The Rocket into Planetary Space 9783110367560, 9783486754636

Table of contents :
Foreword to 2nd Edition
Table of Contents
List of the Most Important Formula Variables and Abbreviations
1. Introduction
Part I Principle of Operation and Performance
2. Most Favorable Velocity
3. Relationships between Time, Mass, Force, Distance, Air Pressure and Most Favorable Velocity
4. Propulsion Apparatus and Jet Velocity
5. The Free Flight of the Rocket
6. Andruck
7. Discussion. Results of Our Investigations Thus Far
Part II Description of Model B: Discussion of Technical Implementation
8. Introductory Remarks
9. The Alcohol Rocket
General
Description of the Alcohol Rocket
Instruments of the Alcohol Rocket
10. The Hydrogen Rocket
General
Description of the H.R
Instruments of the H.R
11. Measurements with Model B
12. About the Technical Devices
Part III Purpose and Prospects
13. Physical Effects of Abnormal Andruck on Humans
14. Psychological Effects of Abnormal Andruck Conditions
15. Dangers during Ascent
16. Equipment of the Rocket
17. Outlook
Addendum
Postscript

Citation preview

Hermann Oberth The Rocket into Planetary Space

Original German Book Oldenbourg Verlag

Hermann Oberth

Die Rakete zu den Planetenräumen

Die Rakete zu den Planetenräumen Hermann Oberth, 2013 ISBN: 978-3-486-74187-2 e-ISBN: 978-3-486-74712-6

Hermann Oberth

The Rocket into Planetary Space Translated by Trevor C. Sorensen, Joachim Kehr, Michael L. Ciancone, Peter A. Englert, Lars Oliefka, Rick W. Sturdevant and Joni Wilson

Translation Team Trevor C. Sorensen [email protected]

Lars Oliefka [email protected]

Joachim Kehr [email protected]

Rick W. Sturdevant [email protected]

Michael L. Ciancone [email protected]

Joni Wilson [email protected]

Peter A. Englert [email protected]

ISBN 978-3-486-75463-6 e-ISBN (PDF) 978-3-11-021809-1 e-ISBN (EPUB) 978-3-11-024509-3 Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2014 Oldenbourg Wissenschaftsverlag GmbH, München Part of Walter de Gruyter GmbH, Berlin/Boston Cover illustration: Irina Apetrei Printing and binding: CPI books GmbH, Leck ♾ Printed on acid-free paper Printed in Germany www.degruyter.com

Preface to English Edition For those of us who have spent our careers in one aspect or another of astronautics, and who in many cases have been steeped in the subject since childhood, the release of this new translation of Hermann Oberth’s classic work is a truly historic event. To hold it in one’s hand (even on an e-reader!) is a profound experience. To read it through, carefully, cannot fail to impress the reader with the magnitude of the debt that we today owe to our pioneers. That debt cannot be paid back, it can only be paid forward, and then only if each new generation comes to understand the magnitude of the contributions to which they are the heirs. With this new translation, the first since a rather hasty and somewhat incomplete work published by NASA in the 1960s, those new generations will have access to this incredible body of work by an old master. The thing that surprises—stuns, really—even the educated reader is the amazing breadth and scope that Oberth addressed in this truly original work. Once that is grasped, the same reader is surprised again by the success with which Oberth treats his subjects, even as viewed with the benefit of hindsight made possible from nearly a century, now, of technological innovation that Oberth could not possibly have foreseen. Yet despite that, and despite the awkwardness introduced both by the necessities of translation and the changes in idiom and phraseology that have come about during the most volatile century in human history, the issues that Oberth chooses to address and the deftness with which he does so are surprisingly modern in their tone. Some who pick up this book, who hold it in their hands, may never get beyond this Preface, or will only leaf casually through its pages. If so, that will be a shame, but if such is to be, if that reader is to carry away only one impression from Oberth’s work, then he or she should know something about the intellectual span attained by this man, thinking and writing in the early decades of the 20th century. In a relatively short work, Hermann Oberth laid down the mathematical laws governing rocketry and spaceflight, and he offered practical design considerations based on those laws. He analyzed the design and performance of oxygen-alcohol rockets, of which the V-2 was the first practical example, in addition to that of the hydrogen-fueled rocket, of which the apotheosis remains the Saturn V. He imagined and considered the problem of launching truly large rockets, offering water launch as a prescient alternative and vehicle staging as a method of attaining the required final velocity. Oberth concerned himself not only with the problems of systems and hardware, but also with the problems of human factors and physiology, offering both analysis and experimental evidence to assess the likely effects of both microgravity and high acceleration on human beings. He proposed the use of tethers and rotating systems to deal with the potentially harmful effects of weightlessness, but he expressed doubt about finding such effects. He introduced risk analysis, he considered the likely failure modes of rockets in the ascent phase and proposed methods to mitigate those risks, and he offered cost estimates for some of the systems and designs that he proposed to be built.

vi

Preface to English Edition

Finally, Oberth devoted considerable effort to considering the practical utility of the satellites and space stations he imagined. He envisioned profit-making commercial applications in addition to public enterprises, including both communications and the collection and distribution of solar power for use on Earth. One could say with very little exaggeration that we, Oberth’s successors, have spent the better part of a century bringing to fruition some of the things imagined by this unique mind. Everyone in astronautics today owes it to himself or herself to become familiar with this pioneering work. Now, with this translation, they can. October 2013

Dr. Michael D. Griffin Chairman and CEO Schafer Corporation President, American Institute of Aeronautics and Astronautics Former NASA Administrator __________________

