credit course of about

a single

engineering and to have a

study .

this

mechanics

answers

" Airplane

has also been extended .

tion was intended to be covered

taking

the last twelve

the University Bookstore of Boulder , Colorado . only has the fund of technical information expanded

instruction in this

lege

in this field in

Be

first edition only in the chapter head text is supplemented in the design field

lithographed text

author's

buted by

This

.

was published .

the

resembles

topics covered

ings and

first edition of this title

important developments

many

second

edition .

Beattie for assistance

in

who

suf

Particular

preparation of

the manuscript .

K. Boulder , Colorado June , 1947

.


1 is due to the high pressures on the front of the body . The base pressure drag , due to the dead - air region seen

tion .

Since skin

in the firing

drag

of such blunt objects

ranges

7 :7.

in Fig . 7:19, makes a minor additional contribu friction and heat transfer are also only minor factors

fairly

are

CALCULATION PROCEDURE

friction for thin

The skin

,

consistent FOR

wedge

if

reasonable assumptions

surface roughness

.

ESTIMATES OF SUPERSONIC

- shaped airfoils

sharp conical noses can be estimated

ter

the data obtained in wind tunnels and

can

SKIN FRICTION .

for cylinders with from the data in the foregoing chap be made as to free - stream turbulence , ,

and

surface temperature , and surface Mach number , so that extent of the the laminar boundary - layer can be estimated and the drag ,

distributed properly between the laminar and turbulent boundary layers . On the other hand , for circular arc airfoils , and for ogival noses involv ing substantial pressure gradients , the estimation is considerably in doubt , chiefly because of the uncertainty of the effect of stream -wise pressure gradient

,

for

which

no

data are given

expansion , as on a double - wedge

in this chapter . Beyond a corner airfoil or a cone - cylinder junction , ex

that the corner usually serves as a trip to initiate a turbulent boundary layer one does not already exist . An example of perience has

shown

if

the calculation of skin

friction

on a double

- wedge airfoil follows :

Example . For the 100 semi - angle wedge airfoil of Fig . 5 : 5 , for which surface pressures and velocities were calculated in Chapter 5 , estimate the skin friction and initial rate of heat transfer per foot of span the airfoil chord is 60 in . , M1 = 2.5 , and the air is standard sea - level at point ( ) 1 .

if

Solution . as calculated

(1 ) ,

Assume

in

air

Chapter

Hoerner , Sighard F.

conditions

in

the free -stream near the surfaces

5 , namely :

" Aerodynamic

Drag . "

Published by author ,

1951 .

TECHNICAL AERODYNAMICS

7-18

Front :

M2

=

2.09 ;

T2 = 623 °R ;

M1

M3

M2 Tw

= 519

/

; P2 = 3940 lb ft2 P2 = 0.00369 slug = 1226 a2 sec ; M3 = 2.95 ; T3 = 425 °R ;

ft/

°R

Rear :

/

P3 = 1142 lb ft2 ; = 0.00143 slug P3 = 1013 / sec . a3

30 "

30"

ft

First

/ft3 ;

/ft3 ;

estimate the transition point location : This requires calculation of free - stream Reynolds numbers near the surfaces . For the front faces , with T2 = 623 ° R ( 163 ° F ) , read in Fig . A1 : 1 or A1 : 2 , H2 = 0.43 / 106 lb sec / ft2 ; calculate v2 = H2 / P2 = 0.43 / 106 x 0.00369 = 0.000117 ft2/ sec ; calculate V2 = M2a2 = 2.09 x 1226 =€ 2560 ft / sec ; calculate_Rex /x = V U = 2560 0.000117 = 22 x 106. Hence on the front face Rex / 106 = 22x , where x is the distance in feet from the lead ing edge . In Fig . 7:16 , read for M 2 and Tw T1≈ 1 ( " experimental trend " ) a transition region from Rex 106 = 1.3 to 2.5 . Since this region equals 22x as calculated above , solve for x = ( 1.3 to 2.5 ) 12/22 = ( 7 to 14 ) in . from the leading edge . For the rear faces , with T3 = 425° R ( -35 ° F ) , read in Fig . 41 : 1 or A1 : 2 , = = = 0.32 106 x 0.00143 = из 0.32 106 1b sec / ft2 ; calculate v3 13/03 0.000224 ft2 / sec ; calculate V3 = M3a3 = 2.95 x 1013 = 2990 ft sec ; calcu late Rex x = V U = 2990 0.000224 = 13.3 x 106. Hence Rex 106 = 13.3x on rear faces . Next estimate the skin friction coefficients and skin friction : For the laminar boundary layer on the two front faces , read in Fig . , at Rextr = 1.3x 106 as estimated above 20f 7 : 6 , interpolating for = 0.0023 , and consider that this is the mean skin friction coefficient for the area 7/12 ft2 per foot of span with a value of 92 = P2V22 2 = 0.00369 x 25602/2 = 12,100 lb/ ft2 . Calculate D2 Lam = 0.0023 ( 7/12 ) 12,100 = 16.2 lb. For the turbulent boundary layer on the front faces , the practice is not well established , but a good estimate is obtained it is considered that the turbulent boundary layer starts at the beginning of transition . = Hence x = 30 in . 7 in . 23 in . = 23/12 ft and ReL Turb / 106 = 22 ( 23/12 ) = 42. Read in Fig . 6 : 5 or 7 : 6 for Re = 42 an incompressible value of 2Cf = 0.0048 . In Fig . 7 : 7 , on the line labeled Tw = Too ( T1 ) , read a com pressibility correction factor of about 0.9 for M = 2. With the same value of q as before , calculate D2 Turb = 0.0048 ( 23/12 ) 12,100 x 0.9 =

/

/

/

/

/

/

/

/

/

/

/

M2

/

if

100

lbs . For the rear faces , the

layer is always turbulent , as the to start turbulence it did not already exist . The Reynolds for the turbulent boundary layer may be cal culated as started at the corner ( though the practice is not well established ) . Hence ReL3 106 = 13.3 ( 30/12 ) = 33. For this value of Re in Fig . 6 : 5 or 7 : 6 read an incompressible value of 2Cf = 0.0050 and in Fig . 7 : 7 read for the " cold model " condition [ since Tr3 = 425 ( 1 + 0.2 x 2.952 x 0.88 ) = 10800R compared with Tw = 5190R ] a compressibility cor rection factor of about 0.83 . Calculate 93 = P3732 2 = 0.00143 x 29902/2 = 6400 lb ft2 and D3 Turb = 0.0050 ( 30/12 ) 6400 x 0.83 = 66 lbs . The total skin friction drag per foot of span is thus , to the nearest lb : = = 16 + 100 + 66 = 182 lbs . D2 Lam D2 Turb + D3 Turb Dskin friction This is one of the answers called for .

if it

/

boundary

if

trip "

sharp corner serves as a

" number

/

/

(

COMPRESSIBLE AND HEAT

- CONDUCTING

BOUNDARY

-LAYER

7-19

FLOW

To estimate the heat transfer , use equation ( 7:11 ) and calculate the Stanton number corresponding to each of the three skin friction coeffi cients estimated above and tabulate the results as shown below . Use Pr St Re Pr = hcL ke , and evaluate kc at free- stream tem = 0.715 and Nu perature from kc = Hcp / Pr .

/

Surface S

B.L.

No. 2

2 3

St

Cf

.58 Lam .0012 1.92 Turb .0021 2.50 Turb .0021

.00075 .0013 .0013

Re 106

1.3

Nu

Too

103

R

0.7

42

39

32

29.7

L

kc 106

623 .43 623 .43 425 .32

106

ft .

hc 103

4.65 .58 5.6 4.65 1.9 96 3.45 2.5 41

Total rate of heat addition

Tr Tr- Tw

R

1090 1110 1080

/

, B sec

Q

2 109 560 57 570

590

168

foregoing heat transfer calculations are based on mean coefficients for the three areas considered ; more accurate estimates are obtainable from local coefficients available in the references cited . Note that heat is being added to various parts of the wing structure at widely varying rates , so that only at the start of a flight can the body surface temper ature be considered uniform . Major structural problems arise from the temperature gradients as well as the high temperatures .

The

PROBLEMS 7: 1. shown

For the wedge

for which

airfoil

surface pres

sures and free - stream tem peratures were calculated in Problem 5: 3 for a = 0 , M1 = 3, and standard sea - level air at point ( ) 1 , assume the wing surface is at a temperature

M1

M2

calculate ( estimating necessary ) the follow 2'0" 2'0" ing : ( a )the transition point location , (b ) the skin tion per foot of span for each surface , and ( c ) the rate of heat transfer from the air to the wing per foot of span for each surface , ( d ) the rate of temperature rise at points 6 in . and 36 in . from the leading edge the wing is hollow with a thin skin of aluminum alloy 24S of thickness 0.065 in . and specific heat 0.23 , neglecting heat transferred from the skin to the internal structure , and neglecting heat transferred between adjacent chordwise stations on the wing . 7 : 2 . Repeat Problem 7 : 1 for the cone - cylinder combination solved in Problem 5 : 4 , for a cone length of 10 ft 0 in . T1 and

where

fric

if

illustrate one step of the series of numer involved in calculating the time - history of the motions is evident that sub and temperatures of a given supersonic missile . stantial progress in missile path and temperature calculation requires a tremendous number of calculations , at present considered feasible only digital computing machines . on automatically programmed NOTE :

The above problems

ical calculations

It

CHAPTER AERODYNAMIC

8

TEST FACILITIES

TESTS . An aircraft (airplane , missile , or helicopter ) is for transporting persons or things rapidly through the air from place to place under the control of a pilot , human or electro - mechanical . The aircraft flies at an altitude or sequence of altitudes determined by FLIGHT

8: 1.

a vehicle

the

pilot .

Measures

its

of

it will travel it can fly , and

merit are the speed at which

chosen altitude , the range of altitudes at which the time required to get from one altitude to another . Quantities

at the

tomarily measured in and

this

connection are :

ceiling (maximum altitude at which the aircraft

can

fly ) .

and landing times , distances , and speeds are also important factors

uting to

the merit of the aircraft .

calculate the mance

in

Manufacturers of aircraft

,

- off contrib

Take

usually

of performance and often guarantee the perfor of a financial penalty for failure to meet the calculated

above items

terms

performance or a

financial

bonus

The purpose of conducting

to establish

cus

level high speed , rate of climb

compliance

for

exceeding

flight tests

with performance

the guaranteed

on performance guarantees , and

is

performance .

normally ( 1 )

( 2 ) to determine

information necessary to permit effective use of the aircraft . test for level high speed at altitudes near the ground can nor

performance

A flight

mally be run by having observers on the ground keeping

continuous

on the location of the aircraft at time intervals and culating speed from the ratio of distance interval to time interval . ground tracking may be done visually ( photographically ) as in Fig . predetermined

Fig .

8: 1 .

Photographer tracking Courtesy NACA . .

aircraft flight

8-1

tally

cal Such 8 :1,

Fig . 8 : 2 . Ground radar tracking aircraft flight . Courtesy NACA .

AERODYNAMIC

The

of

level

change

flight

of

of altitude condition

.

Fig

is ,

16

14

12

10

130 mph

Observed rate of climb for various constant air speeds From Reed JAS February 1941.

(

indication

unreliable

rate

Time min .

an

17,000

.

a

punctured barometer , and gives

.

indicator " consists of

climb

mph 17,500 120

8

The

,

.

160mph mph 140

)

ditions

6

level con usual " rate of

under exactly

18,000

2

fly

it is difficult to

18,500

3 .

altitudes

,ft

,

bar

At higher

altimeter .

for missiles

flight

are normally measured by ometric

indispensable

19,000

Pressurealtitude

Altitudes of aircraft

is

This procedure

8 : 2.

8-2

8 :

in Fig .

which carry no observer .

,

or by radar as

TEST FACILITIES

in many cases , determined by plotting full throttle rate of climb against

horizontal

speed

determining the intercept

and

A for zero rate of climb . flight plan for testing climb performance is sketched in Fig . 8: 3.

The

best rate

principle

is

of climb

that the

may be

termined by a series

de

of short ,

steady climbs at predetermined

air speeds . Full throttle climb

is

usually determined

at

sev

eral altitudes and a sufficient number

of air

that the best has

been

speeds to insure

climbing speed

bracketed , and that

.

.

8 : 4 .

.

Recording equipment being Fig accurately formed curve of installed in test airplane by NACA scientists rate of climb against air speed Courtesy NACA is obtained in the region of best climbing speed . Accurate flight testing requires not only good weather but also , as 1 ) (1 ) complete and accurate calibrated instrumentation stated by Allen : (

an

and Stability . " " Flight Testing for Performance ( Allen and his crew were killed a short time later while flight - testing a military aircraft for Boeing Airplane Company ; have since been named in honor of the Boeing Aeronautical Laboratories

( 1 )Allen ,

Edmund

JAS , January , 1943.

test - pilot Allen . )

T.

TECHNICAL AERODYNAMICS

8-3 so that

all

variables

(2 ) a technique of flying accur

can be measured ,

so that what is measured will be representative of the true optimum performance of the aircraft , and ( 3 ) a mathematically correct method of

ately

interpreting the flight - test

data .

A major step in the development of

flight - test

accuracy comparable with

of techniques for automatic re airplanes helicopters In or this is usually done by

wind tunnel accuracy was the development

cording of

all

data .

collecting the instruments in a panel or by motion picture camera . This device stallation of

is

such equipment

shown

box where they can be photographed

is

as a photorecorder

known

in Fig . which

;

in

In missile tests , in

8: 4 .

photographic records may be landing , instruments are

damaged on

used which

to

radio

send

their readings by

ground -based recorders .

This type of instrumentation

is

in

as telemetering . A model strumented with telemetering equip

known

ment

is

shown

in Fig .

8: 5.

Instrumentation for flight test ing usually includes

for

instruments

measuring the pressure and

perature of the

air , the

ten

vertical

horizontal components of velo city of the airplane , and the thrust of the propeller or jet power plant . and

Such instruments must be accurately

Fig .

8: 5 .

Drop -test model

instrumentation

.

Courtesy

gravity of the airplane

with NACA .

calibrated to eliminate instrument error . The weight and center of

must also be accurately

recorded since the weight

varies in flight as fuel is consumed . A continuous check on the weight of fuel in the airplane is required for accurate weight calculations . Propeller or jet engine thrust is extremely difficult to measure accur

ately

and

is

The

air - speed

can be done only meter may

air flow , fuel flow , and motor tied in with similar measurements

accordingly often derived from

or rotor rpm measurements , which can be made on a test stand on the ground . meter must be

in flight ,

particularly carefully calibrated

as a wind tunnel calibration of an

differ substantially

from that

of the

same

equipment

.

This

air- speed in flight

8-4

TEST FACILITIES

AERODYNAMIC

effect of the location of the pitot head relative to the airplane wing or body . Air - speed meters are usually calibrated by runs

because of the

in

is

In

which the time

measured

Wind effects must be allowed for by running

estimating the performance of a type of

previously

results

for

a given distance

of in both directions and proper corrections for air density included in the plot of the cali bration . A procedure for planning airplane flight tests so as to check conventional performance calculations is outlined at the end of Chapter 18 . over a speed course

flight .

flown , the most reliable procedure

on the most

aircraft for which

aircraft different from any is to use the flight test

nearly similar

flight - test

data

are available , and to estimate ,

on

the basis of other aerodynamic data , the effect of changes in design on changes

in

performance .

For aircraft differing widely from any previously flown , it is usually necessary to supplement mation

with tests

this infor

on scale models

of

the proposed new aircraft , including an

estimate of the effect of

scale of the model and of the ence between the model

the

differ

test condi

tions and the flight - test conditions

.

Models are constructed as accurately

to scale

as shop conditions

permit ,

ef

with proper consideration of the fect of accuracy of model construc

tion and

on cost of the test program , provision is made for moving the

relative to a body of air or moving the air relative to the model . model

8:2.

MOVING MODEL TESTS .

Models

Fig .

have been tested by dropping from a

great height

facilities .

;

the

Eiffel

Tower

More recently

in Paris is

drop - tests

8:6 .

Research

one

model on rocket

Courtesy

NACA .

of the earliest

drop

launcher

.

- test

from airplanes or balloons . Models have also been mounted on automobiles or airplanes or on a whirling arm. For high speed tests models are sometimes shot from have

been made

TECHNICAL AERODYNAMICS

8-5 guns or propelled

by rockets and tracked by

instrumented drop - test model model (a

"bird " )

is

shown

is

on a rocket launcher

of forces

The measurement

A typical

radar or camera .

in Fig .

typical free - flight

8 : 5; a

in Fig .

shown

is

on moving models

8:6.

inherently

inaccurate

,

either on account of the unsteadiness of the motion and poorly controlled conditions , as with models mounted on airplanes or automobiles , or because the forces can be only be

inferred from

flight

Most accurate force measurements can be

models .

stationary

model and moving

as a wind tunnel

tions

partially measured directly , and some forces must in flight path , as in the case of drop or free

changes

around

,

air- stream ,

but since no

and

this type of

wind tunnel can duplicate the

full - scale , free - flying aircraft

tial error in interpreting the flight characteristics . Hence ,

obtained with a

wind tunnel

there

,

is known

apparatus

is

always

test data in

air condi substan of free

a

terms

both types of measurements

large

may have

errors but of different sorts . The most authentic predictions are made by using the results of both moving - model and moving - air - stream types of tests

when

available .

the order of

Much

time

and

fifty

effort in the last

billions of man -hours ) have been devoted aircraft by the world's sovereign

to

years (of

flight - testing

nations as part of a program to develop weapons to fight

and model - testing of

wars , to determine

if

tions , 8 : 3.

any ,

which

shall

WIND

na

of the

endure .

Hun

TYPES .

TUNNEL

dreds of wind tunnels have been

built

air

past

for the a model

of

purpose

while

on the model .

moving

making One

measurements

of the most com

prehensive surveys of the

current

status of the world's wind tunnels is given by Pope , ( 1 ) and abstracts from Pope's summary of available wind tunnel facilities are given in Tables 8 : 1 and 8 : 2 . The exterior view of

Fig .

8:7.

tunnel at

Low Ames

( 1 ) Pope ,

- turbulence

pressure Laboratory of NACA .

Allen .

" Wind Tunnel

is

shown

a

typical

in Fig .

NACA wind

section of a similar

Testing

."

Second

tunnel

8 : 7 , and the cross NACA

tunnel

Edition . Wiley

is

, 1954 .

TEST FACILITIES

AERODYNAMIC

8-6 splitter vanes

Continuous

Drive motor

1

Propeller

Countervanes

Air

-

stream direction

-

Pressure gradient control slots

ANIU

Guide vanes .

Cooling coils

Outer shell of test chamber

Blower

-

-60 mesh screen

Air lock

-

30 mesh turbulence reducing screens

canopy

Observation

NACA

Test section

Langley two dimensional low turbulence pressure Courtesy NACA

-

tunnel

.

.

The

-

Fig . 8 : 8 .

-

:8 9

a

a

,

though

in

few wind tunnels the return flow is undirected in the surrounding building or neigh

tunnel

is

less efficient

circuit

-

closed

.

Some

.

in Fig

as those shown

all of

tunnels because

open

circuit

tunnel

An

does not require the cooling

but

:8 8

.

such

as an

known

.

a

is

Such

circuit tunnel

borhood

shown

to the random conditions

-

left

is

wind tunnel

,

,

another point being

and

a

.

through

a

air flows

of another

are typical of current practice in wind in that closed circuit is provided in which the test section at one point and fan or propeller at

8 : 8

.

: 9 .

.

construction

tunnel

The cross section

Figs

8

in Fig

8 : 8 .

in Fig

shown

open

coils

sort of cooling is necessary on

most

the energy supplied by the motor to

Direction of flow

Sloping ceiling

'

80

Screens

'

12

19

'

cone

Settling chamber

Entrance section

NACA

4

Longitudinal cross section of the foot wind tunnel National Bureau of Standards Courtesy NACA .

.

-

-

9 .

8 :

.

12

'

Exit

Test section Fig

25

JOE

.

!

'.

20

'

112

Upper return duct

of the

S.

# Rect

8x10

1.1D

Round

9

70 96

96

70 96

85.2

Rect Rect Rect Rect Rect Rect

7x10 8x12 8x12 7x10 8x12 7.8x11

8

U

..

U.

.

) (

Round

1.09B 1.0D

325

| 165

1

est

314

1.25B

111

1+

1+

1 1 1

10

200 160

250

0.835 1.255 2.0D

125

0.25

1

1.0B

250 100

1 4 1 1 1

78.5

59 45

Ellip Octa

.. . . .. 10x7.5

150

250

11

1.5D

0.8D

78.5 63.5

Round

10

1.3B 1.3B

... 80 80

70 200 180

LAAT 1 1 1 1

2.5

1.2

3.6

5.5 .8

.7

4.2 1.2

0.7

0.02

1.12 0.1

3.3 2.5

3.2

5.5 1.6

2.5

1.2

0.15 0.15

0.35 0.7 0.3

0.2

3.0 1.0

1.275 2.25

2.25

1.5

0.25

1.2

0.375 2.0

0.8

2.52 0.2 0.5 1.0 2.5 0.02

6.5 3.8

7.0

1.0

7.0

3.5 6.2

3.7 3.5 1.0

3.56

4.0

0.3 4.0

3.5

1.6 40.0 1.1

6.8 8.5

36.0 0.075

2.84 4.6

6.8 18.0

8.0

1.4

2.3

E.R.

1.6

0.9

0.02

0.05 0.6 1.6

2.0

0.02 1.4 1.1

10.2 8.0

2.5

103

Max

turb_hp_

Min

1.5 10

1.8

1

Acft

2.5B

Rect Rect

6.33 8x8 8x10

300 425 120

1 1

4

24 Consolidated Vultee 25 Grumman Acft 26 Lockheed Acft.Co. 27 North American Acft 28 Northrop Aviation

1.03

64

Round Round

11

21 2

19 Georgia Inst of Tech 20 M.I.T Wright Bros. 21 of Michigan 22 New York 23 of Washington

3.6D

19.6 314 126

Round

| | . . . .| . | |

20

250 100

0.27

111

17 DTMB No.2 Navy and Industries Universities 18 Calif Inst of Tech

Ellip Octa

120 500 300

CARL

Field

4.2D

70

2520 14.4

Rect

7x10 40x80 4.5

Rect

Cleveland

2.3 10

120

1 1 1 1 1 1 1 1

Wright

0.93 2.0D 1.4B

1410 314.2

Ellip Round

30x60 20

7x10

360 300

350 76

Lab

Max

3

13 WADC Wright Field 14 Wash.Navy Yard No.1 15 Wash Navy Yard No.2 16 DTMB No.1 Navy

3.7D 1.5B

36 70

6x6

5

Rect Rect

Lewis 45 260

mph Min

Max

Reft 106

33-5321 .ya 6

12 WADC

D.C.

(1

U.

) ) )C( ) A( (

A

S.

scale

)L( )

Altitude Ames 7x10 10 Ames full scale 11 Nat Bur Stds Armed Services

full

# 1

High

7x10

Langley

)L(

Stability Langley

1.5D 1.0h

is

0.75B

.. 22.5 24

3x7.5 4x6

284

19.6

1955

Pressure atm

0111

U.

)) . . -. . ( ( -. ,, . . . . . ) U). ) ) ) ) ) )L( ) ) ) ) ) ) ) ) ) ) ) ) )1( )2( )3( )4( )5( )6( )7( )8( )9( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (

LTT

,.)L( )L L ( ,. (1 )L( )L( - . .

Press

)A(

Dim

Round Rect

Calif Round

ft

vel

IN

1 1

Vertical

5 19

Lab

,. .

Pressure

Ames

.;

ft

is

:

)C( 4

Two

.;

sq

Length

USE Max

. .. , ..

19

Va

.

Langley Lab density

1 8

is

Shape

Area

IN

% 9

Variable

ft

Size

TUNNELS

.

N.A.C.A.

Tunnel

WIND Section

.

and

Test

SOME LOW SPEED

.

Agency

TABLE

8-7 TECHNICAL AERODYNAMICS

1 11

.

.U) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )1()2( )3( )4( )5( )6( )7( )8( )9( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (

88

Lab

6

Transonic

GDF

PWT

19 AEDC

20 AEDC

18 NACA 6x8

21

Supersonic

BuOrd

Daingerfield

Oaks

Mass Minn

Tex

Md White

Tenn

Md

Conn

8.5x12 8.5x12 8x12

102

Rect

Rect

Rect Rect

1.3x1.7 1.3x1.4 1.6x2.3

,

,

1.5x2 1x1

0.8x1

Rect Rect

Rect

11

5.0

to to

2.5 3.0 4.0

to to to to

3.7 0.75

1

3

8.0

4.3

to

5.0 4.4

1.8 to

to to

5.0 4.5 2.2 2.0

to to

0-0.95

2.0D

0.25 0.2

2.0 4.0

10.0

4.0

16.0

13.0

100.0 216.0

50.0 100.0

10.0

83.0

54.0 7.0

45.0

0.350 100.0 14.0 0-1.2 0-1.2 0-1.2

0-1.24 0.8-1.6

27.0 40.0 2.0

16.0 25.0 11.0 60.0 200.0 0.12

hp 103

0-0.95 0-1.22

1.5B 1.16B

1.25B

2.0D

Max

Max

0-1.5

to

1.8

256 2.1

Rect Rect

6x8 3.3x3.3 16x16

Rect

1x3 6x6

16

36 48

Rect

2x2

102 96

Rect Rect

Rect

4x4

Rect Rect Octa

... . . . . . .. . . . . . . 43

.. ., ,

24 JPL 12 in Pasadena Calif 25 MIT Naval Tunnel Cambridge 26 of Minnesota Rosemount

Navy

Army BuOrd Aberdeen Lab 22 Naval Ordnance

Tullahoma

#

23 Universities

Va

Va

Calif Ames Lab Calif Ames Lab Ohio LFPL Cleveland Tenn Tullahoma

#

Supersonic

ft

ft

Field Field

Calif

256

78.5 0.2

Round Round Rect

121 201

Rect Round

1/6

Min

Pressure atm

TEST FACILITIES

16 NACA 1x3 17 NACA 6x6

Langley Langley

Co

ft ft ft

Buffalo

Pasadena

Y.

8

14 NACA 4x4 15 NACA 2x2

op

8x12

U.

Lab

Wash Seattle 8x12 12 Boeing 8ft East Hartford Aircraft 13 United and Armed Services S. Government

Calif

Aero

N.

Southern

0.5 16x16

10

11x11 16

0-0.97 0-1.1

113 201

Round Round 1.5D

0-1.3

0-1.2

Range

No.

Mach

64

1.5D

Length

1955

Poly Rect

.

11

10 Cornell

S.

Ohio Tenn

U.

WADC in Transonic Dayton Tullahoma AEDC PWT Transonic and Industries Universities

ft

Ohio

Calif

8x8 12 16

Area

.

Dayton

Ames

Va

., .

Langley Field Va Calif Ames Lab

Va

8

Field

Shape

IN

6

WADC 10

Services

ft

Size

..

NACA 16 NACA 11 NACA 16

Armed

Langley Field Transonic Transonic Pres Langley Calif Ames Lab

and

Location

Test

USE

IN Section

TUNNELS

.

ft ft ft ft ft

ft

ft

and

. . . . , , . , , . , .. , , . , , . ,. . , . . , . , , ,. . ,. . , ,. , ,1 , . ,. ,. , , , , , , , , . , . , , , ,1, , , , , , "A " , .. . . . . . .

Tunnel

WIND

. .

NACA NACA NACA 12

. :

Government

2 8

S.

AND SUPERSONIC

.

U.

SOME TRANSONIC

.

Agency

TABLE

. AERODYNAMIC

8-8

,,

TECHNICAL AERODYNAMICS

8-9 the propeller

is

the motor

is

air

started the

is

dissipation

delivered in the form of heat to the

,

coils

either cooling

and

or air

test section is usually the smallest area in the circuit

The

followed

by a gradual

settling

chamber , which

all

expansion

is

the

ual as

circuit

around the

way

and

is

to the

followed by a comparatively short contraction

or entrance section ahead of the throat .

The expansion

is

made as

decreasing velocity

permits because the region of

economy

after

To avoid excessive equilib interchange must be provided .

equal to the energy supplied .

rium temperatures

air- stream

continues to rise until the heat

temperature

grad

is

one

of increasing pressure and "unfavorable " pressure gradient as regards the separation and boundary - layer development . Since the pressure inside the throughout

tunnel varies

is at

circuit ,

atmospheric

or

done by leaving a narrow

gap

that

some

This

is

In

point

the

a few low - speed wind tunnels the

the tunnel

must be so constructed other predeterminable pressure , the tunnel circuit at that point .

some

in

test section is

a point

of atmos In tunnels with air - exchange cooling , the atmospheric pressure point is at one of the large sections , resulting in below atmos pheric pressure at the test section . Some tunnels , like Fig . 8 : 8 , have made

pheric pressure .

provision

all

for maintaining

increase the

air

density

and

sections at a high pressure

if

desired to

number of the tests . for maintaining below atmospheric pres been designed for a small fraction of at

therefore

the Reynolds

Such tunnels often have provision

all

sureat

mospheric

points and

some have

pressure at the test section

This permits higher speeds for a

.

given motor power and higher Mach numbers .

for a pressure range from

been designed

providing high Reynolds

number

one

Many of the newer tunnels have

- quarter to four

atmospheres ,

at the high pressure and high

Mach

number

at the low pressure .

principal classification

The

of

wind

tunnels

is

according to

maximum

thirty

section . Table 8 : 1lists about wind tunnels designated as low- speed wind tunnels , and nearly all of them have a maximum speed through the test

speed through the test

lists

nearly

termine

of

section of less than

400

miles per hour

an equal number of higher speed wind

compressibility

or

Mach

number

speeds of over 400 miles per hour

miles per hour

effects

Table

8:2

tunnels intended to

de

, and

all of

.

them

are capable

though none are capable of over 2,000

limitations to be discussed later . In fact , there is no expectation of obtaining test speeds over 2,500 miles per hour except in free flight , regardless of the Mach number attained . on account of temperature

TEST FACILITIES

AERODYNAMIC

8-10

the test section size and the maximum speed obtainable it as well as the maximum and minimum pressure obtainable at the test section for pressurized tunnels . Values are also given of the maxiTable

8 : 1 shows

through

,

mum Reynolds imum

obtainable per foot of reference length

number

turbulence obtainable with existing

free -flight

ally in

Reynolds

screen

fast airplane

number of a

the range from ten to twenty million

,

tion of Table 8 : 1 that none of these low - speed of duplicating full - scale free - flight Reynolds pressurized tunnels can closely approach it .

and the

,

installations

.

min

Since the

based on wing chord

is usu

it is

evident from

inspec

wind

tunnels are

capable

numbers , though some

of the that only a very

Note also

few of the wind tunnels provide an air stream of turbulence less than 0.1 % indicated in Fig . 6 : 6 as necessary to get away from major turbulence

fects on skin friction .

Table

8:1

lists

also

ef

the

maximum horsepower

nec

essary to drive the wind tunnel motor expressed in thousands of horsepower and the energy ratio calculated from the equation E. R. =

which

-

is

in

the ratio of the energy Note

in

Table

the fan

is

mounted as

P AtVt3 1,100

,

(8 : 1 )

Bhp

the jet to the energy supplied by the

that the values of energy ratio given for the typical wind tunnels listed run from 1.0 to 8.5 . In general , a high energy ratio is a measure of the excellence of the wind tunnel design since high energy ratio means low power for a given throat speed and size . drive motor .

In general ,

8 :1

far

from the throat

turbances due to the fan are propogated

installation is seen in Fig shown in . 8 : 9 has the fan too

Such an

The major

the skin

circuit is head loss

with fixed

made up

in

by

each part

area

at

The fan efficiency

well

[

head

the tunnel

it is

/

is

for best results .

wind tunnel

/

=

k

=

APf

=

in

the

that

closed

disc .

The

that part

;

(8 : 2 )

kat throat

velocity at throat , ft/ sec pressure loss coefficient

is defined

to v2

fan

is

also true that

= pv2 2 = dynamic pressure at

Vt

as downstream .

= P + (pV2 2 ) ] around

proportional

dis

The older tunnel

8:8.

rise in pressure APf across the

a

of

ratios

as

near to the test section

in total

loss

upstream

sketch of Fig .

feature of a closed -circuit

aerodynamic

friction

the

as possible , as

by

TECHNICAL AERODYNAMICS

8-11

QAPf 550 Bhp

M₤

of air flowing

where Q = quantity

properly designed value of

8 k (E. R. )

circuit in ft2 /sec .

around the

fan ʼnf can usually be

(8 : 3 )

this

about 0.8 and assuming

made

for the wind

can be calculated

nf , pressure drop

With a

coefficient k tunnels listed in Table 8 : 1 from the values of energy ratio there given . Wind tunnels must be expensive to give accurate results . A study of

the cost of

the wind tunnels listed

in Table

8 : 1 shows

that the tunnel

cost per square foot of throat area , including housing , balances

trols , the

in

expressed

tunnel throat

maximum

ing the results to

of the

number

error

tests ,

(mph VAt large

8 :4 .

dollars is

1955

TRANSONIC

Reynolds

to

requires large expense

AND SUPERSONIC

WIND

pressure

rise

The pressure

and replacing and

cities in

be sonic

the expanding

a " bump "

in

surface of the

building

corresponding to

is

small

;

small

Many

in

subsonic wind

tun

parts of the tunnel by

Chapters 3 and 5 show

in

about twice the test section and supersonic

,

Some

.

subsonic wind

velo tun

test section consisting giving local velocities near the a new

Obviously , this can only be

M = 1.

some

the settling chamber . Also obviously

will

is

region beyond the throat

done with tunnels designed to stand

ocity

the Reynolds

TUNNELS .

developed

the subsonic test section , bump

if

velocity at the throat

nels have been run supersonic by

of

large

(mph VAT )

the motor with one adequate to drive the fan .

flow relationships

will

is

correct

the fan with one designed to give greater

that when the settling chamber pressure pressure there

con

.

nels can be redesigned to give supersonic flow the simple expedient of replacing

, and

where mph

The error in

is

number

proportional

mph² ) ,

+ 0.1

$ ( 500

speed in miles per hour .

full - scale which is )

about

appreciable internal pressure

, a smooth shock

- free

supersonic

in

vel

not normally be

obtained in the expanding area downstream of the throat unless it was specially designed for such conditions . Table 8 : 2 lists a number of transonic and supersonic wind tunnels cur

rently in operation

.

The transonic

tunnels are , for the most part

,

over

speeded and redesigned subsonic wind tunnels . The supersonic wind tunnels have

usually been

designed

for

a

particular

Mach number

or with interchange

able or adjustable test section walls for a range of Mach numbers . The design range of Mach numbers is specified in the table , as well as the

size

and shape

of the test section , the

pressures and the

maximum

horsepower

minimum

required

.

and maximum Because

of

test section the tremendous

amount

of

tunnels

, most

8-12

TEST FACILITIES

AERODYNAMIC

for continuous operation of large supersonic wind supersonic tunnels are either small or operate intermittently .

power needed

The most rudimentary form of intermittent

tank of compressed

air

speeds beyond the hole when the

The

tank pressure

atmospheric pressure ( greater than

30

intermittent supersonic jet

is

supersonic wind tunnel

it .

with a hole in

air

a

at supersonic

flows

is

greater than about twice lbs per sq in . ) . An equally rudi

is

obtained on puncturing a vacuum tank evacuated to less than one - half of atmospheric pressure . Such equip

mentary

useful for small scale teaching demonstrations , but does not per mit accurate measurements of forces , pressures , or temperatures without

is

ment

refinement and expense . The essential elements of two super sonic wind tunnels designed by the NACA for intermittent operation are Quoting from the summary of TN 2189 : "This equipment shown in Fig . 8:10 . consists of an induction tunnel having a 4 in . by 16 in . test section and

considerable

capable of operating at Mach numbers ranging from about 0.4 to 1.4 , and a blow-down tunnel having a 4 in . by 4 in . test section for supersonic Mach The tunnels are actuated by dry compressed air numbers up to about 4.0 . stored at a pressure of

lbs .

300

per sq

in . in

a 2,000

ft

cu

tank by a 150

reciprocating air compressor . This air supply permits inter operation mittent of the tunnels for test periods ranging up to 400 sec

horsepower

onds

(depending

one-half hour 8: 5. made

on the stagnation pressures maintained ) at approximately

intervals . "

WIND TUNNEL

BALANCES

FOR

FORCE

Force measurements are

TESTS .

by mounting the model on a support connected

draulically

,

or electrically

actuated scales

.

mechanically ,

to

hy

The model may be supported

either by wires through the side of the tunnel , struts through the side of the tunnel , or a single strut from behind the model . A typical wire support is shown in Fig . 8:11 , with provision for measuring all six com of force in

ponents

in Fig . Tail

movement .

8:12 . A model supported

by a

tail

" sting "

is

is

shown

in Fig .

8:13 .

system

shown

sting supports are indispensable for supersonic testing because wires

or struts would generate 8 : 6 . OTHER WIND TUNNEL

the purpose Force

A 3 - component strut support

of

measurement

measuring

shock waves which would TEST EQUIPMENT .

forces

equipment

has

,

pressures

affect

the test

Wind tunnels are ,

primarily for

and temperatures

been described

in Art .

results .

8:5.

on models .

Pressures

are commonly measured by manometers or banks of manometers . Equipment for photographic recording of a multiplemanometer bank is shown in Fig . 8:14 .

8:10

Pictorial

. .

Fig

layout

of

small

.

operation intermittent From NACA TN 2189

Schlieren apparatus

AA

11 tunnels

Air dryer

f

Blowdown tunnel

Induction tunnel

developed

Oil filter

Storage tank

by the

. NACA

Air compressor

8-13 TECHNICAL AERODYNAMICS

AERODYNAMIC

TEST FACILITIES

Balance Room

8-14

Angleof Attack Indicator

BO Lift

Manometer

W.Yow Balance W. Rings and Balance Static Sections Moment Moment To Entrance Rolling Balance Balance Working E.Yow Balance E.Lift Balance Drog Balance

To Selsyn Generator

Winch

Xx

Model Wind Direction

Wind Tunnel

Room Observation

rig

Original wire balance system of the GALCIT tunnel . This . ging has since been superseded by an improved system . is reproduced here because shows more clearly the essential features of the force resolution than the more complicated system . (From C. B. Millikan , " Aero Reproduced dynamics of the Airplane , " John Wiley & Sons , Inc. , New York . with permission . ) Fig . 8:11

It

it

Counterweight L2 O-Pivots Screw

Wind Sting '

Fig . 8:12

.

nel balance model .

Simple

Model

type

of wind

tun

using struts to support

Fig . 8:14 .

of

Photographic recording readings . Courtesy

manometer

NACA .

TECHNICAL AERODYNAMICS

8-15

Fig . 8:13 .

Model

in test

section of 6 x 6 ft supersonic wind tunnel at Laboratory . Courtesy NACA .

Ames

The

air

in

is difficult

density in wind tunnels

tunnel wall has glass sides

to measure directly

in density

differences

,

the test section can be measured optically by

meter shown

in Fig .

means

If

the

points

of the interfero used in photo

is usually

The interferometer

8:15 .

.

between various

graphing supersonic flows but can be used either subsonic or supersonic sufficient care is taken in getting the mirrors truly plane . A simpler

if

A

Testsection

of windtunnel

4 M

Condenser Lens1 lens Spark or monochromatic light

Fig . 8:15 .

Diagram

T

Lens2

Camera

-

M Mirror

T =Translucent mirror

of Mach - Zehnder interference refractometer to determine density differences .

equipment

TEST FACILITIES

AERODYNAMIC

in Fig . 8:16.

stop

The

provided at that point

is

.

the " schlieren

equipment

"

sketched

if

S1 may be omitted a point source of light is Ordinarily a monochromatic or spark light source

film in the

used with black and white

used

is

than the interferometer

apparatus

8-16

if

camera , but

light is

a white

with color film in the camera , density gradients appear as color film . An even simpler device is to eliminate the use of

changes on the

51010 Testsection ofwindtunnel

Lens1

Condenser lens

Lens2

Stop Sz

Stop

Spark

S

Camera

Glass port holes

Fig . 8:16 lens

2

in Fig .

sensitized factory

of schlieren

Diagram

.

8:16

for

simply substitute

and

This is

paper .

equipment

sonic flow .

known

getting pictures

for

photographing

of

a sheet

super

photographically

as the " shadow " method and is very of

shock waves .

The

relationship

satis between

these three methods of making photographic records of density changes

explained by

Hilton ( 1 ) by

density changes are large as ing through a shock wave ,

of

use

density , or

its

distance , or

rate of change with

the curvature

of

the

make a

showing

where

record

For the

the shock waves are . dent

who would

field ,

do

laboratory

is particularly recommended of its many helpful detailed

because

( 1 ) Hilton , W. 1951 .

(2)Hilton ,

op .

F.

-

sensitive

to density

Direct shadow sensitivity proportional to

/

curvature d2p dx2 Schlieren

sensitivity proportional

to

/

do dx

recom

8:17 . Variation of air den and refractive index through ck wave , with notes a typical by Hilton . shock

Fig .

sity

" High speed Aerodynamics

cit .

is

Where

work

Hilton

mendations .

Interferometer

stu

the work of

in this

8:17 .

it is evi

density curve can be used to photographic

in Fig .

in pass

from Fig . 8:17 that either the

dent

the sketch shown

."

Longmans , Green & Co.

CHAPTER

9

AIRFOILS AND ASPECT RATIO EFFECTS AT LOW SPEEDS

9:1.

in

FORCES

AIRFOILS ; AIRFOIL COEFFICIENTS

ON

airfoil is

An

.

defined

general as any body shaped so as to get a useful reaction from an

relative to

stream that moves

it ,

but the term

is

to

most often used

air de

KU727

scribe a body of cross - section similar to Fig . 9 : 1 which is acted on by a large force perpendicular to the

I -V

a

tco

D =

planes and

---- Chord

air

stream

airfoil in

.

9 : 1 .

.

Forces on

derived from experimental

lift )

data

on

to

voted laws

and

a small

that direction

tail

(1 )

a

( wind

is de

presentation of the

of force - action on

airfoils

air

fuselages

This chapter

.

force

( drag ) .

surfaces of

airplane

some

airfoils

are

Air

an

(

The wings and

Cpc

velocity

Fig

stream

parallel to

c

Zerolift chord chord Geometric of aa Angle attack

air

Drag

tunnel and

airfoils as free -flight

tests ) at such low speeds (under 300 miles per hour ) that the compressi bility effect of the air is negligible , and ( 2 ) the use of such laws in form to calculate the forces

mathematical

acting on airplane wing and

tail

surfaces at low speeds .

airfoil result from the distributed pressures over the airfoil . As the speed is changed from low subsonic to super

The forces on an chord

of the

typical pressure distribution pattern undergoes a major by the comparison in Fig . 9 : 2 , suggested by Pope . (1 ) In general , the pressure distributions about the airfoils shown in Fig . 9 : 2 can be calculated from the corresponding velocity distributions and the appropriate Bernoulli equation . It may be noted in Fig . 9 : 2 that for sonic speeds

,

the

change as indicated

the typical subsonic flow pattern most of the

lift

is

due

to negative

; whereas , for a supersonic flow pattern , positive pressures to on the lower surface be

pressures on the upper surface most

of the

lift is

due

surface absolute pressures cannot be less than absolute zero . Special consideration of the effect of high speed , as represented mathe

cause upper

matically

by the Mach

A force ( 1 )Pope

is

number ,

will

be given

in

completely specified by specifying

, op .

cit .

9-1

Chapter

its

10 .

magnitude ,

direction

,

AIRFOILS

and

line of

2:1

by

(c.p. )

action

AND ASPECT RATIO EFFECTS AT LOW SPEEDS

Forces

.

lift

specifying

airfoils

on

(L) ,

drag

are

( D) ,

commonly

as in Fig .

specified

center - of - pressure location

and

airfoil .

from the leading edge ( LE ) of the

9-2

Experiments

on

airfoils

-0.6

-0.6 Upper Surface

-0.2

-0.2

Lower

0

Surface

0.2

0.2

BTS

20

0

face

100

of chordwise pressure distributions for low flight at small angles of attack .

speed

60 Per cent chord

0

100

80

20

40

60

Per cent chord

and supersonic

lift

air density ( p) , airfoil sur (S ) , and the square of the relative air velocity (v2) for a given velocity of attack ( a ) between the airfoil chord (c ) and the airvec

that

and drag are proportional

tor , provided that other factors surface , and

foil

Surface

80

40

Comparison

. 9:2 .

angle

Lower

o

1.0

1.0

show

Surface

0.6

0.6

Fig

Upper

0

forces

to

, by

specifying

lift

=

from

The

coefficients

and drag

CL

effect of density , specification the of air

constant .

remain

velocity are usually eliminated

(CL , CD )

defined by

L

(9 : 1 )

qS

D CD = qS

/

where q = pV² 2 and

foil .

and D are the

lift

location of the

The

specified

L

by the

total

(9 : 2 )

lift

and drag forces on the

and drag forces on the

coefficient

airfoil is

c.p.

(9 : 3 )

Cp =

where c . p .

as

shown

An

in

is the Fig

alternate

.

air often

distance from the leading edge to the center - of - pressure 9 :1.

means

of specifying

the line of action of the force on the

airfoil is arbitrarily to

locate the L and D forces at some definite point , leading edge such as the or the 25 or 50 per cent chord point and add a

pitching couple or cient

Cm

is

moment

M

to produce

the

same

result .

A moment

coeffi

then defined by the equation Cm =

M

cqs

(9 : 4)

TECHNICAL AERODYNAMICS

9-3

/

The point

c 4

is

selected as a center of

commonly

location of

and

moments

L and D for subsonic airfoil tests because the pitching moment on most airfoils is approximately constant about this point . With such choice of moments ,

the force system of Fig .

equivalent force system of Fig .

replaced by the

9 : 1 may be

9 :3.

results of tests

The

foils of definite

span

a

/

S )

(A

),

in Fig

Fig

are

.

(

S

=

are

as shown

airfoils

4

9 :

running completely across

airfoil

sections of the aspect ratio

The sec

tion or local characteristics are usually designated by small letters

,

thus

being an

6 .

=

A

center

in Fig

:

6 )

5 )

( 9 :

(9

7 )

9 :

The pitching moment

plotted

is

The aerodynamic

defined as the point about which the pitching angle of attack at which the air strikes the as the

wing

,

.

,

.

,

,

airfoil with c₁ as is shown in Fig 9 : 5

0

abscissa

spanwise

plot of local sec typical

tion coefficients for

"

"

aerodynamic

elementary

distance

28 32

area

the chord and

0.2004

.

a, 8

4

0

9 : 4 .

.

is

the

being

the

9 :

,

0.40.08 dy

Airfoil characteristics of

aspect ratio

moment

respec

a

,

=

cdy

lift

and dM are the

the elementary

on

subsonic

about

,

,

,

tively

10.60.12 dS

-4 12 16 20 24 degrees

dD

and pitching

0

4

Co

coefficient

(

.

12 80 8

dL

.

L /D

1.00.20 drag

A

0

Cp

0.80.16

-4

dD

qds

1.40.28

60

-8

qds

dM

1.20.24 where

20 40

100

dL

cqds

c

S

202

16 22

1.80.36

CL

24 20

Fig

=

Y

:

:

=

2.00.40

1.60.32

Cpl

-8

cd

2.20.44

Airfoil Clark Re 3,700,000 5x30: 68.4ft./sec. Pressure21.1 atm

28

C1

=

CL Co 2.4 0.48

5 .

infinite

have

coefficient the moment

center of

a

simulating an

all

is constant airfoil is varied

moment

.

.

made on

tunnel so that

.

,

the same characteristics

To

"

a

wind

airfoil

de

ratio eliminate the effects by aspect

"

.

-

,

of aspect ratio tests are often the test section of

partly

termined

9 : 1

partly by the cross section of the

and

The curves in

Force system equivalent to Fig .

3 .

.

Fig

9 :

9 : 4 .

14

usually plotted

and

defin

surface and hence aspect ratio ite b² Air velocity Mc

air

on

( b )

center of

AIRFOILS

(For some

airfoils airfoil

section

each

The

is

9-4

EFFECTS AT LOW SPEEDS

such point . )

no

approximately at c

sections and

For

/4

but

is usually

airfoils at low speed the is slightly different for experimentally for

determined

.

results

in Fig .

shown

always some angle at no

is

there

aerodynamic center

different

AND ASPECT RATIO

9 :4

are typical of

many

which the wind can strike an

force perpendicular to the wind direction

(no

airfoils

airfoil

lift ) .

There

.

is

so as to give

Under these con

ditions the resultant air force is parallel to the wind - velocity vector and is drag . The line drawn through the trailing edge of the airfoil in this direction zero -

lift

is

The

chord .

as

known

zero -

tionship to the geometric

is

0.026

lift

The

of

the

airfoil

angles zero -

of attack

lift

chord

9 :4

lift increases lin

beyond which

(CL

as

the

16

changes .

the

stall .

lift The

12 ao

8 0.1Cdo . 14

0

0 CmaC

The

-12 -16 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 GL

-0.4 -0.4 -0.2

Fig .

does not

-4 -8

-0.2 Cmac -0.3

in

of pressure

limit is known

0.008

-0.1

early with the angle , the drag creases at a higher rate , and the center

do 120

0.006

As αa

increased from zero , Fig . that the

0.010

attack and are

usually designated by αa .

28 24

0.002

as

32 Cdo

0.012

ab

solute angles of

shows

Cdo

0.004

known

36

0.014

measured from the

are

40

0.016

with the geometric chord is as the angle of attack (α ) ;

known

is

.

angle that the wind - velocity

makes

144

0018

se

section

c abovechord 0.04 Ja =8,370,000 toinfinite Corrected aspectratio

0.020

lected by the designer for making a drawing

48

aheadc/4 0.011ca.c

0.022

chord ,

arbitrary line

an

152

0.024

no necessary rela

chord bears

which

the

9: 5 .

of

Characteristics

airfoil of infinite

of portion span .

increase with the angle of attack

stalling angle

and

maximum

lift

coefficient

are determined by the separation of the boundary layer , which in as in the flow around a cylinder , depends on the scale (Re ) of the

max )

turn ,

airfoil test coefficient flat plate ) .

and

other factors as discussed elsewhere

(CD min )

is

determined

.

The minimum

chiefly by the skin friction

(

drag

like

a

9 :2 . STRAIGHT - LINE PLOTTING OF LOW SPEED AIRFOIL TEST DATA . The air foil characteristics shown in Fig . 9 : 4 are for a rectangular airfoil of

TECHNICAL AERODYNAMICS

9-5

Clark

Y wing

of

aspect ratio

6,

with rounded tips , with a

taper

2:1

in

thickness ratio , are shown in Fig . 9 : 6 . wing In each case the characteristics are completely specified by graphs graphs only the of CL, CD , and Cp vs. angle of attack α . Of these three

in

planform , and with a taper

of CL vs. a is a straight equation The of this straight graph

CL Co 2.20.44

Planform ClarkY Airfoil:Tapered sq.in,30-in.span Size:150 3,188,000 Re-

2.00.40 1.60.32 1.40.28 1.20.24

Cpt 40

1.00.20

60

0.80.16

80

0.60.12

100

0.40.08 40.20.04 0 0

-0.2 J-0.4 -8 -4 0 4 8 12 16 20 24 2832 a ,degrees .

Conventional plot of tapered Clark

9 : 6.

characteristics of Y wing of A = 6 .

aLo

lift on

04 0.6 0.8

(9 : 8 )

lift - curve

slope and

the angle of attack of zero the intercept

or

axis

a

of the graph

.

graph

The

of

CD

a

vs.

can be

straightened by replotting CDvs . C} , as shown in Fig . 9 : 7 . The intercept

of this

graph on the Cò axis

is

known

effective minimum drag coef ficient of the wing and is here des as the

the symbol CDoe ; the slope , theoretically equal to 1 A

CL 11.1 1.21.3 1.4 1.5 1.6

reasons

/

to be discussed later

may be designated

is a

1

semi - empirical

/

Aew ,

wing

,

where ew

efficiency

factor , so that the equation of the plot of CD vs. c may be written CD = CDoe + CATAOW

(9 : 9)

The graph of Cp vs. a may be

straight

Co 0.10 0.053 ew = =0.91 0.058 0.05

plotting Cp vs. 1 /CL as shown in Fig . 9 : 8 , for which the equation is

ened by

ACO=0.058 1/6 =0.053

2

Fig . 9 : 7 . of CD for

Straight -line plotting Clark Y wing of

tapered

Cp = a.c .

· Cmac /CL

(9:10 )

quantities a.c. and Cmac are the intercept on the Cpaxis and the slope respectively . The quantity a.c. is

The

AC =1

c2

A = 6.

the

is

ignated by

0.15

Срое

is

the

for 0.20

is

where a

-

αLO)

= a (α

CL

1.80.36

Cp 0

Fig

from analytic geometry

line . line ,

thus the distance back from the

lead

ing

center

edge

to the

aerodynamic

AIRFOILS

expressed as a fraction of the chord

in Art .

The three linear equations

(9 : 8) ,

( 9 : 9 ) , and

completely the airfoil characteristics stall . Three intercepts and three

stalling - lift

plus the

,

efficient , in Fig .

In studying

9 :6.

of

number

co

airfoil

large

sections

Cp

airfoils

than

a number of tapered

0.25

wings

a.c.=0.230.02aheadof 0.25c

con

to deal L.E.

3

is giv

( stalling

max = 1.67

aLO =

)

as

follows :

( Fig .

and slope of

9 : 6)

lift

curve

(Fig .

9 : 6)

= =

Cmac

-

0.25

0.02 = 0.23

and slope of graph Cp vs.

plotted in Figs

.

from the graphs

from the table and

may be read

ct (Fig .

Intercept

constants of

seven aerodynamic

vs.

for

(Fig .

-0.071

CD

ew = 0.91

9 : 6,

a.c.

slope of graph of

9 : 7)

A = 6)

-15

(calculate

= 0.058

ΠΑΘΗ

and

9 : 8)

this tapered

wing may also be read

Conversely the con the graphs plotted and

.

intercept

9 : 7,

CDoe = 0.0076

stants

6

0.071 per degree

a =

These

- lift coefficient

intercept

-5.20

5

Fig . 9 : 8 . Straight - line plotting of Cp for tapered Clark Y wing of A = 8.

The aerodynamic

wing plotted CL

4

/

1 CL

for the tapered Clark Y in Fig . 9 : 6 are there tabulated

constants

-0.07

,

in

Appendix 5.

}Acp =Cmac = +4(1 C ) =1.0

9 : 8 .

en

0.15

/

directly with the plotted graphs sim ilar to Fig . 9 : 6 . Such a tabulation

for

0.50.4 0.30.25 0.2

0.50

or wing

and study these aerodynamic

stants of the

2 18

below the

9:6

CL

plotted a

characteristics it is simpler , brief er , and more illuminating to calcu late

in Fig .

shown

0.75

are seen to spec

( 9:10 )

completely specify

thus

airfoil characteristics

the

center being defined as

aerodynamic

,

9: 1.

ify

slopes

9-6

RATIO EFFECTS AT LOW SPEEDS

AND ASPECT

lift

infinite

aspect ratio

independent

gives what

is

in the of

few

ar

ratio

A

next

aspect

called the

.

"

is practically

section

"

to

and experimentally

"

correction

9:10

)

Equation

-

)

,

theoretically

developed (

.

ticles

is

"

,

tion

"

.

(

( a )

( 9 : 9 ) ,

A

appears explicitly in equation The aspect ratio but the curve slope and the wing efficiency ew are also functions of aspect leading to an aspect ratio correc ratio The effect of aspect ratio

TECHNICAL AERODYNAMICS

9-7

characteristics "

and eliminates

effects of

wing - tip shape and

taper ratio included in the table in Appendix mating or calculating

the

The procedure

5.

particular

characteristics of a is thus to correct

the section characteristics

planform

tapered

the section

for

esti

wing

from

characteristics

for the primary effects of Reynolds number and Mach number and to correct the results to the actual aspect ratio , taper ratio , and wing - tip shape . A rational procedure for doing this requires further study of wing theory developed in the next few articles . analysis of the forces relative to the airfoil involves a major assumption that the airfoil deflects a cylindrical stream of diameter equal to the span of the airfoil . A more rational heading for the article might therefore be the cylindrical air - stream analysis of air 9: 3 .

exerted

foil

MOMENTUM THEORY OF

on

airfoil by

an

action .

AIRFOILS . The following

fluid

a

is

This method

stream that moves

elementary , being

based on the momentum

re

lationships developed in Chapter 4 , but it gives several of the results that are usually ascribed to the more elaborate classical treatment or dinarily described as the circulation theory . The rudiments culation theory of this same problem are given in Art . 9 : 4 . As applied to a deflected as

in equation

fluid ,

stream of

Fy

=

i

fluid

the

ond , Fy

and AVy stream .

is in

is

If

on the

is

the

airfoil in mass

stated

,

the y - direction

fluid

of

deflected

per

the y - component of the vector change of velocity of

AVy

is in feet

per second and

in

is

in slugs per sec

pounds .

Let Fig . section of

9:9.

cir

(9:11 )

mVy

of air past

Fig .

may be

(4 : 5) ,

where Fy is the resultant force exerted by the deflecting stream of fluid ,

unit time ,

law

Newton's

of the

Streamlines of flow past an

9:9

represent the flow

airfoil , which is shown an

the cross .

The

air

velocity relative to the airfoil a short distance in front of the air

foil is represented by the vector the airfoil the velocity is Vs , which is nu to Vo but differs from Vo in direction in that it is de through an angle r ( called the angle of down - wash ) , the

airfoil .

Vo ; a short distance behind

merically

flected

subscript AV

is

equal

downward

r

denoting

that the angle

determined , as shown

in

Fig

.

is in

radians .

The change

9:10 , from the difference

of velocity between the

two

velocity vectors

sin

Ertan r

=

is ,

produce

in Fig . 9:11 .

Vor

=

(9:12 )

laws , the force

y

may be added

air

the

on

stream necessary to

If

this

is called

to F and AV .

The

force ex

is in the direction

change

the y - direction , a subscript erted on the

( for which

from geometry

to Newton's

this velocity

of AV for small angles Er

The magnitude

.

Er)

AV and , according

9-8

AND ASPECT RATIO EFFECTS AT LOW SPEEDS

AIRFOILS

of AV .

airfoil is in the opposite direction and is designated by Fy In this figure Fy is shown analyzed into lift and drag

Vo

.

Av

JDi

Vs

Change of velocity air stream .

Fig . 9:10 .

in inal velocity

the usual

components

fluid friction

actually

actually

there are how

thin ) .

the

airfoil

(Do) .

The

total on the

eddies

The sum of the

cross - section

total

stream of air . L is perpendicular to the orig indicating is labeled D , the subscript

The drag

Vo .

drag

the

lift .

induced

The mass

by assuming ameter equal

of

air

greater than ( no

Di because there

matter

is

smooth ) and

how

in the air stream behind the airfoil (no matter friction and eddy drag depends on the shape of ( or

profile

is

may be

the =

)

and

Di

is called

:

(9:13)

+ Do

considered to

by the

airfoil deflects a airfoil .

the drag induced

mean

airfoil

cylindrical

to the span of the

the profile drag

of D and Do , thus

sum

per second deflected

that the

i

is airfoil surface

( Dtotal )

drag

lift

drag

Dtotal The term

Resolution of force airfoil on the de

9:11 .

exerted by

flecting

manner ;

induced drag ; the actual

Fig .

of

This

may be

stream

is called

by the

calculated

of air of

di

by Munk ( 1 ) the

" The assumption of a circular cylindrical stream usually of air deflected is stated as a corollary to other assumptions but can just as well be a major assumption . It is justified only on the area

of " apparent

(1)Munk , Ronald

Max .

mass .

"Fundamentals

Press , 1929 .

of Fluid

Dynamics

for Aircraft

Designers , "

TECHNICAL AERODYNAMICS

9-9 grounds

it

that

correct result .

gives approximately the

The

effective

of air stream for this analysis is usually found experimentally to be 10 to 20 per cent less than that of the circular air stream superim posed on the span of the wing as shown in Fig . 9:12 , and the correction is included in the term ew. For an airfoil of span b , the area of the circular air stream is mb2 4 , area

/

and the mass

air

of

flowing

the area per second

through

m =

Substituting

in

equations =

(9:14 )

Vo

and ( 9:12)

( 9:14 )

,

( 9:11 ) ,

Fy

is

b² VỎE

R™

(9:15 )

For small angles Er , the resultant Fy

is

approximately equal

Front view of air showing area of air stream assumed to be deflected by wing . 9:12 .

plane wing

CL =

,

πAεr/2

=

90S

in Fig .

Note also ,

Dividing by qos ,

L

the

/ 2 , it follows

with L = CLpsv equation ( 9:15 ) that

and ,

Fig .

to

9:11 , that D₁ =

/

Er from equations

( 9:16 ) CDL =

The

total

drag

it

c²

follows

(9:19)

is the " profile - drag coefficient . " If CDo , differentiating equation ( 9:19 ) would give CL then

were independent

where CDO

= ΠΑ

(=

0.053

for

that

is

CD = CDO + CETTA

dcz

L (✯y / 2 ) .

( 9:18 )

ΠΑ

from equation ( 9:13 )

coefficient

from

(9:17)

( 9:17 ) ,

and

lift ;

(9:16 )

CDi = CLEr 2

Eliminating

force

of

(9:20)

A = 6)

Experimental values of dcp / dc for aspect ratio 6 are usually 0.055 to The ra 0.066 , depending on the planform - taper ratio and wing - tip shape .

tio of the ideal to the actual value of dcp / dc of CD vs. c , is the wing efficiency factor ew . ew corresponding to the above mentioned

A mathematical

definition of

ew may

values of

,

determined

from a plot

The range of values

/

dcp dc

thus be written

is

of

0.8 to 0.96

.

9-10

AND ASPECT RATIO EFFECTS AT LOW SPEEDS

AIRFOILS

1

ew =

/ /

A

( 9:21 )

dCp dcz

lift - curve

slope and angle of attack may also be developed from the foregoing considerations . Note in Figs . 9:10 and 9:11

relation

The

between

direction of the velocity makes an angle Ɛr / 2 with the orig inal velocity . The effective angle of attack of the wing chord may thus that the mean

to be reduced by the angle Ɛr / 2 , which is called the induced angle of attack , designated by the symbol air . From equation ( 9:16 ) calculate

be said

air uation

Since

tio A

= oo ,

aspect

(9:18 ) shows that the induced

profile

the

drag

zero , or aspect ra

drag implies no induced

Since no induced

ratio .

is

drag

of as the drag for infinite

may be spoken

the angle =

αor may be spoken

(9:22 )

= CLATA

angle

of attack

- CLA

αr

of as the angle of attack for

,

(9:23)

infinite

aspect

ratio .

Where

finite aspect ratio and CL is the lift coefficient of either finite or infinite aspect ratio wing , assumed to be the same for either finite or infinite aspect ratio . In some NACA reports α is plotted against CL or c1 in presenting the ap

is

the angle of

results

tips

and

airfoil

of

wind

attack for a

the

effect of rectangular

tunnel walls to be described later .

The above simple an

tests

,

with corrections

for

lift - curve

alysis does not permit arriving at any value of finite aspect ratio . To determine this the more follows 9:4 .

tion

and

under

Circulation

Theory

CIRCULATION THEORY

Art .

of

methods

viscous incompressible

closely duplicated

by

pattern with suitably

OF

Airfoils

of

AIRFOILS .

4 : 3 and assumes

elaborate

appears

in

slope for

that

method

to be necessary

.

This theory follows the assump that the flow patterns of non

fluids about cylinders of various profiles may be the vector combination in space of a uniform flow located sources

fairly

,

sinks

,

and

vortices ,

It

all of

which

this Bernoulli's equation , that the lift L of a portion of length b of an infinite rotating cylinder in a fluid stream of density p flowing with velocity Vo is given in the equation ( 1 ) with

can be

handled

method ,

combined with

simple

L

( 1) The

" Kutta

- Joukowsky

mathematics .

=

pvorb

equation . "

may be shown

by

(9:24 )

TECHNICAL AERODYNAMICS

9-11

is

where

the circulation of the vortex determined

tion of the cylinder . shown

It

in Fig .

9:13 .

likewise be

may

rota

by the speed of

The flow patterns with and without rotation are

shown

that the flow pattern around an

cyl

elliptic

inder (determined by flattening and extending the circle ) , inclined at an angle a to the direction of free- stream velocity , may be approximately

similar flattening of the flow pattern The around a rotating cylinder , the lift being given by equation ( 9:24 ) . elliptic Fig patterns cylinders flow around such are shown in . 9:14 . mathematically by

reproduced

a

(b)

(a)

Fig . 9:13

.

Ideal flow patterns ( neglecting fluid viscosity (a ) stationary and (b ) rotating circular cylinders

If

Ideal flow patterns around elliptic cylinders with cylinder axis at angles to the air stream of zero ( a ) and a ( b ) .

9:14 .

the circulation ♪

flow pattern patterns

the angle of attack a are properly

and

around the

elliptic cylinder closely

The necessary

.

circulation is

relationship

slope dc₁ / d

is MO =

dc1

ness

and of

what

less

Fig .

9 : 14b

25

lift - curve airfoils than

also

approximates

may be shown

= 0.1096

shows

per degree

Application

that the resultant

lift - curve

(9:25)

infinite elliptic cylinders tested in wind tunnels is usually

2π per radian .

the

actual flow

that the

per radian

slope of as

,

ratio of the elliptic cylinder ;

dao

or ao The actual

it

zero , = 2

related

between the angle of attack and the

a function of the thickness

as the thickness ratio approaches

at

around

( b)

( a)

Fig .

) .

lift

of

finite thick

found to be some

of Bernoulli's equation on an

to

elliptical airfoil is

per cent of the chord or ( a.c. ) ' = 0.25

(9:26 )

AIRFOILS

AND ASPECT RATIO

EFFECTS AT LOW SPEEDS

9-12

of these relationships it is sometimes considered that an infinite elliptic cylinder behaves like a " lifting - line " vortex located at 25 per For an elliptic cent of the chord of the ellipse from the leading edge . Because

cylinder

of finite an end ;

Bust have

length or for a finite airplane wing , the lifting line (1 ) the condi and according to the Prandtl wing theory

with having a finite lifting line by assuming that the three - dimensional flow pattern around an actual wing consists of a horseshoe - shaped vortex system , as shown in Fig . 9:15 . The tion of continuity

-

down wash

is

made

consistent

pattern behind the horseshoe

system

is

9:16 ;

this

Wing.

Vo

Fig . 9:15

in Fig .

shown

.

Fig . 9:16 .

vortex

Horseshoe

pattern

-

Down wash system

horseshoe

.

vortex .

for

lift distribution along the span of the wing . To of actual wing - lift distributions , Prandtl conceived of the lift being due to a combination of a group of horseshoe vortices as that shown in Fig . 9:17 , giving a lift distribution as shown in

also corresponds to the take account wing such

P

Fig . 9:17 Fig . 9:18

.

Note

.

in Fig .

Composition

of

horseshoe

vortices .

9:17 that at various points

on the span of the

wing there are various numbers of vortices contributing that point , but there

is

considered to be only

( 1 ) Prandtl , L. , NACA Tech . Rept . 116 .

one

to the

lift

lifting line for

at the

9-13

TECHNICAL AERODYNAMICS

Using the calculus

wing .

distribution

spanwise

of

this down

lift

9:19 , the necessary

infinite

conception of an

imal vortices combined in

manner , Prandtl

-wash

velocity

behind

distribution is elliptic

for

a uniform

wing , as

a

as

,

infinites

number of

shows that

in Fig .

in Fig . 9:20 .

shown

w - Downwashvelocity

y Fig . 9:18 .

Lift distribution

due to

vortices .

several horseshoe

Fig . 9:19 .

-

lift

сс 9:20 . bution due

infinitesimal vortices .

also that this

He concluded

for

minimum

induced

elliptic

drag and that

planform ( closely approximated These assumptions

were shown

viously

in

developed

Prandtl

found

it

lift

distribution is the condition

occurs with an

by trapezoidal by Prandtl

good

wings

untwisted

of

to result in

the momentum theory of

experimentally

с

Fig . 9:21 . Chordwise distribu tion of lifting lines necessary to account for low - aspect - ratio wing characteristics .

Elliptic lift distri to infinite number of

Fig .

distribution distribution .

Down wash

elliptic

with

airfoils

2 :1

or

equation

3 :1

elliptic taper )

( 9:18 )

.

pre

.

ex later tests on airfoils between theory and ex

agreement between the theory and

airfoils of aspect ratio 1 to 7 , but of aspect ratio 1 to 3 showed major discrepancies periment , particularly in the lift - curve slope , indicating

periments for

that this theory

for low- aspect - ratio wings and for tail surfaces . More recent studies (1 ) have shown that a chordwise distribution of lifting

was inadequate

lines ,

as

shown

ratio effect of

in Fig . 9:21 , is necessary low - aspect - ratio wings .

( 1 ) Jones , Robert T. Effect of the Chord . "

" Correction

to

account

of the Lifting - line

NACA TN 817 , 1941 .

for

the

Theory

aspect

for

the

AIRFOILS

ASPECT - RATIO CORRECTIONS

9: 5 .

9-14

RATIO EFFECTS AT LOW SPEEDS

AND ASPECT

six

Of the

.

aerodynamic

constants (αLO ,

a.c. , Cmac ) needed for straight - line plotting of characteris tics of a particular wing , four of these ( LO , CDo , a.c. , and Cmac ) are substantially independent of aspect ratio . ew ,

a, CDo ,

ratio corrections

Aspect

lift

for the

is

of aspect

also a function

chiefly

of other factors ,

the

in

- curve slope a . To a lesser extent CL

max

ew ,

are needed for

duced drag CDi , and

ratio but

lift

spanwise

it is

which

determines

also a function of a

distribution

number

which are discussed

,

later . theory

The

elliptic

of

in Arts .

wings developed

9 : 3 and

9 : 4 may be

TTA

written

9:28

(

/

πA

)

(

9:27

)

1/2

+ 1

=

1

/m

CD = CDO + CE /

equations are intended to be applicable only to wings of ellip tic planform The lifting line theory has been applied to rectangular )

, ( 1

Lift curve pa slope factor

Induceddragfactor

5 .

equations given in experimental 9:30 and

bi

1.08

120

1.07

t. 8

1.18

1+

1.16 1.14

1.06

,

.

1.05 8 + 1

1.04

1.12

35

1.03

experimental

data

8

6

4

2

0

Fig

A

10

J1.02 12 14

Aspect ratio factors for 9:22 rectangular wings based on lifting line theory From NACA TN 416.

lift

curve

and

)

.

from the theory

efficiency factor

slope

.

for both wing

-

depart considerably

(

,

the

.

.

.

9:23 and 9:24

.

in Figs

1.10

are

in the wind tunnel

Note that

+ ± 1

1.22

1.09

A

+1

Lift curveslope factor

"

observations

1.10

)

and

)

9:29

,t

theor

between the

1.11

1.26

)

(

)

t

+

( 1

+ d )

.

wings see Appendix

1.28

124

are

for rectangular

values

modifications

)

(

8 ) С

}

/

9:30

TA

9:22

(

etical

the following

) 9:29

πA

and

relation

The

(

9:28

and

/

/

"

tapered

shown

yielding

For trapezoidal or straight

.

wings

Glauert

( 1

factors given in Fig

The

+

(

( 1

+

2π

+ ( 1

CD =

= 1

/

1 m

)

9:27

of equations CDo

wings

(

trapezoidal

+ T )

and

by

.

-

The above

Corrections

must

data in order to agree well with flight test re sults and accordingly the lines through the experimental data are labeled

London

,

,

Press

1942

and

9:23 that the

Airscrew Theory

"

of Aerofoil

in Fig

.

The Elements

note

.

interesting to

.

"

.

It is

"

Glauert University ,

(

bridge

practice H.

recommended

)1

"

,

be based on experimental

Cam

9-15

TECHNICAL AERODYNAMICS

1.0

Elliptical 0.9

Prandtl Theory

;

Rectangular : Glauert Theory

I

1 2 and 3 - to - 1 Taper

0.8 Rectangular Wings

Tail

0.7

Surface Recommended

0.6

Practice

ew

Data : TM 941 , TR 627 ,

0.5

TM 798 , TR 540 , TN 2980

0.4 A = Aspect

0.3

Fig .

4

2

0

8

6

Ratio

10

12

14

Theoretical and experimental variation of

9:23 .

18

20

22

with aspect

ratio .

16 ew

/

dCL da = a .09

Lifting

.085

Line Theory

π2

.08

a =

.075

Lifting

:

ob

A

x A+2

90

Surface Theory by

Points plotted

approximated

.07

a

=

.065

π2

x

90

A A+2.5

Test Data on Surfaces

Tail a =

.06

772

90

X

,

from TR 627 , tests on tapered wings .

A

A+3

=rectangular

tips

• circular tips

DO

=T.M.

941

.055 A

.05

2.5

Fig .

9:24 .

3

Theoretical

Aspect

( Reciprocal

3.5

5

Ratio Scale ) 7 6

10

experimental variation of with aspect ratio .

and

15

20

lift - curve

00

slope

9-16

AND ASPECT RATIO EFFECTS AT LOW SPEEDS

AIRFOILS

is approximately a constant only for a narrow aspect range of ratios from 3 to 10 , and that it drops off to a very small This fact is a major consideration in se value at large aspect ratios . lecting an aspect ratio for an airplane . The effect of aspect ratio on efficiency factor

wing

of wings ,

induced drag

based on

is

Fig . 9:23 ,

shown

in

Fig

.

9:25 .

.20 .18 ew

60

70

.80

•

.40

d (G2 )

.50

.16

1.00

.14 .12

.10

Lifting

.08

=

)

(

d

C

dC .06

Line Theory

1

TA

.04

)

=

as

a

function

parameter

a

9:25

2

2.5

3

5

Induced drag of wings as

.

.

Fig

10

of aspect ratio with

ew

.

20

00

4

(R 0

Aspect Ratio eciprocal Scale

A

.02

-

)

(1

.

-

inFig 9:24 that the experimental data on lift curve slope is sub stantially below that of the lifting surface theory developed by Jones ==

2πA

EA

the form 9:31

the ratio of the semi perimeter to the span of the ellipse

9:31

may be approximated

.

-

is

)

E

Equation

(

where

in

expressed

(

was

)

which

+ 2

wings

(

elliptical

,

for

)

Note

with

fair

accuracy by the empirical

equation 2πA

given to

tion of this

same

form E =

2πTA

cit

.

.op

,

,

( 1 )

Robert

T.

+3 Jones

show that the

lift

curve

-

,

,

however

better approximation by the modified empirical equa 9:33

)

is

rectangular wings

(

slope

on

a

The experiments

)

(

9:32

A +2.5

TECHNICAL AERODYNAMICS

9-17

of aspect ratio

are available , the recommended Aeronautics Administration , ( 1 ) in making aspect ratio

suitable

is

if

( (

if

the

used instead

Also

is

based

of

lift

the

or other test aspect

the correction

ratio

aspect

improved

is

9:23

ew

1.

that

=

9:34

.

shown

improved

is

ratio to on equa

9:35

(

for using published NACA data to estimate the char particular wing is illustrated by the following example

procedure

acteristics of

:

)

instead of

a

A

(

9:33

test

from any

accuracy

in Fig

ratio

from aspect

ratio

an unknown aspect

9:35

) .

,

curve slope correction

tion

equation

by

9:34

A

but the

ratio

ew with aspect

as implied

assuming

ratio

aspect

unknown

due

referred

( 9:28 )

2542

) ,

to any other variation of

and

CETTA

for correcting

can be used

,

Similar equations

/

CL

16

m =

out

drag

6 and then add the induced

61T +

-

CD = CD6

subtract

)

ratio

Thus equations ( 9:27 )

to the desired aspect ratio . to aspect ratio 6 become

6

the induced

first

use equation ( 9:27 ) and

drag due to aspect

)

corrections

,

of Civil , is essentially to

practice

6

3/8

data

A

test

(

If airfoil

-

CL ,

a

3 .

Air

Commerce

Manual

=

04.129V2

4,

/

,

=

/

6,

=

A

and

is

.

0

+ +

=

called for in

0.088 CL

( a ) .

0.242

.

, "

)

( 1

CAA

0.063c

ratio correction

aspect

Cp

0.0630

then

0.0073

=

no

Cp

equation requires

These are the answers

is

equation CD

The

блет

, "

-

The desired drag curve

c

=

CDi

c

of

%

6 .

).

a +

/

a

(

,

.

.

=

A ,

6,

A

=

:

°

=

,

.

=

=

,

a

=

:

5

,

.

,

.

( a )

lift

=

A

c )

.

°,

=

( b )

A

= a 6; ,

CL

.

(

9; a

=

A

( )

CL a

=

5 ,

Given the NACA 4412 wing section data in Appendix find equations for in terms of CD in terms of and Cp in terms of equations for rectangular wing for rectangular wing of equations for an elliptic wing of of Solution Read in Appendix for the 4412 wing the following data 4.0 ao 0.098 Cdo min = 0.0071 a.c. 0.8 ahead alo Cmac = -0.088 0.0073 for 4.28 CD min ть rectangular wing of For use the data uncorrected for and the m6 57.3 4.28 57.3 0.0745 Calculate a6 curve thus For the drag curve 4.0 with aLO = a10 -4.0 write CL = 0.074 rectangular wing of In Fig 9:23 for read ew from Fig 9:23 read ew = 0.84 and calculate Example

EFFECTS AT LOW SPEEDS

AND ASPECT RATIO

AIRFOILS

For a rectangular wing of aspect ratio for the - curve slope

(b ) get

9 , use

lift

ag =

9

20.0745

9 + 3

9-18

equation

( 9:33 )

to

= 0.084

for a rectangular wing of aspect ratio 9 , and read on the line of recommended practice for rec tangular wings ew = 0.77 , for use in equation ( 9 : 9 ) . The estimated equa tions for the rectangular wings of aspect ratio 9 are then To estimate

refer to Fig

the induced drag

. 9:23

CL =

CD

= 0.084

0.0073 +

c²

(α

+

4.0 )

= 0.0073

gnew

+ 0.046c2 0.

Cp = 0.242 + 0.088

CL

These

in

are the answers called for

(b) .

elliptic

wing of aspect ratio 3 use equation ( 9:33 ) for correction from aspect ratio 6 , and equation ( 9 : 9 ) for the induced - drag correction , referring to Fig . 9:23 for ew and assum ing that an actual elliptic wing will approximate the recommended prac tice for a wing of 2 : 1 or 3 : 1 taper in Fig . 9:23 . This procedure gives

( c ) For

an

lift - curve - slope

=

a3

In Fig . 9:23 read

CL = 0.0558 CD = 0.0073

These are the answers 9 :6.

drag than at higher

air

.

ct

=

in

-WALL

from the

= 0.0558

4.0 )

+

0.0075 + 0.123c2

(c). CORRECTIONS

ground

.

An airplane

( or water )

this height ,

Below

9:12 cannot

stream from being

(a

эпет

called for

altitudes .

theory sketch in Fig

lar

+

GROUND EFFECT ; TUNNEL

less than one semispan

3 3 + 3

0.86 , and get the equations

=

ew

x 0.0745 x

6

has

the elementary

b

not necessary for high lower surface of the wing , region of increasing velo

are

Ground plane

a

favors

boundary layer .

laminar

flow in

the

(

-_"

is

which

The

Prandtl

wing

theory

Fig

9:26

Image wing

.

city ,

circu

Wing

The entire

moreover ,

less

.

.

lift .

flying

momentum

apply , for the ground prevents a

freely deflected

Instead , the wing floats on a layer of com pressed air , and high velocities over the upper surface

wing

appreciably

---

Vortex system used

for calculating ground effect

.

the

TECHNICAL AERODYNAMICS

9-19

may be

applied

system

is

so

effects thus calculated are equivalent The equivalent aspect ratio for induced

The

.

ratio

aspect

1.0 0.9

.

1.0

0.8 0.7

Agd

dog da

/

h b

3

0.10

0.2 0.30.40.5

0.10 0.150.2 0.3 0.40.5

/

h b

Fig

Effect of proximity to curve slope or on angle of attack for given lift coefficient a

-

.

.

-

lift

.

.

9:28 ground on

.

.

0.8 0.7 0.05

2.5

Fig 9:27 Effective aspect ratio of monoplane wing near the ground for induced drag computation

.

:

.

Fig

,

= €

6

=

=

,

,

0.10

unchanged

,

=

for

is

ew

/

if

h b

9:27

= 0.089

hence

,

0.88

;

a

"

/

ag

=

11.3π

a

x

c ₤

,

and

,

.

.

+ =

6,

a

A

for

9:26

closed throat wind tunnel the same plus similar effect on the

exists

,

-

a

.

is tested in

in

ft

60

a

as that shown

read

,

effect

= 11.3

0.89

0.075 0.88

span

for

called

When the wing model

.

These are the answers

6

/

=

CL

In Fig

0.10

0.53

= 0.0065

0.10 and

and

are CL = 0.075a CD equations drag and when the wing is

=

=

/

for

h / b

9:28

,

.

In Fig

: =

CD

6/60

Agd =

A

2 : 1

a

h , b .

) 6 ,

Calculate 0.53 Hence

of

wing

in free flight

lift

.

/

A

Agd

/(

ft

Solution read

.

.

lift = .

6

flying

tapered Given and drag equations 0.89 find the from the ground

1.

Example

which the 0.0065+ CL2

-

The effect on lift curve slope calculation is shown in Fig 9:27 Their use is illustrated by the following example shown in Fig 9:28

drag

is

10

0.9

2

A

0.6

LS

0.5 0.4 0.3 0.05

1.0

A

,

in

an increase

Agd

that the horseshoe -vortex

assuming

strength below the ground , that the obvious condition of no flow through the

is fulfilled

ground plane

A

by

matched by an " image " system of equal

as in Fig . 9:26

to

this condition

to

(

-

.

.

-

-

.

a

) ,

out walls

a

tunnel wall For wind tunnel with an open jet test section with an opposite effect occurs because the air stream available is not sufficiently large to provide normal stream deflection as in free flight Wind tunnel tests must therefore always be corrected for the Since the tunnel tunnel wall effect to get free flight characteristics

upper

(

) .

-

, a

a

,

a

,

,

a

wall effect with closed throat like the ground effect is to increase aspect the effective ratio the correction to free air for such tunnel involves decrease in effective aspect ratio an increase in induced drag Numerical values for such correc decrease in lift curve slope tions are commonly put in the form

9-20

AND ASPECT RATIO EFFECTS AT LOW SPEEDS

in

)

9:37

radians

)

8C

9:36

(

-

Δα =

85

(

=

ACD1

c²

AIRFOILS

S is the wing surface and At is the area of the tunnel throat For a circular throat or jet , the values of d are the jet ) . +0.125 and -0.125 , respectively . For rectangular throats and jets of various sorts , Theodorsen ( 1 ) developed the correction factors shown in

in which (or

of

area

Fig . 9:29 . +0.3 Vertical walls only

2

0.2 +0.1

only walls Horizontal

2

0

Closedthroat

8 -0.1 -02

wall

horizontal One

Openjet

-0.4 0.3

1.5

0.5 0.6 0.70.80.91.0 Width Ratio Height

h

0.4

2

-0.3

-

.

.

factors for subsonic flow tunnels and jets

wall correction

Tunnel

9:29

rectangular

in

.

Fig

a

,

"

a

,

-

drag error due to the static For closed throat tunnels there is also hor along gradient pressure the throat which Diehl aptly describes as

,

it

,

2

-

-

"

;

izontal buoyancy since it is proportional to the volume of the model this correction is of the for variable density tunnel tests on airfoils airship may run as high per cent though for tests on models order of

9:37

)

and

(

9:36

for compressibility Fig 9:29 is illustrated

and

.

correction

.

an additional

)

tions

is (

there

,

0.3

)

M >

(

.

as 20 per cent of the drag measured on the tunnel balances For wind tunnel tests in which the Mach number is high say

The use of equa by

the following

:

example

410

.

Rept

.

(

.

NACA Tech

)1

.

=

7

a

=

S

.

,

=

.

Given

a

- 2.

by wing of surface 13.5 sq ft tested in on test results wind tunnel The rectangular tunnel 10 ft closed throat and lift and drag are CL 0.080α CD 0.0070+ 0.040С12 Find the drag equations in free air Example

lift

TECHNICAL AERODYNAMICS

9-21

/

/

== Solution . Calculate b h = 10/7 = 1.43 . In Fig . 9:29 , for b h = 1.43 = 13.5 70 = read for closed - throat tunnels 8 = +0.125 . Calculate S /At 0.193 and 8 ( S At ) = 0.125 x 0.193 = 0.024

/

/

Equations ( 9:36

)

then give

( 9:37 )

and

ACDi = +0.024c2

radians

Δα = 0.024C The corrected

=

when CL = 1.00

= 1.40

1.4CL

results in free air are calculated thus 0.024c2 CD₁ = 0.040C² + 0.024c

CL 0.080

α =

=

=

12.5CL

αι

= a + ▲α =

a'

-

1.00 =

from the

test :

= 0.064c2

12.5+ 1.4

= 1.00

at CL

12.50

at

= 13.90

CL = 1.00

0.072

13.9

lift

Hence , the corrected drag and CD

equations are :

= 0.0070

+ 0.064c2

CL = 0.072α These are the answers

9: 7. FLYING

EFFECTS OF CHORDWISE

is not

IN

SLOT

WINGS ; INTERACTION

OF TWO AIRPLANES

in panels joined to 9:30 . If the chordwise through the joint , the

Wings are sometimes constructed

SIDE BY SIDE .

joint

gether by a chordwise

joint

called for .

,

in Fig .

as sketched

sealed against air leakage

adequately

two halves of the wing behave somewhat b

dependently , with a large adverse

bs

lift .

on the drag and Plan

in

/

is

a reduction

For

= 0.0021

in

a 40

effective

an increase in induced

k

and

=

0.85

aspect

drag

.

in

in

aspect

of the

(kb ) 2/8

wing

(b = 480

Fig

.

in . ) with

9:31 ) .

(9:38 ) induced

a 1 - in .

slot

This corresponds to

ratio in the ratio 0.852 ratio 1 / 0.72 = 1.40 .

the

the

in

ratio of the combination for ( in

on

terms

The reduction

expressed

Aed =

- ft - span

effect

factor " k defined by

.

the effective aspect

calculations .

bg b = 1/480

may be

Munk " span

with chord

wise slot

where Aed drag

Wing

9:30 .

effect

equivalent to a large reduction

aspect ratio

ratio

Front elevation

Fig .

is

drag

The

in

= 0.72

and to

AIRFOILS

AND ASPECT RATIO

flying side

Two airplanes

EFFECTS AT LOW SPEEDS

by side have greatly

9-22 drag

reduced

for

the

reason , and the same graph (Fig . 9:31 ) can be used to calculate the effect with rectangular wings . For two wings of A = 6 flying separately ,

same

is

CDi

tips at

c

/

б

for

If

each .

a distance apart equal

they are flying side by side with the wing to

1/100

of the

. 9:31 to be 0.82 , and CDi = c to a reduction of induced drag in the ratio

read from Fig

6 0.822

x

=

/

combined span , k

12πk² .

This

can be

corresponds

0.75

12

0.9

k 0.8

0.7 0.001 0.002

Fig .

It is

9:31 .

Effect of

thus seen that two

0.005 0.01

0.02

chordwise 50

-ft - span

0.05 0.1

slot in wing

0.2

0.5

1.0

on Munk span

airplanes flying with

wing

factor . tips

if

1

ft

apart have about 25 per cent less induced drag than they keep a large migratory importance may apart This effect be of to birds . distance . PROBLEMS

For Art .

9:1.

A model wing is tested in a wind turmel in which the pressure is the temperature 100 ° F . The wing model is rectangular and has a span of 30 in . and a chord of 5 in . When the air speed is 100 ft per sec , the forces measured on the model are L = 5 lb and D = 1 lb. The pitching moment about the c 4 point is -10 in . -lb . Find (a ) CL, (b) CD , 9:1.

24

( c)

in .

Hg and

/

/

Cmc 4 ,

and Cp . 9 : 2 . A wing of 180 - sq - ft planform surface S carries a weight of 1,200 coeffi lb in level flight in standard sea - level air . ( a ) Find the cient for speeds of 120 , 100 , 80 , 70 , 60 , and 50 mph . (b ) Find the angle of attack from Fig . 9 : 4 . ( c) Find the stalling speed . 9 : 3 . An airplane wing model extends completely across the throat of a wind turmel in which standard sea -level air flows at 100 mph . The wing characteristics are given by Fig . 9 : 5 . The chord of the wing is 18 in . per foot of span of When the angle of attack is 10 degrees , find the the wing model .

lift

lift

For Art .

9 :2 .

9 : 4 . Using the wing constants listed in Appendix 5 , write and plot equations for CL vs. a , CD vs. CL , and Cp vs. CL for the wing of 2 : 1 taper ratio and A = 6 there designated M6 ( 18 ) - ( 09 ) ; 0-0 .

9-23

TECHNICAL AERODYNAMICS

9 : 5 . Repeat problem 4412 - 4412 ; 0-0 .

1

For Art .

for the elliptical

wing

of

A = 6 designated as

9 :3.

9 : 6 . For a particular tapered wing of A = 6 ( wing 2218-09 ; 0-0 in Appendix 5 ) , the following test data are reported : a = 12.480 , CL = 1.00 , CD = 0.068 . Calculate CDi , CDoe , and αo . 9:7. Given the following data on the test of a particular wing of A = 10 and taper ratio 3 : 1 , calculate and plot CDoe and ao as ordinates vs. CL as abscissa . (a ) From these graphs , find CDoe min , CL opt , and dCL da o (b ) Also plot CDoe vs. C12 , and find CDoe and ew.

/

α

-1.2 0

CL 104Cp

0

2

4

8

0.1

0.27

0.43

0.77

85

82

111

156

16

12

318

1.09

1.38 873

555

18

20

1.42 1.50 1,100 1,640

The above data are from NACA Tech . Rept . 627 , Fig . 13 , without corrections . Check these results with data on the airfoil in Appendix 5 designated 23018-09 ; 0-0 . (The data in Appendix 5 have been corrected as specified in a later report , NACA Tech . Rept . 669. )

For Art .

9 :4 .

lift

per foot of span of an airfoil extending completely 9:8. The across a wind tunnel in which standard sea -level air flows at a speed of Using equation ( 9:24 ) , find the circulation necessary 100 mph is 50 lb.

lift

produce this . 9 : 9 . Using equation ( 9:24 ) , find the relationship between the coefficient C1 at any point on the span of the wing of chord c and circulation around the lifting line of the wing at that point .

to

lift

r

For Art .

the

9 : 5.

9:10 . A wing model of rectangular planform , 30 - in . span , and 5 - in . chord , was tested in a wind tunnel and the results of the tests , when corrected for the effect of the wind tunnel walls , were expressible by

the equations

CL

= 0.070

(a

CD = 0.0077

+ 0.80

)

+ 0.0734c2

Using equations ( 9:34 ) and ( 9:33 ) , write the equations for a rectangular wing of A = 3 , and check with Fig . 9:23 . 9:11 . Using the section characteristics of the NACA M6 wing in Appen dix 5 , follow the method given in the example in Art . 9 : 5 , and write equa tions for the characteristics of a rectangular NACA M6 wing of A = 10 . 9:12 . Using the characteristics of NACA 0009 wing in Appendix 5 , low the method of the example in Art . 9 : 5 , and write equations for the characteristics of an elliptic tail surface of NACA 0009 section of A = 4 .

fol

For Art .

9:6 .

9:13 . A 3 : 1 tapered wing of A = 10 , listed in Appendix 5 as 23018-09 ; Using Figs . 9:27 and 9:28 and the data in Ap . has a span of 48 pendix 5 , write equations for CL ( a ) and CD ( CL ) for this wing when is flying 4 from the ground .

ft

0-0 ,

ft

it

AIRFOILS

For

Art .

AND ASPECT RATIO

EFFECTS AT LOW SPEEDS

9-24

9:7.

9:14 . A wing model of 5 - in . chord and 30 - in . span is tested in a wind tunnel of closed throat 39 in . wide and 22 in . high . Equations for and drag characteristics as measured in the tunnel were CL = 0.083α a and

lift

CD= 0.0095

find the 9:15 . of 48

ft .

9:31 and

+ 0.050C12 .

lift and

drag

Using equations

( 9:36 )

and

( 9:37 ) and

characteristic equations in free air .

Fig .

9:29 ,

Each of two rectangular wings of ew = 0.90 and A = 6 has a span They side by side with their tips 4 ft apart . Use Fig . find the percentage saving in induced drag over flying separ

fly

ately a great distance

apart

.

CHAPTER

10

AIRFOIL COMPRESSIBILITY EFFECTS

Airplanes

are of commercial

flight

high speed , and

velocity

ter

is

critical

importance

Mach

must

number "

of their

because

(where

local

some

for

becoming commonplace

indispensable for military

and

signed helicopters

in

beyond the " critical

exceeds the speed of sound )

cial aircraft the

military

and

commer

Efficiently

aircraft .

de

also operate with rotor tip speeds near or beyond

also have satisfactory performance the transonic and subsonic ranges described at the beginning of Chap Supersonic missiles

.

must

5.

of flight is increased beyond M of airfoils begin to be substantially different As the speed

Simple

0.4 , the characteristics

from those at lower speeds . reasonably accurate corrections to low - speed characteristics in the region between M = 0.4 and the critical , which usually

and

can be made comes

≈

between

M =

0.6 and

M =

0.9 .

Transonic corrections

covering

,

in

general the region of partly subsonic and partly supersonic flow , extend ing often up to as high as M = 1.4 , are considerably less accurately known but are discussed

in

in this chapter

the supersonic region

well

as

as

characteristics of

airfoils

.

is

Considerable valuable information

obtainable from a study of two

dimensional airfoil the primary objective of the study predict is to the characteristics of finite aspect ratio wings . This flow even though

chapter

will

consider

first

the

two - dimensional

combined effects of compressibility

and aspect

primarily

Mach number

This chapter concerns

is

not possible to vary the

number .

In the

wind

Mach

tunnel

it

effects ,

and

later the

ratio . effects ,

but

in flight

it

number without also varying the Reynolds is very difficult and seldom done , as a

/

of accurately controlled pressures and or temperatures would provided have to be . For most wind tunnel tests there is a relationship

wide range

between

test

effects

may

mon

practice

Mach

Mach

test

both be large ,

however , to

sen to consider

(2 )

and

number ,

the (3)

Reynolds

number

and they are

for

difficult

try to separate

them .

effects in the following Reynolds

number .

Thus , 10-1

any

particular

to separate .

In this text order :

while

model ; the

It is it is

(1 ) aspect

Chapter

9 has

com

cho

ratio , dealt

10-2

EFFECTS

AIRFOIL COMPRESSIBILITY

with aspect ratio effects , this chapter (Chapter 10 ) will aspect deal with ratio and Mach number , and Chapter 11 with aspect ratio ,

principally

Mach number ,

be

and Reynolds

in

insufficient information

to collecting

-

TWO DIMENSIONAL

10 : 1 .

spite of the billions of

and analyzing data

of

-hours

COMPRESSIBILITY

SUBSONIC

infinite

aspect

from 300 to about 600 miles per hour , and develops

devoted

EFFECTS .

ratio in the speed range first the relationship

/4

Mer

Cmc

In

81

man

always

in this field .

AIRFOILS :

airfoils

This article concerns

will

For most new designs there

number .

.05.5 CL .04

.4

.03.3

.2

.02

CD

.01.1

-.1

/4

Cmc

0

.2

1

.5

.3

.7

8

creases

(

)

and

pitching

numbers below the

that up to and

slightly

)

moment

,

,

: 1

.

on an NACA 4412

airfoil

critical

is

shown

.

Typi

beyond the

in Fig

critical

Mach

10

number

coefficient increases substantially the moment coefficient in slightly and the drag coefficient either remains constant or rises ,

lift

10

,

the

in Fig

drag

cor

effects

.

with high subsonic Mach Note

second

beyond which the

because of excessive shock wave ,

lift

,

variations of

critical

speed

-

limit

rections are inapplicable

of speed

,

of

the upper

(

a

study

: 1 .

)M .

compressible and incompressible flow characteristics and

between

Re

.

(a

constant

cal

for

:

.

a

10

1 .

Force and moment coefficient variation with Mach number = 0.250 for NACA 4412 airfoil small angle of attack From NACA TR 646 increasing with

Fig

TECHNICAL AERODYNAMICS

10-3

Since the test could not conveniently be run at constant Rey nolds number , the effect of increasing Reynolds number would , from con

slightly

.

of boundary - layer skin friction , have resulted in a reduced coefficient . It is evident from Fig . 10 : 1 that there is probably a number effect increasing the drag coefficient to offset the normal

siderations drag Mach

reduction due to increasing

Reynolds

number . M =

0.4

-.5 M =

0.6

Cp .5

1.0 25

Fig .