This year marks the 90th anniversary of the appearance of one of the seminal publications of human spaceflight—Die Rakete zu den Planetenräumen by Hermann Oberth. In terms of primacy, Oberth’s publication is comparable to “A Method of Reaching Extreme Altitudes” by Robert Goddard, an off-print of the Smithsonian Institution, and “Exploration of Space by Reactive Device” by Konstantin Tsiolkovsky, which appeared as an article in the last issue of a Russian science magazine. Goddard, Tsiolkovsky, and Oberth are widely regarded as the “Fathers of Spaceflight.” But whereas Goddard was sparse with his words and Tsiolkvosky was largely unknown outside of Russia, Oberth was at the center of European interest and activity related to spaceflight and rockets that can be traced directly to the V-2 and eventually to the Saturn V. So it has always struck me as odd that, although we mention with reverence this seminal publication, it was never commercially published in English. NASA contracted for a translation in the 1960s, but this translation was restricted to internal uses, and deviated considerably from the original German text. In my role as chair of the History Committee of the American Astronautical Society (AAS), I seek opportunities for applying the collective interests and abilities of the committee to further public understanding of human spaceflight. The notion of translating Oberth’s publication has bounced around for a few years, so I was very receptive when Dr. Trevor Sorensen approached me with a proposal to organize the publication of an English-language translation with the cooperation of the original publishers, R. Oldenbourg. I was pleased to support the effort to bring this important work to an Englishspeaking audience. Of particular interest was to read the words (quite literally translated, in many cases) that were used to describe phenomena that could only be imaged at the time of the writing. The patina of time provides a very interesting sheen to this classic work. I hope you enjoy and appreciate the results. October 2013

Michael L. Ciancone Chair, History Committee American Astronautical Society

Translation Notes It was both a pleasure and hard work to translate Oberth’s first book Die Rakete zu den Planetenräumen from German into English. Especially for the nonGerman speaking members of the translation team, it was wonderful to discover the breadth and depth of Oberth’s thinking in regard to the just barely emerging field of rocketry and astronautics. Oberth’s attention to detail in addition to his foresight into the future of rocketry and astronautics was truly amazing. Discovery was the pleasurable part of translating. The difficult part was how to best express Oberth’s thoughts in English. The translation team faced the dilemma of whether to be true to Oberth’s original language and especially his terminology, which in many cases was fundamental, or to convert it into a flowing, very readable form of English using modern terminology suited for today’s reader. My decisions as team leader were based on what the translation team believed to be the main purpose of this translation, which is to make a very important historical document for the development of rocketry and astronautics available to the English-speaking world in an accurate, understandable format. The anticipated audience consists mostly of academics, students, and enthusiasts of the general public. This primary audience would be most interested in seeing how Oberth thought and wrote, what terms he used (and noting which ones have changed since then). For this reason, the English text is very close to the original German. Where clarifications in meaning were needed, we added them as translation notes (“TransNB:”). Some corrections to errors we found in the original text (most of these were in the typesetting/printing) are also annotated in this way. Oberth’s notes are indicated in the text by numbers, while the translation notes use symbols (*, †, etc.). This book maintains the typical German nomenclature used in the original book to denote chapters (§). Oberth’s term for combustion chamber shows the challenge and illustrates our approach. Oberth actually uses several different words for the combustion chamber of a rocket, among them those most commonly used today. The word he uses most frequently is “Ofen” which means “oven” in English. I believe the word “oven” reflects quite well the purpose of a combustion chamber, referring to something commonly known at that time. As a result, we decided to stay as true to the original book as we could—we used “oven,” “burn chamber,” “fire box,” “combustion chamber,” etc.—whichever was closest to the original German wording. Another technical term for which Oberth used several different words in German was “exhaust velocity” or “exhaust gases.” Again, we endeavored to translate these as closely as possible to the original German words. You will see, for example, “jet velocity,” “exhaust velocity,” and also “outflow gases.” In Chapter 6, Oberth introduced the word “Andruck.” He used it to mean several different things, such as impact force, gravitational force/acceleration, and sudden pressure. It has the units of acceleration (m/sec2). He used the term “lack” or “absence” of Andruck to mean no acceleration and also to mean weightlessness. Because this was such an important word to Oberth and has no comparable single

viii

Translation Notes

English word, we decided not to translate the term, using the definition that Oberth provided and also our own (see footnote on page 33). Finally, translating the title of the book Die Rakete zu den Planetenräumen was intriguing. It has been variously translated as The Rocket to Planetary Space, The Rocket to Interplanetary Space, A Rocket to Planetary Space, By Rocket to Planetary Space, Rockets to Planetary Space, and The Rocket into Planetary Space. We selected the last title because it is how Oberth’s prodigy, Dr. Wernher von Braun, translated it in History of Rocketry & Space Travel, which he coauthored with Fredrick I. Ordway III. Oberth’s seminal work was written and published in 1923, three years before the first flight of a liquid propellant rocket by Dr. Robert Goddard. Despite some of the fundamental, and sometimes even archaic, terminology in this book, we hope you will enjoy reading it and will appreciate the genius of this pioneer, Hermann Oberth, who truly was one of the “Fathers of Spaceflight.” We would like to thank the American Astronautical Society history committee, for initiating and supporting this translation effort; Dr. Michael Griffin for taking the time to read the draft of this translation and writing an insightful preface for the book; Karlheinz Rohrwild of the Oberth Museum, located in Feucht/Bavaria, for providing the scanned version of the second edition of the book for our use in the translation and additional research support; and the publisher, R. Oldenbourg, for the wonderful opportunity of bringing this important book to the English-speaking world. Trevor C. Sorensen (Team Lead/Translator) Hawaii Space Flight Laboratory

The Translation Team:

Joachim Kehr (Chief Translator) German Space Agency—DLR (retired)

Michael L. Ciancone (Reviewer) NASA Johnson Space Center

Peter A. Englert (Reviewer/Translator) University of Hawaii at Manoa

Lars Oliefka (Reviewer) European Space Agency

Rick W. Sturdevant (Reviewer) US Air Force Space Command

Joni Wilson (Copyeditor)

Foreword to 2nd Edition This new edition appeared earlier than I had expected. I therefore allowed the first edition to be reprinted unchanged and am limiting myself to make a few corrections in a postscript at the end of this book. In addition, I note the following: It was my intention to show in this work that it is definitely possible, with the means of today’s technology, to reach the velocities as I have assumed them. However, I had no intention of specifying a definite design for a spaceship. The sketches I made serve more as an illustration and for the better understanding of the text; they are only intended to show what matters in such machines. For practical implementation I would especially make things much simpler. Small models could be simplified still further than stated in § 12 by eliminating the pumps m and n. The content of my book appears to be mainly correct; at least to date I know of no substantive objections. On the other hand, some of the construction information seems to be outdated. Regarding these corrections I refer to the above-mentioned postscript. I considered it necessary to direct the attention of a larger circle of people to my work for only in this way could I hope to attain the means and opportunity for further work. In the third part of my book I make fantastic assertions that indeed cannot be scientifically refuted today, but which one still will not find in scientific works. Unfortunately, this fact has just prevented several serious scholars from considering the ideas and taking the trouble to separate the essential core from the fantastic wrapping. I beg you to consider, therefore, the unusual conditions of the aforementioned third part. If I may be permitted, let me here note the didactic value of the rocket problem. Namely, I consider the questions raised here may stimulate our thinking in a different direction, and indeed, not only for professional engineers, astronomers, physiologists and psychologists, but above all, for the students. The subject is developed from first principles, which we actually encounter daily, but for this very reason we usually do not think about. By virtue of the peculiar relationship among these principles, quite new, and for the young academic, interesting results, now materialize; the “ταυμάζειυ” of Aristotle is evoked. If, for example, a teacher poses a known problem arising from my work, then he can direct the attention of his students to these elementary things in and of themselves, and lead the listeners to explain their science in different ways. In conclusion, it is my pleasant duty to express thanks to my publisher R. Oldenbourg for the kindness provided to me to date, which went far beyond the measure of what an author could expect from his publisher. Medias* in May 1925. Hermann Oberth

*

TransNB: Located in current day Romania.

Table of Contents Foreword to 2nd Edition ................................................................................ List of the Most Important Formula Variables and Abbreviations ............... § 1. Introduction .........................................................................................

1 5 7

Principle of Operation and Performance ............................................. § 2. Most Favorable Velocity ..................................................................... § 3. Relationships between Time, Mass, Force, Distance, Air Pressure and Most Favorable Velocity .............................................................. § 4. Propulsion Apparatus and Jet Velocity ............................................... § 5. The Free Flight of the Rocket .............................................................. § 6. Andruck ............................................................................................... § 7. Discussion. Results of Our Investigations Thus Far............................

9 10 13 24 29 33 36

Description of Model B: Discussion of Technical Implementation .... § 8. Introductory Remarks .......................................................................... § 9. The Alcohol Rocket............................................................................. General ................................................................................................ Description of the Alcohol Rocket ...................................................... Instruments of the Alcohol Rocket ...................................................... § 10. The Hydrogen Rocket ......................................................................... General ................................................................................................ Description of the H.R......................................................................... Instruments of the H.R. ....................................................................... § 11. Measurements with Model B............................................................... § 12. About the Technical Devices...............................................................

48 48 49 49 51 54 56 56 57 58 59 60

Part III Purpose and Prospects ........................................................................... § 13. Physical Effects of Abnormal Andruck on Humans ............................ § 14. Psychological Effects of Abnormal Andruck Conditions .................... § 15. Dangers during Ascent ........................................................................ § 16. Equipment of the Rocket ..................................................................... § 17. Outlook ................................................................................................ Addendum ........................................................................................... Postscript .............................................................................................

68 68 70 76 78 81 87 95

Part I

Part II

List of the Most Important Formula Variables and Abbreviations Here I list only those terms that are used throughout the book. Symbols that are used with a different meaning are only of local significance. The page numbers indicate where a term is first used and defined.* Page