Percent

50

Effect of Mach number on chordwise of a 66 series wing of A = 6.

10 : 2 .

middle

pressure distribution near

From NACA TN 1696 .

insight into the reason for the lift , drag , in Fig . 10 : 1 is obtained by inspection of Fig .

Some shown

effect of

100

75

chord

and moment 10 : 2 ,

variations

which shows the

pressure distribution . Pressures Fig such as those shown in . 10 : 2 can be calculated from the compressible flow equations given in Chapter 5if the velocity distributions are known . In general , it has been shown by Glauert ( 1 ) and Prandtl (2 ) that the Mach

incompressible

number

and

equation

on the chordwise

compressible pressure coefficients are related by the Cp inc Cp

( 1 ) Glauert , Press

,

1942

.

( 2 ) Prandtl , NACA

" Aerofoil

H.

L.

" General

TN 805 ( 1936 ) .

√1

-

( 10 : 1 )

M2

and Airscrew

Theory . "

Cambridge

Considerations on Flow of Compressible

University Fluids . "

AIRFOIL COMPRESSIBILITY

is

where Moo

tion ( 10 : 1 )

critical

the free stream

is in fair results from Cp

inc

use

=

Cp

It

of

M& √1 - M

+

Equa

agreement between the theory and

M2 1

airfoil .

experimental data below the

most

relationship ,

the Karman - Tsien

may be shown ( 1 ) by assuming

10-4

number remote from the

Mach

agreement with

Mach number , though an improved

experiment

EFFECTS

+ 1/1

- M²

isentropic flow

Cp

( 10 : 2 )

inc

from the

free

stream

to

1.0 0 = NACA 4412 Wing , zero

O=

Elliptic

Cylinders

,

lift

zero

lift

.8

Equation ( 10 : 4 ) modified by equation ( 10 : 2 )

.7

Mcr

.6

Circular cylinder .5

Cp inc

mox

2

1

Fig .

Critical

3

function of maximum incompressible pressure negative coefficient . From Sibert , (2 ) Chart 9 .

10 : 3 .

Mach number as a

( 1 ) e.g . , Sibert , H. W. Prentice - Hall , Inc. , 1948 ( 2) op . cit .

" High .

- speed Aerodynamics

,"

equation 9.8 ,

10-5

TECHNICAL AERODYNAMICS

Incorporating

number

:

|

)

|

)|)

3

10

8

×

1

÷

2Y=

+

crit

that the

M = 1,

compressible pressure co

(

Mach

maximum

: 1 )

,

=

Y

: 3 )

(

-

the Prandtl Glauert relationship of equation 10 into gives for air of 1.4 the following relationship be

10

(

equation

YMar

(1

Comas Cpax

local

related to the by the equation + 2

Cpmax

where the

Y F ÷ 7

efficient

airfoil Mer is

[ (

number

☆

Mach

,

ical

*

the point on the

)

:

10

4

·

(

2

[(

0.4M2

0.45 2.4

1 ]

Mar

Mr

3.5

1.431

)

=

incmax

-

Cp

+ +

tween Mer and Cpincmax

1.0

.90

,

-Kaplan calculations Elliptic cylinders

,

.95

TR 624

lift

zero

NACA

digit-

CL

.

Moocr

.80

4

.85

symmetrical ,

airfoils

.75

TR

=

592

20

c,

t/

15

is

zero

angle

sweep of sweep

lift

and

on

critical

instead

of Mcr

coefficient

For swept wings read Mer cos

.

: 4 .

Effect of thickness ratio

30

.

where

10 number

,

Mach

A

.

Fig

25

percent

,

10

5

0

.65

0.4

▲

CL

=

.70

It is

elliptic cylinders

with the experimental

data

cal

in Fig

number

shown

.

The .

Mach

The theory

10

is

: 2 ) ,

seen to be

in

good

effect of pressure coefficient

: 3

and

.

tions

: 3,

.

(

-

a

also possible to derive similar relationship using the more accu rate Karman Tsien relationship of equation 10 and this equation has along with some experimental been plotted in Fig 10 data on wing sec

can be used to calculate

agreement on

criti

the effect of

AIRFOIL COMPRESSIBILITY

critical

.

in Fig

Mach

lift

with

number

coefficient

Mach

number

10

,

critical in Fig

on

data

: 4 .

coefficient

The

and

reduc

seen to be substantial

of the airfoil section and special in developing new airfoils to provide given lift coeffi reduction in critical Mach number for

10

depends on the

efforts have been

shape

NACA

a

the minimum

made by the

,

tion in

lift

are compared with test

.

thickness ratio and

calculations

: 4 ,

such

,

airfoil

10-6

EFFECTS

.

cient by avoiding large negative pressure peaks

1.0

a

Critical

M

9

)

(

deg

8

12

6

7

10

5

8 6

.

coefficient

CL

2

2

Lift

3

4

Experimental

CL with

8

7

5

6

.

6.

section

=

66 series

number Moo number at various constant angles tapered wing of From NACA TN 1697 Mach

A

of attack for

3 Mach

Variation of a

10

: 5 .

.

Fig

.2

,

0

0

Theoretical

to

and

as

lift

also increases in this ratio as sometimes slightly beyond the critical

the

,

: 1 ) ,

10

,

up

,

10

: 5,

.

in Fig

(

given by equation

-

1

,

/

.

-

-

Lift Curve Slope Effect At constant angle of attack on an air foil since all local pressures increase in proportion to √1 M² shown Mach

TECHNICAL AERODYNAMICS

inc

is

in Fig .

plotted

infinite

=

√1

lift

relating compressible

and

is

ratio

aspect

10

130

Figure

10 : 6 .

also shows that coefficient as

which

)

- curve - slope for 80

this

10 : 5 ,

increased

The corresponding equation

ao

and

with

reduced

(

lift

incompressible

is

number

-

critical Mach noted in Fig . 10 : 4 . the

5

line in Fig .

number , designated by the broken

:

10-7

be

10 : 6 shows good agreement

Prandtl -Glauert theory and some experimental values , though slopes accurately - curve are difficult to measure and must be cor

tween the

lift

for

rected

wall

a tunnel

effect of uncertain accuracy , so that

some

of

the experimental data do not agree with the Prandtl -Glauert theory as well as the samples

in Fig .

shown

VI-MO

0.8

0.9

1

10 : 6 .

0.6

0.7

0.6

1.6 1.5

10.7

10

.

: 5

Eq

1.4

4412

TR 646

o a

alo

0.8

NACA

Wing

,

1.2

inc

inc

1.3

0.9

airfoils

,

4A series NACA

c1

= 0

1.1 TN 3162

11.0

0.2

0.3 0.4

0.6

0.5

0.8

0.7

Moo

.

,

often designed with sweep ,

or sweepforward

is aeroelastically

but which

rigidity

A

,

aerodynamically advantageous

the wings have low flexural

major

and

important

number

a

(

,

A

▲ ,

/

beneficial effect of sweep is to increase the critical Mach portion to cos where is the angle of sweep for thickness ratio when viewed normal to the wing axis not 1

aspect

,

-

are

sometimes with negative sweepback

) .

if

4a

flight

(

is also

.

which

,

as

1 :

in Fig

back

speed

-

-

lift

for high

Wings intended

unstable

infinite

compressible flow correction to ratio curve slope zero sweep

Subsonic

10

: 6 .

.

Fig

given

in pro airfoil

as seen normal

AIRFOIL COMPRESSIBILITY

to the lateral axis of the airplane ) .

is

This

/

10-8

EFFECTS

is

because Mcos

line , where effects of sweep ,

the

com

is usually

ponent of Mach number

normal to the wing c 4

sweep

measured .

several adverse

however , and the

There are

selection of the best more

in detail later .

if

sweep ,

of the

One

This effect exists even for

is

any ,

adverse

infinite

a complicated problem discussed effects is on lift - curve - slope .

aspect ratio

40°

.11

:

(

▲

/57.3

1.0

27 a=

.08

cos

:a

=

10 : 7 ,

20°

) cos

Theory

.07

in Fig .

angle

Sweep

.10

a√ -M²

as shown

30 °

A

.09

,

.9

A

аодес

.8 Moo0

Theory

.06

.7

FA

Mo50.6

.6 Data NACA TN 1739

.05

.5

cos A .04

1

0.8

0.7

1.0

0.9

lift

Fig . 10 : 7 . Effect of sweep on infinite - aspect - ratio - curve - slope , including Prandtl - Glauert correction for high - subsonic sub - critical Mach number .

which includes the Prandtl

- Glauert

compressibility

correction

on the Mach

Note that the elementary theoretical correction based on COSA very good . An empirical correction factor FA is better . This can is not number .

the experimental right of the chart .

be read on

Drag and

in thickness ratio

Pitching on

curves in Fig Moment

critical

Mach

.

10 : 7 ,

Effects . number

with the FA scale at the

Since the effect of changes in Fig . 10 : 4 to

have been seen

similar to those of change of maximum negative pressure coefficient (1) shown in Fig . 10 : 3 , it is convenient to consider , as suggested by Stack ,

be

( 1 ) Stack , John . " Compressible Flows nautical Sciences , April 1945 .

in Aeronautics

."

Journal of Aero

TECHNICAL AERODYNAMICS

10-9

airfoil of

that the low - speed

airfoil is

speed

in Fig .

shown

mean line curvature coefficient than the actual ,

in

reduced

airfoil will

Such an

a greater

lift

characteristics as

same

of shorter chord

one

10 : 8 .

the

- M&

Cmac

and

this relationship

is

seen

some

experimental observations .

to be consistent

airfoil .

resulting relationship

The

sible flows

is

tios

The

The

.

Mach number analogous to the

( 10 : 5 )

and

( 10 : 6 )

is ,

lift

however , not

be based on empirical

must

and

repre data

coefficient with thickness ratio for incompres relation between the effective and actual thickness ra

of drag

given by

variation of

moment

Fig . 10 : 8 . Geometric interpretation of subsonic compressibility effects .

similar simple equation but

variation

be

coefficients sug

с

with

variation of equations

on the

,

Lc√1_M²

coefficient variation with

sentable by a

ratio

and a greater angle of attack for a given

in

10 : 1

moment

Mã as

(10 : 6 )

Fig .

The drag

-

have a greater thickness

tween incompressible and compressible pitching gested by Dwinnell (1 ) is

CacincV1

ratio V1

the

high

a given

(t/c ) effective minimum

- (t / c) actual / √1 - M drag

section

NACA NACA

(10 : 7)

coefficient with thickness ratio

digit

4 and 5 66 series

series

.012 Rough

Surface

.008

1

Cd min

Smooth.

.004

Surface

/

t 4

Fig .

10 : 9 .

percent 12

Effect of thickness ratio for use with equation

(1)Dwinnell 1949 .

8

, James

H.

20

16

on minimum ( 10 : 7 ) .

" Principles

of

24

section drag coefficient

Re = 6

x

106 .

Aerodynamics . "

Mc Graw

,

-Hill ,

AIRFOIL COMPRESSIBILITY

for two types of smooth and others , (1 ) is shown in Fig .

airfoils

rough

10-10

EFFECTS

as summarized by Abbott and

,

with equation

10 : 9 and can be used

( 10 : 7 )

to

estimate the effect of compressibility on drag coefficient with zero sweep . Sweep angle also has an effect on infinite - aspect - ratio or section

coefficient

drag

if it is

ing (as

in Fig .

10 : 10b

considered that the

rotation

from the unswept wing by

in Fig .

( as

was

generated

rather than by shear

ratio of the

The thickness

).

swept wing

10 : 10c )

section

streamwise

with Fig . 10 : 9 to estimate the effect of sweep on section drag coefficient , but on airplanes the aspect ratio is always finite and some

may be used

times very small swept

( as

in

" delta wing " airplanes ) ; the

compressibility correction

wing

is

finite

article .

discussed in the next

V

ratio

aspect

V

Normal

Section

Streamwise

Section

(a )

(b)

Unswept

Fig . 10:10 10 : 2 .

Illustration of

.

This

FINITE WINGS

:

Effect

ainc a

CDi

for

.

the

=

effect of high subsonic

1.8

given

infinite - aspect - ratio

VI -

MZ ,

/TA is

independent

of

(10 : 8 )

+

Mach

number ,

but neither

drag and

of these

Ira H. , von Doenhoff , Albert E. , and Stivers , Lewis of Airfoil Data . " NACA Wartime Report L - 560 . othert , B. " Plane and Three - dimensional Flow at High

( 1 ) Abbott ,

lift

resulting

often assumed that the relationship between induced

C

in

Mach number .

- M200

1.8+ A

a swept

EFFECTS .

The aspect ratio corrections

equation (2 )

in Göthert's

lift

COMPRESSIBILITY

of generating

in the lifting - line theory by the factor

curve - slope

-

( c ) Swept by rotating section thinner )

( streamwise

methods

modifying only the

commonly done by

It is also

different

SUBSONIC

9 need to be modified

is

two

section

wing from an unswept wing .

Lift -Curve - Slope Chapter

Swept by shearing

( streamwise same )

S. ,

Jr.

" Summary

()

2 Speeds . "

NACA TM 1105

( 1946) .

Subsonic

10-11

TECHNICAL AERODYNAMICS

is well verified

results on which

by more

and the assumptions

recent experiments

they are based are admitted

validity

by Göthert ( 1 ) to have poor

at low aspect ratio . A desirable

ratio

aspect

for high subsonic

correction

numbers

Mach

should be applicable to a wide range of aspect

ratios (0 to only on

1 ) and

ratios ( 1 to 10 ) and taper major should also cover the effect of sweepback , not

lift - curve - slope

drag , but also on

and induced

critical

Mach

num

information of this sort is ( in 1955 ) , having by by passed this need been recent NACA research because of the even more urgent need for supersonic test data . Murray (2 ) found in a study of wing test data in range aspect

ber .

not yet available

Complete

of

the

3 to 6 , and including

ratios from that Jones

(3 )

lifting - surface

sweepback

theory

up

discussed

to 45° on the c / 4

in

Chapter

9

line ,

could be

modified for high Mach number effect , including a sweep correction factor FA ≈ cos▲ , but requiring additional semi - empirical corrections as yet un determined , by the equation a where ẞ = √1

-

/

AE

1

=

ao inc

57.3 2π 2A

/

AFA B

( 10 : 9 )

small wing - thickness effect

M2 and a

of

Kaplan

(4 )

was

neglected , and E is the same factor used in Jones ' lifting - surface theory in equation ( 9:41 ) , and is very closely approximated for A = (1 to 10 ) by the equation

=

E Combining

equations

and ( 10:10 ) gives

( 10 : 9 )

1 57.3 2π

Equation (10:11 )

becomes ,

for ainc

( 1 ) Gothert ,

, (2 )Murray,

of Predicting 1739 ( 1948 ) .

(3 )JJones ,

B. , op .

Harry E. the Robert

/

/

( 10:10 )

0.94 + 1 A ≈ 1 + 1 A

2+ ( B/FÄ ) ß = 1 and

=

2 πT

for

(1 + A)

ao inc = 2

/57.3 ( 10:11 )

FA = 1 ,

A

57.3 3 +

( 10:12 )

cit .

of Several Methods " Comparison with Experiment Wings in Subsonic Compressible Flow . NACA TN

Lift of

T. , op .

cit .

( 4 ) Kaplan , Carl . " Effect of Compressibility at High Subsonic Veloci ties on the Lifting Force Acting on an Elliptic Cylinder . NACA TN 1834

( 1946) .

AIRFOIL COMPRESSIBILITY

is identical

which

with equation

particular

tests on a

( 9:33 ) and

available , present information ( 1955 ) sug for thin swept wings at high subsonic speeds .

( 10:11 )

Equation

also be written

( 10:11 ) may

A

a ☐ ao inc

( 10:13 )

and

2 + (1 + A)

( 10:12 ) can

be

ainc a

Effect .

effect of

equation

the

form of equation

- M² /FA

√1

3+ A

The

in

combined

= 2 + ( 1 + A)

( 10:13 )

- M² /FA

√1

( 10 : 8 ) thus

Drag

low speed

at

unless special high - speed

,

wing are

gests use of equation

Equations

well verified

Accordingly

ratios .

for a wide range of aspect

10-12

EFFECTS

(10:14 )

on the low - speed induced

Moo

/

(10:15 )

CD₁ = CZ πAеW has been inadequately as are

available

explored , but such spanwise load distribution data

suggest

9:23 should be reduced The the

profile

effect

" rotating

drag

depending

is

that

ew

somewhat

for

as

Moo

also affected

on

whether

approaches

by

the wing .

was

tive thickness ratio sweep reduces the effective thickness ratio

sweep ,

the amount of

swept by " shearing " or by

Increased

of the wing as given by

Fig .

Mor

and by

Moo

A , as given in

ratio

any aspect

as described in Fig . 10:10

"

drag

Moo

increases the

equation

( 10 : 7) ;

effec

increased

factor cos▲ , but in creases the chord and hence the Reynolds number . The net effect of sweep on profile dragis hence partly a viscosity phenomenon ; viscosity effects are considered 10 : 3.

lift ,

in

TRANSONIC

Chapter

by the

11 .

COMPRESSIBILITY

EFFECTS

.. Rules

for the variation of

airfoils covering the range of speeds from the high subsonic super -critical , as in Fig . 5 : 1b , through the low supersonic range involving subsonic flow areas , as in Fig . 5 : 1c , have not drag , and pitching

been , and quite possibly

stall

moment

of

can not be , simply formulated .

and separation as well as

Mach

number effects

This

is

because

are involved

.

How

general rules can be stated for a limited high subsonic super region . This is well worth while because it is the region in

ever , some

critical

competing military aircraft designs are currently for superiority for obvious military reasons .

which

The

airfoil

air

( 1955 )

striving

flow patterns in this regime of speeds and the corresponding pressure distributions are shown in Fig . 10:11 . Figure 10 : 11a

TECHNICAL AERODYNAMICS

10-13

shows the

shock waves which have formed

point ) of

a 23015

airfoil

exceeded .

Figure

slightly

sure distribution

sufficiently

exceeded so that the upper

layer have interacted This

surface .

is

number

Mach

critical

known

of the flow

as

the

number

Mach

-24

,

, 1.0

c

,

b .

.

a

=

in

10:12 that no marked change when Mer

is

reached

corres in

are shown

either the drag

lift

and increase in Glauert rule can be

-

-

a

The

and note also that when

major drop off in there has been that the Prandtl curve the from evident

reached

slightly

coefficient

due to exceeding has started

airfoil

coefficients of this

drag

coefficient occurs

It is

0.73

the symbol Ms.

to

beyond Mer

for the prediction of variation of section and that the onset of serious trouble

with Mach number the

rise

critical

Mach number does not appear

appreciably

This point

,

applied

Moo

,

.

drag

and

in Fig

designated by

.

is

Note

.

.

.

10:12

lift

lift

section

burble

)

.

.

= 0.60

"

a .

,

x

Chordwise station

x

/c

/

.8

Simultaneously obtained schlieren photographs and pressure 20. From NACA TN 1813 for NACA 23015 airfoil section at

"

(

Moo

compressibility

lift

1.0

6

.6

=

4

.2

,

Pressure coefficient

M

ponding

Mg

stall

M 1.0.

Fig 10:11 distributions

or

shock

-1.6

Chordwise station

Fig

of

Crest

Crest

160

or

from the upper

∞

,P

has been

Mach number

surface shock waves and boundary

separation

produce

to

number has

Mach

(highest been only

: 11b shows the shock wave pattern and pres

0.73 when the

Moo =

at

beyond the crest

critical

when the 10

just

until

where the slope

the drag

of the

drag

AIRFOIL COMPRESSIBILITY

10-14

EFFECTS

.

a

,

,

,

a

curve vs. Mach number has attained value of 0.10 is labeled Md At some slightly higher value peak in the but smaller than Mg there is .7 .14

c,

assuming lower Variation of surface lift contribution constant above M 0.65

ratio also

1

1

Aspect

12

.

-

.6

,

See

.10

3

.06

coefficient drag

7 .

coefficient

.08 O

lift

, cd

a

= A = . 2

.

,

a

large has TN 2720 which shows increase in Md from 0.68 at A = to 0.80 at for NACA 0012 wing at 20

effect

cd ./

Mcr

.

Md

02

.6 .7 Free stream Mach number Section lift and drag coefficients 20.

of

Moo

for

sub is evi

beyond the

0.95

indicated by Fig 10:13 which shows that the shocks that form at

a

small loss

pattern

.

small disturbance

of

,

0.85 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Machnumberi front shock

numbers involve

energy

and

hence

of the general flow

n

Mach

0.90

Fig

10:13 Ratio of total pres sure across shock as function of Mach number in front of shock .

critical

-

low super

is

.

Mach number

1.00

.

corrections

sub critical

, M ,

critical

The reason

of subsonic

of

applicability

a

for the

1.05

.

dently no longer applicable

.

correction

Totalheadlossacross shock wave

-

curve and the Prandtl Glauert

sonic compressibility

only

M

as functions From NACA TN 1813 .

a

at

=

airfoil

NACA 23015

lift

,

-

10:12

.

.

Fig

O

8

.5

.4

Section

.04

2

Section

Ms

TECHNICAL AERODYNAMICS

10-15

below which no serious

The Mach number

by the Prandtl

other than those covered

effects

- Glauert

compressibility

due to

or

- Tsien correc

Karman

, is thus seen to be not only greater than Mer but greater usually , , Mg also than Md . It is however less than insofar as compressibility effects are concerned , but the effect is greatly depen Fig dent on angle of attack and airfoil section as shown in Fig . 10:14 .

tions are applicable

ure 10:14 gives calculated

and experimental

values of Mer ,

Md , and Mg ,

as

well as calculated and experimental values of Mg which is defined as the free - stream Mach number giving M = 1 at the crest ( highest point ) of the

airfoil .

The calculated

excellent

agreement and reasonably close to Md .

the newer

airfoils

by

Fig .

Figure

10 : 14a .

larger than

typified

,

values of

are seen to be in also be noted that

Mg may

10 : 14b

than the older

also shows that

Md

is

airfoils

,

critical typified

very substantially

Mer at the higher angles of attack .

For determination of the actual flyable plane , the additional

adverse

Junction

into

must be taken

SUPERSONIC

this is

flight

tests

CHARACTERISTICS .

WING

pressure or pitching

moment

Mach

compressibility

account ;

without special wind tunnel or 10 : 4 .

It

by Fig . 10 : 14b , have a much higher

a given angle of attack

for

Mach number

and experimental

number

for

a given

air

effect due to wing - fuselage almost

impossible to predict

.

The

lift , drag ,

and center

infinite - aspect

coefficient for

- of

-ratio super

sonic airfoils can be calculated from shock and expansion wave theory as in Chapter 5. For thin airfoils at small angles of attack the results , as simplified by Ackeret and presented

by

Sibert

( 1 ) may

be written as

follows : 4α

CL

/2

Cmc

/

where Zc = 2 ( t c ) ² a symmetrical

calculated

=

C²

=0

√M²

-

1 +

( infinite A )

2Zc

√M20

-

(infinite A)

( 10:17 )

( 10:18 )

for a symmetrical double - wedge airfoil and Z = ( 8/ 3Xt /c ) ² bi - convex airfoil . For other airfoil shapes , Zc can be

as outlined

( 1 ) Sibert , op .

(2) Ibid .

( 10:16 )

VM20

CDwave

for

(infinite A )

cit . ,

in

Sibert

. (2)

chapter 19 .

AIRFOIL COMPRESSIBILITY

EFFECTS

10-16

.8

)

(

Mg calc

Ms

(

Melexp

‫יו‬

1

Md

,

Mcr

6

,

section

8

4415

NACA

8

.

deg

.

Airfoil

a

2

of attack

Md

Ms

Mplexp

(

Free

-

Angle

7

stream

Mach

-2

a,

4.6

,

number

M.

.5

.6

MB'calc

Mc

of attack

.

B

0.6

.

stall

-

drag divergence and shock two

different

NACA

airfoil

Mach

sections

.

66,2-215

=

,

a,

NACA

Variation of critical of attack for

numbers with angle From NACA TN 1813

deg

a

section

,

.

.

10:14

Airfoil

,

b .

Angle

Fig

K

2

-2

,

4

.5

TECHNICAL AERODYNAMICS

10-17

Finite

Rectangular Wings .

Except

for

boundary

- layer effects ,

finite

rectangular wings behave like infinite aspect - ratio wings except for the region included in the tip Mach cones , as shown in the sketches in Fig . 10:15 . It is seen in Fig . 10:15 that the difference between

nite

and

fi

infinite

- ratio characteristics is for small flying at low supersonic speeds as in Fig . 10 : 15b .

aspect

aspect - ratio wings

small except

a . High M , Low A

Fig .

10:15 .

Sketch

in tip

conical flow A wings . The

showing

region

.

b . Low

M , High

A

areas of finite rectangular wings affected by Unshaded areas behave nearly like infinite

analysis of Schlichting ( 1 ) as presented by Sibert

, (2)

results in the

equations 4α

CL

√μ20 CDwave

/2

CTRC

( 1-1 / 2A / M2 -1 )

·

=

180

1

A α

3A (M²

/ /M2

-

1 2

in

has the same meaning as

be added to the wave drag

lift

( Delta ) Wings .

drag , and pitching

( 10:20 )

1

( 10:21 )

drag must

,

2Zc

VM20

- 1)

where Zc

Triangular

·

( 10:19 )

equation of equation

( 10:17 ) ,

and skin -friction

( 10:20 ) as

The general problem

moment of tapered

before .

of

calculating

and swept trapezoidal

wings

is

too complicated for presentation here , but has been effectively presented by Cohen (3 ) and others . However , the case of triangular wings with straight ( 1 ) Schlichting ,

1939 .

H, "

Airfoil

Theory at Supersonic Speed , "

NACA TM 897 ,

( 2 ) Sibert , op . cit . , p . 136 . ( 3 ) Cohen , Doris , " Formulas and Charts for the Transonic Lift of Flat Sweptback Wings with Interacting Leading and Trailing

NACA

TN 2093 , 1950 .

and Drag Edges , "

AIRFOIL COMPRESSIBILITY

a

very commonly has been

angle

of the delta leading

TN 1955

are

.

,

"

edge

10:16

The

Ellis

,

aerodynamic

to the

m

well

pointed out

in

characteris

tangent

of the

results of the tests reported in and Hasel draw the following con

:

tan E tan m Jones theory

8/1

(

1000

Y

1.43 1.71 1.75 reference

)1

)

'

(

00

angle

Mach

(

(

--

6

Measuredlift curve slope Theoretical two dimensional ft curve alope

1.0

in Fig

of

it is

wings

their experimental study

clusions from

-

( 1 )

.

tangent

.

,

is the ratio of the shown

For such

factor in determining the

major

a

NACA TN 1955

and Hasel

.

Ellis

by

presented

"

,

known as delta wings which constitute special case of the tapered and swept trapezoidal wing

used

tics

10-18

,

trailing edges

EFFECTS

.2

00

2

.8

.4

1.0 tan E tan m

1.2

1.8

1.6

1.4

2.0

.

0

(

% )4

T

max

с ☐

0

M

1.43 1.71

.08

6

.09

min

O

O

2

4

8

O

O

NACA

1.0

tanE

1.2

1.4

1.6

1.8

2.0

1949

.

October

.

.

From NACA TN 1955

Preliminary Hasel and Sweptback Wings

Investiga

, "

C. ,

,

at

( 1 ) 1955

E.

Macon Jr. and Lowell Supersonic Speeds of Triangular

Ellis

tion ,

series of delta wings ,

Test results on

"

10:16

.

.

Fig

a

tan m

NACA

TN

TECHNICAL AERODYNAMICS

10-19

lift of

thin , triangular plan - form wings may be calcu slender wing theory up to values of tan Ɛ / tan m ≈ 0.3 , where is the wing vertex half - angle and m is the Mach angle . For values of tan ɛ / tan m above 1.0 , the is essentially the same as that obtained theoretically for a two - dimensional wing . 2. The center of pressure of thin , triangular plan - form wings is coincident with the center of area . 3. For low drag coefficients approaching those due to skin friction alone and for the highest values of maximum - drag ratio , both triangular and sweptback wings should be operated with their lead ing edges well behind the Mach cone . " " 1.

The

lated by Jones

'

lift

lift

PROBLEMS

Using the Clark Y ( CY ) airfoil data in Appendix 5 , estimate a 10 : 1 . and cd0 min for a Clark Y wing of 7 - ft chord and 35 - ft span , flying at 450 mph in standard sea - level air , neglecting Re corrections . 10 : 2 . An airfoil is tested at low speed and found to have a maximum negative pressure coefficient on the upper surface of 1.0 . Using Fig . 10 : 3 , find the critical Mach number and critical speed at 40,000 stand

ft

ard altitude . Using equations ( 10:19 ) , ( 10:20 ) , and ( 10:21 ) , write equations 10 : 3 . , drag , and pitching moment coefficients of a rectangular wing for the of aspect ratio 4 , flying at a Mach number of 2.0 . Assume t c = 0.05 . 10 : 4 . Using Fig . 10:16 , calculate the , drag , and pitching moment about the center of area , for a wing consisting of an isoscles triangle 10 ft on each side , flying at a Mach number of 1.5 in standard sea - level

lift

lift

air .

/

CHAPTER

11

AIRFOIL VISCOSITY EFFECTS -

11 : 1 .

SECTIONS . The low- speed Reynolds

SCALE EFFECTS , WING

LOW SPEED

number affects chiefly the boundary layer and hence the skin friction drag and , through effect on separation , the stalling or maximum lift coeffi cient . Since boundary - layer transition (from laminar to turbulent ) and

separation

also affected

are

by

surface roughness

surface

,

curvature

,

surface pressure gradient , and other factors , as discussed in Chapters 6 and 7 , there is a complicated interaction between the boundary layer and the outside air stream , resulting in a number of minor secondary effects which could not be anticipated from any simple theoretical considerations . Some

are evident from Fig .

such interactions

speed scale effects

attack

for

lift

zero

( Fig .

stall

11 : la ) ,

section drag and

maximum

section

results

shown

in Fig .

dimensional low - turbulence tunnel .

" rough

L.E.

"

coefficient

moment

the major

( Fig .

and angle of

effects

ft

10

to

lie

near

11 : 1c ) .

obtained in the Langley two The smooth models were of polished the " smooth on

"

curves

the smoothness

could be maintained in service

on airplanes

and

(c ) on

11 : 1 were

curves , depending

wing construction

ft to

lift

low

minor

shows

free - flight characteristics of an actual airplane

reasonably be expected

tual

pitching

(b )

in addition to

center

mahogany wood ;

from 4

11 : 1 , which

lift - curve - slope

11 : 1b ) ,

The test

of the

on (a )

(Fig .

aerodynamic minimum

below the

with stalling

.

in

might

direction

the

to which the

ac

For wings of chords

speeds of 50 mph to 100 mph ,

is cross - hatched on the c1 max chart of Fig . sizes and level high speeds of 100 mph to 300 mph ,

the range of values of Re 11 : 1c .

For the

same

the lower part of the range of values of chart of Fig . cause of Mach

11 : 1c . number

The most abundant

Re

is

cross - hatched

Beyond 300 mph , the charts

effects discussed in the

next

section test data available

are

on the cd min not applicable be

article

and

are either

elsewhere .

at

Re = 3.2

million (from the NACA variable density tunnel , with turbulence of about 2.5%, as given in Tables A5 : 1 through A5 : 3 ) or Re = 6 million (from NACA Wartime Report L - 560 , as given in Figures A5 : 1 through A5 : 5 ) . Correc tions of these data to other values of Re from 3 million to 9 million 11-1

11-2

TECHNICAL AERODYNAMICS

.11

.10

TH

-1

Smooth

ao per deg

alo ,

deg

Rough

-2

B

L. E. A

L. E.

Rough

.09

/

-3

Re 106

.08

1.0

.5

2

345

10

4

Smooth

/

Re 106 1.0

.5

2

345

10

Section 662-415

Lift

a.

curve effects (minor ) .

-.05 .20

C mac

-.06

Smooth

-.07

or

ac ,

Rough

of

/

1.0

2

Pitching

b.

3

/

.25

Re 106 1

-.08 0.5

fraction chord

4 5

moment

Re 106

1.0

0.5

10

and aerodynamic

center effects

Rough

10

( minor

).

Stall

range

L.E.

Smooth

10

1.6 Smooth

High speed

7

range

of

1.4

airplanes

of airplanes clmax

5 1000

1.2

Cdmin

s

Rough

L.E.

1.0

3

/

Re 106

2

0.5

1.0 C.

Fig .

345

1.8

15

4

2

2

345

Minimum drag

/

Re 106

0.8 10

0.5

and maximum

lift

1.0

effects

2

3

45

10

( major ) .

Minor and Major effects , at low speed , of Reynolds number on section characteristics of NACA 662-415 section . For comparison with other sections see Chapter 13 and Appendix 5 , Fig . A5 : 15 . From NACA TN 1945 . 11 : 1 .

AIRFOIL VISCOSITY are given in Figures

cl

and

max up

data

The

to

11-3

EFFECTS

A5 : 6 to A5 : 8 and A5 : 11

to A5 : 14 ; corrections of cd min given in Figures A5 : 9 and A5 : 10 ,

million are conflicting and nearly

Re = 25

are often

This

incomplete .

always

is

necessarily true because the task of maintaining even a nearly complete catalog of airfoil section characteristics as affected by most of the variables involved is prohibitively expensive . It is moreover unneces of the desired accuracy can usually be estimated , flight condition , by a judicious combination particular specified for a existing of data such as are given in Appendix 5 .

sary

,

as information

For example , suppose it is desired to estimate the low - speed section characteristics of a smooth wing section designated by the four digits for a range of Reynolds numbers from 8 million ( for cl max ' at stall ) to 18 million ( for cd min , at high speed ) , with other characteristics es timated at 13 million . The data here available ( other data may be avail 2418 ,

able ; consult at

Re

3.2 million

first

the

indexes ) are those given

NACA

Item

Data

Table

C1 max

A5 : 1

/

ao deg cd min

of Table

Figs

Data .

A5 :

a.c.

0.239

0.241

3.2

6.0

first ,

1.28 ±0.10

-2.0 ±0.1 0.105 ±0.03

0.0068

-0.045

Re 106

involved

Estimated Values ( see text )

0.098

0.0076

Estimate

listed in

below.

1-5

-2.1

0.094

Cmac

is

test data

A5 : 1

OF PROCEDURE

1.35

-0.038

/

11 : 1

(VDT

These data are

FOR ESTIMATING AIRFOIL SECTION CHARACTERISTICS

EXAMPLE

1.53

-1.9

α10

)

two columns

TABLE 11 : 1 .

in Table

and Figures A5 : 1 to A5 : 5 .

0.00761.001

-0.048 ±0.003 0.243 ±0.002

the minor effects

since the graphs for

8

13

Re

to

Re = 13

18

million

million . Since the effects are unlikely to be very far off ; extrapolation should possible , but here , as often , it cannot be avoided tend beyond Re = 9

An extrapolation

.

corrections of these items minor , always .

the be

do

not

ex

results are avoided

if

The extrapolations

are explained item - by - item below : a10 :

Data in columns 1 and 2 are -1.90 and -2.10 respectively . Refer to Fig . A5 : 6 and note that while data for the NACA 2418 are not given , the effect of Re on alo for other 4 - digit air foils between 3 million and 9 million is less than 0.20 . For may reasonably be judged from inspection of the the 2418 , graphs that no greater change is involved and that a10 changes

it

TECHNICAL AERODYNAMICS

11-4

less than 0.20 up to is -2.00 ± 0.10 .

Re = 13

million

.

Hence , the estimated

alo

in columns

Re 1 and 2 are 0.094 and 0.098 respectively . A5 : 7 and note that ao for other 4 - digit airfoils is in the range from 0.102 to 0.110 with small changes between Re = These data are inconsistent with 3 million and Re = 9 million . Table A5 : 1 for the airfoils given in both Fig . A5 : 7 and Table A5 : 1 ( 0012 , 4412 , and 4415 ) being about 0.005 to 0.010 higher in Fig . A5 : 7 . is recommended that Fig . A5 : 7 be accepted as more accurate because is a more recent study , and that the value 0.094 be thrown out as probably improperly measured or corrected . Correcting the value 0.098 at Re = 6 million to 0.104 , is 0.003 at timated by inspection of Fig . A5 : 7 that a = 0.105

ao :

Data

fer to Fig .

It

it

it

million

Re = 13

.

in

columns 1 and 2 are -0.038 and -0.045 respectively . No general Re corrections are given in Appendix 5 , but Fig . 11 : 1 3 shows the order of magnitude of the correction between Re million and Re - 9 million to be -0.004 for another airfoil ( 662-415 ) . It is judged by inspection of Fig . 11 : 1b that another increase of about -0.003 would be involved in going to Re = 13 Data

cmac

-

million a.c

es

.

-0.045

.:

Hence , the estimated value 0.003 = -0.048 ± 0.003 .

of

Cmac

for

Table

11 : 1

is

No Data in columns 1 and 2 are 0.239 and 0.241 respectively . general Re corrections are given in Appendix 5 , but Fig . 11 : 1 shows the correction on another airfoil ( 662-415 ) to be about 0.002 between Re = 6 million and Re = 9 million . Hence , the es timated value of a.c. is 0.243 ± 0.002 at Re = 13 million .

effects of with similar

The major comparison

Re on

cl

max and

data on other

cd min may also be estimated

airfoils in

Appendix

5 as

by

follows :

Data in columns 1 and 2 are 1.53 at Re = 3.2 million ( and high free - stream turbulence ) and 1.35 at Re = 6 million ( low turbu lence ) . A procedure for taking account of turbulence ( given in second edition of the text ) by calculating an " effective Reynolds number " higher than the actual Reynolds number has been largely abandoned as basically incorrect . The preferred procedure now ( 1955 ) is to use only low turbulence data . Hence , the figure = C1 max 1.53 from Table A5 : 1 will be disregarded as a basis for estimating the free - flight value . No low turbulence data for Re

C1 max :

for

of C1 max NACA 2418 sections are available in , though some might be found by a thorough study of the indexes . Data for Re corrections to c1 max of some other

corrections

this text

NACA

4 - digit

airfoils ( 4412 and 4415 ) are given in Fig . A5 : 14 , and these data are consistent with Fig . A5 : 2 which also shows the 2400 series to be about 0.15 less than the 23000 series at Re = 6 million . the same sort of variation of C1 max with Re is assumed for the 2418 as is shown in Fig . A5 : 14 for the 23015 , the increase in C1 max between Re = 6 million and Re = 8 million should be about 0.03 . Hence , the estimated C1 max for a smooth 2418 airfoil is 1.35 0.03-1.38 . Note , however , that " stand ard " roughness produces a drop of 0.3 . Hence , moderate surface irregularities might well be assumed to produce a drop of 0.1 , and the best estimate for an actual wing is c1 max = 1.28 ± 0.10 . Data listed in columns 1 and 2 are 0.0076 and 0.0068 at Re = min 3.2 million ( high turbulence ) and Re == 6 million respectively .

If

Cd

AIRFOIL VISCOSITY

11-5

EFFECTS

airfoil section are not given , but from other airfoil data as follows : Refer to Fig . A5 : 8 and note that cd min for 4 -digit and 5 - digit = 6 million 15 percent thick airfoils drops 0.0002 between Re and Re = 9 million . Further change to Re = 18 million may be inferred from inspection of Fig . A5 : 9 to be small . In fact , Fig . A5 : 9 shows the drag of 6 - series airfoils to rise between Re = 9 million and Re = 18 million , but this is presumably due to a larg is here judged that on er area of turbulent boundary layer . the 2418 airfoil the same conflicting factors are acting ( reduced cd min with higher Re due to normal skin friction changes for a given ratio of turbulent to laminar areas ; increased cd min with Re due to change of transition point resulting in larger area of turbulent skin friction ) . The net change is estimated as zero but uncertain to the extent of the rise seen in Fig . A5 : 9 for the 633-018 airfoil ( about 0.001 ) . Hence , the estimated cd min for a smooth 2318 airfoil section at Re 18 million is 0.0066 ± 0.001 . Note in Fig . A5 : 9b that standard leading edge rough ness can add 0.004 ; hence , for actual wings in free flight , part of the difference may be added ( say 0.001 ) . The net result estimated at cd min = 0.0076 ± 0.001 . Re corrections may be estimated

for the 2418 or inferred

It

is

For 6 - series

airfoils

which are coming

,

considerably

as the above can be made

airfoil are

discussed above , because

wide use , estimates such

accurately

more

( e.g. ,

data

than

Figs

.

for the

2418

A5 : 10 )

A5 : 9 and

available .

11 : 2 .

COMBINED

HIGH

SPEED

AND

SCALE EFFECTS ,

variations of

results with independent dom

more

into

Mach

WING

and Reynolds

SECTIONS .

Test

numbers are

sel

obtained .

The combined

for high

effects on

minimum

drag

coefficient are usually estimated

subsonic Mach numbers from tests at the proper Reynolds

number

For supersonic Mach numbers , drag estimates usually are based on tests at the proper Mach number , and skin friction

by the methods of Chapter

variation

with

10.

Reynolds

number

is

estimated by the methods of Chapter

7

(which are notably incomplete and often inadequate ) . A few test results of the independent available .

airfoil

Some such

section

( see

effects of

flight of airplanes at high Fig Note in . 11 : 2 that the Mach number effect on factor for values of M as low as 0.2 or even 0.15 independent effects in Fig . 11 : 2 must be combined calculation of stalled

conditions

.

results are

For the shown

M and

Re on c1 max

are

results are shown in Fig . 11 : 2 for an NACA 64-210 also Fig . A5 : 15 ) . Such data are indispensable to

three conditions

in Fig .

11 : 4 .

shown

altitudes or in turns .

cl for

max becomes

according to the

in Fig .

a major

smooth wings .

11 : 3 ,

The

flight

the combined

TECHNICAL AERODYNAMICS

-

number of

The Reynolds

Fig

11

1.65 feet

wing

chord

For condition

.

=

c

of

con

corresponds to

level flight with

sea

mph

2 ,

lof

dition

1.3

M =

standard sea

a

69.

200

200/761

0.26

=

1.4

in

designated -by numbers plotted

6.

flying at level air

For an airplane

: 3

/

Re 106

.

1.5

.

11-6

the wing chord for sea level flight is 4.3 feet At higher altitudes

-

1.2

.

clmax

.

.

;

flight

For supersonic

--- 369--2-

-369-1-369

sort should be lating maneuverability

TN 2824 .

is classified for reasons of military security

available

.

NACA

when

,

11 : 2 .

current

most

information of this sort

,

(

for

inde pendent variations of M and Re on From NACA 64-210 airfoil section . Test results

Fig .

1955

)

.5

.4

.3

this

available for calcu

M

.2

.1

0

of

data

;

0.9

at 50,000 ft times as great

,

1.0

the chords are about

3

Rough

5

the chords are larger

1.1

Condition

Low speed

/

8

4

2

: 2

.

After the effects of as

Re

.

11 : 3 ,

with

M and

in Articles

Re 11

: 1

0 .

: 4 .

C1 max

wing have been estimated

wing can be calculated

,

.

a

a

the

gration over

of wing

variation of

characteristics of finite inte If dS is an element series of chordwise elementary areas area equal to cdy the relationship between the section coefficients

: 2 ,

and 11

finite

10

Combinations of Figs 11 flight showing and

,

.

on each section of

11

smooth

EFFECTS ON FINITE WINGS a

:

3 .

SCALE

Fig

condi

)

8

flight

Mand Re effects

(

Possible

10

.

: 3 .

.

6

0

2

4

combining From NACA TN 2824

Re 106

1.0

6

/

Re 106

11

2

1.1

3

Condition

1

Condition

1.2

1

High airplane Condition Large

.2

Fig 11 tions for

Condition

1.3

altitude

.

High

.3

Clmax

1.4

2

Small altitude Condition

M

airplane

1

.4

3

1.5

.5

by

AIRFOIL VISCOSITY

coefficients specified

and the wing

equations

by the

CLS =

11-7

EFFECTS

( 11 : 1 )

cids

( 11 : 2 )

= Scads CDS

Cmaccavs

is

where cav

when multiplied

lie is

.

is

( 11 : 3 )

/

( 11 : 3 ) ,

the line

about

if

only

the aerodynamic

straight line .

on the same

wings and

jcmaccds

wing

Equation

coefficient

applicable

(about a.c. line )

chord S b . Equations ( 11 : 1 ) and by the dynamic pressure q , give the lift and drag

the average

wing respectively moment

=

in

as noted

of

aerodynamic

therefore

applicable to tapered wings only

,

the

on

gives the

is

centers and

hence

all

centers of

It is ,

parentheses

( 11 : 2 ) ,

if

sections of the wing not applicable to swept

,

the geometry of the taper

in a straight line . flight approximately For subsonic this line is the wing quarter chord ; for supersonic flight it is approximately the fifty percent chord line . A more general statement than equation ( 11 : 3 ) would require writing an centers of the wing

such as to keep the aerodynamic

other integral expression for

the pitching

the root section , of the forces acting

applied

( 11 : 1 ) can be

can be related

only

.

distribution of air

The spanwise

critical

the

distribution of

Mach

of a

number

lift

structed with zero

of construction

chords

, however ,

have , however , a

values of

of

finite

all

is to

have

special

also wing .

spanwise

twist .

α10

known as a " wash ;

positive .

The

A twisted

wing

wing .

to es

the

of

factor deter

Wings are often con

stations

parallel

;

such

An equally common method

geometric

chords

parallel

,

in

said

between the root and

tip sections

built

negative sign

importance

a major

with an intentional twist , the most involving a reduced angle of incidence near the tip . ever , often

twisted

coefficient cl considered in

to have zero geometric twist ; it will then aerodynamic definite twist corresponding to the differ

is

the wing

which case

is

is

This

.

in

Equation

.

loads for structural analysis

lift is

wings are said to have zero aerodynamic

in

lift

local

the

It is of

LOAD DISTRIBUTION .

SPANWISE

a wing .

ence

if

to the angle of attack of the wing

timate the spanwise mining

practice

sections

article .

the next 11 : 4

in

about some point

moments ,

on the outboard

the

- out " of incidence reverse twist

,

and

.

of

of twist

This kind of twist

is arbitrarily

a " wash - in "

Wings are , how

common type

designated by a

incidence

,

is

twist in is has a different spanwise load distribution from Negative twist is often built into a tapered wing to degrees

commonly designated by the

called

symbol € . an un

reduce

TECHNICAL AERODYNAMICS

11-8

the tendency

twist

on

When

of such

wings

stall first

to

stall distribution is

at the

tips .

The

effect of

discussed later in this article . a wing with a positive angle of twist has zero total , the not zero at all points ; zero negative is the result of a

lift is lift near

the middle and a positive

lift lift near

lift

the tips , as sketched in A wing without twist has a spanwise distribution similar Fig , to that sketched in . 11 : 6 with a maximum at the middle and a reduced

Fig .

11 : 5 .

lift

near the tips , the

form

of the

is

wing .

lift

distribution

The Prandtl

obtained with an

elliptic

wing

lift

depending

chiefly

theory concludes

elliptic

planform and an

that

lift

on the minimum

plan drag

distribution

.

Wing Wing

Fig .

11 : 5 .

due The

lift

sidered additive

tion

in Cla

as sketched in Fig

c1c1b

which

is

Fig .

components due to twist ,

+

cla

lift

Additional distri 11 : 6 . bution due to angle of attack .

Basic lift distribution to positive twist .

and .

angle

11 : 7 and

Clb

+

of attack are usually con as represented by the equa

ClaiCL

( 11 : 4 )

clb is the basic lift coefficient at any spanwise station additional lift coefficient . Since cla is proportional

the

and

to

Wing alone

&Wing Wing +2 nacelles

lift

distri Resultant bution on wing with positive twist at positive angle of attack . Fig .

11 : 7 .

Fig .

Effect of nacelles on distribution . ( From Vol . IV , p . 161. )

11 : 8 .

spanwise Durand ,

lift

to the average lift coefficient proportionality is designated by clal on the wing CL . The constant of and may be considered to represent the local additional lift coefficient

angle

of attack

,

it is

also proportional

lift coefficient CL is 1.00 . wings with rounded tips and various taper ratios tapered straight For theoretically calculated values of clal and clb /a € and aspect ratios , widely used in are given in tabular form in NACA TR 631 and have been

when

the average

AIRFOIL VISCOSITY

calculating

lift

spanwise

There is is justified , because

sis .

some doubt ,

distribution for however , as to

the effect of

EFFECTS

11-9

of structural analy

purposes

such a refined

whether

method

fuselage or nacelle interference

is

neglected by this method , and such

neglect results in wide departures from theoretical calculations as shown in Fig . 11 : 8 . Accordingly , an equivalent approximate method , developed by Schrenk ( 1 ) which is explained in detail in textbooks on aircraft structures such as that of Peery , ( 2 ) has been widely adopted . The assumptions of the Schrenk are as follows :

method

1

)

of twist 2

ematic

)

any point

is

equal to the angle

lift chord multiplied by one -half lift - curve - slope . lift distribution is proportional to the arith

aspect ratio

additional

The

the actual wing chord and the chord of an ellipse area as the wing .

mean between

having the

same

These assumptions work

distribution at

measured from the mean zero

infinite

the

lift

The basic

fairly

well

are

difficult

to

justify theoretically

but are found

to

in practice .

1.7

Point of

first stall

C1 max

1.6

CL =1.52 =CL Imax

CLE 1.45

CL

1.5

CL

1.40 1.35

1.4

1.3

0.1

Fig .

If ted

in

11 : 9 .

11 : 9 ,

Semi

and

0.4

0.5

Fraction of - log plot of C1

0.6

0.7

semi - span max and

c

to

0.8

determine

0.9

1.0

CL max ·

if the

lines in Fig .

solution

can be made

(1 ) sSchrenk wise

0.3

the distribution of c1 max along the span of a wing can be estima terms of M and Re , resulting in a plot such as the solid line shown

in Fig . dotted

0.2

distribution of c₁ is also known as shown by the for each of a number of values of CL , a trial for the spanwise location of the point of first stall 11 : 9 ,

" A Simple Approximation Method NACA TN 948 , 1940 .

, O. ,

Lift Distribution , "

( 2) Peery , David

,

J.

" Aircraft

Structures

."

for Obtaining the Span

Mc Graw

- Hill ,

1950

.

TECHNICAL AERODYNAMICS

11-10

for the value of CL

and

if

in Fig .

shown

point of heaviest shading

Fig .

b.

11:10 ,

BOUNDARIES

lift . the lift

of speed and times

These

lift ,

The

tion

is

are constant

In flight ,

.

= nW =

flight

the

if

L

is

speed

constant .

equation

number

Data on the

relationship

that of Fig .

10 : 5 may be

some

Clas

= CLSamph²

,

tapered , and

as shown .

8

, a wing may

stall ,

other combinations by the

following

/391

in miles per hour . In

1481

rewritten

/

p Po

condi (11 : 4 )

Note that

terms of the pressure

qCL

/

and nW S

/

ratio

= p Po '

as

MCL

( 11 : 5)

for a particular wing such as replotted logarithmically as shown in Fig . 11:11 , between CL and

M

this logarithmic replot lines of constant

pressure ratio

lines

airplane

but also under

,

( 11 : 4 ) may be nw

on

on an

relationships are indicated

ds

and

rectangular

load factor , and speed are related by the

L

and Mach

and sweptback

Tapered

in turning or other accelerated flight may be several of the airplane or , in general , L = nw, where n is the

the weight

load factor .

where mph

C.

Tapered

not only at the landing condition argument :

as shown

of rectangular , tapered , and the initial stall occurring at the

sweptback wings .

FLIGHT

11 : 5 .

an outflow on swept wings

Initial stall distributions for

11:10 .

particularly

.

Rectangular

a.

max '

stall distributions

Typical

swept wings are

indication of CL

is

sweptback , as there

11 : 10c .

larger

done by using increasingly

the local c❘ distribution is tan as shown by the heavy dashed line . This

,

however , only a rough

is

the wing

in Fig .

is

until

( 11 : 4 )

distribution

gent to the c1 max

calculation is ,

This

max .

values of CL in equation

are also lines of constant

For level

flight

(n

= 1)

/

wing

loading

nw S and

MCL ,

and are

straight

at sea

level (8

= 1) ,

a wing

100 lb / ft corresponds to the line labeled 100 in Fig . 11:11 . Fig . 11:11 that when the same airplane goes to about 30,000 ft , Note in

loading of

sq

AIRFOIL VISCOSITY where the pressure

11-11

EFFECTS

/Po≈

1/3 , or at sea level in a turn with a load factor the condition is specified by the line nw /ds = 300 , and that under these conditions there has been not only a substan tial reduction in CL max but also the airplane must operate in the re

ratio

gion

d = P

flight

n = 3,

of the peaks of the constant

1.5

100

200

a

300

lines

which , as noted

400

_nw

= 1481 M

8S

.

in Fig .

CL

CLmax

1.0

CImax

-140

.9

-t

CImax at each const a ( High speed

-100

.7

CL

.6

at

each const M

-120.

.8

11:11 ,

buffet )

-80 .

.5 .4 -40.

.3 α

.2

20

.4

.3

.2

3

5

·6

.5 6

7

Moo

/

.7

.9 1.0

.8

Re 106 as tested

Fig . 11:11 . CL variation with M and Re at constant a for a tapered wing of NACA 66 - series airfoil sections and A = 6 (from NACA TN 1697 ) , with Mer and several flight conditions shown . represent a condition of possible high speed buffet ( a condition of un satisfactory handling conditions in flight ) . For the wing whose charac teristics are shown in Fig . 11:11 , it is judged on this basis that values

/

300 do not represent satisfactory flight conditions . of nw 88 In using a graph such as Fig . 11:11 , it is important to know that the

combinations of

Moo

tions in free flight on CL max

and Re as tested

may

not correspond to the combina

of a particular airplane

should be applied

,

if

,

so that a scale

data are available

,

to Fig

.

correction

11:11 .

This

11-12

will result in

TECHNICAL AERODYNAMICS

a

new

Reynolds

number

scale

representing the conditions

as flown or contemplated . PROBLEMS

ft

11 : 1 . A small airplane has a rectangular wing of S = 180 sq and A = 7 and a NACA 4412 section ( see Table A5 : 1 for data ) . The stalling speed at sea level ( determined by CL max ) is about 40 mph with a particular gross weight , and the level high speed at sea level ( determined chiefly by CD min ) is 100 mph with a particular engine and propeller . Using the

methods of Article 11 : 1 , estimate the proper values of CL max and CD min to use for stalling speed and high speed flight calculations . 11 : 2 . The root section of a large airplane has a chord of 15 and a 23021 section . Using the data in Table A5 : 2 , for flight in sea level standard air , estimate c1 max at 60 mph and cd min at 240 mph . 11 : 3 . An airplane of wing loading W, S = 50 lb/ sq ft flies at an tude where the pressure ratio d = P Po = 1/2 and a load factor of n = 2 and the wing characteristics are those given by Fig . 11:11 . From inspec tion of Fig . 11:11 , find the maximum Mach number at which satisfactory flight without high speed buffet is permissible under these conditions .

correction

ft

/

alti

CHAPTER

12

HIGH - LIFT DEVICES

12 : 1 .

ing

FOR HIGH -LIFT DEVICES .

NEED

airplane

are high

speed

speed requires

quirements

are

lift

lift

a high

conflicting

wings without high -

devices , requires

12 : 1 .

Airfoil

conflicting

boundary

- layer

turbulent

flow

boundary

sections

requirements , whereas

layer

in Fig .

high

which

the

section and low Low drag ,

12 : 1 .

lift

devices

,

is

resists

= C1 max Re = 6 x

satisfying the

good low drag and good high

lift

for

extent of laminar

maximum

lift

high -

stall

general , these re

b . Good high section ; 1.7 , but cd min = 0.006 at 106 ( smooth surface ) .

without

of

low landing or

In

section .

illustrated

as

and

drag wing

a low

wing

a . Good low drag section ; cd min = 0.003 , but c1 max = 1.0 at Re = 6 x 106 ( smooth surface ) .

Fig .

Desirable characteristics of an

in level flight

High maximum speed requires

speed .

stalling

maximum

lift .

favored by early development of separation . These requirements

could be simply compromised by the use of a retractible turbulence gener ator near the leading edge . The airfoil section shapes most suitable for the two purposes are also conflicting and velocity gradients involved . An obvious

solution to this

dilemma

lift

vices for

airfoil

sections are

ie chordwise

pressure

is to use a low- drag section for auxiliary retractible or enclosed

the high speed condition and provide an high Various device to get high cl max low - drag

of

on account

shown

used high -

commonly

in

Fig

.

lift

12 : 2 .

devices provide either for change in effective section centerline ture

,

or for delay of boundary - layer separation

sort are currently

( 1955 ) under

development .

ary layer removal and flaps , such as Fig

in cl mum

max ; but

lift

.

12 : 2f

the merit of a device cannot

coefficient obtained ,

as

,

or both .

show

of bound

tremendous increases

be judged

in the last analysis 12-1

curva this

Devices of

Some combinations ,

de

Most of these

solely

by the

maxi

the economic merit

TECHNICAL AERODYNAMICS

11-2

661-212

661-212

Thicker low drag section ; C1 max 1.2 with ca min = 0.0035 . Simula ted .2c split flap shown dotted .

b. Low drag section with plain (sealed ) flap ; C1 max = 2. From

64A010

661-212

a. =

C. Low drag section with leading edge slots ; c1 max = 2 , but at high∞ . From NACA TN 3129 .

NACA TN 2502 .

d.

Low drag

flap : 3007 .

C1 max =

section with slotted

2.5 .

From NACA

TN

661-212 e . Low drag section with nose flap and slotted flap ; cl max = 3. From NACA TN 3007 .

f.

Low drag section with flap and vacuum boundary - layer removal ; C1 max = 4. From NACA TN 2149 , 3093 .

= 0.8 no flaps C1 max = 1.9 opt . flaps C1 max

g.

Fig .

trail

Low drag supersonic section with leading edge flap as well as ing edge flap for high subsonic From NACA TN 2149 , 3093 . .

lift

12 : 2 .

Values of

Various high -

lift devices

applied to low -drag airfoil sections

.

values for low Mach number , optimum C1 max shown are approximate any , optimum flap angle any , optimum boundary - layer slot location any , and suction 106. For specific arrangements and test data ,

if

see Appendix

if

5.

Re6x

,

if

HIGH

-LIFT

12-3

DEVICES

of a high - lift device must be judged from economic considerations of the over -all installation , including the effect of high stalling angles on landing

suitability

design as well as the

gear

devices associated with full - span high -

trol

of possible

lift

devices

lateral con

.

effects of various high - lift devices on wing lift curves are shown in Fig . 12 : 3 . Note in Fig . 12 : 3 that the effect of flaps is to displace The

3.0

the effect of

either flaps , is alone or in combination with to increase substantially the angle of attack at which the wing stalls . This provision

signer as layout of

be made

must

the landing

CL•max . 1.5

0.5 0

for very

gear

+

1.0

de in

a major handicap to the airplane

+

2.0

Fig

high wing angles of attack on landing .

15

Effects of high

12

lift

: 3 .

is

or

2.5

boundary layer removal ,

lift

-

, whereas

Flap Wing and slot slot Suction

3.5

.

slots or

with

devices on so page A5-27

See

al

.

curves

.

of the airplane

lift

in the stalling angle

change

Wing

out major

flaps Wing alone

the angle of attack of zero

have

flaps of

edge

or another

sort

one

since 1945

is

Their purpose

not

in

high CL max for slow landing but also to provide an during steeper glide drag crease in the landing approach which permits landing and smaller fields Such flaps are usually deflected about 600

where

,

,

A5-25

on C1 max

for

due to Reynolds

some

number

are

for

for

from Re

.

a

.

-

.

a

x

15

are indicated in

106

Reynolds

A5-24

constant

it 1.5

The values

Reynolds

substantial

as indicated

number

few low drag

number at

of airfoils

going

Re

Other

on pages A5-21 Mach

types

in

shown

Approximately the

by

correc

sections with .20c

inclusive

. ,

deflected

corrections

on page A5-20

106

to

up

12 2a

higher drag than

split flap

,

than Re

60 °

to less split flaps

=

the test data with flaps down

these data

to

all

a

on

,

number correction

there

but

106

=

for

page A5-8

,

: 2 ,

.

obtainable

have

on low drag sections

.

max

A5

for split flaps x

Fig

line in Fig

off

take

obtainable either with the plain or Re = 6

cl

of

is

max

,

cl

increase

likely to

CL max for landing but is

plain flap at smaller flap deflections for

same

without substantial

:

max

such as that shown by the dotted

Re

are

may be noted

106 to

shown

Typical on page

that the gain

Re =

x

CL

for take

9

in

increase

used

commonly

is

A

good

a

.

a

provides

moderate

split flap

is

=

provide

in drag

smaller flap deflection angle

x

off to

A

.

for landing

a

.

,

a

a

only to provide

built

Most subsonic airplanes

EDGE FLAPS

.

TRAILING

trailing

.

12 : 2 .

106

is

TECHNICAL AERODYNAMICS

12-4

if

entirely lost

almost on page

well as

C1 max as

and

Mach

usually intermediate types of flaps

Reynolds

is

factor in

a major

Actual

numbers .

Note also determining

airfoils will

be

between the " smooth condition " and " rough condition "

data shown on page A5-25 . mon

as high as 0.3 .

the Mach number goes

that surface condition

A5-25

Comprehensive

as a function

of

data

on

airfoil

cl

shape ,

for various com flap angle , surface

max

condition Mach number should be available to permit a wise selection of subsonic flaps but are not now ( 1955 ) available ; the necessary information for design decisions must usually be pieced together ,

and Reynolds

number ,

information . Occasionally tables have been prepared given ( such as those in NACA TR 664 ) for comparing various types of flaps fragmentary

from

flap - slot

and

at a particular value of Reynolds

combinations

number , Mach

surface condition and airfoil thickness but such tables are helpful more misleading than used to select a high device for flight conditions other than the test conditions . Few airplanes use full span flaps because of the necessity of reserving

number ,

likely

,

,

if

to be

lift

the outer 30 to 50 percent of the span of each wing for aileron or other lateral control devices . The effect of using partial span flaps as com pared with full span flaps is a great reduction tainable as shown in Figs . 12 : 4 and 12 : 5 .

. D /L

6

at 0.2

S

0 .

) .

12

60 40 80 20 Flaplengthpercent wing span

Effect of flap

split

1000

span on

wing characteristics 0.15c flaps deflected 60 from NACA ,

tapered TR 611

(

a

8

0.4

Fig span on 60 on

from NACA TR 611

(

3

0.4

16 20

°

.

0.15c tapered wing

5 :

, 4

Effect of flap split flaps deflected

12

: 4

.

-4 Angle attackdegrees 0

-0.4 -16 -12 -8

of

3-0.3

12

50% 100%

-0.2

0.8

°

-0.1

.

0.6

CL max

Wing

1.2

Co

.

-50%

0

Wing

1.6

5 .

0.2

100%

:

0.4

).

0.6

2.0 1.8

CL max

100 50%

%

0.8

alone

C₁ 510

Span Span flap flap

1.2

Wing

and Co

1.4

∞

at

1.6

Fig

--Tapered Tapered

CL

1.8

ob

5 : 5 : 13

2.0

max

12

max O

2.2

in the value of CL

HIGH

If

full

tain

span high -

a value

of CL

lift

max

-LIFT

DEVICES

devices are used

of

12-5

it is

usually

possible to

about 0.9 to 0.95 c1 max ' but special

ob

devices

for lateral control with flaps fully deflected . Some such devices for use with plain , split , and slotted flaps are shown in Fig . 12 : 6 . In general , the highest lifts are obtained with combinations of trailing edge flaps , leading edge slats , and boundary - layer control . must

be developed

The development of the necessary

the determination

of optimum

lift

to say at the present time what tory lateral control , as many

in

lateral control devices configuration

maximum

such

lift

is

,

and

has lagged

it is

behind

not possible

satisfac

obtainable with

devices are under active

development

lateral control devices sketched in Fig . 12 : 6 do not include devices suitable for control at maximum lift coefficients in the range from 3 to 4 indicated in Fig . 12 : 2 and on pages A5-26 through A5-29 , though 1955.

it is

The

not considered

difficult

to develop such devices because minor

/ lift

de

partures of the slat and or slotted flap from their optimum locations pro always involves a re , and control at high duce major losses of duction of

lift

on one of the wings .

It

lift

should also be possible to provide

lateral control by varying the boundary - layer duct pressure or boundary layer duct flow volume in devices where boundary - layer suction is used . For supersonic wings

very thin wing sections

with sharp leading and trailing edges , are needed from considerations of optimum supersonic flight configuration . It is extremely difficult to get a high maximum coef landing wings ficient for slow with such . The best device developed to ,

,

lift

date

(1955 ) appears

to be a combination of leading and trailing

resulting in a thin wing shown in Fig . 12 : 2g , for possible to

make such

structural thin wing ,

design

12 : 3 .

with a which

highly

data

flaps slotted

cambered ,

edge

are given on page A5-30

.

flaps

line

broken , median

It

as

may be

in the deflected position , but the is difficult for such flaps because of the very flaps of this sort appear not to have been reported . when

problem

and tests on

LEADING EDGE SLATS AND SLOTS . An extensible

leading edge slat

,

leaving a slot between the slat and airfoil , as sketched in Fig . 12 : 2c , a simple and effective means of delaying stall and increasing the max

is

lift

coefficient , as shown in Fig . 12 : 3 , either alone or in combina tion with other high - lift devices . Note on page A5-27 that a leading edge slot adds a substantial increment of maximum lift even when double - slotted flaps and boundary - layer control have already produced a very high maximum imum

lift .

For thicker wings

not be so

clearly

,

as shown on pages A5-28 and A5-29 , the

an advantage , as an addition

to boundary

slat

may

- layer control

.

12-6

TECHNICAL AERODYNAMICS

Slot -lip aileron

Flap Plain aileron

WY

NATIONAL ADVISORY COMMITTEE FORAERONAUTICS

A

-

Q15c plain sealedaileronona ClarkY15 wing with020c split flap 62c

Fake

A retractableaileronon a Clark X-15 wing with 6/6c

020c split flap

JAFF⋅

046c

A retractable

Ú

aileron onanMACA23012wing with a 02566cslottedflap

A 0.10c spoiler

hinged at Q50con an NACA23012wing with a 02566c slatted flap

hinged

A QIOCdeflector at Q50c onan NACA23012wing with 0.2566cslotted flap

AQ.10cspoiler hinged at0.50cand010cdefledor hinged at Q60c onan NACA23012wing with a Q2566 slotted flap

I

AQUOCdeflector hinged at0.50cand a retractable aileron on an NACA23012wing with a 02566slotted flap

J

hinged

at

A Q10cspoiler and ac deflector

050c on an NACA23012 wing with a 02566 slotted flap NATI ALADV COMMITTEE FOR AERONAUTICS

A QOC spoiler hinged at 0.50c and a Q10cdeflector hinged at 0.60c with a slot on an NACA 23012 wing with a 0.2566 slotted flap.

Fig .

12 : 6 .

Some

split ,

lateral control devices for use with full span , plain , flaps , reported in NACA TN 1404 .

and slotted

HIGH - LIFT DEVICES

flaps , since

as double - slotted

are obtained without leading

is

fulness on thick wings

maximum

lift

slats ,

edge

12-7

coefficients in

of

excess

but the question of

4

their use

pre

not answered conclusively by the data here

sented . 12 : 4 .

the

BOUNDARY

lift

maximum

in

pores

is

drag ,

minimum

- LAYER

A most effective device for increasing

CONTROL .

of subsonic

wing sections , which

blowing or sucking of

the

air

also decrease

may

the

slots , holes ,

through

or

chordwise locations on the upper surface controlling purpose for the of the boundary layer , which in turn controls skin friction and separation . Suction has been found more effective , and the surface at suitable

more economical

for

been found

of blower power , than blowing . Substantial effects have suction removal of boundary layer anywhere between the

leading edge of the wing and the leading edge of the flap . through porous materials near 4 - digit

symmetrical

to raise the

found

the

section

NACA

lift

maximum

small quantities of suction

leading

air

,

edge

as sketched

12 : 2f ,

.

coefficient from 1.3 to

"

thick

percent

of a 10.5

in Fig

suction

"Area

has

been

1.8 with very

Various types of porous surface were used , including sintered steel as well as perforated plates backed by felt or filter paper . For a quantitative measurement of

air

the suction

flow

it is

flow

customary

( NACA

/

is

3093 ) .

to use a flow coefficient

,

9

CQ =

where Q b

TN

( 12 : 1 )

bc

the volume rate of flow per unit span in

ft3/ft - sec .

For the

leading edge experiment , values of CQ less than 0.001 were found to give nearly the maximum increase in cl max . This flow coefficient repre

porous

sents the ratio of the stream which NACA

tions

suction

would flow through

studies a spanwise

slot

pages A5-28

and

0.1

percent

has been used ;

have been found to be 0.45c

as shown on

flow to the

duct

(NACA

of

amount

of the free

In

the wing area .

air

other

effective suction slot loca

TN 2149 ) and

A5-29 respectively .

0.75c The

(NACA TN

1631 ) ,

flow coefficients

necessary for effective use of such spanwise slots are , however , ten times as great as for a porous leading edge , and the size , weight , and power re quirements

in

of the associated " vacuum cleaner " device

the design of

It is

will

possible

an

airplane

that

" porous

major

factors

.

area suction " at more rearward

locations

installations in connection with slotted flaps and lateral control devices , but no general rules for the design of

permit economical

adequate

become

using such suction slots

12-8

TECHNICAL AERODYNAMICS

such equipment

are

boundary

that economical

slight reduction in crease

in

currently available

- layer

minimum

removal

drag

tice within

Current developments by "area suction , "

coefficient

indicate

providing

a

well as an enormous in = max' 4.0 , possibly higher ) ,

lift coefficient ( up to c1 lateral control , is feasible and

maximum

with adequate

.

as

may become

accepted

prac

a few years . PROBLEMS

12 : 1 .

Using

data from Table

A5 : 2 on an NACA

0012

wing with 20 percent

split flaps deflected 60 ° , write equations for CL vs. a , CD vs. CL , and Cp vs. 1/CL for a rectangular wing of aspect ratio 6 with full span flaps chord

.

Using the graphs on page A5-8 , estimate c1 max at Re = 6 x 106 an NACA 4412 section with 20 percent chord split flap deflected 60º . Referring to Fig . 12 : 5 , find the angle with the horizontal of a 12 : 3 . steady stalled glide of the 5 : 3 tapered wing of characteristics there shown with 50 per cent span flaps . 12 :4 . An airplane weighing 1400 pounds and having a rectangular wing span and 180 sq ft area , is equipped with full span slotted flaps of 35 and with a leading edge slat in the optimum position (data as given on page A5-26 ) . Assuming CL max = 0.93 c1 max , calculate the stalling speed of the airplane in standard sea -level air ; also calculate the Reynolds number at stall , and compare with the Reynolds number specified for the data . 12 : 2 .

for

ft

CHAPTER

13

AIRFOIL SELECTION 13 : 1 .

SYSTEMATIC INVESTIGATIONS AND NUMBERING

have been systematically

investigated

Airfoil

SYSTEMS .

for at least

shapes

a hundred years .

The

primary objectives have usually been to determine a shape which would give high maximum Only within , low minimum drag , and low pitching moment .

lift

the last twenty years , however , have the systematic investigations been reasonably enlightened as to the nature of the air flow in the immediate

vicinity of

an

as noted in

Chapters

so

far

tions Navy ,

airfoil , particularly in 6 and

more an

Air

art than

Force ,

a science .

of

NACA ) , many

many

airplane

educational research organizations

a number

of private

with the

Catholic

investigators

University ,

- layer flow

is

airfoil sec

agencies (Army ,

agencies ( England

,

France ,

( e.g. , Boeing ) ,

manufacturers

Goettingen University )

( e.g. ,

( e.g.

Even today ,

.

optimum

Many U. S. governmental

foreign governmental

, Japan , U.S. S. R. ) ,

layer

on boundary

from complete as to leave the development

Germany many

the boundary

the information

7,

, and

in

1955

Washington , D. C. ) , have studied and

pub

,

Max Munk ,

Dr.

connected

lished results of investigations . The NACA has attempted to serve as a clearing house for information of this sort and is also responsible on its own

for

systematic investigations

the most comprehensive Each investigator and investigating account

of classifying airfoil

Tests of the

shapes .

wind tunnels have appeared

in

many

but most of these discrepancies ences

in

turbulence

,

Reynolds

Prior to

about

wing sections mary

and

variable .

same

have been tracked down as due to number ,

for effects of

most investigations

/

and or surface

wind

differ condi

tunnel wall or open

were made on

relatively thin

the shape of the center line of the section was the

With the development

during World War

I it

seemed

to

many

of structurally feasible investigators

pri

monoplanes

that the study should

attempting to isolate the effects of the upper and lower on which pressure measurements could be made independently . The

be extended surfaces

1910

all .

cases to give widely different results ,

number , Mach

tion , when the proper corrections jet test section have been made .

of

its own system airfoils in different

agency has devised

by

13-1

13-2

TECHNICAL AERODYNAMICS

conclusion was that the lower surface was relatively unimpor systematic variations of the upper surface could lead to

tentative

tant and that

airfoil ,

the best

in flight

out

but

the

tunnel test results were often not borne

wind

of imperfectly

because

differences

understood

tunnel and free - flight flow conditions

between wind

In the alphabetical designation system of Colonel V. E. Clark , with airfoils designated alphabetically from A through Z , a number of very satisfactory airfoils were found to be feasible using a lower surface that was a plain flat surface from trail .

ing edge forward to nearly the leading

edge . For the "Clark Y" , the upper thickness of 11.7 percent at a station 30 per cent of the chord from the leading edge . This Clark Y became one of the

surface reached a

maximum

airfoils

most widely used

Later studies by exploration

the

first

by

ever investigated .

provided for a

NACA

investigating

edge radius , and maximum thickness

ing

usually requires

shapes , including

in

resulted 4

-digit

some

series .

airfoils

" 4 - digit "

numbering

the

) which

This inves system which ,

lead

.

a 5 - digit system

( it did not provided an additional set of center

- digit series

4

and

the thickness .

digits to designate

thickness location

airfoils

include symmetrical

line

NACA

for

symmetrical

a dash and two more

edge radius and maximum

A variant of the

and shape

leading

,

airfoils ,

symmetrical

of

subsequently varying the center line curvature

however ,

geometric

thickness distribution

the

location

distributions found most suitable for tigation involved the so - called NACA

systematic

more

was

trailing

reflexed

edge .

The 5 - digit

series

airfoils

considered to be an improvement over any of the For a number of years the 5 - digit airfoils of the NACA

were considered to be the best .

Later theoretical studies of effect of free - stream pressures

airfoil

pressure distribution layer , resulted

boundary

on

,

and

in

the

another

pressure on the up per surface , and later also on the lower surface , were specified in the numbering system . Such airfoils were found to permit a considerably ex

series of

NACA

tended range system

is

values of of a

maximum

number

which the point

of laminar boundary - layer

currently

provided by pages .

airfoils in

very

lift ,

widely used since

it is

lift

,

of

flow

minimum

and the

even though

considered that

it

" 6 - series " of

this

does not give high maximum

lift

can be

of the high devices described in Chapter 12. Details designation systems are given in the following few of airfoil

some

AIRFOIL SELECTION 13 : 2 .

airfoil shown 13 : 2 ,

Mean

THE NACA

4

- DIGIT

GEOMETRIC

designation involves a

in Fig . 13 : 1 , and laid off at right

The NACA 4 - digit

.

SYSTEM

line consisting

mean

angles to the parabolic

system of

parabolas

two

in

shown

,

as

Fig

.

arcs .

Horizontal tangent to both parabolas here Parabola

Parabola Chord

Location of max . ordinate of

mean line SECOND DIGIT

=

of

thickness distribution as

a basic

line of airfoil ·

Xyc max 4 -digit

13-3

airfoils Fig .

=

max

for

13 : 1 .

Mean

. ordinate of

mean

line

" camber " = Ус max = FIRST DIGIT for 4 - digit airfoils

line

designation for

4-

digit airfoils

=

.

с

0.3c X

y FLE

= 110 (t

ty

t / c ) 2 in

=

0.2969

per cent c

√x -

-

.1260x

.3516x²

+ .2843x3

- .1015x4

air

Basic thickness distribution for NACA 4 - digit and 5 - digit Above airfoil is designated 0020 or 0020-63 , where 6 denotes normal leading edge radius and 3 denotes maximum thickness at 0.3c . See Fig . 13 : 6 for other L.E. radius and maximum thickness location designations . LAST 2 any ) are t c , per cent . DIGITS of 4- and 5 - digit airfoils ( before dash ,

Fig .

13 : 2 .

foils .

if

The two parabolas

of

maximum

in Fig .

ordinate of the

of the 4 - digit designation DIGIT .

horizontal

13 : 1 have a

mean

line

system .

.

The

This ordinate

/

tangent

is

at the point

the FIRST

location of this ordinate

DIGIT

is

the

are the thickness ratio in per cent . The equation for the basic thickness distribution is given below the sketch SECOND

in Fig .

/

13 : 2 .

110 ( t c ) 2.

The LAST TWO

DIGITS

The leading edge

radius

The maximum thickness

Other leading edge radii and other

is

specified by the equation гLE

=

for the basic distribution is at 0.3c . maximum

thickness locations

are

indi

cated by adding a dash and two more digits after the 4 - digit airfoil desig nation . A code table describing the meaning of the supplementary digits

after the

dash

is

given

in Fig .

13 : 6 .

TECHNICAL AERODYNAMICS

13-4

A sample

airfoil for

4

- digit

which

x-

is

layout

in Fig .

shown

and y - coordinates

of the

13 : 3 .

sured from the chord line through the leading

in Fig .

13 : 4 .

designations

-34

omission because " low- drag

in

range

A wide

as shown in Fig . cambers from 0 to 20 to 70 per cent ,

and -35 ,

this

and

is

developed .

the equipment available

2415

airfoils

have been tested ,

them were tested with the dash - number now recognized to have been a major

airfoils

of these

some

NACA

ratios from 6 to 25 percent , mean line ordinate locations of

maximum

all of

though not

the

mea edges are given

trailing

and

4 - digit

NACA

6 per cent , and

airfoils later

"

of

covering thickness

13 : 5 ,

is

This

upper and lower surface

correspond

Even

at the time

,

if such

closely to

very

airfoils

the

had been tested

the low drag would not have been

detected becauseno low - turbulence wind tunnel providing for high Reynolds

available

and Mach numbers was

at the time the tests were run .

0.3c %c

"LE=2.48

t

=

.15c

yc

=

2%c

measurements

of

B = 0.1 Xyc max

=

Fig .

.4c

it

bolas

shown

Principal

13 : 3 .

While the cause

max

4

- digit

NACA 2415

airfoil .

is usually considered obsolete in 1955 be for other mean lines than the two tangent para 13 : 1 , some of the 4 - digit airfoils involving such system

does not provide

in Fig .

parabolas are very close approximations to the Upon re - testing

discovered .

in

" low - drag "

airfoils later

low - turbulence wind

tunnels , they have also been found to have low- drag with the proper leading - edge radius and thickness distribution designated by a dash - number after the four digits . Another range of

mean

THE

was

NACA 5

- DIGIT

GEOMETRIC

ond

to the

with

mean

ordinate

.

two

digits

,

NACA

5- digit

series de

of

The NACA 5 - digit system can system by replacing the

which designate not only the

line but also the

The range

SYSTEM .

from the 4 - digit

be considered to be evolved

digit

provided by the

article .

scribed in the next 13 : 3 .

lines

mean

shape of the mean

lines considered is

ordinate

maximum

line aft of the shown

in

Fig

.

sec

maximum

13 : 7 ,

and

13-5

cent of chord

per cent

ratio

Position of yc max at tenths of chord 4

is

thickness 15 per

is

88STRIN

of chord

2

Among

Maximum

is

NACA 2415 per given Stations and ordinates cent ofairfoil or in Apper Surface Lower Burtes StationOrdinate Station Ordinate

29 28 28 enge

Camber , yc max

FEEBETRERAR

15

no97872393282588

2

NACA

4

AIRFOIL SELECTION

2512

6206

6409

.

Dalala

6418 6421

:

2606

2706

2609

2709

2612

2712

2615

2715

2618

2718

2621

2721

4606

4509

4609

4512

4612

4515

4615

4518

4618

4521

4621

6506

6606

6509

6609

6512 6515 6518 6521

+ 0 +

6612 6615 6618

6621

reported in Technical Report 350 See Airplane Design D. Tenth Edition

,

Wood

1 0 0

! 0=0€ 4506

NACA

.

or

K.

560

,

digit airfoils

-

L -

: 5 .

.

for

4

6221

6412 6415

"

6218

NACA

4421

6209 6215

Report ordinates

4418

6406

6212

Wartime

4415

of

560

FFFFFFFFFFFF

FEIFSC FFGGES

4221

2518 2521

DDDDD

)

4215

4218

,

0025

DDDDD

0021

2515

FFFFFFFFO

FFM FFFFFF

O

FFFFEN

0012

Frrrrr

2509

0018

13

2506

0009 0015

and ordinates

Report

.

.

2406

0006

Fig

designation

From NACA Wartime

-L

-d4

airfoil

, "

igit Example of 2415 airfoil

13

: 4 .

.

Fig

,

2 .

L. through radius 2.48 Slope ofradius L.B.1 0.10

13-6

a.

TECHNICAL AERODYNAMICS

First digit

L.E. radius

Seconddigit

Max.-thickness location, tenths

0 3 6 (standard) 9

Sharp 4 normal Normal 3 X normal

2 3 (standard) 4 5 6

2 3 4 5 6

Meaning of two digits after dash indicating nonstandard leading edge radius and nonstandard maximum - thickness location .

0006-63

0009-33

0012-63

0009-93

0009-63

0009-05

0009-62

0009-35

0009-64

0009-34

0009-65

2209-34

0009-66

2409-34 4409-34

0009-03

b.

C.

NACA

4 - digit

Comparison

airfoils

modified thickness distribution

( From

NACA TR 492.

)

0009-03

0009-62

0009-33

0009-63-0009

0009-63-0009

0009-64

0009-93

0009-66

of airfoils with

modified nose radii

Fig .

with

nose shape .

13 : 6 .

.

Modified

and

Comparison of airfoils with modified location of point of maximum thickness .

d.

NACA 4 - digit

airfoils

.

AIRFOIL SELECTION a sample

airfoil

first

is

designation

in Fig . 5- digit

shown

13-7 13 : 8 .

in Fig .

As noted

13 : 8 ,

system have the same meaning last - two digits of the digit system except , that the first digit is only the approx as for the 4 imate maximum ordinate of the mean line and is actually intended to be a measure of the lift coefficient at which the airfoil is designed to oper ate , usually designated by cli , and actually equal to ( 20/3 ) x Cli ′ The

the

and

Cubic

Straight

yc

line : third digit Inverted cubic : third digit =

max

0

=

1

Approx . FIRST DIGIT , per cent chord

Xyc

max

-One

half of the per cent expressed

(Actually 20/3 of design c₁ )

by SECOND AND THIRD DIGITS

Fig .

13 : 7 .

Mean

line

designation

for 5 - digit airfoils

.

2 30 15

thickness is 15 per cent of chord

ordinate of line is about per cent of chord

Max .

Max . mean

2

ordinate of

Max .

line is at Fig .

second

and

13 : 8 .

Aft portion of mean line is straight

mean

of

3/20

chord

Example

of

5-

third digits constitute

digit airfoil

third digit tells

The

ter the maximum ordinate designating straight and of the

5- digit

along with

some

The mean

ly

was

mean

in

reported

,

NACA

TR 610 are shown

line of

in Fig .

some 13 : 9 ,

also there reported . system were found

the 4 - digit

to provide just as low

system , with a reduction

in pitching

thought at the time to be important , but with the

adoption of high -

af

the symbol o

or an inverted cubic designating inverted cubic . Sketches

the 5 - digit as

twice the

line ordinate

mean

straight

- digit airfoils

lift

which

widespread

4

lines of

drag and high moments ,

airfoils

is 1

maximum

the portion of the

whether

.

is

a per cent of chord which

per cent of chord from the leading edge to the

location .

designation

lift

devices as

fair

described in Chapter

12 ,

the quest for low pitching The basic

moments had to be abandoned . thickness distribution and leading - edge radii for the

system are the same as

for the

4

-digit

system .

Hence , 5 - digit

5 - digit airfoils

TECHNICAL AERODYNAMICS

13-8

also be followed by a dash and two additional digits designating other leading - edge radii and maximum thickness locations . The 23012-34 , shown as one of the collection in Fig . 13 : 9 , is a very close approximation to

can

airfoils later

discovered to have very low drag

not detected at the

time

,

of the

this low

though

tests reported in

drag was

of a

TR 610 because

in the wind tunnel . It is now considered slightly low - drag airfoils only on account of a flat or concave

trace of turbulence

inferior to area near

such

the

structurally

leading edge on the

disadvantageous

is

lower surface which

judged

aerodynamically unimportant

though

to be

Aero

.

characteristics of 4- and 5 - digit series of airfoils as determined high in the - turbulence variable density wind tunnel (VDT ) are given in

dynamic

Tables A5 : 1 and A5 : 2 . 0012-63

0012 68 -60

.

23006

°

0006

23009

43009

63009

0012-64

23009

0012

23012

43012

63012

0012-65

23012

0015

23015

43015

63015

23012-33

23015

0018

23018

43018

63018

23012-34

0021

23021

43021

63021

23012-64

16066

0009

23021 43009

-A

43012

22012

32012

42012

23012

33012

43012

24012

34012

44012

43012

000

21012

60°

62021

63009

63021

64021

airfoil

testing

involving

Mach

the

NACA

to develop

undertook

systematic variations of the

mean

a

an attempt

.

,

)

:

(

.

In

.

number

Note see NACA Wartime Report Tenth Edition for ordinates

series

of line in con

a

of airfoils of high critical

, "

-

SERIES AIRFOILS

,

"

D. ,

THE NACA

digit airfoils

Airplane Design

-

,

.

4

:

13

4- and

Some

Wood

1

or

L -

.

: 9 .

13

560

K.

Fig

5

25012

program

junction with optimization of leading edge radius and thickness distribu tion based on velocity and pressure calculations assuming theoretical

it is

in

to add algebraically the velocity patterns for flow around various mean lines to the velocity pat terns for flow around various thickness distributions The basic symet closely igit correspond trical airfoils tested to those of the NACA

in

which

permissible

-d

4

.

,

compressible flow

-

1

.

,

,

-

In the series series followed by dash numbers -34 -35 or -36 second digit designates the minimum pressure location in tenths of

the the

13-9

AIRFOIL SELECTION leading edge , for the basic symmetrical

chord from the

lift .

For

this

and

a minimum

is

group

pressure at 0.6 chord

often

as the

known

16

,

- series

two

The

.

section at zero

digits are 16 , third digit is the

first

the

lift coefficient cliin tenths , being zero for symmetrical airfoils last two digits are again the maximum thickness in percent of chord A typical 1 - series airfoil designation is shown in Fig . 13:10 . design

.

The

.

1 6-2 15

1

- series

Maximum

Design

Minimum pressure at 0.6 chord for basic symmet

rical

lift

Fig . For most

it

at

section

1

Typical

13:10 .

- series airfoils

1 - series

the

airfoil line is

mean

of

chord

lift coeffi

cient Cli

zero

is

thickness

15 per cent

=

0.2

designation curved

in

.

such a manner

pressure difference that an approximately uniform chordwise between the upper and lower surfaces at the design coefficient , and the designation of such airfoils is often indicated by a = 1.0 following produces

lift

the numerical series designation worthwhile to provide uniform

.

lift

In

some cases ,

however ,

it was

thought

over only part of the chord with a

lin

lift at the trailing edge . In such cases the fraction of the chord designed for uniform lift coefficient is designated as shown in Fig . 13:11 . ear taper to zero

16-215 Same

as

in Fig .

a

=

0.5 Mean line designed to give uniform loading to 0.5c , then linear decrease to

13 : 10.1

trailing

Fig . A

Modified 1 - series airfoil designation with region of unspecified , a = 1.0 ) . uniform loading specified (

13:11 .

more

flexible

was designed

designed

edge

later

sections

if

and

and

is

set of aerodynamically - designed series the most widely used of these aerodynamically

improved

the

6 - series

namic data on some 1 - series

described in the next article

airfoils

are given in

NACA

TN 976 .

.

Aerody

TECHNICAL AERODYNAMICS

13-10

13 : 5 .

-

rently , the

-

most widely used of the NACA The designations

6 series .

The most widely explored and ,

AIRFOILS .

6 SERIES

THE NACA

is

tional information

series

are similar to those of

supplied by

a

cur

airfoils is the NACA the 1 - series but addi

of

third digit in front of

dash as

the

to cli where an extensive region very of laminar flow exists and the drag is low . A typical NACA 6 - series designation is shown in Fig . 13:12 , and the meaning of the third and fourth the range of values of c1 above and below

digits in

terms of a graph of ca against 6 5, 3

-

2 15

is

c₁

line designation , indi cating resultant of upper and lower surface pressure is un iform for 0.5 chord from L.E. Mean

location of mini pressure position is 5 tenths of chord for basic symmetrical section at zero mum

g

thickness is 5 per cent of chord

Maximum

drag is 3 C1 range for low tenths above and below Cli

Fig .

13:13 .

L.

Chordwise

( see Fig .

.

a = 0.5

Series 6

lift

in Fig

shown

Design

13:13 . )

Sample designation

13:12 .

lift

Cli is

of

coefficient

2 tenths

6 - series

airfoils

.

.008

.006

са Low drag range ± 0.3

°1700

of extensive laminar flow Region

.002

-.2 -.1

-.3

Fig .

Cli

L

u

0

.1

1

C1

L

.2

.3

1 .4

lift

Typical Note

surface pressure distributions for symmetrical are compared in Fig . 13:14 with those of an NACA

that

the peak

farther aft troduced

in

each value

.7

Typical " bucket " in graph of section drag coefficient vs. coefficient specified by designation in Fig . 13:12 .

13:13 .

section

foils

.6

.5

on the

the of

negative pressure

airfoil

6 - series ,

cli

to get

NACA 6 - series 4 - digit

air

airfoil .

is

considerably reduced and moved in the 6 - series . The greatest improvement

however ,

is in

in

adjustment

a nearly uniform resultant

of the

mean

line for

pressure over

the

AIRFOIL SELECTION

airfoil

chord of the

is

in Fig .

shown

.8

and the comparison

,

13-11

with

a

similar

4

- digit airfoil

13:15 .

(77/v )2

1

-.4 -.8 .2 a.

NACA

.8

.2

0 x c

1.0

/

b.

0012

.6

.4

1.0

65,2-012

NACA

=

a

=

a

.5 theoretical line

=

0.2 a

0.2

line

Mean

a

0.6 0.8 Fraction of chord

-

0.2 0.4 0.6 0.8 1.0 Fraction of chord NACA 1- and series loadings for given Cli ·

-

6

NACA 64

1.0 b .

a.

+1.0 =

.06 0.4

1.0

Resultant Pressure

a = 0

Mean

-1.0

)

Resultant Pressure

0.5

(

Difference and lower

-1.0.

.

a = 0

of upper surface

-2.0

0.2

.8

Comparison of basic thickness forms and surface pressure distribution of 4 -digit and 6 - series airfoils .

13:14 .

coeff

Fig .

.6

.4

pressure

0

.

with the third digit recently been superseded

more

by

a

is designated

in

which

subscript

as

separated by

sim

the half width shown

in Fig

.

13:12

a

-

6

-d "

pressure distributions

-

has

and resultant

series airfoils ,

.

in Fig

comma

bucket

"

-

.

and

with improved thickness distribution

of the low drag 13:16

shown

igit

,

The designation

4

for

from the second by

ilar series

of mean lines

Comparison

a

13:15

.

.

Fig

TECHNICAL AERODYNAMICS

13-12

as

Same

in Fig .

13 :

a = 0.5

215

653

12

Same

as before

as

in Fig .

13:12

0.3 from cli c1 range for " bucket " of ca graphs , with thickness distribution improved from theoretically derived value specified in Fig . 13:12

Fig .

13:16 .

all airfoil series

Unlike

previously

- series airfoils is a of 6 - series airfoils may ,

bution of the

A

6 - series airfoil section similar to that designated in Fig . 13:12 .

Improved

sub - group

6

discussed , the thickness

function of the therefore

maximum

be obtained by

,

distri

thickness

.

linearly in Fig .

or decreasing the ordinates of an airfoil such as shown 13:12 in a constant ratio . Such a linearly increased airfoil of this sort is designated as shown in Fig . 13:17 . increasing

65 ( 215 ) Same as

in Fig .

-

218

as before 13 :

12

Cli and thickness ratio obtained by linearly increas ing ordinates of Fig . 13:12

new

and thickness from Fig . 13 : 12

Cli ratio Fig . 13:17 .

a = 0.5

Modified

6

- series airfoil obtained by linearly increasing ordinates of Fig . 13:12 .

in

A similar sub - group of 6 - series airfoils is obtained by linearly creasing or decreasing the ordinates of an airfoil such as designated in Fig . 13:16 , and such an airfoil designated in Fig . 13:18 . 65 (315 ) Same

,

with linearly

2 18

Same as

Fig . 13:18

.

,

is

as before

thickness ratio obtained by linearly increasing ordi

ratio

in Fig .

Modified

ordinates

a = 0.5

as in Fig . 13:16

Original thickness

increased

6

New

nates

13 : 16

- series airfoil

ordinates of Fig

in Fig .

13:16

obtained by linearly increasing .

13:16 .

Characteristics of a wide variety of 6 - series airfoils as a function of the digits designating the airfoils at various Reynolds numbers (and

1

AIRFOIL SELECTION a few high subsonic 5 and

will

13 : 6.

2,

While there are

NACA

series designated by

4 , and 5 , they are not widely known

3,

Appendix

later .

SERIES .

OTHER NACA

in

presented graphically

Mach numbers ) are

be discussed

first digits

the

13-13

7 - digit series is , however , fairly widely is shown in Fig . 13:19 . In the 7 - series

used

and

The

a sample designation

is

attempt

an

or used .

the range of favorable pressure gradients over both

made

to specify

the upper and lower

surfaces and the thickness distribution and mean line are specified by a serial letter in the middle . The last three digits designate c11 and the thickness ratio as usual .

2 4 2 A 4 15 7 - series

airfoil

Thickness ratio

Favorable pressure grad ient for 0,4c on upper surface at design q

Design

1S

Series no . wedge ,

(2

-

( 70 ) ( 03 )

-

13:20 .

For supersonic and

inar sonic

boundary

0.4

7

- series airfoil .

L

(70 ) ( 03 )

Max . thickness of lower surface = 0.03

Max . thickness of lower surface at 70 per cent chord

Max . thickness of upper surface at 70 per cent chord

trailing

of

arc )

Supersonic

Fig .

=

Favorable pressure gradient at design c1

1 denotes

circ .

=

Cli

on lower surface

Sample designation

13:19 .

=

per cent

Serial letter designating thick ness distribution and mean line

for 0.7c Fig .

C1

,

Max .

Sample designation

flight , airfoils

with

thickness of lower surface = 0.03

of supersonic

airfoil .

sharp , or nearly sharp , leading

are favored lam - layer is also quite different from that favorable for sub edges

airfoils

.

;

It is

the geometry conducive to extensive

customary

to designate supersonic airfoils

by

13-14

TECHNICAL AERODYNAMICS

separate groups

ilar

digits for

of

thickness

maximum

would have a

airfoil using circular first digit of 2 instead of

tics of

airfoils

supersonic

such

13 : 7 .

ISTICS

In

airfoil

an

is

profitably

on wing

This

chord .

number

on minimum

million

.

will

a,

of

( 2 ) graphs

of ca vs.

six

in

in

mil

,

data

location for

(a )

practically

,

Angle of attack on zero independent

the 4 - digit series

of thickness ratio

and with

considered unimportant

lift

Cli for

in the choice of

It is

simply necessary that order to set the wing , incidence properly

(b ) importance .

of c vs.

c,

5,

beginning with Fig .

in

terms of thickness ,

the 4- and 5 - digit

series ,

negative pressure location

is

, but

in

Fig

. A5 : 1 to be to vary with camber for

seen

It

is airfoil because it deter on the airplane to get low fuse alo be known to the designer in

each of the 6 - series

mines the angle of incidence of the wing .

alo

on ( 1 )

with reference to graphical

Appendix

terms of thickness cli and maximum (second digit ) for the 6 - series airfoils . 1. Lift - curve Effects . ,

effects separately

and ( 3 ) graphs

C₁ ,

considered below

low turbulence data given

camber , and maximum mean - ordinate

airfoils

.

simply

.

lift

The section - curve - slope per degree a is also of little is seen in Fig . A5 : 1 to be almost independent of thickness ,

It

decreasing slightly with thickness for the

slightly

about

to speeds near the stall The effect of higher sub - critical

These graphs present the aerodynamic

lage drag

of

number

character

for by considering only the effect of coefficients up to a Reynolds number of

drag

of c₁ vs. and these are systematically

and

Low speed

.

correspond

convenient to consider the aerodynamic

graphs

summaries

tur

to have

then adequately accounted

about 20

A5 : 1 .

characteristics

compared at a Reynolds

Reynolds

It is

often convenient or desirable

therefore highly desirable

scale airplanes in free- flight .

full

speeds

be

CHARACTER

AERODYNAMIC

ideas as to the effects of minor changes

geometry on aerodynamic

istics can lion based for

it is

, and

reasonably accurate general

airfoil

lines

characteris

the chapter .

-

it is

A sim

section slightly different from any for which low

bulence tests are available some

in

the

behind

13:20 .

The aerodynamic

1.

ON LOW SPEED

the design of an airplane

and

of straight

instead

arcs

are discussed later

EFFECTS OF AIRFOIL GEOMETRY

.

to use

in

in front of is shown in Fig .

portions

the

A sample designation

.

with

value of 0.11

thickness for the per degree

or for

6

4 - digit

series and increasing

- series airfoils from the theoretical very thin airfoils . Small changes in ,

AIRFOIL SELECTION aspect ratio can far

indicated in Fig . (c )

over

- shadow

13-15

the small changes

in

with geometry

a

A5 : 1 .

lift coefficient

Maximum

ness and camber on

c1

max

without flaps .

without flaps ,

ulated split flaps deflected out flaps nearly all reach a

60 ° ,

is

20 per

with

and

effects of thick

The

shown in Fig . A5 : 2 .

cent chord

sim

with for thick

The graphs

peak at c₁ max between 1.5 and 1.6

nesses in the region from 12 to 15 per cent of chord , with slightly higher values for high camber within the range investigated . For airfoils with

flaps , thickness ratios in the region and give values

Much higher values

flaps

and

noted

in

are , however

with the

Chapter

from 18 to 20 per cent are

addition

12 ,

,

obtainable

of slats

significance for

optimum double

with

/

and or boundary

so none of the graphs

favored

full - span split flaps .

for

C1 max around 2.6 to 2.8

of

in Fig .

- slotted

- layer control

of an airfoil , since high lift can best be obtained with auxiliary high - lift devices . Drag - curve Effects . 2.

much

(a)

as

A5 : 2 are considered of

the selection

maximum

Minimum drag

coefficient cd min comparative tests run at Re = for 4 - digit and 6 - series airfoils in Fig . A5 : 3 , but there are major effects due to Reynolds number shown in Figs . A5 : 8 and A5 : 9 and these must also be considered . Low minimum drag at high Rey

6 x

106 are plotted

nolds

number

teristic

is

of an

here

to be the most important aerodynamic charac Note that all the airfoils for which data are

judged

airfoil .

A5 : 3 show an increase of cd min with thickness for 4 - digit , digit , and 6 - series airfoils . Camber and maximum mean ordinate location 5-

plotted in Fig .

are seen to be unimportant for the the 6 - series airfoils portant but the position of

the design

range

lift

minimum

of cambers there plotted

cli is

coefficient

pressure

is

.

seen to be

of major importance

coefficients are obtained with

minimum

drag

position of

minimum

pressure , though the gain from the 66 - series to

67 - series

is

very small .

Minimum drag

or possibly

choice of the 66 - series of all the extensively tested ,

considerations

the 67 - series

airfoil

,

series

.

results are , however , believed to be obtainable series airfoils followed by the dash numbers -34

,

as the NACA has largely

data on these are available

series ,

however modified ,

tion

boundary

and the

hence lead to the

suitable equally good

as the most Almost

from -35 ,

modified or

-36 ,

4

- digit

but few

abandoned the 4 - digit

favor of the wider variety of specifications Major reductions in cd min with suitable suc

in

6 - series . - layer removal

covered by the

NACA

im

farthest aft

the lowest

the

For

have been found possible in preliminary

tests

,

TECHNICAL AERODYNAMICS

13-16

field is

but this

evident , however ,

in Fig .

such as that shown

coefficients could

drag

lowest of the

- layer

boundary

friction ,

in skin

from the basic studies

that the

It is

as yet inadequately explored .

be

divided by

6:5

if the

5

held completely laminar , and tremendous amounts

could be

power would be economically justifiably in the design of an airplane the boundary layer could be kept laminar over the fuselage and tail surfaces as well as wing .

of

boundary

(b )

- layer suction

if

The induced drag

of aspect ratio ,

as

shown

efficiency factor in Fig . 9:23 , has

ew ,

while chiefly a function

been found

4 - digit

for

air

to be substantially higher for

foils

thin airfoils (with proper camber ) , than for thick airfoils ( 1 ) but these effects , like those on lift - curve slope , are far overshadowed by small changes in aspect ratio . 3 . Pitching Moment Curve Effects . (a )

center a.c. The effects

Aerodynamic

on aerodynamic

center location

in

4 - digit

general the

are seen in Fig

airfoils

series

a

show

a.c. with increased thickness movement with increase in thickness

, whereas the 6

aft

little

.

of thickness and

. A5 : 5

slight forward

- series airfoils This

is

camber

to be small , though

in slight

movement

show a

considered to be of

center simply serves as a refer the center of gravity , the distance between aero

importance , since the aerodynamic

ence point

for locating

dynamic center

center of gravity being a factor in the longitudinal

and

stability calculations . Pitching

(b )

airfoil always

moment

coefficient

/

in

geometry on Cmc 4 are shown

small without flaps and

thickness

is negligible .

objectionable

Cm ac

Fig

large with

A high value of

Cm

or

. A5 : 4 .

flaps

c/ 4 is

/

The effects of c 4 The pitching moment is

Cm

;

the effect of

airfoil

considered structurally

to the wing to provide adequate torsional strength and rigidity , but this objection is usually outweighed by the advantage of flaps in producing high stalling speed . Reynolds A5 : 6 through Mach

because weight

number A5 : 15 ,

number effects

13 : 8 .

FOILS .

must be added

effects for inclusive

,

not covered

most

the

in

of the above items are

last

named

Chapter

figure

Some

airfoils

many

in

Figs

.

also

some

SERIES

AIR

10 .

APPROXIMATE EQUIVALENCE OF MISCELLANEOUS developed

shown

showing

years ago are

AND

NACA

known from

flight

tests

to have been very satisfactory , but their characteristics at low turbulence

( 1 ) Dwinnell , James H. " Principles of Fig . 9.8 . Mc Graw - Hill , 1939 .

Aerodynamics , "

First Edition ,

AIRFOIL SELECTION and high

Reynolds

coefficient

drag

not been determined

have

number

13-17 Often the

.

minimum

with better accuracy than from the mea

can be estimated

surements

reported in a high - turbulence wind tunnel by inspection

ordinates

and determination of the equivalent

example , consider

the Goettingen 593

airfoil ,

in Fig .

sketched

specified

listed in

by the ordinates

Table 13 : 1 .

airfoil .

NACA

For

Medianline

Referencechord

is to find

The problem

the equivalent

L.E.-T.E.Chord

13:21 , and

of the

airfoil .

series

NACA

Fig . 13:21

The

Goettingen

.

593

airfoil .

solution follows . TABLE 13 : 1 .

5

%C

ORDINATES

20

10

Find the

1.

is

and

means

13 : 1

same

as a

of the equivalent Find the

Goettingen second

70

80

95 95 100

90

10.85 9.45 7.655.50 3.00

11.70 0

0

0

shows that the

60

0

maximum

maximum

0

10

1.65 0 0

O

- thickness location .

thickness

is

In

11.9 percent

located at 30 per cent of the chord from the leading edge . This that the Goettingen 593 airfoil has a thickness distribution approx

imately the 2.

0.10

50

thickness and the

maximum

spection of Table

12.00

0.15

Lower 3.00 0.85 0.40

40

30

Upper 3.00 7.85 9.75 11.50

593 AIRFOIL .

OF GOETTINGEN

593

NACA

- digit NACA airfoil , and 4 - digit airfoil are 12 .

maximum mean - line

airfoil ,

line of Table

used as a reference

these

items

ordinate

that the last

and

are calculated

its as

location

in Table

two

.

digits For the The

13 : 2 .

represents the ordinates of a line through

13 : 2

leading and trailing TABLE 13 : 2 .

4

the

similar triangles . This line is line of the NACA 4 - digit system .

edges calculated by

line for

the mean

CALCULATION OF MAXIMUM MEDIAN CAMBER AND MAXIMUM LOCATION L OF GOETTINGEN 593 AIRFOIL

CAMBER

Location

,

%c

20

L. E.-T. E. , chord ordinate Mean Mean

- line line ,

ordinate from L.

,

, %c

c

E.-T.

E. chord , %

Inspection

30

40

50

60

2.40

2.10

1.80

1.50

1.20

5.82

6.05

5.85

5.42

4.72

3.42

4.05

3.95

3.92

3.52

of Table 13 : 2 shows that the maximum ordinate of the mean line 4.05 per cent and that it is located between 30 and 40 per cent of chord the mean line is plotted and is judged to be from the leading edge .

is

If

TECHNICAL AERODYNAMICS

13-18

representable with reasonable accuracy by imum mean - line ordinate to the Goettingen 593

Low turbulence be read

Figs

from

closely to

the

A5 : 5 , and

may

by

4312

or

NACA

4412 may

airfoil in flight

University

Goettingen

4412 .

to correspond

be assumed

the Goettingen 593

results published

AERODYNAMIC

digits

4

characteristics of the

number

characteristics of

turbulence and low Reynolds 13 : 9 .

NACA

parabolas tangent at the max airfoil approximately equivalent 2

designated by the

A5 : 1 through

.

the test

than would

then the may be

high Reynolds

,

more

,

at high

number .

AND

STRUCTURAL

It is

COMPROMISES .

important for

the aerodynamicist to realize that airplane wings are not designed and built exclusively from aerodynamic considerations . There can be no com promise should

it is

structural safety

with

;

light

line operation involves

factors

many

Low drag

.

is

It if

operation at high speed .

economical

labor costs

volved is a

in

minimum

the last analysis

is

of wings

the cost

other than the drag of the wings of

important because

and maintain and may also weigh more

in

advantageous .

also

also be remembered that commercial airplanes will only be flown financially profitable to do so , and the financial profit of an air

the airplanes

a

is

weight

it

permits high

Low drag wings

build

All

costs

than wings of higher drag . , ( 1 ) and

only

if the

total labor

a low drag wing economically desirable . ,

as components

speed and

are expensive to

in

Major items

operation rather than

of an airline

as components of an airplane , are maintenance costs and costs of inspec tion and rebuilding to meet certification requirements for safety . Thin wings that are aerodynamically desirable may not only have to be heavier the structural requirements , but also may be so compact in equip design as to be less accessible for repair and rebuilding than thicker Boundary - layer control devices , including porous lead and simpler wings .

to

meet

ment

suction flaps ,

ing edges and

reliable

,

and

more

troublesome

line operation using

them

is

may be

sufficiently

more complicated ,

to repair , that the total cost of the greater rather

than

less

,

less

air

so that apparent

gains may turn out to be economic losses in flight operations . supersonic airplane and missile field , aerodynamic considera In the tions may dictate sharp leading and trailing edges but , at high accelera

aerodynamic

tions

and

high

Mach

numbers , a

knife - like leading

edge

is structurally

( 1 )Wood , K. D. " Airplane Design , " Tenth Edition ( 1954 ) , Chapter 7 , distributed by University Bookstore , Boulder , Colorado . (Eleventh edi tion to be distributed by Ulrich's Book Store , Ann Arbor , Michigan . )

AIRFOIL SELECTION

impossible stresses

which

13:10.

AIRFOIL SELECTION CRITERIA FOR

The forces

AIRPLANES .

SUBSONIC

on an airplane in a glide are shown in Fig . 13:22 . For as flat a as possible , the ratio D L should be a minimum or L D should be a

/

/

flattest

be one of the chief factors determining the

lon of fuel ) of a conventional airplane per gallon of fuel ) of a jet .10 airplane .

.06

Airplane ‫نم‬

Complete

•04

Wing

Alone

Dp .02 KCDP min

/

( L D) max

for for

/)DL(

a

.

1.2

(

13

13

(

divide equation

CL equal to zero and

solve for (

is 13

(

/

, ( L D ) max

by CL

13

2CDp min

)

a

complete

A

is

Effect of Flight

,

and Configuration Variables on shaped Supersonic Wings JAS November 1951

-

in Diamond

1.0

coefficients of

, "

The

"

,

F.

)1

P.

and the corresponding

Durham Thermal Stresses

D ) ,

coefficient for CL (L/ D)

.8

™

lift

=

max

√

The corresponding

.6

.

(L/D),

CD

to

with respect

CDp

CD CL

max =

derivative of

maximum

min

the condition of

for

max

cz πAе

CDpmin

( L /

CD and put

for

wing

Graph showing conditions complete airplane and

and drag

written

/

To solve

for

wing alone

lift

between the

=

may be

. D )

13:23

max

a

relationship

.4

Fig

(

13:22 . Forces acting on airplane in glide . The

.2

0

Fig .

airplane

CL

CDo min

L /

.

D

1

13:23 .

:

in Fig .

complete

airplane

)

CL for a wing alone and for a complete airplane is shown

, for (L/D ) max

.08

(hours

2

vs.

CD

maximum

and the maximum endurance

)

A typical graph of

,

also be shown to range ( miles per gal may

.

of

:

The condition

, ( L / D) max

glide

: 3

maximum.

(

thermal

. (1)

)

glide

failure

cause

involved produce

: 1

acting

will

gradients

temperature

the

because

13-19

TECHNICAL AERODYNAMICS

13-20

/D) max

(L

(13 : 4 )

√πAe /4CDp min

=

, Equation ( 13 : 4 ) states that the highest values of ( L / D ) max are obtained with the highest values of the product Ae and the lowest values of CDp min This requires high aspect ratio , as shown in Fig . 13:24 , though aspect ratios over

are seen to be unprofitable , and low values of

15

CDp

min '

10

8 6

Aew

5

3

2 A

1.5

Fig .

2

By an analysis

sinking speed endurance

4

3

Plot of

13:24 .

Ae

5 6

similar to the

above ,

shown

maximum

is

that for

minimum

=

(13 : 5 )

4CDp min

jet - propelled airplane

,

it

can also be

similarly

that

and (CL1

/2 /CD )

is

jet

also be

range =

(4/3 )CDp min

(13 : 6 )

a maximum .

For each of the conditions should

can be shown

a maximum .

range of a

CD max

may

it

rate of descent ) Vs min . corresponding to maximum ( time aloft per gallon of fuel ) of a conventional airplane

(C₁3 /2 /CD )

For

20

15

10

( vertical

CDys min and

7 8

vs. A , based on data in Fig . 9:23 .

shown

be a minimum

presented

by equations ( 13 : 5 ) and ( 13 : 6 )

it

that the product Ae should be a maximum and CDp min . The foregoing studies indicate that a low value of

CD min is the most important aerodynamic

characteristic of an airfoil sec ratio is also highly important to good airplane perfor mance . The relative importance of low CD min and high aspect ratio is discussed later . tion ; high

aspect

AIRFOIL SELECTION Where the

in

utmost

high

13-21

is

subsonic speed

objective

a major

,

as

in

military fighter aircraft , high critical Mach number is also of major importance . The means for obtaining high critical Mach numbers have been Chapter discussed in 11 and are usually not in conflict with the require ment

of low

13:11 .

drag .

minimum

AIRFOIL SELECTION CRITERIA

sonic missiles

to be supported

by

also a compromise between aerodynamic practices of supersonic missile wing lished

of

adequate

structural

and

is

of solid metal

made

high hot - strength , though a given

if

,

requirements

but the

are less well estab

construction

so that the nature of the compromises

sonic wings are

MISSILES . For super strength , there is

FOR SUPERSONIC

wings

less clear

Many super

.

its

often stainless steel because of strength can

bending

be obtained with

hollow with fairly thick plates for the wing surfaces . wings , for a given strength , will have higher Such hollow drag and require more fuel , which may more than neutralize the weight sav less weight

is

the wing

made

ing due to making the wing hollow , depending on the mission or specifica tion of the missile . Studies reported in TN 2754 provide means for cal culating the " optimum hollowness " of a supersonic wing , but no simple general rules

AIRFOIL SELECTION CRITERIA

13:12 .

as currently

of the blades tabs

operated

( 1955 ) are

through near

the tips ) .

the

importance

to evaluate , copter .

of at least as

much

FOR HELICOPTER

controlled by

In either

a

case

be selected

Helicopters

ROTORS .

cyclic variation of pitch

it

in

( or ,

is

a few cases , by

important

that

for negligible pitching

the

moment

center . The blade section should preferably also drag and high maximum without flaps , though the

aerodynamic

have low minimum

ative

is

.

forces applied at the hubs

helicopter rotor blade section about

profile

as the cross - section

importance

control

be formulated , as the planform

can

lift

of low

minimum

drag

and high maximum

lift is

and depends on the design operating conditions

Inspection

of the pitching

moment

data

in Fig .

rel

difficult

of the

heli

A5 : 4 shows that

only the symmetrical airfoils , among those there reported , have zero pitch ing moment . Recalling from Article 13 : 7 the effect of airfoil geometry on aerodynamic characteristics , it should be noted that only thin airfoils have low minimum

for the

drag , and

66 - series .

It

that the lowest drag reported in Fig . A5 : 3

airfoils

should also be noted that only

per cent thickness have high the most favorable for high

maximum maximum

lift ,

lift .

of over

and that the 66 - series To

find

a

is

is 12

not

better compromise

TECHNICAL AERODYNAMICS

13-22

airfoil for rotor

blades than any reported in Fig . A5 : 3 , several special trailing series of reflex - edge airfoils have been tested by the NACA , ( 1 ) but criteria for selection from those tested are not well established .

is some doubt as to whether a high value of the ratio c1max /cd min proper a measure of the merit of a helicopter blade section , as only

There

is

is

Cd min

involved

if

so

new

or

some

that

it is

weighted

not

The art

possible to say whether

must be maintained .

airfoil

series

not only

of construction

is

drag or maximum

minimum

agreement that the low pitching

It is entirely

with some sort of boundary

minimum

limited by

not

of such blades

also

lift

selec require

combination of the two should be a criterion for

tion , but there is general ment

rotor is

the forward speed of the

retreating blade stall .

drag and high maximum

the complicated mechanical

moment

possible that a symmetrical

- layer control

lift ,

device

but also

cyclic pitch control

( often

eer's nightmare " ) , possibly in conjunction with lieu of a conventional gear - driven rotor .

a

may

66

provide

a substitute for called " an engin

rotor tip jet burner in

PROBLEMS

Describe the airfoil designated 23115-35 . Coordinates of the upper and lower surfaces of a Clark X airfoil are given in Table 13 : 3 ( below ) . Find the constants for straight - line plotting of the variable - density - tunnel characteristics of a rectangular wing of A = 6 using this airfoil . 13 : 1 .

13 : 2 .

05

с

TABLE 13 : 3 10

Upper

4.00

7.96 9.68

Lower

4.00

1.14 0.50

20

40 4

30

11.28 11.70 11.40 0 0.03 0

13 : 3 . An airplane wing mensions : span 40 ft , chord

is

60

50

70

80

90

10.529.157.355.222.80 0

0

10

10

95

100

1.490.12

10

following di in . , location of flat aft of 25 per portion of lower mean line to be lo

measured and found to have the

in . ,

maximum thickness 6 maximum thickness at 30 per cent chord , lower surface cent chord , height of leading edge above plane of rear 50

surface 2.0 in . Assuming the maximum ordinate of the cated at 0.3c , what is the approximately equivalent NACA 4 - digit airfoil ? Using data presented graphically in Figs . A5 : 1 through A5 : 5 , 13 : 4 . write equations at Re = 6 x 106 for CL (a ) , CD ( CL ) , and Cp ( CL ) for a 2 : 1 tapered wing of A = 10 ( without sweep ) the airfoil is a smooth 662-315 Also estimate CD min at section . Neglect " bucket " in the drag curve .

if

Re = 25

x

106 .

( 1) Tetervin , Neal , " Tests in the NACA Two - dimensional Low Turbulence Tunnel of Airfoil Sections Designed to Have Small Pitching Moments and High Lift / Drag Ratios . " NACA Wartime Report L- 452 .

1

CHAPTER

14

DRAG ESTIMATES AND POWER CALCULATIONS 14 : 1 .

lift The

OF ESTIMATING

METHODS

coefficients for data in Fig . 14 : 1

a

typical

DRAG .

The

may be noted

where CD

/

1 TAе

is

is the

is

to be approximated

by the equation CD =

relationship

airplane

complete

between drag and

in Fig .

shown

14 : 1 .

with good accuracy

c

CDL

( 14 : 1 )

ПAе

the intercept on the CD axis of a graph of CD vs. cz and slope , theoretically ( for lifting - line theory ) equal to 1 /πA ,

.12

Line

.10

Test

.08

Data Straight

Typical

Approximating

CD

.06

°170

.02

CDE

CDp

c²

min

.2

Fig .

.6

Comparison

14 : 1 .

between

.8

1.0

typical airplane approximation .

1.2

1.4

test data

and parabolic

but modified by the factor e to take account of discrepancies lifting - line theory for wings and experimental data for airplanes

tion

( 14 : 1 )

parabola

intercept

if

is

called

on the

CD

axis

is

used as coordinates , as sometimes referred 14-1

between .

it

plots

in Fig .

13:23 .

a parabolic approximation because

CD and CL are

1.6

to ( as in

Chapter

Equa as

a

The 13 )

as

TECHNICAL AERODYNAMICS

14-2

min , but is here called CD which small amount shown in Fig . 14 : 1 .

CDp

may

differ

from CDp min by the

very

of estimating CDp min or CDf is to designate the product = Df q , called the " equivalent parasite area of the CDS as equal to airplane , and to estimate this area by adding numerically the values of f for the component parts of the airplane . Each component parasite area One

is

method

/

f

designated by the product CDA , where CD

the component part of the

airplane

A

and

is

is

the drag coefficient

that drag coefficient is based , usually the area Ac of the maximum section . These relationships are summarized in the equation

f

CD S and

typical values of

which they The

= Df

for airplane

CD

are usually associated are

total

f

for

an airplane

component parts plus

5

/9

or

10

=

cross ( 14 : 2 )

ZСDAT

components , and the areas A shown

of

the " proper " area on which

in Table

with

14 : 1 .

is approximately the sum of CD of the per cent to allow for mutual interference

per cent allowance may well be made for small protuberances such as handles , hinges , and cover plates , unless they are specifically included on the basis of data in Appendix 6 . between the components ; an

The drag

additional

coefficients given in Table

5 or 10

14 : 1

are not specific but simply

dicate the range of values usually encountered

flying at

critical

speeds below the

.

for

More detailed

in

full

scale airplanes suggestions for es

the specified range ( sometimes slightly beyond the specified range ) are given in later articles of this chapter and in Ap pendix 6. Their application to a specific airplane is illustrated by timating

within

CD

an example

later in this chapter . efficiency factor "

The " airplane

"wing efficiency factor "

ew

fuselage and other airplane cient

,

as well

An approximate

e

it

differs substantially

in that includes increments parts with angle of attack and

from the

of

drag of

lift coeffi

effects due to wing planform and thickness ratio . rule for estimating e for a complete airplane is given by

as the

the equation е

=

-

—

Σ + = [A

(14 : 3 )

( ÷ ) parts ]

The values of 1 / ew implied by Fig . 9:23 include

(a ) a planform

18

shape cor

theoretical factor in Fig . 9:22 , (b ) equal an airfoil thickness correction factor to 0.005 to 0.010 for usual thickness ratios , and ( c ) a correction to practical wing construction for rection factor ,

given by the

14-3

DRAG ESTIMATES

TABLE 14 : 1 .

APPROXIMATE DRAG OF

AIRPLANE COMPONENTS AT LOW SPEED (M < SPEED AT SEA LEVEL FOR MEDIUM

0.4 ) AND Re CORRESPONDING TO LEVEL HIGH SIZE AIRPLANES . (1 ) SEE APPENDIX 6 FOR Re Length

Part

Description

Wing

Re

roughness ,

Usual

t /c

=

AND M CORRECTIONS

for

Calc .

.

Area for Drag Calc .

Range

CD

Chord

S

.004

-

.1 to .2

.010

Flaps

60% span , deflected 300

Chord

S

.02

- .03

Tail

Usual roughness , t c = .08 to .12

Chord

St

.006

-

Fuselage

Smooth

Length

Ac*

.03

·..08

"

"

.07

.10

:11

:"1 :

/

streamline

body

transport

11

Large

"

Bomber

:00

Small plane , nose

"

-

.08

hull "

"1

Very low drag

Nacelle

performance

Above wing , small

.04

Ac

.08

-

:

:

.07

·

.12

1 =9

"= 1

.04

-

.07

:

.04

Ac

.05

Ac

.07

"

.15

:"1

"

.20

airplane

wing , large airplane

"

In

"

For turbojet engine

:

tip

"

Ext . tanks

Centered on wing

tip

"

"

Below wing

11

"

Inboard below wing ( incl . support ) ( incl .

·-

Ac

Usual for bestwa

ter

.12

.20 ,

.09

engine

Boat

.008

":1 : 3

·

.08 2

.07 .07 .10 .30

Bomb

Below wing

Float

Best

streamlining

"

"

.05

"

Usual

for best wa

"

"1

.12

-

.25

.5

·

.8 .30

support )

ter Landing gear

"

"1

strut

well faired

dwheel

** bdwheels

"

"

.15

·

"

"

.3

- .5

wheels with " pants"

"

11

- .08

performance

Nose wheel and Two

.30

Wheels and exposed

struts

area of cross - section ; ** b = width , d = diameter , for wheels 11 of these data are based on Hoerner , S. F. , " Aerodynamic Drag , .; this published in 1951 by author at 148 Busteed , Midland Park , N. reference should be consulted for more detailed information than that given here or in Appendix 6 . Ac

( 1 ) Most

J

14-4

TECHNICAL AERODYNAMICS

high aspect ratio

involving non - optimum spanwise lift distribution and resulting in the " recommended practice " lines of Fig . 9:23 . The principal incremental value ▲ ( 1 / e ) parts , is due to the fuselage (and nacelles , if any ) . Data for estimating still

/

A ( 1 e ) fuselage are rather incomplete but may reasonably be assumed to be proportional to the ratio of fuselage frontal area to wing area as implied by the plot of Fig . 14 : 2 , which should be noted as limited to the rather unusual case of zero wing incidence . The use of Fig . 14 : 2 is illustrated by the fol lowing example :

Example . Estimate the airplane efficiency factor e for a combination a rectangular wing of aspect ratio 7 and 180 sq ft area , with a rec tangular fuselage of S₁ = 15 sq with zero wing incidence .

of

/

1

attack

An

2 .

.

:

: 3 .

In

and

7.

ficient

can

,

e )

(

/

▲ ( 1

a

of the ,

: 2

.

profitably the

NACA TR 540

check

be

line

of

.

in

the

on

components

made by

cal

total area of

the

parts exposed to the air stream the wetted area and esti

mating 6

.

.

Chart for estimating effect of fuselage on airplane efficiency fac tor for zero wing incidence See also from Chapters

value out

additional

culating

in

" )

14

is

"

(

) 15

8 9

7

5

6

20

A

4

3

10

drag

the case

drag of the airplane

(

0886

2

Art

in

with the test data

0.5

14

little

Constellation fuselage indicated in Fig 14

as having

Constellation Est

Fig

loss

minimum

increased angle of

a

,

which

Round fuselage

0.6

as

Lockheed

Points plottedfrom TR540

10 09 0.8 07

how

.

)

-

very

2.4

fus ST fus

(Al/

is

crease with

1.5

kept to

fus can be

the fuselage so that there

shaping

positive

an additional

of

(

,

.

)

e

is

there

Increments

Rectangularfuselageor 2.0 round fuselagewith cowledengine

)e /S

1.37

a

.

/

to nacelles

by properly

15/180

0.73 With few degrees of wing incidence due to fuselage could be much less

nacelles are involved due

1.75

/e1

If

of

=

= 1

,

,

ever

e

1.37 the loss of

e

Hence

=

1.22

/e

4( 1

x

/

read

14 : 2

culate

9:23 read ew = 0.82 and calculate 1/ ew = 1.22 . In e ) fus ( S fus / S ) = 1.75 . Using equation ( 14 : 3 ) cal +

Fig .

ft

In Fig .

Solution .

the skin

friction

coef

general

be

a

will

-

area

fis

)

4

14

:

CD wetSwet

(

CDS

=

=

f

: 3 ,

.

wetted

.

on

,

the drag coefficient CDf wet substantially higher than that of flat plate of the same Reynolds number because certain pressure drags are in volved as well as skin friction An over all chart for checking given in Fig 14 where based

14-5

DRAG ESTIMATES

is

indicated

the "wetted " area of the airplane

on the chart .

and values of CD wet are estimates based on wetted area are

More detailed

given later in this chapter for the various components

wet

..

CD .015 100

.

-.010 .008 .006

300

.

;

and Swet

.005 .004 .003

70

-

B 29

50 40 30

f

20

C- 47

10 8

L- 5

P - 38

6

4

F - 80

2

flat

plate as airplanes

30,000

8000

of

area of

wetted

)

function

function of Reynolds

ary layer transition

a

of cir to be

on bound

a

)

(

1949

.

"

Airplane

"

Hage

,

Robert E. .

and

Wiley

,

in Perkins Stability and Control

suggested

pressure drag

"

rear of the cylinder and its related ,

( )1

in the

D.

area

Plot

Performance

their effects

numbers and

C.

turbulent

and Mach

in Art

from laminar to turbulent and the effects of tran separation which results in the generation of low pressure

on

,

sition

been pointed out

has

The drag .

,

cylinders

INCLUDING WINGS

6 : 7

and

complex

INFINITE CYLINDERS

elliptic

,

cular

DRAG OF

, "

: 2 .

14

.

.

Parasite

a

1000

4000

(1

14

:

.

Fig

400 600 3 .

200

100

2000

ft

sq

Swet

1

TECHNICAL AERODYNAMICS

14-6

For thin

elliptic cylinders ,

thickness

,

is

coefficient location pends

is

the drag

effects are

almost

accordingly approximately given by

transition

of the

chiefly

for wings of less than entirely skin friction

and

The

in Fig .

on the skin

around an

elliptic

cylinder

The

layer de

if

friction

thermal

in Fig .

is

drag

of the theoretical given

drag

6 : 5.

boundary

turbulence and surface roughness

effect of thickness

taken account of by Hoerner ( 1 ) from consideration

ocity distribution

and the wing

2C

from laminar to turbulent

on free - stream

absent .

or 15 per cent

10

vel

4 : 8 , where

.015

CDo min

Pressure Drag

4 digit airfoils and streamlined

-

.010

=

Cf

struts

0.003

J

W

Skin friction

Skin

0.005

\\\\\\\\\

11

.005

/c)

(1 + 2t

friction

Pressure

LLL

(1

+

Drag

/

1.5t c) 0.0035

164-66 64-66 series

airfoils

t/c .10

.20

.30

.40

wings in Low speed minimum drag coefficient of cylinders and ratio . of thickness range as a function 8 million 3 to from Re sub -critical

Fig .

it is

14 : 4 .

noted that

very close to

1,

/

Vmax Vo = 1 +

it is

t/c .

From the

approximately true that

/

rule for squaring amax

/40 = 1

+ 2t

/c ,

numbers though

of course the average ratio amax o must be less than the maximum . Hoerner finds , as shown in Fig . 14 : 4 , that the minimum drag coefficient of 4 - digit airfoils and the skin friction coefficient and thickness ratio are re lated by the equation

/

/

CDo = t 1 + 2t c + 60 ( t c ) 4 , pres . drag 2C1 skin fric .

(1)Hoerner

,

S.

F. , op .

cit . ,

p . 61 .

( 4 - digit

airfoils )

( 14 : 5 )

DRAG ESTIMATES

first

The

right

two terms of the

hand member

the skin friction effect ; the third

is

term

/

14-7

of equation

represent

( 14 : 5 )

an empirical

additional

term

for the pressure drag based on values of t c up to 0.5 and obviously not intended for extrapolation to the circular cylinder case . For airfoils and struts similar to the

series airfoils with the

64-66

maximum

thick

ness near the 50 percent chord point , Hoerner finds that the increase of the skin friction portion of drag coefficient with thickness is slower , as given by

/c, fric .

1 + 1.5t

CDO =

skin

2Cf

125 ( t / c ) 4 pres . drag

+

(65 - series

airfoils

( 14 : 6 )

)

but the pressure drag term increased more rapidly with thickness in this case as noted . This analysis intends to imply that streamline struts of a given thickness ratio will have about the same minimum drag coefficient as

airfoils

if

tion of Fig .

the Reynolds 14 : 4

it

for

effect

predominant

may

is in

and

Mach

noted

be

From inspec

numbers are the same .

that the skin

friction effect is

thickness ratios of less than 15 per cent

if

the

the

- critical range . For very low Reynolds numbers , of coefficient will be high , partly because of the typical skin friction variation with Reynolds number and partly be cause the flow is more likely to be laminar in the region where there is Reynolds

number

the

super

course , the drag

danger

of separation

14 : 3.

, and a

large pressure drag

STREAMLINE BODIES :

same

build

up .

The drag of spheres

SUBSONIC .

pattern of variation with Reynolds

may

follows

and Mach numbers as that of

the

cir

cular cylinders , as may be noted in Fig . 6:16 . Likewise , the drag of ellipsoids follows the pattern for elliptic cylinders noted in Fig . 6:15 . For streamline bers

bodies at low Mach number and super

gives the semi - empirical

, Hoerner ( 1 )

/ +6 (d/ 1 ) 4

CD wet =

1 + 0.5d 1, skin fric .

Cf

/ is the

where d 1

diameter

experimental data on

in Fig .

frontal area is CDTI

Cf

( 1 ) Hoerner

=

/ length 14 : 5 .

given

1.5+

pres . drag

ratio .

/

, S. F. , op .

num

equation (streamline bodies )

Equation

( 14 : 7 )

is

( 14 : 7)

compared with

as

/

+ 18 (d 1 ) 3

cit . ,

Reynolds

The corresponding drag coefficient based

by Hoerner

3 (1 d)

,

-critical

p . 70 .

( streamline bodies )

( 14 : 8 )

TECHNICAL AERODYNAMICS

14-8

this

and

is

compared with

first

based on a

Equation ( 14 : 8 ) data in Fig . 14 : 6 . relationship in between wetted area and

experimental

approximation

frontal area of to 0.8 )

Swet = (0.7

smaller constant applies to conventional streamline bodies one to ellipsoids and to fuller bodies such as are used

which the

larger

rela

value of 0.75 this results in the

average

With an

.

Swet

/S

/

= 3 (1 d)

.02

14:10

)

for airships tionship

(

and the

.10 CDπ

.04

Drag

0.5 d

/

/1 )

Fig

6

a

d

l/

.

2 ,

.

-

a

surround

given

airplane

(b

.

a

-

6 ) .

69 .

,

F.

cit

distance of laminar

maximum

ratio to

in Fig

14

: 6 .

/

by the

Later low turbulence

varied series of streamline bodies

might be obtained than any shown S.

Hoerner

,

(1

values of CD

body

Reynolds

in Appendix If boundary layer vel transpiration lowing through porous analysis in Fig suggests that lower

data

were reduced

rear portion of the

critical

super

the

incorrect

to maintain

optimum length diameter

the region of

ocity gradient

)

airfoils

in

ratio

and that

but tests on actual fuselages cited by

.p

in

0.03

systematically

6 (

cockpit

low drag

-

"

show an

number

,

flow

like

optimum

)

tunnel tests on

shaped

about

conclusion to be a

this

"

show

.op

)

(1

number

Hoerner wind

is

CD

range at low Mach

.

value of

minimum

inferred that the

circular fuselage is approximately ,

diameter of

. ,

of length to

erroneously be

might

a

: 6

.

it

14

10

CD for streamline bodies 14 at low and super critical Re as function of ratio

/

Fig

8

d

CD wet for streamline 14 : 5 . bodies at low M and super - critical Re as a function of d 1 ratio .

4

1.0

-

.8

2

.6

Fig .

From

31

l/

d 1

.4

1.5+

0.003

.02

0.003

.

.2

+

7 : 8

(1

(

.005

/

Pressure

.06

)d

= 0.003

dra

Cf

.01

:

CD wet

Pressure

.08

.015

the

(14 : 9)

circumference )

max .

M 6 .

in

( length x

14-9

DRAG ESTIMATES

A streamline fers

airplane

body such as an

air

an angle a to an

in

an increase

The relationships

stream , has a

lift

drag nearly proportional

shown

in Fig .

If ,

in

equation

of

for circular fuselages

equation ( 9:33 )

( 14:11 ) , a

is

is

/

A(1 e) fus S fus /S

put equal

=

it

shown

a,

by the

suf 14 : 7 .

equation ( 14:11 )

for rectangular fuselages

/

.

lift

to CL a and the - curve - slope then for zero angle of incidence

may be shown

that

11.6 CD minfus K (A

and equation ( 14:12 ) corresponds

in Fig .

adeg 2 15

and 4 to 6

used to determine

the wing on the fuselage ,

to a² , as

to a and

)

=1 + K

CDπ

inclined at

a wing , when

14 : 7 may be approximated

СDπ min where K = 1

like

,

nearly proportional

+ 3)

²/A

( 14:12 )

closely to the line labeled

" round

fuse

if

lage " in Fig . 14 : 2 CD minfus equals 0.05 (as shown in Fig . 14 : 7 ) . A small and appropriately chosen angle of incidence of the wing on .25

.20 CDπ

Fuselage

.15

Rectangular

.10

Circular CDπ

Fuselage

= CDT

min

(1 + α

/ )

deg 225

.05 a 2 , degrees2 200

100

0

Fig .

+ 5

14 : 7 .

10

α

Variation of fuselage

from data by Hoerner ,

(1 ) Hoerner

, S. F. , op .

cit . ,

.

300 15

400 20

deg .

coefficient with angle of attack and 1 /d = 6.9 . at Rei =

drag

p . 72 .

,

TECHNICAL AERODYNAMICS

14-10

the fuselage can

,

completely eliminate

however , almost

/

the unfavorable

A ( 1 e ) fus indicated in equation ( 14:12 ) for the cruising and climbing range of lift coefficients of an actual airplane . With the zero lift

line of the cruising conditions , equation (14:12 ) greatly over - state the adverse effect of the fuselage .

wing set at 3 to 5 degrees

chord of the fuselage

,

Fig .

and

is

as 14 : 2

common

for

to the

drag

minimum

optimum

The effect of subsonic compressibility on the drag of streamline bodies of revolution as analyzed by Hoerner ( 1 ) is shown in Fig . 14 : 8 , and the

effect of fineness ratio on critical Mach number from the same source is shown in Fig . 14 : 9 . Hoerner develops from rational considerations what 1.0

3

CD wet

2

.8

Mer

comp

/

Mer

0.5

d 1

.6 0.1

f

O

0.2

.4 d

0.3

Effect of subsonic com pressibility on drag of streamline bodies of revolution From Hoerner

.6

209

.

From Hoerner

,

.

.4

.

.

: 8 .

14

.

.2

203

.

.p

1/2

.8 Fig 14 Critical Mach number of streamline bodies of revolution

1.0

.p

.8

,

.6

: 9 .

.4

0

0

Fig

x

M

.2

+

d

.2

p "

203

)

)

(

4

/

d 1

(

p "

"

the

.

p

.

,

cit

(

for several typical values of

show good

numbers up through

.

.op

,

14:14

experimental

the

critical

critical

Mach

.

1

"

.

: 8

to

presented

empirical study that F.

Hoerner

,

(d

14

-

semi

S.

from

(1 )

finds

a

Mach

,

)

is

of this rule for

/1

and other evidence

14:13

VI - M2

this equation is plotted in Fig

cation

¹.5

/

=

p "

where

+ 6

/1

0.5

)

comp

d

= 1

CD wet

+

giving

Cf

and

resulting in the modification of factor l.5 in the last term of "

"

insertion of

by the

a

)

,

that equation

rule

Prandtl

"

14

: 7

equation

the extended

(

calls

he

number

verifi Hoerner Mcr

for

DRAG ESTIMATES

streamline bodies of revolution

is

14-11

single - valued

a

function of

" effec

an

tive " diameter / length ratio defined by the equation ( d / 1 ) eff where

x

thickness

= d

is

the distance from the

.

This ratio

verification

is

is

supersonic missiles

is

older

in

subsonic

+

0.5

( 14:15 )

1)

leading edge to the

plotted vs. Mer in Fig .

14 : 9

point of

SUPERSONIC

based on

.

Much

ballistic

information

research and

on

the drag of

this information

in many respects more extensive than information on flight , but basic studies on shock waves and boundary

and

and their interaction have only recently been extensively comparison

for

the optimum bodies

of

in Fig .

indicated

maximum

with experimental

.

MISSILE BODIES :

14 : 4 .

/( x

14:10 .

Subsonic

made .

bodies layers

A rough

subsonic and supersonic flight is and fuselages have often been

wings

1

с

} t

d

low drag wing section : 0012-0.55 50 ; CD wet = 0.0015 , CD min 0.003 Good NACA

low drag subsonic body : 0.9 ; at Re / 106 .15 ; Mer = CD wet 0.0015 , CD≈ 0.03 1 Good

Mcr.75

/

d 1

= 4

+

d = diameter

T

/

noses

Comparison

14:10 .

of the

been found

NACA

digit airfoils

better than those

fly

required to

sible

4-

X2

at M = 2 but d 10.07 M as in Fig with Re . of near - optimum subsonic subsonic and supersonic bodies . From Hoerner .

low drag missile body : varies considerably with

Good

Fig .

+

2x

X

shown

. CDT = 0.18 . A6 : 36 . also

without subsequent dash numbers have Fig . 14:10 only because they were

in

at wide range of angles of attack . For the lowest pos relatively small leading - edge radii shown in Fig .

drag the

minimum

Good supersonic missiles

14:10 are necessary . a nearly

sharp

curvature

.

point

;

have been found to require

any point , however sharp , has some small radius of

stresses considered , a perfectly sharp point can not highly accelerated supersonic flight ; a nose bluntness of

Thermal

exist long in

the order of a few per cent of the diameter

(1 ) ,Hoerner

,

S. F. , op .

cit . ,

has

little effect

pp . 198 , 210 , and 226 .

on the drag

14-12

TECHNICAL AERODYNAMICS

but permits a large reduction in thermal

sile

in

shown

Fig

.

14:10

coefficient against

(d 1)

is

/

stresses

mis

The near - optimum

.

very long and slender but the graph of drag

ratio is very flat

con

near the optimum , and

in

siderably

shorter missiles have nearly as low drag as the optimum , as dicated in Fig . 14:11 . Note in Fig . 14:11 that for a given nose length

is

the ogive shape

as good as a conical

not

,

nose , but on the other hand

for

a given nose angle the ogive has less drag , as may be seen by compar ing the " proper " drag coefficients for Figs . 14 : 11a and 14 : 11j . The sharp junction between a cone and cylinder , while it shows no disadvantage from shock -wave theory , is actually a substantial handicap in practice , pre

h

.5d

2.5d

°1

FTTTIALL

j

i

It

.

1 .

5d

2.5d

junction

the

A.A

3.5d

layer behind g

d

junction in assisting the

sharp

boundary

a turbulent с

b

a

effect of the

of the

of

new development

f

sumably on account

to provide

tail is

-

,

still

substantial function

exploration

under

the supersonic drag of

"

Mach

in

drag at

number

simple cone

some

in

semi

at

of

a

vertex angle

and boundary

also of nose shape

Data are provided

used

degrees

of 5.7

reduction

of the

quite possibly

and

tail

,

timum boat

bulence

boat

are

but the

op

layer

tur

-

=

-

one diameter

missile

to provide For the tests reported in

noses

+

seen

conical

the drag

,

5

if

between the cone and cylinder

a

,

a

.

is

14:11

.27

-

fairing

smooth

Fig

good

nose and tail shape on 2. From and M

practice

1 d

accordingly

a

is

=

this matter

though

Appendix

cylinder

6

Effects of

-

.

.25

1.64

"

14:11

115.7

.23

.26

M = 2 ,

.29

.24

1.7

.94

.

.25

.45 .47

,

.28

/

Fig .

.21

.

CDπ

is

for estimating

combinations

at

Mach

Flight at speeds beyond is currently being con sidered only at very high altitudes of the order of 100 miles because missiles flying in the lower stratosphere become red hot even at very quickly Such missiles can get out of the lower atmosphere without but the problem of cooling

or of delaying the melting

,

,

overheating

,

.

-

M = 4

)

(

M = 4

numbers up to 4.

upon

225

.

.p

cit

. ,

.op

,

F.

,

S.

( 1 )

Hoerner

;

)

(

reentering the lower atmosphere is as yet 1955 unsatisfactorily solved is some question as to whether the solution will be judged worth

there

14-13

DRAG ESTIMATES

its

if

cost

It

is

obtainable . to analyze the drag of a supersonic missile into three

customary

parts , ( 1 ) nose Figs . A6 : 36 and

drag ,

The pressure

A6 : 37 .

can be calculated

friction ,

skin

(2)

from the conical

lations of this sort are seen to Figs . A6 : 34 and A6 : 35 . Pressure boat -tail angle are shown in Figs .

sonic

skin

Turbulent

.

relative

( or " wave " ) drag

in

flow charts be well

noses

Appendix

4 , and

calcu in

and the

Skin

A6 : 38 and A6 : 39 .

effects of

friction

may be

includes a chart for laminar

7 , which

well

and 4 , as

is still

on the

the missile wall and the recovered temperature

of

of an unsolved problem

somewhat

sub

as

depend greatly

these factors affect transition of laminar to turbulent boundary

How

in

shown

conical

corroborated experimentally

friction coefficients at Mach 2 skin friction is there seen to

temperature

, as

of

coefficients

drag

estimated by the methods of Chapter and turbulent

(3 ) base drag

and

.

layer

indicated by the charts show

, as

ing current status of NACA information on this subject in Chapter 7. There is some evidence to indicate that missiles that are cold relative to the recovered temperature theories

some

Figs .

A6 : 36

)

of the boundary

transition

and

Reynolds

A6 : 37 must

- layer

have very high ( infinite by The drag

number .

analyses given

be considered as only a rough guide

to

in

esti

if

the drag of proposed new missile configurations , particularly they are long and slender and the skin friction is a major factor in

mating

if

the drag

,

because

transition varies with

Mach

and

Reynolds

numbers

in

ways as yet inadequately explored . NACELLE -WING COMBINATIONS

14 : 5 .

largely laminar

have

boundary

.

A smooth wing

- layer flow .

designed

to

A fuselage can also be so

de

can be

signed ; good subsonic designs of

this sort Fig . 14:10 . ever ,

in

have been sketched Combine the

any

way

two ,

in

is

junction .

Usually a substantial

velops are

generated

, no matter

made

turbulent

imaginable and

turbulence

region of separated

laminar

how

at

flow also what

the de

attempts

Fig .

14:12 . Generation of turbulent flow region by wing - nacelle or wing fuselage junction on laminar flow streamline body .

to provide " fillets " at the junction

.

The

effect of

wing - fuselage

junction

on transition in some combined wing - fuselage tests of the NACA on an otherwise completely laminar flow fuselage are shown in Fig . 14:12 . The adverse

junction

at the

effects of

the junction can be minimized by having the rear of the fuselage , as shown in Fig . 14:13 , but this

TECHNICAL AERODYNAMICS

14-14

is flyable

combination

only with a large

the center of gravity of the airplane wing chord .

sweep ,

Forward

turally objectionable

- forward

is

to put

shown ,

as

at the proper location on the main

while aerodynamically advantageous

This

.

sweep

,

is struc

because wing deflections produce increased

angle of attack

, which

further increases

increases

lift

and

This

the deflections .

- elastically critical speed and

combination is said to be aero unstable beyond

Wind

the

c.g. +

critical

less the wing

some

speed may be rather

is

merous combinations

Mean wing

chord

have been

.

un Nu

of wings and nacelles

. Some of Figs in . A6 : 11

tested by the

the test results are through A6 : 18 .

low

rigid

exceptionally

NACA

shown

are seen to show an incremental drag coefficient Some combinations

Fig . 14:13 . Advantageous com bination for maximum laminar due to nacelle of only about ACD = 0.035 , flow (but structurally disad which is very little above the skin fric vantageous ) . drag Reynolds tion coefficient at the numbers tested . Many of the studies are applicable either to fuselages or nacelles . If used for a guide to wing -fuselage combinations

, the drag

of other fuselage parts

must be added ,

particularly the cockpit canopy or enclosure . If used as a guide to con struction of wing - nacelle combinations , consideration must be given to the amount of air flowing into and out of the nacelle for cooling of the power plant or , in the case of turbo - jet nacelles , for intake and dis charge of combustion air and combustion products respectively . Turbo - jet power plants

are often most advantageously located in nacelle pods slung diameter below the wing ( as in Fig . 1 : 4a ) , though nearly

about one nacelle

equally good performance

has been obtained with power plants

built inte

grally with the wings as in the British Comet airplane . In general , it is most efficient to take air in through the nose of the nacelle and to discharge

it

pressure and the tail . 14 : 6.

a fuselage Some

.

is

the

tail

discharged with

FUSELAGES

drag

; COCKPIT

estimate

reported values of

tails , Fig

through

is

CD wet

canopies , protuberances

14:14

, as

air is

the

minimum

loss into a turbulent

ENCLOSURES .

the drag and CD ,

" rammed in " by the impact

coefficient of

a

for

streamline body .

without wings , are shown in Fig . 14:14 . flat plate skin friction data

or slipstream

includes laminar and turbulent

through

starting point

The usual

for fuselage

wake

bodies

DRAG ESTIMATES

for

comparison

with

based on equation ( 14:10 )

scale for CD ratio of about 7. Fig .

CD wet and a

and a length / diameter range of Reynolds

14-15

full

for

numbers

scale

14:14 also

fuselages in

the usual

shows

flight ,

which

is

to be substantially beyond that of all data there reported . Drag coefficients corresponding to less than that of turbulent skin friction on a flat plate are almost never reported . Flow in the slipstream of a propeller is , of course , always turbulent . Minor protuberances generate seen

turbulence ; flow aft of the leading

1.20 o

.005

.10

CD

CD wet

.002

=

/

1 d

Plate

Flat

.08

,0

Data

-

.001

=

7

- Flat

Cf Laminar

for

X

d

Turbulent

.04

body

.02

Transition

on

Plate

Large

A6 13

mph

.01

400

mph

Airplane . ,

Fig

, Small

Int

Wing

Fus

part lam . turb . :

. A6 : 15 , A6 : 15 ,

Fig .

.

Fig

O = NACA , ♂ = NACA , e = .

.0002

100

Fuselage data D = Hoerner p . 122 X = Hoerner p . 123

Airplane

Data

.0005

.004

Re1

in

.

,

,

109

the form of

be

NACA

tests

on

to put

laminar ring of sandpaper

fuselage bodies

in

an

where

a

.

,

,

in

,

,

ingly common practice part of the flow might erator

108

turbulent and any cockpit or canopy to provide vision for usually an additional source of turbulence It is accord

,

pilot is

a

nearly always

3.2

107

Comparison of fuselage drag coefficients without wings tails canopies protuberances or slipstream ,

14:14 .

,

Fig .

106

105

104

a

.0001

the

is

of the wing - fuselage junction

edge

.01

large

artificial turbulence gen

few per cent from the leading

of the fuselage so as to permit more accurate comparisons The effect of fuselage wing junctions may be inferred from data dis cussed in the preceding article to contribute little to the drag coeffi -

.

edge

:

,

.

-

.

:

A6 14

a

fuselage in which the flow is already turbulent if the optimum fuselage wing is selected from the data in Figs A6 13 and combination

cient of

TECHNICAL AERODYNAMICS

14-16

effect of cockpit canopy for Mach numbers less than 0.4 may be in ferred from the NACA tests reported in Fig . A6 : 19 . For a typical ratio The

Scan / S

1/10 , the worst canopies had an incremental drag coeffi cient ACD fus = 0.03 , while the best of the canopies there studied ( X - 1 and X - 2 ) had only one - tenth of this amount or about 0.003 , which may be fus

=

only about ten per cent of the fuselage drag . Inspection of data in Fig . A6 : 19 shows that the canopies must be carefully selected in order to avoid Tests on

critical Mach numbers . tail surfaces reported by /Dprofile of tail = 4% to 8% for most

effects

extreme adverse

on

fuselages with

ratio Dinterference

arrangements , with a very a 2 - surface or V - type The lowest drag

slight

improvement

EXPOSED

conventional tail (to 3 %) for

in interference

tail .

flying boat hulls are

seen

in Fig .

A6 : 23 to have

as low proper drag coefficients as the best fuselages ence and cockpit enclosure are included in each case 14 : 7 .

Hoerner ( 1 ) show a

LANDING

GEARS AND OTHER

landing gears are all but obsolete

wing

when

nearly

interfer

.

PROTUBERANCES

.

Non

- retractable

being used only for airplanes

in which considered relatively unimportant . A wheel has a high drag coefficient even streamlined as well as possible ; a combination of

high speed

is

,

if

or

dinary wheels and round struts would be incongruous wing and fuselage , as the landing gear drag

of all the rest of the airplane . ing gear drag data in Fig . A6 landing gears

shown

in Fig .

This : 26 ,

A6 : 25 .

well streamlined could easily exceed the drag on a

may be seen by

which Drag

consulting

the land

refers to the typical exposed is given in terms of f = D q

/ in

stead of proper drag coefficients to save estimating time . Data on various types of protuberances , including antenna masts and wire and air scoops and outlets , are given in Appendix 6. The proper drag

coefficients of are small

,

these

where otherwise

it

are very high , though

items

effect

the drag

may

did not

"aerodynamic atrocities

, " but

if

the items themselves

is

be small unless turbulence

exist .

Such items such

as

generated

radio masts are

the aerodynamicist should be quick to admit

are not designed for drag alone and that an airplane is a designed to transport persons and things quickly and comfortably

that airplanes vehicle

,

from place to place , and that

it

is

even more

important

for

a

pilot

to be

comfortable , to see where he is going , and to know where he is , than for the vehicle to proceed as rapidly as possible . It may also be true that ( 1) Hoerner , S.

F.

,

op .

cit . ,

p.

112 .

DRAG ESTIMATES

14-17

faulty landing - gear retraction mechanism would be more of a handicap to the sale of a light airplane than its relatively slow speed without retractable landing gear . Making good use of published information on a

the drag of airplane components , it is possible to arrive at an accur ately estimated value of f = D/q for a complete airplane as has been done by Hoerner ( 1 ) in Fig . 14:15 . In Fig . 14:15 the effect of surface fric tion , irregularities , and exposed parts on the drag of each of the major

irreg

rivet

heads ,

ft

and

+

.

L

1.4 1.6 1.8 2.0 2.2

.

Interf

N26

Skin Friction Turbulence Paint Smooth

(

Fuselage

bolt

sq

1.2

NYL 3

Wing

with good

can be estimated

drag estimate , wing

.

include sheet metal

0.2 0.4 0.6 0.8

In Hoerner's

.

edges , surface gaps ,

1.0

0

tail )

power plant ,

,

practice

)

ularities

fuselage

,

little

/

(wing accuracy after a

D q ,

components

Irregularities Additional Parts

537 Radiator

Parts

Engine

Tail

-Induced Drag

DRAG ESTIMATE

: 8 .

14

.

installation exhaust

,

-

,

parts

mast and

,

.

antenna

drag estimate includes

stacks

oil

cooler

FOR

AIRPLANE

COMPLETE

and

air

ventilating

For preliminary

considerably

simpler answer can be obtained by considering major parts without such detailed analysis

due to the analysis of this sort is illustrated

.

a

loss

and wing radiators

,

openings

His

momentum

wheel

by the

following

studies only the drag

An approximate

example

:

intake

and

engine

.

scoop

tail

canopy

His fuselage drag

landing gear ,

pilot

other irregularities

,

estimate includes

aileron gaps aileron edges ailerons and flaps air speed

as

ends of

holes around retracted

and

as presented

,

,

,

head

.

pitot

well

as

gaps at

airplane

,

blisters

metal

aileron balance weights

109

,

sheet

by Hoerner

,

.

.

and several

of the Messerschmitt ,

Drag analysis

14:15

.

Fig

.

Example

.

a

.

151

.

.p

cit

. ,

.op

,

F.

S.

(

(

)2

Ibid

,

Hoerner

)

1

.

.

( )

= a

( b )

"

"

,

( a )

Estimate the flat plate area equal to the parasite drag of assuming the data given below Lodestar airplane Use the result calculated in to write an equation for CD in terms of CL2 for the airplane Use VL 270 mph for calculation of Re at high speed Lockheed

TECHNICAL AERODYNAMICS

14-18

Sπ "

Part Wing , assumed span 65.5

ft

equivalent to

sq

Total .

.

Solution

.

35

0.0054 0.080 0.10

200

0.006

551 40

Fuselage , length = 50 ft Nacelles . total for two , including Tail surfaces , total

cooling drag

.

ΔΙ ,

ACDI

section ,

NACA 23012

.

ft

...

sq

ft

3.0

3.2 3.5 1.2 10.9

Wing Drag Estimate . To estimate the minimum profile drag coeffi cient of the wing , calculate first the mean chord c = S b = 551 65.5 = For V = 270 x 1.467 = 396 ft sec , calculate Re = 396 x 8.4 x 8.4 . 6380 21 x 106. For a 23012 airfoil at Re 106 = 6 , read in Fig . A5 : 3a cd min = 0.006 . To extrapolate to higher values of Re , consider Fig . A5 : 8 , which shows a slight reduction up to Re 100 = 9 , and consider also Fig . A5 : 9 showing a slight increase in cd min from Re 1069 up to Re 106 = 25 . These 6 - series airfoil data may not be applicable as they refer to bottoms of " buckets . " Plotting this point on a skin - friction graph such

ft

/

/

/

/

/

/

/

as Fig . 14:14 and extrapolating from 6 to 20 million , gives a net reduc tion of about 10 per cent or CD min = 0.0054 . Insert this value as the proper drag coefficient in the above table and calculate A fwing and

= 0.0054

insert this value in the table

x

551

=

3.0

.

/

Fuselage . For a fuselage length of 50 ft at 396 ft sec , calculate = 396 x 50 x 6380≈ 1.2 x 108. From streamline body data in Fig . 14:14 , estimate CD = 0.05 , allowing about 20 per cent for cockpit enclo sure , another 20 per cent for interferences , and another 20 per cent for protuberances such as antenna mast , etc. A value of CD = 0.08 is judged

Rel

to be reasonable .

With

this

Affus and

value of

= 40

x

insert this value in the table

calculate

ACD

0.08

=

3.2 sq

ft

.

Nacelles . For the nacelles , refer to Figs . A6 : 15 through A6 : 17 and note that while the best cowlings for air - cooled engines with substantial cooling air flow show proper drag coefficients in the region 0.06 to 0.08 , is conservative to assume additional drag due to non - optimum intake and discharge of air resulting in CD = 0.10 . Using this value , calculate

it

Afnacelle and

= 0.10

insert this value in the table

x 35

=

3.5 sq

ft

.

Surfaces . Calculate Retail 6 x 106 and in Fig . A5 : 3 , assum section consisting of an 0009 airfoil , read cd min = 0.0055 and increase this about 10 per cent for interference with fuselage as discussed in text , and calculate ing

Tail

a

tail

Aftail and

insert this value in

= 200 x 0.006 = 1.2 sq

the table .

ft

DRAG ESTIMATES

14-19

Adding the values of Af in the above table gives a total equivalent Using this value , calculate the = Af = 10.9 sq ft . area of = total parasite -drag coefficient as CDf f/S 10.9 551 = 0.0196 . To get the induced drag , calculate the wing aspect ratio as

f

flat -plate

/

A

=

/551

65.52

7.8

=

/

in Fig . 9:23 for tapered wings ew = 0.87 For the contribution of the fuselage to the

and calculate 1 ew = 1.15 . induced drag , read in Fig .

Read

14 : 2

for

[A( 1/ e )fus ]/ ST round fuselages without

/

This is

as

ances

0.75

0.75 x 40/550

=

0.055

value and can allow for effects of protuber variation with angle of attack and optim

maximum

as normal drag

well

wing incidence

=

nose engine , and calculate

▲ ( 1 e )fus =

a probable

fus / S )

.

Calculate

/

1.15

1 e

and

+

0.055

=

1.205

/

e = 1 1.205 := 0.83

/π Ae

Calculate

=

1

1

/π

x 7.8 x 0.83

lift

The desired equation relating the drag and

answer called

14 : 9.

AND

THRUST

coefficients is then

0.0490-2

CD = 0.0196

This is the

= 0.049

for

POWER REQUIRED FOR AIRPLANES

IN LEVEL FLIGHT

principal forces acting on an airplane in level flight are 14:16 to be the lift L , the weight W , the drag

the power plant thrust T ; there

D,

is also

usually

to balance

lift

on the

clude Ft . velocity

if

Ft necessary L is considered to be

entire airplane

flight

For level

,

it

follows that the

lift

L

= CLPSV2 =

2

The drag

and

lift

D

Fig .

14:16 . an airplane

Forces acting on

in level flight .

( 14:16 )

Clas

coefficient necessary for level flight CL

The

in

at constant

W=

It

can

.

in Fig .

Ft

a tail force

, but

shown

is

/

(14:17 )

= W Sq

coefficients are usually related

by an equation of

the form CD = k1

as shown earlier

in

the chapter , and

+

(14:18 )

k₂CL2

this equation

is

true at

all

speeds

TECHNICAL AERODYNAMICS

14-20

if

altitudes

and

compressibility

of the airplane

The drag

effects are neglected . calculated

may be

from

-

-

D = DW = CDW

Since power force x velocity and required for level flight is

hpr

1 hp = 550

= DV

ft - lb / sec , the horsepower

= D mph

( 14:20 )

375

550

calculation of the

An example

( 14:19 )

power required

for level flight at

sea

level follows : Example . For a Lockheed Lodestar airplane , assume S = 551 ft2 and that and drag coefficients are related by the equation CD = 0.0196 + 0.04901 , as found in Art . 14 : 8 , and calculate the power required for level flight at sea level ( ) with a gross weight of 17,500 lbs at speeds (mph ) of 300 , 250 , 200 , 150 , 125 , 100 , and at stalling speed ( flaps up ) , assuming CL max = 1.55 for a power - on stall with flaps up . Plot hpro vs.

lift

the

mph .

Solution .

Calculate

/

W S = 17.500

/ 551

=

31.7 lbs per sq

ft

Using q = 0.00256 ( mph ) 2 at sea level and equations ( 14:17 ) through the power required for level flight at sea level is calculated 14 : 2 and plotted in Fig . 14:17 . TABLE 14 : 2 .

CALCULATION OF POWER REQUIRED OF A LOCKHEED LODESTAR q = 0.00256 (mph ) 2 , CT CL = 31.7 lb per sq

mph

ft

300 250 200 150 125

160

102.4

57.8 40.0 25.6 20.4

100

89.1 min

1.55

max

AT SEA LEVEL

AIRPLANE =

CDi 0.049C12

0.138 0.198 0.310 0.548 0.792 1.24

230

FOR LEVEL FLIGHT

( 14:20 ) ,

in Table

0.0009 0.0019 0.0047 0.0147 0.0307 0.0752 0.118

CD =

0.0196 + CDi 0.0205 0.0215 0.0243 0.0343 0.0503 0.0948 0.138

D= WCD

CL

lb

hPro

D mph

375

1

2,080

2,600 1,900 1,375

1,268 733 438 370 358 370

1,095 1,110 1,340 1,560

When the horsepower available from the engine and propeller is plotted on the same sheet , the sea - level performance of the airplane can be de termined . Methods of calculating the power available are discussed and illustrated in Chapters 15 and 16 .

Equations (14:16

)

or altitude

conditions

(14:16 ) .

the

If

( 14:20 ) are applicable

through

same

if

the proper

speeds

air

density

are assumed for the

to either

is

used

sea

in

level

equation

calculation of

power

required at sea level , new values of CL and Cp and hp , may be calculated using the proper air density in equation ( 14:16 ) for the specified alti

,

DRAG ESTIMATES

It is

tude .

CL

convenient , however

much more

and CD as were found

sea - level

for the

14-21

,

to

assume

the

calculation .

values of

same

It is

then neces

sary to calculate only the values of mph and hpy for the altitude condi The equations for calculation of power required at altitude are then , for constant CL :

tions .

alt

k₂c²

mphsL √1

=

)

14:21

CL

(

)

14:22

hPr SL 11/0

14:23

)

hpr

/0

k1 +

(

=

mphalt

- CDS CD

(

Dalt = DSL

The calculation of power required at sea level in Table 14 : 2 is continued in Table 14 : 3 for the speed and power at 10,000 ft standard altitude , at

the

same values of CL as in Table 14 : 2 , and the results from both figures plotted are in Fig . 14:18 . Fig . 14:18 differs from Fig . 14:17 only in that 2500 2000

2000

hpa. Chap .

1500

f

1500

leve

1000

1000 900 800

Sea

hpr

700 600 500

500

400

Stall 100

300L 70 80 90 100 125 150 200 250 300350 mph

300

200 mph

Replot of Fig 14:17 Power required for level Fig 14:18 Lockheed Lode- with logarithmic scales and with airplane as calculated in Table power required at 10,000 tude added from Table 14 .

.

.

3

:

Note

A3

: 1 ,

,

chart

.

.

air

standard altitude the or from the standard

10

/

0.7384 from which calculate Table 14:18 that each sea level point plotted is one may

=

σ

is

Fig

√

in

A3

ft

At 10,000

-

.

read from the

Table

used

=

,

table

1.164

scales have been

ratio

: 2 ,

density

.

.

logarithmic

air

ft alti

.

:

2

14

.

14:17

flight at sea level for star

.

ft

10,000

hpro

Fig

16

10,000

moved

a

.

to the right and up the same distance on the logarithmic chart The equality of distances over and up is peculiar feature of logarithmic

TECHNICAL AERODYNAMICS

14-22

scales :

a given

TABLE 14 : 3 .

is

ratio

represented by a given distance on the scale

CALCULATION OF POWER REQUIRED FOR LEVEL FLIGHT AT 10,000 ALTITUDE FOR A LOCKHEED LODESTAR AIRPLANE

ft ,

10,000 Sea Level , from Table 14 : 2 σ mph

CL

hpro

300

0.138 0.198

2,080 1,268

250

0.310 0.548

200 150 125

0.792 1.24

100

1.55

89

FT

σ = 0.738 ,

= 1.164

hpr

mph

2,420

349

1,475

291

733 438 370 358 370

.

233

854

174.7 145.5

431

510

116.4 103.6

416 431

Fig . 14:18 also shows a typical graph of power available from cating engine and propeller at 10,000 ft altitude , as developed

recipro in Chap

of graphs of power required and power calculating available on the same chart permit the performance of the plane in level and nearly level flight at various altitudes , as explained in Chapter 18 . ters

15

and

14:10 . PLANES .

16.

The combination

GENERAL

Fig .

CHARTS OF THRUST

plotted as ratios to

trary standard of maximum L/D

for

an

( 14:18 )

in

14:18 can be put

commonly

selected

(minimum

D

/ L) .

is

condition

of

of this minimum

CL

/

CD CL

CL₁ and

for level flight at

maximum

L/D

given

/

+

The

may be

are

arbi found

by equation

( 14:24 )

K₂CL

with respect to CL =

0 and

D L ( or maximum L/ D ) by ( ) 1 ,

k₂CL1² so that

of

characteristics are

H

Setting the derivative

speed and power .

AIR

first

CL

ing the that

if

the speed and power

the speed and power at the condition

The condition

calculate

follows :

-

AND POWER REQUIRED FOR LOW SPEED

general form

arbitrary standard

some

airplane whose aerodynamic as

air

/

=√k1

/ k2 ;

it is

found

( 14:25)

= k1

CD1

designat

= 2k1

a given gross weight

W,

(14:26)

DRAG ESTIMATES

CLI CL

14:27

is ,

The ratio of the drag to the drag at the reference condition

coefficients

D

CDV2

=

D1

14:28

CD1V12

which

ratio )

14:31

(

1

)

(

-)² speed

V1

in Figs

)

(

)

+

~ +

1

2

= 2

(

14:30

V

14:19 and 14:20 and

and power required

for low

speed

-

constitute general charts of thrust

(1

)²1

+

÷

-

of the

are plotted

ratio as

2

V1

.

14:31

14:29

the speed

terms

V3

=

+

in

+

D1 V1

)

and

(

)

(

14:30

V

= D

2

2

/

P1 Equations

1

can be calculated

of

terms

=

)=

(1 ·+

2

2

ratio

√ )

11/1 Vi

-

23/12

and the power

v2

=

k2

in

so that the drag ratio can be calculated

D1

1

CL2

+

24

=

V /

k₂cz

2k1

/

=

k1

k₂CL2

1

+

k1 + k₂CL12

CD1

2

- k1

CD

k1 +

in

from the

,

)

drag

(

definition of

)

=

(

V V1

14-23

air

.

planes

For any particular airplane

these charts

5.0

specific

charts

6.0

4.0

5.0 D

4.0

D1

3.0

3.0 ala

2.5

2.0

2.0 1.8 1.6

1.5

1.4

1.0 0.9 0.8 0.6 0.70.80.91.0

3.0

2.5 3.0

Fig

General power required 14:20 chart plotted from equation 14:31

) .

) .

(

.

.

,

chart

2.0

(

General thrust required plotted from equation 14:30

14:19

1.5

.

Fig

1.5

.

.5

2.0

,

1.0

>>

SA

1.2 1.0

may be made

TECHNICAL AERODYNAMICS

14-24

by

calculating specific values of

going equations .

V1 ,

to these charts and plained later . An example of the application of Fig . airplane follows : be added

Example .

Given :

CD = 0.0196

fore

In

V1 , D1 , tude .

equation

and P1 , at sea

/

and W S = 17.500 / 551 = 31.7

level

and at 10,000

ft

alti

from the given data ,

( 14:24 ) ,

k₁ k1

14:20 to the Lockheed Lodestar

0.049C12

lb/ft2

Find :

Solution .

as given by the

D1 , and P1 ,

available from the power plant can also used for performance calculations as ex

Power or thrust

k₂

= 0.0196 ,

= 0.049

From equation ( 14:26 ) calculate CL1

/

Vk kz = 10.0196 / 0.049

=

CD1 = 2k1 = 2

definition of

From the

91

For standard V₁ or at

10,000 V1

alt

sea -level =

√91

ft =

=

/

/

W S CL1 = 31.7 0.632 = 50.1

air

/ ( p /2)

/

with

SL V170

,

calculate

/ 0.00119

D1V1

,

with

= CD1 W = 0.0392

0.032

for

calculate

sea

= 205

ft / sec

/

= 239

ft/ sec

17,500 = 1,085

level

( 140 mph )

= 0.738 σ = p Po

x 1.164

= 205

CL1

calculate

p 2 = 0.00119 ,

= 150.1

V1

D1

0.0196 = 0.0392

CL calculate

standard altitude

For any altitude

Since P1

=

x

= 0.632

and 10,000

/

= 1 1.164

( 163 mph )

lb

ft

standard altitude

ft lb/ sec = 403 hp 259,000 ft lb / sec = 470 hp

P1 SL = 1,085 x 205 = 222,000 P1

alt

=

1,085 x 239

=

To check Fig . 14 ; 18 against Fig . 14:20 , read a point on Fig . 14:18 , such = altitude . Calculate for this point as mph 349 , hpr = 2,420 , at 10,000

ft

V = 349 = 2.14 V₁ 163 Above

this value of

/

V V₁

in Fig . P

= 5.1 x 470 = 2,390 hp

This value checks the value 2,420 hp calculated

in Fig .

14:18 .

/

= 5.1 , and calculate 14:20 , read P P1

in Table

14 : 3 and

plotted

DRAG ESTIMATES

.

14:11

DRAG ESTIMATES

FOR

14-25

Inhabited

SUPERSONIC VEHICLES .

vehicles

( supersonic airplanes

) are limited by the " thermal barrier " to M = 1.5 to troposphere 2 in the and lower stratosphere from considerations of cockpit

refrigeration

lent

( tr = 215 ° F in the lower stratosphere at M = 2 with turbu layer ) and from considerations of hot - strength of transpar

boundary

suitable for windshields

ent materials

siles )

limited in

are likewise

flight

speed of prolonged

mis in the

( guided

Uninhabited vehicles

.

to

M = 3

troposphere and lower stratosphere from considerations of hot - strength of

available structural materials ( tr = stratosphere at M = 3 with turbulent

flights

at

M = 4 and

1030

°F , or

" red - hot , "

boundary

layer

lift of some

wings

in

the

lower

though

short - time higher are possible without structural disintegra ) ,

tion . Data

for estimating the

able for supersonic timating the drag of

vehicles

have been

drag and

flight

have been presented

in Art .

data for es suitable for supersonic

bodies (cone + cylinder ) given earlier in this chapter .

some

wing + body combinations can

, however , NOT be

suit

(rectangular )

The

10 : 4 ;

lift

and drag

of

estimated with useful accur

ef

acy from knowledge about the separate components , as the interference fects for typical supersonic configurations , unlike subsonic , are likely to be larger than the separate effects . Bonney (1 ) portrays this graphi

cally ,

in Fig . 14:21 . The wings are usually not greatly affected but their effect on the body is often large .

as shown

XXX

by the body ,

missile

have enough

lift

cit

at

weight without wings but this in Fig 14:22 and the resultant

Engineering Supersonic Aerodynamics .

.op

,

can

characteristics .

ahead of the usual center of gravity

"

)

is

E. Arthur . A.

Bonney

,

)

(

2

(1 )BBonney , Hill , 1950 .

(

to the axis

E.

normal

N

,

angle of attack to support its mostly on the nose as sketched

body

is

body with wing

not

From

small

lift is force

location

,

sum of the separate

a

,

speeds

a

At supersonic

characteristics of

aerodynamic

. "

of

,

Sum

even approximately equal to the

,

14:21 .

.

Fig .

McGraw

TECHNICAL AERODYNAMICS

14-26 a wingless

and such

missile

attack unless stabilized

not maintain a constant angle of

rifle

in

shells )

and gun

(as in Fig . 14:23 ) . Resultant normal force

=

fins

N

or

will

body

by spin ( gyroscopic , as

Noody N

tail

-80

Net pressures normal to axis

=

Wind

Wind

Axial force

W

Forces on wingless

.

14:23

fin stabilized missile

usual c.g. location

.

.

on

when of semi vertex angle eg to the inclined at an angle

Behind the cone usual junction the net normal ,

.

as

/

3

pressure drops to

a

deg

tity in

M

.01

vertex angle

,

-

Semi

calibers

so that the

is not far from the centroid of the platform area

center of pressure

deg

20

15

of the nose

.

5

10

few

negligible quan ,

α

q8

cylinder

a

d

dCN

=

N

2

.

1.5

.03

,

,

wind

1.0

.02

)

may be estimated from the re sults of theoretical calculations shown in Fig 14:24 where CN =

83

,

T

t..

a (d

,

-

nose

.05 .04

conical eg ,

N

The normal force

cap

body

flight

able of steady level

a

tail for

.

.

.

out

Fig

Sketch showing unbal on missile body with

14:22

anced forces

-

Fig

W

Triangular fins are usually pre

more

movable

,

"

all

because add

,

(

)

1 :

must be

A

)

.

.

480-483

information

Inclined

Body

of this sort Revolution

, "

little

of

very

an

,

(

"

but

Supersonic Flow Over

pp

.

,

1938

"

tunnel tests S.

H.

,

Tsien October

( 1 )

fins

they

in the

large flaps are very ineffective at supersonic speeds interference lift data is currently 1955 being compiled from

supersonic wind

JAS

Guidance

given area

as

7a

edge

"

body of

"

"

trailing

to the body

.

lift

interference

a

for

Fig

.

inical

ferred over rectangular Nike missile

"

.

Tsien

as

Normal force coefficient cal noses as calculated

,

co

(

for

,

14:24

by

slope

.

.

Fig

14-27

DRAG ESTIMATES

has been published

It ents

.

customary to analyse

has become

, one independent

which

is called

lift

of

two compon

) and one nearly proportional

(CD

CDi by analogy .

missile force data into

Hence , for a

it is

missile

write

to

customary

this

analysis

cients are largely

is

not very useful because

for

body

not yet

stability

wing +

fin

been formulated

, but

of such missiles

flight test

lift ,

students

if it is

The

coefficients are not ,

drag , and pitching

may

moment

supersonic

and

wind

- tunnel

between wind

- tunnel

data will be due to the large difference temperature

have

the performance

calculate

assumed that

coefficients

M and dimensions

principal discrepancy

conditions as the missile surface path ( see Chapter 7 for details ) .

to

while the subsonic coeffi

combinations as a function of

test data are available . and

,

independent of M , the supersonic

Simple rules for estimating

,

(14:32 )

CD = CDo + CDi

but

CL2

in

boundary

changes along

layer

its flight

PROBLEMS 14 : 1 . For a particular wing - fuselage combination , the drag added by the fuselage per sq ft of fuselage frontal area at 100 mph at sea level is 10 lb. Find ACD for the fuselage . 14 : 2 . For a streamline body of revolution of / d = 5 , read CD in Fig . A6 : 15 and compare with general data of Fig . 14 : 6 .

l

Using Figs . A6 : 34 through A6 : 37 , estimate CD at M = 1.5 and cylinder missile body without boat - tail for flight Tr for a cone in standard sea -level air . Cylinder diameter = 10 in . , cone , length = 25 in . , cylinder length = 25 in . Assume transition at Re = 106 . 14 :4 . A " streamlined " wire of nominal 1/4 in . size ( diameter of threaded end ) has a cross - section 0.087 in . wide and 0.348 in . long . Using the drag data on elliptic cylinders ( Fig . A6 : 2 ) , estimate the drag per ft of length of this wire at 100 mph in standard sea - level air . 14 : 5 . For the Ercoupe airplane sketched in Fig . 1 : 3 , assume the data given below . ( a ) Estimate the equivalent parasite flat plate , and ( b ) write the equation for CD vs. CL2 . Use mph = 120 to calculate Re for the high - speed wing -drag estimate . Tw

14 : 3 . =

Part section , b = 30 ft · Fuselage , length 20 ft 9 in . Tail surfaces • Nose wheel ( low pressure ) and support Main wheels and supports . ·

Wing , 4412

Total .

Sπ , sq

ft

Af, ACDπ

142.6 12

30

0.60 1.50

0.12 0.006 0.6 0.4

sq

ft

TECHNICAL AERODYNAMICS

14-28

For the Lockheed Constellation airplane , a photograph of which 1 : 4d , assume the data given below . ( a ) Estimate the equivalent parasite flat plate , and ( b ) write the equation for CD vs. CL² . Use mph = 350 to calculate Re for the high - speed wing - drag estimate .

is

14 : 6 . shown

in Fig .

effective section 23015 , span 123 ft Fuselage , length 95 ft . Nacelles , total for four , with cooling air flow Tail surfaces ·

Wing , mean

Total

tion

ft

1,650 100 70 700

ACDП

sq

ft

0.070

0.080 0.006

•

14 : 7 . 14 : 5 ,

Af,

Sπ ,

sq

Part

For an Ercoupe airplane assume that the drag and

for which drag was estimated in problem coefficients are related by the equa

lift

CD = 0.030

0.066012

the power required for level flight at sea level with a gross weight of 1,260 lb at speeds ( mph ) of 120 , 100 , 80 , 70 , 60 , 50 , and minimum speed , assuming CL max = 1.50 at minimum speed , and plot hpr vs. and calculate

in Fig .

mph as 14 : 8 .

14:17 . a Lockheed Constellation airplane , Fig . 14 : 6 , assume that the drag and

For

for

lift

timated in lated by the equation

CD = 0.0154

which

drag was es

coefficients are

re

+ 0.0426C12

calculate the power required for level flight at sea level with a gross weight of 86,250 lb at speeds ( mph ) of 400 , 350 , 300 , 250 , 200 , 150 , = 1.60 at 125 , 100 , and minimum speed ( flaps retracted ) , assuming CL max flaps plot Fig hpr speed , mph , minimum ( retracted ) and vs. as in . 14:17 . 14 : 9 . For the Ercoupe airplane , calculate the speed and power quired for level flight at 12,000 ft standard altitude at the same values of CL as in problem 14 : 7 and plot on logarithmic ruled graph paper . Check and

re

by

Fig .

14:20 . 14:10 . For the and power required

Lockheed

Constellation

airplane

,

calculate

the speed

for level flight at 20,000 ft standard altitude at the same values of CL as in problem 14 : 8 , and plot on logarithmic ruled graph paper . Check by Fig . 14:20 .

CHAPTER

15

AERONAUTICAL POWER PLANTS

15 : 1 .

siles )

POWER PLANT TYPES .

are

to

combustion

rearward

titative terms

the

( airplanes ,

aircraft

energy of discharge of

mechanical

helicopters

plants which convert chemical

air

energy

/

of

gases

It is

forward .

summary of typical quan the student or engineer can

chapter to present a brief

of this

on such power plants

data

mis

,

and or exhaust

generating a thrust which propels the aircraft

,

the purpose make

Most

propelled by power

so

that

rapid and reasonably accurate estimates of the propulsive thrust in of fuel consumption , as a basis for estimating the performance of

aircraft . Typical

15 : 1 ,

and

power plants

aircraft some

sketches of Fig . as the British

are

shown

in the

photographs

of their engineering characteristics are The engine

15 : 2 .

more

- driven

screw propeller

descriptively characterize

it , is

of Fig .

shown

in the

or " airscrew , "

the most efficient

of aircraft propulsion yet devised for flight speeds under 400 mph . The efficiency of screw propellers is considered in Chapter 16 in some detail . At speeds around 450 mph , with the usual optimum propeller blade settings in the region of 450 , the Mach number along the helical blade

means

unity

path approaches

Under these circumstances ,

near the propeller efficiency . propulsive losses of thrust and propulsion by means of high - speed jets gener shock waves begin to

and

blade tips , with substantial

ated by internal combustion more

efficient

.

At

still

turbines

For flight at very high

optimum ramjet be by rockets as

designs (Fig .

( " turbojets , " Fig .

15 : 1c ) become

higher speeds the turbines are unnecessary

the impact or " ram " pressure of the air plant operation and the " ramjet " (Fig .

ical .

form

become

is sufficient for

, as

power

economical

reasonably econom 15 : 1d ) becomes altitudes where air density is very low ,

prohibitively large

15 : 1e ) , which

,

carry along their

and own

propulsion

oxidizer

must

as well

fuel . For these various types of power plants the thrust

propulsive of speed

efficiency

in Fig .

,

15 : 2 .

efficiency

-all efficiency are summarized as functions civil aircraft in use or under construction

and over Most

, thermal

15-1

,

TECHNICAL AERODYNAMICS

15-2

a.

Gasoline engines

, unsupercharged supercharged .

b.

Turbine

and

propeller ( turboprop ) .

c. Turbojet ( Pratt and Whitney

J57.

40 Ramjet ( Marquardt ) . d. ( Courtesy Aviation Week ,

April

HYDROGENPEROXIDELINE

e.

Fig .

STEAMTURBINE PUMP

18 ,

STEAM EXHAUST

1953 .

ROCKET MOTOR

Rocket ( liquid propellent , using gasoline and H202) . 15 : 1 . Current common types of aircraft power plants . ( See Fig . 15 : 2 for characteristics . )

AERONAUTICAL POWER

Accelerating Thermal force -Thrust efficiency ( T) (n₁₂)

mph

mph

0

.8

4000

.4

.1

mph

AL 500

500

8

2

Prop

° F

1

.2

Jet

.1 mph

moh 1000

1000

mph

500

500

8 1500

F

O

.2

Turbojet

mph

500

.3

mph

Jet

mph

500

.1

°

moh

500

.2

mph

500

1500

Prop

Turboprop

(16)

mph

500

0

500

( p)

L

propeller

efficiency

0

.1

Overall

efficiency

L

engine and

Propulsive

0

Piston

.3 .2

1

Prop

2

D

° F

m

15-3

O

Mass per second

PLANTS

.4

.2

moh

moh 1000

1000

mph 1000

12

Ik .2

mph

Rocket

possible

placement of

internal

O

0

2000

engines

that the next few decades engines

are

will

by turbines

driving

.

)

screw pro

under construction

,

combustion

propelled airplanes

combustion

mph

types of aircraft power plants Westinghouse Engineer March 1945.

internal "

it is

by

turboprop

"

.

and

few

2000

, "

: 2 .

1955 are propelled

mph

2000

common "

0

Characteristics of Presentation suggested in

15

A

in

2000

.8

5000

mph

2000

(

.

mph

2000

0

mph

pellers

mph

.2

0

Fig

L

2000

k

.5

mph

2000

0

mph 2000

.2

°F

2000

0

mph

0

1

Ramjet

0

8

.8

see the gradual re

for propeller drives

TECHNICAL AERODYNAMICS

15-4

under

of the inherent lightness

mph because

400

simplicity of the

and

turbine compared with the internal combustion engine (wt /hp for turbo props is about half that of piston engines ) . Such developments , however , take many years , but most

the gas turbine

experts agree that there

is

where weight

The supersonic missile field in . always be dominated by turbojets , ramjets , and rockets ;

course ,

transonic military

field of

the

for

a good future

airplanes

at even more of a premium than

will , of

is

particularly in the field of helicopters

,

aircraft , is

speed commercial

aircraft

expected

and , to a

to be

lesser extent , high by the

dominated

turbojet

power plant . 15 : 2 .

PISTON ENGINES .

first

The

power driven airplanes

were powered

by steam engines . Consideration has also been given to the powering of large airplanes by steam turbines from steam generated by nuclear reac

tor boilers

.

The

principal

steam

ternal

engine of equal

combustion

turbines

are

to be used for

to

condensers

to the use of steam or other

handicap

fluid in an engine is that turbine is usually about ten

mediate

inter

the "water rate " of a steam engine times

power .

airplane

the fuel consumption Thus ,

if

of the

steam engines

or

in

or steam

power , they must be equipped

with

for recirculation of the water in order to have Suitable steam condensing equipment has thus far proved

provide

reasonable range

.

excessively

it is quite possible that wing surface condens at a reasonable weight similar to the wing surface radi

ers can be

heavy , though

built

ators used with

liquid -cooled gasoline

some

Internal

Intake manifolds ThrottleCarbureter Float E

-

Gasoline

15

: 3 .

a .

Fig of

Air

Stroke jacket Water

Cylinder head Intake valve ... port Intake

-k

Exhaust valve Exhaust port Spark plug Cylinder Piston rings -Piston pin

Bore Piston

ConnectCrankcase ingrod Crank shaft Crank Crankpin

Principal

elements

(

gasoline engine From Chatfield and Taylor The plane and Its Engine the study

Fig .

15 : 3

.

. "

)

,

"

.

Air

which burn

inders

engines . combustion

air

and

" piston " engines ,

and gasoline

drive

a

in

metal

of pistons and connecting rods ,

by means

are the principal current type of plane power plants . The principal ments

of

cyl

rotating crankshaft

one

combustion

cylinder of engine

are

air ele

internal Fig in . 15 : 3 .

such an

shown

While the construction of such engines assumed

to

be

familiar to

is

most students

it

of Technical Aerodynamics , is consid ered worthwhile to review here the basic operating principles

in

connection with

of the characteristic limitations of such engines . Note in that the cylinder surrounds a piston which is connected by

15-5

AERONAUTICAL POWER PLANTS

of

means

peller

.

a connecting rod to a crankshaft

is

There

also a carburetor

air ,

and a manifold that conducts

also

a system of valves

in

the proper time open

manifold to form a combustion

burning .

pipe after

starting the

The valves

.

to permit the products of combustion

exhaust

combustion

in

is

There

the

the fuel in There

the mixture into the cylinder

the stroke of the piston

the cylinder from the

atomize

the mixture to the cylinder .

for admitting

pro

that delivers power to the

with jets that

,

first

at

close

chamber , and

off

later

discharged through

to be

is

an

also a timed ignition system for

cylinder .

Measurements of the pressure inside of one of the cylinders while the engine is running yield an indicator diagram similar to that shown in

Fig .

of

15 : 4 shows

operation consists

is

the mixture

approximately adiabatical

ly

and at the end of which

the mixture

is

ignited

a

rise in

and burns ,

with

ucts of combustion piston

on the

;

bustion flow out

;

(3 )

prod

the

expand and do work

(4 )

an exhaust

four - stroke cycle and engines .

atmosphere .

is

Fig

15 one engine

Bottom dead center

for

Indicator diagram cylinder of an airplane

stroke during which the

of the exhaust

discharged into the

Power stroke Compression stroke 15 stroke Exhaust s troke Intake O 4 0 Top dead center PistonPositionIn

resulting

pressure and temperature

a power stroke during which

1000

100

, .

compressed

( 2 ) a compression

;

which

4,400

.

stroke during

500 .I.n8 400 , 300 200

.

into the cylinder

600

Lb.per Sq Pressure $

of four strokes of ( 1 ) an intake the piston as follows : during stroke which the mixture flows

cycle of

that the

°F

diagram

°F

indicator

The

.

15 : 4 .

: 4

Fig .

valve and through

an

products of com exhaust pipe to be

is known as the in most airplane

The cycle of operation

the cycle

of

operation used

A lighter engine

can be built , with some sacrifice in fuel economy , slight positive if a intake pressure is maintained by means of a blower and the exhaust and intake occur simultaneously at the end of the power

stroke cycle

,

.

in

which case

Such engines

the cycle of operation are

" outboard" motorboat engines . They have also gliders , and some small helicopters . The

at the center "

ratio of the

is

cheap and simple and

volume contained

known

as the two - stroke

are most widely

been used

in the cylinder

for target when

" bottom dead center " to the volume when the piston

is

known

as

the compression

ratio

.

With a

is

known

as

drones ,

the piston

is

at " top dead sufficiently high

TECHNICAL AERODYNAMICS

15-6

ratio , the isentropic rise in temperature on sufficient to ignite the fuel without an ignition system .

compression

in this

operates

occasionally

is

manner

fuel

where

that

engine ; such engines have

known as a Diesel

aircraft

on

been used

is

compression An engine

economy

is

a primary con

sideration . indicator

The net area of an

is

diagram

a measure of the work per cycle done

is

what

delivered by the crankshaft

,

is

( Bhp ) ,

known as the mechanical

efficiency

the torque

( Ihp )

15 : 4

and determines

of the engine

The power

.

sometimes measured by a brake and therefore

called brake horsepower power . The ratio of the

If Q is

inside the cylinder

horsepower

as the indicated

known

in Fig .

such as that shown

always

than the indicated

less

brake horsepower

horse

is

horsepower

to the indicated

.

is

delivered to the crankshaft and rpm rpm , then

the rate of

3500

Characteristics of typ for light airplanes

engine Note

in Fig

15

: 5

a

)

.

a

the mixture flowing

through

manifold and valves

The

is

being

that

if

somewhat

termined

arbitrary

primarily

by

the

rating

de

considera

tions of durability of the engine

propeller the re rpmis determined by the propeller

the engine

drives

between propeller power and for fixed pitch propeller the horsepower varies approximately as rpm3 Specific fuel consumption based on brake horsepower for propeller load Ratings of many and full throttle conditions are also shown in Fig 15 airplane engines currently manufactured in the United States are shown in page A7-1

.

Appendix

7,

: 5 .

.

.

a

;

lationship

to increased friction power loss of pressure in

and increased

2000 2500

rpm

.

.

parts

1500

due

a

5 .

:

15

ical

are

,

Full

1000

engines

.

0

throttle

800

proportional

,

8

bhp

20

is

brake horse power and rpm where the torque has not yet begun to drop off with rpm

throttle

,

.

usually rated at

load

x

airplane

full throttle

Airplane

a

50

:

(

A

=

-

.

.

full

small

that the

rpm

rpm shown

Propeller BSFC

Approximate Propeller fixed

Bhp also BSFC 100 lb.fuel perBhp

15

This corresponds to constant torque over the range of

BSFC

60

.

with rpm for

in Fig

to the

RatedBhp and rpm

70

Fig

15

brake horsepower

100

hr 80

,

Note

rpm

5,250

horsepower

.

.-

rpm 2π 33,000

: 5 .

typical variation of brake is shown in Fig 15

engine

: 5

A

Bhp

1

rotation of the crankshaft in

15 : 3 .

SEA

- LEVEL

built lighter for

is

cylinders

SUPERCHARGERS

such as that

shown

in Fig .

15 : 6 ,

are

supercharged

percharger

only

.

horsepower

into the

"Scroll"

Diffuservanes Air -fuel mixture tomanifolds

Geardrive

(Powerfromshaft engine ) "Scroll "orcollector

gases for compressed

Cutaway view of gear -driven centrifugal supercharger .

15 : 6 .

but

70

about 300 horsepower

Fig

be

admitted to the cylinders .

Rotatorvane and impeller

The supercharger would add ,

air

Fuel injector nozzle

su

about 700 horsepower .

about 370 horsepower would require about

the

usually

can

flowing

blower , or " supercharger , "

it is

before

deliver

might

a rotary

of

engine

Fuelline from carburetor

15 : 7 .

Such an engine without

if

power

Carburetor Air inlet

engine

in Fig .

shown

airplane

An

by means

The relationship between indicated and brake horse power for a typical sea

level

.

a given delivered

compressed

15-7

POWER PLANTS

AERONAUTICAL

to run

it ,

resulting in

with only a slight increase

in

a net gain of

weight

(necessitated

by the requirement for designing the engine to withstand the extra stresses and higher

signed

resulting from

temperatures

for use

on

the higher pressures ) .

land and water vehicles

less important , rarely

,

in

which weight

which is

ButnotALLof thispoweris available for "outside work" ..... Some ofitisused toovercome friction engine within the . -andsome ofitisrequired to things pumps , drive such asfuel oilpumpsmagnetos . on -endasexplained , some poge ofit 18 isused torunthe SUPERCHARGER

BRAKE HORSEPOWER

ical

15 : 7 .

Engines

is what'sleft for drivingthepropeller

1150 H P.

minus

15.0 H.P ●quals

1000 H.P

Relationship

horsepower Motors Corporation . ) 1000

de

considerably

use sea - level superchargers or " ground boosting . "

INDICATED HORSEPOWER power developed means within thecylinders

Fig .

is

between indicated and brake horsepower sea -level - supercharged engine . (Courtesy

for

typ

General

Without supercharger , or with a sea - level supercharger , the indicated

is

horsepower which

the

density of the air in flying and hence drops off markedly with increasing

approximately proportional

engine

is

to the

altitude . Since the friction and blower power does not drop off in pro portion to the air density , the reduction in power with altitude is accen tuated .

For an airplane

engine

in

which the

friction

torque

Qf

is

13

per

15-8

TECHNICAL AERODYNAMICS

)

15

15

)

2

is

and

a

)

: 8,

a

a

.

4 .

,

as shown

various

,

-

been used

altitude Fig in 15

power with

Note

: 9 .

7

have

ENGINES

SUPERCHARGED

In order to avoid excessive loss of

.

of blowers

arrangements

uni

shown

.

: 8 .

.

engine

also

:

15

variation of torque with altitude for sea level Typical

15

is

which

.5

with

resulting in uniform scale of altitude of

.

-

)

(

.6

plotted a,

(

)

non

Uniform scale

.8

.9

.

.

,

is

form scale σ

like

15

altitude relations for

-

many power

: 1

15

Fig

,

(

0/00

Equation

1.0

is available Fig

to the contrary

.5

in

that superchargers may operate in either one or two stages and either gear driven or driven by an exhaust turbine sometimes with inter cooler between stages or an after cooler after the second stage

Fig

.

in

Such

the

right

is

-

,

.

.

page

(

15:10

considered independent

in the left

given

hand graph

involving

in Fig

shown

hand graph and

al

ratings

Several sea level

"

performance

15:10

ratings

is

limitations of both manifold pressure

read from the chart are shown

in

Table

15

.

.

and rpm

-

.

are shown

such engines

"

level titude performance in Sea

A useful

the intake manifold

and manifold pressure are

rpm

,

)

variables

for

in

: 1

graph of performance

in which

power

can be set by The constant rpm

predetermined

.

to

.

governor

-

of

15-10

,

form

a

operate at any throttle then determines the pressure of

means

level

sea

.

are

of 30,000

-

Such engines

superchargers

on the

altitudes ft or more ordinarily used with propellers that

up to

can be maintained

.