A.R. a b

 0 1

c

γ d e F Fd Fm G g go H’ H h H.R. x= L L’ ln log m m M m O *

alcohol rocket……………………………………………………………….. Andruck [contact pressure—see note on p. 33] …………………………….. actual acceleration ………………………………………………………….. = in the first second of thrust flight L ideal acceleration: bx  b  g  …………………………...………..……. m I have used this symbol both for air pressure and for air density. Confusion is not possible. air pressure in kg/m2 at the start of A.R. thrust …………………………….. air pressure at the start of H.R. thrust ……………………………………… to denote in Chapter 4, I used the letter c for jet velocity in general, flow velocity in the throat of the nozzle, for the exhaust velocity at the nozzle exit, and c for at any other point in the nozzle. In other paragraphs, only is of interest, which I have simply shortened to c drag coefficient …………………………………………………………….. nozzle exit diameter; when used as an index e.g., Fd , p d , cd , d denotes the parameter as being at the nozzle exit …………………………………... base of the natural logarithm largest cross section of the rocket. In § 4, F also stands for the cross section of the nozzle at the point under consideration width of the nozzle exit …………………………………………………….. width of the nozzle throat …………………………………………………... weight of the rocket (as force) ……………………………………………... acceleration due to gravity at altitudes h or s ………………………………. acceleration due to gravity at Earth’s surface ……………………………… when the rocket ascends from s to s + H', then  decreases by a factor of e 1 1 2 is so defined that   …………………………………………….. H H' r distance from the center of Earth …………………………………………... hydrogen rocket ……………………………………………………….……. specific heat at constant pressure ………………………………………. specific heat at constant temperature force of air resistance [i.e., drag]. In §5, if is maintained ……………….. force of air resistance if the velocity is less than ………………………… natural logarithm common logarithm mass of the rocket in general ……………………………………………….. mass of the fueled rocket in general ………………………………………... mass of the empty rocket in general ………………………………………... refers to the throat of the nozzle ……………. as index: e.g., , , , mass of the A.R. mass of the H.R. oven [combustion chamber]; o as index: e.g., , , refers to the oven ...

24, 49ff 33 9, 17 17, 18

15 56

11, 13 24 ff

24 24 9, 11 15 15 15 15 30 24, 56 ff 25 9, 11 30 9, 17 10, 17 10, 17 24 ff

25 ff

TransNB: Any comments in this list that are in [ ] are translator notes and do not appear in the original text.

6

List of the Most Important Formula Variables and Abbreviations

Page

P p

total required thrust ………………………………………………………… pressure pressure in the oven [combustion chamber] ……………………………….. pressure at the [nozzle] exit ……………………………………………….... sum of all forces opposing ascent ………………………………………….. = P – Q …………………………………………………………………….. Earth radius ………………………………………………………………… altitude to which a given rocket must ascend to achieve the most favorable velocity. For investigations about Andruck, s is used for the braking distance. temperature; (if not otherwise indicated, T always relates to absolute temperature) absolute nozzle exit temperature …………………………………………… absolute oven [combustion chamber] temperature ………………………… reduced oven temperature ………………………………………………….. time internal overpressure ……………………………………………………….. velocity in general most favorable velocity in general …………………………………………. ideal velocity ……………………………………………………………….. velocities with reference to a coordinate system having the center of Earth as origin and a fixed direction in space ………………………………... most favorable velocity for s and ds ………………………………………. denotes at the start of thrust [flight] denotes at the end of thrust; In § 5, is also used to denote velocity with reference to the surrounding air in general. tangential velocity of a layer of air due to wind and Earth’s rotation ……... as index: denotes thrust in space free of air drag and gravity, e.g., , …

Q R r s T Td T0 T1 t ü v vg vx

,

w x

=

Z, z

*

2

∙ ∙

; =

∙

9, 17 25 25 9 9

28, 29 28, 29 28, 29 26 11, 12 18 29 ff 11

29 17, 18

2∙ ∙

sprayer* ……………………………………………………………………...

24

TransNB: This definition of “Z” is missing from this list in the original text. Although we have translated it as “sprayer” it could also be called the “atomizer” or the “injector”.

§ 1. Introduction 1. At today’s state of science and technology, it is possible to build machines able to ascend beyond the limits of Earth’s atmosphere. 2. With additional refinement these machines will be able to attain such velocities that—left to themselves in the ether*—they will not fall back to Earth's surface, and will even be able to leave the gravitational field of Earth. 3. These kinds of machines can be built in such a way that people can ascend within them (probably without health disadvantage). 4. Under certain economic conditions, the construction of such machines may even become profitable. Such conditions might arise within a few decades. In the present document I intend to prove these four statements. First, I will derive some formulas, which will give us the necessary theoretical insights into the functioning and performance of these machines. In a second part I will show that their construction is technically feasible, and finally in a third part I will discuss the potential of this invention. I endeavored to be concise. I could frequently simplify the mathematical derivations and formulas by using approximate values for certain parameters that simplified the calculations. I used this approach especially if it made the nature of a subject clearer when discussing a mathematical formula. (In addition, I have often supplied the accurate result or at least shown how it could be derived indirectly from the approximated value, and sometimes I simply estimated the error margin). I have only briefly discussed technical problems whose solvability no one doubts. In the third part, I have limited myself to suggestions, because the subjects dealt with lie still rather far in the future. I did not want to provide more here than deemed necessary for understanding the invention and evaluating its feasibility, because: First of all, by no means did I intend to describe in all details the design of a particular machine, but only to show that such machines are possible. [e.g., I do not have to calculate the maximum performance a specific rocket might actually achieve, if I can just show that it is able anyway to meet the defined requirements. Thus I assumed, for example, a constant exhaust velocity c (cf. p. 9), even though this value can vary by as much as 9% in some cases, and I discussed the case of a rocket traveling at a velocity v (cf. p. 11), although in this case the fuel is not at all optimized, among other examples. If I estimate the performance of a rocket based on v and the most unfavorable value for c, and find the rocket capable of reaching a required final velocity and altitude under these assumptions, then I have also proved that it surely can attain them in reality]. I am even convinced that the whole thing becomes much clearer if I do not go into too much detail. Second, there are some things that I want to keep to myself (in particular, apparently quite favorable technical solutions) as they are unprotected intellectual * TransNB: First postulated by Aristole, many people, including scientists, believed that outer space was filled with an unknown substance called “ether” that enabled the propagation of light and other electromagnetic waves. This was brought into doubt by the Michelson-Morely experiment in 1887, but only definitively disproved by Albert Einstein in the early 20th century.