-

,

-

-

With suitable pressure regulators

-

.

:

9

15

may be

an

represented

assumed to represent the

unless information

engines

Fig

15

loss of power with altitude at given rpm e.g. in NACA TN 579

.6

.4

is

in Fig

graphically commonly

.8

0.13

: 8 ,

Equation

-

:

-

ft

-

(

.9

1.130

(

Qalt

Non uniform scale

variation

the

given by

)

1000

.

.

is

.

Alt

Std

is typical ) ,

( which

Q

20

15

10

5

1.0

torque

with altitude

torque

: 2

full - throttle

of

(

sea - level brake

cent of the

altitude chart is plotted on the following basis at constant rpm very nearly proportional horsepower and full throttle the brake is to the density ratio which is the uniform scale abscissa of the right hand chart ).

hence non uniform

-

(

altitude scale is

Accordingly

,

,

-

:

The

lines of constant

rpm

AERONAUTICAL POWER PLANTS

15-9

SUPERCHARGER TYPE 1ALTITUDE SINGLE STAGE WITH ONLY ONE SPEED ho Below 1000 High gear Air 4000 feet Carburetor Throttle ratio engine engine Critical altitude Sea level has Power from advantage TYPE I Manifold She Latitude Fuel mixture Versuspressure engine TYPE feet &000 Above toengine SEA Type Supercharger provides LEVEL Isubstantial Control Supercharger gain Altitude output 2 ALTITUDE SUPERCHARGER hp inpower TYPE 500 ; TWO engine SINGLE ,MECHANICAL STAGE SPEED CLUTCH Two -speed drive Sea dutch mechanical AirThrottle level Carburetor engine engine from Power Manifold pressure mixture Fuel Sea control Supercharger level toengine 10,000 20,000 30,000 infeet Altitude above sea level SUPERCHARGER TYPE, 3 ALTITUDE SINGLE STAGE WITH VARIABLE SPEED CLUTCH speed Variable hydraulic Carburetor AirThrottle clutch 1000 ho engine -Power from CriticalTYPE 4 Manifold Type Caltitude mixture Wet Fuel 3 TYPE Versuspressure 4 atas good 3 control Superchargertoengine TYPE lower as stage TYPE 4 No.3Auxiliary but altitudes inoperation TYPE 4 SUPERCHARGER bethrottled must TWO STAGE WITH MECHANICAL CLUTCH hp 500 Mechanical clutch Air engine Power from Auxiliary stage Supercharger toengine Micure Carburetor Engine stage supercharger 10,000 20,000 30.000 ALTITUDE Altitude infeet above sea level TYPE 6 SUPERCHARGER ,VARIABLE AFTERCOOLER WITH SPEED STAGE TWO speed Variable Critical jaltitude clutch (hydraulic hp 1000 Air auxiliary stage Since TYPE engine Power from 7 Auxiliary byexhaust , stage isdriven supercharger to Mixture the total increase in engine power gain Engine isanet stage Carburetor Aftercooler supercharger hp ALTITUDE 500 TYPE 7 SUPERCHARGER ,WITH TYPE7 EXHAUST DRIVEN INTERCOOLER TURBO byexhaust engine Versus Turbine -run from TYPE 6 driving Turbo unit runs Turbo Sea auxiliary stage supercharger regulator level engine from Power 10,000 20,000 30,000 Auxiliary Mixture toengine Altitude infeet above sea level stage Air Engine stage Intercooler Supercharger

-

Fig .

I

Types of supercharger arrangement and their effect on engine 15 : 9 . power at altitude . ( Courtesy General Motors Corporation . ) TABLE 15 : 1 .

Point

on S. L.

throttle

Take - off Max . continuous

2,100

36.5

1,800

34 26

on the

will

pres

rpm

Cruising

are plotted

Man .

Rating

chart

KB

SEA - LEVEL RATINGS

graph as

sure ,

1,900

straight .

in

Hg .

Point

Bhp

alt .

760

on

chart

L

675 430

For each altitude

give a determinable manifold pressure

;

and

therefore

rpm , ,

full

lines of

constant full - throttle manifold pressure may be drawn and these are the arcs sloping diagonally upward from left to right . The other diagonal lines XY , LE , VW , and CA are graphical constructions to determine various power

fold

throttle limitations at other altitudes with pressure

.

For a given

increases with altitude because of reduced

tion should

be a

function

a

given

rpm and

mani

rpm and manifold pressure , brake horsepower exhaust

of pressure ratio

,

pressure and

interpola

but the density ratio scale

2100 rpm 1100

&

TO 1.

.

.. , , .C +7 ,A B.A .T: ) °

on on

to

of Ts

by

hpat hp

Ts +

2. 3. 4. By

[

off-

Take

SR

000L

5000 4000

C

s $

horsepowerBrake

in

hp

pressuremanifoldRated

atD

%

10Ts

,.

airplane

0009

. .

1820F

53.

engine

000'11 0000

(

Wright

12,000 altitude

feet

13,000

supercharged

8000

Standard

14,000

,

No ram

2100rpm

performance

data

25,000 24,000 23,000 22,000 21,000 20,000 19,000 18,000 17,000 16,000 15,000

Typical

34

0 50

15:10

+42

-

Hg

Hg

S0006

Standard altitude temperature Ts

-11,300

Absolute manifold pressure

in

..

150

1800 1700 1600 1500

50

200

N

P

300

D 51

250

R Normal horsepower 2100rpm

33

350

H

400

450

G

.,

F °

temp altitudeStandard

Fig

pressureand temperaturestandard

600 HORSEPOWER VS 550 MANIFOLDPRESSURE at SEA LEVEL PERFORMANCE 500

. . 650

..

Absolutemanifold pressure in Hg

,

222

. Y 32

11

700

TECHNICAL

B.

C D 750

:1

850

WRIGHT AERO ENGINE NORMAL PERFORMANCE Engine SR 1820F Propeller gear ratio 6.40 Compressionratio 8.31 Blower gear ratio 11 Impellerdiam ins Carburetion Fuel Date 53

800

HORSEPOWERAND MANIFOLD PRESSUREALTITUDEPERFORMANCE

:: 1

900

950

1000

1050

.

FINDACTUALHP GIVENDATAFOR 2000 ALTITUDERPM MAN.PRESSCARB.AIR TEMP Locate fullthrottlealt.curve for givenrpmandman pressure 1900 Locate sealevelcurvefor rpm andtransfer andmanpress Connect and straightline 1800 andread givenaltitude Modify forvariation carb air temp fromstd.alttemp 1700 formula 460 Actual Hp.at DxV460 1600 correction Approx.1 for Full throttle each F.variation horsepower from 1500

15-10 AERODYNAMICS

.

)

POWER PLANTS

AERONAUTICAL

15-11

if

use is restricted to standard altitudes , for which P / Po definitely and p Po are related and if corrections are made for departures from standard temperature . A graph of standard temperature is given on

/

facilitate

the chart to

such corrections , which are noted on the chart to

a function of √Tsta /T .

is

in Table 15 : 2 .

shown

is

15 : 2 , which

PART - THROTTLE

TABLE

for

The procedure

OPERATING LIMITATIONS

S.L. ratings pres sure

Max . continuous 1,900 Cruising 1,800

34 26

AT ALTITUDE .

Alt . ratings ( full -throttle Man .

Man .

rpm

altitude interpolation

an extension of Table 15 : 1 .

(part- throttle ) Ratings

such

pres sure

Bhp

rpm

675

1,000 1,800

443

Alt

hp

22243

be

. ,

can be used

ft

Point E A

8,000 14,000

750 550

26

)

If

.

it

?

delivering Solution

Hg

,

a

.

Example the above engine is cruising at 2,050 rpm and 29.2 in manifold pressure at standard altitude of 11,300 ft what power is

shaft

chart

.

TUVW on

given horsepower to be supplied to

combustion

gas

turbine can be

built

a

a

.

For

internal

an

,

:

ler

.

.

TURBOPROPS

.5

15

See points

Read the answer as 650 hp

propel

for approxi

etic

energy

,

ler

this

is

though

is left

(

AB

,

.

,

shown

tend to either are provided

in the sketch of a in Fig 15:11

.

substantial

amount

of

kin

after the gases pass through the turbine wheels jet which augments the thrust of the propel discharged in propulsive power due to the jet is usually the additional over

a

and

,

through reduction gears the propeller

,

and

controls

they

which drives the compressor A

CD

)

turbine

(

and

a

BC

)

chamber

(

.

.

15:11

combustion

typical turboprop power plant are compressor The principal parts are a

Parts of Fig

with minor in unless complicated electronic

they

) ,

,

,

or stop

speed

a

"

"

run away

piston engines

unlike

changes

;

-

are not self regulating

.

have an inherent disadvantage in that

,

light

,

.

,

.

a

a

mately half the weight of piston engine and with small fraction of the currently number of moving parts Such turbines are under intensive de velopment by power plant manufacturers Such power plants while very

,

.

h -s

.

from

to

B ,

compressor

A

.

P

-v

.

less than 10 per cent of that supplied by the propeller The principle of operation of the turboprop power plant is shown in diagrams of Fig 15:12 the and which is labeled to correspond 15:11 Air is compressed approximately isentropically in the to Fig where

fuel is injected

and combustion

takes

place

TECHNICAL AERODYNAMICS

-Fuel line -Fuel pump

Jet

D

Propeller

JUL

hub

chamber

and Whitney T57 turboprop power plant on manufacturer's photographs

,

of Pratt

Sketch

based

°

t≈ 1500

F

.

.

.

15:11

Turbine

Combustion

Compressor

Fig

nozzle

HI

0

0

0

0 0 0 0

Reduction gears

.

15-12

Combustion

D

Intake Pressure

diagrams

for

gas turbine

power plant

.

and

h -s

-v

S

P

.

.

15:12

exh

and

V

Fig

Turbine

Combustion Pressure

.

B Compression

h

P

Turbine

Compressor

B

a

.

C

D ,

B

at approximately constant pressure between and C. The products of com bustion expand approximately isentropically in the turbine from to where they are discharged at nearly atmospheric pressure The efficiency cycle is limited by the maximum temperatures which are permis of such .

feasibility

of various turbine blade cooling

Efficient fuel air ratios are far

/

.

vices

now used

above the stoichometric

de

ideal

(

1500

temperatures

-

the

blade material and the

Maximum

limited by the hot strength of the turbine -

in

row of turbine blades

F,

are

first

region of

°

sible at the

POWER PLANTS

AERONAUTICAL

ratio

for

needed

all

burning of

complete

15-13

in

oxygen

air ) .

the

Since the

exhaust gases have a great surplus of oxygen , they may be "burned

again "

by feeding

called

fuel in

more

an " afterburner . "

a tremendous

behind

is

increase

in

is

This arrangement

the turbines .

Such combustion

very inefficient

It is

thrust of the jet .

result in

but can

seldom used with tur

on military turbojets for short bursts of high or for getting through the " sonic barrier . " turbine engines , given in Table A7 : 2 , show that ( except

boprops , but often used

for

speed ,

take

-off ,

Data on gas

for

small turboprop power plants being developed by Boeing ) the only United States turboprops now under development are the T56 by the Allison some

Division of

General

Corporation

Motors

Pratt

and the T34 and T57 of the

Aircraft

Typical 15:13

thrust

as under development

full - throttle is

in

England .

turboprop data are shown

a generalized

plot of shaft

in Figs

horsepower

. 15:13 and 15:14

( Shp )

.

gross jet

and

against rpm in terms of the rated values ( ) r , as analyzed by 15:14 is a similar plot of fuel and air flow rates . The

( Fg )

(1 ) Fig .

parameters

turbine

(rated at 5,500 and 15,000 shaft horsepower respec eight large turboprops are listed in recent aviation

At least

statistics

Durham .

Aircraft Division of United

Corporation

tively ) .

Fig .

at 3,750 shaft horsepower )

( rated

and Whitney

used

inlet

the analysis

in

by

Durham

(which

is

based on a

limiting

temperature ) are :

8t1 =

0 +1 =

Pti Tti

inlet total pressure standard sea - level pressure

(15 : 3 )

inlet total

( 15 : 4)

compressor

Po

= compressor

To

temperature

standard sea - level pressure

In

equation ( 15 : 3 ) the compressor inlet total pressure is to be calcu lated from the isentropic pressure rise ( designated by a prime ) and the

ram

efficiency

Пram

defined by Pt1 Пram =

/P - 1

(15 : 5)

/Pa · 1

Pt1

/

where Pt1 Pa = ( 1 + 0.2M² ) 3.5 as

( )a

total

denotes

ambient

temperature

condition .

is to be

( 1 ) Durham , Franklin P. 1951 .

given

In

calculated

" Aircraft

in

Chapter

equation

( 15 : 4 )

5 and

subscript

the compressor

assuming Tt1 / Ta-

Jet

the

Til / Ta-

inlet

1 + 0.2M² .

Powerplants , " Prentice - Hall , Inc.

15-14

TECHNICAL AERODYNAMICS

1.50

/

SHPr

1.0

SHP

1.00

10 t1

Pt1

8t1

.90

2.00

Pa

.80 HP

.70

,

Shaft

.60

1.40.8 1.2 =

ram

1.1

mph

0.8-

=

400

.50

1.50

,n ram

1.0

1.00

mph

-200

t

-1.2 1.11

Jet

-1.0

.30 .25 75

80

Fig .

15:13 .

Gross

Fg Fgr

Thrust

/

.40

811

/

( rpm /rpmr ) √0t1

85

90

.50 100

95

105

110

General plot of turboprop power and thrust data .

1.5

/

Wa War

/

St1 10t1 and

1.0

Pti t1 /Pa

/

.9

we Wfr

.8

St110t1

1.4

.7

1.2 1.0

.6

Air Fuel

1.2

/

rpm rpmr

14

60

Durham

90

flow data

)(

General plot of turboprop fuel and air 15:13 and 15:14 replotted from Durham

, F. P. , op .

110

100

.

igs

.

(1 ) .

15:14 .

(F

Fig .

Vet1 80

70

cit . ,

p . 81 .

)

.3

1

.4

.

1.0

/

.5

AERONAUTICAL POWER PLANTS

The use of Fig . 15:13 for calculating boprops

is

best illustrated

off- rated

by the following

15-15

items of tur

performance

example taken from Durham's

work . Example . Given a turboprop power plant , whose performance is given 1513 , which has a sea - level rated shaft horsepower and jet thrust of Shpr 3,000 and Fgr = 1,000 lb at rpmr = 9,000 . The rated air flow = = 0.6 lbm sec ( air fuel 50 lbm sec and the rated fuel flow war ratio = 83.3 lb air 1bm fuel ) . Find the shaft horsepower , gross thrust , and fuel and air flow rates , at 35,000 standard altitude at an air speed of 400 mph and at 8,500 rpm , the ram efficiency is 85 per cent . Solution . In Appendix 3 , at an altitude of 35,000 , read the am

by Fig .

/

is

/

fr

/

ft

if

ft

bient conditions Pa

= 498

lb/ft ?

Ta

= 394 °R

To get total pressure and temperature

Ma

Fig .

and from

/

Pt1

/Pa

and calculate

/

Tt1

0t1

Tt1 /Ta

=

(1

=

0.2

x

0.602

= 1.072

+ 0.2M2 ) 3.5 = 1.275

ram = 0.85

10.85

x 0.275

= 1.234

394 = 422 °R

x

= 422 =

0.815

15:13 ,

as calculated

/

519 rpm

t1 = Voti

Pti

rpm

1

rpmr

10 t1 Noti

=

8,500

=

8 +1

1

lb/ft2

498 = 615

=

615

2,116

= 0.290

=

1.05

9.000 V0.815 V0.815 rpm

Shp Shpr = 1.50

/

x

ratio is then

for the above corrected above , read

Fg Fgr t1

= 1.234

0.905

8t1 Vet1

the

calculate

= 0.60

1 + 0.2M2 = 1 + = 1

= 1.072

The corrected

From

inlet ,

at compressor

= 400/665

665 mph

next

and

In Fig .

=

from

,

Pt1 Pa

Calculate

=

aa

A4 : 1 read

Tt1 Ta and

/

1.60

given values of Shpr , Fgr , Wfr , above , calculate

ratio

for

and

/

wf wer

/

Pt1 Pa

= 1.234

= 1.20

8t√t1

/

Wa War

8+ 10+1 and war and

=

1.05

the values of 8t1

and 0 t1 calculated

Shp = 3,000 x 1.50 x 0.290 x 0.905 = 1,180 hp

TECHNICAL AERODYNAMICS

15-16

lb thrust

Fg

= 1,000

x 1.60 x 0.290

= 464

wf

= 0.60

x 1.20 x 0.290

= 0.209

x

50

wa =

/ 0.905

1.05 x 0.390

=

/

lbm sec

16.8 lbm/ sec

are the answers called for . Application of the above data to and airplane is considered later .

These

a

propeller

is

While the foregoing analysis

general , and valid for altitude as well

as sea - level performance , some modification

is

power plant control

inlet

desirable

to have the

re

sults directly applicable to flight performance of turbine - powered air planes at altitude , as pointed out by Domasch . (1 ) The usual turboprop system involves

a turbine

(semi -automatic ) .

( automatic ) and an rpm control

limitation effects of altitude

temperature The

inlet temperature are shown in the British turboprop calculations plotted in Figs . 15:15 and 15:16 . Note on performance at constant rpm and turbine

as 8

.7

for variation

.6

)

power

.4

400 -200 200

δ = p Po 8

.4 .5 .3 Fig 15:16 British calculations 81.5 of Fig 15:15 plotted vs.

.4 .5 .3 British calculations on .6

Fig . 15:15 . Bristol Theseus turboprop performance 1944 .

From " Aviation , " December

.8 .7

.

450mph

cessive shock losses at the blade tips

it is

,

ex the

jet alone

diagram

.

a

4,

Flight Test

Manual Courtland Perkins Performance of Turbojet Airplane

"

Agard

Chap

.

0.

Daniel

Editor Vol

I

,

turbojet

.

General

)

(

Typical

Dommasch

)

1

.

15:17

for

"

and some design data

have

economical to eliminate

where propellers

A flow means of typical axial flow turbojet are shown in Fig thrust and fuel consumption data are shown in

and propel the airplane by

,

propeller

a

.

: 6 .

TURBOJETS

,

For speeds beyond

15

.6

/

.7

.

.8

/

8 01.5 λ

.

1.0

1

.3 1.0

8

/

ft

mph

SHP O

.5

/0.8

1000

SHP

1000

.

HP

Std .

40

30

Alt . ,

.

Shaft

(jet

7

mph

1.5 .

,

Shaft HP

/

D.

2000

SHP

.9 .8

graphs

1500

ft

1000

Necessary slope of

8

20

. "

Alt

10

.

Std . 2500

.,

oe or

to

30 1 .

, " (

3000

proportional

400

20 T

10

Shp

200

that these calculations show

POWER PLANTS

FundamentalData GE TG-180

EXHAUST SYSTEM

--

,

15:17 .

(

-

Flow diagram for design data for General Electric ( Courtesy " Aviation Week , " July 7 , 1947. )

TG 180

turbojet .

24

20

20

Thrust

,

24

. )

)

)

(

Fig .

-

(

TG- 180 Turbojet

Schematic Flow Diagram of GE

(

)-

-

(

AND ACCESSORIES GEAR DRIVE ACCESSORY

.

. )( (

Maximumdia. 36% in. length 166in. Maximum Weight ) -2,380 (includingall accessories lb. (av.) ; 2,450lb. (guaranteed max .) military rat (15 min. takeoffand Thrust ing)-4,125 ; 3,750 lb. (av.) lb. (guar anteedmin.) 7,700 Rpm takeoffand military deg F. max Exhaustgastemp 1,250 rating -3,420 lb. Trust max continuous av. Sfc. lb./hr./lb. thrust) -1.026 av. cruise) Fuel Gasoline ANF28 or Kerosene ANF34 Lubricant 3606 hydraulic fluid or 1065 engineoil .

IGNITOR PLUG SYSTEM COMBUSTION FUIL HOZZLE

15-17

( )

AERONAUTICAL

lb

/

100

16

Thrust

10,000

12.0

8

1.5

4

1.0

0

Fig . 15:18 . level , Jumo

800

600

TSFC

lb

Fig

400

mph

800

600

Thrust at altitude with 15:19 Jumo 004B turbo TSFC as parameter jet at 8700 rpm .

,

.

Thrust and TSFC at sea 004B turbojet at 8700

rpm .

True Airspeed 200

,

mph

400

40,000

,

True Airspeed ,

30,000

.

TSFC

200

-

1.5

TSFC

20,000

lb

8

ft

1.9

, /

12

1.7

/100

lb

1.6

Thrust ,

the

which

in

.

shown

is

the

by 15

One

-

.

two values of rpm need be considered

be a

for calculating the sea Usually only ratio is the rated rpm for full throttle

maybe used

function of rpm and pressure

.

15

: 5

.

in Art

to

.

e2

Fig 15:21 that found factor at constant rpm and turbine inlet temperature

)

VeVa

in

as given

is

net thrust

two

Fig

: 6

-

level gross thrust as

a

The methods outlined

is

(

ram drag

in

.Vj

-

= where Fg Wa V .. Note the net thrust parameter

inlet

15:21

"

in Fig

temperature

"

and turbine

Fg

minus the

ratio on gross jet the thrust ef

.

,

15:20

Fn

"

"

gross thrust

plotted

which duplicates

-

The thrust

rpm and ram pressure

altitude effect studied separately for

The

"

.

15:21

.

.

fect shown in Fig 15:13 turbojets at constant rpm

.

shown

in Fig

.

are

effects of

The

"

15:18 and 15:19

.

.

Figs

jet thrust

is

12

hr

16

TECHNICAL AERODYNAMICS

15-18

1.8 1.5

/

Fg Fgr

8t1 1.0

.9 .8

Pt1

Pa

.7

1.4

1.27 1.0

.6

.5

/

.4

rpm rpmy

I

Vet1

.3

60

80

70

90

90

Fig .

100

15:20 . Effect of rpm and ram pressure ratio on turbojet gross thrust (General Electric Co. ) . Note that both 8 and 8 must be varied for tude performance , and that turbine inlet temperature is proportional to 0 .

alti

1.0 1.0K

.8 .7 .6

.9f

•.5 5

0/0

.8

.25

4

- 8/02

I

.7

x = G.E. - 16 + = Jumo 004 B

.6

/

Fn Fno

.5 .4

X

.3 Std .

.25 0

Fig .

15:21 .

10

20

Alt

. 1,000

30

Effect of altitude

of two turbojets inlet temperature

at

.

ft 40

on net thrust constant rpm and turbine (SAE Journal , Sept. 1946. )

AERONAUTICAL POWER PLANTS

15-19

operation and the other is a reduced rpm of about 80 or 85 per cent of rated rpm for cruising . Also , only two values of ram efficiency are com monly involved

in

is

and 100 per cent

installations in aircraft . A value between 95 usually reasonable for nacelle or " pod " installations

turbojet

-

value of between inlets at the side of a fuselage

as on the

for

B 52 ; a

- layer

selage boundary

Fig .

is

reduced

ature at altitude

.

inlet

with

temperature

preferable

and for

in

cent

is

is usually

which a substantial

assumed

amount

of fu

For altitude effects ,

if it

is desired to assume that the turbine inlet in proportion to the reduction in absolute temper

The more reasonable assumption

this

given by Fig . 15:21

,

diminishes the ram recovery .

15:20 may be used

temperature

80 and 85 per

altitude

Inlet cowling

constant turbine

is

,

reasonable .

more

(

of

giving better altitude performance

the variation of net thrust with altitude

purpose

-Supersonic spike Diffuser cone )

,

Subsonic diffuser Flameholder

Fuel injection manifold

Exit

Fuel inlet

nozzle

line

Total head probe

Combustion chamber

Inner body rear cone

-air- turbine -driven fuel pump

Fuel control

Fig .

15:22 .

15 : 7 .

ramjet

ical

is

Ram

Cutaway sketch

(Courtesy

RAMJETS . A cutaway shown

in Fig .

15:22 .

of typical supersonic ramjet Marquardt Aircraft Co. )

power plant .

sketch showing typical parts of a supersonic Ramjets will also operate subsonic , a typ

subsonic ramjet having been

in Fig .

shown

is

subsonic speeds the ram pressure ratio ciency , as noted in Fig . 15 : 2 . With a fixed inlet configuration

15 : 1d , but even at high

such as to give very poor

the shock

wave

from the

effi

conical

nose

is

" captured " by the inlet cowling with good efficiency only at a partic ular design Mach number , as indicated in Fig . 15:23 . With a variable

position inlet

cone , as shown

in Fig .

tained over a wide range of

Mach

iable , satisfactory control

can

15:24 , good

numbers .

also

be

efficiency

can be

ob

With the outlet area also var obtained to provide a thrust to

TECHNICAL AERODYNAMICS

or airplane

match the missile Capture area

steady

level

at any desired

within

the

Mach number

Designcondition

c .

Swallowedshock

-

for useful configurations

,

(

security

classified

.

15:24 are those of an example worked out by

of course

,

(2 )

and are

)

)

1

in Fig

The values given ham

1955

) (

(

.

From Durham

ap

pear to be at the present time

.

,

.

.

Fig 15:23 Effect of off design condi tions on inlet flow for supersonic ramjet

Numerical

values of thrust coefficients

not typical of the best

Dur

of current practice

but are judged to be feasible and usable for preliminary

design studies

.

b .

a .

ramjet and vehicle Spillover

flight

limitations of the .

Capture area

Capture area

for

drag

.

15-20

1234 .

EXIT AREA FIXED AT MAX IMUM PRACTICAL VALUE

NORMAL

COEFFICIE ENT

1

1

SHOCK

Fn =

.

-

yob

.

/

FUEL GASOLINE STOICHIOMETRIC FUEL AIR RATIO

INFINITELY VARIABLE INLET

1.0

THRUST

THRUST

SUPER

CRITICAL

MAXIMUM SUBCRITICAL

NET

1

TYPICAL

£ 0.5

1.0

AIRPLANE

1.5

0.5 FIXED INLET AREAS DRAG

CHARACTERISTICS

2.5

2.0

3.0

.

FLIGHT MACH NO

280-284

266

.

.p

cit

. ,

.

,

op

.

,

Ibid

pp

.

(2 .)

,

Durham

P.

F.

).

(

1

(

)

)

( 2

.

)

,

.

15:24

(

.

inlet

.

Effect of inlet geometry on ramjet with infinitely variable Courtesy Marquardt Aircraft Co. Bulletin MP 520. Typical nu merical values of thrust coefficients added from Durham Fig

POWER PLANTS

AERONAUTICAL

15 : 8 .

differ

Rockets

ROCKETS .

all

from

Gas

other power plants pre

viously considered in this chapter that they carry along their

oxidizer

Fuel

in

dependently of the surrounding

at

mosphere or beyond the earth's

at

Gas

Fuel

typical liquid propel lant rocket systemis shown in Fig . 15:25 and a typical rocket combus tion chamber in Fig . 15:26 . Typi shown

Table

page

15 : 3 ,

-

Valve

exhaust

are

Rocket motor

15-22 .

as a function

of the are shown in Fig .

liquid

propellant

for

system

rocket

From

Dur

Injection plate

15:27 , page 15-22 . feed Propellant

Typical fuel

Fig 15:25

area ratios

.

pressure and

pump

Valve

ideal thrust coefficients ob

tainable from rockets

Oxidizer

Turbine

.

The

in

Shaft turbine

pump

mosphere . A

combinations

Oxidizer tank

tank

own

and hence can operate

cal propellant

generator

. (

in

15-21

Throat

Ab

Combustion chamber

.

)

2

,

"

.

a

The

specific thrust

/

1

: 3 .

. ,

Ibid

.p

( 2 ).

290

cit

. ,

.op

,

( 1 )

Durham

reactors are

288

-

,

of quantitative F.

the publishing

on

using uranium

security classified basis that prohibits technical data but some non classified .

under development

plants

Power

.p

.

PROPULSION

a

NUCLEAR

,

: 9 .

15

currently

P.

some

tremendous rate

in the form of in lbs for lbm sec

often stated

obtainable

.

.

for

rocket

of fuel and oxidizer specific optimum Values of thrust for mixture ratios are given of the fuel combinations in Table 15

meaning the thrust consumed

is

rocket at

"

consumption

in

consumed

a

rate of fuel

are

a

(

Fuel and oxidizer

liquid propellant

(

)

combustion chamber for From Durham

Typical

.

15:26

.

.

Fig

Nozzle

TECHNICAL AERODYNAMICS

gasoline

)

hydrazone hydrogen

242 255 239 243 238 255 259 335

Red - fuming

aniline

220

White-fuming

furfural alcohol

214

Hydrogen

hydrazine ethanol

methane

ethanol

,

%

25

%

75 ethanol methanol

Oxygen

water

ammonia

nitric

)

/

lb in.2

2

)

300

(

and Pp about

/

Fuel

Oxidizer

/(

Specific thrust lb lbm sec with optimum mixture ratio ,

.

1

BIPROPELLANT COMBINATIONS

LIQUID

: 3

TABLE 15

(

15-22

ethanol

acid

nitric acid

peroxide

methanol 2.0 200 Ptb Po

1000

*

A

Pb

/

Fn

=

CT

1.8

500

,

333

200

1.6

100 50

33.3

Thrust coefficientCT

1.4

20.0 10 Lineof maximum thrustcoefficient 5.0

LO

+3.5

/

08

2.5 2.0 30

/

.

From

)

y

=

,

306

101.

Wiley

,

Elements

.p

Propulsion

, "

Rocket

100

.

p .

. ,

cit "

.

op

P.

,

)

,

George

.

J.,

F.

Sutton

,

Durham

F.

( )1,

(2 .

1949

80

60

1.2 Ideal thrust coefficient for rockets with Jour Franklin Institute October 1940.

,

Malina

P.

15:27

.

.

Fig

40

(

TO Arearatio

A

8

0.6

AERONAUTICAL

POWER PLANTS

15-23

published which are worth discussing here to show the

studies

have been

sort of

development

is

that

being given

consideration .

A hypothetical

airplane driven by uranium - powered turbojets , as studied for Life Maga zine by physicist Lyle Borst and aeronautical engineer Frederick Teichmann of New York University and presented in Life Magazine for February 7 , 1955 ,

is

shown

in Fig .

15:28 .

Possible details of the

power plant considered

helf klep

Fig .

15:28 . Hypothetical nuclear - powered turbojet - propelled supersonic long - range bomber . ( Reproduced with permission of artist Rolf Klep and Life -Time , Inc. , from Life Magazine of February 7 , 1955. ) for such an airplane are shown in Fig . 15:29 , page 15-24 . While the power

plant goes

is

into

feasible by its designers , the article in Life Magazine detail as to the extensive precautions which would be neces

judged some

sary for servicing this type of power plant and the limitations of crews due to radiation absorption in spite of the elaborate and heavy radiation shielding . was the judgment of the designers that crews for the

It

plane might safely

make

only a few long - range

flights

air

per lifetime

,

so

that while the power supply might last practically indefinitely the useful range of the airplane would be limited by radiation absorption by the crews .

15-24

TECHNICAL AERODYNAMICS

TAIL ET ENGINE CUTAWAY

JET ENGIN VARIABLE EXHAUSTCONE

COMPRESSOR TURBINE SUPERHEATED COMPRESSED AIR STEAMBOILER

CONTROLRODS

TURBINESHAFT HEATEXCHANGER

LIQUIDMETAL PUMP

CCC

STEAM TURBINE

COP

AUTOMATIC UNCOUPLE

LIQUIDMETAL

TAT

COMPRESSED AIR

COMPRESSOR

REACTOR

URANIUM FUEL

POWERDRIVE FOR PLANE'S ELECTRICAL SYSTEM

LAYERSOF SHIELDING

AIR INTAKES

WING

Fig . 15:29 . Hypothetical nuclear turbojet power plant for supersonic long - range bomber . (Reproduced with permission of artist Rolf Klep and Life-Time , Inc. , from Life Magazine of February 7 , 1955. )

AERONAUTICAL

15-25

POWER PLANTS

PROBLEMS

15 : 1 . For the engine data given in Fig . 15 : 5 , read values from the graphs and calculate , ( a ) the full - throttle torque , ( b ) the fuel consump tion rate in lbs hr at 2,550 rpm, full throttle , and ( c ) the fuel con sumption rate in lbs hr at 1,550 rpm on propeller load . 15 : 2 . The engine shown in Fig . 15 : 5 is rated 75 hp at 2,550 rpm at sea level . Using equation ( 15 : 2 ) , find the power developed at 12,000 ft standard altitude at ( a ) 2,550 rpm and ( b ) 2,000 rpm . 15 : 3 . For the engine data in Fig . 15:10 , at 14,000 ft standard tude and 1,800 rpm , read Bhp = 550 with 26 in . Hg manifold pressure ( point A on the graph ) . For the same rpm and manifold pressure at sea level read Bhp = 430. Using the method of Art . 15 : 4 , ( a ) find the brake horsepower available at this rpm and manifold pressure at 8,000 ft standard altitude , and ( b ) find the brake horsepower available at this rpm and manifold pres sure at 8,000 ft pressure altitude and a temperature of -10 ° F . 15 : 4 . A turboprop is rated as follows : Shpr = 3.750 , Fgr = 500 , rpmr - 50 lbm/ sec . Find the Shp , Fg , wf , and = = 10,000 , wfr 0.56 1bm sec , war 9,000 rpm wa at . Using the turbojet data in Figs . 15:14 and 15:20 , ( a ) calculate 15 : 5 . Fn Fno for standard air altitudes of 10,000 ft , 20,000 ft , 30,000 ft , 40,000 ft , and 50,000 ft for constant rpm ( rpm /Ve variable ) ; ( b ) calcu late also turbine inlet temperature ( Tti ) if Ttio = 2,000 R. Assume a constant Mach number of 0.5 ; ( c ) calculate the thrust specific fuel con estimate the effect of keeping Tti constant as sumption ( TSFC ) ; ( g ) tude is changed . Using the ramjet data in Fig . 15:24 , (a ) calculate the net thrust 15 : 6 . of a ramjet of 24 in . burner diameter at M = 2 at 30,000 ft standard titude , assuming a capture area ( Fig . 15:23 ) corresponding to 18 in . ameter and a fuel air ratio of 0.06 ; ( b ) estimate the fuel consumption 925 . Using the rocket data in Table 15 : 3 and Fig . 15:27 , ( a ) esti 15 : 7 . mate the ideal thrust at sea level of a rocket which burns gasoline and oxygen at a combustion chamber pressure of 300 lb/ in.gage pressure with air area ratio Aj A** = 4 and a throat area of 7 sq in .; ( b ) estimate the 1,000 lbs of ( fuel + oxidizer ) with optimum mixture burning time for

/

/

alti

/

/

alti

al

/

/

ra

tio .

(1 )Durham, F. P. 1951.

Chapters

" Aircraft 4 and 5 .

( 2 ) Ibid . , Chapter

( 3 ) Ibid . , Chapter

12 .

13 .

Jet

Powerplants , "

Prentice

- Hall

,

Inc. ,

CHAPTER

16

AIRPLANE PROPELLERS

propeller , or British call it two or more rotating airfoil - shaped blades driven by a piston engine or turbine . A propeller blade element and the forces acting on it are shown in Fig . 16 : 1 . The lift 16 : 1 .

PROPELLER CONSTRUCTION

airscrew as the

and drag

AND GEOMETRY .

,

An airplane

usually consists of

forces on the blade element can also be analyzed into thrust and tangential force components dT and dF , dr respectively , as shown in Fig . 16 : 1 . The thrust force propels the airplane tangential

dD

known as the " effective pitch ' of the pro

and

Propeller blade el forces acting on .

it

is the

same at all radial sta effective pitch angle must therefore decrease in going radially out ward from the hub to the tip of the blade .

tions .

and

The

chord chord direction thrust wind Zero Geometric




25 20

(

is

fifth

calculation of the

).

The

AIRPLANE PROPELLERS

PROPELLER PROBLEM

16 : 5 .

the selection lems

is

and use

TYPES AND

16-18

A guide

METHODS OF SOLUTION .

to

of the proper equations for various types of prob 16 : 2 , which is illustrated by examples follow

provided in Table

ing the table . TABLE 16 : 2 .

OUTLINE OF PROCEDURE FOR SOLVING OF VARIOUS TYPES

Given

Problem type

1. Selection of diameter

2.

Thrust

power calcu

V, n, P, P

To

if

fixed- pitch )

V , n , P , P,

T , 1 , Thp

Thrust

lation , const .

v,

Q,

P, D,

B

T , Thp , 1 , n

torque .

4. Best cruis ing fuel con sumption .

Calc . Cg , equation or (16:38 ) .

2.

Read V nD and on " max " line , as in Fig . 16:18 .

3.

Calc

1. 2.

Calc . Cp , equation or ( 16:39 ) . Calc . V/ nD .

4.

Calc . Thp

3.

rpm .

3.

1.

D

lation , const .

power calcu

Procedure : Calc . calculate Read = read on chart

find

T, n , (also ẞ

D,

1. 2.

3.

V, C=

T,

p , D; n) ,

f (P ,

lb/ (hp ) ( hr )

n, P , n, best fuel lb mile

/

PROPELLER PROBLEMS

/

.

V/D ; T = TP.

D =

V/nD

( 16:25

)

in Fig . A7 : 9 . Bhp ; P = 550 = Bhp ; and T = np v . ,

Read

as

/

, equation ( 16:33 ) . Read CT CQ and V nD , as in Fig . 16:17.

Calc . Cos

/

Calc . T

/

=

CT& D са

V/D V nD

n =

/

4.

Calc . Thp = TV/ 550

1. 2.

3.

Calc . Pc , equation ( 16:37 ) . Assume several V / nD values . Read , as in Fig . A7 : 10 .

4.

Calc . P

5. 6. 7.

/

= TV n ; n =

Select best of

of

fuel .

V / nD

/

; n = TV P.

V /D

/

V nD or Fig.

Read C , Fig . 16:20 A7 : 2 . Calc . fuel lb / mile = PC / mph . ues

550

val

assumed minimum

for

to are typical only ; the most recent chart of the type specified should be used . Charts referred

( 16:32 )

available

TECHNICAL AERODYNAMICS

16-19

Example 1. Propeller - selection problem , Lockheed Lodestar airplane . in Tables 14 : 2 and 14 : 3 , Given the airplane power - required calculations the engine data in Fig . 15:10 , and the propeller data in Figs . A7 : 5 through A7 : 9 . Find the propeller diameter for maximum efficiency at a speed of 240 mph at 10,000 standard altitude and 2,100 constant rpm ; also find n , Thp , and T. Solution . Following the procedure outlined in Table 16 : 2 , calculate first Cs . In the specified engine data read Bhp = 780 per engine , and for this brake horsepower and the specified =rpm and altitude read in Fig . 21.3 ; and calculate 16:19 : σ 1/5 = 0.941 ; Bhp1 5 = 3.79 ; rpm² 5

ft

/

= 0.638

Cs

In Fig .

for this

A7 : 8 ,

24.5 degrees

/

/

x

3.79

240 x 0.941 = 1.79

x 21.3

value of Cs , read on the " maximum " line Bo.75R At the same Cs , read = 0.88 .

=

and V nD = 1.01 . D =

/

V n

/

V nD

= 240

x ( 88 / 2,100 ) 1.01

=

9.95

ft

Calculate also 0.88 x 780 = 687 per engine

Thp

and

T

= 687

x

375/240 = 1,073

lb

called for .

These are the answers

-

Example 2. Power available calculation , Lockheed Lodestar airplane . Given the airplane , engine , and propeller data in Example 1 , and assume that a propeller diameter of 10 ft 6 in . was selected on the basis of ad Find the full - throttle ditional considerations to those in Example 1. power available at 10,000 ft standard altitude 2,100 constant rpm , and airplane speeds ( mph ) of 291 , 233 , 175.5 , 145.5 . 116.4 , and 103.6 ( same speeds as in Table 14 : 2 ) . Solution . Following the procedure outlined in Table 16 : 2 , calculate first Cp (which applies to all airplane speeds , because P and n are known and V is not involved in the definition Cp = P / pn3D5 ) . A more useful form of equation ( 16:25 ) defining Cp for practical calculations is Cp =

Using

Bhp

= 780 ,

σ

= 0.738 ,

Cp =

Calculate

0.5

/

Bhp 1,000

/

( rpm/ 1,000

) 3 ( D 10

( 16:39 )

)5

rpm = 2,100 , and D = 10.5 , calculate

0.5

0.780

0.738 2.13 x 1.055

also = mph

= 0.045

88 = x 2,100 x 10.5

mph 251

list this value opposite each value of mph as in Table 16 : 3 below . For each V/ nD , with Cp = 0.045, read ẞ0.75R in Fig . A7 : 6 and ʼn in Fig . = 780 x 2 for two engines , giving the results A7 : 7 , and calculate Thp and

shown .

Table 16 : 3 gives the answers called

for in this

example .

16-20

AIRPLANE PROPELLERS

CALCULATION OF FULL - THROTTLE THRUST HORSEPOWER AVAILABLE FOR LOCKHEED LODESTAR AIRPLANE AT 10,000 FT ALTITUDE

TABLE 16 : 3 .

/

V nD

mph

1.16 0.93 0.70

291 233

175.5 145.5 116.4

Thp 1,360 1,340 1,280 1,230 1,120 1,060

0.87 0.86 0.82 0.79 0.72 0.68

260

22° 180 160

0.58 0.464 0.412

103.6

n

Bo.75R

150

14.50

Power - available calculation , Piper Cub airplane with Given a Piper Cub airplane for which

Example 3.

pitch propeller . W = 1,400

lb

ft

S = 180 sq

fixed

CD = 0.046 + 0.060 C12

powered by a Lycoming six - cylinder opposed - type engine rated 120 hp at 2,000 rpm and equipped with a fixed - pitch propeller of diameter D = 6.5 set at 0.75R = 180 of characteristics shown in Fig . 16:17 . Find the full - throttle power available at sea level at speeds ( mph ) of 120 , 100 , 80 , 70 , 60 , and 50. Calculate also the thrust at mph = 0 . Solution . Following the procedure outlined in Table 16 : 2 , calculate first CQs = V√√pD3 Q , equation ( 16:37 ) , using Po = 0.00238 = 1/420 , D3 = 6.53 = 275 , Q = 120 x ( 5,250 / 2,600 ) = 242 lb - ft , and V = mph x 1.467 .

ft

/

Cos

1.467 mph

=

V420 x

For each speed ( mph ) , calculate CQs

in Fig .

16:17 ,

for

Bo.75R

242/275

For each Cos and list as in Table 16 : 4 . Calculate 18 ° , read CT CQ and V nD .

/

/

=

/

/

= moh 13.1

/

/

T = ( Cr Cq ) ( Q D ) = ( Câ / Cq ) ( 242 6.5 ) = 37.2 ( GT CQ )

/

Thp = (T x mph ) 375 , and rpm = 60n =

giving the results shown TABLE 16 : 4 .

in

Cos

100

9.16 7.64

80 70 60

5.35 4.58

120

50

0

/

16 : 4 .

CALCULATION OF FULL - THROTTLE FOR 120

mph

Table

88 mph

6.5 (V nD)

6.11

3.82 0

Cr

CQ

6.3

6.9

7.45

7.9

8.15

8.5 9.8

HORSEPOWER

/

PIPER

V nD

T

0.74 0.65 0.57

234 257 277 294 303 316

0.51

0.45 0.38 0

364

=

13.5 mph V nD

/

THRUST HORSEPOWER CUB AIRPLANE

Thp

75.0 68.5 59.1 54.9 48.5 42.1 0

AVAILABLE

rpm

2,190 2.010 1,830 1,800 1,740 1,720

Indeterminate

TECHNICAL AERODYNAMICS

16-21

Since the values of rpm in Table 16 : 4 come out well under the rated is evident that the propeller is not properly selected or set ; proper diameter and setting could have been determined by the method the of Example 1 , the data in Fig . A7 : 12 being used . Example 4. Calculation of best cruising fuel economy for Lockheed Lodestar airplane . Given the same airplane , engine , and propeller data as in Example 2 , plus the specific fuel - consumption data in Fig . 16:20 . Find the engine rpm and brake horsepower for most economical cruising at 233 - mph true air speed at 10,000 ft standard altitude , and find the cor responding number of miles the airplane will go on 6 lb ≈ 1 gal ) of fuel .

2,600 ,

it

(

0.55

perbhp

,

0.50

500

hp

600

350 hp

hp hp

400 he 450

lb. BSFC

hp

hp 300 hp

hr

700

800

0.45

0.40

800

1400 1600 1200 Crankshaft rpm

1800

for

engine

2000

.

data in Fig

15:10

: 2

)

,

:

=

0.078

2

x

,

=

)

(

on the

, S

/4

X

π

=

/4

x

=

interpolation

551

86.5

cruising propeller chart in Fig

.

by

0.0243

.

line

(

с

=

,

2, .

=

про

Draw this A7 10

data

=

:

ft

consumption

Following the procedure outlined in Table 16 taking the value of CD Calculate Pe from equation 16:37 14 as CD 0.0243 for 200 mph at sea level or 233 mph at = 10.52 86.5 ft2 пD2 Then with Ad 551 ft2 2

Step from Table

10,000 and ne =

fuel

1. .

Solution

:

Assumed

-

16:20

.

.

Fig

.

,

1000

.

. -

,

/

V

,

C = .

.

=

=

)

V /

,

(

= .

/ C

/

.

: 2, =

/

/

V

/(

,

x

=

/

=

V

,

(

=

) V /

,

/ x

, = a

/ 6

(

$

).

/

,

6

: 3 .

/

7.

).

=

/

lb /

.

.

/D ) /(

V

,

:

.

,

(

V

V / =

C

.

6. - 5.

/

,

/

,

/n

n

3.

.

: 2

:

,

5

,

/

V

.

.

,

;

V /

a

,

a

V /

Step 2. As guide to the range of values of nD to assume for the specified trial calculation range to the right of the peak of propeller efficiency is suggested for high nD values will give lower values of rpm and Fig 16:20 shows that low rpm favors low fuel consumption Ac cordingly the range of values of nD from 1.4 to 2.2 is chosen for tab ulation as in Table 16 below for each value of nD assumed as out lined in Table 16 Step Read from Fig A7 10 e.g. at nD 1.4 read 0.889 Step 4. Using Thp = 854/2 = 427 per engine from Table 14 calcu = = late Bhp Thp for each nD e.g. at nD 1.4 Bhp 427 0.889 480 1,400 rpm For this condition 60 nD 88 233 10.5 1.4 Step Read in Fig 16:20 For the same nD as above read 0.495 lb hp hr Calculate fuel mile = Bhp mph Step For the same nD as above calculate fuel lb mile 480 0.495 233 1.02 per engine 2.04 lb mile for two engines Step Select the lowest fuel lb mile in Table 16 In this case the best rpm is 980 corresponding to Bhp = 500 per engine and giving 1.82 fuel consumption of 1.82 lb mile for the airplane gas mileage = 3.30 miles per lb gallon

AIRPLANE PROPELLERS TABLE 16 : 5 . LODESTAR

V /nD

CALCULATION OF BEST CRUISING FUEL ECONOMY FOR LOCKHEED AIRPLANE WHEN CRUISING AT 233 MPH TRUE AIR SPEED AT 10,000 FEET STANDARD ALTITUDE Bhp , 1 engine

η

1.4 1.6 1.8 2.0 2.2

0.870 0.855 0.815

500

CORRECTION

0.467 0.444

0.425 0.425

890

, 2 engines

2.04 1.94 1.87

0.495

1,400 1,220 1,080 980

523

fuel lb / mile

с

rpm

480 485 490

0.889

0.880

16 : 6 .

16-22

1.82 , optimum 1.91

Wind - tunnel

FOR PROPELLER CHARACTERISTICS .

FACTORS

cruising

tests on propellers are seldom available for the exact arrangement contem plated in a proposed new design . In making performance estimates it is accordingly necessary to use such test data as are available and make cor rections for conditions .

at

the difference

principal

The

1.

Number

items

for which corrections

are

are :

made

of blades .

2.

Blade width and planform .

3.

Blade thickness

4.

Blade

5.

Body interference

6.

Tip

airfoil

ratio .

section

.

between propeller

(compressibility

speed

the blade tips )

and nacelle

correction

due

or fuselage

to high Mach

.

number

.

Each of these items has an appreciable

the

and the proposed

between the test conditions

optimum diameter , on

,

the efficiency

though sometimes minor ,

for

, and

effect

on

fixed - pitch propellers

on the blade angle necessary

(a ) tests

Number

to absorb a given power at a given rpm . of Blades . The results of a large number of NACA

have been summarized by Weick

is usually desirable propellers . " This

(1 )

as follows : "Two -blade propellers are used in all ordinary cases , for the fewer the blades the lighter , cheaper , simpler , and more efficient will be the propeller ; and two is the smallest number of blades with which proper balance of mass and air forces can be obtained . ..· Vibrations are however set up in two - bladed propellers when the air plane is turning , due to the varying gyroscopic moment of the two bladed arrangement and , when the airplane is sideslipping , due to the uneven air loading . . . . Vibration difficulties considered , it on propellers

statement

is still

to have three or

good

develop a one - bladed propeller ( 1 )Weick

,

F. E.

" Aircraft

in ,

It

1955 .

using

more

may

blades

in

have inspired

large geared attempts

a blade - stump counterweight

Propeller

Design , " McGraw

- Hill ,

for

to

mass

1929 , p. 252 .

TECHNICAL AERODYNAMICS

16-23

a rubber -mounted

balance and

pivot to permit the centrifugal couple to balance the

air

forces and give

of pitch . usually This is not considered satisfactory , for the simultaneous adjustment development

drag of the blade - stump balance more than offsets the gain in

ef

ficiency blades

.

due to reduced number Moreover , as

designs have developed

forward speeds and slower

tive

speeds , the

ofblades

of

airplane to larger

effect of

rota number

on efficiency has become

small to negligible and while three -blade designs predominate

simplicity and smooth Fig . 16:21 . Eight -blade counter - rotating because of propeller . ( General Motors " Aeromatic . " ) ness , many careful studies have yielded four , five , six , and even ten blades as optimum design . An eight blade "counter -rotating " design , with four blades rotating in each

is

rection ,

shown

in Fig .

when a large amount

of

16:21 .

is

Counter- rotating

di

designs are often used

installed in a small airplane to eliminate in efficiency due to inter sets of blades rotating in parallel planes a small

power

the " torque reaction . "

While there are losses

ference between the two

distance apart , there are compensating gains due to elimination of the energy of slipstream rotation ; in general , counter - rotating designs will

efficiency as high as , or higher than the best single -plane propellers . Test data on counter - rotating designs of four , six , and eight blades

have

are given on pages A7-13 through A7-16

tractor

A7-17 and

plane and cedure

they

, and composite design charts for propellers of two to eight blades are given on pages A7-18 . Special test data on each number of blades , both single counter - rotating , appear to be necessary because a general pro

and pusher

for

will

different

correcting be

the results of tests on one number of blades so that

applicable

number

to

of blades ,

calculations not available .

performance

is

on

a

propeller of

(b )

Blade Width and Planform . The effects on power absorption of blade width , and blade -width distribution along the radius , are usual

ly

properly accounted

and calculated

for in

in Art .

16 : 1 .

terms The

of

the activity factor , as defined

effects of activity factor

on maximum

AIRPLANE PROPELLERS

propulsive efficiency

recent 70 =

Fig .

gible loss of efficiency . In fact , the highest efficiencies thus far reported

(c ) Blade is usually

Thickness Ratio taken as a

blade thickness ratio ports tests on

16:22

1

.

8

n

/bh n

per cent

thickness on maximum propulsive efficien cy is shown in Fig . 16:23 , the efficiency being used as

thick propeller

0.97

Airfoil

blade

Fig .

Section .

0.6

0.4 0.94 0.070.080.090.10 0.11 0.120.13 at 0.75

Fig

high values of Jm the effect of thickness on maximum propulsive Blade

0.8

20.96 0.95

16:23 shows that at (d )

1.0 Jm

= 0.98

.

a reference value .

1.00 0.99

/

cent

propeller

the

h b

of a 7.5 per

thickness ratio

measure of

re

effect of blade

The

max

The blade - section

typical single

NACA TR 1126

per cent , though values around are more typical .

.

Effect of A.F.

on

blades as thin as 5

some

80 90 100 110 120 100,000 16 ffx³dx

=

Fig

0.075

at 0.75R

70

between 150 and 200 per blade .

range

max

factor

cent are the activity

.

in

with very thin blades

0.96 60

93 per

of about

1126 )

0.97

AF

maxat

( NACA TR

Jm 2.0 1.0 0.6 0.4

12100 9004

negli

FAF

with

1.00

at 0.99 0.98

16:22 that relatively wide blades can be used under these conditions

1.01

b

evident from

(

is

J

.

it

and

more

are

as

R

2.5 or 3.0

In

Jm may be as high as

.

shown

as a parameter .

propeller designs ,

of V/ nD , designated

which the design value

in

16:22 ,

Recent

16:23

.

is

in Fig .

(1 )

as studied by Thomas , Caldwell , and Rhines ,

max Пmax AF

shown

16-24

on

efficiency

Effect of max

is

/

h b

very small .

designs of propellers with

air

high efficiency at high tip speeds have favored low - drag , high - speed foil sections , such as those shown in Fig . 16 : 7 . For conditions where

tip is

not operating near sonic velocity tion has been proved relatively unimportant . This

the blade

at the usual Reynolds

numbers

,

the blade

is

airfoil sec

presumably

for propeller blade - tip operation

because ,

, the

bound

is mostly turbulent with service leading - edge roughness . Re gardless of the airfoil section , for a given thickness ratio , the maximum

ary layer

propulsive

No systematic correction

it is

best to use data

tip

about the same

for

available the effects of blade section

data are not

at low

all good airfoil sections . factors for blade airfoil sections are available ; based on the proper airfoil section , but if such

efficiencies are

may be

safely neglected

speeds .

( 1 ) Thomas

,

Caldwell

,

and Rhines , JRAS , January 1938 , pp . 1-86 .

TECHNICAL AERODYNAMICS

16-25

(e)

This is partly because the propulsive efficiency , as defined , includes

Diehlp.334

stream . Most propeller data are obtained with a propeller mounted in front of a na celle ; often the nacelle is mounted on a wing . A propulsive efficiency correction

0.90

D B

0.85 0.1 0.2 0.3 0.4 0.5 0.6 0.7 = Body diameter Propellerdiameter

max Speed

critical

plot of maximum propulsive particular configuration number for

for cruising

speeds

-

propellers operate at speeds beyond the high speed of the airplane some even oper

Many

flight

.

.

efficiency against helical tip Mach shown in Fig 16:25 These tests involved

is

thin blade section oper angle of attack Maximum ,

.

a

relative low lift coefficient and efficiency corrections to other thicknesses and angles of attack

ating at

in

,

ate at super

given

;

the level

is

A

critical for

body interference

.

Tip

.

)

(f

n

/D B

factor due to Fig . 16:24 .

Effect of

.

.

16:24 on

slip

the effect of the drag added by the

Tractor

0.95

a

= 1.00 D

Fo

in front propulsive

on the

efficiency .

1.06

Fig

effect

adverse

a

/B

has serious

or fuselage

-

max 0.42 maxfor

of or behind the propeller

η

A large nacelle

Body Interference .

as

re

31HARM

(

( 3 )

062

-045

)

10-

NACA

efficiency

,

Maximum

.8

.6

stream Mach number

-

Air

!

-

Air

stream

Mach

)

number

08 -045

3 )(

(

NACA 10-

,

.8

.7

.6

.

.

Fig 16:25

for

Effect of tip

Leading edge

.9 Mach

1.0

1.1

NACA

1.3

1.2

number on maximum propulsive efficiency reported in NACA TN 2881

the particular configuration

.

H4T

Helical tip Mach number

M

………………………… ++++++

.2

Rhines ,

and

16-26

are

in

shown

Figs

16:26

.

Caldwell

Thomas ,

)

ported by

(1

AIRPLANE PROPELLERS

and

16:27 . 140

.

Yor

sections

.

EHTS= HTS Fcxfhx fa 1.20

fa 1.10

Fig

0.75R

deg

of

.

16:27 Effect of angle attack on limiting Mt.

AND VERTICAL

TAKE OFF AIRPLANES

.

:

: 7 .

SLOW VENICLES

Bo.75R

-

Effect of thickness limiting Mt.

STATIC THRUST

16

=

α

.

16:26 on

1.5

.

.

Fig

1.0 at 0.75

.

0

/

h b

0.5

10

5

1.00

R

LOOL

,

speed

High

15

tipsections

-

Clark

1.10

1.30

RAF

6

fn 1.20

tip

130

propeller at zero forward speed called the particular importance in the calculation of the static thrust is of airplane take off of an and is basic factor in the design of verti

power coefficient increases

a "

.

= 0,

nD

/

V

.

-

.

rotating

rapidly

the static thrust

wing

to the blade angle

of total

As would be expected

16:28

setting

;

in Fig

,

of the blade as

cient is nearly proportional

a

.

shown

three blade 5868-9 propeller .

are

227

a

=

activity factor

data on

stalled

.

of

,

static thrust

usually

is

greater than Bo.75R150 most the blade may be seen by inspection of Fig 16:13

as

For blade angles at

are seldom available

0

nD

=

at

/

Wind tunnel tests

V

,

static thrust considerations

consideration

,

.

,

V /

,

primarily

Typical

Air

5b

Since such propellers operate at very airplanes they may usually be designed compared nD with

small values of from

in Fig

for the propulsion of slow vehicles

used

sleds and bicycles

meaning

sometimes VTOL

such as that shown

" ) ,

-

"

vertical propellers are also occasionally such as boats

VTO

1 :

take off and landing

.

"

usually designated

,

airplane

off

-

take

(

cal

.

-

a

,

"

"

,

airplane

The thrust of an

from

coeffi

the corresponding

relationship

.

between static static thrust coefficient is found to be approxi mately parabolic as shown in Fig 16:29 More careful and more extensive hovering required helicopters power Chapter 17 studies of for show that usually 3/2 For the three blade pro better approximation The

)

-

.

cit

.

Rhines

.op

and

,

)

a

Caldwell

,

(

,

Thomas

)

1

(

CPS CTS

is

(

.

,

and

.

coefficient

power

more

TECHNICAL AERODYNAMICS

16-27

peller data in Fig .

16:28 ,

it is

seen

CPS

=

0.006

in Fig .

16:29 that the

static

power

by the equation

thrust coefficients are related

and

( Fig .

+ 3CT3

16:29

)

( 16:40 )

.16 .14 .12

.10

CTS

CTS

and CPS

.08 .06

.04

CPS .02

$0.75 R

0

-5 Fig . 16:28 .

0

20

10

Static thrust data on three - blade 5868-9 propeller of total activity factor = 227. NACA data .

Studies of power for

the static condition

of

other propellers

indicate

or zero thrust value of Cpg is a function of the total activity factor of the propeller , and accordingly the data in Fig . 16:28 generalized by writing in the form may be somewhat that the

minimum

If , mum

as

thrust

angle

in

may be

For a

it is

the design of a slow vehicle ,

for

a given

(16:41 )

= 0.006 (A.F.total/227 ) + 3CT3

CPS

amount

selected from the following

specified tip

Cps

maximum

InD

:

/

maximum

T

( 16:42 )

1,730 Bhp

/

propeller blade

considerations

speed , maximum T Bhp requires

стя For a specified rpm ,

desired to get the maxi

of horsepower , the proper

T Bhp requires

maximum

AIRPLANE PROPELLERS

/

CT3 2 205 13/2

/2

=

)

(

requires

BT Bhp

PDp1

CPS

/Bhp

T

maximum

maximum

16:44

720

)

diameter ,

16:43

Tn2

(

For a specified

T

P

5/2

R2

1/4

=

75/403

=

CPS

/

4

/

CT5

16-28

.151

Test Data approximation 2 3

+

+

/

CT

CP

/

of

3/2 CT

max =

CTS

/

5/4 CT CP = max

.

0.006

CP = max

.

.05

CPS

.

CPS

=

.10

:

Parabolic

2

→

104 CTS O

.

:

ample

/

.

16:30

/2

C3

In Fig ,

rpm

Bhp

/

Cp ,

,

speed

.

.

The known values

factors in the design

thrust for and

is

or diam

the optimum blade angle has a

or

(

read from Fig 16:28 from similar the propeller of desired activity fac

for

and number

of blades

).

blade section profile

of

,

blade thickness

When

Cpg and CTs can be used calculate the unknown This procedure is illustrated by the following ex to

tor

,

,

CPg and CT can been selected graph experimentally determined

design

tip

.

in the

,

specified

on whether .

assumed

depending

16:28

the design

the optimum blade angle for maximum

be

,

is

eter

degrees

,

3,5 or 7.5

about

16:28

in

T

"

.

are plotted against blade angle for the data of Fig note that for this propeller

maximum

CT5

.

static

/

desired to have

/4

.

also

Values

,Cp

it is

figure of merit

/

where

given power and diameter

called the

CT

,

sometimes

"

is

16:44

of helicopters

of

Equation

(

.

.

16:29

225

Parabolic approximation to static thrust data of Fig )

Fig

200

150

100

50

Cp a

0

TECHNICAL AERODYNAMICS

16-29

2.0

10

₹9.0

1.77

CTS

= 0.0775

CPS

= 0.024

( Specified

8

1.8 D)

1.6 5/4 CTS

7 6

3/2

10 CTS

CPS

5

3

CTS

CTS

= 0.0575

CPS

=

/1

514

0.016

( Specified

3.70

CTS

rpm

)

1.2

+ 1.0

CPS

0.045

CTS

=

CPS

= 0.012

0.8

(Specified

nD )

0.6

CPS

2

0.4

1

0

Fig .

1.4

CPS

0.2

B0.75 R -10 16:30 .

/

0

0

20

10

30

Thrust power ratios for optimum static thrust designs with various criteria , based on data in Fig . 16:28 .

Example . Given a bicycle , to be propelled by an air - cooled outboard motorboat engine rated 5 hp at 4,000 rpm, ( a ) for a direct drive at 4,000 rpm, find the maximum thrust and corresponding propeller diameter ; ( b ) for

diameter propeller with a belt drive of ratio to be determined , maximum thrust and the corresponding rpm ; ( c ) for drives at con stant tip speeds of 900 , 700 , 500 , and 300 ft/ sec , find the maximum thrust and corresponding diameter and rpm . Solution . (a ) For this propeller may be noted that CT5 4 Cp = 1.77 at Bo ..75R = 50 and Cp = 0.016 . For the example above , using Bhp 5 and = rpm = 4,000 , use Cp 0.016 to calculate the optimum diameter of a three blade propeller thus : a 24

in .

find the

//

it

Cp = 0.016 =

D = 10

0.0025 0.016 x 64

and , from equation ( 16:43

(0.5 x Bhp)/ 1,000 (rpm/ 1,000 ) 3(D/ 10 ) 5 D =

=

5/410 5/1410

),

10

3.33

=

/

2.5 1,000 x ( D/ 10 ) 5

64

= 3.00

ft

= 36

in .

AIRPLANE PROPELLERS

39

8.16

/ /

27

(

) x x x

= (

,

=

=

)

,

2

(π

πD

nD

)

(

rpm = 60

)

=

900

ND 3/2 = 1,000

3

πnD 100

)3

(

2,980

and

nD

that gives at sea level

Cp

/

=

54,500

107

of

=

рCp πnD

read CT = 0.045 5x 1,730 3.70 nD

50

300

64.0

550,3 Bhp

lb

)

45.7

3/2

/ /

(

.

T

,

==

700

35.6

ND

38.8

60

6,880

calculate

and

;

x

6,88012 x 24

the diameter from the definition

D =

32

16:30

500

900

or

1,000

=

=

/

/

D²

rpm

rpm

( c ) For CT CP max 3.70 and 0.75R and Cp = 0.012 . For the specified Bhp calculate 32,000 nD thus : πnD T

105

6.88

in Fig

ẞ0.75R

1,000

=

‫لوسو‬

0.0775

=

3/326

For the ex

at

2.5

(

/

=

0.00238

x

0.0775

=

) 3 ( D 10 ) 5

=

read CT

,

thrust Ts

( rpm/ 1,000

x

32

=

To calculate

Bhp 1,000

σ

250 0.024

rom

1,000

ft

/

0.5

= 0.024 = Cp =

for

132

lb.

(b) Note that Cr3 2 Cp max = 0.90 at ẞ0.75R = 7.50 . , use Cp = 0.024 ( read ample above , using Bhp = 5 and D = 2 7.50 ) to calculate the necessary rpm , thus :

Solve

0.221

=

2,750

x

1.77

=

) =

=

0.00238

√66.7

/

or Ts

5 x 550 x

= 1.77

In

x

/4 Po 1/4

/

= C5 Ts5 4 Cp

16-30

12.2

5.2

2.02

2.95

4.47

7.65

8,500

4,530

2,140

750

.

18.5

speed is limited by noise or by compressibility of limit on thrust and diameter is seen above

the effect of the

.

tip If choice

300

,

rpm

500

=

ft

700

=

D

) "

(

which gives

( b ).

a )

.

(

;

a

,

a

These answers permit wide choice of diameter and rpm based on conven ience but it should be noted that they do not give the maximum thrust for given diameter or rpm these items have been found in parts and These are the answers called for

16-31

TECHNICAL AERODYNAMICS

22 22 DETAIL - DESIGN CONSIDERATIONS .

16 : 8 .

structed of

dural

wood ,

or steel in the

,

manner

Brass tipping

of propeller blade construction

is

hollow steel construction 8

feet . Propeller

tion of

and

forces , as shown

carefully

be

tensile stresses

in Fig .

Curtiss Hollowsteel

(From Nelson . ) ( 1 )

.

usually lighter for propeller

hubs and blades must

bending

16:32 .

If

analyzed

set up by the thrust

Tilt

T

diameters over

for the combina and centrifugal

fails

the blade or hub

Centrifugalforces.

16:31 . The

Weld

Aeroproducts Hollowsteel

Solid Dural

Types

16:31 .

in Fig .

shown

Brazed. joints

Solid wood

Fig .

are usually con

Propellerblades

it is

,

thrown

In

out with

enormous

such

event , the unbalance

an

of the

blade usually

remaining

tears the airplane

energy .

engine

tilt

being

approximately 1/2 degree

.

The

this

out

of the

of disaster Fig . 16:32 . Forces acting on propeller has occurred on several occa blades . sions in experimental testing of airplanes . The centrifugal and thrust forces can be made to offset each other partly by having a small amount of forward tilt in the blade , as shown in Fig . 16:32 , the usual amount of ;

type

propeller in . at the tips for

deflection of

blades under load , which sometimes amounts to

2

or 3

the

gives an additional effective tilt maximum thrust that must be considered in making an accurate stress analysis . A system (1 ) Additional gy atic procedure for doing this is outlined by Nelson . large propellers under

,

stresses are added to the propeller blade

roscopic bending

plane has a rapid rate of pitch or yaw ; a procedure for

when

the

air

calculating the

stresses is also outlined by Nelson . A rotating propeller blade that is free to turn about the blade axis

gyroscopic bending

is

acted

on

zero pitch . 16:33 ,

in

by a powerful centrifugal couple tending to set the blade at The cause of the

which

spection of Fig

blade

the

equivalent of two .

weights

16:33

( 1 ) Nelson , Wilbur Inc. , 1944 .

Sons ,

is assumed to be represented by its dynamic displaced slightly from the blade axis .

In

shows

C.

centrifugal couple is illustrated in Fig .

that the centrifugal forces tend to

" Aircraft

Propeller Principles

,"

rotate

John Wiley

&

AIRPLANE PROPELLERS

its

the blade about

axis

own

in

as to reduce the pitch .

such a way

propellers the centrifugal couple

some

is

16-32

balanced

pair of

out by a

In

weights

located in a plane perpendicular to the mean plane of the blade , but in most controllable - pitch propellers this centrifugal couple represents sim

ply

load to be taken by the pitch - changing

an additional

pitch - changing be either

mechanism , which may

electrical

mechanical ,

or hydraulic

,

Bladeaxis

( as shown in previous

,

Shaftaxis Shaft axis

photographs ) must not only overcome

friction of

the

The

mechanism .

but also

must

trifugal

couple

the blade bearings

Fig . 16:33 . Sketch showing source of centrifugal couple tending to reduce pitch of controllable blades .

counteract the cen

pitch

the

when

Blade axis

is

being increased and the aerodynamic

couple

pitching

due to the

moment on

the blade , which usually acts in the same direction as the centrifugal couple . The efficiency of the pitch - changing mechanism is usually made somewhat

than 50 per cent

less

to

make

it irreversible

.

in pitch ( for

that do not have to be feathered or reversed

namic brakes ) a rate of pitch change of 5 or 6 degrees

For propellers use as

aerody

per second has been

found satisfactory , but rates of pitch change as high as 45 degrees per (2 ) to be necessary for quick feathering or second are reported by McCoy aerodynamic

braking by

sary to avoid

ing by

means

damage

means

in

of reverse pitch

case of engine

of reverse pitch

is

Quick feathering

.

failure in flight ;

is neces brak

aerodynamic

incorporated in most large propeller

signs because aerodynamic braking has been found to be considerably effective than braking by means of wheel brakes . On

airplanes

for the pellers be

pilot

with three or

it

propellers

to synchronize the propeller

This

is

usually accomplished

in the propeller - governing

propeller

governors

synchronization

by means of synchronous

made

speed

is

approached

to avoid hunting .

and

( 2 ) McCoy ,

, W.

C. , op .

H. M. ,

"

liquid

must

motors

propellers

in that

governor

they

.

in

speed as the

mechanism " dead - beat "

are also equipped

for spraying the blades with antifreeze

( 1 ) Nelson

the

makes the governing

Most propellers

operated

" anticipatory

lude an accelerometer element that decreases

iesired

of constant - rpm pro

governors

circuit for electrically are being

more

is practically impossible

manually ; therefore , some means of automatic

provided .

Most

more

de

with

slinger - rings

to minimize the detrimental

cit .

Jour . Aeronautical Sciences , July

1944 .

TECHNICAL AERODYNAMICS

16-33

effects of ice formation

Rubber de - icers , such

on the blades .

times have been used on the leading edges of wings

useful on the inboard portions of

some

propeller

, have

also

as

Some

been found

blades .

PROBLEMS

16 : 1 . Using equation ( 16 : 4 ) and the method outlined in Table 16 : 1 , calculate the activity factor for the 37-3647 propeller for which blade form data are given in Fig . A7 : 4 . 16 : 2 . Using equation ( 16:13 ) , calculate the slipstream velocity ratio of 90 per cent . Vs Vo necessary to get an ideal efficiency 16 : 3 . An airplane traveling at 500 mph is propelled by a jet that has a discharge velocity ( Vs - Vo ) of 1,000 ft/ sec . Using equation ( 16:13 ) ,

/

calculate

i·

/

A propeller operates at a disc loading T Ad = flying 200 mph in standard sea - level air . Using equation 16 : 4 .

late ni .

10

lb/ ft²

( 16:14 ) ,

16 : 5 . An Ercoupe airplane is to be powered by an engine 2,550 rpm . Using the design chart in Fig . A7 : 12 , select a

rated

while

calcu

75 hp

at

propeller diam at sea level , and

eter and blade angle for maximum efficiency at 120 mph find the propulsive efficiency at this speed . 16 : 6 . Assume that a two - blade propeller of diameter 6ft set at Bo.75R = 16 ° is selected for the Ercoupe airplane powered by the engine of char acteristics shown in Fig . 15 : 5 ( direct drive , no reduction gear ) and with the propeller characteristics shown in Fig . 16:17 . Assume the same air plane speeds as in problem 14 : 1 . calculate the maximum full -throttle thrust horsepower available for level flight at sea level and the engine rpm at each flight speed . Using Fig . 16:17 , calculate the static thrust ( V nD = 0 ) for the 16 : 7 . airplane - engine - propeller combination in problem 16 : 6 . 16 : 8 . Assume the Lockheed Constellation airplane to be powered by four engines of characteristics shown in Fig . A7 : 2 , with a propeller reduction gear ratio of 0.4375 . Assume the propeller characteristics shown in Figs .

/

A7 : 5 through A7 : 8 , and select a propeller diameter for maximum efficiency when delivering the maximum rated power ( 1,800 hp at 2,400 rpm ) at 10,000 standard altitude at a true air speed of 375 mph . Find also max . 16 : 9 . are selec Assume three - blade propellers of diameter D = 15 ted for the Lockheed Constellation airplane powered by the engine of char

ft

ft

acteristics given in Fig . A7 : 2 and with given in Fig . A7 : 5 through A7 : 8 . Assume

' problem

14 : 2 and

calculate

the

maximum

the

propeller of characteristics

the

same

airplane speeds as in thrust horsepower 10,000 ft altitude at

full -throttle

from four engines available for level flight at 2,400 rpm . 16:10 . For the Lockheed Constellation airplane with engines and pro pellers as in problem 16 : 5 and power - required calculations as in problem 14 : 2 , use the cruising - propeller chart in Fig . A7 : 10 and find the mini per mile for sea - level cruising at 250 mph . Find also mum fuel consumed the brake horsepower and rpm for most economical cruising . 16:11 . A four - blade hollow - steel propeller blade of 12 ft diameter weighs 65 lb and has a center of gravity 40 per cent of the radius from the shaft axis . is acted on by a centrifugal force of 150,000 lb and has a maximum centrifugal blade torque of 10,000 in . -lb . Using a blade friction -torque coefficient of 0.014 in . , pitch - changing - mechanism ciency of 50 per cent , and a rate of pitch change of 45 deg / sec , calculate the maximum power required to change the pitch .

It

effi

AIRPLANE PROPELLERS

16-34

Using the methods and data of Art . 16 : 7 , find the blade angle available from a 2 ft propeller of three blades driven at 2,200 hp gasoline engine . For an engine developing 1 hp driving at 2,200 rpm a three blade propeller at the static - thrust characteristics shown in Fig . 16:30 , find the maximum static thrust that can be developed and the corresponding propeller diameter and blade angle . 16:14 . For an engine developing 1 hp driving a three - blade propeller of the static thrust characteristics shown in Fig . 16:30 and a propeller diameter of 36 in . , find the maximum static thrust that can be developed and the corresponding rpm and blade angle . 16:15 . A sled used for servicing high - tension lines in the mountains is powered by a small airplane engine rated 75 hp at 2,550 rpm at sea level . The sled , carrying power plant , equipment , and two servicemen , weighs 800 lb. At 10,000 ft pressure altitude and a temperature of 0 ° F (σ = 0.77 ) , the engine develops 55 hp at 2,550 rpm . With this rpm specified , find the optimum blade angle and propeller diameter , using the three - blade - propeller data in Fig . 16:30 . Also , find the static thrust and the steepest grade climbable . 16:12 . and thrust rpm by a 1 16:13 .

CHAPTER

17

HELICOPTER PERFORMANCE ORMA

( 1)

is a vehicle of military become of considerable and commer cial importance with the satisfactory solution of the control problem . The invention of the helicopter is often attributed to Leonardo da Vinci 17 : 1 .

DEVELOPMENT

ancient lineage

( 1452-1519 )

,

HELICOPTER .

though he appears

,

several centuries

well in Fig .

OF THE

The

helicopter

only recently

(2 ) .

1 : 6 , pages

The helicopter

(3 )

the Chinese by

history of the helicopter

The more recent

handled by Gregory .

by

to have been anteceded

Several current

has been

types of helicopters are shown

1-6 and 1-7 . consists

essentially of

a body which encloses the pay

rotor or rotors which provide lift by action sim airplane propeller , and a control system . The dominant

load and power plant , a

ilar to type of

that of an

helicopter

has

become

that with a single main

lifting rotor

and

an anti - torque rotor in a vertical plane in the rear , as shown in Figs . 1 : 6a and 1 : 6e . The control system for a helicopter of this type consists of a controllable pitch anti - torque rotor for control about the vertical

axis ,

and a " cyclic pitch

about the other two axes .

pitch control

" for the rotor blades

control The

main

rotor blades for control

must also have a " collective

either vertical climb , hovering , or safe descent without power . The collective pitch control is very similar to that of a controllable pitch propeller . The cyclic pitch control changes the pitch " to permit

(1)Much of

the material on this chapter was presented by the author at the 23rd annual meeting of the Institute of the Aeronautical Sciences , 11 Jan. 24-27 , 1955 , as a paper entitled " Aerodynamic Design of Helicopters , which constituted an abstract of a Ph.D. dissertation of the same title at the University of Michigan . Microfilm copies of the original 95 - page dis sertation are obtainable from the Graduate School of the University of Michigan , at about 3 cents per page . The IAS supply of preprints of the paper was exhausted early in 1955. As of June 1955 no arrangements have been made for publication . , ( 2 )Magoun

,

Hill , 1931 , p . (3 ) cGregory ,

F. A. 8.

and

Eric

Hodgins .

"A

History

Colonel H. F. " Anything a Horse Helicopter , 11 Reynal and Hitchcock , N. Y. , 1944 . 17-1

of Aircraft Can

Do , The

, "

Mc Graw

Story of the

HELICOPTER PERFORMANCE

17-2

C Fore and aft

cyclic

Lateral cyclic

Collective

(a )

(b)

( Above ) Bell Two blade Mechanism .

( Right ) Sikorsky

Three -blade Mechanism .

Figure 2.

Pitch

Two Types

of

Control Mechanism .

Fig . 17 : 1 . Types of pitch - control mechanism . ( Courtesy Bell and Sikorsky advertising . )

TECHNICAL AERODYNAMICS

17-3

of each blade each time the rotor goes around , providing small pitch - angle The as the blade goes forward and large pitch -angle as the blade retreats . pitch control

mechanisms , which have made safe

helicopter flight possible

,

are complicated and expensive ; they are also heavy because they must be designed for fatigue limits much lower than yield stresses ; they are also troublesome because they introduce vibration problems . Common types of

pitch -control

in Fig . 17 : 1 . The principal com cyclic pitch mechanism . On small is due to the helicopters great control simplification is obtainable by substituting weight shifting for cyclic control , as shown in Fig . 17 : 2 , though only very mechanisms

are

sketched

plication of the control

inher

slow forward speeds are obtainable with this device because of the ent limitations of center - of - gravity from

lift

rolling of the

over sidewise as advancing

and

it

movement

moves

necessary to keep the machine

forward , due to the difference

in

retreating blades .

-

Fig .

Helicopter ( de Lackner , DH 4 ) without cyclic pitch - control , 17 : 2 . steered by shifting of the weight of the pilot . ( Courtesy " Aviation Week , " April 4 , 1955. ) The problem ment of

with which this chapter

simplified

methods

is chiefly

for calculation , rapidly

concerned and

is

a develop

accurately

,

of the

nearly level , flight performance of single - rotor helicopters It is found convenient to use such as those shown in Figs . 1 : 6a and 1 : 6e . the hovering performance as a point of reference .

level ,

and

17 : 2 . ment

LIMITATIONS

of helicopter

OF HELICOPTER

performance

is an

theoretical treat extension of airplane propeller theory THEORY .

The usual

HELICOPTER PERFORMANCE

and has been

well presented

by Stepniewski , (3)

17-4

by Gessow and Myers ,

(1 )

by

Dommasch ,

(2 )

and

of the theory are only very the resulting equations require empirical coeffi cients to be applicable with good accuracy to the helicopter performance but since the assumptions

fulfilled

approximately problem .

In helicopter based on

tip

propellers .

work

it is

customary

to

speed (Vt

= ПnD )

The usual

coefficients are

rather

CT

use torque and thrust

than forward speed

coefficients (V ) as used for

given by the equations

T

A

PAdVt

( 17 : 1 )

2

P

СО

( 17 : 2 )

PAdVt3 The momentum theory

in Fig .

16:10 ,

is

of propellers , involving the flow pattern shown to climbing helicopters ; and , in the

commonly applied

case of zero climb , to hovering helicopters , even though the airflow pat tern through a hovering helicopter , as typified by Fig . 17 : 3 , bears little

similarity to that of a climbing helicopter or an advancing propeller . On this basis it is shown in the references previously cited that CQ for a helicopter is proportional to C3 /2 .

Fig .

Streamlines of flow through a hovering rotor .

17 : 3 .

(Official

NACA

photograph . )

A careful integration of a blade element analysis

including

the effect of " inflow " at the disc , for uniform chord blades of optimum twist is shown by Gessow and Myers (4 ) to yield an expression for hovering torque coeffi

(1 0Gessow , Alfred and Garry C. Myers copter , " Macmillan , 1952 .

)

( 2 )Dommasch , Daniel 0. 11 namics , Pitman , 1953 .

I,

( 3 )Stepniewski , " Performance

."

W.

Z.

" Elements

Jr.

"Aerodynamics

of Propeller

" Introduction

Rotorcraft Publishing

( 4 ) Gessow , A. and G. C. Myers ,

,

Jr. ,

of the Heli

and Helicopter

Aerody 11

Aerodynamics , Vol . Committee , Morton , Pa . , 1950 .

to Helicopter op .

cit . ,

p . 83 .

TECHNICAL AERODYNAMICS

17-5 cient of the form Cq =

in

a

+

CT

+

/

c CT3 2

d

+

c²

(17 : 3)

which a , b , c , and d are constants for a particular rotor . The quantity

is the zero thrust torque coefficient usually designated by Coo The quantity b is usually a small negative quantity depending on the shape of a

the blade

profile

drag curve near the zero

and d are nearly the

same

for

all

lift

region .

helicopter rotors

The

quantities

and depend

chiefly

c on

the " tip loss , " or on the extent of the blade tip (Fig . 17 : 3 ) , on which there is upflow rather than downflow . For a simplified analysis of the

it

hovering performance of helicopters is desirable , convenient , and rea sonably accurate to replace equation ( 17 : 3) by either of the following two approximations

Cqk1

+

k₂C+2

(17 : 4 )

= k3

+

k₁G3 / 2

( 17 : 5 )

CQ

A

of the accuracy of

comparison

the basis of

rotor test

all

tower

these

two approximations , as judged

the full - scale hovering test data available (Fig . 17 : 4 )

is

in Fig .

shown

C3/2 is

mation involving

within

on the NACA

Note that the

17 : 5 .

on

approx

nearly always

a few per cent of the

test data .

The approximation involving CT2 is some times better at high values of CT , such as are often involved

but

Fig .

17 : 4 .

mounted on

tower .

of

Helicopter rotor NACA hovering test

is usually CT , more

in propeller tests ,

poorer at the

low values

typical of current helicopter

hovering condition has been used

.

in

The CT2 approximation

Chapter

16

in

handling

static thrust data on airplane propellers , and has also been used by the 1) author ( for a simplified helicopter design procedure . The C3 / 2 approx

will be used here in the interests of slightly for lightly loaded helicopters . imation

17 : 3 .

HOVERING

PERFORMANCE

ANALYSIS .

( 17 : 5 ) is the torque coefficient at zero theory (2 ) to be given by the equation

(1 )Wood,

K. D.

( 2 ) Gessow ,

" Airplane

Design , " Tenth

A. and G. C. Myers ,

Jr.

, op .

The quantity

lift

Co

Edition cit . , p .

and

improved

accuracy

in

equation

k3

is

indicated

( 1954 ) , Chapter 60 .

5.

by

55

Fig .

ce

/

te

.

.

50

17 : 5 .

,0

T

5

.076

2 11 12

090 Scele

5 59

-

T

Comparison

40

30

25

40 19 8 20 я10

( (

Scale .042 20

8758

105c 60

8

0

O

P

.

of approximations in

20 6

4

.038

ga

la

00

)G2 (

equations

15 2

Scale

30

20

9 to

4

)A

=

VLLE

5

Scale

.027

+++++

20

270.5

1050Q Scale 60 40 40

5.5

6.5

4.5

3.5

2.5

1.5

60 30

)A (

Scale

T

C)

1

( 40

Also

.σ6σ

teg 20

1000

GT

80

(

σ

2

1.5

Scale 2086 TN .027 .023

Scale 70

5

e =

x

)

=

Scale .038

2.5

(

.(

10000

3.5

)G (

4.5

.

)A)

=

A

30 10

Scale 1000CT

6 10

3/2

-

5.5 12

T

1000 .060 Scale

T

) (

4 3 3 7

x

(

A)

, .

(

.076

3

+

Scale

, 14

( (

4

20

( , .

5

10 Scale

? )

)

(

k₂

)

=

=

7

)

C

X

)

. 1698 .042

)

A

k₂

)

B

.

T.4

7

1000

k₂

te

.20 .15

■

16

co

/

18

of

3 *

46.5

105

2318 .027 2277 .038

3/2

0.5 -80 twist 1.0 0.5 .15 1.0 .12 1698 .060 T.0 0.5 Fabric not smooth 1.0 .20 11.5 X 2318 .076 8 ARRL5F25b Full scale tunnel test check points

Sym

,

x

20

K4

.20 5.5 -80 twist .15 .15 .12 Fabric not smooth .20 14 scale tunnel test check points

Helicopter tower test data fitted by family of straight 2.7 lines form CK3 1000GT with FE of Notes Ref TN 105kg 105

) (

2318 .027 2277 .038 1698 .042 1698 .060 2318 .076 ARR15F256 Full

22

k

T.A

Sym

Helicopter tower test data fitted by family of straight lines of form 105ca 3 1000GT with 1.15 FE of Ref TN Notes 105K1 105

HELICOPTER PERFORMANCE

17-6

YAAR

σ 19 819

۲۲ 89to

C

B

O

188-8

JIG

D

B

( 17 : 4 ) and ( 17 : 5 ) .

10

O

C

TECHNICAL AERODYNAMICS

17-7

#

K3

is

where σ

solidity defined

the

Cao

= Ocde

(17 : 6)

8

by

Bce

D =

( 17 : 7)

πR

in

which B

is

ce Equation ( 17 : 8 ) integrates

= 3

blade ce

is

f₂ cx²dx

is

ratio of the blade area to

the

weighted

( 17 : 8 )

thus ,

a blade of uniform chord c .

in

the case of a uniform chord

For

the disc area .

a

tapered blade

weighting each chord in proportion to square of and hence , for constant angle of attack , in proportion

rational

A more

.

mean

be CeQ comparison

which would involve torque

The quantity

·/·

in

purpose

would

( 17 : 9)

cx3dx

O

blade

on the

elements

is

thrust difference usually neglected .

is

Cde

effective chord for this

= 4

of

than equal

rather taper ratios , and

, but the

equation

is

basis of equal

small for the usual

effective minimum drag Studies of the relationship between

( 17 : 6 )

coefficient for the blade airfoil .

a mean

CQ and a show a range of values of Cde from 0.008 for rotors with 3 drag blades to 0.012 for rotors with 2 relatively high - drag blades .

to

1

low

( 1 ) to be indicated by theory The slopes of the curves plotted in Fig . 17 : 5 differ from

The quantity equal

,

mean chord ,

the local velocity , to the thrust

defined by

cc for

to give

The meaning of the term " solidity" ,

is

the number of blades and ce

in

k

/√2 .

equation

this theoretical value by

( 17 : 5 )

is

a factor of about 1.2 because of blade

tip losses

non - uniform downwash .

This factor is called kå and is the correction factor from ideal to actual hovering induced torque coefficient . and

and k in equation ( 17 : 5 ) as modified above with the definitions of thrust and torque coefficients for a helicopter given in equations ( 17 : 1 ) and ( 17 : 2 ) , permits writing an ex

Using the coefficients k3

and combining

pression for hovering rotor horsepower which

is

here called Ph

( 1 ) Gessow

=

Bhphr

/

W 1,000 , A.

per thousand

pounds gross weight ,

Ph , as = 1,000

550

Poocde V+3 + 1,000 8w

and G. C. Myers ,

550

Jr. ,

op .

cit . ,

Kn √w

1200

p . 30 .

( 17:10 )

HELICOPTER PERFORMANCE

17-8

where W Po

W =

(17:11 )

Ad P

The appearance of equation

simplified , and its plotting fa specific case of helicopters with three

( 17:10 )

cilitated , by restricting to low - drag blades , and writing still fairly general

can be

the

Vt / 100

Ph P₁

=

=

For this special case

v.

kg K5 Ov³

+

, which

is

(17:12 )

kg √w

where k5 = 4.32 for three low - drag blades ( 6.48 for two high - drag blades ) and k6 = 31.9 for the usual tip loss and downwash correction kn = 1.2 . Since equation ( 17:12 ) has too many variables for a simple network chart

,

it is

dividing by

considered desirable

30

to reduce

giving

/ /3

Ph = v3 15 To w 02 Equation

( 17:13 ) may be

abscissa

respectively

the

number

of variables

/ / /3

by

(17:13 )

+ x6 V

w 02

plotted as a network chart using as ordinate Ph

and

(17:14 )

Зго

/ /

= w 02 3 X =

and

this

maxima

has been done

in Fig .

17 : 6

may be shown

are characterized

ratio =

Th

where

It

17 : 6 .

and minima that the bottoms of the " valleys

speed curves power

in Fig .

(17:15 )

Phi

=

k√w

( 17:12 ) and Php tion (17:12 ) . Note that

-

Fig .

power per 1,000

and

is

/ is

of the constant of the hovering

( 17:16 )

= 2

Php power "

term

in equation

the " hovering profile power " term in

is , for

of

tip

by a value

the " hovering induced

k50v³ w k5 °v³ /w 17 : 6

Phi

"

by the calculus

a given

lbs of gross weight

solidity

, a

equa

plot of hovering horse

against disc loading

( corrected to sea

and that the " optimum line " of rh = 2 gives minimum power for a given diameter and tip speed , though it does not necessarily represent the best design . In fact , Fig . 17 : 6 is not very useful for design , as it pro

level )

vides no guidance for selection of

ity . It is

a

tip

speed , diameter , power , or

simply a chart which satisfies hovering requirements

.

solid To be

TECHNICAL AERODYNAMICS

17-9 400

300

"Optimus line" 3√0

200

N

Pap

const

Vt

250

-

1600 500 400 300

Vft /bec

150

100 90 80 6

5

Fig .

7

8

v12213 20

9 10

First draft of

17 : 6 .

useful , it must consider the special copter operates . 17 : 4 . may

be limited by

tips of the

itation ,

it is

Cb

cient "

stall

advancing

customary

To develop

to think

/

When

ition

is

in

defined by W B =

where W

speed

of the retreating

blades .

the gross weight

equation

( 17:17 )

is

CLb b

and

B

35 40

limitations

R

50

.

under which

, the speed

of

a

helicopter the

retreating blade stall

lim

the

lift coeffi

( pV2 / 2 ) cdr

the number

it

may be shown

CLb = 6CT / 0

(17:17)

of blades .

integrated and combined with the usual

of thrust coefficient CT ,

heli

a

blades orby shock waves on

terms of a " mean blade

[S*0 is

30

hovering power chart

In forward flight

LIMITATIONS .

SPEED

25

15

defin

that ( 17:18 )

17-10

HELICOPTER PERFORMANCE

It in

is

customary

terms

where V

to think of the speed of forward

of the ratio

is

a helicopter

of

movement

/

the forward speed

με V QR and R is the tip

(17:19 ) speed Vt .

Elementary

the

that with a given stalling angle of at degrees , , tack such as 12 or 16 an increase in forward speed requires a reduction in the blade lift coefficient to avoid stall of the retreating blade and that the reduction should be proportional to the square root of

oretical

considerations

indicate

the mean blade lift coefficient . Flight tests and wind tunnel tests on rotors show this to be the case , as shown in Fig . 17 : 7 , where the " rotor limit " data of Brown (1 ) (based on Bell Helicopter flight tests )

0.6

are

com

0.35

g

0.30

G

11/2

( Squared scale )

0.5 Equation :

α = ((d290

0.25

· 0 . V = 0.475-0.63μis =

)

16°

0.20

"Rotor Limit "

0.4

/

PL Gessow 0.3

0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07

0.2

0.06

0.3

0.05

0.4

0.2 -Equation :

Va )

(α 270=12°

9.2 = 0.425-0.63μLS

0.3 0.4

0.04 0.03 0.02 0.01

0.1

M15 0.1

Fig .

17 : 7 .

R

0.3

0.4

of retreating blade stall limitations . Solid lines and Myers . ( 2 ) " Rotor limit " line from Brown . ( 1 )

Summary

from Gessow

(1 ),

0.2

VIS

Brown , Eugene "Helicopter Performance and Aerodynamics , " craft Corp .. Helicopter Div . Document , 1954 . ( 2 ) Gessow , A. and G. C. Myers , Jr. , op . cit . , p . 266 .

Bell Air

TECHNICAL AERODYNAMICS

17-11

flight

pared with a summary of

(1 ) ,

test and wind tunnel test data presented by

in which the total drag / lift ratio P/ L is considered to be a minor parameter . Equations for the limiting speed ratio μLS in terms of CT o are given in Fig . 17 : 7 .

Gessow and Myers

/

flying at the speed of retreating blade stall , the advancing blades may be limited by shock waves at the tips . For a retreating blade stall limitation of When

mphLS

if

critical

the

tion

on

stall is

parameters

itations Two

speed due

(QR)LSC

Equations .

-

=

( 17:20 )

about 0.8

, the combined

limita

blade shock and retreating

-

( 840 to 900 )

( 17:21 )

1.467 mphLS

to Fig .

blade

since the

same

to provide a hovering power chart with speed Such a chart is Fig . 17 : 8 .

lim

( 17:20 )

( 17:21 ) can be added

and

are involved

17 : 6 ,

,

shown

in Fig .

17 : 8

relative to the One of these

of shock - free landing from a descent without power .

limitations is that of

a mean blade

corresponds approximately to CL Another limitation added speed of

involving

/ /o

√w

22

to advancing

additional limitations are also

problem

cal

0.50R

number of the tips is

Mach

rotor tip

=

gliding

unusual

the vertical

is

skill for

conditions of forward

a

that of approximately , which

30

is

ft / sec

descent

will

have been more

also includes scales for rotor diameter

minimum

verti

judged to be a region

a safe power - off landing .

gliding

flight

for

coefficient of about 1.4 , which typical helicopter blade section .

without power

descent

speed of

max

lift

The estimation

of

be discussed later after the carefully studied . Fig . 17 : 8

and hovering rotor horsepower

per

1,000 lbs of gross weight to facilitate performance calculations and de sign selections . The use of Fig . 17 : 8 is illustrated by the following example : Example . Given a helicopter rotor with a solidity of σ = 0.04 and a rotor diameter of 27 ft . The helicopter weighs 1,000 lbs and operates at a rotor tip speed of 600 ft / sec . Find the power required to hover at sea level out of ground effect ( at an altitude greater than 1 or 2 rotor dia meters ).

Solution . In Fig . 17 : 8 , for a sea level diameter of 27 ft and a solid of σ = 0.4 , read w /o2 / 3 = 15 ; at a tip speed of 600 ft / sec read on the horsepower scale for σ = 0.04 a value of Bhphr = 63. An engine of greater power than this would be required to provide also the usual tail -rotor Since these losses usu power , cooling losses , and gear friction losses . ally total 15%, a 75 hp engine would provide satisfactory hovering . Ad ditional information provided by this chart is , ( 1 ) that the advancing blades would not be shock - limited , since the upper shaded area is avoided ,

ity

( 1 )Gessow ,

A. and G.

C.

Myers ,

Jr. ,

op .

cit . ,

P. 266 .

HELICOPTER PERFORMANCE 30

-

0.04 0.0

30

350

25 2000 and

25

1

.

S

120

for

W

.. Dam

13015

17-12

σ

400

0.06

150 0.01

110 140 19

1000 and

18

17

16

-0.09

15

τσ

|

for W-

locating

.

20

Diam

σ

SL

.

35

.

130 110

1525

100

0.08 300

diameter

cal

20 90 100 110

250

Tip speed

80 90

1

ΩR

Advancing blade shock in at phys

100+

1

Zod

wm 108

106

200

165

phys

70

60

= 0.04 //////////

70

600

80+

σ

60 50

J

70

gliding

.

Approximate 30 ft./sec

=.04

descent

150

ph

Bat

-is -

55

65+

150

for σ

specified

3.09

60

MO 100

50

QR 35

40

45

)

(

Shock free landing not possible if Laax 14 =

phs

00

(

GLb1.4

400

55

-

50

10 )

‫ایک‬

σ

300

100 NIT

Lo

9

10

15

20

Hovering power chart with speed

25

30

limitations

35 .

17

: 8 .

Fig

8

8/02/3 7

specified

80

6

0

.

σ

/

W

0

.

σ

5

= 60

for

.04

BuPhr 1000

=

90

'

= 290

30

40

50

TECHNICAL AERODYNAMICS

17-13

and ( 2 ) that the forward speed would about 160 mph .

POWER REQUIRED FOR LEVEL FLIGHT .

17 : 5.

stall - limited until it

not be

The

rotor blade profile power is to increase the turn the rotor . While the velocity increase

effect of forward

torque on

reached

speed

on

and power required

to

the advancing

is

blade

the

as the decrease on the retreating blade , the forces vary as the square of the velocity and the net effect is an increase in the ratio

same

Pp Php

= 1 +

also a body drag which forward which the

it

flat

must

well

may

allow for rotor hub

to

( 17:22 )

(17:22 )

higher values than

though various authors have suggested

cient of μ² in equation

3μ²

be overcome by

additional

the

3 as

drag .

tilt

coeffi is

There

rotor

of the

Designating by

be considered at the same time .

f

plate area of unity drag coefficient equivalent to the body drag that

may be shown

f

Ppb = 1 + 3µ² + Rp = Php Cde Ao

43

,

( 17:23 )

effect of forward speed on induced power is quite the opposite of the effect on profile and body power , since the rotor acts on a much larger volume of air when a component of forward velocity is added to the inflow . The

The usual assumption would

flow

normal

through

to the

flight test

a

flight

data

is that the stream of air affected is the stream circle of diameter equal to the rotor diameter path .

show

it

curacy of this assumption

prising

if it power

is

Equations ( 17:23 and

to be of the

)

glance

order of On

and

=

Pi Phi

=

1 8μ

( 17:24 ) are

thrust coefficient respectively

power

in

-1

/

W =

ν

20 per

cent would not be

the basis of this assumption

ratio R₁ of induced given by the equation Ri

and

this seems optimistic , but substantially correct , though an inac

At

could be detected .

be shown that the induced

first

that

52μ

plotted

forward

flight

as parameters .

.

17 : 9

sur may

to hovering

(17:24 )

1,000 CT

in Fig

it

with drag

ratio

Since the variation of

each of the two components of hovering power with forward speed has been determined

and

plotted

in Fig .

17 : 9 ,

if

the ratio of these two

components

= when hovering is known ( e.g. , гh Phi / Php 2 ) a proper weighting of these plotting permits general factors a chart of power required for level flight .

This has been done in Fig . 17:10 for гh = 2. A similar chart for any other can be plotted from the equation

value of г

0

=

Fn

Right

+ 72 15

R

9

flight

of

required =

for =

/ Php

chart

profile flight

(

Phi

and

level

body

level

.

power

in

induced

+

ratio

0.1

)

helicopters

optimum

17:10

: . .

Fig

) ) ( .( . of

power with speed Above General

Drag

17

P7 0.3

-By

hi

0.1

0.2

1000CT

defo Cdokamra

3424

except where shownbroken

-

+

Fig

0.2

0.2

0.3

3.4

0.5

0.7

Rp

Variation

0.1

μ

1000 CT

High

0.5

гороха 1.0 0.9 0.8

3

0.6

4

0.7

5

0.8

,

1000 CT

- Ppb1 Php dray

Xbox

0.3

Ασ

f

0.9

.

=

1.0

2R

10

98 7 6

1.5

2.0

1

HELICOPTER PERFORMANCE 17-14

37.

.)2 =

rh

(

TECHNICAL AERODYNAMICS

where R

is

P

= Rp

rn

the ratio of power required

Ri

17:25

)

=

(

*

R

1 + +

17-15

rh

in

level

flight

to hovering power

. The use of Fig . 17:10 is illustrated by the following example : Example . Given the helicopter for which hovering calculations were made in Art . 17 : 4 . This helicopter has a body of " low drag " specified by the ratio f/ cdeAσ = 12.5 , and it flies at a thrust coefficient of CT = 0.02 . Find the minimum power necessary for level flight and the forward

required

speed at which the power is a minimum . Solution . In Fig . 17:10 , for " low drag " and 1,000 CT = 3 , read in Fig . Since 17:10 a minimum value of R* of 0.56 at an advance ratio µ = 0.14 . 63 hp was required for level flight , the minimum power for forward flight is 0.56 x 63 = 35 hp . Since the tip speed of the rotor was 600 ft sec and the value of u at minimum power was 0.14 , the forward speed of the copter under minimum power conditions is 0.14 x 600 = 84 sec = 57 mph .

/

17: 6 .

HIGH SPEED AND MAXIMUM CLIMB CHARTS .

ft/

If more

power

heli

is available

at the rotor than the minimum necessary to hover , the ratio of the avail able power to the hovering power may be plotted on Fig . 17:10 ( or similar may be read ( which chart for the appropriate value of г½ ) , and a value of is designated HL) . This is the ratio for the level high speed of the helicopter . A chart of this sort is plotted in Fig . 17:11 . For each of

a number of values of tip speed (Vt = R ) such as 500 , 600 and 700 scales of level high speed can be added to Fig . 17:11 as shown.

ft / sec ,

Level high speeds

in mph for R shownbelow ( IF NOT LIMITED BY VIBRATION) .60

=

12.5 1.50

t,/

cdeσ

150 200 190 180 170 160

170 160

150

130

110

140

120

100

130

11c

,

120

High

/

30

25 80

speed chart

2.0

for helicopters

15

2.5

designed

with

гh

2 .

level high

-

Sea

Pa ph

1.5

=

NR

& C

/

=

20

= BOOK

80

70

600

700 ↑ .

35

M

1.0 .

37.5

90-

= R

17:11

drag

000-

90

100

100

Fig

40

Looger

7

1405

110

drew

130

150

120

Low

140

HELICOPTER PERFORMANCE

A

sea - level rate of climb chart

maximum

for

17-16 any given

ratio of

avail

able to hovering power can be plotted in a similar manner , measuring the net available power from the bottoms of the " valleys " of the curve in Fig . 17:10 . This has been done in Fig . 17:12 . Since the climb ratio calculated

in this added

manner

for

is

Ch max / 33Ph , scales

of rate of climb in

This has been done

value of Ph .

= 40 , 60 , and 80 ;

values of Ph

tion

is

any specified

for

other values of Ph .

ft / min

in Fig .

can be

for linear interpola 17:12

satisfactory . MAX. CLIMB, FT./MIN . FOR VALUES OF Ph AT HEADOF COLUI .

·P

80

6000

values

2.5 -1000CT

1.5

-

4500r 3000

2.0

100077 5000

2500 3500+ 3000 2000

drag

2000 2000

High

Approx

1000 1000

.

.

1500-1000

climb

Low

1500

vertical

2500+ 3000

1.5

10000 drag

max

4000

1.0 Comax

0.5

500

sea

2.5

level rate of climb chart designed with rh =

Maximum

2.0

1.5

.

The use of Figs

level rate of climb of in Art

17

for

helicopters

the level high speed and

may be

illustrated

by con

: 4 .

example started

a

tinuing the

.

sea

-

maximum

17:11 and 17:12 to calculate

helicopter

3.0

2 .

17:12

.

.

Fig

1.0

-

0

0

500

helicopter

,

.

.

=

"

it

.

-

"

a

is

.

,

,

with

: 4

The

.

Example equipped

.

on which calculations were made in Art 17 125 hp engine of which 20 hp is used in the cooling blower tail rotor and gear losses so the net available horsepower per 1,000 lbs gross weight Pa 105 hp Assume the body of the helicopter may be and its rotor hub are exceptionally well streamlined so that classified as low drag helicopter Find the level high speed and maximum sea level rate of climb of this helicopter

is

TECHNICAL AERODYNAMICS

17-17

/

Solution . Calculate w = 1,000 x 13.521.75 ; v = 6 ; 1,000CT = 42w v2 x 1.75/ 36 = 2.04 . Calculate also Pa / Ph = 1.67 . In Fig . 17:11 above = 1.67 , read L = 0.41 and above QR = 600 read a level high speed Pa Ph of about 165 mph . Note , however , that the hovering power chart showed a retreating blade stall limit of 160 mph . The top speed would be , there fore , 160 mph at which point roughness would develop and the helicopter could not safely be flown at the level high speed corresponding to wide

= 42

/

throttle . In Fig . 17:12 , above Pa / Ph = 1.67 , interpolation between the two low drag lines given permits reading Ch max / 33 Ph = 1.1 . The maximum sea - level rate of climb for Ph - 60 is read as 2,100 ft / min ; at Ph = 80 read Ch = 2,900 ft / min . Interpolate linearly to the design value of Ph = 63 , and get Ch = 2,220 ft/ min . These are the answers called for . By calculating rate of climb at each of a number of altitudes , plot ting rate of climb against altitude , and reading the intercept where rate open

of climb equals

zero

solute and " service

ceilings are

"

forward

some practical value such as 100 ft / min , the ab ceilings of the helicopter can be determined . These flight ceilings ; they are substantially higher than

or

the hovering ceiling determined 17 : 7 .

AUTOROTATIVE DESCENT

equipped

with a " free- wheeling

tion

from the hovering chart OF HELICOPTERS .

minimum

rate

descent

the pilot

rotor

stops .

the engine

is

are

usually

and the

tail

rotor

will con

Rotation at a favorable speed for

greatly enhanced by prompt action on the part of

the engine

, when

Helicopters

device between the engine and the reduc

"

gear box , so that both the main

tinue to rotate after

.

stops ,

in setting the collective pitch

down

to

position . In most helicopters the " rate of stable auto windmill is not far from that of the design level flight

a good windmilling

rotation "

as a

, though

condition

flow conditions

flight . since

trol .

air

there may be a substantial difference because the windmilling are quite different from those of level

when

is

The condition of windmilling

all

the main rotor

Under windmilling

must

the middle of the blade radius

it

blade drives

is

drive the

lift

, and the

blade

a large

of

there

,

forward , overcoming

the inner third of the the presence

do

conditions

approximately that of zero torque ,

is .

If

the

minimum

, the rate of descent power required for level гh

of the " valleys

"

in Fig

.

17:10 )

rotor to maintain

stalled

Approximately

under these conditions ;

a handicap

to the

calculation of

the rate of stable autorotation

may

flight

be

flight

is supplied

con

force on this portion of the

be assumed to correspond to the design level

sign value of

tail

a high angle of attack near

the drag of the tips .

usually

stalled area is

the rate of stable autorotation

is

condition at the

can

de

calculated by assuming that corresponding ( to the bottoms

by gravity .

This assumption

HELICOPTER PERFORMANCE

is

admittedly poor

17:10

,

and

(approximately

imum rate of descent

the horizontal .

In

violates the conditions

level flight )

, because the

in

are usually

17-18

in

assumed

flight

the neighborhood

path angles at

of

a few cases , however , nearly correct

ues have been obtained by

this

method and the

deriving

results of

45 degrees

flight

these

Fig .

min with

test val

assumptions

800 700

QR, feet per second

600 500 400 v 300

60 50

/02/3.1

9 10

20

MinimumSinking Speed, feet per second

:/ Nort

40

041

10004

Lines

for

h=2

/

0.006 CT 0.004 CT 0.0015 S01e7

30

Lines

for

Drag gh Drag Yow Drag

20

h

=3

cois

HighDra Low

15

Glide test check points on Bell H- 13- B plotted x = Calculated = Flight Test

Drag Low 10

Drag High Drág Low

o

w, pounds per square foot

8

3

Fig .

‫ڈن‬ 4

5

6

7

8

Simplified approximate calculated min 17:13 . imum sinking speed of helicopters in autorotative descent at the autorotative speeds specified above . are therefore tionary words

presented

in

graphical form

" simplified approximate "

in Fig .

17:13 , with the precau

title . A analysis of this maneuver is sorely needed as a design cri as the providing of shock - free landing without power is considered in front of the figure

more adequate

terion , to be one of the principal sales advantages of helicopters compared with other forms of transportation . A rough check on the general validity of

TECHNICAL AERODYNAMICS

17-19

Fig .

rates calculated by this well established rate of vertical descent given by

17:13 may be made by comparing

method with the

fairly

the descent

the equation ( 17:26 )

Vy = 29 VW where Vy Note

is

clined glide descent

the vertical descent

in Fig .

is

speed

17:13 that the minimum found to be

in ft /sec . sinking speed for the optimum

between 40 and

60

in

per cent of the vertical

speed . PROBLEMS

17 : 1 . A helicopter weighs 2,000 lbs and has a rotor diameter of 34 The solidity is 0.0625 . The normal rated tip speed is 640 sec . Using Fig . 17 : 8 , calculate ( a ) the power required to hover out of ground effect at sea level ; ( b ) the retreating blade stall - limit speed ; and ( c ) the ratio of hovering induced power to hovering profile power . (d ) Will the advancing blades be shock - limited at the stall - limit speed ? 17 : 2 . Consider that the helicopter of problem 17 : 1 has a body drag corresponding to the " low drag " line in Fig . 17:10 ; calculate ( a ) the power required for level flight , and ( b ) the forward speed at minimum which the power is a minimum . 17 : 3 . The helicopter of problem 17 : 1 is driven by an engine rated 240 hp at sea level . Assuming 15% losses in gears , cooling blower , and tail rotor , use Figs . 17:11 and 17:12 to calculate ( a ) the level high speed at sea level , and ( b ) the maximum rate of climb at sea level . 17 : 4 . Calculate the rate of climb of the above helicopter at 10,000 standard altitude , assuming the engine power varies with altitude as specified by equation ( 15 : 1 ) . 17 : 5 . Using Fig . 17:13 , estimate ( a ) the minimum speed of vertical descent at sea level , and ( b ) the minimum speed of gliding descent at sea

ft/

feet .

r

ft

level .

CHAPTER

18

AIRPLANE PERFORMANCE

18 : 1 .

SPEED

CLIMB

AND

OF

PROPELLER - DRIVEN AIRPLANES .

in

such as have been presented

Chapters

From tabular

of power calculations power airplane flight required for level available from an en and of an gine propeller unit , it is customary to plot power required and available ,

speed and solve graphically

against

designated by the subscript

in

the manner outlined

( ) L,

for the

speed of

maximum

and the maximum rate

in Tables 14 : 2 and Figure Fig . 18 : 1 . in

requirements were calculated

available

are reproduced from the engine

titude the power - required

level flight

of climb (Ch

,

max )

below .

For a particular airplane , the Lockheed Lodestar 14:18 , and

14 and 16 ,

- propeller units in

as a parameter , as determined

level flight

14 : 3 and 18 : 1

power

plotted in Fig .

also shows the power

as a function of speed with

Chapter

power -available graphs

and

,

15.

The

any given

of

al

intersection of

maximum speed of level flight at that altitude . Fig = 250 at sea in . 18 : 1 , read mph 2500 level and 280 at 10,000 ft . For

resents the

altitude rep For example ,

full

Ch The rate

being given by

= 33,000

W

(18 : 1 )

500

alti

400 300 70 80 90100 125 150 Mph

a given

tude varies with the

airplane

speed

in the

in Fig .

18 : 2 ,

which

manner shown

also

maximum

climbing

shows

the

definitions of max and

best

Since Fig .

18 : 2

rate of climb Ch speed mph .

Max.X710hp at sealevel

700 600

X

of climb at

the

1000 900 800

18-1

Fig

200 250 300

18 Power required and available at sea level and 10,000 ft for Lockheed Lodestar airplane

.

ft /min

climb in equation

climb , the rate of

1 .

will

:

the airplane

ft

10000 level Sea 10,000

18 : 1 , and

.

in Fig .

as indicated

1500

-

for level

.

flight

over that required

,

available

2000

Horsepower

throttle flight at speeds lower than mph there is an excess horsepower X

TECHNICAL AFRODYNAMICS

18-2

is

15

$

a

max.

I

18

is

point

a measure of the angle of climb , and a line drawn through the origin tangent to the graph is the maximum angle of climb , as any

10

5

plot of vertical vs. horizontal speed , line drawn from the origin to the graph at a

Best climbing Max.angle speed ofclimb 100 200 Mph

shown

in Fig .

18

: 2.

Choice of the

Lodestar as an airplane 300

example

in this text

in

sonably appropriate

Fig .

18 : 2 . Rate of climb at sea level as a func tion of speed , for Lockheed Lodestar airplane .

availability in Fig .

for

is

an

Lockheed

illustrative

considered to be view of

its

rea

current

modified form , as shown

in

18 : 3 .

0 Leerste

Fig . 18 : 3 . Modified Lockheed Lodestar ( " Learstar " ) , distributed in 1955 by Lear , Inc. of Santa Monica , Calif . ( Courtesy Aero . Digest , March 1955. ) 18 : 2 .

formance

full - throttle per plotting the maximum Fig . 18 : 4 . For airplanes

CEILINGS OF PROPELLER - DRIVEN AIRPLANES .

of

an

airplane

is

commonly

The

summarized by

rate of climb Ch max vs. altitude , as shown in with gear -driven superchargers , the graph of Ch max vs. altitude is very nearly a straight line above the critical altitude ; for airplanes without superchargers , it is a straight line from sea level up . For any airplane

is

of climb is zero , ceiling airplane Since the rate and this is known as the absolute of the . of climb is zero , the absolute ceiling is attainable theoretically only in infinite time . A ceiling can be attained only if there is a positive small rate of climb ; it is customary to define the service ceiling as the there

always

altitude at

in

some

which the

altitude at

which the maximum rate

rate of climb

is

100

unfavorable weather or over mountainous

craft a true

in

maximum

terrain

and

commercial

flight

for military

100 ft /min rate of climb feasible operating altitude of

formation , this arbitrary

picture of the

ft /min . For

air

does not give the airplane ,

AIRPLANE PERFORMANCE

it is

and

ceiling

accordingly

for

customary

some

18-3

purposes to speak of an operating

higher rate of climb , usually set at ceilings 300 to 500 ft /min . These three are shown in Fig . 18 : 4 for the Lockheed Lodestar airplane . corresponding to a

35 30

somewhat

35

Absoluteceiling, 29,800 ft ft Serviceceiling, 28,200

30

25

ceiling ,26,000 Operating ft.

20

Critical Typical altitudeof climb variationwith engine unsupercharged engine (130hp CubCruiser )

h 100015 10

25 20 1000 15

5

2.4

6

8

/

10 12 14 16

0

Ch max 100

18 : 5 . Variation of stalling speed , best climbing speed , and level high speed with altitude for

Lodestar airplane . The speed

of

- shaped

is

and

it

and outside

in Fig .

shown

area of speed

Lodestar airplane

Figure

18 : 5 .

altitude within

fly .

.

its relation

of climb in

rate

maximum

and level high speeds

YAYL 50 100 150 200 250 300 V

Fig .

Fig . 18 : 4 . Graphical determin ation of ceilings for Lockheed

dome

LVC

10

5 0 0

Vs

to the stalling

18 : 5 shows a

which an airplane

typical can

fly

exists be

Such a dome - shaped

of which cannot area cause the stalling speed increases with altitude and , above the critical altitude of the engine , the level high speed decreases with altitude .

Below the critical altitude of the engine , there is seen to be an increase in level high speed with altitude , and this increase is usually represented by a straight line of slope such that the level high speed increases almost

alti

exactly

1 per cent for each 1,000 ft of altitude up to the critical This feature of the performance of supercharged airplanes is what made possible a new order of high - speed performance unattainable with un engine airplanes . supercharged For example , an airplane that will reach

tude .

a

level high

speed of 300 mph at sea

of nearly 400

mph

To determine and

h₂ ,

18 : 6 .

it is Since Ch

if

the

its

engine had a

time At required

level

critical altitude to climb between

convenient to replot Fig . max

= dh

At

/dt , it =

իշ

18 : 4

in the

high speed

of 33,000 two

form

ft .

altitudes hi shown in Fig .

follows that

Sh² at

ել

would have a level

dh =

իշ

Sh1

1 Ch max

dh

( 18 : 2 )

TECHNICAL AERODYNAMICS

18-4

If Ch

30

titude 20

arbitrary varia tion of rate of climb with altitude , the time for

10

/

Fig .

in

0.3

0.1 0.2 1000Ch max

termining time to climb between

altitudes

two

CL , as

tween CD and

in Art .

quired

-

Assuming a parabolic

the development

charts for

of general

power

from the engine

opofv3 + 550 Thp = 2

in

which may be put

Equation =

2 w2

( 18 : 3 )

поρ еb² (V)

the form

550 =

v3

840

840 (Thp / of )

π

W

1

eb

σThp / V

( 18 : 4 )

permits solving for the level high speed of the airplane

( 18 : 4 )

VL/ 1.467 in terms of the parameters

/1

and Lt

is called is called

( 18 : 4 )

has

where Lp

abscissa

plot

re

for level flight to -propeller unit , it may be

that

shown

mph

AIR relationship be

the power required

equating

available

in

may

Fig .

PERFORMANCE OF PROPELLER DRIVEN

PLANES .

14:10 , and

the thrust horsepower

general , for any

to climb between two altitudes

minutes

18 : 3 .

.

in

t ; in

be represented as an area , as shown 18 : 6 , and integrated graphically .

Plot for de

18 : 6 .

as

straight line can be substituted in equation ( 18 : 2 ) resulting in a logarithmic expression

Min time(minutes to climb from 10,000 ft.to20,000ff

1000

,

plots as a straight line vs. al in Fig . 18 : 4 , the equation for 8

max

,

( 18 : 5)

= W eb2

( 18 : 6 )

Lt

= w Thp

( 18 : 7 )

/ /

the " parasite loading , " Lg is called the " span loading , " (1) Equation horsepower loading " by Oswald .

the " thrust

been plotted and

↳p = W

Lg

LL /

in Fig .

18 : 7 with mph

o as parameter .

(2 ) suggested by Perkins and Hage .

for the level high

This

is

Fig .

speed of an airplane

in

as

18 : 7

terms

/

ordinate , Lp oLt as of the Oswald

a modification

permits a quick solution

of the

maximum horsepower

available without calculating the complete charts of power required and available , as in Art . 18 : 1 . The equation on which Fig . 18 : 7 is based ( 1 )Oswald

, W.

B.

Airplane Performance

(2)pe Perkins ,

C.

" General ."

Formulas

NACA TR 408 ,

D. and R. E.

Hage ,

and Charts

for the Calculation

1932 .

op .

cit . ,

p . 168 .

of

18-5

AIRPLANE PERFORMANCE

500

400 mphL

( Uncorr

for

.

compr . )

300 250

LsLt 200 100 -200

150 Lp

It

120 20

Fig .

40

30

propeller -driven airplanes , neglecting Level high speed of Prppell compressibility corrections . ( 1 ) See Fig . 18 : 8 for corrections .

tions

no compressibility

and

correcnecessary to take

it is

separate account

of the effect

high

on

Mach

the

mph .

number

This

if

fect

on wing drag

is

and

.

the major

500

critical

Mach

wing , additional

in Fig .

.18 -10

.12

Amph

O

ef

-10

com

35000

-20

AmphL

numbers than the

are involved

.

18

20000

-20

15

ft .

t/c=

0

-10

ft .

t/c =

,

, have

corrections to those

18 : 8

(1 ) ,Replotted

of

If other items

nacelles or cockpits

0

speed

the compressibility

pressibility effect

shown

400

of

can be done by the use

18 : 8

such as

level high

region between

Fig .

lower

1000

500

300

18 : 7 .

involves

in

200

100

50

Amphi

--- CL =0.2 -C₂ =0.4

SEA

0.18

LEVEL

Uncorr .

mph

from Oswald , W. B. -200 450 TR 408) as modified by Perkins , 500 C. D. and R. E. Hage , " Airplane Per- Fig . 18 : 8 . Effect of wing thickness formance , Stability , and Control . " ( unswept ) on compressibility correc Wiley , 1949 . Chapter 4. tion for propeller driven airplanes ( 1 )

( NACA

TECHNICAL AERODYNAMICS

18-6

Similar charts are available for maximum sea - level rate of climb and for absolute ceiling . The Oswald charts for climb and ceiling of airplanes with unsupercharged engines are shown in Figs . 18 : 9 and 18:10 . Figures airplanes in 18 : 9 and 18:10 show the climb and ceiling for unsupercharged terms of the ceiling parameter A = LgLt4 3 / Lp1 /3 . The climb chart uses

/

altitude as a parameter as well as the design Cg (CSm) of the propeller . The ceiling chart has a single family of absolute ceiling charts for var ious values of Csm of the propeller . The absolute ceiling corresponds , by definition , to the service ceiling with L = 0. For other values of Lt designated

on the

responding to

100

18 : 4 .

chart

ft / min

of

ting drag and

rate of climb .

turbojet

a

cor

service ceiling

is the

shown

OF TURBOJET PROPELLED

PERFORMANCE

performance

ceiling

, the

AIRPLANES .

The full

is

analyzed by

propelled airplane

thrust against speed .

commonly

is

high speed

The level

of the graphs of airplane

throttle

plot

determined

thrust available , just as speed for a propeller - driven airplane was deter mined from thrust horsepower required and available . A maximum angle of from the

climb

is

intersection the level high likewise

drag

thrust available to

from the maximum excess

determined

of gravity along the flight

overcome a component

and

path .

Charts for level high speed , maximum rate of climb , and absolute ceiling of jet - propelled airplanes may be developed in a manner similar to those

It is

customary to

/

to

make

drag gives (

18

98

W2

8292

solved graphically

subsequently

18

(

q 1

L

Ls

1,000

as

made by means

in Fig

18:11

.

and

1,000 π

of Fig

.

can be plotted

with compressibility correction

=

+

W

feb²

q 1

W

,

: 9 )

(

18

= q +

1

T Equation

(

thrust

to

written π

which may also be

= D =

+

T

equating

,

)

speed calculation

1/8

level high

For the

, and

)

.

8

for propeller - driven airplanes

:

18 : 3

assume the parabolic approximation CD (CL2 ) for this purpose subsequent correction for compressibility .

18:12

.

in Art .

: 9 )

developed

usually cover the range from 400 to 600 mph instead of the 400 to 500 mph range common for propeller driven airplanes jet propelled airplane assuming The maximum rate of climb of con corrections

stant thrust Ta

and

.

a

,

√πT

,

is 18:10

)

eb2

path

(

-

/

-

D1 = Ta

flight √1

forces along the

2

balanced

-

a

-

Compressibility

17

6 16 5 15

4 14

3 13 2 12

F11

10

.

9

Ch +

L

8

7

6

5 сл

4

3

3 3 4 +/

15

=

10,000

117

9 8 7 6 5

2

1

0

1 airplanes TR

/

NACA

with 408.

Fig

:.9

.

Oswald unsupercharged

. . with

18:10

0

for

A 9 8 7 6 5

(

. From

T

chart

Absolute engines

ceiling

20

25 30

40

0

LT =

50 60 70

chart for airplanes From NACA TR 408.

28474 Lp13

=

1

climb

ceiling

10

15

engines

== =

50 60 70

/

Oswald

40

.. ..

30

3

unsupercharged

20

Service

284 Lp

5000

10,000

15,000

ceiling

18

ft

10

feet Ceiling = H

Peak eff prop All Csm Best perf.prop Csm 1.6 " Csm 1.2 " " Csm-0.9

-

Fig

level

1000

20,000

25,000

30,000

dP 1.00 aN

..

5000

Sea

10

35,000

=

dN

dP

Peak eff prop All Csm Best perf prop Csm 1.6 Csm 1.2 Csm 0.9

AIRPLANE PERFORMANCE

18-7

)

(

.

)

18-8

TECHNICAL AERODYNAMICS

.

600

ft

9

500

at

10.

35000

8 7

mphy

6 5

( Uncorr .

91 100

for

comp .

400

700

3

600

776

2.5

2

-300 500

1.5

250

Ipa 100g

T100

10

Fig tion

400

2.5

1.5

200

3

Level high speed of turbojet propelled airplanes from equa neglecting compressibility corrections See Fig 18:12 for compressibility corrections ,

.

.

.

: 9 ) ,

18

(

.

.

-

18:11

where

/

18:11

(

ZW SCL1 Po

)

V1 = and

obtained by neglecting 18:10

from

,

sea

(

/0

18:13

level

The condition

)

.

0

at

emp

.

/(T

)

.

=

the

.

(

can be determined

-

a

,

Temp

(

and

=

Po

/

=

P

where

σ

Ta To

)

(

V1 may be

-

term

)

first

approximation to Ch

of the right hand member of equation jet propelled airplane The absolute ceiling of the consideration that as shown in Fig 15:21

second

)

(

/s

hand member

/

a

,

first

of equation 18:10 is often small jet airplanes for with adequate thrust for take

of the right

compared with the

off so

18:12

).

term

VAеf

-

The second

=

CL1

for

AIRPLANE PERFORMANCE

t/c

-10 Amphi

35,000

ft

O

t/c

-10

17

-20

20,000

-10 Amphi

·CL

=

0.2

CL

=

0.4

Uncorr .

ft .15

t/c

=

. 12

18

mphL

400

Fig .

= .12

.15

18

Δmphi

-20

.12

.15

18

-20

=

18-9

SEA

LEVEL 600

500

Effect of wing thickness ( unswept ) on compressibility correc tion to level high speed of jet - propelled airplanes . ( 1)

18:12 .

absolute

ceiling

( altitude

for zero climb)

(0/0 )ch= 0

/

is

/

2 √£ ob2 √π To W

=

/

( 18:14 )

To W in the range from 0.2 to 0.3 , which are necessary for reasonable sea - level take -off , absolute ceilings of 50,000 ft to 60,000 ft are quite common , but are rarely used in civilian jet aircraft because of

For values of

the high pressures necessary for cabin supercharging which impose a se vere structural penalty on the fuselage design . The use of the foregoing methods in calculation of the full throttle performance of the civil jet airplane ( Morane - Saulnier 760 , shown in Fig . 18:13 , is illustrated by the following example . Example . For the airplane shown in Fig . 18:13 , assume the following data and calculate ( a ) the level high speed at sea level , ( b ) the maximum rate of climb at sea level , ( c ) the level high speed at 20,000 ft standard altitude , and ( d ) the absolute ceiling .

( 1 )Replotted from Perkins

, C. D. and Hage , R. E. ,

op . cit ..

Chapter

4.

18-10

TECHNICAL AERODYNAMICS

lb

W = 8,480 e = 0.85

ft2 b²/s = 5.6

S

= 194

A

=

Rated thrust at sea level To Thrust variation with altitude as =

Solution . ( 1 ) Calculate

VAеf /S

=

2f /S

=

CD1

=

D1

in Fig .

=

√ x

33.3

ft

( 2 Turbomeca Marbore 15:21

/

5.6 x 0.85 x 4.4 194

.

engines ) .

= 0.584

= 0.0453

= 582 CD1 W = 0.0453 7,480

0.534

/

12W/ SCL1 ° Po =

V10

=

at (L/D) max from equations ( 18:11 )

the conditions

and ( 18:12 ) thus CL1

= 1,760

b

f = 4.4 ft²

1/840

x

7,480

lbs

/194

x

0.584 = 235

ft/ sec

( 160 mph

)

-WGVOE

F

Fig .

-

Morane Saulnier 760 four - place civil turbojet airplane , in in 1955 at Beech Aircraft Corp. plant in Wichita , Kansas .

18:13 .

production

(2)

Plot

(3 )

W

V1 =

(4 )

on

mph

Ch = T

Ch

-

0.157

=

D1 =

1,760

L1

7,480

x

At 20,000

ft

D1

14:19

/

0.235.078

ft/min

=

0.62 x 1,760

=

1,909 582

=

= 0.157

( checks published 2,260

standard altitude , read in standard 0.86 , 0/0 = 0.62 , and calculate

Ia =

Ta a

In Fig .

0.0453 = 0.584

235 x 60 = 2,230

0.533 , 0 = 4470/5180

mphL =

/

/

/

Fig .

14:19 : Ta D1 = 1,760 582 = 3.03 and read VI V1 2.45 x 160 = 394 mph at S.L. From equation ( 18:10 ) calculate at sea level

2.45 , hence

ft /min )

air table

σ =

= 1,090

1.88

/

read V V1 = 1.85 . Calculate V₁ = 160 10.533 = 219 mph , and = 405 mph (checks published value ) .

1.85 x 219

18-11

AIRPLANE PERFORMANCE

( 5 ) For the absolute ceiling

//

2 Vf

=

(0/0 ) ch = 0

V1

eb2

, =

To W

from equation ( 18:14 ) calculate

/

2 14.4 0.85 x 33.32 1,760 7,480 Υπ

=

/

0.33

ft

From standard air tables , for o / 8 = 0.33 , read absolute ceiling = 39,000 ( published value 36,000 ft , presumably based on a slightly less favorable variation of thrust with altitude ) . (6 ) As a check on the level high speeds , use Fig . 18:11 . Calculate

first

Lp

7,480

=

L's

7,480

=

=

1,000 x 4.4

1,000

LpLs

7.95 x 1.70

=

1,000

7.95

=

0.85 x 33.32

/f

/

1.70

=

13.5

= 1,760 sea level , with T 4.4 read in Fig . 18:11 mph = 390 mph . 20,000 altitude , with T / = 1,090 44 = 248 and the same value of = 0.533 calculate LpLs , read qL = 225 , and with o

For For

ft

/

are the answers called for

to

x 25.6

is

" Range "

endurance .

Airplanes are

are of

endurance

it is

customary

and endurance

for

is

to

make

can

corresponding time

the

for both

importance

proposed

commonly cruised at the interests of long range

in

the distance an airplane

running out of fuel ; " endurance " major

= 405

.

75 per cent of rated power or thrust

or long

and

/

CRUISING RANGE AND ENDURANCE .

18 : 5 .

50

/

= 1001225 0.533

mph

These

f

civil

and

.

fly

without

Range

and

military operations

,

extensive and careful calculation of range designs . The basic equations for these

new

calculations are Range

R =

= E =

Endurance

is

where AW

the weight of

AWf

fuel

AWf

calculations in Chapter Propeller - driven Airplanes .

equations

,

usually attributed

consumed

,

and the rates

/

of fuel

consump

and or engine data as

in the

16 .

The basic incremental range and endurance

to Brequet

dR = -375 dE =

( 18:16 )

(lb -fuel /hr) av

tion per mile or hour are based on propeller sample

( 18:15 )

(lb - fuel /mi ) av

L

CD

,

are

dw

( 18:17 )

/2

W

18.91 C13 CD

( 18:18 ) 33

18-12

in

TECHNICAL AERODYNAMICS

which

-dW

consumption

is

the change in airplane

if it

weight

fuel

differential

due to a

Both of these equations can be conveniently integrated

dwp .

is permissible to assume CL , CD , n (propulsive efficiency ) , C (brake specific fuel consumption ) , and σ ( altitude density factor ) constant be tween the limits of integration . While the optimum values of these fac tors are not truly constant , it is customary to assume reasonable mean

).

)

( W₁

(

18:20

1 )

√W

/

08

18:19

(

D

- 37.9

=

Exax

giving

,

10910 Wo

HIA

- 863.5

)/2

Rax

the equations

)

order to integrate

023

in

them

(

values of

Wo

80

)

70

hours

10

for

60

1.89

60

.

80

= 1.89

100

.85 for 7 = .45

12

Endurance

,

J

in

mi .

1000

=

Range

1

(a)

14

(b

16

50

HA

20 8

40

6

30

S

20

4 =

-5

-

).

in Fig 18:14 for typical val is plotted for the no wind

Figure 18:14

"

.

/

"

0.45-1.89 no effect on the endurance but it is customary to as function of altitude for various values of winds ex

18 0.85

Wind has

at each altitude in order to determine the operational using in general the optimum cruising speed for the airplane ,

which

is different

from the optimum

cruising

speed

in

utility

of

each wind

still

air

.

range

pected

velocity

18:20

(

and

.

are plotted

18:19

)

) ,

(

C

/. ¶

)

(

)

(

18:20

.4 .5 propeller d riven for

.6

a

calculate

.

n

/c

of

condition

and

root scale

)

(

.7

.8

1.0

.

.

ues

18:19

.

/ .4

Cruising range and endurance no wind 18:14 See equations airplanes with typical values of Equations

Sq

0

)

WO

(

Fig

.5

.6

.8 .7

1.0 .9

W1

T

10

Log scale

0

Wo

(

/

W1

2

18-13

AIRPLANE PERFORMANCE

pounds

08

/ L

C11

MP

CD

W

18:21

dw

18:22

(

D W

10910

(

/

)

-

(

WO

W1

1

18:23

Wo

18:24

)

)

max

to

(

2

(

)

Wo

CD

for typical

val

W1

in Fig

are plotted

18:15

.

(1) 18:24

:2

and

18:23

(

(

-

2.3

Bmax

Equations

1

/

-

39.6

Rmax

GL1 2 )

assuming constant value of C ' , CL , CD , and σ , integrate

,

equa

endurance

and

)

1391W

=

dE

=

as

range

)

to write the basic incremental dR

which

Since turbojets are characterized by a fuel per hour per pound of thrust ,

.

in

C'

)

Airplanes

consumption

customary

tions

of equations

(

-propelled

specific fuel

is

by means

and ( 18:20 ) .

Turbojet

it

/C

to other values of

18:14 can be corrected

( 18:19 )

/2

Figure

8

)

.

(

(

)

.

,

,

C '

Graphs for other values of these parameters may ues of CL and CD be constructed by use of equations 18:23 and 18:24 As for propeller

'

C

CL CD

Endurance

,

14

1.10

0.4 0.025

'

for

=

hours

1.10

L D

10

-100

5

= = =

for

6

(

in mi

1247

1000

C

Range

.

7

b )

(a )

16

8

4

80 60

3

6

:

40

.7

.6

.5

.4

.8 .7

Log scale

.6

)

/

W1

1.0.9

Wo

(

J

0

1

1.0 .9

Fig

.8

root scale

)

Sq

(

W1 WO

O

.

/

1

2

2

4

.

Wg

.4

.5

).

18:24

(

and

)

(

-

)

.

(

,

C ' ,

.

.

Cruising range and endurance no wind of turbojet propelled 18:15 airplanes with typical values of CL and CD See equations 18:23

TECHNICAL AERODYNAMICS

18-14

calculations are customarily made at various altitudes with various head and tail winds at each altitude to determine opera

driven airplanes and

,

utility .

tional

in general the comparative range and and 18:14 . For a given ratio of empty

Note 18:13

endurance weight

to

in Figs .

scales

original weight

(W1 /Wo) , the range and endurance of turbojet - propelled airplanes are only to 40 per cent of the corresponding values for propeller -driven air planes for the no - wind condition . With the usual adverse winds , the jet 30

airplanes

show up

In

more favorably .

" long

general , however , the terms

range " and " jet propelled " are contradictory . Elaborate techniques for refueling in flight are necessary for " long - range jet bombers . " For long range commercial

transoceanic hops

order of 3,000 miles ) there

( of the

is

considerable question as to whether the small pay load remaining ( after the necessary fuel is pumped aboard ) will willingly pay the premium for the

mph

100

- is

DC 8

18 : 6 .

cause

extra

speed .

TAKE

- OFF

primarily

a take -off runway length take

is

CALCULATIONS .

take -off distances

plane designed

if

(This

to say

the financial success

of the

not assured . )

-off

-off calculations are

often limiting factors

from

flight

in excess of

occasionally

must

Take

are

is likely

considerations commonly

those

be made from an

important

in design .

An

be air

to require

available , especially a high altitude

airport at

level .

above sea

Take -off calculations

difficult

accurately because the take piloting technique relative to off distance varies considerably with the the ground and wind conditions , and because the principal forces involved cannot

are

be very accurately

distance

velocity ,

,

tions of velocity equations ,

it

and

and

to

estimated .

acceleration

acceleration

follows that take

As

-off

in

any simple problem involving

basic equations are the

, the

V

:

make

= ds

/dt

gration

VTO

/

and a = dv dt .

distance can

be

defini

From these

obtained by the

inte

V

( 18:25 )

a = Net Force Mass

(18:26 )

xto

=

√

V dv

where

and VT

is

the take - off speed in

of the stalling partly down at

It is

speed

in the

a predetermined

customary to make take

ft / sec ,

which may be any speed

take -off configuration optimum

( usually

in

excess

with flaps

position ) .

- off calculations

from a standing start to

AIRPLANE PERFORMANCE

a

point

18:16 .

xtı ,

shown

,

and a climbing

in Fig .

, as shown

as

distance xc

= xg + Xt1

(18:27 )

+

general , the lower the

take - off speed

will

high could be cleared

into which it is customary to analyze the take - off in Fig . 18:16 to be a ground run xg , a transition dis Xto

In

ft

50

The components

distance are tance

obstacle

an

where

18-15

the

,

shorter

total horizontal distance to clear an obstacle . An airplane can actually be be the

pulled off the

round

at

a

speed somewhat lower than the

stalling

calculated

speed

Ground run

ob

tained by using a wind - tunnel

test value of CL a higher under

value

again .

To avoid " mushing

practice to specify take 20

conditions

involves

- off stalling

per cent

, hence

a take

a

in" - off

Components

of

-Xc

take

- off

that

speed at some

arbitrary

This margin of safety

common

per cent above the

is

commonly set at

to assume ( 18:28 )

VTO = 1.20V STO A smaller value

of

dis

the airplane will settle down after a too early take - off , it is a common

hazard

speed VSTO

it is

18:16 .

50ft.

h₁

tance over a 50 ft obstacle . of increasing angle of attack . This pro

obtainable

the transient

cedure , however ,

Fig .

climb 10,

·Xti

-Xg¨¨

max because

is

Transition V=VTQ

VÃO may be assumed

if it

is

desired to get a shorter

take -off distance with a correspondingly higher risk . Forces acting on the airplane during the three phases of the assumed take -off are shown in Fig . 18:17 . An analysis of the horizontal distance

for these three

phases

is

made

separately in the following three para

graphs .

L=1.44W O R=μW

Fig

a. .

N=W

вер

W

-

Tc Dc Vw

C. Climb b . Transition Ground run phases of assumed 18:17 . Forces acting on airplane during three take -off .

TECHNICAL AERODYNAMICS

18-16

(a )

Ground Run .

tion of the three forces T ,

Equation ( 18:29 ) assumes that

is

tion for

most favorable

very high

( as

R = μW ,

D , and

T ually the

accelerates horizontally under the

The airplane

·

D

lift

· is

IEa

HW =

(18:29)

zero during ground run

condition unless the coefficient of

field )

on a muddy

any wing as low as the

ac

so that

is

since there

is us

, which

fric

rolling

/

of L

no value

coefficient of rolling resistance of wheels

D

on

surface . Typical values of rolling resistance coeffi cient for braked landings as well as for rolling take - off , are shown in Table 18 : 1 . is often not possible to take off at zero because of a reasonably hard

It

lift

TABLE 18 : 1 Brakes off , average ground

Type of surface

Concrete or Hard

turf

Firm and dry . · Soft turf · Wet concrete . · Wet grass Snow or ice - covered

zero

lift .

placed by ground

may

effect )

is

0.07 to 0.10

set on the airplane

prevent take -off with

in

as calculated

( 18:29 )

the

Chapter

nose

, as

landing gear

the

sufficiently

a take

The acceleration

9.

in equation

should be inserted

- off distance

.

( 18:25 )

to get

down

the ground run based net thrust

is

on

=

(T

-

D

-

)

and

determined

integrated

To avoid a graphical

quicker but less accurate calculation may be the average net thrust during acceleration by

, a

TNav

age

0.30 0.20

0.10 0.02

field

graphically to determine defining

0.33

In this event , the term µW in equation ( 18:29 ) should be re L) and D must include the induced drag of the wing ( with μ (W

by equation gration

0.4 to 0.6 0.4

0.07 0.05

the angle at which the wing arrangement

coefficient

μ

0.03 to 0.05 0.05

macadam

•

, average

wheel -braking Hb

resistance

coefficient

fully

Brakes

applied

made as

corresponding to the aver

1 vto xg = 29 TNav W

( 18:31 )

/

Studies of the relationship between average

:

(18:30 )

HW av

a constant acceleration

inte

follows

and

initial

net thrust

during

18-17

AIRPLANE PERFORMANCE

in

by Diehl , (1 ) show that the

equation

is

18:18 ) , and

( 18:31 )

if a

initial

correction factor

used instead of 1 / 2g

Ig

in equation Kg vto

net

/

=

For

18:32

TNI W

accurate calculations

more

should be integrated

in Fig .

giving

( 18:31 )

Note in Fig . 18:18 that Kg is a function of the ratio of to initial net thrust , thesenet thrusts being determined 18:19 .

thrust TNI can

Kg (as plotted

)

be used

made

(

take -off , as

graphically

, the

net thrust

final

net thrust

in Fig .

as shown

shown

in Fig .

18:19

. Tor D

0.040

Thrust

0.035

available

0.030 Tc-Dc

Ks 0.025

TNI

flight level Drag

D+μW

/

Fig

Distance .

.

-

Variation of forces dur showing the values of necessary for use in Fig

.

TNI and TNF 18:18

transition

The

from the level

ground run to

given by the equation 01 =

Tc-

Dc

18:33

W

take place at constant normal

to

)

81 ,

may be considered

off

(

(b) Transition climb at an angle

18:19

ing take

Fig . 18:18 . Diehl's ground - run coefficient for use in equation (18:32 ) .

.

0.4 0.5 0.6 0.7 0.80.91.0 TNF TNI

,

0.3

μW

.

0.015 0.2

2

Takeoff

0.020

acceleration

due

to

lift

a

,

a

.

)

(

18:35

W

revised edition

)

vio 0.44g

(

=

Engineering Aerodynamics

"

W. S.

18:34

approximately

Xt1r91 ( 1 ) Diehl ,

vio

0.44g

.

is

r=

Dc

the horizontal distance

is

, "

path

To

flight

-

dius of such

a

a

at

operating CL max while traveling speed VTO- 1.2VSTO giving equal to 1.44w and The ra normal acceleration of approximately 0.44g

18-18

TECHNICAL AERODYNAMICS

and the corresponding

vertical distance

is

x+19

b1 =

In

the distance hi

cases

some

which

will

be calculated

to reach

50

50

ft ,

ft altitude

in

. may

relationship

from the approximate

Climbing Distance .

ter than

turn out to be

Itxt1 /50/ (c )

,

(18:36)

the transition distance necessary

case

the geometry of Fig . 18:16

, from

Equilibrium

(18:37)

h1

of

in Fig .

the forces

18 : 17c

for

steady climb at an angle 81 requires that W , Te , and De be related as in equation ( 18:33 ) . The horizontal distance necessary to climb a vertical distance of 50 - hy is accordingly xc =

50

(Tc

-

- hi

(18:38 )

Dc) /W

10

Typical

8

long runways

Take -off

7

distance

6

1000

ft

,

Typical short

5

runways

Propeller -driven

--Jet

4

ft

3

50 Over

2

---run

Ground

1 i

W W

1

5

CLTO

100

Bhp 200

or

W W

2

1

I

STOCLTO

300

400

500 600 700

Fig . 18:20 . Approximate ground run (no wind ) and total take - off distance for either propeller or jet airplanes , replotted from Perkins and Hage . ( 1) An over - all picture of the effects of wing loading , power or thrust loading

,

air

density

, and

as studied by Perkins

and

take - off

(1 ) Hage ,

18:20 that high wing loadings

lift

coefficient is shown in Fig .

and high

on take 18:20 .

power or thrust

-off

distance

, C. D. and R. E. Hage , op .

cit . ,

p . 197 .

in Fig .

Note

loadings require

take -off distances nearly to the limits of current typical runways

( 1 )Perkins

,

.

Figure

AIRPLANE PERFORMANCE

is

18:20

plotted for no headwind or typical small values of headwind

there is

a substantial

shortened

, as

18 : 7 .

headwind , the take

in Fig .

shown

DISTANCE

LANDING

18:21 .

der development ) .

Reasonable landing

tance for airplanes

on ice requires

,

- off

distance

,

0.6 Xq go

dis

,

like

cannot

Diehldata for landplanes

0.4 Xa·=(1 Vw2 X90 SK Forseaplanes fromR&M 1593 )

(

0.2 0

pro

.

Calculations for landing distance

08

either

reverse - thrust jets or reverse - thrust

take

1.0

CALCULATIONS .

sign , particularly with jet airplanes which have no provision for reversing the thrust of the jets (such items are currently un

calculations for

If

.

-off distance is very appreciably

Landing distance , like take - off distance is important as a limiting factor in de

pellers

18-19

0

Fig .

0.2

18:21

0.4 0.6 VW VTO

/

.

1.0

0.8

Effect of wind

on

take -off ground run xg , replot ted from Diehl . ( 1)

be made with very good accuracy because they are capable of major reduc tion by proper piloting technique , particularly the " sideslip " on landing ,

For commercial airliners the sideslip is usually not considered a permis sible maneuver except in an emergency , because it tends to frighten the passengers ; high - drag flaps are often chosen for the primary purpose of avoiding the necessity of a sideslip landing .

of landing distance over

50

foot obstacle

.

Components

18:22

.

.

Fig

-Xt

a

-Xg

50ft.

,

a

,

rolling distance before

revised edition

.

Engineering Aerodynamics

a

,

, "

S.

,

W.

Diehl

transition distance

, "

ground run

of the

( 1 )

sum

a

.

.

.

a

,

-

are commonly made for landing as for take off over 50 Typical phases of the landing over foot obstacle 50 foot obstacle are 18:22 shown in Fig The total landing distance is considered to be the Calculations

TECHNICAL AERODYNAMICS

reverse pitch propellers

braking distance which

calculation

is the stalling

based

+

X

( 1 ) that the glide is at a speed of 1.3VSL , speed in the landing configuration ; ( 2 ) that the

a deceleration

if reversed - pitch

propeller braking until the airplane stops . The relationships these are applied

CLA

1.3V SL at

where

Dg

= Dg

)

18:42

(

2

/)

at

18:41

(

1

VSL

Xt =

18:40

CDg

)

50

)

=

Xg

)

(

( and ,

is

used , the reversed thrust

(

are applied

equations that express

from Vg = 1.3VSL to Vg = VSL ; ( 3 ) that required before the brakes are applied ;

is

time of about 3 seconds

( 4 ) that the brakes

is

(1 ) is

V

a

by Crocket and Bonney

recommended

assumptions :

transition involves

rolling

18:39

Xp

V &

where VSL

procedure

Xt

by

as indicated

W + g

on the following

B Xg

+

XL The

jets ,

or reverse thrust

include the use of

may

)

, and a

+

brakes are applied

(

18-20

18

assumed

) )

be given

.

18:47

K2

"

Reverse Pitch pp 441-447 .

,

,

E.

,

B.

, "

,

to

+

K₁

=

T

.

.

.

)

( (

( F

,

is

Crockett Harold and Arthur Bonney JAS October 1945 as Airplane Landing Brakes )

retard

Subscripts

of the form

Fig 18:23 Forces acting on K₂V² airplane during braked ground run with the coefficients K1 and

(1

the net

-

by an equation

N =W- L

is

18:23

refer to glide and stall respec If the variation of reverse pitch

thrust with speed

μ(W- L)

o ) ,

in Fig

(

.

18:46

.

and

tively

shown

.

equation

S

g

18:46

(

In

ing force nT

)

Fg

a W

18:45

)

where

a

)

VSL

(

=

1

Xx

18:44

3VSL V

=

Xr

18:43

CDS ground

V &

1.69C

Dg +

=

(

Xt

W1S

giving

determined

Propellers

AIRPLANE PERFORMANCE

)

(

a

18:46

is

and

applied

integrat

complicated expression for

ground run

braked

propeller

)

( CLS

CD

)/

-

18:45

integrated

may be

graph

.

)

)

18:49

HDCL

(

equation

Но

(

/

calculation

CD

,

more accurate

ically

loge

CLS

Hb

( a

For

)

-

HCL

mph

(

0.0334

Xb

2

,

.

For the simpler case in which the terms involving thrust are removed the result of the integration is

)

(

18:48

reversed thrust

into equation

rather

CLOP

+ Hb

on which the

18:48

)

(

K₂V² )

becomes

.

of engines

Putting the force of equation ing equation 18:45 gives

+

force

,

is the number

where ner

ner (K₁

+

-

)

v2s

= спорот 2

F

the net retarding

,

2

characteristics

(

from the propeller

18-21

The forces acting on an airplane

= 0 ,

ΣFx

,

= 0

glide

steady

and 2Fy = 0

(

)

18:50

8

18:51

(

)

sin

W

in

equa

these

e

=

D

shown

,

as

= W COs

L

x

y

.

Since acceleration axes

(

D

)

.

propeller

with and give tions

.

W ,

D ,

L,

.

.

:

8 .

GLIDINGAND DIVING

a

in steady glide without power are shown in Fig 18:24 The tail force is negli gible compared with or but its moment about the center of gravity is not negligible and must be considered when calculations of balance in glide are made The drag force must include the drag of the idling 18

and

.

)

Fig

18:24 Forces acting on airplane in glide

elevator

.

.

,

)

)

D ]) D )

/

/( L /

(

/

sin

e

and

L

(

18:53

8

+ (

e

1.0

SCL

²

0.002560 mph (

=

L

)

(

and

/S cos

sin

are negligible

then 18:54

)

W

0.002560CL

(

mphg =

/S

;

compared with 1.0

glide

,

For small angles of

18:50

W

-√0.00256 0.002560CL cos e

mphg

from equation

mph

,

glide

in

of

The speed

,

is

stabilizer

.

settings

by the

is de

The angle

W

.

with the horizontal termined

(

the angle of the path of glide

.

is

-√

where

18:52

8

HIP =

D

cot

TECHNICAL AERODYNAMICS

a

vertical dive ,

sin

= 0,

cos

w /s

mphg max

For any

assumed

18:55

0.002560CD min

of glide

angle

9 = 1.0 , and

)

For

(

18-22

8,

L / D can be calculated

from equation

corresponding angle of attack , CL , and Cp can be read from a graph of the airplane characteristics ; thus equation ( 18:53 ) can speed of glide is plotted be used to calculate the speed of glide . ( 18:52 ) and the

If

against angle of glide as in Fig

gliding - velocity

10

Stall

18:25 , the

.

resulting

graph

diagram , a

is called

special

a

form of

" hodograph . " The

limiting

speed of

monly calculated

Pancake

in connection with the

lem of determining design loads on the

300

Vertical dive

is

vertical dive

com

prob

wings

of the airplane . Under these conditions drag of the idling propeller is a major

60°

tor

90°

and

can not be neglected .

which the propeller

will

rotate

the

fac at

The speed

idling

when

Fig . 18 : 5 . Polar diagram depends on the friction horsepower of the en of gliding speed vs. angle gine glide if " dead " and on the idling - jet adjust of . Terminal dive calculations for de ment of the carburetor if throttled . termination of design loads for wings are

commonly

made

on the assumption

is or limited to some arbitrary value . Since the propeller drag coefficient depends on V/nD , the propeller drag can not be estimated until the terminal dive velocity is known , hence , the solution for terminal dive velocity must be by trial . governed

on airplane

r is

( 18:56 ) and

cos

L sin

in horizontal

tions

lift

is

= W

18:56

)

L

where

must

flight ,

available for supporting the weight . In Fig . 18:26 , 2Fy = 0 and ΣFx = w gry2. hence

Forces acting

turn without sideslip

a

gr

of bank .

Solving equa

=

18:57

.

is the angle the radius of turn and ( 18:57 ) together gives tan

❤ =

v2 gr

18:58

)

18:26 .

W

L

in

(

Ľx

Fig .

lift

turn are shown in Fig . 18:26 . The be greater in a turn than in horizontal for only the vertical component of the

.;

W

on an airplane

)

R=

The forces acting

,

properly banked horizontal

TURNS .

(

LEVEL AND GLIDING

22/225

18 : 9 .

rpm

(

that the propeller

AIRPLANE PERFORMANCE

For

lift

radius of turn , the wings

minimum

coefficient

,

the airplane

and

18-23

operate at

must

at the

must be banked

their

maximum

angle at

maximum

which the power available will supply the speed necessary to support the weight . A logarithmic graph of hpr and hpa against speed , as shown in

Fig .

for graphical determination of

18:27 , can be used

radius of

minimum

turn in the following manner : at a given angle of attack ( e.g. , at CL max ) hpr varies as v³ ; hence , a line through hpr at CL max with a slope of 3 : 1 the locus of power required at CL max at different speeds . The at which the power available will propel the airplane at CL max is

represents speed

in Fig .

determined by the intersection A plane

for

curves are plotted

be 70

mph ; whereas ,

which

) , L / W = sec and is stalling speed ,

equation ( 18:56

radius

and Vs

For the

if

XV

Вес ф =

Vt

is

at CL

;

tan

= 702

x

32.2

x

is

where imum

0.98

= 335

s

gCL max

chiefly

Equation

on wing

loading

From

Hpa

HPF

1

90

ft

80

sin

( 18:60 )

Logarithmic 18:27 . horsepower - speed graph for

(18:60 )

, more

maximum

points

heavily

70 80 90 100110 Speed=v , mph

60

Fig .

determined from equation ( 18:59 ) .

fields .

air

seen to

100

radius of turn of his airplane for

small

ΤΑ

❤ = 0.98

w/ 0.00119

li

7: 3

140

A general equation for rmin , derived from equations ( 18:56 ) and ( 18:58 ) , is Imin

t+

Hp 120

= 1.41

(88/60)2

is

max was 59 mph .

180

18:27 ,

(70/59) ²

speed

speed of turn at minimum

the

and , from equation ( 18:58 ) ,

"min

this

160

in Fig .

❤ = 44.50

flight

(18:59 )

=

example

18:27 ,

200

2

sec

in Fig .

the speed of level

For the particular

18:27 .

graphical determination , of minimum radius of turn . ( 1 ) A

pilot

should

know the

min

safety in maneuvering around

out the

fact that

loaded airplanes

rmin depends

requiring a larger

radius to turn . Calculations on gliding turns are of practical importance because they permit determining the minimum altitude from which a return to the airport is possible in the event of motor failure soon after take - off . The forces

(1 )

Diehl ,

W.

S. , op .

cit .

TECHNICAL AERODYNAMICS

18-24

acting on an airplane axes shown

in Fig .

in

gliding

a

=

ΣΕΖ

and 2Fy = R =

0,

=

/

(W g )

r,

shown

in Fig .

angle of bank =

❤ , and

For the

18:28 .

a constant speed of glide

for

18:28 and

path of radius of curvature

turn are

in

a

helical

angle of glide

= 8,

(V² / r) .

e

VW

Fig .

Forces acting on airplane

18:28 .

in gliding turn .

From ΣFx = 0 , D = W From

ΣF₂

= 0,

sin

( 18:61 )

0

LW Cos COS

(18:62 )

From ΣFy = R ,

L sin The radius wound

is r

of the

cylinder

cos2 8 , and the

♡ =

loss of altitude

about 45 degrees

,

(18:63 )

r

it

sine for

can be solved

ing turn in terms of wing loading minimum

g

on which the helical path may be considered altitude lost in a complete turn is h = 2πr

The above equations

W v2

,

(18:64 )

cos e

minimum

parasite

loss of altitude in

drag , and aspect

glid

a

ratio

.

For

can be shown that the angle of bank should be

and the wings

should

operate

at

maximum

lift .

PROBLEMS

For the Ercoupe airplane for which calculations of power required at sea level and 12,000 ft altitude were made in Probs . 14 : 7 and 14 : 9 , and for which full - throttle power available for a 75 - hp engine at sea level was calculated in Prob . 16 : 6 , ( a ) calculate and plot a graph of rate of climb vs. speed at sea level , and find the steepest climbing angle , the maximum rate of climb , and the corresponding air speeds at sea level ; ( b ) the maximum rate of climb and level high speed at sea ; ( c ) plot rate of climb vs. altitude as a straight level and at 12,000 line , and find the absolute ceiling , the service ceiling , and the ceiling for 300 ft / min rate of climb . Use the general logarithmic plot of power required for level flight . 18 : 1 .

for level flight

ft

AIRPLANE PERFORMANCE

18-25

18 : 2 . For the Lockheed Constellation airplane , for which calculations altitude power required for level flight at sea level and 20,000 were made in Probs . 14 : 8 and 14:10 , and for which full -throttle power available at 10,000 ft from four engines was calculated in Prob . 16 : 9 , ( a ) find the maximum rate of climb , best climbing speed , and level high speed at altitudes of sea level , 10,000 ft , and 20,000 ft ; ( b ) plot maxi mum rate of climb vs. altitude , assuming a straight line above 10,000 ft , and find the absolute ceiling , the service ceiling , and the ceiling for min rate of climb . 300 Use the general logarithmic plot of power re

ft

of

ft /

quired for level flight

.

For an Ercoupe airplane with W = 1,260 bs , S = 142.5 sq ft , b = , and e = 0.76 , , and Bhpm = 75 , assume f = 4.28 sq ft , n 30 max = 0.71 ( a ) use Fig . 18 : 7 to find the level high speed at sea level , ( b) calculate ▲ from LsLt / 3/ Lp1 3 and use Figs . 18 : 9 and 18:10 and a peak - efficieny propeller to find the maximum rate of climb at sea level and absolute ceil 18 : 3 .

ft

/

ing .

Repeat Prob . 18 : 3 , ( a )

18 : 4 .

( b ) for

f

per cent increase

f

ft

in

for

30

per cent increase

in gross

weight ,

horsepower , ( c ) for 30 per cent de crease in , and ( d ) for 30 per cent increase in wing span , keeping all other items constant in each case . design changes : W in 18 : 5 . Repeat Prob . 18 : 3 , with the following creased from 1,260 to 1,600 to allow for one more passenger and heavier engine ; brake horsepower increased from 75 to 130 by shifting to six cyl- . inder engine ; reduced from 4.28 to 2.80 by retracting landing gear ; b increased from 30 to 39 to improve altitude performance . 18 : 6 . Given the following data on an Ercoupe light airplane , find ( a ) the horizontal distance necessary on landing , at sea level with no wind to clear a 50 ft obstacle and come to a full stop using brakes , and neglecting the drag of idling propeller ; and ( b ) the horizontal distance necessary on take - off , from sea level with no wind , to clear a 50 ob stacle after starting from rest . All data are intended to be the same as in previous problems on this airplane . Airplane data : W = 1,260 lb , S = 142.6 sq ft , CD = 0.030 +0.066012 ; no flaps ; CL max = 1.50 ; h b = 0.085 on ground ; CL = 0.30 on ground . Engine data : Full - throttle sea level Bhp rpm = 75/ 2,550 direct drive . Propeller data : D = 6 ft 0 in . , fixed pitch Bo.75R = 16 deg , charac teristics in Fig . 16:17 . Ground data : Rolling - traction coefficient for take - off , μ = 0.05 . Sliding -friction coefficient for tires on landing , b = 0.60 . 30

brake

ft

ft

/

/

airplane , 18: 7. Given the following data on a Lockheed Constellation find ( a ) the horizontal distance necessary on landing , at sea level with no wind , to clear a 50 ft obstacle and come to a full stop , using wheel brakes only ; ( b ) the landing distance , at sea level with no wind , to clear a 50 ft obstacle and come to a full stop , using full - throttle reverse pitch on two engines , as well as brakes ; and ( c ) the horizontal distance neces sary on take - off , from sea level with no wind , to clear a 50 ft obstacle after starting from rest . Airplane data : W = 86,250 lb , S = 1,650 sq ft , Cp = 0.0154 + 0.042C ( retracted flaps ) , CL max = 1.60 ( retracted flaps ) . For take - off flap setting assume CD = 0.020 + 0.043CL to CL max ==1.8 . For land ing flap setting , assume CD = 0.030+ 0.043C to CL max = 2.0 . Engine data : Sea - level take - off Bhp / rpm = 2,200 / 2,800 . Propelier gear ratio 0.4375 to 1 ; characteristics as in Fig . 15:10 . Propeller data : D = 15 ft 2 in . , three blades ; assume the character

istics in

Figs . A7 : 5 through A7 : 8 ; constant rpm governed reverse -pitch characteristics as in forward flight , K2 = 0 .

; assume

TECHNICAL AERODYNAMICS

18-26

Rolling - traction coefficient for take - off µ = 0.05 . b = 0.60 . the Ercoupe airplane for which data were given in Prob . the angle and speed of flattest glide , ( b ) find the ter minal velocity of vertical dive , neglecting propeller drag , and ( c ) plot a gliding diagram similar to Fig . 18:25 . Using logarithmic charts of power required and power available 18 : 9 . for the Ercoupe and Constellation airplanes , use the method of Art . 18 : 9 to calculate the minimum radius of level turn at sea level ( a ) for Ercoupe and ( b ) for the Constellation . 18:10 . For the Ercoupe airplane for which data were given in Prob . 18 : 6 , find the minimum loss of altitude in a 360 ° gliding turn , without power , neglecting the drag of the idling propeller . Ground data Braking , 18 : 8 . For 18 : 6 , ( a ) find

:

CHAPTER

19

CONVERTIPLANES

19 : 1 .

The term " convertiplane "

TYPES OF CONVERTIPLANES .

applied to aircraft which are combinations of airplanes The attempt

like

is

being

the helicopter

large landing

made to develop

an

aircraft which

and thereby avoids the necessity

fields usually

associated with airplane

is

helicopters .

and takes

is currently

off

of long

and lands

runways

and

-off , and which blade stall or ad take

not so severely limited in high speed by retreating vancing blade shock losses as the helicopter . Current developments

are

classifications : ( 1 ) the vertical take -off airplane , and (2 ) the " unloaded rotor " or winged helicopter . Airplanes with rotatable propeller axes are shown in Figs . 19 : 1 and 19 : 2 . If the goal is a military vehicle which will take off vertically

of two

major

and achieve a 600

mph

high speed

jets rather than propellers are limited in high speed to about 450 rotatable

necessary , since propellers but no configurations are yet

appear mph ,

,

achieving this

goal .

Fig .

1 : 5b )

19 : 3 ( and

requires

a rotatable

in

sight which have any promise of The vertical take - off (VTO ) turboprop shown in Fig .

is the

highest speed convertiplane yet developed

pilot's

seat

pay loads or to more than one or

,

but

and does not appear adaptable to large

possibly

two

seats .

rotor helicopters shown in Figs . 19 : 4 and 19 : 5 , while they promise show of raising helicopter level high speeds to 200 or perhaps 250 mph ( from the current maximum of around 160 mph ) , are not usually re The unloaded

garded as very promising developments

high speed over normal helicopters 19 : 2 .

propeller

is

because the possible not

sufficiently

improvement

in

great .

- PROPELLER -AXIS AIRPLANES . Airplanes with rotatable such as shown in Figs . 19 : 1 and 19 : 2 , may be designed and

ROTATABLE

axes ,

air

calculated on the basis of information given on planes and propellers in previous chapters . The propeller selection for such airplanes must be primarily from static thrust considerations , as

their

performance

discussed problems

in

Art

at the

.

end

16 : 7 ;

such

calculations are called for in

of this chapter . 19-1

one of the

CONVERTIPLANES

19-2

E

Courtesy Aero Digest

.

span

175.

)

rota

(

:

W ,

&

P

,

ft

,

: 1 .

.

ft

30

-3

convertiplane with XV Specifications axes height 13 engine mph

19 Bell table propeller

.

Fig

L

Fig

1

,

7,

(

1

19

G :2 .

.

Transcenden convertiplane with rotatable propeller axes flight tested in Courtesy Avia 1955. tion Week February

tal

,

3

I

1

445

)

1955.

.

)

-

(

rising tail landing gear 40 turboprop power plant

vertical

-

XFV

using Allison

T

Lockheed

-1

.

Fig

19 : 3 .

NAVY

airplane

TECHNICAL AERODYNAMICS

19-3

19 : 3 .

UNLOADED

In

ROTOR HELICOPTERS .

a normal

helicopter the retreat

ing blades carry about the same weight as the advancing blades , compensat ing for the lower relative air velocity by higher angle of attack . a helicopter has a substantial wing area to carry nearly all of the weight at high forward speeds , both the collective and cyclic pitch of the blades

If

canbe greatly reduced

An

.

additional

improvement

tip

of the rotor tip speed , though lower pitch to keep from completely unloading them

" fly

results from reduction

speed requires

increased

cyclic

the retreating blades and having propulsion Forward of a winged helicopter by means

backwards . "

of a nearly horizontal rotor is very inefficient , so a separate horizontal axis propeller is usually provided , as shown in Figs . 19 : 4 and 19 : 5 .

convertiplane with gear -driven rotor and pro ft , length 22 ft , height 10 ft , Wempty 3,475 lb , Bhp 350 (Jacobs R - 755 EM ) , mphL = 175 , Ch max = 1,400 ft/ min , range 300 miles with 50 gallons fuel . (Courtesy Aero Digest . )

Fig . 19 : 4 . Jacobs Model peller . Specifications :

The performance

of

104

D = 36

a convertiplane , such

as

shown

in

Figs . 19 : 4 and

as a helicopter up to nearly the level high speed helicopter may of the and be calculated as an airplane beyond (and some what below ) that speed . It is desirable for the airplane to have a stall ing speed somewhat less than the level high speed of the helicopter in 19 : 5 , may be calculated

order to permit reasonably safe transition between helicopter airplane flight . 19 : 4 .

OUTLOOK

FOR CONVERTI PLANES .

dustry regard a convertiplane

Many

as both a poor

persons in the

airplane

and a

flight

and

aircraft in poor helicop

ter , and there is some justification for this point of view in terms of calculations of economics of the operation . There is , however , a tremen dous military demand for a high speed helicopter for military evacuation

will be less of a " sitting It is , therefore , evident that a

and supply missions that normal

helicopter .

duck " target number

than a

of rotatable

19-4

CONVERTIPLANES

axes airplanes similar to those shown in Figs . 19 : 1 and 19 : 2 will be built , with level high speeds perhaps as high as 300 mph . It also seems likely that a number of tail - landing gear (VTOL ) airplanes will be built for spe cial military missions in defense of unarmed merchant vessels .

EXP

Fig .

19 : 5 . McDonnell LXV - 1 convertiplane with pressure - jet driven rotor , and engine -driven propeller . Specifications : span 26 ft , length 30 height 10 ft , engine Continental 500 hp drives blower and or propeller . (Courtesy Aero . Digest , March 1955. )

ft

/

PROBLEMS

19: 1 . A rotatable - propeller - axis airplane

similar to Fig .

ified by the data below . Estimate ( a ) the level high and (b ) the maximum rate of climb as a helicopter . b

19 : 1

is spec

speed as an airplane ,

ft

= 44 e = 0.9 S = 176 ft2 W = 6,000 lb

CDf = 0.025 Shp = 800 (turbine ) Wfuel = 1,200 lb D = 40 for each of 2 rotors C = 0.8 lb-fuel hp -br at 400 hp cruise = 2) = 0.9 ( rotor data as in Chapter 17 ; rh Propeller data as in Figs . 16:28 and A7 : 5 through A7 : 8 19 : 2 . An airplane similar to Fig . 19 : 3 is powered by a gas turbine rated 6,000 hp , which drives the six - blade counter - rotating propeller . Using the data below ( a ) estimate the maximum static thrust at nnD = 1,000 sec , and (b) estimate the level high speed .

ft/

= 26 ft e = 0.8

b

ft

/

S

= 350

ft²

W = 10,000

lb

ft

D = 16 CDf = 0.030

Propeller data as in Fig . A7 : 15 Static thrust data as in Figs . 16:28 through 16:30 , with CTS and Cps doubled due to higher activity factor .

CHAPTER

20

MISSILE PERFORMANCE

20 : 1 .

fines

a

FOR

OUTLOOK

missile

execution

, as a

MISSILES .

as " a weapon

or intended to

thrown ,

lance , an arrow , or a bullet . "

twentieth century , while

still

Dictionary "

"Webster's 20th Century

be thrown ,

The " missile "

for

de

doing

of the mid

a weapon of death and destruction ,

is

more

aircraft or finned artillery shell , usually guided by radio . Table A8 : 2 lists 32 varieties of "U. 8. Missiles and Pilotless Aircraft , " the development of which constitutes the largest single item of current defense expenditures . The importance of the missile as a weapon stems chiefly from the ther often an

unmanned

fact that it is readily deliverable by aircraft , fact that satisfactory radio guidance systems have been developed for such aircraft and for anti - aircraft rockets .

monuclear or H -bomb , the and the

system development

The weapon

craft

neering contests to provide centers of weapon production means

programs ,

are participating

manufacturers

(a ) and

the

in

, may be

means

which

all

briefly

major U. 8.

described as

for destroying the industrial

their civilian populations

for preventing such destruction .

air

engi

, and

Granting this concept

,

( b ) the

the prime

target of Soviet weapons would be the people of the City of Los Angeles and their food , water , and transportation , though many other U. S. cities are also major contributors

to the U. S. defense

Long range H - bomb guided )

aircraft

carriers may be either The probability of scoring

.

effort

manner

a hit on

or

. unmanned

(radio

their intended

tar

is greatly increased by increased speed , since high speed increases the difficulty of interception . Subsonic bombers , like the Boeing B - 52 gets

( Fig .

1 : 4a ) , are

as the " Nike "

interceptor

" sitting

( Fig .

1 : 7a )

for anti - aircraft rocket batteries , such with suitable early warning detection , or for

ducks "

fighter aircraft

equipped

with

anti - aircraft

rockets such as

( Fig

the " Sparrow " . 20 : 4 ) , though experience shows that a small percent age of any attacking force nearly always " gets through " to the target and a small percentage of a large attacking force might deal crippling blows

to the U.

S.

retaliation capability .

Long range supersonic 20-1

aircraft

such

MISSILE

20-2

PERFORMANCE

X -3

D558-2 Skyrocket

wwww

Jet researchplane, performanceclassified

Fig

.

20 : 1 .

Douglas supersonic airplanes .

First planeto fly double speedof sound

( Courtesy Douglas Aircraft Co. )

Fig . 20 : 2 . Boeing F- 99 BOMARC surface -to -air guided missile ( an unmanned airplane ) . Data ( Courtesy Aero . Digest ) : span 36 ft , length 66 ft , height 16ft , gross weight 8,500 lb. Propulsion : 2 ramjets plus solid propellant booster rocket . Performance : speed M = 2 , altitude 60,000 ft , range 100 miles plus . Guidance : radar or infra - red homing , command guidance .

r

Convair " Terrier " surface - to - air anti -aircraft rocket for 20 : 3 . launching from U. S. Navy ships . Data ( Courtesy Aero . Digest , March 1955 ) : span 4 8 in .. diameter 12 in . , gross weight 3,360 1 in . , length 13 , lb. Propulsion : solid - propellant booster rocket . Performance : M = 2 Guidance : command , beam rider . altitude 60,000 ft , range 8

Fig .

ft

ft

miles .

TECHNICAL AERODYNAMICS

20-3

ballistic missile

as the intercontinental

(Fig .

azine for March 7 , 1955 these

will

airplane

unmanned

sile ) is

shown in

are

opment

shown

in

are

are

process of development

and

.

in Fig .

shown

20 : 1 ,

a super

as a surface - to -air guided

classified

(also

Mag

to intercept

supersonic piloted airplanes

Typical sonic

20 : 5 ) ,

difficult

be extremely

in Life

( " IEM" ) described

Fig . 20 : 2 . Anti -aircraft rockets currently in Figs . 20 : 3 and 20 : 4 .

mis

under devel

Fig . 20 : 4 . Sperry " Sparrow " air- to -air anti - aircraft rocket . Data ( Cour tesy Aero . Digest , March 1955 ) : span 2 ft 3 in . , length 8 ft 3 in . , dia Propulsion : solid propellant rocket . Per meter 6 in . , weight 280 lb. Guidance : beam rider , semi - active homing . formance : M = 3 range 5 miles . 20 : 2 .

PERFORMANCE

OF

for supersonic aircraft ,

in

the

Chapter 18.

In

be made

same manner

essence ,

AIRCRAFT . Performance calculations piloted airplanes or guided missiles , may as for subsonic jet airplanes , as outlined in

SUPERSONIC

whether

this

flight

is to

method

and weight at each of a sequence

of

times

position from the vector This is = Rg W , where R is the vector resultant force . conveniently done by analysing the vector acceleration a into

path determining each succeeding

most

components

path , where

/

time and

/

acceleration

usually

/

at along the flight path and an = v2 r normal to the flight r is the radius of curvature of the flight path , and at =

/

dv dt = vdv ds , s being distance . along the

It is

drag

if

in

lift

, drag , thrust , or positions along the intended

estimate the

also customary terms

, as

frontal area of the Many supersonic

wings .

If

body , the

missiles

path .

for subsonic airplanes

of coefficients

the missile has

flight

CL and CD

the wing

frontal

have no

,

respectively area

is

to think of , based

lift

and

on wing area

small compared with the

body area may be used instead . wings

( for example

,

Fig .

1 : 7c ) ,

es

pecially if they are intended primarily for vertical flight or for flight chiefly in the remote stratosphere . For flight at M = 2 and higher , most missile bodies will support their weight in horizontal flight with a small

ft

,

-

,

Magazine for Life from sketch as copied vehicle ballistic of intercontinental configuration is assumed to rocket primary Underhill The Garrett and Earley by John on calculations based Ramus by Michael 37 burning after altitude at 38,000 each wing are dropped under rockets the booster thrust 60,000 lbs have Inc. Time Ramus and Life of Michael permission with Reproduced mph seconds top speed 10,600 Possible

20

Possible

.5: .

Fig

MISSILE PERFORMANCE

20-4

.

.

,

;

.

20-5

TECHNICAL AERODYNAMICS

angle of attack on the body

, but

control

or guidance

to hold the body at the necessary angle of attack

aft

guidance

fins

is

chiefly

determined

flight .

As

for airplanes

from the intended take

must

be provided

as well as typical shift of

, and forward

necessary to provide for the

may be

the center of gravity during area

fins

-off

,

the necessary wing or launching condi

tions . Some

in

data

Chapters

wind

,

and

lift

respectively

10 and 14 ,

ference effects

special

the drag

on

The

.

especially that

tunnel tests

of missile wings and bodies

difficulty

of estimating

of the wing on the body

, has been noted

in

are given

Chapter

14.

lift ,

One

inter without

of the best

available unclassified collections of supersonic drag and lift data on (1 ) and bodies is that of Hoerner . Supersonic missiles and airplanes are usually powered by rockets , ram jets (with rockets to boost up to design Mach number ) , or turbojets ( with

wings

afterburners

, or sometimes

rockets

,

to boost through

the " sonic barrier " ) .

in

Selection of the best power plant for a given speed and range usually

trial

volves many repeated

calculations ,

as the

flight

path

as

well

the power plant and body must be optimized .

/

high - speed analogue Some

,

of use for preliminary design are presented by In general , rockets are good for only a few seconds or min

utes of propulsion

"

" IBM

(Fig .

region of about

of several

25

only a few miles of powered flight ; the long range : 5 ) comes from the glide back to earth from high

and 20

titudes with several

al

off the lower atmosphere in the shown in Fig . 20 : 6 . Ramjet vehicles

" skips " or " bounces "

miles altitude

hundred miles range ,

terburning turbojet

iseing

digital

generalizations

(2 ) Sutton . of the

and or

as

For reasonably quick answers computing machines are necessary .

,

as

like

Fig

The af 20 : 2 , appear feasible . currently is considered a most prom pilotless aircraft at speeds near the .

( or turbo - ramjet )

power plant for long range " thermal barrier " between M 2 and M = 3. Accurate this region are usually security classified .

power plant data

Distributed by ( 1)Hoerner , Sighard F. " Aerodynamic Drag , " 1951. 1951 . thor in 1955 from 148 Busteed , Midland Park , N. J. (2 )Sutton , George P. " Rocket Propulsion Elements , " Wiley , 1949 .

in

au

20

flight Possible permission with Reproduced of March Magazine from Life

Fig

. of

of

artist 1955.

path

NEWYORK

:

GALAPAGOS IS

FLIGHTPATH

BOMB RELEASE ALTITUDE37 MILES

85 MILES

)

intercontinental Ramus Michael

ballistic Life

95 MILES

and

25 MILES

Time

-

vehicle Inc.

25 MILES

LENINGRAD

POWEROFF 38 MILES

113 MILES

MISSILE PERFORMANCE

20-6

., ,

.6: . 7

,

(

CHAPTER

21

STABILITY AND CONTROL

21 : 1 .

STABILITY

ered

to

trols

, can make the

have

AND CONTROL

CONCEPTS .

satisfactory control airplane

take

It is

if

is usually consid

An airplane

the pilot

off , fly in

by manipulating the con

,

any desired

if

direction

, and

, when the pilot said to have satisfactory stability airplane , releases the controls the maintains a condition of steady flight .

land safely .

is

An airplane when

it is

stable

if it is

from a condition of steady

,

said to be statically

disturbed

that ,

forces are devel

it

cally stable successively smaller and smaller An airplane

so designed

to that condition . It is said to be dynami – the oscillations in returning to the stable condition are

oped that tend to return

if

flight

need not be

flyable , provided that

.

statically

or dynamically stable in order to be

is satisfactory . In general , the more is , the less sensitive it is to the controls ; some mil itary airplanes are purposely made marginally stable or slightly unstable the control

stable an airplane

pri

in

order to increase their maneuverability . A commercial airplane for vate pilots should probably be made statically and dynamically stable , in the interest of safety ; but a commercial airliner , intended to be flown by professional pilots and equipped with

sibly

be unstable

in the free - control condition

exists . Satisfactory design

stability

an automatic

procedure

for

an airplane

pilot ,

as

may

quite permis

this condition rarely

requires

that

the con

while the airplane design is still in preliminary stage , the and that the preliminary calculation of stability and control be thoroughly verified by wind tunnel tests before the design

trol

and

be investigated

has progressed so

far that changes in the control surfaces are expensive . chapter This deals with such preliminary calculations . The calculations here given are limited to aerodynamic calculations on a body structure as sumed to be perfectly rigid and containing no partially filled fuel tanks .

Partially filled tanks noses down the

are a destabilizing influence

fuel flows to the front of 21-1

, as when

the airplane

the tank and exerts an additional

STABILITY nosing

flexible

moment ;

down

21-2

AND CONTROL

undergo

structures

changes

in

shape under

load which are often destabilizing . This field of calculations , known aero - elasticity , is neglected in the present chapter for simplicity can not be neglected in practice

as but

.

In general , rigid airplanes with full fuel tanks and conventional con figurations , if statically stable , are also dynamically stable . This chap ter will be limited chiefly to static stability calculations . 21 : 2 .

bility

AXES , ANGLES , AND COEFFICIENTS .

is

calculations

systematic

,

in Fig

shown

.

Conventional notation for

sta

This notation is logical

and

21 : 1 .

though often confusing because

of the use of the symbol L for

Positive directions of axes and angles (forces and moments) are shown by arrows Angle

)

Roll Pitch Yaw

relative

neutral

gbS

yawing

.

)

.

Conventional notation for stability calculations of back cover of all NACA reports

Found inside

)

surface

.

control

Indicate surface by proper subscript

(

of

of

X

to

Y

Angle set position

Linear Symcompo- Angular bol nent along axis

.

Z

Z

---

Y

X

Designation

)

(

: 1 .

)

21

.

Fig

CN (

qcS

pitching

)

=

qbS rolling

(

moment

M Cm=

(

C₁ =

L

Positive direction

), 8.

247

244

Absolute coefficients

Rolling Pitching Yawing

. . ..

X

Longitudinal Lateral Normal

LMN

)

( Sym bol

Designation

Velocities

(

Moment about axis Force parallel to axis Sym symbol Designation bol

(

Axis

TECHNICAL AERODYNAMICS

21-3 nearly

because

all

analyses are expressed

rather than the moments many persons find them

If

the X -axis

is

is called

in

terms

the coefficients

of

the coefficients are not

ambiguous , though

difficult to memorize . in Fig . 21 : 1 is the longitudinal axis of the air of axes shown is called " body axes . " If the X - axis

shown

plane , the system shown

, and

the direction of the remote wind velocity , the axis system shown "wind axes . "1 Wind axes will be used in this chapter because

most wind tunnel data are presented

in this

form and the explanations

are

simpler in terms of wind axes .

It is

to simplify the stability

customary

sidering separately

( a ) motions

in

the plane

problem

and control

by con

of symmetry of the airplane

are treated under the heading of " longitudinal stability , " (b ) mo tions relative to the plane of symmetry which are treated under the head ings : directional stability and control ( yawing ) , and lateral stability

which

control

and

21 : 3 .

( rolling ) .

STATIC LONGITUDINAL STABILITY .

The physical

and

mathematical

for statical longitudinal stability is that increases in angle of attack result in changes of moments of air forces about the center of gravity which tend to decrease the angle of attack . The starting condition

condition

for such calculations must be the condition of balanced flight . A wing flying alone , without body or tail , will be stable or unstable in balanced

flight

depending

on

airfoil

the shape of the

section and the corresponding

position of the center of gravity ( c.g. ) relative to the aerodynamic center ( a.c. ) for balance . A conventional wing , such as a 4- or 5 - digit series or 6 - series section , is longitudinally unstable starting from a balanced

flight

condition

,

as shown

in

Fig

.

21 : 2 , because

the c.g.

must

be behind

LIE Ma.c. a.c.

Relative wind

W, balanced byL2

Fig

. 21 : 2 .

Wing with negative Cmac ;

c.g. aft of a.c. for balance ; longi tudinally unstable .

a.c.

OC.G

Relative wind

Mac. W, balanced byL2

Fig . 21 : 3 . Wing with positive Cmaci c.g. ahead of a.c. for balance ; lon gitudinally stable .

STABILITY

the a.c. for balance

as

balanced condition

= L2 )

creased nosing -up

If ,

(L

moment

21 : 3 , and

is

which

in

increases

stable

can not be equipped

edge , as

must

in Fig .

.

tail

surface .

The simple addition

of a

therefore for given

Hence ,

wing area than an

This simple consideration

uneconomical

surface and fuselage

therefore have a

21 : 3 , and

flap - type high - lift devices .

speed , a " flying wing " must have much more

tail

in

(L =

wing " airplane

trailing

makes a "flying wing " airplane a

attack from the

angle of attack result in increased diving

A " flying

.

with

plane with a separate

with

of

L3) results in an about the center of gravity , which is unstable

wing section with swept - up

stalling

lift

to a higher

section has a swept -up trailing edge , as in Fig . flight condition is with c.g ahead of a.c. , as shown

21 : 3 , the balanced

in Fig .

An increased angle

shown .

airfoil

however , the

moment

21-4

AND CONTROL

air

usually

as compared with an airplane

.

tail

surface

does not make an

, however ,

air

This is seen in Fig . 21 : 4 , in which the " tail . "wing area , " resulting in a " tandem monoplane . "

plane longitudinally stable area " is

Fig . with

equal to the

made

C.G.

Tandem monoplane two symmetrical wings of equal incidence ; c.g. mid way between a.c.'s for bal ance ; neutrally stable . 21 : 4 .

Relative wind

Relative wind

F W ‫ت‬

Fig

Tandem monoplane symmetrical wings with wing at lower incidence ;

. 21 : 5 .

C.G.

of two

Relative wind

rear c.g. nearer to front a.c .; stable

k

.

Relative wind d,

d2

W

The wings shown are symmetrical

- section

for simplicity . If the incidence of the of gravity must be midway between the two and changes

in

two wings

is the

aerodynamic

same ,

moment

the center

centers for balance ,

of attack result in no changes in pitching neutrally is stable . This combination can be

angle

so the combination

ble ,

zero pitching

wings with

moments , made

sta

however , by moving the c.g. forward and setting

incidence

, as

shown

of attack increases

in Fig .

21 : 5 .

an equal amount

rear wing at a smaller arrangement , when the angle For this on both wings , the percentage

increase

TECHNICAL AERODYNAMICS

21-5 on the rear wing

is

greater

,

and

the pitching

gravity changes so as to produce a net diving

will

of

the principle , in

that

reduce

This arrangement is therefore stable and , the arrangement used in all present day airplanes , though the rear wing

angle of attack .

is

center

about the

moment moment

is usually of gravity

made

substantially smaller

location

farther forward is

even

stability is thus

tudinal

than the

front

wing so that a

required for balance

.

center

Longi

horizontal location of c.g. in glider flight were killed principle . This principle is

seen to depend on the

for satisfactory balance .

Many experimenters

failure to discover this elementary equally valid whether the larger surface is the forward surface or the surface , though only a few airplanes have been built with the smaller through

face forward

( for example ,

stability relationships

the Naugle

1 : 5e ) .

sur

Static

here only for the conventional case

are developed

with the wing ahead of the

in Fig .

N - 6 shown

rear

stabilizing

and control

surface , but the same

can be used to develop relationships for the " tail first " or "canard " type of airplane . The static longitudinal stability is also seen in Fig . 21 : 6 to depend on the vertical c.g. location . With the center of procedure

L24

Zerolift chord

D

Mac 1 ZC

Relative wind

C.G. -XC

W

Fig .

Effect of vertical c.g. location on stability .

21 : 6 .

gravity

located

some

distance below

Fig .

Sketch for calculating 21 : 7 . moments of wing forces about a c.g.

of arbitrary location

the aerodynamic

.

center , an increase

in angle of attack causes a diving moment of the lift force about the center of gravity . This wing arrangement was first developed by Spratt of Coatesville , Pennsylvania , about the time of the Wright brothers ' first flight , but does not usually lend itself to efficient aerodynamic design and

is

accordingly seldom used .

For the general a.c. and zc below

case where the c.g.

it

( Fig .

21 : 7 ) ,

is

located

the equation

a

for

distance xc aft of the moments of the aero

STABILITY

center of gravity

dynamic forces above the

- c²/ m)

Cmw = xCL + z (CD

For

airplane

for

wings

good , equation

which

m

is the

for

Cm

CD = CDo min +

/ - 1/m)

lift - curve - slope per radian for

may be considered as

( 21

zc (( 1 Ae min + zcz

CHW = xCL + zCDo

in

effects ,

and

Millikan

= 0.02

to 0.04

A (a.c. ) 2 nacelles

= 0.025

are

methods

Equation

,

( 21 : 2 )

results

values of

(1 ) are

.

to be usu

addition

fuse

(21 : 3 )

to 0.045

for estimating part

available

the fuselage effect

( 21 : 2 )

nacelles to the wing appears

as given by

▲ (a.c. ) fus

Theoretical

: 1)

the center of gravity

ally satisfactorily accounted for by assuming that such in a forward movement of the aerodynamic center . Typical and nacelle

,

c² /TAе is

+ Cmac

the wing .

the wing alone about

The effect of adding fuselage

lage

of attack

written

may be

( 21 : 1 )

angles

+ Cmac

approximation

the

which

for small

,

is

to coefficient form

converted

21-6

AND CONTROL

but

not

all of

since the wing fuselage interference is hardly suscep tible to mathematical analysis . ( a.c. ) ' is the effective aerodynamic taking fuselage center location account of and nacelle effects ,

If

I

(a.c. )

Hence , equation ( 21 : 2 )

if

is

the center of gravity

(a.c.

' =

( a.c. ) wing

applicable location

) wing , and Cmw may be called

· A (a.c. )

(21 : 4 )

to a wing with fuselage and nacelles

is

x

measured from

( a.c.

) ' instead of

Cmwfn '

4F+

Fig .

21 : 8 .

Sketch

€

Windbehind wing

·It' illustrating

relationship for

wing

C.G.

downwash and

Wind

aheadof

Downwash angle

and angle

horizontal

wing

of attack

tail .

With the horizontal tail behind the wing , as shown in Fig . pitching moment coefficient for the tail may be written Cmt

( 1 ) Millikan p. 149 .

,

Clark B.

,

=

at at

21 : 8 ,

at St t

" Aerodynamics

of the Airplane

the

( 21 : 5 ) , "

Wiley ,

1941 ,

TECHNICAL AERODYNAMICS

21-7 where the subscript

( ) t denotes conditions at the horizontal tail . Since the angle of attack on the tail surface at differs from the angle

effects and

)

6 )

:

: 7 )

(

)

: 8

(

: )9

(

in

as indicated

equations

21

(

21

Static stability requires that an in in or CL be accompanied by re duction in Cm or

stability

=

dCm

a

α

crease

dCL

-0.3

21

Cmt

index

21:10

)

1

en

on the

(

-0.2

Cmwfn

,

nacelle (

° °

CMt

is

coefficient

is the moment coefficient of taking account of fuselage and

the wing

-2

-3

21

where Cmwfn

: 3

° .

-1

= 0)

is

=

Cm

Cuwfn

CM -0.1

(ig

moment

airplane

+0.1

S -0

( 0 )

A resultant

tire

21

+

Ε

ε

( ·

-CL at 1t at St (1

Cmt = +0.2

21

to give

( 21 : 7 ) may be combined

and

in

write

· ig

18

/α

-

lift

the stabilizer

chord , we may

/

: 5)

=

1

at/a

·

& and by

: 4 ) .

Equations ( 21

= 0 , becomes

= d

at for ig

which ,

angle

downwash

to the wing zero

ε α )

is relative

=

of attack on the wing a by the cidence

is

,

and 21

complete

airplane

are

shown

:

.

.

: 9 .

21

.

tail Typical plot of Cm vs. CL in Fig a

Fig

,

1.5

a

1.0 CL

.

0.5

9

-041

a

.

negative for positive static longitu dinal stability Typical plots of Cm vs. CL for wing

lifting

+2

)

/

C

/α

(A

2πA

=

and

.

TA

,

According to

/

2C

21:10

,

Fig

.

in =

ε

9 ,

shown

since

with

)

21:11

(

wings

)

elliptic

(

)

+ 2

/

(A

ε

actual wings in the region of typical tail surfaces departures from the theory as indicated in Fig 21:11

made on

.

.

show substantial

,

Measurements

tail is

in radians

/α

and

Ɛ

a

both

wing and

from Chapter ,

of

line theory

= 4

vicinity

a

A

.

Accurate calculation of longitudinal stability is limited chiefly by the accuracy of predetermination of the downwash in the vicinity of the physical picture of the vertical velocity distribution in the tail

STABILITY

21-8

AND CONTROL

CL TAR

Actual

CL TAR

-Theoretical

=

= 9

6 0.2

10.1 0.2 0.2 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Tail length wing span

h / b o

h /b = 0

0.3

Lt

,

/ b

,

%

WING

RECTANGULAR AR

= 9

h / b = 0,

0.1 0.2

0.3

AR

h /b = 0

0.4 018

AR

h /b = 6 = 0

0.5

20.1 0.21 0.2 0.3 0.4 0.5 0.6

= 12

0.4

AR 12

Theory

h /b 0

w18

0.6 0.5

WING

AR

-

0.7

the

.

From

ELLIPTICAL AR

distribution Millikan

)

tail

wing and

.

a

vicinity of

( w

Vertical velocity

21:10

.

.

Fig

0.1 0.2

0.2

0.1 0.2

0

0.1

/

AR

-

9

= 6

AR

h /b = 0 .

0.6

h / b = 0

-0.11

0.4

-0.1

-0.2

0.3

th /b = 0⋅

0.5

w18

TAPER WING

AR

0.7

= 12

2 : 1

,

, Lt b

%

0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Tail length wing span

. ,

.op

,

B.

,

cit

/

(

.

144

and tapered

NACA TR 648.

)

rectangular From surfaces ,

tail

,

b

elliptical

.

behind

p .

Downwash

the region of typical C.

in

Millikan

)

1

(

21:11

.

.

Fig

wings

,

, %

0.1 -0.2 0.2 0.2 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Tail length wing span Lt

21-9

ratio of

The

is

TECHNICAL AERODYNAMICS

at

/

to be unity unless the horizontal tail

a may be assumed

located partially in the

of the wing

wake

in

,

which

graphs

case

for

/q are available in NACA TR 648 and elsewhere . Propeller slipstreams , if any , have a destabilizing effect difficult (1 ) The ef to calculate but explained in some detail in Perkins and Hage . fect of releasing the elevator so that it floats free ( " free - elevator " ) is also destabilizing . Flap and stabilizer positions usually have minor estimating at

is stabilizing

though proximity to the ground

effects ,

cussion of these factors see

(2 ) Perkins and Hage . 21 : 4 .

STABILITY .

STATIC DIRECTIONAL

right (or

is

,

fuselage

, and

tail

as shown

produce

field ,

an airplane

When

sideslipping to the left ) ,

forces on the wing

For further

.

extensive works in this

more

in Fig .

a moment

is

dis

such as

yawed to the

21:12 , the

air

the airplane

N on

.

in flight

is tunnel tests distinction is made between the angle y referred to an arbitrary time t * 0 , and the sideslip angle , more often designated by B. The yaw Fig arbitrary positive , , and moment directions shown in . 21:12 are the

The angle of yaw

tests

designated y in wind

,

though

a

values of the

NACA

in Fig

conventional notation shown in

Fig .

as the angle of yaw

Wind

is

. 21 : 1 .

if the

21:12 ,

w

With the directions moment

increases

,

N decreases

the airplane

said to have positive static

directional Static directional stability is usually obtained from the results of wind tunnel tests by plotting yawing moment coef

stability .

ficient

Cn vs.

angle of yaw y , defining Ca

by the equation Cn =

Fig .

Yawing moment on airplane at angle of yaw . 21:12 .

In Fig . vs.

stability ;

W

N qbs

positive slope of Ca vertical tail indicates

21:13 , the

without a

(21:12 )

in

with the vertical tail the negative slope indicates stability . Tests are also usually run with various fixed rudder angles and with free rudder . Note that with fixed rudder angle , the effect of rudder displace ment

is

,

to displace the yawing

( 1 ) Perkins ,

(2)Ibid .

C. D. and R. E.

moment

Hage ,

curves

op .

cit . ,

vertically without changing p.