8

§ 1. Introduction

property. Should my ideas be realized one day, I certainly would be happy to furnish exact plans, calculations, and methods of computation. Finally, I will not hide the fact that I consider some of the devices in their present form by no means as definitive solutions. As I worked on my plans and computations I naturally had to consider every detail; and in doing so I could at least see that there were no insurmountable technical difficulties. At the same time, however, it was also clear to me that some specific questions could only be solved after most thorough research and perhaps years-long experimentation in order to find optimum solutions.

Part I

Principle of Operation and Performance The flight of these machines is based on the reaction principle; i.e., the machine is lifted and moved by gases that are expelled under corresponding pressure like a rocket. Therefore, allow me a few words first on the theory of rockets. +P A completely sealed vessel, in which the internal pressure is greater than the external pressure, stays at rest because the total pressure (which is the result of all pressure forces on any part of –P the vessel wall) is canceled by an equal and opposite pressure on the rest of the wall. But if part of a wall is missing (cf. Fig. 1), then 1. the content of the vessel is expelled through the opening Fig. 1. and, 2. the vessel seeks to move in the opposite direction, because the total pressure on the side of the wall with the opening is now less than the pressure on the intact opposite side. Therefore, the force that would propel the vessel rearwards (we shall call it the reaction force and denote it with P) is equal and opposite to the force that propels the contents in the forward direction. If I denote the element of mass flowing out during the time period dt as dm and the exhaust velocity as c, then: | ∙ |=| ∙ | Henceforth, I will call every flight machine that moves in reaction to expelling gases a rocket. Here we need only to investigate the case of a rocket ascending vertically. Let its velocity be and its mass m. The vectors are pointing vertically either up or down; those pointing upward (e.g., P, ) we will define as positive, and those pointing downward (e.g., c), as negative. Part of the reaction force P is used to overcome drag (-L) and gravity (-G); we will call this part Q (of course, we must consider Q, just as P, to be positive). The remaining force R provides the rocket with a certain acceleration b =

.

We

therefore have: ∙

=

∙

(1)

10

Part I. Principle of Operation and Performance

P  dt . Here c is an absolute number; P and dt are c positive, so it follows that dm < 0, i.e., that the mass decreases with time. It also t 1 1 follows that, if c is constant, then for a given c, m0  m1   P  dt ; that is to c t0 We can also write dm = 

t1

say the decrease in fuel is proportional to the momentum integral P  d t t0

= ∙ =

∙

∙

∙

=

=

∙

∙

∙

∙

=0

(2)

§ 2. Most Favorable Velocity In order to provide a basis for our further considerations, let us consider the following: We think of a layer of air at an altitude s with a density β and a thickness ds, which should be small enough that β and m can be considered constant throughout the entire layer. The rocket passes through this layer with a given velocity , and its momentum increases by a prescribed amount ( m  ). In doing so it, in any case, suffers a loss of mass (dm). Now, at what velocity will dm become a minimum? In order to pass through the layer, the rocket needs the time dt =

and we have

[according to (2)]: Q  ds  cdm  0 v dv Q dm m  c 0 ds v ds

m  dv 

(2a)

m· and ds are predefined, thus constant, and we obtain through differentiation with respect to : Q  dm       v    c  dm  c   d s   0 (3) dv v  v ds

For my rocket, c has a maximum value, which is limited for technical reasons. It varies only slightly and can be attained for any reaction force P that is feasible. Now I consider c to be constant, thereby making the second term of equation (3) equal to 0. If dm is a minimum, then also  dm     ds   1    dm   0 dv ds v

§ 2. Most Favorable Velocity

11

and we have Q    v  0 v

(4)

Now using (cf. p. 9) Q=L+G G = m  g ( g: gravitational acceleration at altitude s. ds should be so small that g will be constant for the entire layer). For the drag we have: = ∙ ∙ ∙ Here F is the largest cross section of the rocket. The factor γ (the drag coefficient) depends on the velocity, and the shape, i.e., for a given rocket, only on . =

= ∙

=

∙

∙ ∙

∙

∙

∙

∙

If this expression equals zero, then according to (3) with the same performance, the mass loss over the distance ds is at a minimum. We denote the velocity at which this occurs and define it as “the most favorable velocity for s and ds.” In the following, we shall examine the case in which the rocket travels with this velocity, i.e., m g v2  v 2  (5)  d  F    v     dv  N o t e : is the most favorable velocity at position s if it is simply a question of achieving the best possible performance at this particular location; however, need not necessarily be the most favorable velocity if we consider the entire ascent. be the value for at the start of the ascent at altitude . The rocket is to obtain its Let drive from an external force. should be so large, and the mass loss so small, that the external air pressure β and thus also L decrease more rapidly than the weight of the rocket. Then will increase, let us say, until the rocket has reached velocity at altitude s. If there is just enough fuel to reach and , then, as can be shown by indirect calculation, it will reach its highest altitude, let us say, , if it travels at a velocity of m/sec at . If it reaches sooner, then the greater air resistance below slows it down so much that it does not even have velocity at , and thus will not reach . If it has not yet reached at , then it must fight against its own weight for too long and again will not reach . , and are given, then , the most favorable velocity between and , is If defined such that (cf. p. 5):

∙

reaches a minimum.

=

∙

∙

=

∙

∙

12

Part I. Principle of Operation and Performance

Now  Q  dt is at a minimum at velocity , so all Q  dt are minima then [cf. (3)]. On the other hand, ∫ m · is at a minimum when acceleration is initially zero and what was missed is made up after a substantial portion of the fuel has been used to overcome gravity and drag. This has the is smaller than in the lower part of the flight path, the difference remaining more effect that can be derived as a function of s by or less constant until it suddenly reaches at . = 500 m/sec, c = 1400 m/sec and atmospheric indirect calculation. For the case where conditions, for example, the difference amounts to a maximum of 200 m/sec (for = 2000 m/sec). It thus becomes smaller as c becomes larger. As increases, it decreases relatively, but it increases absolutely (for = 10,000 m/sec, for example, it would be 250 m/sec in the example above). The gain in propulsion performance here is 10.3 and 12.5 m/sec, respectively. Now, the inaccuracies entering into my calculations are significantly larger (mainly because I did not have a sufficiently accurate value for c, and could not have provided one accurate enough at all). An additional deviation from is due to technical conditions. This is likewise larger than - , but is of no interest to us in this purely theoretical section.

I therefore base my derivations initially on the assumption that the velocity is equal to at all times, which considerably simplifies the formulas. From (5) it follows that:

m

F   2  d  v  v   g dv  

(5a)

and because here all variables are functions of a single independent variable: ∙

=

∙

∙

∙

  d 2 d v  2  d  dg 2dv 2 d v  d v      dv d v g     v dv  

∙

(5b) contains the expression short designation z. = =

∙

=

∙ ∙

∙

∙

= ∙ 2

∙

I denote this expression with y.

2∙

which I replace by the

∙ ∙

(5b)

∙ ∙ 2

∙

∙

∙

(5c)

(5d)

§ 3. Relationships between Time, Mass, Force, Distance, Air Pressure

13

§ 3. Relationships between Time, Mass, Force, Distance, Air Pressure and Most Favorable Velocity If we multiply (2a) with

ds we obtain mc ∙

(6)

=0

∙

According to (5a) and (5b): 2∙

=

∙

According to (5d): = ;

∙

∙

∙

=

∙

∙

and (6) can be written: ∙

2∙

∙

∙

= 0.

(6a)

Here we can now express all terms by means of and t. By definition (p. 11),

=

∙ ∙ The shape of the rocket, particularly the nose cone, is similar to that of the German S-projectile,* which has the following curve for γ (according to Crantz and Becker†).

200

400

600

800

1000

1200 u

Fig. 2.

We are not interested in the absolute value of γ. It is approximately constant up to 300 m/sec, rising rapidly after reaching sonic velocity up to a maximum of 425 m/sec (about 2.6 times the value for subsonic velocities), and then asymptotically approaching a value that is about 1½ times the value for subsonic velocities. Rothe, Krupp, O. v. Eberhardt et al.‡ obtained similar curves for artillery projectiles, and for Siacci§ this was the mean curve for various projectiles. Other authors have derived this curve based on theoretical considerations. *

TransNB: The German S-projectile was an artillery shell used in the First World War. TransNB: Lehrbuch der Ballistik, 1. Band, 2. Auflage, by Dr. Carl Cranz and Capt. Karl Becker (Vol. 1, 2nd Ed.). Oberth misspelled the name as “Crantz.” ‡ TransNB: R. Rothe, Artill. Monatshefte, 110-111, 1916; O. von Eberhard, Artill. Monatshefte, 69, 1916. Otto von Eberhardt was a pupil of Krupp's artillery expert, Fritz Raufenberger. § TransNB: Balistica (1888) by Italian mathematician Francesco Siacci. †

14

Part I. Principle of Operation and Performance

What is the reason for the initial rise and then the drop of γ? The explanation for the rise between 300 and 400 m/sec is simple. If a projectile travels slower than the speed of sound, the air compression at its tip can be compensated by: 1. air flowing off the sides, and 2. the elasticity of the air to the front enabling compensation. If is greater than the speed of sound, then only the flow off the sides is possible; thereby the compression of the air in front of the projectile naturally increases. Both above and below the speed of sound, the effect of the air compression, the pressure, is proportional to the square of the velocity. Behind the projectile a partial vacuum arises. Its effect (base drag) initially also increases proportional to the square of the velocity, but reaches a limit at the speed of sound1) as the air behind the projectile cannot be rarefied to more than absolute vacuum, and it cannot come together behind the projectile faster than the speed of sound. Therefore, at high velocities the base drag being constant plays an ever decreasing role compared with the pressure, and as a result the expression: pressure base drag ∙ ∙ asymptotically approaches the value: pressure = ∙ ∙ For a rocket under power, the base drag is generally absent because the space behind the rocket is filled with the exhaust gases. The progression of γ is similar to that indicated by the curve in Fig. 3. =

200

400

600

800

u

1000

Fig. 3.

Fig. 3a further gives y (dashed line) and z (solid line) for my alcohol-rocket Model B:

y u 200

400

600

800

1000

1200

z

Fig. 3a.

1)

More precisely, just above the speed of sound, at around 400─450 m/sec. Namely, the air next to the projectile experiences a certain impulse forward. Relative to this moving air, appears to be smaller. Hence the continuous and differentiable, not sudden, transition.

§ 3. Relationships between Time, Mass, Force, Distance, Air Pressure

15

Earth’s gravity g is inversely proportional to the square of the distance from the center of Earth. Let r be the radius of Earth; s the altitude; then: = 9.81 = =



9.81 ∙

m sec

2∙

∙

2∙

∙

2∙

,

g

In the second term of formula (5a):

 y  dt we want to use in first c approximation a constant mean value for g (e.g., for so = 5000 m; = 50 km, the best value is 9.7 m/sec2). Air density β (considering atmospheric conditions, such as temperature and weather, as given) is merely a function of the altitude s; (s = ∫  dt ). We do not know the exact value of β for the upper layers of air, and we actually do not need to know it exactly, as I will show later. For lower air layers, β can be calculated quite accurately using the barometric formulas given in meteorological textbooks. It appears, however, that we would come upon unsolvable integral equations if we were to employ these formulas directly. We must therefore take recourse to indirect computation.