231 .

STABILITY

stability

over the fixed rudder condition .

coefficient angle ,

-0.1

as implied by the equation

Cnf

Cn

indicated by the slope of the yawing

dy

The yawing

moment

slope due

slope Cnfy

to fuselage

may be analysed

location on the length of the fuselage plus propeller interference designated respectively ,

increments

an angle of

due to wing and

sidewash

,

by analogy

)

21:15

with the similar

written

av 2v By

av

ACny props

analogous

21:16

to the

)

+

,

may be

"

is

vertical tail

)

the

tail

0

for

the horizontal

Cavy where

basic

of gravity

ACny wing and ACny props

ACny wing

-

The yawing moment slope

Cnfy basic

(1

#

=

Cnfy

effect of

into

by the center

by the equation

, "

as indicated

21:14

Cnvy

principally

determined

,

moment

coefficient

)

+

dcn = Cny = Cnfy

yawing

moment

written for simplicity

,

which

may be

(

yaw ,

a

stability is

vs. angle of

(21:13 )

Cav

(

The

10

trol

components due to fuse

tail ,

lage and

20

yaw

Fig 21:13 Typical wind tunnel test plot of directional stability and con

coefficient into

moment

Angle

(

two major

to analyse

customary

-10

.

the yawing

mo

W =

it is

ments ,

Cn -0.2 -20

.

in

the case of pitching

0

control . As

10

directional

a measure of

Ly

and are

Rudder +10 Rudder Rudder

°0

a given rudder

be held by

can

-

moment

angle of yaw that

show the

of

zero yawing

yawing

of

Withoutvertical tail

Rudderfree

moment

fixed The intersections of the rudder angle lines with the axis

.

rudder float

reduction in the

a

0.2

free , however ,

+

is

let

effect of

The

10

ting the

coefficient

the stability .

21-10

AND CONTROL

downwash

angle

in

the

.

( )

158

.

p

.

cit

. ,

.op

,

C.

B.

,

Millikan

)

(

1

,

,

longitudinal stability calculations and denotes vertical tail Millikan (1 ) states that Galcit tests show values of -Cay in the range

21-11

TECHNICAL AERODYNAMICS

to 0.0015 tobe desirable .

from 0.0007

(W/ S ) , which gives the same loading W/ S of 14 to 30 lb / ft² .

as 0.00005

for

1) Diehl ( states a desirable value results as Millikan's recommendation (2 ) suggests

wing

Perkins

a desirable

value of Cny = 0.0005 (w/ b² ) 1/2 . The suggestions of Diehl and Perkins take account of the fact that the wing makes only a minor contribution to

stability ,

the directional

coefficient

but the wing span appears

The conditions

.

which must

rectional control are discussed in

be

the yawing

moment

fulfilled for satisfactory

di (3) related design textbook .

the author's 21

in

: 5.

LATERAL STABILITY .

is

an airplane

When

in

yawed , as

21:12 , the side wind component

erts not only a calculated in Art

rolling

a

21:14 .

cient

is

C1

& Fig .

21:14 . component

angle

where

is

Effects of side

rolling

on

L

rolling

seen moment

is

in

also Fig .

coeffi

defined by the equation

the

(21:17 )

rolling

moment

and

nearly proportional to the angle

of yaw

wind

position of the

The slope dC₁ / dw = Clw

W.

depends

moments .

, but also on the

but

21 : 4 ,

.

C1 = ci - qbs

Wind

ex

yawing moment as

as

moment

The

Fig .

chiefly

on

dihedral

the

fuselage and the

wing on the

vertical position of the vertical tail relative to the fuselage center line . These effects are indicated by the equation C1y = The

relationship

If

+

0.00025°

(21:18 )

the lateral stability of has excessive vertical tail area and small

the airplane

.

dihedral

a

sideslip

may

be

spirally

unstable

said to

=0

between Cly and Cny determines

the airplane ,

C1r

excessive dihedral

result in .

and marginal

If

,

a on

spiral dive . the

cit . ,

airplane is

airplane sideslip to

hand , the

directional stability ,

( 1 ) Diehl , W. S. , op . cit . , p . 204 . C. D. and R. E. Hage , op .

( 2 ) Perkins ,

other

Such an

a

p . 326 .

K. " Airplane Design , " Tenth Edition . Distributed University Bookstore , Boulder , Colorado . Eleventh edition to be buted in 1956 by Ulrich's Book Store of Ann Arbor , Michigan . ( 3) Wood ,

D. ,

has

the

by the

distri

STABILITY

right will which

slip

movement

is

followed by a

right ,

yaw .

in Fig

sketched

lateral

stability .

roll

and

roll . "

An

types of

two

in

directional

The rate of

yaw and

rate

also affect both yawing and

rolling moments

.

eral

is left

dynamics

vanced

21:15 ,

.

carefully propor

must be

tioned to avoid these combined

resulting

The

described as a " Dutch

airplane

of

left , left side

cause yawing to the

may be

and

21-12

AND CONTROL

texts

21 : 6 .

Calculation of to

lat ad

more

Fig .

.

CONTROL

sonic airplane

CHARACTERISTICS .

SURFACE

are usually

movable

constitute the rear portion of as ailerons , elevators

an

flaps

21:15 . Dutch roll lateral directional instability . The

control surfaces of

sub

a

in their neutral position , Such flaps may be designated

which ,

airfoil .

, depending on whether they control the longitudinal , lateral , or vertical axis of the air plane , respectively . In order to make calculations on the control of an airplane , it is necessary to know the aerodynamic characteristics ( lift , movements

,

or rudders

about the

drag , and pitching moment ) of such hinged surfaces . The control forces necessary to move such hinged surfaces depend on the moment of the aero dynamic forces about the hinge axis ; thus , studies of control also involve the aerodynamic hinge moment of the movable surface , designated by Hp . The control surfaces are often modified by means of a tab that constitutes a portion of the trailing surface

,

ventional

flap

, and tab ,

edge

is

of the flap .

shown

in Fig .

notation as to dimensions

,

A typical combination of fixed

21:16 , which

angles , forces

,

also shows the

con

and moments .

N

D wind Relative direction

Fig .

21:16 .

d cf--

.=

-a.c

Forces , moments , angles , and dimensions surface with movable flap and tab .

of

a

control

TECHNICAL AERODYNAMICS

21-13

At high subsonic speeds fectiveness

because

,

such

control surfaces lose

of local shock

much

ef

of their

At supersonic speeds

formation .

wave

they are almost completely ineffective and " all movable " control surfaces are necessary . Effects of Mach number on control are treated separately in the next article , the present article being limited to low speed con

trol effects . The usual

coefficients

of hinge surfaces

characteristics

used to describe the aerodynamic

such as those

in Fig .

shown

21:16 are

=

N qs

or

cnc = acc

( 21:19 )

CDC =

D q8

ΟΙ

Cdc

(21:20 )

ΟΙ

CMC =

CNC

Cmc =

CHI

Mc

qccs Hs

=

or

qcfsf

Chf

qcc

=

( 21:21 )

qcc

hf

(21:22 )

qc+2

in

which the subscript ( ) designates the complete control surface , and the subscript ( ) designates the flap or major movable portion of the surface The

normal

.

flap angle of force

has a major commonly

) , drag ,

pitching

effect only

neglected .

Chf

on the

moment , and

flap hinge

on the

kồ

hinge

lift

( studied

moment .

f)

or

Effects

CNC = ac (α + kƐ

in

terms of

The tab angle

moment .

effects are representable

The other

Cnc = aoc (α Cmc =

effect

has a major

on drag

åt are

by the equations

f)

(21:23 ) ( 21:24 )

-mfdf

= hocne + hộp

+

h8t

( 21:25 )

in which each of the coefficients k , mf , ho , hi , and h , is an influence coefficient representable also as a partial differential equation , such as aock

=

cnc

adf

(21:26 ) α =

const

Values of each of these coefficients can be developed rationally in terms of lifting line theory for infinite aspect ratio control surfaces , but such calculations

flight

are

not of

much

value because actual

wind

tunnel

and

tests rather widely from the theoretical calculations . The agreement with theory is fair in the case of the coefficient k in equation depart

STABILITY

21-14

AND CONTROL

I

1.0

IGA

% C

= C

k :

Definition of Сn aoα αok8f

C °6α 0,4

1.0

C

Noses

for

A

0.9

10

0

0.2

420

0.3

8

k k Cf c -/ 04

71 actual theory

‫نا‬

0.5

256

(=k

Gap0.457.c

+

)-

0.6

=

const

.

% C

. ik actual

0.7

Gap0.45 -

k

theory

0.8

-

Gap0.45

0.9

Cb %

30

0

0.1 0.2

0.4

0.3

0.5 Cf

0.6

0.7

0.8

0.9

1.0

/C

E =

0

0.1

.

surfaces

From NACA TR 721.

)

hinged

(

Lift of

.

21:17

.

.

Fig

0.012

Const

=

0.006 0.004 0.002

0.3

0.4

Cf

as seen

in Fig

Pitching

moment of hinged From NACA TR 721.

(

and also

21:17

,

.

,

)

(

21:23

0.8

0.7

0.9

1.0

surfaces

)

21:18

.

.

Fig

0.6

0.5

.

0.2

/C

0.1

E =

0

36

Actual

/

)(

Definition of Cm -mf8f

0.008

:m

Theory

0.010

for the pitching

moment

influence

.

,

.

,

,

in

.

as seen

h,

,

mf

.

Fig 21:18 The hinge moment parameters desig subscripts nated with various are seen in Figs 21:19 21:20 and 21:21 to depart rather widely from lifting line infinite aspect ratio theory

coefficient

"

.

"

"

"

Calculations intended to verify wind tunnel or flight test results should evidently use the graphs labeled actual rather than theory for studying these relationships is to develop the free elevator factor Fe shown in Fig 21:22 since this factor can be applied to pitching- or yawing moment calculations with fixed surfaces corresponding to zero hinge moment to get the free control stability ,

-

"

"

.

conditions

,

of the major reasons

.

One

TECHNICAL AERODYNAMICS

21-15

-0.24 Actual

-0.024 -0.022 -0.020

-0.22 -0.20

Theory

-0.18

.

-6

(

-0.012 Definition andho cho hộp Chỉ

-0.008 -0.006

-0.10= ho

cn of h

-0.010

och

-0.12 Theory

Actual

= h

-0.14

-0.014

h .

c₂

.

-0.16

const

-

no

const

-0.018

-0.016

-0.08 -0.06

. 9 : 4

SeeFig forbalanceeffect at 0.40

-0.04

E =

-0.004

-0.02

0

-0.002 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

E =

0

0.1

====

for

sealed hinged

balance

+

0.003 0.002

GAPEFFECT ON ++ Nose 0.20.40.60.8 Gap% C

0

FLAP NOSES

)

(

.

Gap 0.005 0.004

A+

surfaces

From NACA TR 721.

L

IIIC

without aerodynamic

h B + C

Hinge moment

21:19

.

.

Fig

0.016

. 9 : or 2, E = '

No gap balance FromFig 0.40

0.014

0.10 0.08

0.012

ho

10.06

0.010

-ho 10.04

-h 14

0.008

0.02

0.006

0

Th

0.004

0

0.002

/

=

0

±

c .

=

%

)

h

,

,

E

.

;

.

moment

E.

(

.

0.04 From

Effect of aerodynamic balance and gap on parameters in Fig 21:19 0.40 for Curves for ho and are for gap 0.5 JAS April 1945. Root

21:20

L.

.

Fig

hinge

0.30

0.10 0.20 Per centbalance Cb Cf

STABILITY

21-16

AND CONTROL

-0.022

/

-0.016

0.10 0.3

-0.014 -0.012

Theory

CTABCFLAP0.2

/

-0.010 10.1

-0.008

+ h, h 8t ,:

ach hoc

) (

and

of

0.20 -CTABCFLAP

-0.018

N

const

.

0:30 -0.020

Definition of hocn+ hôf Ch = +

-0.006 -0.004

0

0

-0.002 0.1

0.2

0.3

0.5

04

0.6

0.8

0.7

0.9

1.0

21:21

.

.

Fig

full

Effect of

hinge

/C span trim tab on

moments

flap

.

E₁ =

Cf

1.0

9 : 3

2"

"

BASEDON ACTUAL GRAPHSIN FIGS.9: AND

0.9

= 1 + h:

EQUATIONS

0.8

Fe

1 -

hoak

a =

AR t ++ 3

0.11At

0.7

00

0.5

AR + =

Fe

0.6

0.4 0.3 0.2

0

0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Free elevator factor for tail surfaces without aerodynamic balance or gap

21:22

.

.

.

Fig

/C

E =

Cf

TECHNICAL AERODYNAMICS

21-17 21 : 7 .

in

outlined slope with number

ical

Chapter

Mach number

surface flap

lift is

also indicate a

lift - coefficient

with

more

is

due

to incipient

deflected

,

the

lift

seriously limited

reduction

marked

-off in

a major drop

, and

airfoils in lift - curve in critical Mach

subsonic effects

while they show a minor increase

10 ,

number ,

Mach

The high

AT HIGH SPEED .

CONTROL

lift

beyond the

shock wave formation .

coefficient increases

on

crit

When a control , but the maximum

the higher the Mach number .

A high speed

is accordingly likely to " run out of control " before the level is reached , and control limits are nearly always reached in a high speed dive . Such limits have resulted in numerous casualties in the development of high speed aircraft , because of inability of the pilot to airplane

high speed

pull out of

a dive .

this

for

to be developed

case ; the development

(1 ) described by Sibert .

For control of supersonic aircraft most completely

little

effect

istics

may be

21 : 8 .

eral

ineffective

because

of

calculated

STABILITY

stability

as

Gessow and Myers .

(3)

It is

controls is well

al

flap - type control surfaces are trailing edge flap movements have

must be "

OF HELICOPTERS .

have had

,

all

for supersonic

of helicopters

controls

such

on surface pressures ahead of the hinge

surfaces for such aircraft

control

longitudinal

Special supplementary

line .

movable " ;

in

wings

Accordingly

their character

Chapter

10 .

The problem of longitudinal

treated by

has been well

pointed out

in

,

Doumasch

and

(2 )

lat

and by

these references that current

with low c.g. and teetering or flapping rotor have neutral static longitudinal and lateral stability in hover

conventional helicopters

,

blades , ing , have " stability with speed " associated with

" cone blow- back due to with angle of attack . " Dommasch points out that satisfactory handling qualities , as regards control position and

flapping

, " and have " instability

control force stability , are attainable

ity

with angle of attack

pitch controls

.

,

in spite of the natural instabil taking account of the usual collective and cyclic

However , neither

author considers specifically

fects of vertical c.g. position with rigid rotor blades , ( 1) Sibert , H.

Chapter 26 . (2 ) p

W. ,

" High

Speed Aerodynamics

, "

Prentice

- Hall , Inc. ,

Dommasch , Daniel O. , " Elements of Propeller and Helicopter Chapter 6 . namics , " Pitman Publishing Corp. , N. Y. , 1953. ( 3 ) Gessow ,

Alfred

and Garry

copter , " The Macmillan

C. Myers , Jr. , " Aerodynamics Y. , 1952. Chapter 11 .

Company , N.

the

ef

which has recently

1948 .

Aerody

of the

Heli

STABILITY become important through

similar to Fig 21:23 .

.

the development

of

a number of small helicopters

effects are considered specifically in Fig .

These

17 : 2 .

21-18

AND CONTROL

Rel . Wind

Do Rel . Wind

Rel . Wind

a . Rotor tilted from hovering ; neutral sta bility regardless of

verticalc.g . position .

Advancing

b.

rotor ;

blade forces stabili zing ; body forces de stabilizing for low body ,

stabilizing for

high body

c.

Tilting rotor .

Blade

forces more destabiliz ing with increasing rate , regardless of of vertical c.g. position .

tilt

.

Fig . 21:23 . Sketches illustrating effect of c.g. position relative to rotor on static longitudinal or lateral stability of a helicopter . Note that net effect of high c.g. is increased stability , ( more stability with speed , no reduction

of

instability

with angle of attack ) .

Figure

21 : 23a indicates that a hovering helicopter , when tilted from the normal vertical axis position , is acted on by no forces tending to up

it

set or to right it and regardless of the vertical

therefore considered to be neutrally stable c.g. position . A man standing or sitting on

is

top of such a rotor can right it by minor and natural shifts of his weight . Fig . 21 : 23b indicates that when the helicopter starts moving sidewise or forward , the rotor is acted on by a righting moment even though the blades do not

flap

this effect is substantiated by tests on rigid propellers (1 The effect of body position relative to rotor is yaw . 21 : 23b to be stabilizing for bodies above the rotor and de

and

at large angles of

)

in Fig . stabilizing for bodies below the rotor . Accordingly , the arrangement with the body above the rotor is more favorable from this point of view , and a helicopter designed by Th . von Karman about 1916 ( photograph included in seen

(1 )

See NACA TN 3228 , p . 47 .

TECHNICAL AERODYNAMICS

21-19

(1 ) ) had this configuration . sketch of Gregory

the historical

bility

( or rate of tilt ) is indicated to be unaffected by vertical c.g. position .

due to angle of attack

While these considerations

, they are indicative of some promise small one -man helicopters of the sort sketched

Fig .

21:24 .

Possible

type

blade

it only

in the

trailing

insta 21 :

23c

heli

for future development of in Fig . 21:24 , which elim

arrangement of one - man " flying motorcycle " ( composite photograph ) .

of helicopter

inates the complicated tains

.

for large

are not of major importance

copters

in

The

Fig

and

expensive

embryonic

cyclic pitch control

( or at most

form of small solenoid - operated

edges to produce

tabs

cyclic twisting of the blade )

on

re the

.

PROBLEMS 21 : 1 . Given the data below for an airplane similar to the Ercoupe , ( a ) estimate the a . c . location for the wing and fuselage , ( b ) write an equa tion for Cmwf in terms of CL and numerical coefficients , ( c ) write an equa tion for Cmt in terms of CL and numerical coefficients for is = 0 and fixed elevators , ( d ) plot the equations of parts ( b ) and ( c ) like Fig . 21 : 9 , and ( e ) find the farthest aft location of c.g. for positive static stability . Wing data : S := 142.6 ft² , b = 30 ft , rectangular 4412 section . Fuselage data : assume A ( a.c. ) = 0.03 due to fuselage . Tail data : 1t = 14 ft , St = 19.6 ft² , At = 4 . c.g .: 0.3c aft of leading edge , 0.02c above zero chord . Downwash and wake : assume = 0.35a and at = q .

lift

21 : 2 . Find the same items as in Prob . 1 , but use the following data , which apply to an airplane like the Lockheed Constellation .

( 1 ) Gregory , Colonel H. F. , " Anything a Horse Helicopter , " Reynal and Hitchcock , N. Y. , 1944 .

Can

Do ; The

Story of the

STABILITY

lbs ft2 , b = assume (a.c. )

Gross weight = 86,250 Wing data : S = 1,650

21-20

AND CONTROL

123

ft ,

tapered

3:1,

23018-09 wing .

Fuselage data : = 0.04 for fuselage , 4 ( a.c .) = 0.06 = Tail data : 45 ft , St = 347.3 ft² , Sf = 106.8 ft² , At = 3.6 , elevator balance = 25% elevator chord ; gap = 0.005c . Center of gravity location : 0.22c aft of leading edge of geometric mean chord ; vertical location assumed to be exactly on the zero

It

lift

chord . and wing wake : assume ε = 0.30a and at = q . Trim speed = 150 mph . 21 : 3 . For the Ercoupe airplane , the total horizontal - tail area is 19.6 sq ft , of which 9.4 sq is elevators . Assuming that the effect Downwash

of

twin vertical

is

no aerodynamic

ft

at the end of the horizontal tail ratio of 4.5 , write equations for CN and

tails

is

to give an

effective aspect Cm in terms of the flap deflection åƒ . 21 : 4 . airplane has The horizontal tail of the Lockheed Constellation a total area of 347.3 sq ft , of which 106.8 sq ft is elevators . Assuming that the effect of the triple vertical tails is to give an effective as pect ratio of 4.0 , write equations for CN and Cm in terms of the flap de flection of . 21 : 5 . A horizontal tail surface similar to that on the Ercoupe air plane has an area of 19.6 sq ft , of which 9.4 sq ft is elevators . The effective aspect ratio is 4.5 , the actual aspect ratio is 4.0 , and there balance on the elevator and no gap between elevator and

stabilizer . Find : (a ) an equation for CH in terms of CN and df ; ( b ) an equation for CH in terms of a and 8f ; ( c ) the free - elevator factor Fei (d ) CH for a = 4 degrees and of = 8 degrees ; ( e ) the elevator hinge moment for the conditions in part d when air of 6,000 ft standard altitude flows by the tail at 80 mph ; ( f ) the control - stick force in part e if the geometry of the control system is as follows : distance from pilot's hands to control - stick pivot = 20 in . , distance from control - stick pivot to elevator cable connection = 4 in . , elevator - horn length from elevator hinge = 3 in . - tail surface similar to that on the Constellation of 347.3 sq ft , of which 206.8 sq ft is elevator . effective aspect ratio is 4.0 , and the actual aspect ratio is 3.6 . A horizontal has an area

21 : 6 .

airplane

The There is an aerodynamic balance on the elevator , with nose shape A , and a gap of 0.005c between the elevator and stabilizer , as in Fig . 21:20 . The elevator balance is 25 per cent of the mean elevator chord . There is a full - span trim tab of 10 per cent of the elevator chord . Find : (a ) an equation for CH in terms of CN , 8f , and 8t ; ( b ) an equation for CN in terms of a , df ; ( c ) the free - elevator factor Fe ; ( d ) CH for a = -2 de grees , & = -15 degrees , and 8t = 5 degrees ; ( e ) Hf for part d at 2,000 standard altitude and an air speed of 80 mph ; ( ) the control - stick force in part e , the geometry of the control system is as follows : distance from pilot's hands to control - column pivot = 36 in . , distance from control- column pivot to elevator cable = 6 in . , elevator - horn length

ft

f

f

if

from elevator hinge

= 6

in .

APPENDIX NOTATION

ABBREVIATIONS

,

,

1

AND CONVERSION FACTORS

Most of the notation here used has been used in reports or notes of the National Advisory Committee for Aeronautics ( NACA ) . The only depar ture from NACA notation intended are those involved in a much wider var iety of topics being covered here than in any one report or note of the NACA . The order of listing is ( 1 ) English Letter Notation , with some subscripts ; ( 2 ) Greek Letter Notation , with some subscripts ; ( 3) Summary of Subscripts , Sub - subscripts , and Superscripts ; and ( 4 ) Abbreviations . Some notation , when used at only one or two places in the text , is not listed in this summary . is intended that such notation be explained where is used .

It

it

(1) a

English Letter Notation

/

/

lift

acceleration = dV dt , ft sec ; - curve - slope slope of graph CL vs. a ( subscripts denote object , such as w = wing , t = hori zontal tail ) ; speed of sound , ft sec ( subscripts denote condi tions such as 1 at point 1

/

ao

infinite - aspect ratio

A

area ,

b

wing span ,

B

British thermal unit or rotor

Bhp

brake horsepower

с

chord

lift - curve

slope

ft2 ( subscripts denote locations such as A₁ at point 1 ; aspect ratio = b S ( subscripts denote parts , such as w = wing )

/

ft

( subscripts

denote parts such as bs = span any radius r

propeller blade width of =

= 550

ft

ft - lb / 778 ;

number

of slot ) ;

of blades for propeller

ft - lb / sec

( subscripts

denote locations , such as ct = chord such as ( subscripts denote conditions specific heat at constant pressure ) ; critical velocity , Cp ft sec ; section coefficient ( subscripts denote force component , section drag coefficient ) such as ca

at

of

wing ,

tip ) ; specific

heat

/

£

section drag coefficient , ( subscripts denote conditions , such as cdo = section , or profile , drag coefficient for an airfoil sec

tion

/

= dD qds )

lift

( subscripts

section such as

Cm

section pitching moment coefficient ( subscripts denote locations , such as Cmac = pitching moment coefficient about aerodynamic center )

Cli

coefficient

dL/ qds

5

=

design

=

lift

coefficient )

A1-1

denote

conditions

,

A1-2

Cn ‫نآ‬

section normal force coefficient

‫نش‬ ср

specific heat at constant pressure ,

‫یم‬

specific

‫ن‬

coefficient tions

CD

CDf

/1bm

at constant volume , B

heat

,

/lb

B

, such as wing such as CL =

lift

( deg F)

coefficient ( subscripts coefficient )

/

drag coefficient = drag qS ( subscripts Cdi = induced drag coefficient )

drag coefficient based on the proper area

Cf ‫نم‬

skin-friction coefficient

=

wing = CD

/

F S PV2 2

/

rate of climb

lift

coefficient

=

/

L

qS

/

Cm

pitching -moment coefficient foil unless specified

Cp

location of

Cp

power

Ca

torque coefficient for propellers

Cos

speed - torque

Cs

, such as

- CL2MA

CDπ

F

condi

drag coefficient due to friction ; intercept of the graph of CD vs. CL2 ; approximately the effective minimum profile or para site drag coefficient

profile -drag coefficient of

‫یسک‬

conditions

denote

CDo

‫یھب‬ Ch

denote

for

speed

wings

lift

leading edge of

= M cqS ; about

and drag forces =

coefficient for propellers

c.p./c

pressure coefficient

;

or rotors or rotors

coefficient for propellers

-power coefficient for

propellers

CT

thrust coefficient for propellers

d

diameter ,

D

drag ,

e ew

-drag efficiency factor for airplane Napierian logarithms induced -drag efficiency factor for wing

E

ratio of elevator

f

flat - plate

F

force

lb ;

air

ft ;

length or distance

diameter of circle

tips revolve

or rotors ,

in

ft ; differential of which propeller or rotor blade =

induced

chord

to

horizontal

area equivalent to

lb ; factor

minimum

tail drag

/

1 TA dCp dCL

/

base

of

chord

of

a wing or airplane

A1-3

Ex

g

of

Fahrenheit degrees due to

acceleration

temperature

gravity

= 32.2

ft / sec²

specific enthalpy of a gas B/1bm ; vertical location of the hori zontal tail relative to the zero - lift chord of the wing

h

‫هت‬

horsepower

‫هش‬ hc

convective heat transfer coefficient

hPa

horsepower

available

hpr

horsepower

required

hpro

horsepower

required at sea level

H

total enthalpy of

Habs

absolute ceiling

Hs

service ceiling

,

/

B hr

ft2 Fo

gas

is

angle of incidence , radians unless specified part , as = incidence of wing )

Ihp

indicated horsepower

J

i

ratio for propellers

advance

=

a constant (various

кс

thermal conductivity

Ky

radius of gyration of the airplane

K

a constant

1

length

L

distance or length

,

constants at various locations

E

/

in

= CLaS , chord ; loading

lb ;

air

handled ; mass

speed

M

Mach number

Mer

critical

Md

Mach

Mach

number

median camber type of

denotes

of fluid flowing per

miles per hour

mph

maximum

( subscript

slope per radian

per second of slugs sec

mass

in text )

around the span axis

ft ; lift

)

lift - curve

denote

constants at various locations on text )

location , fraction of

loading

( subscripts

V/nD

k

(various

;

number

( Moo when

for substantial

Mtotal

drag

rise

= 1)

second ,

A1-4

per second

n

revolutions

ne

number

P

power loading

P

absolute pressure = F/ S lb ft ; brake power of engine period of vibrations , sec

q

dynamic pressure = pv² 2 ;

of engines

/

torque or B 1bm go

source and sink strengths

go max Qo

full -throttle

r

radius ,

ft ;

rpm

revolutions ute

R

radius

R°

Rankine

air

flow ,

level

sea

ft³/ sec ; heat brake

,

energy

torque

torque at sea level , lb - ft

rotor ; ratio per minute

speed

;

of rotation in revolutions

ft - lb/ lbmR ° ;

gas constant ,

universal

;

ft³/ sec ;

,

ft - lb / sec ;

ft²

lb

lb - ft ; volume of

moment ,

/

8

for helicopters

temperature

degrees

= ( Fahrenheit

per min

ratio

temperature

degrees ) +

460

/ lb Ro

S

specific entropy ,

Sh

specific humidity , lb

S

wing surface ,

B

per

1bm

Shp

shaft

STT

proper area , plan or frontal ,

ft²

t

airfoil

T

deg

H20

air

ft²

horsepower

F;

thickness

ft ;

,

time , sec

absolute temperature

thickness ratio

on Fahrenheit

propeller thrust or other force

thrust

u

specific internal

V

specific

3

specific weight , lb

/ ft3

weight rate of flow

, lbm

horsepower

volume ,

W

weight , lbm

X

distance

,

,

,

Fahrenheit

(Rankine )

lb

delivered by the propeller

Thp

·Σ

dry

energy , B/ 1bm

ft / lbm ;

v

/

= 1 w

/ sec

length , or thickness

,

ft

scale = nBhp

temperature ,

=

t

+ 460 °F

A1-5 ‫א‬

excess horsepower ; distance

y

length or distance

Z

liquid pressure

(2 ) a

Greek

(alpha )

ft ;

,

head ,

( for landings )

spanwise

ft ;

distance on wing

vertical distance

ft

,

ft

,

Letter Notation angle of attack radians unless specified

da

absolute or aerodynamic

angle of attack

άo

section angle of attack

(

ai

induced

α10

angle of attack for zero

lift

of wing section

απο

angle of attack for zero

lift

of wing

αo

angle of attack (CT TA)

angle

of attack

B (beta )

propeller -blade angle propeller , deg

Bo.75R

propeller -blade angle

Y (gamma )

angle between

r ( Gamma)

circulation

Г огго

dihedral

♪ (delta )

angle ,

=

lift

heats

2K

- angle , radians

aspect ratio )

radians unless specified

for infinite aspect ratio

/

of specific

,

infinite

measured

,

radiant

measured

at 0.75 propeller radius

component and the resultant = c, Сраст

force

unless

specified

/

( subscript

denotes

ε ( epsilon )

angle of twist , radians unless specified ; angle of radians unless specified

in

efficiency ( subscript or ram

part ) ;

P P )

increment or increase

Пram

ratio

;

radians or degrees

also pressure ratio

ciency

R

/L, sq ft/sec

▲ (Delta )

(eta ) '

of

= Vob

partial derivative of

ʼn

r-

from plane of rotation

(delta )

a

=

a quantity

prime denotes

special

-

down wash ,

kind of

effi

efficiency

e

(theta )

angle of glide path with horizontal , radians unless fied ; temperature ratio T/ To

A

(lambda )

slope of graph of temperature ard air )

vs. altitude

( 0.00356

speci

for stand

A1-6

viscosity coefficient

/

- /ft2 ;

Fx SV , 1b sec

(mu)

dynamic

u

( mu)

kinematic viscosity

ʼn

(pi )

3.1416

p

( rho )

air

density

Po

air

density at sea level , slugs per cu

σ ( sigma )

air- density ratio of

,

=

/

= H P,

ft2 / sec

slugs / ft³

/

p

--

o;

(Sigma )

sum

↑

( tau)

unit shearing stress

(phi )

angle of bank , radians unless specified

w

( omega )

(3)

()a ( (

Summary

(

angular velocity of Subscripts , atmospheric

braking

( ) B ,C ,

at point

)(

centrifugal

at point

,

;

control

and Superscripts

to aerodynamic

center

A

B , C , etc. ;

climbing

;

related to heat convection

compressible

Ver

critical

( cruis

cruising

7014

du dy

available

; ambient ;

surface

()cyl

/

=

at altitude

Ob

comp

of fluid flow

radians / sec

- subscripts

absolute

(A

(

Sub

abs

average

(

= 2mm,

related or referred

av

between layers

angle of yaw , radians unless specified

ac

( alt

ft

solidity for helicopters

Σ

V (psi )

rolling - resistance

( applied to Mach number ; where Mlocal = 1 ; applied to Reynolds number ; where major changes in separation take place )

cylinder related or referred to quarter chord position

A1-7

(D (a

(

(

(wing )

drag (section

referred

ed

of equivalent drag

eff

effective

(F

()g On ()i ()I (

inc

) 1w

( jet

( (L 1

( LE LS

( )( ( (

LSC

friction ; flap fuselage

final gross ; ground

indicated and corrected

hovering

for

weight

relative to jet

lift

( section )

lift

( wing ) ; landing

referred to leading

;

level

edge

limited by stall limited by stall

max

maximum

min

minimum

∞

;

incompressible

mean

()

to altitude

initial

mean

)(°

gliding

induced ; indicated ; intended ( design ) condition

moment

N

; gauge ;

related or referred

W

On ( ).nacelle

;

to propeller disc

effective

elevator

( fus

(

) ;

e

()f

(

drag

and compressibility

normal

nacelle net

original

;

sea

level

at infinity , or

remote

A1-8

( opt

(p

( )P

optimum

at constant pressure or related to pressure ; related to pro peller ; parasite ; profile

(a ( (r

power

()s

ram

as

ram

()sat ()sc ( SL

( std ( () STO

sub

() ()surf

super

()t

( tail ( ( ( (

time

torque torque and speed related to rudder ; related to root of wing radians ; required ; rated ; ratio

stall ;

stall sea

span

and compressibility

level

;

stall in

also

landing configuration

standard

stall in

take

- off

configuration

subsonic supersonic on surface

at tip of wing tab ; thrust related to

;

at throat of wind tunnel

tail of

TO

take

-off

turbulent

vertical

(or

wave

wave

wet

wetted

()w

transition

airplane

;

at constant volume

referred to wing

(

;

time

total

()

slot ;

( for angles ) in

saturation

total

turb v

related to a

;

due to pressures )

( area )

related to weight

;

for vertical tail

; trim

-

;

x

-y

axis

-

about the

axis axis

z

direction

;

the

about the

;

in

direction

-

the

about the

-y

in

direction

-

the

z

in

x

A1-9

specified

some

conditions

or process

e.g.

isen

)

tropic

,

referred to

where

(

at critical condition

M = 1

)*

(

referred to proper area

vector quantity ABBREVIATION NOTATION aerodynamic

BSFC

brake specific fuel consumption

C.F.

centrifugal force

c.g.

center of gravity

c.p.

center

of

E.R.

energy

ratio

Eu

Euler number

Fr

Froude

Gr

Grashof number

Hg

the element mercury

L.E.

leading edge

log

logarithm

center

Nu

Nusselt number

Pe

2

Peclet

Pr

Prandlt

2 Re

Reynolds

sin

sine

St

Stanton

S.L.

sea

tan

tangent

gb

/

liquid

v²

waves

,

for

heat transfer

)

(

number

in

pressure

2

number

level

)

subscripts

denote length used

in calculation

)

number

number

heat transfer

(

number

(

2

a.c.

A1-10

T.E.

trailing

edge

VTO

vertical

take

VTOL

vertical take -off

- off and landing

REFERENCE

ABBREVIATIONS

JAS

Journal of the Aeronautical Sciences

NACA

National Advisory Committee

TN

Technical Note

TM

Technical

TR

Technical Report

WR

Wartime Report

Memorandum

for

Aeronautics

APPENDIX

UNITS

1

AND CONVERSION FACTORS

TABLE A1 : 1 . LENGTH EQUIVALENTS Centimeters

1

2.540 30.48 91.44

Feet

Yards

Meters

0.3937

0.03281 0.08333

0.01 0.0254 0.3048 0.9144

10-5

0.0,6214

0.0,254 0.0,3048 0.0,9144

1

12

1

0.01094 0.02778 0.3333

36 39.37 39,370 63,360

3

1

1

100

100,000 160,935

3281

1.0936 1093.6

5280

1760

3.281

TABLE A1 : 2 . Square meters 1

1

1,728 46,656 57.75 231

61.02

1000

1

0.6214

1609

1.609

1

Square feet

Square yards

10.76 0.006944

144

1

1296

9

1

1

TABLE A1 : 3 .

0.001

0.0.1578 0.0,1894 0.0,5682 0.0,6214

1.196 0.0.7716 0.1111

1550

0.09290 0.8361

Miles

meters

AREA EQUIVALENTS

Square inches

0.0,6452

Cubic inches

Kilo

Inches

VOLUME

Cubic yards

Cubic feet

0.035787 1 27 0.03342 0.1337 0.03531

AND CAPACITY

0.0,2143 0.03704 1 0.001238 0.004951 0.001308

U.S.

EQUIVALENTS

quarts ,

U.S. gallons ,

liquid

liquid

0.01732 29.92 807.9

0.024329 7.481 202.0 0.25

1

4 1.057

Liters

0.01639 28.32 764.6 0.9464 3.785

1

0.2642

1

¹ In the following tables , the subscripts after a cipher , e.g. , O. , indicate that the cipher is to be repeated the indicated number of times .

TABLE A1 :4 . Grams per cu cm 1

27.68 0.01602 0.1198

Lb per

SPECIFIC WEIGHT EQUIVALENTS Lb per cu ft

cu in .

62.43

0.03613

1728

1

1

0.035787 0.004329

0.1010

A1-11

Lb per U.S. gal 8.345 231

0.1337 1

A1-12

TECHNICAL

TABLE A1 : 5 . Cm per sec

Meters per sec

0.6

1

1.667 27.78 30.48 0.5080 44.70 51.479

VELOCITY EQUIVALENTS

Meters per min

0.01

1 100

Ft per

Ft per

sec

min

0.036

1.9685 0.02237 0.03281 196.85 3.281 2.237 3.281 0.05468 0.03728 0.9113 54.68 0.6214 1 60 0.6818 1 0.01667 0.01136 1 88 1.467 1.68894 101.337 1.15155

0.06

1

16.67 18.29 0.3048 26.82 30.887

TABLE A1 : 6 .

Km per hr

3.6

60

0.01667 0.2778 0.3048 0.005080 0.4470 0.51479

AERODYNAMICS

1

1.097 0.01829 1.609 1.8532

Mph

Knots

0.01943

1.943 0.03238 0.53960 0.59209 0.00987 0.86839 1

FORCE AND WEIGHT EQUIVALENTS Tons

Avoirdupois Kilograms Short

Long

Metric

35.27

2.205 0.0625

0.021102

0.001 0.0,2835

1

0.0005

1 16

32.000 35.840 35.274

2000

1

0.039842 0.042790 0.0.4464 0.8929

2240

1.12 1.102

0.9842

2205

TABLE A1 : 7 . Megabars or mega dynes per 8q cm

Lb per 8q in.

1.0197 1 0.07031 1.0333 1.3596 0.03453 0.09991 0.002538 0.03045

14.50 14.22 1 14.70 19.34 0.4912 1.421 0.03610 0.4332

1

Atm

Columns of Hg at temperature 0°C and g 980.665 cm per sec²

Meters

1 0.9807 0.06895 1.0133 1.3333 0.03386 0.09798 0.002489 0.02986

0.0.4536 0.9072 1.016 1

PRESSURE EQUIVALENTS

Kg per sq cm (metric atmos pheres)

0.043125

0.9869 0.9678 0.06804 1 1.316 0.03342 0.09670 0.002456 0.02947

0.7500 0.7355 0.05171 0.76 1 0.02540 0.07349 0.001867 0.02240

In. 29.53 28.96 2.036 29.92 39.37 1 2.893 0.07349 0.8819

Columns of water at temperature 15°C and @= 980.665 cm per sec¹

Meters

10.21 10.01 0.7037 10.34 13.61 0.3456 1 0.02540 0.3048

In. 401.8 394.0 27.70 407 2 535.7 13.61 39.37 1

Ft

33.48 32.84 2.309 33.93 44.64 1.134 3.281 08333 1 0

1016 1000

Pounds

121

1

0.02835 0.4535 907.2

Ounces

APPENDIX TABLE A1 : 8 . Joules 107ergs

Kilogram

1 9.80665 1.356 3.6 X 10 10 2.648 2.6845 X 10 4183 1054

0.10197 1 0.1383 3.671 X 10 2.7 X 105 2.7 X 105 426.6 107.5

meters

X

Kilo-

Chevalvapeur hours *

Horsepower hours

calories

0.062778 0.0.2724 0.063766 1 0.7355 0.7457 0.001162 0.032928

0.063777 0.0537037 0.0651206 1.3596 1 1.0139 0.001580 0.033981

0.063725 0.063653 0.0650505 1.341 0.9863 1 0.001558 0.033927

0.032390 0.002344 0.033241 860.5 632.9 641.7 1 0.25200

Kw

POWER EQUIVALENTS

Cheval vapeur *

Meter -kg per sec 76.04 102.0

1

0.7457

1.341 0.9863 0.01315 0.00182 5.610 1.414

1

1.014 1.360

0.7355 0.009807 0.001356 4.183 1.054

0.01333 0.00184 5.688 1.433

Lb /sq ft (Ft sec ) 2

LIFT

.

Lb

/

/sq ft

550

737.6 542.3 7.233

1

1

0.1383 426.6 107.5

AND DRAG

1

2.151 1

52.7 24.5

0.0409 0.532 0.00510 0.00256

13.0 0.125 0.0622

Btu per

0.1783 0.2390 0.1758 0.002344 1

0.7074 0.9486 0.6977 0.009303 0.001286 3.968

0.2520

1

0.033241

3086

777.5

- COEFFICIENT

/sq M (Km /hr)

/ /

0.464 0.0190 0.247 0.00237 0.001185

Kg - cal per sec

sec

Kg

Kg sq M (M sec ) 2

Mph2

12pv²; p

Ft-lb per

75

1

horsepower.

TABLE A1 : 10

/

0.039486 0.009302 0.001286 3415 2512 2547 3.968

EQUIVALENTS

British

L

2

1

sec

2qS

4.05 1.88 0.0769

421

843

196

392

1

104

16.0 208

1

2.0

8.02

0.00958 0.00479

0.500

mass density of air , any units ; v = speed, same units .

TEMPERATURE EQUIVALENTS

TABLE A1 : 11 . Deg C Deg

F

1° centigrade = 1.8 ° Fahrenheit = 5%( F Deg C abs . = deg 32 )

9%

-

deg + 32

TABLE A1 : 12 .

Deg

NACA 212

Hp

q =

Btu

horsepower .

TABLE A1 : 8 .

* Metric

Kilo gram

watthours

Foot - pounds

Fabs .

= deg

C

F

+ 273

+ 460

VISCOSITY EQUIVALENTS

1 poise = 100 centipoise = 1 dyne - sec per sq cm = 0.00209 lb - sec per sq ft 1 lb-sec per sq ft = 478 poise = 47,800 centipoise

1

* Metric

AND WORK EQUIVALENTS

ENERGY

0.7376 7.233 1 2.655 X 10 1.9529 X 10 1.98 X 10" 3086 777.52

A1-13

1

APPENDIX

2

PROPERTIES OF SOME LIQUIDS AND GASES TABLE A2 : 1 .

Alcohol methyl

CH ,OH

Benzene

C&H

Gasoline

42

C₂H ,

32 68 104 140

49

175

32 68 104 140

54.4

7.3

5.8

C

6.55

Variable

32 88 68 140

43 mean

-40

32 88 68

78 mean

0.90 0.647 0.492 0.389

18.8 13.5 10.2 8.1

0.42 mean

0.092 mean

0.53 mean

0.078 mean

0.164

4,800 815

106 17,000

0.58 mean

6.8 mean

3.0 1.9 1.3 0.9

62.5 39.6 27 19

0.47 mean

0.086 0.084 0.082

1.7 1.6 1.5 1.4

35.4 33.3 31.2 29.1

0.033 mean

4.83

0.027

0.65 0.55 0.43 0.36

13.5 11.5 9.0 7.5

0.50 mean

0.084 0.082 0.081

8.0 6.4 5.4

1,500 520 250

0.5 mean

0.08 mean

5.420 1.460 670

15 mean

0.08 mean

0.542 0.573

0.153

0.074

21

0.323 0.343 0.362 0.377 0.398

13.6

Hg

-38

675

32 68 104 140

847 845 841 839

Octane

C&HIS

-71

256

32 68 104 140

43.5

5.8

Lub. oil SAE 10 (mean )

C₂Hy

Variable

32 68 104 140

About 57

About 7.6

Lub. oil SAE 30 (mean )

CH

Variable

32 68 104 140

About 57

About 260 70 7.6 32

Ethylene glycol

C2H6O2

290

32 68

68 mean

9.1

14 420

32 68 104 140

2

54 mean

7.2

2.2 1.54 1.03 0.86

21.5 18

0.42

32 68 104 140 176 212

62.42 62.32 61.96 61.37 60.61 59.76

8.34 8.32 8.28 8.21 8.10 8.00

1.793 1.008 0.653 0.469 0.357 0.283

37.5 21.0 13.7 9.80 7.47 5.92

1.009 0.998 0.997 0.999 1.002 1.005

64

8.55

.

†

. "

ChemicalEngineersHandbook

"

DatachieflyfromPerry, At saturatedpressure

A2-1

2898899090

CO

CHE

27.5

'

,

Water sea

72.0 25.0 12.0

46

†

Mercury

IS

51 mean

212

7.0

10.4

32 68 104 140

32

hr ) .,

0.124

Variable

H₂O

/(

0.57 0.60 0.67

CH

Water, pure

( F ) = )(d ke

.

/(

(d

10

16.8 12.4 9.35 7.27

Kerosene

Turpentine

Therm. conduct Prandtl Btu number eg Pr ft

0.808 0.593 449 0.349

4321

554

F . ) lb ) ,

.

2

148

Centi- Lb- sec poise sqft

882

C₁H SO₂

ft

Sp bt Btu eg

SO

Glycerine

-145

Viscosity

0

melt

)

mula

(

Liquid

Spec wt. Temp. of data, Lb per Lb per degF cu gal boil 10 U.S.

Critical points, degF

For

LIQUIDS *

71

4.36 3.00 2.18

2

zN:

Air Paz

0.00242

-66

32 130 277 425

+8

Carbon dioxide P32 0.00383

CO2

Helium P32 0.000342

He

Hydrogen P32 0.000174

H2

Nitrogen P32 0.00242

-66 32 130 277 425

-66 32 130 277 425

-66

32 130 277 425

N2

-66 32 130 277 425

Oxygen P32 0.002765

O:

-66 32 130 277 425

Ср

.

Ce

0.297 0.357 0.413 0.487 0.555

0.239 0.239 0.240 0.241

0.171 mean

1.405

0.228 0.286 0.342 0.448 0.526

0.203 0.211 0.220 0.230

0.168 mean

1.28

0.333 0.391 0.442 0.501 0.577

1.26 1.26 1.26 1.26 1.26

0.76 0.76 0.76 0.76 0.76

0.148 0.175 0.200 0.234 0.263

3.48 3.48 3.50 3.51

0.287 0.344 0.396 0.467 0.531

0.248 0.248 0.249 0.250

0.357 0.426 0.492 0.583 0.665

0.217 0.218 0.219 0.220

Pr

.,

53.3

0.77 0.77 0.75 0.77

34.9

0.005 0.0061 0.0078 0.0104 0.0138

1.10 1.07 1.10 1.01 1.03

0.0698 0.0801 0.0895 0.1016 0.1129

0.70 0.715 0.725 0.725 0.745

0.0771 0.0916 0.1048 0.1233 0.1385

0.775 0.77 0.77 0.77 0.775

54.9

0.0110 0.0131 0.0151 0.0178 0.0203

0.75 0.75 0.76 0.76 0.76

48.3

0.0111 0.0134 0.0156 0.0189 0.0213

0.80 0.80 0.78 0.80

386

2.48 mean

2.48

767

0.177 mean

1.41

0.156 mean

1.40

.

Prandtl number

0.0107 0.0128 0.0149 0.0179 0.0200

1.66

,

,

.in

,

.

,

)

per deg abs

Data chiefly from Boelter Cherry and Johnson Heat Transfer California Press Berkeley Hg absolute pressure Data at 29.92

*

Therm con duct Btu hr deg = ke

/(

R,

ft

F

-

k

.

mula

Spec. ht. per lb

*

913

For

Gas

Temp . Viscos ity , of lb-sec data , 10° 8q deg F ft 10μ

GASES

( F ) ft ) (

TABLE A2 : 2 .

A2-2

Notes

, "

APPENDIX

University

of

TECHNICAL AERODYNAMICS

A2-3

1

/

lb 10

sec

T*

=

ft²

μ*

0.8

sea

-

level

air

0.9

0.8

H 106

1.

standard

0.7

with

°

and Too = 393

R .

/

1 + 0

+

T 0 *

1

0.505

T *

=

$ *

0.5

@ =

0.5

μ

T* *

Sutherland

ooo

0.55

through

0.6

0.45

0.4

Sea

0.35

level

standard

0.3

T,

0.25

used

Comparison

in

text

800

100 200 300

LI

1000

1500 1000

500

2000 1500

3000 2000 2500

of air viscosity data with some approximations Replotted from Van Driest JAS MARCH 1951 .

A2 : 1 .

-100

600

,

Fig .

-200

500 0

-300

400

300

.

200

,

0.2

RO

APPENDIX

3

PROPERTIES OF AIR TABLE A3 : 1 .

AIR AT SEA LEVEL AND AIR AT ALTITUDE

STANDARD

EQUATIONS

FOR STANDARD

British Symbol

Το

407.15

407.15

lb ft2

2116.23

2116.23

2116.23

lb ft3

0.097928

0.076506

0.068855

ft3

0.0030437

0.0023779

0.0021401

ft²

3.0420x10-7

3.7250x10-7

4.0455x10-7

0.99944 10-4

1.5665x10-4

1.8903 10¯ 1176.60

.

n

986.61

1116.22

mph

672.69

761.06

802.23

knots

584.16

660.90

696.55

sec

ft

0.1891x10-6

0.2421x10-6

0.2690

ft

0.1887x10-6

0.2415x10-6

0.2683

ft

0.1890

*

6

sec

×

/ / -

sec

× 10

free

40715

water at

ft

of

path of

576.0 29.9212

/ /

-ity

518.4

ft2

%

viscos

116.6

29.9212

slugs

lb

ity

Kinematic

59.0

×

Но

-54.5

maximum temperature

405.0

°F

Coefficient of viscos

At probable

temperature

29.9212

/

"

985

Density

At stendard

°C

15

90

weight

Mean

in

Po

Specific

minimum

abs

in.Hg at 32

Pressure

Speed sound

of

system

temperature

&F O

to

Absolute temperature

Unit

probable

.

Temperature

At

/

Quantity

engineering

nitrogen free

path of

O

oxygen

10

-6

0.2419 10 ×

air

.

free path of air

×

molecules

Mean

-6

. 0.2688x10

molecules Average mole culer weight

Ratio of specific heats

Relative ume of oxygen

10

vol

ΤΟ

28.966

28.966

28.965

1.4

1.4

1.4

0.2095

0.2095

0.2095

A3-1

-6

× 10

molecules

Mean

-6

APPENDIX

TABLE

A3

3

A3-2

AIR AT SEA LEVEL AND EQUATIONS AIR AT ALTITUDE ( Continued )

STANDARD

: 1 .

FOR STANDARD

Atmosphere Tables

Quantities used in deriving values for Standard

to

=

To

= 288 C =

Pressure at sea level

Po

=

80

15°C

Temperature at sea level Absolute temperature at sea level

=

518.4 °F

29.92117

in . of

ft/

lb

sec² = .002378 = = .0065 ° C / meter = .00356617 OF

o

tropopause Subscript refers to standard sea

the Tropopause

° F

/2 )

isothermal tempera absolute ture level conditions the Tropopause P loge Po Po Pogło

)ht

P

12

T =

σ

Ti

-

( Pt h

=

P

/

Po

) )

^

-1

/

P₂

/

) (

PA

b )h ) PoɛTo

) (

h

PosTo

ft

in

Above

loge

h

+

1

−

-

−

(1

=

(1

=

a

Alai

(

=

Below

C

pause

O

Ti

pressure at the

absolute

height of the tropo

=

,

pressure

in

10-8 T3

+ 114

°

T

T

absolute temperature

=

3.059

ht

/ft4

−67

x

= = =

(

ft

Hg .

/ft

-55

1.4000

=

= = = =

h SEP T

Pt

altitude in

/

2116.229 lb ft² sec² 32.1740

=

Y

viscosity

Absolute

°

μ

ti

Isothermal temperature Ratio of specific heats

= 59° F

°C

λ

ρ

Acceleration of gravity Density at sea level Temperature gradient

Day :

.

Technical Note No. 1200

.

,

:

Reference Warfield Calvin N. Tentative Tables NACA for the Properties of the Upper Atmosphere

:

FIGURE A3 -5 120 110 100

-60

1.0

0.9

Pressure

-

altit

0.8

0.7

0.6 0.50

) (

0.45

in

=

0.40

0.35

0.30

40,000 0.25

AIR

CHART

45

420 6380

// ==

Po

=

0.002378 Vo 0.0001567

-

0.200.190.180.170.160.15

-80

-70

-60

-50

-40

2

40 . F °,

50

60

50 120 110 100 90 80 P70

TECHNICAL AERODYNAMICS

d

ha

10,000

)( ,p) (

of

)( c

,)

po

p

/(

),b(h 14 )ha v) of ( /v is (/

is

a

)(a

at F.

)(;b

Po

/P σ , ;)(

ft h

2

of

p p

./ .

at

of

)( ;ihn

toa

is

1

)(

Density ratio CHART Example use chart Given pressure altitude hp altimeterreading 38,000 temperature -20 deg Find density altitude density ratio density air and kinematic viscosity Solution Locatethe pointonthechart theintersection linesfor 38,000 and -20 deg this pointreaddensity altitude 40,500 and ./ 0.227 onthescale the bottom thechartreadthe density ratio corresponding thiscaseread 0.238 Calculate 0.002378 0.000566 and 0.0001567 0.000574 Explanation plotting chart Temperature scale logscale absolutetemperature Tt 460 labeled degrees density ratioscale logscale thebase the temperature scale Withthesescaleslines constantpressure assuming pg 53.37 plot straight linesof slope andlines constant./v assuming To 6.80 which an approximation within percentforthe temperature lines slope 0.40 plottedandassuming vp at 59 deg plotas straight range Wood by 1955 Copyright

1.1

XIX

40

11

1.2

-80

Temperature

-70

5

-50

XM

XXXXXX

V

35

Temperature

-40

5000

-30

15,000

STANDARD AIR

20,000

-20

9JO

30

1

709

P

Ş

15

. F ° ,

. ft

XX

1000 30

.ft

XV

Density altitude 20 25

A3-3

)a(p./p , =t .: . .p/ of .p)/ of /vo of of ( , of -A. ,

-

;)(c

.

1

.

p p

of

) /T(

./ ,

;F/

in

=

of

D.

,° , p)

of

K.

)(;d(,

+

ofas

,

/P ,F

APPENDIX

f

.00248 .002413 .002378 .002343 .002309 .002275 .002 242 .002209 .002176 .00214 .002112 .002080 .002049 .002018 .001988 .001957 .001928 .001898 .001869 .001840 .001812 .001784 .001756 .001728 .001701 .001675 .001648 .001622 .001596 .001571 .001545 .001521 .001496 .001472 .201448 .001424 .001401 .001378 .001355 .001332 .001310 .001288 .001267 .001245 .001224 .001203 .001183 .001163 .201143 .001123 .001103 .001084 .001065 .001046 .001028 .001010 .000992 .000974 .000957 .000939 .000922 .000906 .000889

.0296 .07878 1.0147.07764 1.0000.07651 .9854 .07540 .9710 .07430 .9568 .07321 .9427 .07213 .9288 .07106 .9151 .07001 .9015 .06897 .8880 .06794 .8747 .06693 .8616 .06592 .8486 .06493 .8358 .06395 .8231 .06298 .8106 .06202 .7982 .06107 .7859 .06013 .7738 .05920 .7618 .05829 .7500 .05739 .7384 .05649

445.3 443.5 441.7 439.9 438.2 436.4 434.6 432.8 431.0 429.2 427.5 425.7 423.9 422.1 420.3 418.5 416.8 415.0 413.2 411.4

2194.1 1.0367 2155.2 1.0182 2116.4 1.0000 2078.1 .9821 2041.3 .9644 2003.8 .9469 1967.8 .9296 1931.7 .9129 1896.3 .8962 1861.7 .8798 1827.7 .8636 1793.8 8477 1760.5 .8320 1728.0 .8165 1696.2 .8013 1664.3 7863 1633.2 .7725 1602.1 .7570 1571.7 .7427 1542.0 .7286 1512.3 .7147 1484.0 .7010 1455.7 .6876 14.27.4 .6743 1398.8 .6613 1372.2 .6484 1346.0 .6358 1319.2 .6234 1293.7 .6112 1268.2 .5991 1242.8 .5873 1218.0 .5756 1194.0 .5642 1169.9 .5529 1146.6 .5418 1123.9 .5309 1100.6 .5201 1078.7 .5096 1056.7 .4992 1034.8 1,890 1013.6 .4789 993.1 4690 972.6 .4593 952.1 .498 932.2 .4404 912.4 .4312 893.3 .4221 874.2 .4132 855.9 houl 837.5 .2958 819.8 .3874 802.1 .3790 785.1 .3709 768.1 .3628 ? 751. .3550 734.9 .3472 718.6 .3396 703.1 .3321 687.5 .3248 672.0 .3176 657.1 .3105 642.2 .3036 628.1 .2967

30500 31000 31500 32000 32500 33000 33500 34000 34500 35000 35332 36000 37000 38000 39000 40000

409.6 407.8 406.1 404.3 402.5 400.7 398.9 397.1 395.4 393.6 392.4 392.4 392.4 392.4 392.4 392.4

614.0 .2900 599.8 .2835 586.4 .2770 572.9 .2707 559.5 .2645 546.8 .2584 534.0 .2524 522.0 .2465 509.3 .2407 498.0 .2351 489.4 .2314 474.6 .2242 452.0 .2137 431.5 .2037 411.0 .1942 391.9 .1852

41000 42000 43000 44,000 1,5000 46000 47000 48000 4,9000 50000

392.4 392.4 392.4 392.4 392.4 392.4 392.4 392.4 392.4 392.4

373.5 356.5 339.5 324.0 308.4 294.2 280.8 267.4 255.3 243.3 232.0 220.7 210.8 200.9 191.7 182.5 174.0 166.2 158.4 150.7 143.6 137.2 130.9 124.5 118.8

392.4 392.4 392.4 392.4 392.4 392.4 392.4 392.4 392.4 392.4 61000 392.4 62000 392.4 63000 392.4 64,000 392.4 65000 392.4

$1000 52000 $3000 54,000 $5000 56000 57000 58000 59000 60000

1119.7.0002419 1117.8 1115.9 1114.0 1112.0 1110.1 1108.2 1106.0 1104.3 1102.3 1100.4 1098.5 1096.6 1094.5 1092.6 1090.7 1088.7 1086.8 1084.7 1082.8 1060.7 1078.8 1076.8

.7268 .05561 .7154 .052.74 .7042 .05388 .6930 .05302 .6820 .05218 .6712 .05135 .6605 .05053 .6499 .04972 .6394 .04892 .6291 .04813 .6189 .04736 .5088 .04658 .5988 .OL582 .5890 .04507 .5793 .Oh432 .5697 .04359 .5603 .04287 .5509 .a4215 .5417 .04145 .5326 .04075 .5236 .04.006 .5148 .03939 .5060 .03872 .4974 .03805 .4889 .03740 .1.804.03676 4721 .03612 .4640 .03550 .4559 .03408 79 .03427 11:00.03367 1323 .03307 .1246 .03249 11171.03191 4096 .03134 11023.03078 .3950 .03022 .3879 .02968 .2809 .02914 .3739 .02861

3.504 3.194 3.186 3.172 3.463 3.452 3.4 3.430 3.422 3.411 3.400 3.390 3.379 3.268 3.360 3.347 3.335 3.326 3.314 3.304

2.028 2.054 2.081 2.107 2.135 2.163 2.192 2.220 2.250 2.280 2.310 2.341 2.373 2.404 2.138 2.170 2.50 2.539 2.573 2.608

1074.9 1072.8 1070.8 1068.9 1066.8 1064.8 1062.8 1060.8 1058.7 1056.7 1054.8 1052.7 1050.7 1048.6 1046.6 1044.5 1042.4 1040.4 1038.L 1036.3

3.293 3.283 3.271 3.262 3.251 3.242 3.230 3.217 3.206 3.195 3.184 3.173 3.163 3.153 3.140 3.131 3.117 3.106 3.099 3.085

2.645 2.682 2.719 2.757 2.795 2.836 2.876 2.917 2.958 3.000 3.087 3.332 3.178 3.224 3.272 3.320 3.369 3.420 3.470

1034.2 1032.2 1030.0 1027.9 1025.9 1023.8 1021.8 1019.6 1017.5 1015.5 1013.3 1011.3 1009.1 1007.0 1004.8 1002.8 1000.6 998.5 996.3 994.1

.000873 .000857 .000841 .000825 .000810 .000795 .000780 .000765 .000751 .000736 .000727 .000704 .000671 .000640 .000610 .000582

.3671 .02808 .3603 .02757 .3537 .02706 .3471 .02656 .3406 .02606 .3242 .02557 .3280 .02509 .3218 .02462 .3157 .02415 .3096 .02369 .3057 .02339 .2961 .02266 .2823 .02160 .2692 .02059 .2566 .01963 .2446 .01872

3.076 3.064 3.052 3.039 3.030 3.019 3.008 2.995 2.986 2.971 2.961 2.961 2.961 2.961 2.961 2.961

3.523 3.575 3.629 3.684 3.741 3.797 3.856 3.915 3.976 4.037 4.080 4.212 4.418 4.633 4.860 5.098

992.0 989.8 982.6 985.4 983.2 981.0 979.0 976.8 974.6 972.4 970.9 970.9 970.9 970.9 970.9 970.9

.1765 .1683 .1605 .1530 .1458 .1390 .1326 .1264 .1205 .1149

.000555 .000529 .000504 .000481 .000458 .000437 .000416 .000397 .000379 .000361

.2332 .0178 .2224 .01701 .2120 .01622 .2021 .01546 .1927 .01474 .1837 .01405 .1751 .01340 .1669 .01277 .1592 .01218 .1517 .01161

2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961

5.347 5.609 5.883 6.171 6.473 6.790 7.122 7.470 7.836 8.219

.1095 .104 .0995 .0949 .0905 .0862 .0822 .0784 .0747 .0712

.00034 .000328 .000313 .000298 .000284 .000271 .000258 .000246 .000235 .000224

01107 .1379 .01055 .1315 .01006 .1253 .00959 .1195 .0091 .1139 .00872 .1086 .00831 .1035 .00792 .0987 .00755 .0941 .00720

2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961

8.521 9.042 9.485 9.949 10.436 10.947 11.482 12. 12.633 13.251

.0679 .0647 .0617 .0589 .0561

.000213 .000203 .000194 .000185 .000176

.0897 .00687 2.961 .0855 .00655 2.961 .0816 .00624 2.961 .0777 .00595 2.961 .0741 .00567 2.961

13.999 1.579 15.293 16.041 16.825

970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 970.9 .00326

3 .

:

1.527 1.545 1.564 1.583 1.602 1.621 1. 1.661 1.681 1.702 1.723 1.744 1.766 1.788 1.010 1.833 1.856 1.879 1.903 1.927 1.951 1.977 2.002

: ::

20500 21000 21500 22000 22500 23000 23500 24,000 24500 25000 25500 26000 26500 27000 275.00 26000 28500 29000 29500 30000

3.738 3.728 3.719 3.708 3.699 3.688 3.679 3.669 3.658 3.649 3.639 3.628 3.619 3.608 3.598 3.587 3.578 3.566 3.557 3.46 3.535 3.527 3.516

:4

522.0 520.2 518.4 516.6 514.8 513.1 511.3 509.5 507.7 505.9 504.1 502.4 500.6 198.8 497.0 495.2 493.0 491.7 489.9 488.1 486.3 484.5 482.7 481.0 479.2 477.4 475.6 473.8 472.0 470.3 468.2 466.7 464.9 463.1 461.3 459.6 457.8 456.0 454.2 452.4 450.6 448.9 ‫ايلم‬ 7.1

.

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 6000 8500 9000 9500 10000 10500 11000 11500 12000 12500 13000 13500 14,000 14500 15000 15500 16000 16500 17000 17500 18000 18500 19000 19500 20000

.

-1000

- 500 0

A3-4

UP TO 65,000 FEET Density SpecificCoefficientKinematic Speed of anFree Viscosity Sound Pathof Ratio Weightof Viscosity ν ▼ a Molecules σ μ (ft) (lb/ft³) (lb-sec / ft²) (ft2/ sec λ x107 x103

AIR

)

STANDARD Altitude Absolute PressurePressure Density TemperatureP Ratio a / ) (Slugs P/Po I .) (F abs (lb/ft2) . x1050

sec ) ( ft /

TABLE A3 : 2 .

3

Altitude ft

,

,)

/P

/(

,

1b

).

, (

) (

33333

3383 ‫لاسامال‬

.

28 2008 2000FFRyng ON~~26692

×

annot

defconang 533 508 185 462.7 441.1 420.7 401.2

2

DEC

...

33333333 &&&&&

88888888888888888888888888888888 58580 RES FRF 8788128588 8282 88983

dap

emofing motor 987 2222 &&076 809

OON 486 11326 ay 387

500

$$

888

1132 1101 1149 1157 1166 1174

:

,

TO

0.08279 0.09115 0.1002 0.1101 0.1207 0.1122

8888

.0404 0.0447 0.0495 0.0547 0.0604 0.0664 0.0731 0.0802 .0879 0.0961 0.105

NIGHT

270 6266 20

278 253.3 230.8 210.0

2.961 2.961 2.961 2.961 .987

2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961 2.961

-- British

413.8

1065

1802 1718 1637 1561 1419

2.961 2.961 2.961 2.961 2.961 2.961

.

: 3

65,000 FEET

132,000 134,000

(

OR

106,000 108,000 110,000 112,000 114,000 116,000 118,000 120,000 122,000 124,000 126,000 128,000

/ 2.961

dard Temperatures Based on an

Force

1404 1339 1277 1160 1106 1054 958.6 871.3 831.1

,) ~~22

AIR

392.4 392.4 392.4 392.4 392.4 392.4 392.4 392.4 392.4 396.5 404.5 412.6 20.6 28.7 436.7 454.8 52.8 160.9 68.9 76 185.0 193.0 501.1 309.1 517.2 525.2 533 541.3

, 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 sm.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 971.1 .1 971.1 971.1 971.1 971.1 971.1 971.1 m.1 976.2 986.0 995.8 1005 1015 1025 1034 1043 1052 1062 1071 1080 1089 1097 1106 1115 1124

of Gravitational

1699 1620

v( 0.00326x103 0.00342 0.00359 0.00377 0.00395 0.00414 0.00435 0.00456 0.00478 0.00502 0.00527 0.00553 0.00580 0.00608 0.00637 0.00668 0.00701 0.00735 0.00771 0.00809 0.00848 0.00890 0.00933 0.00979 0.0103 0.0108 0.0113 0.0119 0.0124 0.0130 0.0137 0.0143 0.015 0.0158 0.0166 0.0174 0.0191 0.0210

DAY

-

, ) =/

STANDARD

392.4

(

947.1 903.1 861.0

/

~

-/

392.4 392 392.4 392.4 392.4 392.4 392.4 392.4 392.4

, )(

2.961

5 V

971.1 971.1 971.1 971.1 971.1

/

0.001680 0.001761 0.001848 0.001939 0.002034 0.002133 0.002236 0.002346 0.002461 0.002582 0.002710 0.002844 0.002985 0.003127 0.003279 0.003439 0.003607 0.003784 0.003968 0.004163 0.004366 0.004579 0.004802 0.005037 0.005286 0.005547 0.005818 0.006101 0.006399 0.006713 0.007038 0.007380 0.007743 0.008128 0.008523 0.008946 0.009837 0.01082 0.01134 0.01212 0.01383 0.01572 0.01783 0.02016 0.02273 0.02558 0.02876 0.03224 0.03605 0.04024 0.04485 0.04989 38 0.055 0.06137 0.06795 0.07505

, ()

2.961x10 61 2.961 2.961

free Specific Coefficient Kinematic Speed of Mean pathof veight of viscosity viscosity sound olecules 88 lb ft³ lb sec ft² ft sec ft² sec ft

) ( , )

1763x107 7414x105 5672x10 5407 7068 1602 6738 6423 1456 6123 388 1324 22 1262 4060 1203 1147 1094 1042

Density ratio •

,

561210-5 5350 5100 4862 4635 4419 4213 4017 38.30

Density slugsft³

TABLE A3

;

Absolute tempera-Pressure Pressure ture ratio T ft² Po abs

A3-5 TECHNICAL AERODYNAMICS

262,467 FEET

Properties of the Upper Atmosphere

for Tentative Stan Arbitrary Constant Value Engineering System

.

Nang Montmore

HARMON 65

HÅRFORAR

.

$

888888888

3288

nevror

200 SETONG

59506

050

.

888888888888888888

BBB 255

88888 55

.

moa

B

8888888

66 65 A

696nne .

4TOMBGHTO 2592500 co 54330 55555555

25699 24000 CG 6COU - DUOUTH www.von 24 244

C.C 1

,

88 88

:

Q

Atmosphere

4

Upper

Ms2

Technical

Tentative

33

.

NACA

ESBEAST 88 Q888ESSO

the

8 22

Tables

for Note

the No.

.

1200

Prop

ING

of

ne 50588 730 2:56 8877665555

N.

443mm

Calvin

-666

209 .500

.2222

219 2.952 893

1057 1050 1042 1034 1026 1019 1019 1019 1019 1019 1019

1159

1220 1214

~mmmmmer

Warfield

.006 4.590 209 3.859 3.732

8106

6565 6844

coNDOREN

432.0

33332 ~~~~~ .195 1.190 1.091 001

not 282080

199 4.172 3.825 3.507 3.216 3.151

8P

0.00025 0.08809 0.08095 0.07422 0.05806 0.06660

996

0.1699 0.1572 0.1453 0.1341 0.1237 0.1133 0.1048

828

y

noo

do

0.3504

589955,686988 home AAAAA22222

(

)

:

3 .

:

,

262,467 FEET

erties

696 who

619.4 612 012.7 606.0 599.3 592.6 585.9 579.2 572.5 565 559.1

86_8Fh7228

630.0 630.0 630.0 630.0 630.0 630.0 630.0 626.1

333 hmm

3

Reference

000

999999

65,000 FEET TO STANDARD AIR DAY OR NIGHT Continued

262,467

869L8 BHOJE 8

1231

obamme

240,000 42,000 244,000 245,000 248,000 250,000 252,000 054,000 .. 905

2222

0.3748

824

,

6665 20 4596966 1993 offro30 229

X

&

686 MO

630.0 630.0 630.0 630.0

;

TABLE A3

200,000 202,000 204,000 208,000 210,000 212,000 214,000 216,000 218,000 220,000 222,000

OF

630.0

629.8

APPENDIX

A3-6

.

986

Altitude

,

b

T 0.3158 0.2937 0.2735 0.2546 0.2374 0.2367 0.2224 0.2088 0.1960 0.1842 0.1730

0.2416 0.2247 0.2092 0.1948 0.1816 0.1811 0.1701 0.1597 0.1500 0.1409 0.1324

3.777 3.799 3.822 3.844 3.867 3.867 3.889 3.911 3.933 3.955 3.977

3.546 3.569 3.593 3.616 3.639 3.662 3.685 3.708 3.731 3.754

50.30 54.40 8.75 63.50 68.48 68.71 73.54 78.77 84.38 90.30 96.67

21.73 23.75 25.90 28.25 30.79 33.47 36.38 39.51 42.86 46.45

31.5 34.0 36.6 39.4 42.5 45.7 49.0 52.6 56.4 60.5 64.7 69.2 73.9 79.0 84.3 84.5 89.9 95.8 102 109 116

1248 1257 1266 1275 1284 1285 1289 1294 1298 1303 1308

13.8 15.1 16.4 17.9 19.5 21.1 22.9 24.9 26.9 29.1 1160 1169 1177 1186 1195 1204 1213 1222 1231 1240

1072 1081 1089 1098 1107 1116 1124 1133 1142 1151

,

:

4 .

:

262,467 FEET

7.509 6.984 6.504 6.054 5.645 5.628 5.288 4.965 4.661 4.380 4.114

0.5252 0.4837 0.4463 0.4119 0.3804 0.3519 0.3258 0.3020 0.2801 0.2600

8.380 9.273 10.25 11.30 12.46 13.70 15.06 16.54 18.13 19.86

DAY ONLY

0.3804 0.3584 0.3380 0.3187 0.3009 0.3002 0.2841 0.2687 0.2541 0.2404 0.2274

0.6865 0.6322 0.5833 0.5384 0.4972 0.4599 0.4259 0.3947 0.3661 0.3399

3.306 3.331 3.355 3.379 3.403 3.427 3.451 3.475 3.499 3.523

6.40 10-3 6.84 7.45 8.12 8.83 9.61 9.74 10.5 11.5 12.6

AIR

16.32 15.03 13.87 12.80 11.82 10.94 10.13 9.386 8.705 8.082

1.269 1.155 1.053 0.9616 0.8791 0.8048 0.7371 0.6761 0.6210 0.5707

1019 1022 1026 1030 1034 1038 1038 1046 1054 1063

FEET

0.7228 0.6750 0.6314 0.5908 0.5531 0.5185 0.4866 0.4570 0.4296 0.4040

× 1.659 1.510 1.377 1.257 1.149 1.052 0.9635 0.8837 0.8117 0.7460

3.572 3.835 4.208 4.612 5.051 5.531 5.610 6.136 6.818 7.559

×

39.45 35.91 32.74 29,89 27.32 25.02 22.91 21.01 19.30 17.74

3.212x10-7 3.212 3.212 3.212 3.212 3.212 3.212 3.232 3.257 3.282

sec

ft

Mean free path of molecules

STANDARD

0.008050 0.007585 0.007153 0.006744 0.006368 0.006353 0.006012 0.005686 0.005377 0.005087 0.004812

527.5 531.5 535.5 539.5 543.5 543.6 547.5 551.5 555.5 559.5 563.5

) (

320,000 322,000 324,000 326,000 328,000 328,083 330,000 332,000 334,000 336,000 338,000

°F(

0.01530 0.01428 0.01336 0.01250 0.01170 0.01098 0.01030 0.009671 0.009091 0.008550

.

487.4 491.4 495.4 499.4 503.4 507.4 511.5 515.5 519.5 523.5

/P

300,000 302,000 304,000 306,000 308,000 310,000 312,000 314,000 316,000 318,000

,

0.03200 0.02956 0.02736 0.02535 0.02351 0.02184 0.02029 0.01888 0.01759 0.01639

(

447.4 451.4 455.4 459.4 463.4 467.4 471.4 475.4 479.4 483.4

/

280,000 282,000 284,000 286,000 288,000 290,000 292,000 294,000 296,000 298,000

, 2.893x10-6 2.695 2.456 2.241 2.046 1.868 1.842 1.695 1.537 1.397

1

3.782x10-5 3.522 3.210 2.929 2.674 2.442 2.408 2.215 2.009 1.826

ft² sec

Speed of sound

/(ft

89.93 10-9 83.75 76.33 69.65 63.59 58.07 57.26 52.67 47.77 43.42

, ) -v / (

( sec ft²

Kinematic viscosity μ .‫ע‬

,)

0.06669 0.06241 0.05724 0.05257 0.04829 0.04438 0.04381 0.04082 0.03760 0.03469

Coefficient of viscosity

) / ( ,) / )(

μ

) (

432.0 432.0 432.0 432.0 432.0 432.0 432.0 435.4 439.4 443.4

Specific weight gp lb ft³ λ

262,467 264,000 266,000 268,000 270,000 272,000 272,309 274,000 276,000 278,000

,)

slugs ft³

Density ratio σ

,

1.512 1.397 1.293 1.198 1.111 1.032 0.9588 0.8920 0.8310 0.7746

) /l(b , )

ft²

Density

TABLE A3

3.151x10-5 2.949 2.705 2.484 2.282 2.097 2.070 1.929 1.776 1.638

Pressure ratio PO

,

abs

Pressure P

ft

Absolute tempera ture

PROPERTIES OF THE UPPER ATMOSPHEREFOR TENTATIVE STANDARDTEMPERATURESBASED ON AN ARBITRARY CONSTANTVALUE OF GRAVITATIONALFORCE BRITISH ENGINEERING SYSTEM Continued

A3-7 TECHNICAL AERODYNAMICS TO

393,700

lb

Altitude

Pressure

,

T

b

.

°F , (

)

(

380,000 382,000 384,000 386,000 389,000 390,000 392,000 393,700

/P

0.001640 0.001564 0.001492 0.001423 0.001358 0.001296 0.001237 0.001190

, 4.423 4.443 4.464 4.484 4.504 4.525 4.545 4.562

0.03925 0.03719 0.03526 0.03343 0.03171 0.03009 0.02854 0.02732

€ 362.5 384.3 407.3 431.6 457.0 483.9 512.3 537.3

197.7 210.4 223.9 238.2 253.2 268.9 285.7 303.5 322.2 341.8

223 236 250 265 280 296 313 331 350 370 390 411 434 458 483 509 536 560

1358 1362 1367 1371 1376 1380 1384 1389 1393 1398 1402 1406 1411 1415 1419 1423 1428 1431

:

Atmosphere

Upper

,

the

.

Note

Tentative

,

N.

No.

1200

Tables

,

Technical

for

.

Calvin

the

Properties

of

)

(

:

3

.

NACA

,

Warfield

,

4

:

.

262,467 FEET DAY ONLY Continued

AIR

Reference

ft

123 131 139 148 157 167 177 188 199 211

1312 1317 1322 1326 1331 1335 1340 1344 1349 1353

sec

FEET

where the meen free paths of The values for viscosity listed in these columns are not applicable at the higher altitudes Furthermore the values listed the molecules are comparable to or longer than the dimensions of the body being considered has been made for the effect no allowance consequently are based on the conventional Sutherland formula for normal air and oxygen in the atmosphere at the higher levels of dissociated

0.05130 0.04861 0.04609 0.04369 0.04145 0.03933 0.03731 0.03571

1.220 1.156 1.096 1.039 0.9856 0.9352 0.8872 0.8491

4.214 4.236 4.257 4.278 4.299 4.319 4.340 4.361 4.382 4.402

0.06860 0.06477 0.06116 0.05779 0.05464 0.05166 0.04886 0.04624 0.04376 0.04144

103.4 110.5 118.1 126.2 134.8 143.7 153.4 163.6 174.4 185.7

ft2 sec

Mean free path of molecules

STANDARD

0.07751 0.07390 0.07049 0.06724 0.06417 0.06126 0.05847 0.05624

0.08967 0.08466 0.07994 0.07554 0.07142 0.06753 0.06387 0.06044 0.05720 0.05416

(

647.6 651.6 655.6 659.6 663.6 667.6 671.6 675.0

/

2.132 2.013 1.901 1.796 1.698 1.606 1.519 1.437 1.360 1.288

Speed of sound

TABLE A3

0.1271 0.1208 0.1148 0.1092 0.1039 0.09887 0.09411 0.08962 0.08536 0.08133

,

(

0.002690 0.00255 0.002429 0.002311 0.002199 0.002092 0.001992 0.001897 0.001806 0.001721

, )

607.5 611.5 615.5 619.6 623.6 627.6 631.6 635.6 639.6 643.6

(

360,000 362,000 364,000 366,000 368,000 370,000 372,000 374,000 376,000 378,000

lb

3.999 4.021 4.043 4.065 4.085 4.108 4.129 4.151 4.172 4.193

2

0.1244 0.1170 0.1102 0.1036 0.09755 0.09196 0.08660 0.08163 0.07697 0.07264

/ )(

0.1626 0.1529 0.1440 0.1354 0.1275 0.1202 0.1132 0.1067 0.1006 0.09495

Kinematic viscosity

ν

3,866 3.636 3.424 3.220 3.032 2.858 2.692 2.537 2.392 2.258

-v l/b

ft³

Coefficient of viscosity 11 sec ft² μ

0.004556 0.004315 0.004091 0.003875 0.003674 0.003485 0.003306 0.003136 0.002978 0.002829

· -

Specific veight gp

/f(t , ) ./ , )(

567.5 571.5 575.5 579.5 583.5 587.5 591.5 595.5 599.5 603.5

)

slugs ft³

Density ratio

,)

340,000 342,000 344,000 346,000 348,000 350,000 352,000 354,000 356,000 358,000

P

) (

0.2153 0.2039 0.1933 0.1831 0.1736 0.1647 0.1562 0.1482 0.1407 0.1337

) /l(b ,)

ft²

Density

,

abs

Pressure ratio PO

,

ft

Absolute tempera ture

APPENDIX

A3-8

to 393,700

.

1

Altitude

Absolute tempera ture

Pressure

Pressure ratio PO

,

,

h

lb

T

.)

(s)t

°F (

0.6643 0.6151 0.5699 0.5286 0.4906 0.4556 0.4233 0.3935 0.3660 0.3407

0.3171 0.2955 0.2753 0.2569 0.2397 0.2238 0.2090 0.1953 0.1826 0.1709

0.01406 0.01302 0.01206 0.01119 0.01038 0.009642 0.008958 0.008327 0.007745 0.007210

0.006711 0.006253 0.005826 0.005437 0.005073 0.004736 0.004423 0.004133 0.00 3864 0.003617

487.4 491.4 495.4 499.4 503.4 507.4 511.5 515.5 519.5 523.5

527.5 531.5 535.5 539.5 543.5 547.5 551.5 555.5 559.5 563.5

320,000 322,000 324,000 326,000 328,000 330,000 332,000 334,000 336,000 338,000

(

300,000 302,000 304,000 306,000 308,000 310,000 312,000 314,000 316,000 318,000

/

1.481 1.363 1.255 1.156 1.066 0.9832 0.9079 0.8384 0.7748 0.7168

)

0.03134 0.02884 0.02656 0.02446 0.02256 0.02081 0.01921 0.01774 0.01640 0.01517 0.7065 0.6489 0.5963 0.5487 0.5052 0.4654 0.4290 0.3957 0.3653 0.3374 0.3116 0.2882 0.2665 0.2469 0.2286 0.2119 0.1965 0.1823 0.1692 0.1572

7.410 6.853 6.337 5.871 5.436 5.039 4.673 4.335 4.023 3.738

3.777 3.799 3.822 3.844 3.867 3.889 3.911 3.933 3.955 3.977

3.546 3.569 3.593 3.616 3.639 3.662 3.685 3.708 3.731 3.754

34.2 37.3 40.6 44.1 47.9 52.0 56.4 61.1 66.2 71.7 77.6 83.9 90.8 98.0 106 114 123 133 143 154

1082 1087 1091 1096 1100 1104 1109 1113 1117 1122 1126 1130 1134 1139 1143 1147 1151 1155 1160 1164

21.11 23.13 25.34 27.71 30.30 33.08 36.13 39.41 42.95 46.79

60.31 65.47 71.14 77.18 83.69 90.73 98.31 106.4

14.1 15.5 16.9 18.5 20.3 22.2 24.2 26.5 28.9 31.5 1037 1042 1046 1051 1055 1060 1064 1069 1073 1078 8.103 8.945 9.873 10.90 12.01 13.22 14.54 15.98 17.57 19.27

,

:

262,467 FEET

0.2384 0.2205 0.2039 0.1889 0.1749 0.1621 0.1503 0.1395 0.1294 0.1203

0.5405 0.4964 0.4562 0.4198 0.3865 0.3561 0.3282 0.3027 0.2795 0.2581

12

5.40x10-3 .84 7.46 8.13 8.87 9.67 9.80 10.6

: .

5

AIR

15.43 14.18 13.05 12.01 11.07 10.20 9.409 8.686 8.023

3.306 3.331 3.355 3.379 3.403 3.427 3.451 3.475 3.499 3.523

1019 1019 1019 1019 1019 1019 1019 1023 1028 1032

.

1.313 1.198 1.093 0.9976 0.9120 0.8339 0.7638 0.6994 0.6410 0.5881

3.572 3.818 4.164 4.541 4.951 5.401 5.475 5.974 5.620

ft

FEET

1.726 1.566 1.429 1.304 1.192 1.090 0.9984 0.9142 0.8378 0.7687

ft² sec

Meanfree path of molecules λ

STANDARD

40.80 37.24 33.98 31.01 28.34 25.92 23.74 21.74 19.92 18.28

=

) /b v l(

( 3.212101 3.212 3.212 3.212 3.212 3.212 3.212 3.232 3.257 3.282

lb

1

447.4 451.4 455.4 459.4 463.4 467.4 471.4 475.4 479.4 483.4

-

2.893x10-6 2.707 2.482 2.276 2.087 1.913 1.887 1.741 1.583 1.441

/ )(

3.782x10-5 3.538 3.244 2.975 2.728 2.501 2.467 2.275 2.069 1.884

μ

1

280,000 282,000 284,000 286,000 288,000 290,000 292,000 294,000 296,000 298,000

P

/)(

89.9310-9 84.13 77.14 70.74 64.87 59.47 .67 54.10 49.20 44.80

(

)

sec ft²

Speedof sound @ ft sec

/

, ()

Kinematic viscosity y

,)

0.06669 0.06239 0.05720 0.05246 0.04810 0.04410 0.04351 0.04044 0.03712 0.03408

, ) (

432.0 432.0 432.0 432.0 432.0 432.0 432.0 435.4 439.4 443.4

Coefficient of viscosity

,

262,467 264,000 266,000 268,000 270,000 272,000 272,309 274,000 276,000 278,000

,

slugs ft³

Specific Weight gP ft³

TABLE A3

3.151x10-5 2.948 2.703 2.479 2.273 2.084 2.056 1.911 1.754 1.611

/P ,) /( ,

ft2

Density ratio 8

,

abs

Density

CONSTANT VALUEOF GRAVITATIONALFORCE BRITISH ENGINEERINGSYSTEM Concluded

-

PROPERTIESOF THE UPPERATMOSPHERE FOR TENTATIVESTANDARD BASEDONAN ARBITRARY TEMPERATURES

A3-9 TECHNICAL AERODYNAMICS

NIGHT ONLY

TO

393,700

Altitude

,

,

h

ft

Absolute tempera Pressure P ture T ft2 abs

1b

.

F °

(

) ( 0.02660 0.02497 0.02345 0.02204 0.02073 0.01951 0.01838 0.01748

535.0 572.5 612.5 654.5 698.9 746.2 795.7 839.5

331 353 376 400 425 451 479 508 539 571 604 639 676 714 754 795 838 875

1256 1267 1277 1287 1297 1308 1318 1328 1339 1349 1359 1370 1381 1391 1401 1412 1422 1431

of

the

:

Upper

Atmosphere

Tables Note

No.

.

ties

,

Technical

.

Tentative

,

N.

for

the 1200

Proper

3

. NACA

,

Calvin

,

Warfield

262,467 FEET Continued )

(

:

AIR

Reference

,

NIGHT ONLY

484 504 .525 4.545 4.562

4.423 4.443

278 4.299 .319 4.340 4.361 4.382 .402

258.2 278.9 301.1 324.3 349.2 375.9 403.7 433.5 465.7 499.3

: 5 .

STANDARD

0.03477 0.03264 0.03065 0.02881 0.02710 0.02550 0.02402 0.02285

4,214 .236

0.05251 0.04887 0.04550 0.04243 0.03959 0.03698 0.03458 0.03235 0.03027 0.02837

FEET

0.06864 0.06388 0.05947 0.05546 0.05175 0.04834 0.04520 0.04229 0.03957 0.03708

ft

166 178 192 195 206 221 237 253 271 290 310

sec

1168 1172 1176 1177 1185 1195 1205 1215 1226 1236 1246

ft

Mean free path of molecules

TABLE A3

The values for viscenity listed in these columnsare not applicable at the higher altitudes where the meanfree prths of Furthermore the values listed the molecules are comparableto or longer then the dimensions of the body being considered are based on the conventionel Sutherland formule for normal ir and consequently no allowance has been madefor the effect of dissociated oxygenin the atmosphereat the higher levels

0.8268 0.7761 0.7288 0.6851 0.6444 0.6064 0.5712 0.5434

0.05000 0.04757 0.04528 0.04313 0.04112 0.03920 0.03741 0.03598

) /( , )

0.001058 0.001007 0.0009582 0.0009127 0.0008702 0.0008096 0.0007917 0.0007614

/

647.6 651.6 655.6 659.6 663.6 667.6 671.6 675.0

P

380,000 362,000 384,000 386,000 368,000 390,000 399,000 393,700

( 1.632 1.519 1.414 1.319 1.231 1.149 1.075 1.006 0.9409 0.8817

(

0.08576 0.08098 0.07648 0.07235 0.06848 0.06488 0.06151 0.05836 0.05537 0.05260

-/ 1d

0.001815 0.001714 0.001618 0.001531 0.001449 0.001373 0.001302 0.001235 0.001172 0.001113

(

607.5 611.5 615.5 619.6 623.6 627.6 631.6 635.6 639.6 643.6

,) lb

-

1

360,000 362,000 364,000 366,000 368,000 370,000 372,000 374,000 376,000 378,000

/ )(

3.999 4.021 4.043 4.048 4.065 .086 4.108 4.129 4.151 4.172 4.193

H

(( )

0.1118 0.1038 0.09663 0.09494 0.08936 0.08263 0.07644 0.07075 0.06560 0.06083 0.05748

v

0.1461 0.1357 0.1263 0.1241 0.1168 0.1080 0.09992 0.09248 0.08575 0.07951 0.07383

=

3.474 3.227 3.003 2.951 2.777 2.568 2.376 2.199 2.039 1.891 1.756

/ /)i

ft² sec

Speedof sound

/

0.1599 0.1496 0.1402 0.1380 0.1314 0.1234 0.1159 0.1089 0.1025 0.09646 0.09090

Kinematic viscosity

, ()

115.1 124.6 134.6 137.2 146.4 159.1 172.9 187.8 203.6 220.6 238.8

800 ft²

Coefficient of viscosity

, )

0.003384 0.003166 0.002967 0.002920 0.002781 0.002611 0.002453 0.002305 0.002169 0.002041 0.001924

, ) (

567.5 571.5 575.5 576.5 579.5 583.5 587.5 591.5 595.5 599.5 603.5

Specific Weight gP rt3 λ

340,000 342,000 344,000 344,487 346,000 348,000 350,000 352,000 354,000 356,000 358,000

· -

Density ratio

,) /

slugs ft³

Density

,

PO

Pressure ratio

APPENDIX

A3-10

TO 393,700

.

APPENDIX 4 COMPRESSIBLE TABLE A4 : 1 .

( From Symbols :

/

P Po

P/Po

/ / / /

T To a ao A* A q/p po

12

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90

1.0000 1.2100 1.4400 1.6900 1.9600 2.2500 2.5600 2.8900 3.2400 3.6100

2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90

ISENTROPIC

NACA TN 1428 ; see

FLOW FUNCTIONS

also

NACA TR 1135 ) Machnumber ratio of static pressure to total pressure ratio of local density to stagnation density ratio of local temperatureto stagnation temperature ratio of local speedof soundto speedof soundat stagnation conditions ratio of area, of throat to local cross sectional area of a streamtube ratio of to static pressure y2 to total pressure ratio of the factor V - 1 angle-of -turning of a supersonic streamfrom 1 to M Machangle ap 1/6 TT P Q aa A* A

/

£

M

FLOW CHARTS

ampPo

/

elfo

/

/

/

.5283 .4684 .4124 .3609 .3142 .2724 .2353 .2026 .1740 .1492

.6339 .5817 .5311 .4829 .4374 .3950 .3557 .3197 .2868 .2570

.8333 .8052 .7764 .7474 .7184 .6897 .6614 .6337 .6068 .5807

.91.29 1.0000 .7000 .9921 .8470 .8973 .8811 .9705 1.008 .8645 .9378 1.183 .8969 1.372 .8476 .8502 1.575 .8305 .7998 1.792 .8133 .7961 .7476 2.023 .7790 .6949 2.268 .6430 2.527 .7620

4.0000 4.4100 4.8400 5.2900 5.7600 6.2500 6.7600 7.2900 7.8400 8.4100

.1278 .1094 .09352 .07997 .06840 .05853 .05012 .04295 .03685 .03165

.2300 .2058 .1841 .1646 .1472 .1317 .1179 .1056 .09463 .08489

.5556 .5313 .5081 .4859 .4647 .4444 .4252 .4068 .3894 .3729

.7454 .7289 .7128 .6971 .6817 .6667 .6521 .6378 .6240 .6106

.5926 .5444 .4988 .4560 .4161 .3793 .3453 .3142 .2857 .2598

3.00 3.10 3.20 3.30 3.40 3.50

9.0000 9.6100 10.2400 10.8900 11.5600 12.2500

.02722 .02345 .02023 .01748 .01513 .01311

.07623 .06852 .06165 .05554 .05009 .04523

.3571 .3422 .3281 .3147 .3019 .2899

.5976 .5850 .5728 .5609 .5495 .5384

.2362 .2147 .1953 .1777 .1617 .1473

3.60

12.9600

.01138 .04089

.2784

.5276

.03702

.2675

.5172

.03355

.2572

.03044

3.70 3.80 3.90 4.00 4.50 5.00 6.00 7.00 8.00 9.00 10.00 15.00 20.00 100.00

13.6900 9.903 x10-3 14.4400 8.629 x10-3 15.2100 7.532 x10-3 16.0000 6.586 210-3 20.2500 3.455 x10-3 25.0000 1.890 110-3 36.0000 6.334 1104 49.0000 2.416 x10 64.0000 1.024-4 x10 81.0000 4.739 x10-5 100.0000 2.356 x10-5 225.0000 1.515-6 110

/

Po

.3698 .3967 .4157 .4270 .4311 .4290 .4216 .4098 .3947 .3771

0 .4583 .6633 .8307 .9798 1.118 1.249 1.375 1.497 1.616

0 2.182 1.336 1.508 3.558 1.204 6.170 1.021 8.987 .8944 11.91 .8006 14.86 .7274 17.81 .6682 20.73 .6190 23.59

2.800 3.087 3.388 3.703 4.032 4.375 4.732 5.103 5.488 5.887

.3579 .3376 .3169 .2961 .2758 .2561 .2371 .2192 .2022 .1863

1.732 1.847 1.960 2.071 2.182 2.291 2.400 2.508 2.615 2.722

.5774 26.38 .5415 29.10 .5103 31.73 .4828 34.28 .4583 36.75 .4364 39.12 .4167 41.41 .398743.62 .3824 45.75 .3674 47.79

6.300 6.727 7.168 7.623 8.092 8.575

.1715 .1577 .1450 .1332 .1224 .1124

2.828 2.934 3.040 3.145 3.250 3.354

.353649.76 .3408 51.65 .3290 53.47 .3180 55.22 .307756.91 .2981 58.53

.1342 9.072

.1033 3.458

.289260.09

.1224 9.583

.094903.562

.2807 61.60

.5072

.1117 10.11

.087223.666

.272863.04

.2474

.4974

.102110.65

.080193.770

.265364.44

.2381

.4880

.0932911.20

.07376 3.873

.2582 65.78

.01745

.1980

.4450

.0603814.18

.048984.387

.2279 71.83

.01134

.1667

.4082

.0400017.50

.033084.899

.2041 76.92

5.194 x10 2.609 110 1.414 -3 x10 8.150 x10 4.948 x10 6.968-5 x10

.1220

.3492

.0188025.20

.015965.916

.169084.96

.09259

.3043 .2692

.05814

.2411

8.285 6.928 x10 4.589 7.937 x10-3 2.687 8.944 210-3 1.649 9.950 10-3 2.386 14.97 x10 5.854 4-519.97 x10 1.953 100.0

.144390.97

.07246

9.602 34.30 210-3 5.260 44.80 x10-3 3.056 56.70 10-3 1.866 70.00 x10-3 2.663,157.5 x10-4 6.503 280.0 x10-5 2.157 7000.0 x10-8 O

.02766

.04762 .2182 .02174

.1474

.01235 .1111 400.0000 2.091 1.694-5 x10 x10-7 .02236 104 2.790 5.583 4.998 x10 110-12 110-9 0 0 0 0 Mach

angle

= am =

408 0

sin - 1 ( 1/M) omitted

A4-1

.126095.62 .1118 99.32 .1005 102.3 .06682111.5 .05006116.2 .01000127.6 0

130.5

APPENDIX 4 TABLE A4 : 2 .

(From Symbols

: P /Po P2 P1 P2 P1 T2 T 82/81 P3/Po P2 P3 P2 Po

/// / /

Va

A4-2

NORMAL SHOCK WAVE FUNCTIONS

NACA TN 1428 ; see

also

NACA TR 1135

)

Machnumberupstreamof normalshockwave Machnumberdownstream of normalshockwave ratio of static pressure to total pressure upstreamof shockwave static pressure ratio across shookwave density ratio across shockwave temperatureratio across shockwave local speedof soundratio across shockwave ratio of total headdownstream of shockwaveto total headupstream ratio of static pressure to total pressure downstream of shockwave ratio of static pressure downstream to total pressure upstreamof wave ratio of velocity ( correspondingto M ) to the speedof soundwhere

Va

/

P1 Po

/

P2 P1

/

P2 P1

/

T2 T1

/

*2 a1

P3 Po

P2 P3

/

P2 Po

/

V₁ a*

.5283 .4684 .4124 .3609 .3142 .2724 .2353 .2026 .1740 .1492

1.000 1.245 1.513 1.805 2.120 2.458 2.820 3.205 3.613 4.045

1.000 1.169 1.342 1.516 1.690 1.862 2.032 2.198 2.359 2.516

1.000 1.065 1.128 1.191 1.255 1.320 1.388 1.458 1.532 1.608

1.000 1.032 1.062 1.091 1.120 1.149 1.178 1.208 1.258 1.268

1.0000 .9989 .9928 .9794 .9582 .9298 8952 .8557 .8127 .7674

.5283 .5837 .6286 .6652 .6953 .7202 .7411 .7588 .7728 .7867

.5283 .5831 .6241 .6514 .6662 .6697 .6635 .6493 .6289 .6037

1.000 1.081 1.158 1.231 1.300 1.365 1.425 1.482 1.536 1.586

.5773 .5613 .5471 .5344 .5231 .5130 .5039 .4956 .4882 .4814

.1278 .1094 .09352 .07997 .06840 .05853 .05012 .04295 .03685 .03165

4.500 4.978 5.480 6.005 6.553 7.125 7.720 8.339 8.980 9.645

2.667 2.812 2.951 3.085 3.212 3.333 3.449 3.559 3.664 3.763

1.688 1.770 1.857 1.947 2.040 2.138 2.238 2.343 2.451 2.563

1.299 1.331 1.363 1.395 1.428 1.462 1.496 1.531 1.566 1.601

.7209 .6742 .6281 .5833 .5401 .4990 .4601 .4236 .3895 .3577

7978 .8075 .8159 .8233 .8299 .8357 .8408 .8455 8496 .8534

.5751 .5444 .5125 .4802 .4482 .4170 .3869 .3581 .3309 .3053

1.633 1.677 1.718 1.756 1.792 1.826 1.857 1.887 1.914 1.940

3.00 3.10 3.20 3.30 3.40

4752 .4695 .4643 .4596 .4552

.02722 .02345 .02023 .01748 .01512

10.33 11.05 11.78 12.54 13.32

3.857 3.947 4.031 4.112 4.188

2.679 2.799 2.922 3.049 3.180

1.637 1.673 1.709 1.746 1.783

.3283 .3012 .2762 .2533 .2322

8568 .8598 .8626 .8652 .8675

.2813 .2590 .2383 .2191 .2015

1.964 1.987 2.008 2.028 2.047

3.5

.4512

.01311

14.13

4.261

3.315

1.821

.2129

.8697

.1852

2.064

.4474

.01138

14.95

4.330

3.454

1.858

.1953

.8716

.1702

2.081

.4439 9.903 x10-3 .4407 8.629 x10-3 .4377 7.532 x10-3 .4350 6.586 x10-3 .4152 1.890 x10-3 .4042 6.334 7-0 x10 .3974 2.416 x104 .3929 1.024 x10 .3898 4.739 x10 .3876 2.356 x10 .3823 1.5156 x10 .3804 2.091 x10-7 .3781 2.790 x10-12 O .3780

15.80

4.395

3.596

1.896

.1792

.8734

.1565

2.096

16.68

4.457

3.743

1.935

.1645

.8751

.1439

2.111

17.58

4.516

3.893

1.973

.1510

.8767

.1324

2.125

18.50

4.571

4.047

2.012

.1388

.8781

.1218

2.138

29.00

5.000

5.800

2.408

.06172

.8881

.05481

2.236

41.83

5.268

7.941

2.818

.02965

.8936

.02650

2.295

57.00

5.444

10.47

.01535

.8969

.01377

2.333

74.50

5.565

13.39

3.659

2.359

94.33

5.651

16.69

4.086

5.724

20.39

4.515

7.631 110-3 .9005 4.470 x10-3 .9016 2.745 x10-3 .9041 3.974 x104 .9050 9.753 x10-5 .9061 3.255 x10-8 O .9061

M

2

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90

1.0000 .9118 8422 .7860 .7397 .7011 .6684 .6405 .6165 .5956

2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90

3.6 3.7 3.8 3.9 4.0 5.0 6.0 7.0 8 9

8 15

8

20 100

8

116.5

/

3.236

262.3

5.870

44.69

6.685

466.5

5.926

78.72

8.873

11,666.5

5.997 1945.4 6

44.11

/

8.488 x10-3 4.964 x10-3 3.045 x10-3 4.395 6-4 x10 1.078 x10-4 3.593-8 x10 O

.8990

2.377 2.390 2.423 2.434 2.449 2.449

A4-3

TECHNICAL AERODYNAMICS

2.0 1.6

1.9 1.8 1.5 1.7

1.6

1.4

ala

Pt 1.5

Pt

1.3

1.4

1.3

1.2

1.2 1.1 1.1

M

1.0

0

.2 .3

I

11

C

4

.6

1.05

Tt/T

││││

1.0

Fig .

.5

A4 : 1 .

?

i

1.10

1.0 1.0

.8

1.15

Pt / P , Tt / T , Pt / P , isentropic ,

SUBSONIC .

1.20

A4-4

APPENDIX 4

10

9 8

Pt +

P

10

(

n

104945 A

6

Pt P

-

)

1

n = 10

1

7

and

P

1

x

Pt

10n

*

5

104

4

M =

Read

1.4

T2.25 = 17.0 0.38

1

(

n

A

P

and

A

111

Mmmm

2.5

3

Tt

/ /T

,

/T

Tt

Pt / P,

A4

: 2 .

.

Fig

2

1.4 1.5

A * A ,

1.1 1.2

3.5

isentropic

3.5

SUPERSONIC

.

2.5

,

1.5

3

1.0

1

.7

M

T

Subsonic A4 Fig

.

2

13

Supersonic

see

,:

Pt

= 2

100

)

A

2

Pt

=

with 2.5

/A /P Tt/

,

Example

For

y

3

TECHNICAL AERODYNAMICS

A4-5

.

60 °

▬▬▬▬▬▬▬▬▬▬▬

M3

‫دمحم‬

1

M1 =

2ta

70 °

Given

400

=

M3 after flow around = 100 corner Δφ Solution For M2 = Read For 26.3 read M3 = 238

Find

26.3

°

=

2

100

=

+

°

2,

=

24

36 30

.

3 =

:

of

:

50°

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬T

:

M2

2

:

Example

300

20 °

100

3.5

)

-

Expansion angles around OUTSIDE CORNERS Meyer flow solution ISENTROPIC

4

2

2.5

;

:

A4

Prandtl

(

.

Fig

3 .

1

1.5

3

M

0

A4-6

APPENDIX 4

20

PPt2 +

4.0

10

Pt1

3.5 Pt1

10M2

P1T1 P1

12

P2 M2

M1

Tt1

10

=

Pt2 MEYEN

P1

P

‫مام‬2

15

Tt2

2.5

9

/ .

-10 Pt2 Pt1

8

T2 T1

10M2

6

2

7

-

1.9 5

1.8 1.7

4

1.6

3

1.5

2.5

1.4

P2 P1

2

1.3

1.2

15 1.1

.

A4

4

.

Fig

:

2.5 Ratios across

NORMAL

3

1

1.5

SHOCKS

.

1

M1

3.5

1.0

A4-7

TECHNICAL AERODYNAMICS

4.01

5 °

S

3.5

+

es =

W 10

100

S

3.0

150

200

M2

M₁

250

.

‫دمحم‬

2.5

200

250

2.0

300 300 350

400 350

$

1.5

°

450 50 550

600 650

1.0 0.9 0.8 0.7 0.6

M2

Normal

w =

(

shock

)°

90

0.5

wiluu M1

1.5

A4

: 5 .

.

Fig

2.0

Angles

and M2

for

2.5

‫سک‬ 3.5

3.0

WEDGE SHOCKS

.

0.4 1.0

4.0

A4-8

APPENDIX 4

20 M1

P1

15

P2

T

M1

M2

S

10

350

P2

300

9 8

250

7 Norme

6

200

5 4.5 4

150

3.5 3 2.5

100

2

50

1.5

A4

: 6 .

.

Fig

2

2.5

Pressure ratio across

3.5

WEDGE SHOCKS

.

1.5

3

1.0

4

s

0

es

TECHNICAL AERODYNAMICS

A4-9

T1

4.0

T2

M1

50

380

es

3.5

$

3.0

300

T2

TPLION

250

s

2.5

50

200

2.0

1.5

B

100

M₁

1.5

2

2.5

3.5

.

.

Temperature ratio across WEDGE SHOCKS semi angle as parameter

Wedge

-

A4

:

Fig

7 .

1

.

1.0

S

4.0

APPENDIX 4

A4-10

es 4.0

↓

es

3.5

M

0w Msurf

3.0

=

100

7

BW

150

200

BS

50

200 250

250

2.5

300

300

2.0

Msurf

350

350 400

400 1.5 500 450

550 600 650

500

1.0 0.9 0.8 0.7 0.65

Minimum M1

for

constant es

0.6 0.55 0.5 0.45

‫لس‬

0.4 1

2.0

1.5

3.0

M1

Fig .

A4 : 8 .

Angles

and Msurf

for

CONICAL

SHOCKS .

4.0

TECHNICAL AERODYNAMICS

A4-11

20 8

M₁ 15

P1

500

7

Psurf

PP1

Psurf

45 °

400

10 350

9 8

300

7 6 250

5

4

200

3 150

2

100

1.

1

es

M₁ 1

1.5

Fig .

A4 : 9 .

2

2.5

Cone surface pressure behind

3 CONICAL

3.5

4

SHOCKS .

A4-12

APPENDIX 4

°

3.0 40

M1

Tsurf

es

2.5 Const shock

Tt = Tsurf

300

Normal

T1

2.0

250

200

1.5 150

100

50

Temperature

2.5

near surface behind

CONICAL

3.5

SHOCKS

.

.

A4 10

:

Fig

2

3

M1 1.5

1

.

1

TECHNICAL AERODYNAMICS

A4-13

1.0 M₁₂

P1 subter 8S

.9 Росу ) P1

D

.

4.0 I

L .8

3.5

.7

3.0

.6

2.5 .5

2.0

1.5 M1

θα

.4

0

10

20

30

40

A4 : 11 . Surface pressure just behind CONE - CYLINDER JUNCTION . Plot ted vs. Os with M₁ as parameter , calculated from Figs . A4 : 2 , A4 : 3 , A4 : 8 , and A4 : 9 . Scatter of points is due to cumulative inaccuracy of a series of chart readings .

Fig .

1

APPENDIX

5

WING AND TAIL SURFACE DATA SECTION CHARACTERISTICS

NACA

,

SERIES AIRFOILS * a.c.

from

Go per deg

Clopt

Cdomin Cma.c.

771 per 6

alo, deg

Cimax

A

-DIGIT

round tips

044

Airfoil

FOUR

= 6,

1.

% c

TABLE A5 :

Ahead

Above

ra

CD min

2.6 3.4

0.099 0.14 0.098 0.13 0.098 0.18 0.095 0.09 0.092 0.06 0.091 0.02 0.096 0.16

0.0058 -0.048 0.0060 -0.051

0.096 0.098 3.8 0.099 -3.6 0.099 3.9 0.096 -3.6 0.099 3.5 0.095 3.6 0.091

0.16 0.28 0.28 0.24 0.27 0.10 0.16 0.04

0.0059 -0.036

1.2 0.9

0.5 1.4 1.1 1.4

0.0064-0.054 0.0071-0.050 0.0075-0.047 0.0082-0.044 0.0063 -0.062

0.3 1.0 0.9 1.1 2.3 1.4

0.0065 -0.075 0.0067 -0.060

0.6

0.4 0.6

-

3.9 0.100 0.32 0.0062 -0.087 T 3.9 0.096 0.26 0.0066-0.088 4.0 0.098 0.32 0.0071-0.088 4.0 0.097 0.22 0.0076-0.085 - 3.7 0.092 0.13 0.0079 -0.078 3.4 0.089 0.08 0.0088 -0.071

-

4.31 4.28 4.28 4.18 4.02 4.04 4.20

0.0060 0.0061 0.0066 0.0072 0.0075 0.0083 0.0066

4.20 4.28 4.31 4.31 4.20 4.31 4.18 4.04

0.0068 0.0072 0.0073 0.0071 0.0073 0.0076 0.0083 0.0090

4.34 4.20 4.28 4.24 4.07 3.96

0.0071 0.0072 0.0073 0.0079 0.0081 0.0089

5 2

0.0061 0.0062 0.0069 0.0076 0.0084

1.0 0.5 0.7 0.9 1.2 1.3 1.8

A5-1

4.31 4.31 4.28 4.24 4.14 4.11

0.7

0.0065-0.075 0.0068-0.073 0.0069-0.076 0.0076 -0.069 0.0082-0.065 0.0089 -0.058

-

446330 4 5

-

54548 3

-

2.0 2.0 1.8 2.3

0.0063 0.0060 0.0064 0.0065 0.0070

443122

1.32 1.77 1.74 1.72 1.57 1.41

-2.1

4.31 4.34 4.31 4.24 4.28

0222242

4406 4409 4412 4415 4418 4421

0.4

2.0 2.0

0.0051 0.0058 0.0060 0.0064 0.0070 0.0080 0.0094

3 3 2 2 312233433 3

1.80 1.83 1.28 1.71 1.74 1.67 1.56 1.38

0.0056 -0.039 0.0060-0.044 0.0061-0.043 0.0068-0.040 0.0076 -0.038 0.0083 -0.035

0

2712 4212 4306 4309 4312 4315 4318 4321

0.18 0.08 0.14 0.10 0.06 0.06

0.099 0.099 0.098 0.097 0.094 0.093

-

2.7

0

|

1.06 1.48 1.73 1.64 1.58 1.48 1.78

1.2 1.7 3.0

0.8

1.7 1.7 2.0 1.7 1.9 1.7

4.28 4.28 4.32 4.24 4.20 4.11 3.82

0.6

0.0062-0.037 0.0064-0.039 0.0070 -0.034

0.12 0.14 0.14 0.12 0.08

-

1.0

0.9 0.4

0.099 0.100 0.099 0.097 0.098

-

0.7

0.0062-0.029

1.8 ――― 1.8 - 2.0 1.9 1.7

-

0.0051 0.0058 0.0060 0.0064 0.0070 0.0080 0.0094

0

2506 2509 2512 2515 2518 2521 2612

0.098 0 0.098 0 0.099 0 0.097 0 0.096 0 0.093 0 0.085 0

OOOOOOO 0 0 0

1.04 1.62 1.72 1.66 1.53 1.44

OOOOO 0 0 0 0

2406 2409 2412 2415 2418 2421

-

- -

1.72 1.11 1.62 1.72 1.65

0

-

2212 2306 2309 2312 2315

0

-

0.91 1.39 1.66 1.66 1.53 1.48 1.28

-

0006 0009 0012 0015 0018 0021 0025

2 1 1 122

dian

0.8 1.0 1.4 1.9

APPENDIX

TABLE A5 : 1 .

A5-2

5

round tips

alo deg

Clopt C40min

Cma.c. Ahead

Above

m6 per

CD min

га

Ci max

Airfoil

Go per deg

= 6,

A

from

44

a.c. %

c

SECTION CHARACTERISTICS , NACA FOUR - DIGIT SERIES AIRFOILS . * ( Concluded ) .

dian

-

-

5.6 5.9 5.9 5.7 5.7 5.2

0.100 0.097 0.098 0.095 0.095 0.092

0.50 0.48 0.33 0.25 0.25 0.10

0.0073-0.129 0.0075-0.133 0.0078 -0.133 0.0087-0.125 0.0093-0.118 0.0099 -0.110

-0.7

0.40 0.48 0.40 0.25 0.10 0.10 0.25 0.35

0.0070 -0.159 0.0075-0.158 0.0079-0.155 0.0094 -0.147 0.0099-0.139 0.0106 -0.129 0.0086-0.185 0.0097-0.199

0.096 0.100 0.095 0.097 094 0.093 0.097 15 0.098 0.10 0.107 0.095 0.66

0.0054 0.0060 0.0058 0.0069 0.0066 0.0083 0.0059 -0.020 0.005 0.0063 0.0076 0.0111 -0.196

1.0 0.6 0.6 2.0 0.8 2.5 1.1 1.0

6.3 6.3 6.2 6.0 5.7 5.3 6.6

0.097 0.099 0.097 0.095 0.091 0.090 0.095 7.3 0.096

-

-

-

0

0 0

0 0 0

-

1.5

-0.6

0

0.2

-11.7

0.0082 0.0087 0.0158 0.0090 0.0086 0.0089 0.0092 0.0100

4.34 4.24 4.28 4.18 4.18 4.07

0.0107 0.0087 0.0088 0.0091 0.0096 0.0101

-

4.24 4.31 4.24 4.18 4.04 4.00 4.18 4.20

0.0099 0.0093 0.0088 0.0096 0.0100 0.0108 0.0094 0.0102

-16

4.20 4.34 4.18 4.24 4.14 4.11 4.24 4.28 4.57 4.18

0.0055 0.0061 0.0058 0.0069 0.0066 0.0083 0.0061 0.0062 0.0076 0.0060

000220

1

4.11 4.20 4.37 4.34 4.24 4.24 4.14 4.07

021200

1.2 1 3 040

0.8

-0.4 0.6

0.7

0.9

0.7

212

0.7 1.3 1.5

-

1.3 1.7

0.1 0.8 1.0 1.6 1.8 1.7 1.2

-1.5

2

111

-

-

† †

{ $

-

-0.143 -0.089 -0.109 -0.112 -0.111 -0.105 0.0091-0.098 0.0098 -0.090 0.0078 0.0077 0.0078 0.0079 0.0077 0.0088

-

8 7 5 3 3 6 924

0.91 1.13 1.10 1.60 1.38 1.50 1.64 1.61 1.64 2.19

-

0.26 0.45 0.57 0.27 0.35 0.22 0.15 0.10

0.0081 0.0076 0.0073 0.0083 0.0087 0.0094 0.0077

T

0006T 0006B 0012T 0012B 0018T 0018B 2R1121 2R212 0012Fo 0012F18

-

0.093 0.096 0.101 0.100 0.097 0.097 0.094 0.092

4.34 4.31 4.11 4.24 4.07 4.04 4.14

11 11 203322322 2

1.38 1.83 1.87 1.79 1.72 1.60 1.96 2.05

-

5.0 5.2 5.2 5.4 5.5 5.4 5.2 5.2

0

6506 6509 6512 6515 6518 6521 6612 6712

-

0

1.53 1.80 1.82 1.70 1.62 1.51

-

-

0

6406 6409 6412 6415 6418 6421

0.5 0.3 1.1 0.9 1.4 1.6 1.0

OOOOOO 0 0 0 0

1.95 1.87 1.65 1.78 1.78 1.66 1.53 1.41

4.3 0.100 0.34 0.0071-0.110 4.1 0.099 0.27 0.0071-0.106 4.2 0.093 0.21 0.0070-0.106 4.1 0.097 0.17 0.0082-0.097 3.9 0.092 0.13 0.0086-0.093 --- 3.4 0.091 0.06 0.0093 -0.082 4.6 0.094 0.24 0.0074-0.124

0

4712 6212 6306 6309 6312 6315 6318 6321

-

0 0 0 0 0 0 0

1.18 1.67 1.81 1.73 1.65 1.50 1.88

1│││││

4506 4509 4512 4515 4518 4521 4612

R≈

-

:

in .;

≈

.

,

.

,

.

.

Tech Rept 669 .

specified

in

as

610 corrected

"

,

"

,

D.

Airplane Design Tenth for ordinates of some of these

K.

.

Wood

A2a

: 7 , 8

,

foils

.

tion

p

See also

,

.

From NACA Tech Rept 628

or

:

.

.

-

;

;

B "p

-

†

T

;

V

ft

3,500,000 Turbulence 0.025 300 lb per sq 80 per sec refers to exceptionally thin nosed sections refers to exceptionally blunt nosed sections R1 and R2 refer to airfoils with reflexed trailing edge Fo and Fi refer to airfoils with flat trailing edge Fo straight Fi deflected down

Edi

air

t

0.7 0.9 1.0

23015 23018 23021 24012 25012

1.73 1.58 1.50 1.71 1.67

1011

1.1 1.2 1.2 1.5 1.6

0.10 0.08 0.07 0.08 0.10

0.0067-0.008 0.0074-0.006 0.0080-0.005 0.0062-0.013 0.0064-0.019

1.1 1.7 2.3 1.3 1.1

32012 33012 34012

1.74 1.80 1.80

111

1.2 0.100 0.15 1.7 0.099 0.10 2.1 0.100 0.20

0.0064-0.005 0.0064-0.014 0.0064-0.022

1.1 1.0 0.6

42012 43009 43012 43012A

1.76 1.72 1.84 1.78

-

1.8 2.4 2.3 2.2

0.20 0.18 0.26 0.29

0.0067-0.009 0.0060-0.021 0.0068-0.019 0.0070-0.017

1.1 0.8 1.0 1.2

43015 43018 43021 44012

1.76 1.63 1.48 1.82

2.4 2.4 --2.8

2.3 0.101 0.18 0.096 0.16 0.093 0.10 0.098 0.25

0.0070-0.015 0.0078-0.013 0.0085-0.010 0.0069-0.028

1.2 1.8 2.4 0.5

62021 63009 63012

1.52 1.77 1.84

63015 63018 63021 64021

1.76 1.63 1.48 1.46

001260 2300960 2301260 2300975 2301275

2.35 -13.1 2.31 -14.0

0.091 0.092 0.088 2.30 15.1 0.089 2.54-15.6 0.085

0.0141-0.200 0.0144-0.233 0.0142-0.236 0.0177-0.210 0.0172-0.228

0.6 0.9 1.2 0.9 1.2

2301575 2302175 4300975 4301275 6300975

2.70 2.74 2.35

0.0168-0.245 0.0156-0 300 0.0178-0.208 0.0171-0.225 0.0178-0.230

1.1 2.3 0.8 1.0 2.6

- 3.1 -3.5

-

-

0.094 0.12 0.098 0.57 3.5 0.100 0.40

0.0087-0.006 3.2 0.0071 -0.042 2.6 0.0075-0.033 2.7

0.25 0.15 0.21 0.13

0.0078-0.024 1.6 0.0080-0.020 2.1 0.0089-0.018 3.1 0.0091 -0.031 2.7

3.5 0.098 3.4 0.097 0.097 4.2 0.094

-

-3.6

.

111

16.2 0.086 16.5 0.094 17.5 0.080 2.6517.3 0.082 2.40 19.0 0.078

in sq in .;

-

0.100 0.100 0.100 0.102

2.4814.3

; ; ; ; ; ° ° ° ° °

f f ff ff f

; ; ; ; ; ° ° ° ° °

0.098 0.097 0.092 0.100 0.100

12.00 1.8 12.00 1.8 12.00 1.8 15.00 18.00 21.00 12.00 12.00

12.00 2.3 12.00 2.8 12.00 3.1 12.00 9.00 12.00 12.00 15.00 18.00 21.00 12.00

21.00 4.6 9.00 5.5 12.00 5.5 15.00 18.00 21.00 21.00 12.00 9.00 12.00 9.00 12.00 15.00 21.00 9.00 12.00 9.00

1.8 1.8 3.7 3.7 5.5

f

;

some

1.6 2.1 2.4 2.7

4.34 4.34 4.34 4.34

0.0063 0.0065 0.0064 0.0065

1.1 1.5 1.8 1.8 1.8

4.32 4.34 4.34 4.32 4.34

0.0060 0.0062 0058 0.0060 0.0061

4.24 4.14 4.18

1.8 1.8 1.8 2.1 2.3

4.28 4.24 4.07 4.34 4.34 4.34 4.32 4.34

0.0066 0.0065 0.0066

3.1 3.7 3.7 3.7

4.34 4.34 4.34 4.41

0.0068 0.0065 0.0071 0.0073

3.7 3.7 3.7 4.2

4.37 4.20 4.11 4.28

0.0071 0.0079 0.0087 0.0070

4.14 4.28 4.34

0.0089 0.0176 0.0087

5.5 5.5 5.5 6.2

4.28 4.24 4.24 4.14

0.0081 0.0081 0.0092 0.0093

1.8 1.8 1.8 1.8

0063 0063 0.0063 0068 0.0074 0.0080 0.0063 0.0065

4.04 4.07 3.93 3.96 82 3.86 4.14 3.64 3.72 3.57

0.2-chordsplit flaps

.

,

Airplane Design

for ordinates of

Tenth Edition of these airfoils

"

.

as

;

"

lb

"p

ft

,

,

D.

K.

8,

,

:

7

See Wood A2a

.

pp

,

.

; . V

≈

Turbulence 0.025 80 persec ≈300 per Re≈ 3,500,000 From NACA Tech Rept 631and610 corrected specified NACA Tech Rept 669.

CD min

.

0.0061-0.010 0.0062-0.011 0.0062-0.010

ra

dian

,

|||

1.2 0.097 0.25 1.2 0.094 0.13 1.0 0.095 0.10

7716 per

0

1.52 1.49 1.71

0

23012-33 23012-34 23012-64

12.00 12.00 6.00 9.00 12.00

=

1.5 1.3 1.0 0.9 1.2

5887

0.0060 0.001 0.0061-0.005 0.0057-0.012 0.0059-0.009 0.0060-0.008

65877

0.04 0.10 0.15 0.08 0.08

744

0.6 0.099 0.9 0.100 0.100 0.099 -1.2 0.100

64997

- 1.2 -1.1

-

665

1.63 1.72 1.17 1.66 1.74

6677

21012 22012 23006 23009 23012

12.00 12.00 12.00 12.00

5675

1.0 1.5 1.4 1.3

873

0.0062 0.001 0.0064 0.002 0.0064 0.0064-0.002

89990 6 66

0.06 0.08 0.10 0.08

37777

0.8 0.100 0.100 0.9 0.100 1.2 0.100

69677

-0.8

0

1.64 1.73 1.67 1.62

-

Ahead Above 22112 23112 24112 25112

6

.

max. %

0 0

Clopt Cdomin Cma.c.

Max cam ber % ,

do per deg

from 422

alo, Clmax deg

=

с % c

a.c. Airfoil

FIVE - DIGIT

NACA

,

SERIES AIRFOILS *

0

SECTION CHARACTERISTICS

.

TABLE A5 : 2 .

AERODYNAMICS

3

TECHNICAL

A5-3

B B B B

106R. 111 111 (inv.). 112. B 112(inv.).

1.48 1.68 0.89 1.69 0.70

S GS-M S GS-M (inv.) . S GS-I. S GS-I (inv.). St Ae. 27A. RAF34.

1.69 7.9 0.89 1.78 -6.8 1.16 1.72 -10.2 1.58 0.8

USA27 USA27(inv.) USA35-A USA35-B USA35-B (inv.) .

1.71 1 4.7 0.094 0.300.0075 -0.078 0.52 0.080 0.094 1.52 8.0 0.095 0.380.0094-0.111 1.81 5.2 0.099 0.350.0072-0.076 0.081 0.102 0.81

1.8 1.9 0.8 0.5 1.3

C C C C C

62. 72. 72(inv.). 80 80(inv.).

1.06 1.74 0.83 1.24 0.81

0.6 1.0 1.0 0.2 0.4

2481423

N N N N N

22. 22(inv.). 60. 60R. 68.

1.72 0.84 1.73 1.50 0.96

0.6 5.4 0.096 0.170.0075-0.075 0.082 0.8 0.098 5.5 0.097 0.300.0074-0.078 1.5 0.098 0.090.0066-0.001 -0.1 0.7 0.0054 0.097

N N N N N

69. 71 71(inv.) 75. 75(inv.)

1.00 1.67 1.24

46255 614205

0.4

50551 402052 41324O7 2

0

14

.

= 6

A 19.80 8.0 12.64 1.8

18.18 7.3 11.61 4.6 8.04 1.9 11.73 4.0 8.58

1.3

12.37 4.0 12.37 2.8 8.00 10.94 11.54 2.0 11.50 2.0

11.54 2.0 11.54 2.0 14.85 5.9 13.75 4.9

10

0

00

)

-

-

A5-5

13.98 4.5

11.50 2.7

]

00

concluded on

11.50 2.8

0

46132

0

0

0

0

T

:

13.06 2.0 11.50 3.0

0

0

0

0.9 0.7

8.3 0.095 0.180.0084-0.084 -0.4 0.1 10.0058 0.100 0.102 0.2 0.0057 0.5 4.4 0.098 0.220.0071-0.061 0.099 0.062 0.6 6.1 0.101 0.370.0068-0.095 0.8 0.101 0.095 2.9

13.06 3.5

12.37 4.3

0.8 0.7

0.7 0.4 1.9 1.0 1.7 0.5

4.24 0.0076 4.28 4.28 0.0067 4.34 4.14 0.0070 4.11

11.12 5.6

0.7 2.1 0.096 0.190.0067-0.032 0.032 0.5 0.095 2.2 0.098 0.16 0.0060-0.044 -0.1 0.043 0.100 0.2 2.2 0.100 0.140.0062-0.041 0.101 0.038 0.1 6.6 0.097 0.30 0.0076-0.093 6.0 0.094] 0.150.0076-0.081 0.086 0.097 6.1 0.095 0.40 0.0072-0.086 6.4 0.090 0.450.0071-0.093 2.2 0.098 0.100.0070 -0.005 7.7 0.101 0.350.0080-0.096

12.68 4.2 10.38 3.2

16.05 5.5

66 5547

0

0

:

1 11

0

-

:

0.1 1.1 0.4 1.2 0

100

:

1 1

0.300.0080 -0.105 0.105 0.25 0.0070-0.094 0.093 0.400.0102-0.177 0.200.0061-0.006

.p

)

Table A5

-

3

.

)

G

.

G

1.51 1.61 1.65 1.68 0.76 1.91 0.73

11

1.70 1.68 0.83 1.20 1.19 1.46 1.61

-

1111

367 398. 398(inv.). 398A. 398B 398R 413.

*

0.099 0.101 0.097 0.100 100 0.098

1.8 0.095 0.150.0059-0.038 5.6 0.095 0.230.0071-0.084 0.085 0.096 1.0 0.098 0.050.0057-0.015 0.100 0.018

00

G G G G G G G

420. 429AG 429J 436 436( inv. G 532 532(inv.

0.3 1.3 0.9 0.7 0.7

1

1.63 0.99 1.74 1.17 1.79 1.26

G G G G

1.1 0.095 0.05 0.0065-0.001 2.1 0.096 0.17 0.0062-0.033 0.033 0.096 2.0 0.096 0.20 0.0062-0.023 0.023 0.096

0.0058 0.093 2.0 0.099 0.180.0058 0.029 0.030 0.099 1.682.2 0.097 0.150.0065-0.045 1.09 0.046 0.096

80 80(inv.) 81 81(inv.).

N 76.

0.6 0.9 0.5 0.8 0.8 1.4

-

N N N N

N 76(inv.)

4.8 0.097 0.150.0075-0.065 0.069 0.098 3.8 0.098 0.17 0.0065-0.053 0.058 0.100 -4.4 0.094 0.140.0069-0.052 0.057 0.093

m6 per CDmin radian

0

13.62 13.48 13.75 16.45

4.5 4.5 3.5 5.0

18.75 4.5 11.20 11.78 11.10 3.9 13.00 4.8

4.18 0.0066 4.20 0.0063 4.20 4.20 0.0064 4.20 4.31 4.37 4.24 4.34 4.34 4.28

0.0084 0.0072 0.011f 0.0061

14 0.0084 14 4.18 0.0099 4.31 0.0075 4.41

44

1.76 0.96 1.74 0.85 1.64 0.88

725052

103 . 103 (inv.). 103A 103A(inv.). 106. B 106(inv.).

40065

-

B B B B B

Max cam ber

% C ,

Ahead Above

max. %

4.18 0.0060 4.18 0.0075 4.20 4.28 0.0058 4.34 4.20 4.28 4.24 4.28 4.24

0.0076 0.0077 0.0067 0.0055

4.11 0.0058 4.31 0.0060 4.31 4.24 0.0067 4.20 4.20 0.0070 4.18 4.28 0.0062 4.34 4.34 0.0064 4.37 4.24 4.14 4.24 4.18 4.00 4.28 4.37 4.18 4.34 4.41 4.28 4.31 37 4.37

4

Cma.c.

00

Cdo

from C t

,

el max alo deg

MISCELLANEOUS

c

a.c. ao per cl opt deg

с % c

AIRFOILS

*

SECTION CHARACTERISTICS

TABLE A5 : 3 .

Airfoil

A5-4

5

APPENDIX

0.0081 0.0079 0.0092 0.0104 0.0070 0.0087 0.0086 0.0058 0.0059 0.0074 0.0730

TECHNICAL

AERODYNAMICS

SECTION CHARACTERISTICS

AIRFOILS

from

2222

0.150.0060 -0.043 0.170.0060-0.045 0.250.0060-0.047 0.250.0061-0.049 0.17 0.0056-0.044 0.24 0.0056-0.048 0.200.0064-0.038 0.040

1.0 0.100 0.18 0.0055-0.007 0.103 0.150.0059 0.105 0.0063 0.008 0.9 0.104-0.05 0.0065 0.008 1.3 0.102 0.100.0053-0.010

-0.8 -0.8

2 5 1 7 2 43 664 6 5

-

0.3 0.7 0.4 0.6

11.70 3.1 12.01 2.4

1.2 0.5 0.4

-10

0.5

-0.1 -0.1 -0.3 -0.2

0.0073 0.0083 0.0077 0.0084 0.0059 0.0050 100068 0077 0.0099 0.0113

4.18 0.0066 4.18 4.18 0.0066 4.24

2.0 2.0 2.6 2.6 2.0 2.0 2.4

4.14 4.18 4.18 4.20 4.11 4.00 4.20 4.24

9.00 12.00 15.00 18.00 6.00

2.0 2.0 2.0 2.0 2.0

4.34 4.44 4.51 47 4.41

0.0061 0061 0.0065 0064 0059 0.0067 0.0066

0.0057 0.0060 0.0062 0.0065 0.0054

"

.

;

.

; N = .

. in .;

in

lb

; C

; ; p G ." =

as

Airplane Design

for ordinates of

,

D.

"

ft

D. ,,

.

8 ,

,

7 ,

:

.

K.

.

;

S

: B

See Wood A2a

4.28 4.20 4.28 4.20 4.07 3.96 3.93

12.00 12.00 12.00 12.00 12.00 12.00 12.00

Goettingen = Clark Boeing; Sikorsky Abbreviations U.S. Navy Re 3,500,000 Turbulence≈ 0.025 V≈ 80 per sec 300 per sq From NACA Tech Rept 628corrected specified NACA Tech Rept 669

pp

1.9 2.6 3.2 4.6 6.3

4.07 4.28 4.96 4.14 4.24 4.04 4.14

some

Tenth

Edition

,

1.65 1.67 1.54 1.46 1.14

2.0 0.094 0.095 0.095 0.096 1.9 0.093 2.2 0.090 2.1 0.096 0.097

6.00 8.00 10.00 14.00 18.00

13 22.00 8.0

2.9 0.095 0.080.0065-0.027 0.7 0.095 0.032 1.6 0.095 0.030.0066 0.002 -0.4 0.097 0.007

-2.1

18.00 4.0

-10

-0.8

-1.9 -2.0

...

11.46 3.3 15.00 4.0

of these airfoils

.

23 24 25 26 27.

.)

1.17 1.64 1.53 1.69 1.01 1.02 1.71 1.08

(BRTREEE2

15. 16. 17. 18. 19. 20. 21 21 inv

11.70 3.9

13 NOWNWO

1.58 0.96 1.51 1.19

-

0

NACA : CYH CYH (inv.). -M6. -M6(inv.)

0.15 0.0055-0.038 0.140.0054-0.045 0.230.0065-0.059 0.15 0076-0.080 0.230.0095-0.098 0.101 0.150.0111 0.107

0

inv

0.098 0.096 4.5 0.098 0.096 7.6 0.092 0.089 -9.3 0.088

-3.6

-

06100

]

0.7 0.7 0.7 1.2 1.5 0.3 1.8

- 2.9

0

22

. .)

CY

1.07 1.37 1.68 72 1.48 0.89 1.36

0

C C C Y - - - Y - - -8 -6 . 18 . (

CY Y

C Y 10. 14. CY 18.

1.1 1.7 1.3 1.1 1.3 1.4 2.2

T

. .) ).

C

- - - 18 (

CC

YM 15. YM 15(inv CYM 18. YM inv.

1.68 1 5.0 0.092 0.120.0071-0.069 0.92 0.098 0.072 1.14 -5.4 0.089 0.350.0062-0.075 1.70 5.2 0.094 0.100.0076-0.068 1.23 0.097 0.071 1.00 5.1 0.091 0.07 0.0085-0.064 0.094 0.650 1.39

88886 7 8

C Y (inv.) .

CY -B .

m4 ra- Comin dian

0

%

0

max.

00

Cdo Cma.e. Ahead Above

CY

Max cam ber %

.

cl opt

4

alo deg

,

ctmax

Airfoil

% e

)

* (

a.c. Go per deg

MISCELLANEOUS

Concluded

C,

TABLE A5 : 3 .

C

A5-5

APPENDIX TABLE A5 : 4 .

5

A5-6

CHARACTERISTICS OF TAPERED WINGS , DENSITY - TUNNEL TEST RESULTS *

VARIABLE

a.c. form taper ratio

Wingst

0015-09;0-0 .. 2415-09;0-0 . 2415-09; 15-0. 2415-09;30-0 .. 2415-09;30-8.5 .. 2R115-09 ; 15-8.5. 2R: 15-09 ; 15-0.. 0015-09; 15-3.45. 0015-09; 15-3.45. 2218-09;0-0 .. M6 ( 18) - (09) ;0-0. CYM - 18-09;0-0 . 23015-09;0-0 .. 23018-09;0-0. 23018-09;0-0. 23016-09;0-0. 23018-09;0-0. 23016-09;0-0. 23020-09 ;0-0. 0018-09;0-0 . 23013-43010;0-2. 4412-4412;0-0 ...

2: 1 2: 1 2: 1 2: 1 2: 1 2: 1 2: 1 2: 1 4: 1 2: 1 2: 1 2: 1 2: 1 2: 1 3: 1 5: 1 5: 1 5: 1 5: 1 2: 1 1.6 : 2 Ellip .

As

CL max aLo , deg

pect ratio

tion

a per CLopt CDemin CM a.c. ahead deg

of root

6 6 6 6 6 6 6 6 6 6 6 6

1.53 1.68 1.63 1.43 1.51 1.59 1.50 1.48 1.32 1.60 1.49 1.67 1.71 1.66 1.51 1.50 1.49 1.46 1.42 1.48 1.67 1.81

10 10 10 12 12 6 6 6

0

0.075 0.074 0.075 0.072 0.7 0.076 1.2 0.076 -0.7 0.078 1.0 0.076 0.7 0.076 -1.8 0.071 -1.1 0.070 -5.2 0.071 -1.3 0.074 -1.3 0.073 -1.2 0.083 -1.2 0.083 -1.2 0.083 -1.2 0.086 -1.2 0.084 0.074 -0.7 0.074 0.074 -4.0

-1.7 -1.9 -1.9

0.0065

0.04 0.14 0.19 0.16 0.36 0.26 0.16 0.06 0.10 0.15 0.18 0.22 0.17 0.11 0.04 0.03 0.05 0.02 0 0

0.0065-0.040 +0.022 0.0065-0.043 -0.352 0.0065-0.042 -0.775 0.0071 0.002 -0.786 0.0078 0.003 -0.348 0.0066 0.004 -0.351 0.0069 0.007-0.346 0.0070 0.005-0.334 0.0074-0.029 0.028 0.0071-0.006 0.017 0.0076 -0.071 0.020 0.0067 -0.007 0.014 0.0071-0.007 0.020 0.013 0.0070-0.011 0.0067 -0.009 0.011 0.0071-0.011 0.013 0.0066-0.014 0.016 0.0069 -0.007 0.010

0.15

0.0071-0.100

0

0 0.0069 0.0064 -0.009

0.014

0.020

0.89 0.90 0.90 0.88 0.92 0.93 0.89 0.90 0.90 0.91 0.90 0.91 0.91 0.90 0.80 0.78 0.81 0.76 0.74 0.90

0.018

0.92

30 deg sweepback on

line

.

,

8.5 deg dihedral on

line

.

;

2409 tip airfoil

; .

:

.

,

.

=

2415 Root airfoil

.

Reported in NACA Tech Rept 627 corrected as directed in NACA Tech Rept 669 Numerical designations have the following significance in the example 2415-09 30-8.5

* †

frac

114

Plan

TECHNICAL AERODYNAMICS

3357 camoodore sedToshop

-Rough

.10

012 00 00.2 40.4 v0.6

.08

,

8

48040

,

8

6

ADVISORY NATIONAL CONDITTEE TICS 10 12 16 14 percent Airfoil thickness of chord BACA 64-series

.12 .10 4640

"

Rough

.08

8

12 10 16 18 14 percent of aberd Airfoil thickness 65-series NACA

20

23

.

(a )

,

,

,

Lift curveslopeperdegree

ry

.

(e )

Smooth

A

Lift curveslopeperdegre

.

8

(4 )

of serolift sectionangle Measured 7 L 404

0.4

.

(b )

odore sedTattop 3517 earno

.

,

(e )

2116

8

4 4400

4

-Rough

08

-

,

20

.10

-

20 12 16 percent Airfoil thickness of abord MACA 65-series

12 14 10 16 18 percent of chord Airfoil thickness NACA 63-series

2mooth

ADVISORY NATIONAL FOR AERONAUTICS COMITTEL .06 20 12 24 percent of chord Airfoilthickness 64-series NACA

,

-d

mooth

.12

,

1

.

,

(a )

,

8

(b )

44049 .

,

*

22

.14

20 12 16 percent of chord Airfoilthickness 63series NACA

▾ 230( digit 10 12 18 20 16 14 percent Airfoil thickness of chord igit series four-and five MACA )

.06

Rough

digit

)

14400

Series

.08

,

0000

9

4

sectionangle of serolift of zerolift deg Measured sectionangle Measured P 7 2

-Smooth

.10

-

20 8 12 16 24 percent Airfoil thickness of chord d igit MACA four-andfiveseries

of serolift sectionangle Measured

.12

8

)

)

sy

Lift curveslopeperdegree

deg Measured sectionangle of serolift 4 _____ (a 48069 ) 4 81433 (5

H4digit 250 digit

,

symbols Plagged rouch condition indicate

,

5.14

-

14

.

Series

?

83432 5 (4

A5-7

.12

Booth

.10 011

.08

-Rough

8

6

.

,

(e )

.

L -

.

6 "

von NACA

H. ,

106

.

,

"

,

,

S.

.

,

-

: 1 .

.

A5

,

lift

curve data for some airfoils at Re Section Albert Ira against thickness ratio From Abbott Jr. Summary of Airfoil Data Stivers and Louis Doenhoff 560 Wartime Report

Fig

plotted

E. x

.

a

-

a

(

.

)

,

4

8

ADVISORY NATIONAL ADVISORY NATIONAL FOR AROMANTICS COMMITTEL FOR COMBETTER 12 16 20 18 24 20 10 16 22 12 14 percent percent of abord Airfoil thickness Airfoil thickness of chord 66-series NACA 66-series NACA angles slopewithairfoil thickness A. Measured section of serolift for nus reticandcamber of lift curve Variation andrough conditions berof MAGA airfoil sections of various thicknesses and inboththesmooth of MACA airfoil sections for number camber

APPENDIX 5

011 0.6

digit

A .4

·

DO

14 series (4 digit )

4400

00-series (4 digit )

‫م‬

$ 8

445 M

00

011 0.6

-

24 series

digit

A .4 .2 00

.

( 4

.8

)

1.2

444

021

499

-

digit

)

(4

-

44 series

1.6

.2

Airfoil

)

( 5

-

230 series

Plain airfoil

00- series (4 digit )

2.0

)

(4

-

44 series digit

AL

14-series (4 digit )

2.4

PAOD ..

2.8

with split flap

A5-8

Smooth Rough

Smooth Rough

Symbolswith flags correspondto simulated split flap deflected 60 12

16

20

24

,

16

20

24

.

NACA65- series

.

-

12

Airfoil thickness percent of chord ,

Airfoil thickness percent of chord NACAfour- and five digit series

8

0

8

0

0

°

60 °

Symbolswith flags correspond to simulated split flap deflected 4

.4

3.2

011

&

011

.8

011 -A 0.4

-0.2

0.6

A .4 .2 00

◊

°

Symbolswith flags correspond to simulated split flap deflected 60 16

20

24

,

Airfoil thickness percent of chord .

NACA66- series

.

-

lift

coefficient

,

Maximum section

12

8

240

,

8

4

0

00

Smooth —————Rough

°

Smooth Rough Symbolswith flags correspondto split flap simulated deflected 60 12 16 20 Airfoil thickness percent of chord NACA63 series

Plain airfoil

.

0.6

00

1a

.

A 0.4 .2 00

6.4

.4

with split flap

.2

011 1.2

400 288

Qα

"

09

1.6

Airfoil

4

011

2.0

As

2.4

444

011 0.4 .2 BO

RR Lop

#

PAPP

DO

LINEA

011 2.8

bmax

.

-

L

,

.

,

x

6

2 .

:

.

=

plotted 106 Section C1 max for some airfoils at Re A5 against thickness ratio with and without simulated split flaps and stand From NACA Wartime Report 560 ard roughness

Fig

TECHNICAL AERODYNAMICS

▲ →

cd min

-

063 series

64 65 66

Cd min

A◊ ☐

.008

NACA airfo

.012

NACA632-215 NACA642-215 XACA652-215 NACA662-215 NACA67,1-215

65,3-818

800

°

O

A5-9

.ool .004

.8

.2

/

lift

Design section

A. Variation of minimum drag coeffi cient with position of minimum pres sure for some NACA 6 - series airfoils of the same camber and thickness .

coefficient

011

,

.6 .4 Position of minimumpressure , x o

Variation of section minimum drag coefficient with camber for B.

series airfoil sec percent thickness ratio

.

18

-

NACA

tions of

6

several

Series

)

-

14 digit

digit

)

44 230

-

Rough

▼ 0.6

12 16 HACA64- series

20

24

.

-d

240

20

16

igit series

(c )

12

.

8

4

)

▲ 0.4

Smooth

NACAfour- and five

(a

0.2 0.2

H

Smooth

.ool

00

Rough

cd min

8

.008

4

.012

00

(5

OBOAD

.016

.012 Rough&

.008

Rough

00

Calmin .004

0.2 0.4 ▼ 0.6

A

Smooth

Smooth

0 0 0.2L

ed

.

,

in

Variation of section mini mum drag coefficient with airfoil thickness ratio for several NACA airfoil sections of different cam C.

bers

in both

24

20

.012

.008

.col

Rough

011

00

0.2

40.4

Cd min Smooth

ADVISORY NATIONAL FOR AROMASTICS COMMITTEE 16 20 Airfoil thickness percent of chord NACA66– series

smooth and rough con

12

-

Report

106

,

Re

6

airfoils at

From NACA Wartime

560

plotted

.

.

some

x L -

Section cd min for against thickness ratio

3 .

A5

:

.

Fig

.

)

(•

,

4

.

ditions

12 16 NACA65- series

.

(a

,

)

(b

NACA63- series

Minimum section drag coefficient

) 8

0.6ICS 20 240

16

8

12

Airfoil thickness percent of chord

4

8

4

A 0.4

5

APPENDIX Eagle flaggedsymbols split flap are for 60° simulated .1

A5-10 .1

NATIONAL ADVISORY FOR COMMITTEE AROMANTICS

-.3

digit

20

24

O

&

-d

NACAfour- andfive igit series. 16 12

digit

230

)

▼

•

A4

)

• GO O 14

A

-.1

36

Series

¿

904

,

-.1

Moment coefficient

i

•

24 (5 4

QU SHOTOTOO

11

-440

24

,

4

8 12 16 20 Airfoil thicknesspercentof chord ● NACA 66-series.

( )

.1 .26

0 0.2

Moment coefficient ano

,

.24 NACA230 series

/

-

.22

b

c x

,

.26

24

O

series

+ 16

8

12

20

0

0 0 0.1 O 0.2

NACA

1

22

aerodynamic

20

-

16

4

B

12

center

2

63-series. NACA

.26

:

.24

-.3

.22

position

-

NACA24 series

line = 0.5mean

Chordwise

8 a

011 00 0.2 0.4

.24 14

NACA

series

-

O

.22 26

-.2 .24 -.3

-

.

-d

and aerodynamic 106 plotted

From NACA Wartime Report

560

.

against thickness ratio

at Re

,

coefficient

airfoils

6

moment

x

some

=

for

.

.

center data

Section

L -

,

A5

: 4

.

Fig

24

,

24

8

1 12 16 20 Airfoil thickness percent of chord igit series NACAfour- and five

0

4

.

12 16 20 Airfoil thicknesspercentof chord 8

-.4

NACA00 series

.22

HACA 65-series 4

110

,

ADVISORY NATIONAL FOR ADORANTICS COMMITTEE 12 16 20 24 .26

NACA 64- series.

.

7

-.4

Mament coefficient

of

O

4

mo Good

-.2

TECHNICAL AERODYNAMICS

A5-11 .28

28

/

8

x c

.26

012

.24 .28

/

x c

.26

= 0.4 and 0.6

.24

O

.26

O

8

011

.24 .28 O

4

•

.26 02₁ = 0.2

/

011 = 0 12

16

20

24

/

xc

(0)

021

.24

8

16

20

*

.28

xc

O

011

.24

.26

/

xc

= 0.4 and 0.6 .24

011

28 X C

/

= 0.2

0%1

X C .26

.28

x/ c

.26

= 0.4

.28

.24

011

.24

011

= 0.2

= 0.1 .28

24

.26

.26

₁ =0 0

8

12

16

20

NACA64- series . Airfoil thickness, percent of chord

24

.24

O

x/ c

O

X C

.24

=0

12

NACA65- series .

.28

.26

= 0.2

@

NACA63- series .

.26

= 0.4 and 0.6

x

0

x c

011

.24 .28

.24 .28

.26

x/c

.26

=0 OVL 12 16 NACA66- series .

0

8

c₁

= 0.6

Chordwiseposition of aerodynamiccenter,

106 ,

A5 : 5 .

plotted

1

Airfoil thickness, percent of chard

Symbolswith flags correspond to

Fig .

20

/

xc

Section aerodynamic center data for some airfoils at Re = 6x against thickness ratio . From NACA Wartime Report L- 560.

APPENDIX 5

A5-12

ONACA 64-409 NACA641-412 NACA642-415 ANACA 647-418

-2.0

deg

O

-4.0

, ,a

A

4.0

-6.0

NACA6414212 NACA641-412 NACA641-612

NACA 632-415 NACA 642-415 NACA 652-415 NACA 662-415

▲◇□O

Measured section

O

angle of sero lift

-2.0

-2.0

O

4.0

-2.0

NACA 4412 NACA 4415 NACA23012 NACA 23015

4.0 NACA

A5

: 6 .

.

Fig

for

Airfoils with

Variation of section some

airfoils

4.0 5.0

/

smooth surfaces

angle

of

without flaps

10.0

106

lift

zero with Reynolds From NACA TN 1945

.

.

a

3.0

number

,

Reynolds

.

2.0

Re

1.0

.

-6.0

number

TECHNICAL AERODYNAMICS

A5-13

ONACA 64-409 NACA641-412 NACA642-415 ANACA 643-418

-2.0

..

▲◇ □

.

-4

NACA 64A212 NACA641-412 NACA641-612

□

ONACA 632-415 NACA642-415 NACA652-415 NACA662-415

A

Measured section

angle of zero lift

deg

, a ,

-2.0

A

-4.0

X 2.0

NACA 4412 NACA 4415 NACA23012 NACA23015

0

-4.0

NACA

zero

lift

with

NACA TN 1945.

Reynolds number Concluded )

Variation of section angle of airfoils without flaps From

.

some

106

standard leading edge roughness

.

A5

for

: .6

.

Fig

number

10.0

(

b .

Reynolds

Airfoils with

3.0

4.0 5.0

.

2.0

/

1.0

,

.5

Re

-6.0

APPENDIX 5

A5-14

.12

Δ

O

.10

A

/

NACA 64-409 NACA 64-412

da

.08

do

,

NACA 642-415 NACA 643-418

per degree

.12

A

slope

O

.10

641-012 6414212 641-412 641-612

curve

°

180

NACA NACA NACA NACA

-

OOP

O

.10

▲◇

Section

lift

.12

NACA NACA NACA NACA

632-415 642-415 652-415 662-415

.08 NACA

.12

.10

A

O NACA 0012 NACA 4412 NACA 4415 NACA 23012 NACA 23015

airfoils

/

106

lift

curve slope with Reynolds From NACA TN 1945

without flaps

.

some

10.0

-

Variation of section

for

number

4.0 5.0

with smooth surfaces

-

.

A5

: 7 .

.

Fig

Airfoils

,

Reynolds

a

3.0

.

2.0

Re

1.0

.5

.

.08

number

TECHNICAL AERODYNAMICS

A5-15

.12

.10

.12

.10

NACA 6443-418

dor da

/

per degree

.08

|

A

|

ONACA 64-409 NACA 641-412 NACA 642-415

ONACA NACA ONACA ARACA

.08

641-012 6414212 641-412

64-612

.12

curve

slope

,

.10 NACA 632-415 NACA 642-415 NACA 652-415 ANACA 662-415

□ O

Section

lift

-

.08 .12

.10 NACA .08

1

▲

O NACA 0012 NACA 4412 NACA 4415 NACA 23012 NACA 23015

106

/

,

standard

10.0

leading edge roughness

-

-

Variation of section lift curve slope with airfoils without flaps From NACA TN 1945.

Reynolds number Concluded . )

some

Airfoils with

.

A5

for

: 7 .

.

Fig

number

4.0 5.0

(

b .

Reynolds

3.0

.

2.0

1.0

Re

.06 .5

APPENDIX 5

A5-16

.010 64-409 ONACA 641-412 ONACA ONACA642-415 NACA643-418

A

.008

.006

.004 .008 □

ONACA641-012 NACA6414212 NACA641-412 NACA 641-612

at

.010

▲

.006

.004

□O

NACA632-415 NACA642-415 652-415 NACA NACA 662-415

.008

A

Section dragcoefficient

experimental

% 0

.006

.004

.002 .010 O NACA0012 ONACA4412 NACA4415 ANACA23012 NACA23015

.008 A .006

NACA

Reynolds

Airfoils

4.0 5.0

10.0

106

with smooth surfaces

.

.

a

number

3.0

/

2.0

Re

1.0

,

.oa .5

8 .

lift coeffi

.

:

.

Fig A5 Variation of section drag coefficient at design cient with Reynolds number for some airfoils without flaps .

TN 1945

From NACA

A5-17

TECHNICAL AERODYNAMICS

.016

A◇□

ONACA64-4.09 MACA 641-412 NACA642-415 NACA643-418

.014

.012

.010

.008 014

A ◇ □O

MACA 641-012 NACA64 4212 NACA641-412 NACA647-612

012

Section dragcoefficient

at

.010

.008 .016 XACA632-415 NACA642-415 MACA 652-415 ANACA662-415

◇ □O

experimental

% 0

.01

0

.010 .016 ONACA 0012 ONACA 4412 NACA4415 ANACA23012 NACA23015

.01

.012

.010 NACA

number

4.0 5.0

)

.

(

Concluded

number

10.0

106

/

Re

,

3.0

standard leading edge roughness

for

some

airfoils

.

Reynolds

Airfoils with

cient with Reynolds TN 1945.

2.0

Variation of section drag coefficient

8 .

A5

:

.

Fig

1.0

at design without flaps

lift

.

b .

.008 .5

coeffi

From NACA

APPENDIX 5

A5-18

.0080

.0060

a

.

.0040

Effect of thickness

.

.

a .0080

.0060

.0040

.0040

.0020

Effect of thickness

form

.

Minimumsection

-

.0060

b .

drag coefficient

,

b .

@dmin

.0020

.0100

.0080

.0060

.0040 NACA 63-006 NACA 63-009 NACA 631-012 NACA 633-018 NACA 63-209 NACA 631-212 NACA 64-006 NACA 64-009 NACA 65-006

DODO

.0020

ARADA

♡

.0080

.0060

/

20

15

25

30

NACA

x

25

up

NACA

to

.

camber

TN 1773

106

.

.

cd

Variation min with series airfoils From of

A5

: 9 .

.

Fig

Effect of

Re

C.

106

9

6

6

C. 3

.0020

Re

.0040

for

some

TECHNICAL AERODYNAMICS

A5-19

1.8 ◇

ONACA 63-006 NACA 63-009 NACA 631-012

ANACA 633-018

1.6

Flagged

symbols denote

-

leading edge roughness

Clmax

,

coefficient

1.4

lift

1.2

section

1.0

10 O

15 .

a

Effect of thickness

20

25

30

.

Maximum

3

2

.8

1.4 ONACA 63-006 NACA 63-009 NACA 64-006 NACA 64-009 NACA 65-006

1.2

/

to

x

Re

up

with

106

From NACA TN 1773

.

airfoils

25

,

Re

C1 max

106

number

.

Variation of series

25

30

some

NACA

.

b . .

:

.

A5 10

20

Effect of thickness form Reynolds

Fig

15

9

3

2

.8

6

1.0

for

APPENDIX 5

A5-20

2.01

Maximumsection lift coefficient cimax

,

)

NACA 63-009 NACA 631-012 NACA63-209 NACA 631-212 NACA 63-009 flap

(

▷

1.8

1.6

1.2

Effect of

25

30

to

.

up

.

)

x

(

6

/

106

25 106 for some NACA C1 max with From NACA TN 1773. Concluded

airfoils

Re

Variation of series

.

.

A5 10 :

.

Fig

number

,

Reynolds

20

camber Re

C.

15.

9

6

3

2

1.0

TECHNICAL AERODYNAMICS

A5-21

3.0

2.8

A

ONACA 64-409 NACA 641-412 NACA 642-415 NACA 643-418

Airfoils with .20g split flaps deflected 600

2.6

1.8

1.6

airfoils

lift Maximumsection

Pota

2.0

,

to

max

2.2

coefficient

2.4

Plain

1.4

BQ

IN

1.2 1

1.0

NACA Flagged symbols and broken lines denote with standard leading edge roughness

Variation with

thickness

Re

4.0

5.0

IL

10.0

106

/

,

Reynolds

series

-

number

number

of maximum section

airfoils of

From NACA TN 1945

.

and various

NACA 64 .

11

.

:

.

A5

ficient for four

3.0

2.0

Reynolds

Fig

-

I

1.0

airfoils

0.4 design

lift

lift

coef

coefficient

APPENDIX 5

A5-22

2.8

with .20c split Airfoils flaps deflected 600

▲

2.6

ONACA 641-012 NACA 641A212 NACA 641-412 NACA 641-612

max

2.4

coefficient

,

2.2

2.0

1.6

airfoils

O

1.4

Plain

Maximumsection

lift

1.8

1.2

1.0

NACA .8

airfoils

3.0

number

4.0

5.0

10.0

106

/

Reynolds

2.0 ,

1.0

Re

-

Flagged symbols and broken lines denote with standard leading edge roughness

:

12 .

. -

camber

.

.

Fig A5 Variation with Reynolds number of maximum section lift coef ficient for four NACA 64 series airfoils of 0.12c thickness and various From NACA TN 1945

TECHNICAL AERODYNAMICS

A5-23

3.0

with .20c split Airfoils flaps deflected 60

▲

2.8

ONACA 632-415 NACA 642-415 NACA 652-415 NACA 662-415

2.6

°

Maximumsection

lift

coefficient

,

2.2

2.0

1.8 Ope

max

204

airfoils

1.6

XX

Plain

1.4

1.2

NACA 1.0

airfoils

-

Flagged symbols and broken lines denote with standard leading edge roughness

Fig

3.0

number

4.0

10.0

5.0

106

/

Reynolds

2.0

Re

1.0

,

.8 .5

lift

.

-

6

,

,

lift

.

13

.

:

.

Variation with Reynolds number of maximum section coef four NACA series airfoils of 0.4 design coefficient From NACA TN 1945 and various thickness distribution 0.15c thickness A5

ficient for

APPENDIX 5

2.8

TTTT

O NACA 0012 NACA 4412 NACA 4415 ANACA 23012 NACA 23015

with .20c split Airfoils flaps deflected 60

3.0

A5-24

°

2.6

bax

2.2

coefficient

2.0

1.8

Maximumsection

,

lift

2.4

airfoils

1.6

Plain

104

11

1.2

--

#

10.0

5.0

/

106

section

lift

coef

digit series -

and two NACA

-

maximum

5

-

4

-d

1945

.

.

:

4.0

Variation with Reynolds number of igit series airfoils

ficient for three NACA airfoils From NACA TN .

number

Re

Reynolds .

3.0

2.0

1.0

.5

A5 14

airfoils

-

Flagged symbols and broken lines denote with standard leading edge roughness

.8

Fig

NACA

,

1.0

TECHNICAL AERODYNAMICS

A5-25 1.2

1.0 max

,

+7

.8

NACA65-006airfoil

• 5 x

Re

å

VADODO

coefficient

of

Maximum section lift

V

NACA64-009airfoil

106

6.0

▲ 9.0

1.6

1.4

1.2

1.0 NACA 0 .1 .5 Free streamMachnumber

.2

.5

1.0

oz

. ,

DA

1.2

NACA 64-009

Re

1.5 2.5 3.0

airfoil

106

4.5

▷

9.0

1.0 NACA

.1 .4 .3 Free stream Mach number

Rough condition

.4

airfoil

lift

.

Variation of maximum section coefficient 15 series airfoil sections with Mach and Reynolds numbers From NACA TN 2824 for discussion

:

.

.

)

.

11

.3

.

NACA 642-215

-

.

ter

A5 6

Fig

NACA

,

airfoil b .

NACA 64-210

.2 M

for

several See Chap

(

.2

-

.1

0

.8

*

0 0

airfoil OO

NACA 65-006

lift

.6

x

.8

coefficient

To

Maximum section

.

.4

,

Smooth condition

a

.3

NACA642-215airfoil

.

NACA64-210airfoil

51

.3

-

.2

.1

. ‫اه‬

.8

APPENDIX 5

A5-26

3.2

coefficient

2.4

lift

-

=

x17 106

2.8

2.0

Section

Leading edge slat

17.00

line Airfoilchord

,

Re

1.6

O

-

coefficient NACA

-.6

NACA

0

-8

in

,

a

,

x

4

Re =

lift

O

pitching Section

percentchord

Doubleslotted flap

0.45 Flapchord

Airfoilchord line

-

Trailing edgeflap None flap Double slotted

i

All lineardimensionsare

55.0 Sdst 52.7

line chord Flap

25.00

17.23

-

Section angle of attack

Fig

O

-

cm

,

°

.

.8

moment

by

Slatreference point

1.2

8

16

24

deg

106

-

.

°.

.

-

-

.

:

.

A5 16 Section and moment characteristics for the models with the leading edge slat extended Slat in optimum position for From NACA TN 3007 model with the double slotted flap deflected 52.7

pitching

TECHNICAL AERODYNAMICS

A5-27

4.0

Slat flap

and double -slotted extended and boundary - layer control

3.6

3.2 Double

- slotted

2.8

2.4

c1

NACA LMAL 48071

flap extended ( optimum position )

Slat

extended

(optimum

INCHES

position )

2.0

Plain wing with boundary layer control

1.6

1.2

&

0.8

0.4

α

24

Lift characteristics of NACA

.

:

641A212

airfoil

layer control

-

.

,

-

).

(

,

.

double slotted flap and boundary smooth surface From NACA TN 1293

section with LE 106

x

16

6

8

=

A5 17

O

Re

Fig slot

-8

at

-16

,

0

APPENDIX 5

A5-28

0.862c

0.450c

0.021c

0.092c

0.010c rad rad 0.005c

rad 0.062c 0.021c

Airfoilchord line

0.021c 0.235c 0.375c

0.167c

Airfoil 4.0

A ON 0

cQ Slot sealed .015 .020 .025

)

sealed .015Slot .026

)

(

OBAV

3.6

with flap retracted

.

0.781c

3.2 2.8 2.4 =

°

Of 55

55

°.

of

2.0

=

Sectionlift coefficient of

,

1.6 1.2

A

exoood

.8 = 0 °

of

4

= 0 °

8p

0

÷ NACA

2.2x

in

6.0x

,

, 8 a

0

smooth condition

16 dog

106

NACA 652-415 airfoil sec lift characteristics of thelayer boundary control slot at 0.45c slotted flap and

.

.

-

Section

double From NACA TN 2149

a

a .

:

.

Fig A5 18 tion with

Re

106

Model

-24

-8 -16 Sectionangleof attack =

,

, a

=

Re

16 24 deg

.

-8 Sectionangleof attack 8

-16

0

-.8

TECHNICAL AERODYNAMICS

A5-29

0.65c

Chord

.

Slots at 0.650 4.4

1

3.2

20

.

3.6

)

0

Slot sealed .005 .010 .020 .030 D .034 Flap deflected

)

(

Slot sealed .010 .020 V .030 D .035 Flap deflected

(

0

4.0

2.4

2.0

Section lift

,

1.6

1.2

.8

Flap retracted

a

c

coefficient

2.8

Flap retracted

.4

-.4

Model in smoothcondition

lift

0 16 -8 deg Section angle of attack Model in rough condition a

,

0.018c slot Re =

106 .

of

.

-

.

:

A5 19 Section characteristics NACA 655-424 airfoil section From NACA TN 1631 with boundary layer control slot at 0.65c

.

Fig

-16

32

8

24 deg

x

16 ao

6

,

8

-8 Section angle of attack

,

-.8 -16

24

NACA

APPENDIX 5

A5-30

25

2.0

1.8

4.50 4.23 7.5

to

1.4

168.7

7.5

50

1.2

section

lift

coefficient

cimax

,

NoteAll dimensionspercent chord Flapsnotdeflected for datashown

Trailing edge

flap

deflection

°°

°

DABDO

° ° ° °

20 40 50 60

91

.6

NACA

20

,

Variation of

C1 max

airfoils

.

.

A5 20 :

.

Fig

40

30

Nose flap deflection

with

deg

flap deflections

From NACA TN 2502

.

10

0.000467

in

10

for

double

wedge

-

Symbol

-

Maximum

1.0

Plapsection

airfoil MACA designation ‫هرد‬

0.30

0.80

0.30

0.30

0.30

0.50

0.30

0.30

6000

6000

6000

6000

8000

8000

,,

,,

Sealed 0.0018

,

Bluntnose

0.0003.0068.100.048

to

;

,

;

)

.

,

lift

Overhang

.090.052

Sealed0.001 0.00500.0100 -.0054-0074

,

Sharp nose

.094 .052

Sealed0.001a 0.00500.010 -.0032-0048

.048

.084 .058

-.0116.088

Test Reynolds number 1,430,000 Mach number 0.1 turbulence factor Experimental tunnel wall corrections applied only 1.93 ,

-

6

-

-

: 5 .

INFORMATION REGARDING TWO DIMENSIONAL FLOW MODELS NACA 4- BY FOOT VERTICAL TUNNEL

Overhang

Medium nose

-.006

.052

.092 .052

-.0124.092

Sealed0.0016 0.008 0.010 -.0024-0036

,,

Overbang

Bluntnose

Modified sharp nose

,

333333 0.55

Overbang

0.0060

Sharp nese

IIII

,,

0.35

-.006

.0104 .088 .045

-.0104 .088.Oll

Sealed0.001 0.008 0.0108 -.0064-0125

,

Overhang

.096 .03

.

(

TAIL AIRFOIL TEST

0.80

,,

0.006

,

Modified medium noss

-.0052

Sealed0.0010 0.00500.010-006

€

Medium nose

0.005

-,.

Modified bluntnose

.025

188

Sealed0.0010 0.010 0056 -.0094 .092 .056 0.0050

,,

,,

Bluntnose

,

.

0.80

. , -

Overbang

Overbang

0.20

0.30

6000

Overhang

0.20

0.30

0009

Overhang

0.20

0.30

6000

Overhang

0.80

0.30

0009

Sealed0.0010 .- 0064-012 0.005 0.0100

Circular are

Unbalanced plainflap

0.09

0.30

6000

xe

TABLE A5

-.0116.1000.045

Sealed0.008-0043

Circularare

Unbalanced plainflap

0.10

0.20

6000

0040-0082.09

.Sealed0.006

Hovegap распр xe ses

Circular are

0.18

0000

‫ه‬ Unbalanced plainflap

Description ofbalance

/

0.10

of balance 30/20 Type

A5-31 TECHNICAL AERODYNAMICS DATA

TESTED IN

0.30

0.30

9100

20

Overbang

Overhang

Medium nose

Bluntnose

-.0048-0068

Sealed 0.0050

.036

.08

.Oll

.078 .052

.0052.082

-

-006-0048

-.0034 Sealed 0.0050

Sealed 0.0056

,

;

0.1 turbulence factor only applied to

)

.

,

lift

0.50

0.80

Medium nose

.Oll

.04

)

(

-

-

TWO DIMENSIONAL FLOW MODELS

0018

Overbang

.09

;

Continued

0.35

-.0064-0044.084

81unt nose

Sealed 0.0050

Overhang

-.008

.056

.05

.05

Mach number

0.38

-.0024

Sealed 0.0056

Unbalanced Circularare plainflap

.0116.1 -.0026-0012.102

-.0092

.1

TUNNEL

0.15

Sealed

Ventat 0.560 andat 0.690

Internal

Sealed

Ciroular trailingedge

Profile modification

-.008-011

-

0.50

0.09

Sealed

-6

FOOT VERTICAL

0.30

0.30

6000

Kliptical trailingedge

Profile modification

1,430,000

0.09

-.0096.084.036

REGARDING

0018

0.30

6000

Sealed 0.0060

Experimental tunnel wall corrections number

-.003

Beveled trailingedge

Profile modification

BY

0.09

.05

-.004-0084.088

:

.5

4-

0.30

0.30

6000

° Sealed 0.0000

flap Bulged profile

Profile modification

Reynolds

0.09

NACA

0015

0.30

0009

.052

-.0014-0028.094

Sealed 0.00150

Modified sharp nose

Overhang

0 09

.

(

INFORMATION

0.30

0.30

0009

.094 .06

-.0014-006

.092 .05

-.002

1.93

Sealed 0.00150

-.001

.096 .064

-

Test

Sharp nose

Overhang

0.80

Sealed 0.00180

Modified medium nose

-

A5

0015

0.30

0009

Overhang

0.00

Sealed 0.00180

Medium nos

TABLE

0.30

0.30

0009

Overhang

0.00

TAIL AIRFOIL TEST

6000

0.30

0009

APPENDIX 5 A5-32

DATA

TESTED IN

Plapsection

Reference :

Sears

acteristics of Airplane Control Surfaces

Richard

I. ,

"Wind 0.80

0.30

64-009

64-000 0.26

0.35

66-009

Biantnos

Sealed 0.001

-

-.0022-0048

-

Sealed 0.0050

.092 .052

.076 .064

.0100 .092 .060

-.0126 .096 .056

;

,

)

.

;

,

Test Reynolds number 1,430,000 Mach number 0.1 turbulence factor Experimental tunnel wall corrections applied to 1.93 only ,

lift

Overbang

Bluntnose

-.0064

-.008 Sealed 0.006

Sealed 0.008

-

Overhang

Bluntnose

Circular are

€

Overhang

Unbalanced plainflap

0.11

44-009

-0030.0032.092.032

Sealed

Coverplatespant 0.80station

Internal

-.0096.096.048

-004

Sealed

bent Coverplates in andout at0.650 station

.088 .030

,

0.60

Internal

,

0.80

,

Large coverplates

Sealed0.00110 0.00850.0064-0058-0038

.088 .028

.088 .030

.

(

-

6

:

)

-

INFORMATION REGARDING TWO DIMENSIONAL FLOW MODELS TESTED IN NACA 4- BY FOOT VERTICAL TUNNEL Concluded

(

-

5 .

TAIL AIRFOIL TEST

0018

0.30

0018

Internal

,

0.80

,

0.30

Sealed0.00110 0.008 .0052-0036 0.00250

,-

0015

Medium coverplateb

,

Internal

-.0032 .092 .028

1

-.003

Sealed0.00119 0.0060024.0028 0.00230

,

0.80

Narrow coverplates

0.005

T

-.002

-

-.002

.0028

.092 .048

aa

-.0096

.

0.30

Internal

Sharp nose €

0.80

Overhang

Bluntnos Overhang modification

a

-.0038-008

θα

-

0015

0.30

0.008

,S

0.50

0.50

0.008

,2

Bluntnoe Overhang modification

,1 €

0015

0.30

0018

0.50

Hooegap

0.005

Bluntnose Overhang modification

Description ofbalance

!!!! €

0.30

0.30

0018

0.50

of balance Type

TABLE A5

0015

0.30

90/08

s

0018

NACA airfoil designation08/0

A5-33 TECHNICAL AERODYNAMICS DATA

-tunnel Data on the Aerodynamic Char . NACA Wartime Report L- 663.

Planform

1

Reference :

-

-

acteristics of Airplane Control Surfaces

Sears , Richard

-

I. ,

DDT

" Wind

-

.

-

NACA Wartime

3.7

0.67

0.27

0.27

0.09

0.50

.053

.052 .04

.056 .028

.048 .03

.052 .03

.06

.056 .038

)

7- BY 10 FOOT TUNNEL Turbulence factor 1.6

-

-

-

DIMENSIONAL FLOW MODELS

-

- tunnel Data on the Aerodynamic

Report

elevator Cedro

0.57

=M R

Bevelede

3.7

=M R

noseglerator Sharp

= =N R

Bluntnoseplerater

0.50

=M R

0.27

=M R

0.57

+

3.7

+

0.35

-

0.27

-

0.87

-

3.7

0.35

-

noselevator Sharp

0.27

M R

0.67

0.09

.054 .036

.024 .05

(

THREE

3.7

0.27

tailon Modified Complete 66 stubfuselage NACA Sealed 0031 .0056 1,510,000 series =0.1 tail Horisontal on Sealed NACA pursuitfuselag0.005e .0012 .0035 0009 502,000 =0.1 tail Horisontal On Sealed MACA pursuitfuselage .0018 .019 0009 502,0000.0050 =0.1 tail Horisontal OD Sealed NACA pursuitfuselage -.006 0009 502,000 0.005-004 0.1 tail Borisontal on Sealed MACA pursuit fuselage -.005 0009 502,0000.005-0032 =0.1 tail Horisontal on NACA Sealed 006-008 fuselage pursuit 0009 502,000 =0.1 tail Borisontal on NACA pursuitfuselage Sealed 0009 602,000 0.008-005-0044 0.1

.034 .05

NACA LMAL

Bluntnoseelevator

0.57

tallon Sealed Modified Complete 66 stubfuselage NACA 0.113 -.0022-0068 1,510,000 series inch No.1

-

REGARDING

3.7

0.20

0.31

I

6 .

:

SURFACE

elevator Unbalanced

0.42

0.42 R

rudder balanced Internally

0.47

0.47

tailon Sealed Modified Complete 66 stubfuselage NACA 0.113 1,510,000 inch series 0.1

.053 .024

049 .028

.054 .014

TAIL

2.41

2.41

0.20 = =M R

noserudder Mediue

0.42

= M R

rudder none Medium

0.47

tallon Sealed-.0010-0072 Modified Complete 0.113 NACA 66 stubfuselage 1,510,000inch series 0.1

= M

2.41

0.13

model 0.020-0010-0024 Semispan NACAR 0.50 Modified symmetrical 1,920,000 0.1

.009

IN

rudder Unbalanced

росли OaD Da

INFORMATION

A

0.42

0.30

R

0.47

0.88

Test condition

-

2.41

3.98

Airfoil section

TABLE A5

Bluntnoseelevator

/

0.41 model -40 Modified NACASemiapan 0.020-0015 .38 symmetrical 1,920,000 0.1 .36

30/30 or Sp35

/s

3.96

0.43

or 3p

/

0.58

, 3

Aspect Taper raile λ

-

noee elevator Medium

of section Typical controlsurface

APPENDIX 5 A5-34

TEST DATA TESTED

-

= =M R

L- 663.

Char

APPENDIX

6

PARASITE DRAG DATA 2.4

Vc

416-18

0.4

12

14

7=

V=

+

d

/

2212

.

Wieselsberger

= 1 32

Half tube cylinders

2.0 1.8 1.6 1.4 1.2

#

1.0 0.8

Coo 0.7 0.6

1

wire

Streamlined

0.5 0.4

106

of circular cylinders

.

5

105

2

2

5

5

2

104 103 Reynolds number

2

5

102

Subsonic drag

.

.

:

A6

1

Fig

2

10

0.2

5

0.3

)

(

From NACA TR 619. 1.4 1.2

Wieselsberger

1

02

0.44

0.6

Wind direction

0.4

:

-2

1

:

0.6

Wind direction 1

Coo

8 :

0.8

Coo

4 :1

1.0

1.0

0.8+

1

1.2

:

1.4

0

/

and elliptic From NACA TR 619.

)

cylinders

.

of circular

V

Drag

=

0

=

6 8

2

4

3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Vc Mo

(

.

: 2 .

A6

106

6 8

4

2

105 Reynolds number

3

0 104

Fig

0.2897

Mo 0.4

0.2

2.41 2.81

2.0

=

Mo 0.4

2.4

Coo

Wind direction

1.2 0.8

0.8 0.4

triangular cylinders

NACA TR 619.

A6-1

.

/

and

=

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Vc Mo

V

of square From

0

6 8

3

105

)

Drag

2

6 8

3

4

104 Reynolds number

(

3 .

A6

:

.

Fig

2

103

4

0

0

0.4

Wind direction

1.6

Coo

1.2 4D

1.6

2.0

A6-2

APPENDIX 6

24

---

2.0

)

=

(

8

O 1.2

-

8

.

.

-

-

.

-

·

.

8

-

. -

3 .. -

24

20

1.6

12

3

. - -1 1-

t"

-1. -p

"

.

11

"

.

- .-

" 3 "

critical Reynolds

numberrange

.

Reynoldsnumber in

" "

O

by 0.5 dia Foot WT by 34 Foot WT 0.3 dia A unknown dia ref 15 by dia Foot Supersonic WT and dia ref dia Langley Foot WT -3 dia. Langley 16 Foot WT dia force measurements ref 13 dia ressure measurements ref 13 .10. 0.5 dia fineness ratio 60 ref 12

·, I"

∞

Drag coefficient Co

,

Newtonian theory M co

1.6

2.8

3.2

Supersonic drag of circular cylinders

.

A6

:

.

Fig

4 .

,

Mach number M.

(

)

From NACA TN 2960.

2cos¹8

,

/ ),

P =

( re < ₤ 14

Theory -Newtonian

0-8

Incompressiblepotential 1-4sin

'

,

P -

theory

,

2

T




critical R

O

R

40

80

120

160

)

From TN 2960.

(

Pressure distribution on circular cylinders

.

: 5 .

.

A6

.

,

8,

Circumferentialangle deg

Fig

TECHNICAL AERODYNAMICS

0.20 0.70

Fig . A6 : 6 . Reversible fairings for cylindrical gun barrels . ( From Hoerner , Fig . 8:28 . ) Blunt -nose sections

)

M=1.5

( 1 /M)

sin

1

Bi

. .

V

CD

CD

tan

CD

CD

/

-t

(

M =

.

Comparison of cylinder 1.5 From Hoerner

: 9 .

Fig A6 fairings at Fig 12:21

0.59

)

,

drag of airfoil From Hoerner (

.

=

0.62

.

.

1

.2

c

friction

)

12:20

1.5

0.62

drag

.

1.2 1.0

0.4

CD

V

0.8 0.6

CD

Cnormal

CD and

CL

0.2

Friction

60

)

.

.

of cylindrical cables inclined to Fig 8:31

From Hoerner

,

Drag

(

.

A6 10 :

Fig

CL

α

30

.

.

Fig

Profile M

8 .

:

.

A6

1.5

1.2

Total

.

oubleSkin

Amondeorlin ardhm

sections at

:

/ 33

Drag of faired circular Adopted from Hoerner

wedgeincompr.

Fig

.03.65

3.0

CD convex

.4

,

=

8:27

-1.0.13

90

wind

.

1 μ

.35

.4

=

Cdo

Fig

?

A6

cylinders

1024

2

Fig

.73 1.5-3.0.16

,

0.38

=

3.9

0.60

.4

=

0.17

2.0-3.5 .24

.82

=

0.44

1.5-4.0.4.4

?

2.3

1 d

→

0

crit Mer

2

0.08 0.55

3.0

1.2

4

h

1.20 0.50

O

=

1.0

+

CDT Red Sup

3

Re≈2.105

CDT 105

Sub crit crit

1

Shape

(

Mer

: 7 .

CD

.

/

h d

1 d

)

/

Shape

.

A6-3

APPENDIX 6

A6-4

·

0.080c

C₂

с

-NACA 65-210 modified

C

)

Position Position Position

(

Position

C,

20810

2.66c a66c

C

Vertical variations

of nacelle positions

.

.

a

0866

0.160c

0.156c

0J25c

C

1.20

Q66c 035c

Position A

Position D Position C

B

Position

variations of nacelle positions

.

b .

Longitudinal

0660

-Position C25

sition

111

fuselage on 65-210 wing and drag data

for fuselage ordinates

)

NACA

See next page

of incidence

.

Position of

) (

11 .

:

.

Fig A6 From NACA TN 1593.

angle

.

Variation of nacelle

C.

(

C.2.5

C

.

Position

A6-5

TECHNICAL AERODYNAMICS

Station

1.583

2.392 5.167

6.183 6.925 7.483

25.00 30.00 35.00

0

nacelle length

.08

-

used

04

ACTO

a.2.5

°

α 0 =

ACD 08

)

(

From NACA TN 1593.

.

in

[

tests .08

percent

Ordinates of NACA in wing fuselage

A6 : 12 . ( Above )

fuselage

radii

and

5.100 4.092 3.092 2.075 1.033 .520

95.00 97.50 100.00

8.333 8.333 Stations

6.033

90.00

7.900 8.183

40.00 45.00

70.00 75.00 80.00 85.00

]

20.00

8.217 7.933 7.483 6.833

60.00 65.00

3.592

4.467

10.00 15.00

111

Radius

50.00 55.00

of

1.25 2.50 5.00 7.50

Fig .

Station

O

0

Radius

.04

.08

May

°.

"

α.0

ACD

0

12

°

04

16 Nacelle position

08

·

12

A

B

.04 08

2.5

-

°

α

CDT

O 20

04

06

NACA

a.5

ACT

°

:

0

12

• 0 A

5550

16

position

0

•

Nacelle

.6

(

11 .

:

.

fuselage )

for

.

A6 13 :

.

Fuselage drag incre positions on wing shown in Fig A6 From NACA TN 1593. ment

0

λ 06

O

C

2.5

-

•

:

Nacelle position C

5

M

α

02 08

2.5

.04 2

Fig

3

2

/

0

NACA

5

=

α

ACDT

°

04

=

.04

08

02

.1

.2

.3

M

.4

=

2.50 .5

.6

.7

A6-6

APPENDIX 6

os

C

8 Tail outlet

Streamline body

B

47

05

.8

az

NACA Cowling

NACA cowling

20

04 03

Nose C

CO

Streamline body Nose C

02 Transition fixed Fixed transition .03 .01 .02

Natural transition .07 0 01 .03 .06 .02 Flow coefficient pQ FV

.06

07

wing

.

)

L -

a

.

(

.10 Wose ...

.05

.

Drag of good ducted body mounted on From NACA Wartime Report 300

A6 14 :

.

Fig

.04

a

.05

,

.04

,

0

/p

( a )

.01

(b )

-

%

.06

External dragcoefficient Cor

,

Tail outlet

É

07

.10

-

Nose Body

Opening

Nose 2

Body 3

Body Nose3

C

Nose2 Cowling C ..

Cowling

2

7

Cowling

2

EffectivefuselagedragcoefficientCa

,

.06 0

-

+ )

,

x

,4

.3 .5 Mach numberM T 12 8 16 10 ReynoldsnumberRe approximate

)

.

L -

(

.

.

Effect of Mach number on drag of nacelles with various A6 15 From NACA Wartime Report 542 noses with normal transition

6

;

C,

2 -

:

2 4

)

(a

,

12 16x108 8 ReynoldsnumberRe pproximate

Fig

P •

13567 6

.5

▸

(

4 3 MachnumberM ,

2

Combination Condition Body nose - 2 2 cowling closedexit open open 2 2 18 2 19 closed 2. nose A 3 3-4

B O a O D

open closedexitopen ,

•

.02

Condition

, C,

1, 1;I;

O D

04

6

Combination Body nose вод2 cowling

s

:

02

‫ه‬

. ; ; 2; 2; ; 2 :

04

5

136750202

06

.

Effectivefuselagedragcoefficient

Ca

-

7

.08

1

Body

|

,

Body

.08

TECHNICAL AFRODYNAMICS

M 0.5 α

CDF

PQ

=

21 EXT DRAG AT O

=

INTERNAL FLOW

MODEL ARRANGEMENT

родеть

/

0.05

74

/

Prope "INEST LINE ENCERZ

0

A6-7

680

ORIGINAL NACELLE

C COWL

-

/

.051

.085 335

-

MIDPOSITION

-

COWL C

L

IA

.051.080 AFTER TMPROVED LOW POSITION BODY FOR AUXILIARY AIR OUTLET

E COWL PLAN NEW PROFILE

2

315 -

118.061 240 POSITION MID TOP OUTLET CLOSED

E

My

BE

.053 .088 345

2B

.053

"

088 345

,

SAME ASZALOW POSITION

20

.074

4

2A

.090 350

,

SAME AS28LARGE OUTLETS MIDPOSITION

C COWL

3

-

E [

0.126 0.056 180

MACELLE !

LONG AFTERBODY

SECTION CROSS ELLIPTICAL

.093 054

3A

BOTTOM OUTLET CLOSED

E

4

CIRCULAR CROSS SECTION

093.061

200

.065.053

145

040

110

089 .052

140

SAME AS34 SHORT AFTERBODY .

E

3B

SHORT AFTERBODY

5

113

5A

RIGHT OUTLET CLOSED

5B

089 045 120

,

SAME ASSA SMALL FILLET ON LEFT SIDE

229

.

reported in NACA Wartime Report

L -

A6 : 15a .

M =

for 0.3 Nacelle arrangements

*

Fig .

APPENDIX 6

A6-8

.12

*

10

00

.00

NACELLE ZA NACELLE 2A

COF

2

06

2

CDF .06

04

.04 Outlets open

NACELLE SC

8

NACELLE SC

8

9

SA

0⁰ 10

.20

.30

M

.40

outlets L- 229 . )

IA,

NACELLE

OR

PUSHER

.06

38

0

.10

.20

M

(Pasher )5 40

.50

Fig . A6 : 17 . Comparison of drag co efficients of nacelles . WR L- 229 .

No.

).

,L

.( : . A6

Notation :

°

236

of

5 NACELLE

-Fillet outline

.12

.5

- Free streamvelocity Massdensity of air in internal -Free -stream density

flow

Volumerate of flow Free- streamdynamicpressure(1/2 Por² Maximum cross sectional area of engine F Maximum cross sectional area of nacelle CDF • External drag coefficient of nacelle (total drag of combination) - (wing drag) (drag from internal losses) qF.

·

)

--

/

-

222

6

O

.14

CDF

.60

Nacelle

Rear view

-Air outlets

18 ORIGINAL NACELLE

.50

Report

α =

arrangement

O

NACA Wartime

160

General

A6: 16 . Effect of air ( NACA WR on nacelle drag .

Fig .

.50

From

M

.40

18

.30

Fig

20

inches

.10

Scale

α = 20

A6-9

-

Ordinates

1

X

TECHNICAL AERODYNAMICS

24 1 652042

.x

.

36

2 30 3.1.20 78 1.4289 5 153.96 136 98 1.55600 8.147 .97 9 1.37 101.24 86 11 -38.75 121.90-66 14:47 3

windshield

:

6 4

52

9-1-2

,

8-45

40

3.30 PasiūñíðbavauAGN

Ao

12 2.98 200 275

10-1-2

-

3-1-2

106 391

2-0-3

4.4 278 3.00 307 8 605 473 8 7.01 321 8 7.97 1441.00 8 0.541 1.00 8 811 9.51 10.65360 2 |

22 ye 0 357 bud 410 1.73 8.101450 1634 3.45 867 516 2230 6.502324 0.0 2738 200 14 4450 13.40 14.12 324 2000 17.36 2.323 13.50 21.08 1300 ELAB2/33 1851 24.26 25.22493 27.03 4071 23.ON 23 30.58 22,0 10 !

x

4-0-3

2 8

12.70 1.2485 13.70 1.1087 14.69933 7 18.65741 5 16.M 842 7 57.50344 4 18.94150

-

X 2

-

?

1

xX

M

462

.

WR

-

-

From NACA

) .

Ordinates canopies

.

:

Fig A6 20 of low drag

L

)

-

.

L

(

.

.

.

:

Fig A6 19 Drag of cockpit canopies based on frontal area of canopy From NACA WR 462

.

= -0.670

(

a

,

Mach number

Crdinates

y

3-1-1

.16 12

X

2

,,,,

Drag Coefficient

6-1-2

C C

Section

Section

A A

·

B B

Section

B.B Sestron Section A -

-J

A

-3.00⋅

1

tc

Å

3.30

91

From NACA WR

windshield

462

)

2

-

The

.

canopies

inches

X

in

-

of low drag

are

15

L

dimensions

34.64 10

(

Sketches

25.

Ja

.

All

-

A6 21

.

.

Fig

28.35

windshield

:

1

-

The

X

< -c

A6-10

APPENDIX 6

17.95

20

4.97

Sternpost

44.5832.87

F.P.

12.91

Center of moments

Base

110.19

(a )

line

A.P.

Model 213 ; == 6 .

Extended

afterbody shown 20

broken TN 2762 37.64

51.04

9.85

116.65 (b )

Model

203 ; = = 9 .

20

121.78 (c)

(From

41.42

56.17

8.13

Fig . A6 : 22 . Lines NACA TN 1686 . M=

of

Model 214 ;

some

0.22 , Re2

= 12 .

flying boat hulls tested for drag . = 15 x 106 , transition fixed at 0.05L .

.09

Strut

.08

Wing

.07 .06

.05

CDM

° 170

.03

5

support

support

Planing min

tests

tests

Fig . A6 : 23 . Minimum drag coeffi cient of conventional hulls ( above ) and planing tail hulls ( below ) .

.

tail hulls L/b

10

15

Fig .

Planing tested for drag with wing sup ports . (NACA TN 2762. ) A6 : 24 .

tail hull

A6-11

!! TECHNICAL AERODYNAMICS

2

Fig

Landing

.

:

A6 25

.

(

gear arrangements for which drag data are given below From .

ITTIT

518

,

,

NACA TR 485

and

)

522.

,

See also Hoerner Aerodynamic Drag 128 1951

for

(

,

" , .p "

S. F.

various other

)

0

ar

includ wheels tail

,

-

ing nose wheels and

,

,

rangements

partly re .

tracted wheels

ATAU 214

:1

7

0.86 1.13 1.05

,

0.31

,

1

0.47

1.25

data

for

.

A6 26 :

.

Fig

Drag

landing

gear arrangements sketched above .

.

0.51 1.52 1.02 1.60

,

..

.

0.53

Alo

.

,

8.50-10wheels. 8.50-10-wheels, not faired.. 8.50-10wheels, faired. 8.50-10wheels, not faired. 24-in. streamlinedwheels, in tersectionsfilleted 8.50-10wheels no fillets 8.50-10wheels Low ressure wheels inter sectionsfilleted Low ressurewheels no wheel fairing Streamlined wheels round strut half fork no fairing .

0.84 0.68

above

,

0.98

no

-p

3.83 0.74

4. 5. 5. 6. 7.

-p

1.67 1.50

,

1. 8.50-10wheels, not faired .. 1. 8.50-10wheels, faired.. 1. 8.50-10wheels, no streamline members.. 2. 8.50-10wheels, faired. 2. 27-in. streamlinedwheels, not faired. 3. 27-in. streamlinedwheels, not faired 3. 8.50-10wheels, faired. 3. 21-in. streamlinedwheels, not faired..

Sketch

11

9. 8. 7.

|r=

9.

no . above

9.

Sketch

S

DO

APPENDIX 6

b

B.L.

A6-12

to

= 2

4h h

L

L CDπ

CDπ

/

Approx

$ .1

h 8

10

15

.2 h x

.3

/

.4

CDI

0

= .002

/h

L/h

20

10

L

Fig . A6 : 27 . Drag of half - bodies of Fig . A6 : 28 . Drag of fairings ( bumps revolution on plane wall as affected or blisters ) on plane walls and fus by boundary layer thickness . Replot- elages , with h several times bound ted from Hoerner , " Aerodynamic Drag , " ary layer thickness ( Hoerner , p . 99) . p . 98 . h s at h s Shape of opening ( d/ s) Dr 5 p q Shape of opening (d s) Domin W V V V *

/ /

ŁS

( 2)

Al

/

/

3

1.0

2

J

0

S

Tw

(2)

p = Pout

1

0.15 0.9

/

0

0

3

0.30-0.25

3

1.20-0.5

2

0.10 -0.2

2

-0.1

W

2

In

Tracing

Fig . A6 : 29 . inlet scoops

0.8

0.35

1

Kalf - circular

dk

Gur 7777

of drag of ) . CD based Typical variation

Comparison

/

( Hoerner

on Sπ = Пd2 4 . with w V below .

/

3

10.10

1.2

As Outlets

Fig . A6: 30 . Comparison of drag of outlet scoops (Hoerner ) . Outlet pressure given for w V = 0 . CDπ for w V = 0.5 based on S₁ = d2 /4 .

/

/

CDO

0.8

N

As

0.4

W

b) -0.4

-0.2

Fig .

A6 : 31 .

Inlets

0.5

0

+0.2

Effect of inflow

+0.4

+0.6

¥

+0.8

and outflow on scoop drag .

Airplane

Fig .

A6 : 32 .

-

-

-

#

-

-

Vanesinstalledin rear underslung fuselage duot

-

)) 0 ( ( )) (a (

-

-

-

.000 39

-.000l 37

.0005 39

))6 ) ( ( (

)) ) (a ((

)

.

dragcoefficient Estimated buodifications

-b 5( .000 39

))a ( (

))0 ( ( ) ) ( (

)) (b (

modification Canopy

(

.0017 33 34

.0005 3540

.0005 25

0.0007 20

.0007 30

4016

)) ( ) ) ,) )0( a ( ( (

Redioantenna

) (

.0009 30

.0009 29 .0004 35 .0005 30 .0005 51

))a ( (

Tail surfacegapleakage

) ) ( (

.0005 29 .0007 .0002 36 35

)) ( (

Tail wheelandarresting hook

) (

.0014 27

.0007 25

.0005 20

0.0017 10

0.0173 .0208

0.0171 .0221

) (

Armament

.0008 32

) (

.0012 22 .0010 26

) (

Landing gear

) ( .0004 24

.0021 0.0010 19 17

0.0005

))e (7(

Wing fold axis leakage andgunaccess doors

.0008 18

) ))a ( (

0-0.0034 13 .0002 15

0.0005

12

13

)) (b (

Sanded walknova

0.0040 21

0.0004

)a (7(

installation Supercharger

ACD

)) ) a ( b( ( (

0.0021 12 .0018 .0008 14 12 1416

0.0004 0.0041

10

) (

Exhaust stacks

2

))b (7(

Carburetor scoops

[ )6 (

Coolantradiatorinstallation

3

011coolerinstallation

4

ingductinlets

5

Cowling flapandhingeline gapleakage

in

6

0.0040

] 0.0160 C.0219 0.0215 0.0210 .0280 .0284 .0293

7

CD 0.0183 0.0313 0.0282 0.0222 .0337 .0386 .0293 0.0361 .0264

8

Enginecooling

0.0205 .0243

Numbere parentheses referto figures 9

sealedandfaired Airplane in servicecondition Airplane

Item

A6-13 TECHNICAL AERODYNAMICS

) ( )a( ( 40

))b ( (

) (

)) a ( (

) (

))0 ( (

)) a (3 (

.

Drag data on complete airplanes shown on opposite page . ( From NACA Wartime Report L- 108 . )

A6 : 14

APPENDIX 6

NACA LMAL22001

LMAL MELS

Service condition; propeller removed g) Airplane 7. Tunnelmock installed . -up; propeller (a) Airplane 1.Wing ( sq. ft. area 256.0 sq.ft. Wingarea = 170.0

NACA NACA LMAL22146 MAL31581

(b) Airplane 2.

. Service condition; propeller removed Wingarea 290.0 sq.ft.