We set = ∙ , e being the base of the natural logarithm and H' a constant. We thus obtain as a first approximation a formula in which s is expressed using only . With this s we could then determine β and the other quantities more precisely; therewith again compute s, and so on. So we set: =

∙



=

∙



=

=

1

∙ ∙

Formula (6a) is now written: ∙ 9.7 m/sec

and we summarize

∙

∙

2

v 2v v in the form:  ' H r H

∙

2

∙

∙

=0

16

Part I. Principle of Operation and Performance

We then obtain: 1 2  z dt  c v v g dv  y H c

(7)

At speeds below 330 m/sec we can use any interpolation curves for y and z. This method fails when 330 < < 460 m/sec. We cannot express t by in this segment because is not defined at all here. Because γ is so much smaller for subsonic speeds than for supersonic speeds, increases only very gradually between 300 and 330 m/sec, and then jumps suddenly to 460 m/sec. In this way the reduced drag can (of course only theoretically) be most effectively utilized. is actually nothing more than the mathematical optimum between drag and gravity. However, because we cannot provide unlimited acceleration to a rocket, rockets cannot maintain velocity if the ratio between weight and drag falls within these limits. Thus we cannot use as the starting point for our calculations either. For the apparatus I describe later, must be at least 500 m/sec, so the behavior of is of no further interest to us. Above 460 m/sec becomes steady again. For > 460 m/sec, γ becomes (almost) constant and thus we have: = 2; = 0; = .

1 2  dt H v  2c  c v   2 gH  dv v  2  g c  v v   H c c  

(7a)

by integration 2 =

∙ ln

∙ ln

2

(7b)

N o t e : For calculations with a slide rule one should use

2 g H c

v ; lo g v0 

2 gH c ; lo g 2 gH c

v

2 gH

c  v0 2 gH v v0  c

then

2 gH 2 gH  v v c v0 H c c    lo g t  t0  2 . 3 0 2 6    lo g 2 gH v 2 gH c g  v0  v0   c c

    

§ 3. Relationships between Time, Mass, Force, Distance, Air Pressure

17

T h e a c c e l e r a t i o n b is equal to the differential quotient of the velocity with respect to time: 2 ∙ ∙ 2 (7c) = = ∙ = 2 2 ∙ (This naturally applies only if the velocity was everywhere equal to everywhere > 460 m/sec.). M a s s o f t h e R o c k e t : If we substitute the term

yg  dt and if c

and if

Q  dt in (6) by its value mc

> 460 m/sec everywhere, i.e., y = 2, we obtain: 2∙

∙

(8)

=0

and by integration: ln

m0 1   v  v0  2 g  t  t0   m c 

N o t e : For technical reasons,

(8a)

soon reaches a limit and so does

. But if I place

several rockets on top of one another in such a way that the lowest one operates and is then discarded as soon as its fuel is consumed, then all the velocity limits are added together. In sequence, they result in the following terms, if M, m, μ ... are the masses of the individual rockets:

ln

M 0  m0  0   M 1  m0  0  

; ln

m0  0   m1  0  

; ln

0   ; 1  

and the total velocity increase results, if we use in (8a):

m0 M 0  m0  0   m0  0   0   :    m1 M 1  m0  0   m1  0   1   This value can of course be made any size. In my apparatus, two rockets are placed one on top of the other.

Technically important is the required reaction force, or thrust, P. We had: ∙ = ∙ and  dv y  g  dm  m     dt  , c c   so, P  dt  m   d v  y  g  d t  ,

(1)

(8)

 dv   y  g  m b  y  m  g P  m  dt  For

> 460 m/sec: =

∙

2

(9)

18

Part I. Principle of Operation and Performance

N o t e : The term (b + 2g) corresponds to the acceleration the rocket would experience in airand gravity-free space. I will define this as the “ideal acceleration” denoted as bx. It can be described in terms of as:

bx  ∙ = I call the integral the ideal propulsion and the mass:

v



H

vc  2 gH v  2c

 2g 

c v 2  4 gH  . H v  2c

the “ideal propulsion.” There is a simple relationship between

c  d m  m  d vx  0 ln

(19)*

=

In our calculations, the mass is often of lesser interest, because does not really depend on the mass but rather on the shape and the cross-sectional load. Therefore, the magnitude of ⁄ is more useful for a general discussion. =

∙

The right side here depends only on and A l t i t u d e : ds = ∙ 2 = ∙ ∙ 2 (for

2

and is therefore valid for any m.

(10)

> 460 m/sec). Through integration: 2 ∙

=

2∙

∙ 1

∙

∙ ln

2

(10a)

These are the most important formulas for a first approximation. It will now be interesting to estimate the margin of error, at least for m and . The most obvious error was that I made H' a constant value in the

. The actual air density could vary from this value by a formula: = factor of two or three. Now let me first examine the effect of this error at final, high velocities using a somewhat schematic example. Let the requirement be: = 11,000 m/sec becomes large and = becomes particularly Thereby, inaccurate. I now set H ~ H' = 6300 m. This is much too low, and if βo was correct, then β1 would certainly be fundamentally wrong. At the instant t0, when our consideration begins, the rocket will have already reached its most favorable = 500 m/sec. Then according velocity and the variables will combine so that to (10a):

*

TransNB: This equation is probably numbered out of sequence, although it could be numbered incorrectly.