(h) Airplene 8. Sealedandfaired condition; propeller removed . Wingarea = 442.0 sq. ft.

T NACA MAL30781 LMAL2 302 Service condition except for sealed . (e) Airplane 5.cowling Service condition; propeller removed . (1) Airplane 9. Wing holes; outer-wingpanels removed area 314.0 sq.ft. Wingarea 465.0 sq. ft .

NACA LMAL20474

NACA 32402 LMAL

propellers removed (d) Airplane 4. Service condition; sq . (3) Airplane 10. Service Condition. Wingarea 534.0 sq. ft . Wingarea 527.5. . ft .

LMA

-nacelle installation ; propeller (e) Airplane 5. Engine installed . Wingarea

(f) Airplane 6.

1048.0sq.

Y

A6: 33 .

(k) Airplane 11. Service condition.

ft.

. Service condition; propeller removed Wingarea 490.0 sq. ft .

Fig .

50 Wingarea

(1)

248.0 sq.

ft .

Airplane 12. Sealedandfaired condition; . Wingarea=255.2 sq. ft . propeller removed

Fig . A6 : 32 . Airplane photographs for data in (From NACA Wartime Report L- 108 . )

TECHNICAL AFRODYNAMICS

A6-15

.8

..21

Shock detaches °19

&

11.

ε

CDA nose cone

-d

300 .

.8 .4

=

·6

200

.4 CDA .2

Ε

M

N

10 °

.2

/

( log scale ) 2

1

d x = 2 tan €

4

3

.4

Fig .

Fig . A6 : 34 . Drag of conical noses vs. M for three semi - vertex angles . (Hoerner . ) .5

A6 : 35 .

.8 Drag

/

M =

Skin

friction

vs. d x at

1.2

1.6

of conical noses 2. (Hoerner . )

1.0

X 404

.8

.4 Base

.3

.6

CD π Wave drag

.2

of conical

drag

.2

friction )

Base drag

Base drag 2

1

Wave

nose

Skin

.1 0

4

zzd/ x 4

3

Fig . A6 : 36 . Drag analysis of cone cylinder bodies vs. M for d x = 0.4 . (Hoerner . )

/

.3

Tail

.4

/

.

Base drag

cone

CD Constant forebody drag

.1

/

Sh S .2

0

Fig .

and

.

2

drag to

.8 1.0 .6 Effect of boattail on base total drag in the region M = 1.5

A6 : 38 .

.4

.6

.8

1.0

Fig . A6 : 37 . Drag analysis of cone cylinder bodies vs. d x for M = 2 . (Hoerner . )

Flow separation

.2

.2

0

APPENDIX 6

-24

/

-2 7M

From Ref

Present tests Model 8

-c

/0-7

. .

0

-12

Ogive ylinder with boattail

From Ref 9 From Ref 10

O

pressure

/0-7

Ogive ylinder

4 9

1 -c

O

.

From Ref

)

-16

σ

.

Vacuum limit

(

coefficient

-.20

Present tests Model 3

1

,R

A6-16

-08

Base

-.04 30

2.0

5.0

4.0 M.

6.0

,

Mach number

-24

x

=

/

Vacuum limit

7

SSWT

-12 pressure

=

1-

-

.

)

(

-2 yM

-16

-

4

Present tests Model 3 Ogive cylinder From Ref O From Ref 9 1/0 7 Present tests O From Ref 9 cylinder From unpublished Ogive data NACA Ames with boattail by 3- foot 1/0 . .

-20

coefficient

10

-

,P

,

(a)

Laminar boundary layer Re 3.0

-08 D

Base

-04

NACA

4.0 3.0 Mach number M.

2.0

5.0

6.0

,

9.0

coefficient reported

= PbSb

where Sp

= 0.365 and ogive boat semi angle ≈ 100

= 0.6042

=

ACDπ

x

=

,

ACDST

106

.

-

base pressure

tail

-

For above tests

on

NACA TN 3393

.

=

tail

in

-

Po

boat

/S

90

/S

= Pb

Effects of

S

Pb

A6

:

.

Fig

39 .

(b )

Turbulent boundary layer Re 5.0

base area

equivalent to

.5

.4

Fig

9

.3

.2

COEFFICIENT

DRAG

.1 for

2.2

2.4 NACA

CDB

CDT

100

NACA RM 10

4.5 106

106

to

)

test measurements From NACA TN 2944.

, flight

M

.) : .

. : .

Comparison of wind tunnel and in Fig A6 42 photographs

1 Number

2.0

= == 2.7 2.66

x

Mach

"1

1.8

Re Re

Re

11

tests

30

1.6

tunnel 11 11

inches inches

x

A6 40

x

inch

'x6 '8 wind

,, ,

41

146.5 73.25

(( x

1.2

model

41

Models 11

8E, 7C, 6B, 5A

inch

Flight

*--

))

1.0

146.5

wwwш

***** ** *******

2.6

A6 : 17 TECHNICAL AERODYNAMICS

-

(

(

APPENDIX 6

.,

A6-18

O

drag

-

2

D

D

B

coefficient

.

Predicted variation laminar flow

ord

3

CDa

Predictedvariation-turbulentflow

Boundary layer condition Laminar Partially turbulent Turbulent Unknown

-

-

Facility

lift

Present test

zero

9

'

4'x4

inch

'

8'x6

PARD

Total

D NACA

,

RM 10

-

=

NACA

.

.

missile with laminar 5.5

106.

and turbulent From NACA TN 3171.

)

RM 10

Re

body nose

(

of

trip at

x

;

M

.

.

Shadowgraphs A6 42 boundary layers :

for

layer

Turbulent boundary layer

.

1.6

)

(

M

min with Re at From NACA TN 3171.

-

Fig

boundary

3,

)

(a (

)

b

Laminar

R

-

Variation of CD missile .

:

A6 41

.

.

Fig

109

108 107 Free stream Reynolds number

106

Octane822888888 132333

, Y.

, 6 66

- -- -- - --

, ,

u opp

44 4 6 6 6

,-6

A

-

. ,

A7-1 2,200 2,200 2,500 275 2,300

6.5

7.21 .666 1,425 2,700 100/130 54.95 7.21 800 2,600 G.5625 50.45 91/98 7.21 1,425 2,700 Direct 100/130 54.95 800 2,600 7.21 Direct 50.45 91/98 7.21 G.5625 1,475 2,700 100/130 54.95 7.21 .5625 1,525 2,800 115/145 55.74 800 2,600 7.21 Direct 50.45 91/98 7.21 G.663 1,425 2,700 100/130 54.95 7.21 Direct 1,525 2,800 115/145 55.74 7.21 50.5 G.5625 800 2,000 91/98 118 2,800 81 2,350 6,500 80 22.53x32 Direct 140 2,800 100 2,350 6,000 80/87 22.81x32.24 Direct 150 2,700 112 2,450 7,000 80/87 24.68x32.24 Direct 190 2,550 142 2,300 6,500 80/87 29.59x32.24 Direct 200 2,800 142 2,300 6,500 80/87 24.65x32.24 Direct Direct 260 3,400 187 3.200 9,00091/96 28.21x33.12 280 3,400 196 3,100 5,000 80/87 33.12 Direct G.642 280 3,400 180 2,750 6,000 80/87 29.59x33.12 G.642 300 3,400 195 2,750 10,00091/98 32.36x33.128.6 G.642 280 3,400 195 2,750 6,000 80/87 33.12 340 3,200 210 2,750 18,000 G.642 100/130 33.12 11.27 375 3,300 240 2,750 13,500 G.642 91/98 30.75x33.18 400 3,300 249 1,750 11,000100/13030.75x33.187.91 Direct 7.91 400 G.642 3.300 252 3,750 11,000 100/13030.75x33.187.91 Direct 7.9 400 3,300 280 8.000 12,000 100/130 33.18

44 44

" "

Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad Ho Ho Ho Ho Ho Ho Vo Ho Ho Ho Ho Ho Ho Ho Vo

73 73 80/86 73 80/86 80/86 80/86 80/86 80/86 80/86 80/86 80 80 91/98

(

)b .

:1

676 777

AB

---

,.

-1,380 1,065 1,350 1,056 1,404 1.445 1,080 1,385 1,460 1,092 236 200 268 392 362 383 396 422 488 432 492 592 580 597 585

505 505 758

200 200 278 278 294 282 307 297 372 170 182 186 257 265 263 355 385 352 485 431

dryweight Gross•

&

76B 826C9HD3 R1820-76A 853C7BA1 R1300-1A 863C9HD11R1820-103 865C7BA1 R1300-2 866C9HE1 R1820-80 867C9HE1 R1820-82 871C7BA11R1300-3 896C9HD1 R1820-86 895C9HE11R1820-84 890C7BA1 R1300-4 C1 0235 0290 D2 0320 0435 0435 K11 0435 0435-4 0435 C2 G0435 GS0435 GO480 080480 GS0580 80580 D G80580 0580 80580 0580-3

6 66

.

ON U.

Division Lycoming AvceMfgCorp. Stratford Conn

FREE

R755-11

2,300 2,575 2,655 2,550 2,700 2,600 2,600 2,650 2,600 2,200 3,100

65 85 95 125 145 150 205 225 225 240 260 300 275 350

91 80

(

cowling without Diameter

Direct Direct Direct Direct Direct Direct Direct Direct Direct Direct G.69 Direct Direct

2,300 2,550 2,600 2,800 3,000 3,100 3,100 3,100 3,275

90 100 150 165 178 185 200 200 245

ratio Blower

Ho Ho Hǝ Ho Ho Ho Ho Ho Ho Rad Ho Rad Rad Rad

:1

Jacobs Aircraft Engine Co. Pottstown Pa

Direct Direct Direct Direct Direct G.632 Direct Direct Direct

Propeller drive DATA

B

arrangement Cylinder

Ho Ho Ho Ho Vo Ho Ho Vo Vo

. )(d

power cruise Normal

A65-8F C85-12F C90-12F C125-2 C152 0315A E185 E225-8 0470 W670-23 GE260-2 R755 R755 EH R755

cylinders No. 4 of

)

(

)

TABLE A7-1

Continental Motors Corp. Mich Muskegon

B3 4A4-90 B3 4A4-100 B3 6A4-150 6A4-165 B3 B32B331 0335-3,4 6V4-178 B12 6AG4-185 6A4-200 C6 C321 C331 0335-5 6V4-200 B16F10425-1 6V6-245

Designation

y power takeoff Max

Aircooled Inc. Motors N. Syracuse

Manufacturer andAddress

PowerRatings

S. PISTON ENGINES

"

1 : 1:

G

5 &

. .,

of

(

1955

)

APPENDIX 7

POWER PLANT AND PROPELLER DATA

.

° " " " " ""

"""

11

: : :1 1:7

97 979 97 997 4

"

:1 :1

:1 :1

G

666

-B - -C - - A- H- - -V - - D- -V

B

55.8 55.6 84.95 54.95 55.6 50.45 54.95 56.6 50.45 54.95 55.74 50.45 55.6 50.45 54.95 56.6 56.6 55.75 59.6

2,200 2,8001,400 2,300 12,100 100/130 2,500 2,8001,470 2,400 11,000100/130 1,4252,700 100/130 1,4252,700 100/130 2,700 2,900 115/145 800 2,600 91/98 1,4252,700 100/130 3,250 2,900 115/145 800 2,600 91/98 100/130 1,4752,800 1,5252,800 115/145 800 2,600 91/98 2,7002,9001,600 2,400 12,100 115/145 800 2,600 490 2,130 10,50091/98 1,4752,800 890 2,400 13,000 100/130 115/145 3,2502,9001,910 2,400 11,400 2,8002,9001,600 2,400 12,500115/145 1,5352.800 890 2,400 12,200 100/130 3,4002,900j1,910*...** 11,600

.500 G..500 .450 450 .450 .450 .450 .450 G.450 .375

G.4375 G.4375 .666 .5625 G.4375 .5625 Direct G.4375 Direct .5625 G.5625 Direct G.4375 .5625 .5625 G.4375 G.4375 G..5625 4375

Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad Rad

14 14 18 18 18 18 18 18 18 28

18 745C18BA3 18 749C18BD1 -76B 826C9HD3 R1820-76A 826C9HD4 R1820-101 836C18CA1R3350-26WA18 853C7BA1 R1300-1A 863C9HD1 R1820-103 R3350-30W 18 856TC18DA1,2 865C7BAI R1300-2 866C9HE1 R1820-80 67C9HE1 R1820-82 871C7BA11R1300-3 18 956C18CA1 957C7BA1 ...... 968C9HE1 972TC18DA1 R3350-347 18 18 975C18CB1 976C9HE1 18 EA1 988TC18EA R3350

-

.

&

. ,

G

-

- - -- - -- 99

.

,

-79 G

79

7

,

5 &

,

$

:1 :1 :1 1: :1 :1 :1 :1 1: 1: :1 :1 :1 :1 :1 :1 :1 1: 1: 1: 1: :1 :1 :1 :1:1

GG

9 G

111111

9

,2 114

(of )

(

7

.

.-

.:1 :1. :1.

1• * •

-

.

.

. .

lotlas

1955

).

March

le hs

Week

•

2,780 2,944 1,380 1,380 2,848 1,065 1,380 3,408 1,056 1,380 1,445 1,080 2,957 1,065 1,390 3,514 3,029 1,460 3,609

takeoff R3350-30WA similar buthas 856TC18DB1 weight wet 3,600 anddrygross power butweighs 3,438 lb. dry Somehave -30WA manifold absolute pressure regulator Military engine rated 3,700 hpmax

° °°"

Aviation

°°°

( Courtesy

GG G °

Forhelicopter installation Manufactured under Curtiss Wright license Or10.14 Or8.89 Or8.67

°°°

(

.

)

PISTON ENGINES Concluded

of

... .

at

)

,

,"

"

(

S.

U.

DATA ON

Brake mean effective pressure Geared opposed -Horizontally Radial -Sea level opposed -Vertically

" °"

Rad Rad

6.46 6.46 7.21 7.21 6.46 7.21 7.21 6.46 7.21 7.21 7.21 7.21 6.46 7.21 7.21 6.46 6.46 7.21

1.585 1,605 2,317 2.357 2.357 2,350 2,350 2,390 2,390 3,670

TABLE A7-1

Rad

$

Div Wright Aeronautical Curtiss Wright Corp. Wood Ridge N.J.

"" ° "" °"

Rad Rad

49.10 49.10 52.80 5280 52.80 2.80 52.80 52.80 52.80 55.00

6,400100/130 5,000100/130 6,000100/130 8,500100/130 8,500108/135 6,000100/130 6,000100/130 8,500100/130 8,500108/135 5,500108/135

1.450 2,7001,200 2,550 1,450 2,7001,200 2,550 2,400 2,8001,800 2,600 2,400 2,8001,800 2,000 2,5002.800 1,800 2,600 2,400 2,800 1,800 2,600 2,400 2,800 1,800 2,600 2,400 2,8001,800 3,600 2,500 2,8001,800 2,600 3,500 2,7002,650 2,550

G G G GG G G G

D5 Aireraft Div R2000 Pratt Whitney United Aircraft R2000-2SD13 Corp. CA3 R.2800 East Hartford Conn R2800 CB3 CB4 R2800 CA15 R2800 CA18 R2800 R2800 CB16 CB17 R2800 CB2 R4360

1955

)

APPENDIX 7 A7-2

Manufacturer AFJ AFJ AFP

Designation

J65W J67 T49

Туре

--

Curtiss Wright Corp. Aeronautical Division Wright

112

1 222

1 -R -

&

- - -3 --111

-A -A -A -A 1--A - --1

& 3

⠀⠀⠀⠀ 2

-

3

68 - ----3,250 lb. 7,500 lb. 7,500 lb. lb. 4,000

1.06 4.1

.

:

.

-

-.

..

---

March

(

)

2,080 2,650 1,233 3,000 3,500

120 186

14

t

2,564

/.w -B,

158

is

110 157

1955.

- Pounds thrust

.Lb

Week

24 40 40

51 34

34

107 1.765 107 1,820 160 1,750 196 2,8307,400 lb. afterburners 2.25 145 1,610Commercial versionModel 501 D10 F3H 66andP6M Powers

.;fc-

.

Aviation

CFJ Centrifugal flowturbojet eshp Equivalent shafthorsepower

-

8

Abbreviations AFJ Axial flowturbojet AFP Axial flowturboprop

.t t. .t .t . .t .t .t .t . . .t . .t .t .t t. lb. 7,200 lb. 10,000 15,000 lb. 6.7 5,500 eshp 15,000 eshp 1.14 7,250 lb. 6,000 eshp 0.63

4.4 4.4 4.25 5.2 37 9.5 39

GAS TURBINES

( Courtersy

1

11

13

1111

AFJ AFJ AFJ AFJ

-

J34WE34 J40WE J40WE J46

2

Westinghouse Electric Corp. Aviation GasTurbine Division

22

11 14

1.14 1.14 1.14 1.09 0.54

333333 55358

AFJ AFP

stages turbine No.

S.

CFJ AFJ AFJ AFP

88 4,600 lb. 4,600 lb. 4,600 lb. lb. 5,600 3,750 eshp lb. 10,000

:

.

2

DATA ON U.

United Aircraft 348 Corp. Aircraft Division J57 Pratt Whitney J75 T34 T57 JT 7H PT2G

1 14 14 14

.t .t .t .t

CFJ CFJ CFJ AFJ AFP AFJ

2,554Powers Boeing47B RB47E 3,196Powers NAA 86Dhasafterburner NAA 86H Powers

- -; --

145 228 148

-

J33 18A J33 35 J33 37 J35 35 T56 J71

... 5.35 37 5.35 37 37

& 12 R to B F F

345 Flown Ryan Firebee BellVTOL dataapplies -14-20 -24

, ,, ,E

89

in

lb. 6,970 7,650 lb. 9,000 lb.

&

10

1.50

-4 rated at 7,800 lb.t.

240 Flown Cessna XL 19BandKaman 245 copters

;

General Motors Corp. Division Allison

AFJ APJ AFJ AFJ

-,5 ,-,-32 1

J47GE 25 J47GE33 J73GE J79

. . .t t.

lb. 1,000

40 43

,

. in

7,220 lb. 15,000 lb.

-

.

-

General Electric Co. GasTurbine Aircraft Division

1

12 12 12

rpm Compression max at ratio

210eshp 1.3 3.0 270eshp 1.02 4.25

envelope in diameter Max .

. ,

TABLE A7

Fairchild EngineAirplane Corp. J44 Fairchild Engine Division

2

13

stages compressor No. 1 1 combustors No.

:::

.

. ,

envelope in length Max

CFP CFP

..

. , Dry ib alipips lessweight

T50 502-10B

powers Max .

eshp lb./hr./lbpower max consumption fuelSpecific

,

.

1

Boeing Airplane Co.

.

L

ator .

A7-3 TECHNICAL AERODYNAMICS

1955

)

,

,"

"

Type

Designation

,

address and Manufacturer

,

,

, .

, AFP CFP CFP CFJ CFJ CFJ CFJ AFJ AFJ AFJ AFJ AFJ APJ AFJ APJ AFJ AFP

DartMk 506 DartMk 510 Mk Depwent Nene 10 Nene 101 Nene 102 Avon503R.A.25 AvonMk 521 AvonR.A.7 AvonR.A.7R AvonR.A.14 AvonR.A.21 AvonR.A.28 Soar Mk 101 Conway R.Co.2 RB 109

AFP

22 1

221

,

&

:..

..

,

8

.

, Aviation

999 98 8 8 8

(.

. . t. t. t. t. t. t. t. t. t. t. t. t. .

.

)

.

March

4,405 eshp

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

14

1955.

39 8

42 42 42 42 42 16

23783873TTEET

Week

A A

A

1,540 eshp0.73 5.5 1,690 eshp0.71 5.5 3,600 lb. 1.05 4.0 lb. 1.06 4.0 5,100 5,000 lb. 1.09 4.0 5,100 lb. 1.06 4.0 7,000 lb. 0.91 10,000 lb. 0.86 7,500 lb. 0.92 9,500 lb. 9,500 lb. 0.84 8,000 lb. 0.93 10,000 lb. 0.86 1,810 lb. 1.26

6 5 6

43 50 50 50

...

95 97 83 105 78 97 103 113 110 120 113 110 113 77 107

3,000 eshp0.62 7.0 122 36 83 19 750gbp 0.68 eshp0.56 7.0 122 36 4,000

1.16 3.7 101 50 1.16 4.5 121 53

1,850

2,440 2,790 2,460 2,485 2,860 2,520 2,900 275

1,044 1,107 1,280 1,620 1,618

available from Jan. engines 1,575Production 1956 495 Gasgenerator P.74 Percival forHunting belicopter 1,775

1,619 versionMk 104 2,154Latest

BRITISH

( Courtesy

32 2 2

10 12 10

¦¦

AFJ

4

t. t.

Oryx E.153 Eland

2222 3,500 lb. 5,050 lb.

.

is

Eland E.141

8 16

3,000 under license byWright 3,650Made asJ67 850 Medium power for lightweight fighters andtrainers turboprop withconstant Supercharged anywhere TO power

-

.

RollsRoyce Ltd. Derby

. CFJ CFJ AFJ

4,150 eshp0.48 7.2 113 40 124 40 lb. 0.77 11,000

:

3 . DATA ON SOME

D.NapierSonLtd. W.3 London

3 3

,

Goblin 35 Ghost Mk 103 Gyron

chambers Combustion 661

. t.

eshp 4,000

,

,

S. U. in

DeHavilland Engine Co.Ltd. Middlesez Edgware

stages Turbine

. . . t. t.

...

rating Max

AFP

length envelope Overall Compression ratio 58 29 780 80 53 2,100 120 3,450 35 45 465 83438

Orpheus B.E.25

.

in envelope diameter Overall

eshp 0.80 5.4 1,475 2,950 cebp0.80 5.4 4,110 eshp0.80 5.4 lb. 10,200 1,640 lb.

u

, Dry tallpips lessweight

755 Proteus Mk 101 Olympus

11

/

.

,

Remarks

Bristol Co.Ltd. Aeroplane PiltonBristol

compression of Stages 12

hr lb./eahp or hr lb./lb cons fuelSpecific . ., .

TABLE A7

ACFP 12A1C AFJ AFJ

GREATBRITAIN AFP Armstrong Siddeley Motors Ltd.Mamba ASM Parkside Double Mamba Coventry ASMD.1AFP Python Mk AS8.7 AFJ Sapphire ASV.5 Viper AFJ

.

.

APPENDIX 7

A7-4

GAS TURBINES

)

,

,"

1

"

HORSEPOWER BRAKE

-

)

(

10 15 ALTITUDETHOUSAND FEET 20

.

25

- 5(

-

or

-

( ,- 9-

in

1470 2300SLto 13000 1400/2300/14500 21000

..2100 2400SLto5500 1800/2400/9500 to16000

Approximate Weight 35 lb 20 lb lb

.

,,,, , -

35

-

-

At Fig

ALTYA

Performance

.1: . A7

HIR "

Wright

18BD

Engine

, , ,

Data

Optional Equipment andResulting Variations fromStandard Weight Approximate Increase Manifold 15.8lb pressure regulator Gear driven fan including afterbody andfandrive 168 lb Propeller speed fan including afterbody 80 lb gear Reduction with ratio 10 lb Waterinjection including control unitanddischarge butnotincluding nozzles regulator tankrubing etc. 3.8lb Approximate Decrease Reduction gear with5625 30 ratio 10 lb

Standard NotIncludedTotalDryWeight Equipment SixPointDynamic Suspension Assemblies FrontCylinder Exhaust Pipe Extensions Pressure Transmitter Torquemeter

, ,

SL

..

-

200

-

2

400

/

25002800 SLto 3800 1900/2600/11500 to15500

,

Model lb 951C18BD12869 Model749C18BD12884 lb Standard Equipment IncludedTotalDryWeight fordouble Provision acting propeller pitch control Torquemeter Priming system on engine flange Firesealadapter airdeflectors Cooling drives Accessory drivecovers Accessory Reduction gear with4375ratio drive single Supercharger speed twospeed indicated Bendix 58-18 B3Afuelinjection system including master controlinjector anddrivespump pumps and supply injection linesandinjector nozzles Scintilla DLN lowtension ignition system including magneto distributors andhigh tension coilsalsoradio andspark shielding plugs as

600

13000

)

;

800

) ( in

RATED POWER METO AT2400 RPM

on

,

1000

1470 2300 SL

/ /

1200

HIGH RATIO

3800

2100 2400 SLto 5500 to

1400

-

LOW RATIO

)

/ /

WEIGHTS Standard Engine TotalDryWeight

of

25002803SL

/ /

/ /

1600

. to

to

1800

1 : Take off minutes maximum LowRatio HighRatio Rated PowerMETO LowRatio HighRatio Power Cruise LowRatio HighRatio

DATA

grade fuelandoperating mixture strengths 951C1880I 74C188D1 RPM ALT RPM ALT BHP BMP

INSTALLATION 30

OFFAT TAKE RPM 2600 RATIO HIGH

AND

/:

TAKE OFFAT 2800 RPM LOW RATIO

OPERATION

/ /

/ /

2000

.

/ /

2200

:1 &

/

2400

1 :

Standard Atmospheric Conditions with Operating Mixture Strengths Unless Otherwise Specified

(

PERFORMANCE All ratings arebased theuse 100

.)

2600

. .

COMP RATIO 6.50 IMPELLER DIA13in SUPER RATIO 6.468.67 FUEL GRADE 100/130

ALTITUDE PERFORMANCE CURVE

MODEL 749C18801 RED GEAR RATIO 4375

A7-5 TECHNICAL AERODYNAMICS

.

,

;

➢

FUELSPECIFIC BRAKE .HR / BHPLB CONSUMPTION

/

-

46

At

600

.

%

At

.

,

Wright

18BD

Engine

5

.2: .

Performance

(

A7

140 BMEP FULL THROTTLE

(

Fig

SL

200

400

600

800

1000

-

15 10 FEET ALTITUDETHOUSAND

)

Data

800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 HORSEPOWER BRAKE

BRAKE HORSEPOWER

°

MAXIMUM RECOMMENDED O SIGNIFIES MEP OF140 LBPER CRUISING LONG RANGE SQINFOR OPERATION

.

44

2008

SPECIFIC MINIMUM ESTIMATED CONSUMPTION FUEL

.

.48

.

2400 2300 2200

2130 70

2200

2300

200 RPM 2300

2600

TAKE OFFPOWER BHP 2600 RPM 1900

.

NOTE THROTTLE LINES OF2300 FULL RPM & LESS AREESTIMATED 20 25 30

2100 2200 RPM 2100 1900 2000 1800 1900 RPM 1700 1800 1600 1700 1500 1600 1500 1400 1300 1200

)

1200

1400

PROP LOAD FULL THROTTLE

RATED POWER METO 1800 BHP AT2400 RPM

.

8

.

❖

( 1600

1800

2000

2200

2400

2600

-

2225 80%

% 2320 90

OFF TAKE

RATING NORMAL IMETO

.

O SIGNIFIES ESTIMATED RICH 5.7.C. ONPRO AUTO LOAD PELLER

SIGNIFIES S.F.C. ATWHICH METO RATED POWER NORMAL ISGUARANTEED

RPM 2600

-

72

.

78

..

.80

:1 :1

.82

.in .

.84

.

Unless Otherwise Specified withOperating Mixture Strengths Standard Atmospheric Conditions

.

Otherwise Specified Strengths Unless with Operating Mixture Standard Atmospheric Conditions

COMP RATIO 6.50.1 RATIO 8.67.1 SUPER

IMPELLER DIA13in GRADE 100/130 FUEL

ALTITUDE PERFORMANCE CURVE HIGH RATIO MODEL 749C18801 RATIO 4375.1 REDGEAR

. .

.86

DIA13 IMPELLER 100/130 GRADE FUEL

-

6.50 RATIO COMP RATIO 8.67 SUPER

-

749C18801 MODEL 4375.1 RATIO REDGEAR

ESTIMATED SPECIFIC FUEL CONSUMPTION CURVE HIGH RATIO

APPENDIX 7

A7-6

.

TECHNICAL AERODYNAMICS

A7-7

solid dotted

F. Y6

R.A Clark

/

bD h/b 0.110.44

12.2

)

(

Propeller 37-3647

1D /D

Bladecrosssection

2.0

0.100.40 Set35° at 0.75R

LB

.

0.090.36

16

0.070.28 8 8 0.060.24 0.050.20 8

All

0.080.32

0.040.16

150 Allpropellers

40.8

)

. (

LO

10.6

ggg

0.010.04

0.2 10

37-3647

04

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

r/

x = R

0

195

0.020.08

0

4371

2

)

25

0.030.12

5868-9 5868 -R6

14

-

$(

)

Propellers 868-9 and 5868R6 propellers

5868

R6

From NACA TR 640.

0.20 0.18 0.16 0.14 0.12 0.10 CT 0.08 0.06 0.04

/

V

0

0

0.02 40 50 60° Bladeangle15 20 25 30 35 45 55 Lat 075R 0.2 0.40.6 0.810 12 1.4 1.61.82.02.22.42.628 30 32 34 36 38 40 42 44 46 48 nD

/

CT vs. V nD, three blade 5868-9 propeller spinner . From NACA TR 640.

)

-

A7 : 5 .

(

Fig .

with

and

37

form curves for

)

3647.

Blade 5868-9

,

A7

propellers

and TR

-

Fig

Propeller blade

NACA TR 639

,

in

: 4 .

A7 : 3 .

(

shapes 640 .

.

Fig .

A7-8

APPENDIX 7 0.64 0.60

0.16 0.15 014 0.13 012

0.15

0.56 0.52

Lo.il

0.48

0.10 CT 0.09

0.17

.

0.44

X0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01

0.40 0.18 10.17 0.16

0.16

.

0.32 0.28 0.24 0.20 0.16 0.12 0.08 0.04

45° 50° 55 Bladeangleat0.75R 60 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.82.0 2.2 24 2.6 2.8 3.0 3.2 3.4 3.6 3.84.0 4.24.4 4.6 4.8 5.0 5.2 5.4 5.6 V nD

with CT as parameter propeller with spinner nD

three blade 5868-9

.

-

: 6 .

.

vs.

,

Cp

A7

,

/

Fig

V /

0

1.0 0.8 0.6 0.4

I

R

40 45 angle 0.75 50 15 20 25 30 35 55 Blade 1 0.2 0.40.60.8 1.01.21.4 1.61.82.0 2.22.42.62.8 3.0 3.234 3.6 3.84.04.2 4.44.64.8 nD

three blade 5868-9 propeller with spinner

1.0

25

.

-

nD

,

vs.

/

5.2

35

0.8

° 4.4

-60°

04-20 25 0.2 35 40

4.8

4.0 -55

3.6

0

%

‫ף‬

60

°

°

50 55 60

0.6

°

A7 : 7 .

n

Fig .

V

/

V

0

0

0.2

at

7

°

-50 °

2.0

25 20 Bladeangle 0.75R

1.2 0.8

Cs 4.0 4.5

0.4 5.0

0

of

1.6

5.5 6.0

three blade 5868-9 propeller with spinner

.

chart

2.5 3.0 3.5 Cs

-

Design

efficiencyfor maximum

1.5 2.0

,

0

A7

: 8 .

Fig

1.0

1 at

15 + ° °

35

0.5

2.4nD

° °

-40

Line

3.2 2.8

45

.

Cp

0.36

0.7

0.8

0.9

0.5

0.20

0.18 0.8

0.22 Cp

nD

→

1.4

parameter

/V

,

/V

1

.9: .

spinner

1.2

0.36

nD

0.28 0.26 0.24 1.0

0.34

.

( From

2.5

Cp

3.0

)

5868-9 blade 658. TR

1.8 2.0

three NACA

1.6

-

,

with

0.9

0.38

vs.

0.16 0.14 0.7

0.45

A7

0.6

0.50

0.4

0.4

0.5

0.08

4.0

propeller

3.5

TECHNICAL

Fig

-F

0.6

0.12 0.10

0.04 0.06

0.02

A7-9 AERODYNAMICS

0.85

0.90

45n

0.5

:

.

A7 10

0.04

vs.

0.7 0.8

..7

Pc

0.9

/V nD

nD

parameter

1.2

1.4

,n

n

From

→

/V (.

NACA

three

1.6

1.8

.

spinner

Pe

1.1

2.2

TR

658.

blade

2.0

0.04

-

with

1.0

0.06

3.5

propeller

2.6 2.8 3.0

5868-9

2.4

7

Fig

0.6

of

0.08

0.70

Values

0.45

250

900

0.75

0.80

0.40

0.35

10.221 0.24 FQ26 10.28 0.30

18

0.08

APPENDIX

A7-10

)

TECHNICAL

AERODYNAMICS

n

A7-11 1.0

0.8

0.9

0.6

0.7

0.5

5.0

0.02 4.5

0.03

4.0

0.04 3.5

0.05

fe

neD2 0.06 0.07

3.0

0.08 0.09

Values of Cp

0.10

2.5

Jo

0.60 0.15

0.55

0.20 0.50

2.0

0.40

0.45

0.30

1.6

0.20

0.25

0.35

1.8

0.9

0.8

0.15

1.2

0.7

0.6

31.0 0.4

0.5

parameter

-

,

three blade From NACA TR 658. )

.

5868-9 propeller with spinner

(

Cp

/

Cp

.

vs.

J/2

η

.

A7

:

.

Fig

11

n

1.0

0.05

=

0.10

Cp

1.4

1.3

B

12

°

=

J

$

0.5

0.7

B=

0.6

n

November

1944

50

R.

Woodward

SAE

parameter

, ., Journal

Reference

CT

0.015 0.35 0.40 0.45 0.50

0.6

0.7

0.8 0.9 nD →→

16

W.

nD

180

12

20

and

A7

1.0

22

D.

vs.

-

0.02

°

°

1.2 1.3 1.41.5

C₁

K.

as

Cp

8

°

°

2

0.03

0.04

0.05

√240

Fig

AF

0.02

0.025

0.03

0.04

0.09

28

Wood

propellers

same

.

Right

=

0.115

3.0

=

,

A7 13

0.75R

light

2.5

Cp

0.05

0.06

0.07

0.08

0.09

7

Fig

propellers

Design

for

1.6 1.8 2.0

chart

1.4

/V : )b/ . h ) (, ) .

.p, ( ( . . : : , . .

airplane 93

AF

:

Reference W.R. WoodK.D.andWoodward SAEJournalNov1944 50

0.75 0.115

DESIGN CHART PROPELLER NO.2

93 =

Above

12

)/(

A7

16

b h

.,p

Fig

1,2 and Gs

0.8 0.9 1.0

240

0.10

26

0.31 0.4

B

80

=

0.4

=

8

+

0.5

B

V

°

nD

= B 8 B

° °

=

0.6

=

12

20

280

B =

0.7

24

-B

0.8

=

16

20

Line of max efficiencyfor

=

0.9

1.0

B

11

C

1.1

1.2

APPENDIX

A7-12

1.1

/V

140

:,

A7-13

TECHNICAL AERODYNAMICS SUMMARY OF PROPELLER CHARTS ON PAGES (From NACA WR L 286 .

-

Made Propeller Number Figure activity of Rotation location factor blades

Body configuration

Reference

Bureau of Aeronautics 5868-9 Radial engine nacelle without wing

Biermann David Hartman Edwin

and Tests

.:

P ,

Tractor

of Pive Pull Scale Pro pellers in the Presence of Radial and Liquid a

a

-

Single

A7 : 14 THROUGH A7 : 18 .

, ,

80

3

,

Blade design 1

)

-

TABLE A7 : 4 .

, ,

.

.

Biermann David Hartman Edwin

,

Liquid cooled engine nacelle without wing

and Tests

.:

P

--do ---

of Two Pull Scale Pro pellers with Different Pitch Distributions at Blade Angles up to 600

.

,

-

110o-

,,

80

-

2

3

,

.

Cooled Engine Nacelle Including Tests of Two Spinners Rep No. 642 NACA 1938

.

,

.

3

--do-

1-10-11

-do

3

--do--

-do

90

--do

--10 ---

90

110o-

1-10-1

90

6

--do--

--do ---

--------

--do-

op- ---

-do -------

Single

Pusher

--doDual --do-

--do 1 --do ---

Gray W. .: Wind Tunnel Tests of Single and Dual Rotating Tractor Propellers at Low Blade Angles and of Two- and Three Blade Tractor Pro pellers at Blade Angles up to 650. NACAA.R.R. Feb. 1943. H

Streamline nacelle without wing

,

-

-

90

,

Tractor

8

,

2

Single

3

Hamilton Standard 3155-6 and 3156-6

404

3

,

Rep No. 658 NACA 1939

Blade design

,

,

,

Biermann David Hartman Edwin P. and Pepper Edward Pull Scale Tests of Several Propellers Equipped with Spinners Cuffs Airfoil and Round Shanks and NACA16 Series Sections NACAA.C.R. Oct. 1940.

,,

-------

Gray W. .: Wind Tunnel Tests of Single and Dual Rotating Tractor Propellers at Low Blade Angles and of Two- and Three Blade Tractor Pro pellers at Blade Angles up to 650. NACAA.R.R. Feb. 1943 H

Streamline nacelle with wing

,

P ,

,

Biermann David and Hartman Edwin .: Wind Tunnel Tests of Four and Six Blade Single- and Dual Rotating Tractor Propellers Rep No. 747 NACA 1942

-

.

.

.

.

,

,

.

-do --------- do-------

Biermann David Gray W. H. and Maynard, Julian D.: Wind Tunnel Tests of Single- and Dual Rotating Tractor Propellers of Large Blade Width NACA A.R.H. Sept. 1942

-

Streamline nacelle with wing

-------- do

,

--do ----10-1 1110111

,

Tractor

--do-

Dual 11871

,

,

.

.

Hamilton Standard 3155-6-1.5 and 3156-6-1.5

Single

,

3 894

4567

,

Blade design

.

135 135 135

,

15 16 17

-

135

Biermann Dayid and Gray W. .: Wind Tunnel Tests of Single- and Dual Rotating Pusher Propellers Having from Two to Eight Blades NACAA.R.R. Peb 1942

,

14

--do---

Streamline nacelle without wing ----- do ---- do---------- do--------

H

90 90 90

.

90

11 12 13

-

10

-

,

.

-

-

-

,

,

Biermann David and Gray W. .: Wind Tunnel Tests of Eight Blade Single- and Dual Rotating Propellers in the Tractor Position NACAA.R.R. Nov. 1941

,

90

II

9

,

.

--- do--------

-

879

.

,

-

-

90

,

5

-I

.

,

-

, ,

,

-

:

90

APPENDIX 7

A7-14

(1block 6/60°)

.90 FOUR -BLADE SINGLE -ROTATING TRACTOR PROPELLER WITH WING 8d

.75

.70 TEN -FOOT PROPELLER , NACA ,3155-6 TESTED ATPRT APRIL1980 . SEENACA REP . NO . 77.

.65

.60

.55

nin percent .50

.40

.35

.30 .25

.20 .15

.10

.05

0

B-20 at 75R25 .5

1.0

40 30 35 2.0 1.5

45 2.5

$0 3.0

55°

/

v n Fig .

A7 : 14 .

1.0

3.5

4.5

60. 5.0

5.5

6.0

D

Four -blade counter - rotating ( From NACA WR L- 286 . )

propeller tests .

6.5

A7-15

TECHNICAL AERODYNAMICS

(1block- 8/60)

2.0

1.9

1.8 SIX-BLADE DUAL -ROTATING TRACTOR PROPELLER WITH BING

1.2

1.6

1.5

1.4

TEN -FOOT PROPELLERS , MACA , 3155-63136-6 ATPRT TESTED APRIL1980 . SEENACA REP . NO . 757 .

1.5 1.2

1.1

1.0

.9

.8n pertent

3

.7

.6

.5 .4

.3

.2

0

Bat 75R- 20 5

25 30 35° 40° 1.0 1.5 2.0

450 2.5

50° 3.0

/

55° 3.5 4.0

60° 4.5

5.0

5.5

65 6.0

V ND

Fig .

A7 : 15

.

Six- blade counter - rotating propeller tests . ( From NACA WR L- 286 . )

6.5

60-)

$ /

(1

block

4.8 4.6 4.4 4.2 4.0

-

-

EIGHTBLADE DUAL ROTATING PUSHER PROPELLER WITHOUT WING

3.8 3.6 3.4 3.2

TENFOOT PROPELLERS 3155-6& 3156-6 TESTED ATPRT NACAJAN 1941 SEENACA A.R.R. WIND TUNNEL OFSINGLETESTS AND DUAL ROTATING PUSHER PROPELLERS HAVING FROM TWO TOEIGHT BLADES BYBIERMANN ANDGRAYFEB 1942 .

.

,

.

,

2.8

.

--

,

-

3.0

2.6 2.4 2.2 2.0

Cp

1.8 1.6

percent

1.4

J

1.2 1.0 .8 .6

35 30

.4

50 3.0

3.5

Bat

55

5.5

75R 65 6.0

-

45

2.0

286

.

From NACA WR

)

L - -

-

Eight blade counter rotating propeller tests (

.

:

A7 16

.

V /

nD

Fig

.

,

5.0

A7-16

in

1IITITIT

APPENDIX 7

75R

MA

40

9

Fig .

159

A7 : 17 .

Composite skeleton design chart , TRACTOR ( From NACA WR L- 385 . )

32 3.6 40

14

48

69 52

N

C.

blode

60

4

8

Har D

12

1.6

20

-l

36

4.0 15

44

48 4

12

16

Boy

& t

Efficiency envelopes

40

propellers

1.4 18 82

Pa

5.6 60

blode 468

454646

20 t t&

of °

23460

∞

.

56

56 05 5.2

Loo

197

28

Efficiency envelopes

H

468

20 24

pey

8

1.2

1.6

20

t

>

40

44

48

5.2

5.6

A7-17 TECHNICAL AERODYNAMICS 0

19

o

0

APPENDIX 7

A7-18

48

CCCC

5.2 5.6 09

88

64

0

Blodes

2.0 2.4 2.8 3.2 3.6 40 2

9

8

478

8

° 5 S 45

робо 35+40

°

1.2 91

2

lo

1.2

1.61

2

loz

#

84 .

tak obtok

6

40

.

36

ge

S

T 6

2.4 28

Mig

gp

to 8

Glodes

99-4

Efficiency envelopep

80

6

60

2.8

423

-0

O

48

4.4 3

3

7

8

5

8

5.2

:

10 9

6

R

‫و‬.

6

5.6

68

6.4 By 4

175A

sobe

7.2

1

7.6

sappig

Lo

C

2

GO

Fig .

A7 : 18 .

3

00 8 2

2

Composite skeleton design chart , PUSHER ( From NACA WR L - 359 . )

9

propellers .

Personal

and

andAddress Designation Manufacturer

U.S.

). (ft

f-t.,

. of

(. .

.

) (lb.

) lb. (

Fuel Weights .) (

galcapacity fuelNormal fuelauxiliary weight @gross without range airstill Max wtgross ceiling @ Service

.)ft (

.) mi ( , ). . (

Dimensions

) (

Price

.

TABLE A8-1

FAF price model Standard $ ft sqailerons Wing including area "2 height Overall 7 ″ 2 length Overall

' 4'

span Overall

weight Empty

weight Gross

, , . of

Seats

21 190 25,000 34 D2 135hp 120 100 1,225750 500+12,000 350 24 1,9501,400 Inc. 21 Lyc0290 Aerocar Flying Auto Wash Longview 950 34 14 242.5 66,000 197 1,700 24,000 1,150 1 505,500 3,800 900 AeroDesign Aero Commander 5205-7 LycGO435 C2B 260bp211 Corp. Engineering Okla Bethany 219 210 429 25 22 Streak 165 2,00025,5001,06040 1,6951,045 Aircraft Corp. 21 Fr. 165hp AeroFlight Beach Calif Long 22 120 + 110 GreenwoodAG14 85034 Anderson 700 + 450 23 120 4,495 1,400 19,000 21 ConC90-12FP90hp Co. Tez Bellaire 213 27 10 ConC145 145hp 1701,500 800 1,25018,000 750 75 3,5002,250 41 Baumann Aircraft Corp. Brigadier 290 Pacoima Calif TwinBeech WR985 47 349 87,050 Beech B5 450hp Aircraft Corp. D188 2111,7601,4601,19020,500 9852068,7503,770 100,000 WR985 234 E188 TwinBeech AN 14B 2,0801,5701,25023,0001,455 Wichita Kan .... 9,3006,150 450hp 194 184 1,009 7071,30019,000 830 39 2,7251,675 3210 177.6 19,990 E35Bonanza 41 ConE225-8 225 2 B50TwinBonanas 45 277 69,950 1348,0003,940 LycGO435 C2 260 205 185 1,2581,3751,45020,0001,088 14 44 410 21018 72 700 500 350 9,000 75 Associates Inc. WeeBee 11 Kiek043-35 hp Beecraft 1610 96 880 61028 110 500 400 1,00018,000 240 Bee Honey 11 ConA65-8 hp SanDiego Calif 130 Bee 175 100 1,000 7001,00016,000 700 36 2,1501,190 32 Queen 41 Lye0320 150hp 23 34 6'2 161.5 180 Bellanca Cruisemaster 41 Lyc0435 190hp Aircraft 1,40022,500 900 54 2,6001,560 Corp. 14-19 NewCastle Del 23 181.6 6,425 105 Callair 2-31Lyc0290 D2 140hp 1,00017,500 656 25 1,55097535 5,320 1,6501,000 8-1B1 1,20017,500 600 Super Cadet 21 Lye0290 D2 135hp 125 115 AftonWy 350 28 32 Central Lamson 320 50 5,5002,955 Corp. AirTractor101 11 WR985 450hp & 105 1,1301,000 510 Wash Seattle 170 175 8.295 25 Cessna Co. Aircraft 120 36 41 ConC145 145hp 69015,500 540 42 2,2001,205 76 175 12,950 180 26 36 Wichita Kan 41 Con0470 150 A225 hp 1,15019,800 675 60 2,5501,460 195LC 126A 27 218 24,700 51 Jacobe 36 165 1,20018,300 750 80 3,3502,030 R755300hp 310 175 49,950 36 110 1004,6002,850 Con0470 240bp 220 205 1,70020,0001,000 23 10 150.6 12,500 Colonial Corp. 125115 Aircraft Skimmer 34 700 700 40 1,9501,300 2-31Lyo0290 130hp 2 Huntington N.Y.

.ft - .,

.)ft (

Performance .)

SL@ wt@gross fpmclimb rateInitial no wt SL@wind gross @ obstacle50 Landing over distance no wtgross wind obstacle50clear to distance Takeoff + mphspeed Cruise

(

.)

Aircraft

+ mphwt @gross speed Maximum

Number makemodel andmaxtakeoff ). power engine (.

Powerplants

Business

DATA

@

ON PERSONAL

$

"

′ "' ' ° '1' ' '

2

3 8 "4

″

′

'8 '

44

3

- - .

)

(1

. . ., . . . ,, , , , , ,

&

-

&

A8-1

8

APPENDIX

AIRCRAFT DATA AND BUSINESS AIRPLANES

*

$

$$ $ $

°

. .

@

. .

. .

2

2 5

@

&& PP 22 8

$$

59

2 6

-B

-

,. . ,

,

$$ $ $ $

" " " ' 811 6'614'11 '5 8""7 5'8 "7F 611 7'6 2'7"32 8' '5 "3 "2' "7 "2 " 1″′ "5'" " 4 6 ' '34 25'31 ' ' 22 ' 24 " "27 ' "8 " " ' '3'4 "1'0 "2' 9'"8'35 7 "2"1' '

"

"

40

+

2388 . ..hp . . 82 . . . @ hp .. .. . .. 28 @ @65 @ -- @- @@ @-A -- @ - -B @-D .

. ... . .. P .. . .

&

-L

2 5

-

-2A

-1C

., ., .,

, ,

1. L.

HelloAircraft Corp. Norwood Mass

. . . . .. ...... . .. . . .. .

1 ConC90 90hp

-

H

4 2

.

@

-

2 23

26

38 22 4 3 3 3 °3 3 29

44

44

. . .. . . . .

65 @@ @ @@@ E @ @ @

.

- - - ---

2 4

. ,. . . , , , , ,

7

- - -- - - -23 -1

,

. , 5

. . ... .. . . 65 87 @

@@

A 1818

T

. ,

26 3 87

8

45

@

1 2 4 4

″ ″27 ″4

′

33

60

885

@

2 4

D

-

. . , ,, .,

Experimental model which beingdeveloped twoplacer withfolding wings Builtunder license fromAeroFlight Aircraft Corp. 166 ofStreak maker builtsingle Ryan North American Plusoriginal airframe engine

2

.

•

-

& P

*

.

.

.. . $. . &

-

in

1 *•

.)

. ( .. .

- . .. .

1954.

. or

15

.is

March

6 9

"

Week

″6

9'6 178.3 28,500

183.7 3,060 7'1 186.3 8,950 $$ $

W Pratt Whitney Aircraft SL -Sea Level Alsoavailable withConE185-11 @ 205hp This version costs18,990 Deluxemodel Allfuel tiptanks

9

21 24

888888

3.50 710 600 15,000 450 25 1,20078036 36 1,250 560 92517,300 400 42 3,0151,505 700 6501,40020,000 600 3,3502,300

$

Aviation

′ ′ ′″ ' ′′ ′ ′ ′ ' ' '' ′ ' ′ ' ' ' ′ ' ′ ′ ′ ' " °° ° '° ' ' °" ° ° ' 4' ' ' ' ' ' ' ' ′ ' ' 38 36.5 90 2,500

,

75 43 584 393 10 11 8001,0001,000 10 800 8001,600 660 452 100 17 54020 350 6001,60014,000 450 16 490 22 2 5 2,81027,0001,35060 1,9641,170

9,750 16,000

)

(

Concluded

of

23 5$ $ $$ $ $ 5

.

ON PERSONAL

( Courtesy

″ " ° " ″ ″ " ″ ]″ ″ ' 8" 263' 76 76' 76' 7'648 69 37' 2′4 5' 35 18 6 "" 7 " 5 4" 4° 4" 2° 6° 4° " 4″ 6″ 8 95 34 166.9 178.5 5,095 178.5 4,195 178.5 195 147 6,275 147.5 6,475 204.2 32,500 167

$$

DATA

Approximate Continental Aircooled Motors Franklin Horsepower Klekhaefer Lycoming

155 160

24,500

TABLE A8-1

Con Fr. Hp Kiek Lyc

2110 600 575 960 18,000 600 32 1,9101,250 30 30 1,05018,000 700 2,6001,625 11 780 520 10417 1,09019,400 28 1,26021,900 718 35 2,0001,049 500 6001,05020,500 500 36 1,500 89535 22 22 952 800 62413,500 360 18 1,500 80035 22 210 6001,00019,500 500 36 1,500 93035 20 80015,000 580 36 1,950 05029 80015,000 580 36 1,9501,085 20 900 6701,35020,000 850 72 3,5002,168 37 27 600 600 90019,000 600 33 24 1,9001,275

60

145 200

107

94 231

'8 '6 "4

Aircraft Co. Meyers Mich Tecumseh Aircraft Inc. Mooney Tex Kerrville Aircraft Corp. Piper Haven Pa Lock

22

30

' ' '39 '5'

20

2,8001,900 $

21 ConC145-2H @145hp 166 160 41 Con0470 @225hp 196 182 Mite 18LA 11 Lyc0145 B2 hp 140 125 20 ConC145-2H145hp 176 161 21 Lyc0290 PA Super Cub D2 135hp 127 112 110 100 PA 95Super Cub 21 ConC90 90hp PA18 135 1-21Lyc0290 D2 135hp 135 110 PA20Pacer Lyc0290 D2 135hp 139 125 PA22Tri Pacer 41 Lyc0290 D2 135hp 137 123 180 167 Lyc0320 150hp PA Apache 140 130 Bros. Aircraft Inc. Rawdon 21 Lyc0320 150hp Kan Wichita 185 165 Junior StitsAircraff 11 ConC85 hp 215 185 P.O.Box3084 11 ConC85 112hp Skybaby 170 155 8A3A Pla boy 11 ConC85-8 87hp Calif Riverside 238 225 Streak AeroCorp. Stre-225 21 Lyc 225hp P.O.Box181 Calif Hollydale 105 95 BC12 DeLuxe 21 ConC65 hp Taylorcraft Inc. 131 122 Pa 11 Con 225hp Conway 15AG Topper 180 170 Temco Aircraft Corp. TwinNavion Lye0320 150hp Tez Dallas

Paraplane

157 500 500 1,10027,000 600 124 108 300 250 1,225 8

.

LycGO435 C2B 260hp @

Lanier Aircraft Corp. N.J. Marlton

391 Courier YL 24

APPENDIX 8 AND BUSINESS AIRPLANES

A8-2

to

-

)

,

,"

"

W W & & P

P 4 2

passengers ofNo. 44 13,000

JT3

10,000

550

Model

t.

Name

Manufacturer 86

.

- -

crow ofNo.

3

5

- -- - - -

,

(( ( (

7

... .. . .

@@@ 171617@@@ @

-----

W W && PP& P 4444 4 4

0

))))

47 7

&

-

P

:

.

4

. ..

& USAF Navy Navy BuAer Buder BuAer

-

ft boostar lesslength Overall ,

.

. ,

.

. ft ,

. ft

Body diameter wings fins span Overall of

or

lb. booster lessghtweTakeoff ,

,

spr spr

,

Name

Category

-

in

designation andtypeManufacturer

designation andtype Manufacturer

.. 1

contractor Sperryprime

-

None

useService Production Development

onConvair103 Tested mid1954 Canceled

Remarks

-F

spr spr spr

None None

,

. ,

mi range Maximum number Machspeed Maximum ,

,

Aircraft Per- Current Launcher form- Status ance

:

Pilotless Powerplant

1

and

is

Data Physical

Footnotes Figuresealevel rate climb Includes twocabin attendants of

Missiles

lb.t.Pounds ofthrust Horsepower hp

5,830 5.840 73,016 137,500 113,000 123 113 24 Wr972TC18 DA3 3,250 hp 370335106 7956,630

97

..

Manufacturer

Hughes Martin Philco Douglas

106 28 106 106 108 108 28 112 10

'

8

Designation

-4N -N7 2-N-3N -4N - - - -- -

12 3

Falcon GAR98 Oriole XAAM Sidewinder XAAM SparrowXAAM SparrowXAAM Sparrow XAAM

4936,100 5,160 5.00051,316 107,000 88,200 117 4605,680 4,995 3,720 55.357 100,000 85,000 117 4936,100 5,160 5,000 58.340 107,000 88,200 117 5,510 3,625 64,480 122,200 97,000 117 4815,830 117 5,990 5.072 68,073 125,000 102.000 5186,560 127 5,400 6.010 72,643 139,000 107,000 5074,040

'

:

.

2

,

AND PILOTLESS

Airtoair

length takeoff fieldCAA

′

" 8" "8 7" 7" " ″8 8

′° ′

U.S.

Weight lb. empty

4

" "28"28"28" "31 "6 "6 "6 " "11"3 " " " 11" " " 6" 6" "6 6" 6" 6 """" '

MISSILES

Basic Missile Data

′ 2″′

29.48647,000 46,500 105 79 228 1,260

″

-

130 128 38

. ft ,

DATA ON TRANSPORTS

Lockheed Aircraft1049G Super Constellation 5-1147-99 Corp. Abbreviations W Pratt Whitney Aircraft Wr Wright Division Aeronautical

gross lb. weight Maximum 190,000

. ft ,

Dimensions

3

R2800 CB 2,500 hp370 315 Douglas Aircraft Co.DC6ALiftmaster 3-5 30,500 Inc. version 54 16,780 W R2800 CB 2.400 hp370 315 95 DC6B domestic DC6B overwater R2800 CB 2.500 hp370 315 97 version7189 11,930 370 Wr972TC18DA4 DC domestic version 66 12,310 3.250 hp 410 17,730 Wr972TC18DA4 361 DC7B overwater 3,250 hp 406 version 55-58 DC7CSeven Seas 58-62 18,100 Wr988TC18EA1 359 3,400 hp 406

landing length fieldCAA

1,220 4,675

,

landing lb. weight Maximum

2,400 hp314 284

,

,

Weights

BUM

R2800 CB

fpm climb route enoutEngine mphdown gear landing Landing andflapsspeed mphspeed cruise Best mphspeed Maximum -.

mi range airstillMaximum -

. ,

length Overall

2-3

lb. @ 16 powerplants rating of maximum anddesignation Number @ P

,

Transports Performance . .ft ft . , ), ), . . , ( ( , , , height Maximum

Convair Division 340 Convair Liner General Dynamics Corp.

Cargo lb.capacity ,

Commercial

TABLE A8

Airplane Co.707 Boeing

U.S.

Aircraft General Data

A8-3 TECHNICAL AERODYNAMICS AIRCRAFT

is

...

1

1

Cognizant service

Airtosurface Bullpup Dove Gorgon Rascal

-

5

- -

1

Terrier

Talos

1

-5 4

21

8 -N2

3

- 2- -

Q

. -- -- . . . . . . R -

1.3 1,690AeroIpr

.

. .

1

1

Aerospr

.

.

1

1

-

:

..

-N- F

--- /

--

March

,

14

1955.

-RR

-

-

P

Week

. - r| 1 &

Aviation

1

&

of of

of

,

- -

---

(

Courtesy

2

-

)

,

AND PILOTLESS

-

-

-

-

of ✓✓Holdsalt record 158 mi

Extreme altitude targot

) ) ( 2 1 - (1- -

RM None RMI XLR10 3.0 42-49,9-13 Viking RTV 12aMartin pr Abbreviations Herc Hercules Powder Co. W Pratt Whitney Aircraft Division Aero Aerojet General Corp. UnivApplied Physics Lab JHU APL JohnsHopkins Division —-Ramjet All Allison LabCalTech JPL Jet Propulsion RMI Reaction Motors Inc. Army Ordnance ArmyOrd rocket propellant RollsRoyce Ltd. BuAerNavy BureauAeronautics Ipr Liquid Marquardt Aircraft Co. Mar rocket sprSolidpropellant BureauOrdnance BuOrdNavy McC McCulloch Motors tj Turbojet Con Continental Motors Corp. NAA North American Aviation Inc. USAF United States AirForce Engine Division Fair Fairchild NRL Naval Research Lab Division Aeronautical Wr Wright Central Aircraft GC Grand

20

R 11111

USAF Navy NRL

1 tj R T

Aerojet

11 2 1

.tj . .

Aerobee

.

RadioplaneUSAF 12.311.5 BuOrd 14.0

-- -. . . . rj. . . .tj

tj 14 A

OQ19D

.

Armyand AlsoXM KDA Navy

tj

>

> Soar AeroX102F2 spr0.91.5 1,848FairJ44 20 ConJ69 19tj 0.3 McC piston eng Catapult spr X220A8 spr

(

MISSILES

Pogo

A 0.9

- $:

Firebec

. Sled launcher

P

RadioplaneUSAF 17 14.3 USAF 17.311 Ryan

tj 2

All

1

.

4.5

.

32

&

YQ IB

8

.

Northrop USAF

0.9600 3.0

Concluded

Research

1 -A-7

-

SM62

11 spr NAAlpr None spr

:

spr ArmyOrd All J33 37 Martin USAF 39.528.84.512,000 American USAF North Wr Chrysler ArmyOrd lpr All J33 Chance Vought BuAer 33 14.5221

: 2 .

DATA ON TRANSPORTS

Snark

. . ..

JPL lpr 2.512,000 2.5 Hercspr

ballistic Intercontinental missile JPL Originated Unguided range compar ableto longrange ar tillery missile Closesupport each Cost 90,000 Atleast three versions missile Tactical land have Testvehicles inggear has Development W J57 at

Lacrosse Matador TM 61 Navaho SM64 Redstone Regulus XSSM

.

Firestone ArmyOrd40 Douglas ArmyOrd21

1 None None

.

CorporalX88M John Honest

1 NAAIpr

spr

✓✓

More than100 sites near 13cities APL JHU Originated Bumblebee

2.0 18 ✓✓

20

hassystems Boeing contract

2.5

Aerospr

None Hercspr

/

SM

1pr

GC spr AeroIpr

5,000Mar.

on

Surface toSurface Atlas

USAF

XSAM

-A-7 6-N -7N-

XSAM Convair

McDonnell BuOrd

XSAM

25

2

1 1

BuOrd

ArmyOrd ArmyOrd20

. 1

Convair

USAF

Boeing

contract Bellhassystems Forantisubuse

TABLE A8

Target

EastCoast Douglas

Noneairlaunched 1.5100 ✓✓

. .

0.7 Noneairlaunched 1

Loki Nike

BellIpr

. tj. rj. . .. .

Fair344

1

Bomare IM 99

4.5

None

-; - .. ; -

Surface toair

20

spr

3

BuOrd

Fairchild

XAUM

11 1

Petrel Airtounderwater

7 -N- -4-N -5-N 2--N -

Martin Navy EastKodak Navy Martin Navy BellAircraft USAF

.

XASM XASM XASM GAM63

APPENDIX 8 A8-4

AIRCRAFT

..

,

)

,

,"

"

1 1 3 1 0 1

-4B -5B -6B

-1 5

- -3

A

,

,

"0

′

' " '" '

7

0

1

5

1

-

,SR -1

of

K 240 HTK HTK

..

-B

Kaman Corp. Aircraft

-

104

' 69 7'" """ "" "" "' "" "0 '" "8' "" "'° "'" ° "'" " 0 ' 0 8′ 0' ′ ' '

-H -H

-

12

0

Aviation

47 47

0

0

of

0

22

6

-1

-

6

-1

(

Courtesy

12 12

66

HOK

& P P 1 1 11 1 12 1 1

Week

190 600

Boeing 502-2 W R1340

",

March

14

240 190 Lye0-435 Boeing 502-2

.

11

40 40

11 0 0 32 00

12

14

42 42 42 42

-

21

,

1955.

HJ andHOE also

-

Development project only project Development only

300 Convertiplane

3,200 140

250 Coaxialconfiguration 1

1010 2,3503,475 3,475Jacobe R755EH 3501758.L

hassemi conven tionalcontrol has stick single

Design studies on family oflarge copters

-

680 36

450878.L

220 1401182,0004,200

340 40090 1,0007,000

1

14

Gyroglider Gyroglider

260 100 S.L 8,000+ 90 converti Fourrotor plane

. . . / / / C33 200848.L 1,6282,500 2,500AM6V4-200 381 10 6301,080 1,080Hiller8RJ2B

" 8

Jacobs Co. Aircraft Engine

"8 7

&

23B 1-21-2 440 35 40 32 11 30023 23

1

3,8005,750 5,800 WR985 BPI

Lye 290D2

1

12

' 1,1501,655

-O.

-

HillerHelicopters

Con 90

40758.L 60S.L 608.L

175 S.L

/

-

48 48

2,200

3,2005,000 5,000LycSO580

" 3

10

"6

.

R

24 XRON 10

0 2

D -

;8

K 225

00 0 111

6

1

′ ′ ′ '° ′ ′ ′ ′ ′

0 1

32 35

"

1,9002,600 3,000ConFSO470

Lyc0-320

3R ramjet None None

1

/

-

Co. AmerInc. GCA2C Gyrodyne

1,200 48

″0 ″0 ″0 ″ ° °0 0

. . .

- C

40

"

/+

a

Glenview Metal Products Co.

1

YH 31

19

' ′ ′ '6 "68' 10 8251,350

99 372 86 336 103 353

2

.

LZ

200 35 42

11

″″ 1 455

4

-1

-

Flettner Aircraft Corp.

23 525

0

5015 15 75180 18 75,2020

1

///

...

Doman Helicopters Inc.

0

0

--

Inc. Convertawings

23 1 WR985

212 3,600 10,000 200+ engine Derated 200+ 5,000 Derated engine Twintandem rotors derated engine twin Convertiplane rotors onwingtips 6,000

-

CH

13

55550

800

,

B2

H 16 & P 1

Brantly Helicopter Corp.

1

,

Aircraft Co. Cessna

14

' ' ″′ " " " '" " ' ' ' '" '" '" " ' ' '' ' "4 6" 9

24 30

P 111111

ConArtouste C32 200100 2,350AM6V4-200 8.L 2001008.L 2,350LyeVO435 C32 200100S.L 2,350AM6V4-200 200 2,550LycVO435 WR2800-501,900 138 S.L

... . . /// / /

Bensen Aircraft Corp.

1,4352,350 1,5552,350 1,4652,350 1,6262,550

"

HSL

95 95 94

I- - . . .&

XV

610 35141 35 41 490 351'41 525 622,3541 51 70

14220

,

212

--

XH 13F 12 13G 12 12

Weights

:

3 .

TABLE A8

200

201 47G 47G 47H 47J 61

528

Dineralens

DADES FREE

BellAircraft Corp.

Data General

A8-5 TECHNICAL AERODYNAMICS DATA ON ROTARY WING AIRCRAFT

)

Kellett Aircraft Corp.

KH 15

- -1 2- - 4- - - - H H HH

XV

- -35 41 800

2

2

8-56 HR2S 18-58 HSS 8-59 XH 39 22

.

′ ′° ′ ′° ′ '

-G1

-1 1- -

222

Week

0

0

' :.

March

″8

14

1955.

1

1

:

,

. -& .

P

"

Aviation

9 7 160

test Convertiplane vehicle

Concluded

)

(

:

3 .

WING

of

211

-

II

Footnote lb thrust

1

(

LycGO290

405 Also 19C HO48-1 2,200 HRS -2 395 Also 19DHO48-2 12,500 HRS H048-3 AlsoArmy 37A AlsoArmy 34A 8,500 255 Holds speed 166mph records andaltitude 24,500 ft

-H 1- H-

&

Engine abbreviations AM Aircooled Motors BPI Barmotive Inc. Products Con Continental Motors Corp. Division Lyc Lycoming W Pratt Whitney Aircraft RMI Reaction Inc. Motors Wr Wright Aeronautical Division

. &P . .

..28,500 WR2800-501,900 Wr R1820-84 1,525 8.L 2,2003,560 3,560ConArtouste 400146

7001108.L

600101 8.L

. . / /

DATA ON ROTARY

(

Courtesy

5,0457,500 7,900Wr R1300-3

. , ) , , -3, -HH- ( .) &

Transcendentai Aircraft Corp.

Rocket 4,7957,200 7,200 W R1340 & P 1

17

102,200 53 62

-H -H

53

19B

0 1 101,800 62

by 450 Power limited 14,900 transmission 400 6,000 400 6,100 YH 16AhasAllison T388

TABLE A8

---

44

″4 ″4 ′° 13″ 7 ′″ 7″ 0 ′9

19A

13

8,600 13,30015,000 Wr R1820-1031,425 140 8.L 140 8.L Wr R1820-1031,425 8,600 13,30015,000 W R2180 1,650 30,000

11 2

8-55

Wr R1300-3 700 1408.L 8,300 11,20014,500 Wr R1820 103 1,150

Convertiplane 490 7,000 490 Navyequivalent 7,000 HUP

. . . .. / / / //

8.L 550108 5501088.L

-

Div Aircraft Sikorsky

11 1

. . &P

CraftCorp. Rotor

-11

21B 1-220 86 21C 1-2204,500 44086 16 YH 16 2-3 40 82 134 31

12

′′ ′ ′′ ′ ′ ′ ′′ ′ ′ ′

44 88

11

HUP 21A 1-214

161 550

-3

PH42 PH 42

1 is

PD22

Con

RMI rockets

. .. ..

4,1005,750 6,100ConR975-42 3,9285,750 6,100ConR975-42

″2 ″6 "0' 0"' 0 0″′ 13 ″11″11 16 ″4 16 ″4 °4 0″′ ″0 °0 ″0 ″0 ″0′

5-61,500 35 56 5-61,500 35 56

0 1 1

Plasecki Helicopter Corp. PD 18 HUP PD 18 25A

82

2

McDonnell Aircraft Corp.

APPENDIX 8

A8-6

AIRCRAFT

. /

-

.

,

)

,"

ANSWERS TO PROBLEMS

While most of these answers have been carefully checked to slide - rule accuracy in previous editions , many problems are new with this edition and some answers are withheld pending more careful checking . A " ditto " proc ess set of SOLUTIONS TO PROBLEMS will be supplied gratis by the author to teachers adopting this text for 10 or more students , and , with the teach er's approval , to his students at $ 1.00 per copy after January 1 , 1956 through the University Bookstore , Boulder , Colorado . 2 :1.

2:2. 2: 3. 2 :4 . 2 : 5. 2 : 6. 2 : 7. 2:8. 2 : 9. 2:10 . 2:11 . 2:12 . 2:13 .

2:14 . 2:15 .

2:16 .

lb/sq in .

( a ) 14.70

2:18 .

/

(b )

1.033 kg sq cm P = 32.50 lb sq in . abs AWork = 41,200 - lb W = 54 lb cu ; v = 0.01853 cu ft lb W = 0.0890 lb cu ; v = 11.22 cu lb L = H p = 19.35 106 sq ft sec

/

/

ft ft

/

Pr P:

ft/ /

/

=

0.77

Pg Pg Pg Pg ( a ) u2 - u1

(b) (c)

/

$2

/

/ /

/

/

/ ft/ ft/ 1.6x103 ft - lb/lbm

( a ) 23.1B

(b )

23.1B ( a ) SPdv = 65,200 (b ) AQ = 83.9B ( c ) Au =: 0 (d ) AS == 0.0360 ( a ) V2 = 3.04 cu

ft - lb ft/lbmi

2:23 .

(b) sh

2:17 .

ft/ lbmi / cu ft ; - u1 = -11.81 B/ 1bmi u2 9,010 ft lb/ lbm ; SPdv hj հշ = -16.5 B/ lbm

V2

= 18.48

W₂ = 0.0541

cu

lb

a =

Straight line through ( T 120 , a/ 1,000 = 1.184 ) ; ( T = −80 , a/ 1,000 = 0.959 ) ( a ) Rel . humidity

air

= 20

( e) 2:24 .

W = 0.0722 = 0.988

2:25 .

2:26 .

( a ) Rel .

( a)

=

10.0042

= 0.001132

(( a ) σ (b) σ

228

/T

/

N-1

.

slug/ cu

ft

ft ;

) 2.47

= (P P ) 0.712 ; P = 0.000545 slug cu u = 0.000573 sec sq ( a ) p = 0.00126 slug cu (b ) u = 0.000263 sec sq ( c) Bad = 20,200 (d ) o = 0.529 = ; 3d = 21,900 Bp

/

/

200

=

0.575

ft ;

ft

ft ;

ft

2:30

/ 540)

slug / cu

lb/sq

= 0.000324

= (T

ft

8%

/ ft

P2

2:29 .

lb/ cu

σ = 0.552 at 20,000 σ = 0.181 at 50,000 = 902 lb sq ; P1

P1

2:28 .

ft

= 0.999+ =· (

(b) P2 = 2:27 .

lb/ cu

humidity

( a ) P/PO

(b)

67%

=

Wmoist = 0.713

(b) F

=

lb/ 1,000 lb dry

(d ) F

ft ;

/

= 977 = 946

(c)

≈2 = 19.2 cu = 492 °F abs T2

( b ) Pdv = 125,000 ft - lb ( c ) AQ = 0 ( d ) Au = -25.3 B 1bm = -160B ( e ) AS = 0

ft /lb

ft/ sec ft/sec 1184 ft sec

a a

= 5.13

=

;

= 0.0333

2:19 . 2:20 . 2:21 . 2:22 .

B 1bmi lbm ; v1 = 13.1 cu V2 = 13.87 cu lbm

Pdv

/ cu ft

AQ = 17.3 B 1bm : 13,480 SPdv - lb

/ ft

15.1 lb sq in . = 8.22 lb sq in . = +0.0538 lb sq in . = 0.405 lb sq in . +17.83 lb sq in . ( PA -PB )

ft/ lbm ;

V2 = 21.1 cu W2 = 0.0470 lb

ft

ft

ft / /

ft ft

N-2

=

T1

=

185

.00126 slug cu

;

/

0.217

°)

=

α

;

;

+

/

; ;

)

α +

+

/

;

=

;

10.03 13.50 15.28

17.43

=

0.0082 0

=

/

=

=

/

°) ;

+

a

;

( +

lower than graph

);

= 0.722

0.8

0.1264C2

=

0.0066 +0.042502

=

0.254

0.240

;

;

° )

+

CL

/

- 0.002

0.0885C2

;

0.0058

0.8

;

= 0.065a

)

=

0.084

CD Cp

on graph

0.84

CL

0.80

/

;

ew

=

CL

and

0.097

=

)

b

(

=

r

c₁

9 : 9: . 8 . . 9

9:12

0.0077

+

0.1082

/ 4

Cmc

9:11

=

=

CD

0.0525

e3

360,000

= 0.542 =

CL

Re

3.22 6.60

25 Voc

=

.

Eff

=

C1

CD

0.40 per cent

=

1

lb

lb lb

.

ft

=

Drag

17 = 17

.

/ /

ft

1.51

CDoe 0.0081 143 sq ft sec

CL e6

=

Drag Drag

-1.20 -0.18

between 0.10

=

CL

;

ft ; 9:10

CD

lb

=

=

9.31

( ( b a ) )

F

opt

dCi da

sq

;

ft

sq

lb /

1,745

0.0150

;

/

ft

R

/

sq

.

b )

(

( a )

;

/

R;

lb

lb /

=

P2

= = = =

ft

/

lb

= 550

P3

b )

(

CDoe min

ft

Re = 7,700,000 Re = 26,850,000

( ( ( ( (a )c )b )a b) )

6 : 6 : 6 : : 6 2 1 4 . .3 . . 9:1.

cu

3.070 sq

= 2,450

12

slug

.475

230 = 1,770 P2

ft

CDoe CDoe

16 18 20

ft

sq

lb

.00485

;

туб

M2

=

( a P3 )

5 : 4 .

5:3. О

in

.

497

sq

4.0

0.0577C2

0.0082 0.0082 0.0087 0.0097 0.0129 0.0177 0.0267 0.0386 0.100

12

R;

T2

( )c

= .937 = 4,110

P2

ft

+5.0 +9.2

1.1

0.0590c2

0.0530

-1.2

.0103 slug cu

P *

A

432.5

/

p

= =

T✶

+0.5

0.100 CL

α

/

sec lb sq

+2.5

0.006 CL

9.40

ft

0.53 0.725 1.04

a

α O

8 4 2 0

ft

= 670 a1 P * = 7,600

0.0071

CDi

-2.5 -1.5

mph

( ( ( a

/

P1

=

R ;

ft

398

P

lb

sq

+

1,086

(

466 1,065

0.074

+

487

0.233

=

504

0.0071

0.232

0.181 0.261 0.407

1.49

= =

T₂

=

max

=

846

ср CD

643

40.9

=

CL

CL

9 : 5 .

/V₂

Calc 0.80

.6

Extrap 0.69 1.065

Calc P2 P1 0.90

(a)

v V

(

ძვ

(b)

6 : 5. 6: 6 .

(

)

(a

)c

to

=

= = 0.704 Mo = 30 °

=

51.9 lb 0.070

=

CL

1.375

max

so

CD = =

/

L

: :9 9 .4 3.

Vmax max

1.30

o =

C₂ 1,103 5: 2 .

.

/ ft

9 :

5: 1 .

80 70 60 50

9 : 7 .

4:9.

4:10 . 4:11 .

100

;

4 :8.

/

CT

120

;

4: 5 . 4 : 6. 4 : 7.

mph

/

.

4: 4 .

and

ft

u = 0.000214 sec / sq Wt sec = 32.6 lb Wt sec = 12.75 lb Thrust = 528 lb ( a ) F = 33.5 lb (b ) Angle = 3.40 = 0.00477 lb Drag uy + VX s = Plots ( 3 ) and ( 4 ) , Table 4 : 1

( c)

4: 1. 4: 2 . 4: 3 .

ft ;

14,000

0.650 ;

9 : 2

(a) d = (b) σ =

/

2:31 .

N-3 9:13 .

;

16 : 4 .

CD = 0.0070+ 0.0196C2

16 : 5.

( a + 1.2

CL = 0.091

9:14 . 9:15 . 13 : 1 .

=

CL

°)

0.0755α a camber located 15% leading edge trailing 15%, reflexed

max .

aft of

t

=

edge

3.4 %

13 : 2 .

max . camber located leading edge = 11.7%

t c CL = 0.0745 ( a CD = 0.0068

+

16 : 7 .

+ 0.063CZ

16 : 8.

/

NACA 3312

CD = 0.39 (a ) = 4.29 sq

f

14 : 5 .

(b) CD

14 : 6 .

14

f = 25.4

(b)

CD = 0.0154

hpr

120 100 80

56.6 36.9 24.3 21.0 19.2

144.1 120.1 96.1 84.1 72.1 60.1

68.0 43.8 29.2 25.2 23.1 23.0 23.1

19.1 19.2

50

48.2 14 : 8 .

)

14:10 )

15 : 2 . 15 : 3 . 16 : 1 . 16 : 2 . 16 : 3 .

57.9

at

12,000

548 479

15,900 10,920 7.350

1,922

1,925 2,025 253 mph

( a ) 154.4

/

(b)

/ ni

A. F.

at

= 38 =

49.0 hp 37.4 hp

20,000

16:11 . 16:12 .

Bo.75R = 25.6 °

T

=

528 Bhp = 113

= 1.222

0.595

8.2

3,270

2,630 2,635 2.770

ft

lb

8.0 lb

D = T =

17 : 1 .

2.86 17.4

lb lb

ft

lb

rpm = 1,820 = 7.5° B 0.75R

6.12 362

( a ) 156 ( c ) 2.0

ft

lb ;

grade

(a )

41 hp

17 : 3 .

(a )

mph = 154

(b )

2,000

17 : 4 .

900

17 : 5.

(a )

18 : 1 .

(b )

Fig .

(b )

(a)

85

50%

(b) (d )

hp

17 : 2 .

ft / sec

175 mph No

= 58 mph

(well

rotor limit )

below

ft/min

ft /min ( extrapolating

/

17:12 to Pa Ph = 0.88 ) 42 sec = 2 21 ft sec = 4033 minutes max

ft/

if

/

mphs

505 Bhp ( point D on graph )

S Vo Vs =

155

lb - ft

Fuel hr ( c ) Fuel / hr

(a ) (b ) ( a) (b )

171

4,815

1,000 Bhp and

rpm 11.5 hp

16:15 .

11,620 7,980

342 274 205

lb/mi at

ft

400 350 300 250 200 150 125 113

3.515 2,390

1,460

D = T =

hpr

411

6.75

16:14 .

mph

5.370

16:10 .

T = 16.3

hpro

=

274 205 171 155

16:13 .

mph

V1 15 : 1 .

86.5 mph

Thp , 4 engines 6,200 6,680 6,920 6,920 6,680 6,360 6,120

342

0.0426c2

Alt

70

= 0.88

411

mph

60

lbs

mph

ft

sq

rpm

2,510 2,330 2,060 2,030 1,950 1,880

ft

479

hpro

V1

53.0 48.0 41.6 38.9 35.2 30.5

T = 270 D = 13.9

16: 9 .

mph

=

Thp

120 100 80 70 60

max

ft

S.L.

: 7. )

14 : 9 . )

mph

0.030+ 0.06602

=

(a )

ft

50

3.4°)

Cp = 0.243 + 0.075 CL 13 : 3 . 14 : 1 .

16 : 6 .

0.4c

aft of

/

= 0.978

D = 5.22 B = 21.50

n = 0.78

22%

1.8 %

Mi

= 60 = 470

Ch max

mphc = 73

(b ) S.L. 12.000

h

ft/min

VL

ft

115 104

Ch max 470 120

N4 18 : 1 .

( c)

habs = 16,500 hserv = 13,000 = 6,000

hoper 18 : 2 .

( a) S.L.

10,000 20,000

(b) habs 18 : 3 .

mph

=

=

18 : 6 .

(a )

=

1,393

(b) XTO 18 : 7 .

( a)

(b) 18 : 8 .

=

1,985

VL

Vc 193

361

211

337

172 338

ft ft ft

= 25,500

108 126 125 118 163

215 680 468 560 900

ft

2,620

3,133

(a) 01

=

+

5.10

V1 = 71.3 mph

(b) v

339 mph

for

= 280

❤ = 450

max = 2,500

( a ) Ts

max = 25,000

(b) mphL =

(d )

= 0.212

Cmwf = 0,088

0.0034CL =

Cmt

Max . (a ) ( a.c.

+ 0.08801

)'

=

c.g. = 0.331c 0.137

0.011+ 0.083CL

Cmt = 0.274GL c.g. Max .

aft

= 0.412c

0.066 ( a + 0.578₤) Cm = -0.00748 ₤

19,500

21 : 4 .

CN = 0.0625 Cm = 0.00948

17.500 14,600 25,000

21 : 5.

brakes

CN =

(a )

(b)

(a

+

0.578₤ )

CHF = 0.135CNc CHF = 0.0085a

( c ) Fe

=

(a) CHp

0.54

-0.00658f -0.00138 ₤

= 0.14

(e) Hf = 21 : 6 .

-

0.119GL

aft

Cfn mwfn =

(d )

lb

410

)'

(a ) ( a.c.

ft/min

21 : 3 .

+ 625 + 40 =

ft

ft

7.500

ft

1,320

ft ft

205

(b) G

(b) (c)

habs

540 + 500 + 210 + 143 =

only XTO

21 : 1 .

21 : 2 .

XL = 655 + 3,500 + 449 + 560 = 5,160 , =

19 : 2 .

(c)

ft

=

= 940

18:10 . h = 225 19 : 1 . (a) mph

(b)

ft/min max

min

"min

730

VLCh

(d ) (+Ab)

18 : 9.

1,880 1,590

= 28,000

14.500

(a ) ( +AW) ( b) (+AP ) ( c ) ( Af )

:5.

ft

490

18 :4 .

18

ft

116 =

Ch max habs

Ch max

= 29,000

hserv hoper

ft ft ft

222 lb - in . ( f ) Stick force = 15 lb (a) CHF =

0.0520-0.00488

384+ 129 =

(b )

.00870t

CN = 0.063

(c) Fe =

0.70

(a

+ 0.618

(d) CHF = 0.065 ( e ) H = 3,860 lb- in (f) Stick force = 207 lb

₤)

INDEX Pages are numbered by chapters ; thus 18-2 means Chapter 18 , page 2 . Appendix pages are designated by prefix A ; thus A6-5 means Appendix 6 , Title page , page 5 . Answers and Index pages are designated by prefix N. prefaces , and Table of Contents are numbered by small Roman numerals .

Absolute ceiling , 18-2 chart for , 18-7 Activity factor , 16-7 Adiabatic flow , 3-4 steady , equation for , 3-4 , 4-1 steady flow energy equation , 5-2 steady incompressible , 4-1 Airfoils , 9-3 aerodynamic center of , 9-3 aspect ratio effects , 9-14 circulation theory of , 9-10 compressibility effects , 10-1 data on , A5-1 efficiency factor of , 9-15 forces on , 9-1 ground effect on , 9-18 low drag , 14-8 momentum theory of , 9-7-9-10

digit - digit

system , NACA 4 system , NACA 5 NACA 1 series , 13-8

13-3 13-4

6

viscosity effects ,

Airfoil coefficients

,

Ailerons , 1-16

11-1 9-1

-

9-4

Air

chart for , A3-3 density of , 2-15 humidity chart for , 2-16

isentropic

expansion

of ,

moist , 2-15 physical factors of , 2-17 properties of , A3-1 standard , 2-19 viscosity of , 2-25

Aircraft

performance

of ,

principal parts of , 1-19 types

Airplane

of,

1-1

axes of , 1-15 control , 1-15 ,

-

on induced drag , 9-14 curve , 9-14 on slope of Atmospheric pressure , 2-1

lift

standard , 2-2 of airplane , 21-2

Axes

longitudinal , 21-3 wind tunnel balances for tests , 8-12 Balanced controls , 21-15 Bank angle of , 18-22 Barometer definition of , 2-6 , 2-7 Bernoulli equation , Boattail , 14-12

2-17

force

4-1 , 4-2

Body

missile ,

14-11 , 14-7 Boundary layer , 6-1 control , 12-7 isothermal , 6-1

streamline

laminar compressible , 7-5 laminar incompressible , 6-4 of high speed flows , 7-1 separation of incompressible , 6-11 temperature near a surface , 7-1 transition , 6-7 , 14-5 turbulent compressible , 7-7 turbulent incompressible , 6-5

construction 1-7

21-1 14-17 nomenclature of , 1-3 , 1-5 , 1-20 operation of , 1-15

drag estimates

18-1

propulsion of , 1-7 1-7 types of , 1-3 www Airspeed , for best climb , 18-2 Altitude , 2-26 density , 2-26 pressure , 2-26 temperature variation with , 2-26 time to climb to , 18-3 variation of density with , 2-26 Angle of attack , 1-19 Aspect ratio , 1-12 , 9-14 , 18-24

1-17 ,

(cont . ) of,

performance

Balance , 21-3

series , 13-10 plotting , 9-4

NACA

Airplane

,

Cable

drag of A6-3 N- 5

N- 6

INDEX

Efficiency propeller ,

Ceiling absolute , 18-2 hovering , 1-14 , 17-17 service , 18-2 Circulation theory of airfoils

,

9-10

Circling flight

,

18-28

effects of ,

Endurance , 18-11 Energy , 2-2

conservation of , 3-3 equation of , 3-3

Climb

chart for , 18-7 Cockpit enclosures , 14-14 Compressibility , 2-1 , 2-5 Compressibility corrections

16-13

Elevators , 1-15 construction , 1-12 , 1-24 free , 21-9

kinetic ,

Engines ,

10-1

10-10

3-4

characteristics of , 15-2 variation of power in , with altitude , 15-8

Compressible flow around spheres and cylinders , 7-17 Excess power for climb , 18-1 one dimensional subsonic , 5-1 Figure of merit , 16-28 ranges , 5-1 Flaps , 12-3 subsonic , 5-1 trailing edge , 12-3 supersonic , 5-1 Flap deflection , 21-13 transonic , 5-1 Conductivity , 2-1 full span , 12-4 on flap hinge moments , 21-13 thermal , 2-5 , 21-13 on Continuity equation of , 3-5 , 4-2 on pitching moment , 21-13 partial span , 12-4 Control plain , 12-4 boundary layer , 12-7 longitudinal , 21-1 slotted , 12-4 split , 12-4 Convertiplanes , 19-1 Flight boundaries , 11-10 Curvature effects , 6-10

lift

Flow

Cylinders

circular , 4-9 , 14-5 drag of , 14-5

elliptic

between streamlines ,

frictionless

duct , 4-1 pipes , 4-1 steady flow , 3-3 uniform flow , 4-5 Flow patterns

in in

4-9 , 14-5

,

Density , 2-1

of air , A3-1 , A3-3 of liquids , A2-1 ratio , 2-26 , A3-3 Diameter of propeller , Directional stability , Dive , speed of , 18-22

16-18 21-9

angle , 21-10

Downwash

coefficient , 6-7 effective minimum , 1-12

Drag

induced , 9-8

of complete airplane , 14-17 of fuselage , A6-4 of landing gear , A6-11 of nacelle , 14-13 , A6-8 of spheres , 14-7 Drag estimates for supersonic vehicle

Drag of Dynamic 21-1

,

14-25

4-5

incompressible

cylinder , 14-5 longitudinal stability ,

around infinite double , 4-7

,

4-1

cylinder , 4-9

streamline equations , table of 4-8 transonic , 5-1 two - dimensional in perfect fluid ,

4-5

unsteady , 6-1 Fluids , 2-1 definition of ,

2-1

flow of, 3-2 perfect fluid , 4-1 Fluid flow , 3-1 free molecule flow

slip flow ,

,

3-1 , 3-2

3-1 , 3-2

turbulent , 6-1 Forces exerted by jets , 4-2 Forces on airfoils , 9-1

N-7 INDEX

Friction ground

Jet

,

18-16 skin , 7-3 , 6-10 Fuselage , 1-25

Laminar

Gases , flow

of

,

15-16

flow , 6-1 ,

6-4 1-26 , 1-27 details 1-26 exposed , 14-16 , A6-11 Landing over obstacle , 18-19 Landing run , 18-19 Lateral stability , 21-11 Leading - edge slats and slots ,

Landing gear

cockpit enclosures , 14-14 construction of , 1-25

Gas dynamics ,

propulsion

3-2 , 3-3

at constant entropy , 2-11 definition of , 2-10 dynamic viscosity of , 2-4 non - flow , process relationship of , 2-12

perfect , 3-5 properties of , 2-1 , A1-2 statics of , 2-8 , 9-10 , 9-14 Gasoline density of , A2-1

Gliding flight , 18-21 Ground effect , 9-18

, of ,

Lift coefficient

9-3

,

maximum , Chap . slope , chart

12 and 13 .

for

9-15

12-5

determining

Lift - curve effects ,

,

13-14

chart for determining , 9-15 compressible , 10-7 incompressible , 10-7

Liquid definition of , properties

of,

statics of , 2-6

2-1

2-1

stability ,

Heat

Longitudinal

Helicopters , Chap . 17 blade construction , 1-27 , 1-28

Mach number , 2-6 , 5-8 , 7-8 , 10-2 Manometer , 2-6 , 2-8 , 2-28 , 2-29 Maximum speed , 18-5 , 18-8 Missiles , Chap . 20

transfer , 7-3 estimate of , 7-19

control ,

1-17

general arrangement

,

1-7

performance , 1-14 photographs of , 1-2 , 1-8 , 1-9 , 1-18 rotor limit , 17-10 stability , 21-10 types , of , 1-7 High devices , 12-1 needs for , 12-1 sketches , 11-2 Hinged surfaces , coefficients for , 21-12 Humidity , 2-16 chart for sea - level air , 2-18 relative , 2-16 specific , 2-16

lift

Incidence , angle of , 14-9 Infinite cylinders , 14-3 drag of , 14-5 flow patterns around , 4-5

Isentropic , definition dry , 2-11

2-10 , 2-10

expansion angles , A4-5 subsonic chart , A4-3 supersonic chart , A4-4 Isothermal , 2-10

airfoil

selection

13-21 body , 14-11 control , 1-19

,

21-3

criteria for

drag estimates , 14-25

major purpose classification , performance , 1-14 photographs of , 1-2 , 1-10 satellite , 3-2 take - off , 1-14 types of , 1-11 Moist air , 2-15 Moment Moment

1-11

coefficients , 9-3 , 11-7 effects , 10-8

drag , 10-8 , for steady flow , 3-4

Momentum

Nacelle drag of , 14-7 , A6-6 wing combination , 14-13 Normal shock wave function , 5-5 , 5-6 , A4-6

Nusselt number , 7-4

Parasite drag , Chap . 14 , Parasite loading , 18-4 Perfect gas

18-24

-

INDEX

Perfect

gas (cont . ) laws of , 2-12 Performance calculations , absolute ceiling , 18-2 maximum

Chap .

speed , 18-5 , 18-8

Performance problems diving , 18-21

gliding , 18-21 gliding turns ,

18-22

landing over obstacle , 18-19 take -off over obstacle , 18-14

18

N 8

Rotors , ( cont . ) operation of , 1-9 tandem , 1-9 twin , 1-9

Roughness effect , 6-9 , 7-11 Rudder , 1-17

construction

of ,

1-23 , 1-24

Scale effect , 11-5 , 11-6 Section characteristics of air foils , A5-1 Service ceiling , 1-12 , 18-2 Shock waves , normal , 5-5 , A4-6

Pitch propeller , 16-2 Pitch control , 1-18 inclined , A4-7 sideslip , 21-9 collective , 1-19 , 17-1 cyclic , 1-19 , 17-1 sidewash , 21-10 Simpson's rule , 4-4 Pitching moment coefficient , 11-1 Pitching moment curve effects , 13-16 Skin friction , 1-12 Pitot tubes , 4-9 chart , effect of Mach number sketch of , 4-10 surface temperature on , 7-7 coefficient sketch , 6-5 , 6-6 Power loading , 1-12 definition , 7-7 Power plants , Chapt . 15 Prandlt number , 2-5 effects , 6-10 Pressure , 2-1 absolute pressure , 2-2 atmospheric pressure , 2-1 gauge pressure , 2-2 measurement of , 2-2

and

in

pipes and ducts , 6-10 laminar , 6-4 turbulent , 6-4

Solidity , 16-7 , 17-7 Sound , speed of , in air , 2-6 , 2-14 Span load distribution , 11-7 , 11-10 wedge shocks , A4-8 ratio acro Span loading , 18-4 Pressure altitude , 2-26 Specific heat , 2-3 Pressure distribution , 4-9 , 4-10 Speed body , 4-9 ratio , 5-3 critical , 10-2 cruising , 1-12 Pressure gradient effects , 6-9 , 7-14 Pressure head , 2-7 effects , 11-5 high maximum , 12-1 Propellers , Chap . 16 activity factor of , 16-7 level high , 1-12 low landing , 12-1 blade - element theory , 16-10 minimum , 1-11 coefficients , 16-11 Speed , 16-1 - power coeffic ent , 16-13 for factors correction Stability , Chap . 21 effective pitch of , 16-22 directional , 21-9 momentum theory of , 16-8 dynamic , 21-1 static thrust , 16-26 longitudinal , 21-3 Propeller efficiency , 16-13 Stabilizer , 1-24 charts of , A7-8 A7-12 logarithmic plot of , A7-9 construction of , 1-24 Stalling speed , 11-12 Psychrometer chart , 2-16 Standard air , 2-25 charts for , 2-24 Range calculation , 18-11 Statics Rate of climb , calculation , 18-1 Recovery factor , 4-2 , 7-3 , of gases , 2-8 , 2-9 Reynolds number , 3-1 of liquids , 2-6 Stanton number , 7-4 transition chart , 7-11 Static thrust , 16-26 Rolling moments , 21-11 Steady-flow , 3-4 Rotors , 1-1 , 1-9 , Chap . 17 applications , 3-5 anti - torque , 1-9

-

N- 9

INDEX

- flow (cont . ) continuity equation of , 3-3

Troposphere ,

Steady

energy equation , 3-3

equation , 3-4

momentum

relations , 3-4 Stratosphere , definition of ,

2-20

-

for

procedure

esti

mates , 7-7 Supersonic wing characteristics 10-15

,

effects ,

Surface curvature 10-10 Surface temperature effect , 7-14 Systematic investigation of

foils ,

air

13-1

Take -off , calculation Temperature

of ,

18-14

2-2 case of uniform surface , 7-6 dry - bulb , 2-17 recovery factor chart , 7-3 stagnation , 7-1 variation with altitude , 2-22 wet -bulb , 2-17 Tests low- speed test data , 9-4 absolute

,

moving model , 8-4

straight - line plotting of , 9-4

wind tunnel , 8-12 Thermal barrier , 14-25 Thermal stresses , 14-11 Thermodynamics , 2-1 , 3-1

Thrust required

flight ,

for

airplane

in level

10-12

correction

,

effects

,

7-11

of aircraft ,

of

helicopters

Variable

Velocity

-pitch

1-1 , 1-7 , 1-7

propellers

,

effect

16–2

, 5-3 laminar and turbulent boundary layers , 6-3 Venturi meter , 4-11 maximum

sketch

for

Viscosity

dynamic , 2-4

kinematic , 2-5

of air , 2-1 , A1-3 of gases , A2-2 of liquids , A2-1

, normal shock , 5-5 shock , 5-1 , 5-2 Wetted area , 14-4 Wheels , 1-23 1-26 construction of , 1-23 , 1-26 Wind , effect on take -off , 18-19 Wind tunnel , 8-5 Wave

-

balance , 8-12 data on , 8-7 - 8-8 high speed , 2-19 model test , 8-4 supersonic , 8-11

test

equipment , 8-12

transonic , 8-11 turbulence in , 6-8 types , 8-5

Wing

of , 1-12 , 1-23 efficiency factor , 14-2

construction

finite , 10-10 finite rectangular

, 10-17 1-12 , 1-21 scale effect on finite , 11-6 types of construction , 1-22 , 1-23 Wing loading , 1-12 , 18-24 definition of , 1-12

of ,

Yaw , 1-15 , 21-9 Yawmeter , 4-11

11-1 7-10

Transonic compressibility

9-18

Types

photographs

14-19 , 16-26

static Transition , 6-7 boundary layer , photographs of ,

,

Turboprop , 1-7 , 15-11 Turbulence , 6-8

Streamlines equations for , 4-5 flow between , 4-5 Streamline bodies , 14-7 Struts , drag of , A6-1 Subsonic compressibility effects , 10-6 10-2 ranges of compressible flow , 5-1 streamline bodies , 14-7 Supersonic flow , 5-7 one -dimensional , 5-2 ranges of compressible , 5-1 Supersonic airfoil , 13-13 Supersonic skin friction , 7-17

calculation

definition of , 2-20

Tunnel -wall correction Turbojets , 14-14

Zero

lift

angle of attack for , 9-5

10-1

1895

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9015 00097 4785

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