§ 3. Relationships between Time, Mass, Force, Distance, Air Pressure

2 =

2

∙

2 ∙

∙ ln

2

We further specify: g = 9.70 m/sec2, c = 3000 m/sec. 2  g  H 2  9.70  6300   19.4  2.1  40.740 m/sec. c 3000 2 ∙

=

40.740 = 0.01358 3000 2

log

= log

2

10,959.260 = 1.377721 459.260

ln " = 2.3026 ∙ log " = 3.17233

2

2

2

∙ ln

= 2.01358 ∙ 3.17233 = 6.37882

2

10,500 = 3.5000 3000

=

= 3.5000 =

6.37822 = 9.87822

∙ " = 6300 ∙ 9.87822 = 62,232.8 m

Fuel consumption: log

=

∙ 0.4343

2 ∙

∙ 0.4343

1

(namely when (8a) is multiplied by the modulus of the common logarithms). 2 ∙ 0.4343 =

∙ log

2

2 ∙

∙ log

2

(It follows from the note to (7b):) c/g = 309.28 sec 2 log

2

∙

= 1.37772

2.69897

4.04139 = 0.03530

19

20

Part I. Principle of Operation and Performance

∙ 0.4343 = 309.28 ∙ 0.03530 2.1 ∙ 1.3772* = = 10.918 + 2.893 = 13.811 sec 2g · " = 13.811 · 19.4 = 267.93 m/sec † · 0.4343 = 10,500 · 0.4343 = 4560.15

( m0 log   4560.15  267.93 : 3000  4828.08 / 3000  1.60936 m1 m0  40.678 m1 At an altitude = 62,223 m, according to our approach: s s 0  e H  e9.87882  104.2907  19,530 1 0 1

But, as stated, 1 

0

since H > 6300 m. If, for example, = 5000 m and 19,530 = 67,233 m, then would actually be four to six times greater. But now if I could be maintained under all regulated the speed of the rocket so that circumstances (possibly by means of a device that would reduce the exhaust flow would only be reached at when L > G, and vice versa (cf. § 9.8)1), then simply a higher altitude and somewhat later. The apparatus would have had to fight longer against the air and gravity and consumed more fuel. I will now assume for this instance that β is not four to six times greater for an altitude of 67,233 m, but rather 60 times greater, as I previously calculated. It is therefore: ,

then

= 10

.

= 10

.

62,233  2.5125  log e  I  H II : 62,233  4.2907  log e  II  and through division 6300 I 4.2907 H  6300   10,758.8 m 2.5125 H  3.5863 sec c 2 gH  19.4  3.5863  69.574 m/sec c 2 gH v1  c  log10,930.426  log430.426  log 2 gH v0  = 4.03864 – 2.63390 = 1.40473 c

1) In this text I now and then refer to later sections. The sections concerned complement the previously made remarks, but are not necessary for their understanding. * TransNB: Due to typesetter error, the original German book shows “137772”. † TransNB: Similarly, the original German book shows “10,500” when it should have been “10500”.

§ 3. Relationships between Time, Mass, Force, Distance, Air Pressure

log " ∙

= 1.40473

2.69897

∙ 0.4343 = 309.28 ∙ 0.06231

21

4.04139 = 0.06231 3.5863 ∙ 1.40473 = 24.309

2 g  " = 471.59 log

m0  4560.15  471.59 : 3000  m1 = 1.67724 (for H = 10,758.8 m) m0  47.560 m1

But now certainly during the entire thrust period 6300 m < H < 10,759 m (even if we take the statements on p. 60 into account), and so it is also certain that m 40.678 < 0 < 47.560. m1 So if I denote: m0 = 44 m1

this value will never deviate by more than 7.5% from the true value if all the other assumptions are correct. ln ln

for

= 10,759

for

= 6300

=

1.67724 = 1.60936

1.0404

m0 is approximately proportional to 1/c. I would also m1 have obtained the same uncertainty if c would be uncertain by 2.02%. But c has an uncertainty of ± 7 to 8%, and further varies by more than 4% (cf. p. 26). So for is likewise proportional to now, this approach is quite sufficient for β. 1/c at high velocities. So we can solve what we previously said was our main m problem, namely to calculate from 0 to within ± 7 to 8% for high velocities m1 because the other quantities in the formula have very little influence on the relationship between m and . The drag coefficient γ can be determined fairly accurately from measurements of projectile velocities up to = 1000 m/sec. That it remains constant beyond this velocity is actually only a hypothesis, but it is as good as proven through theory and also by the measurement of the drag coefficients of moving bodies in water. But even if γ deviated from this value by a factor of two or three for high velocities, this would not change the performance. We previously let the drag vary by a factor of 60 without noticeably influencing the result. The error we introduced when we assumed a constant mean value for g is even smaller.

According to (8a), ln

22

Part I. Principle of Operation and Performance

The underlying reason why the result changes so little if we estimate β, γ, and g incorrectly for the upper air layers is the fact that dt is of the same order of magnitude d v / v [cf. (7a)] and with increasing v , d v increasingly dominates dt. In the differential equation (6), which controls the performance, the increase of Q  dt g 2  g  dt dv  y   dt  loses its importance compared to as v increases. mc c c c β, γ and g are all three contained in Q and occur only in this term in (6). At low velocities, we would therefore get much larger errors if we estimated Q incorrectly. But one factor here is very important (at least for my apparatus). already amounts to 500 m/sec, becomes small if Namely, because is also small. Over this short distance, H and g also deviate much less from the mean values, and thus can be more easily replaced by constants, whereby the result would be even more precise (if c were known exactly!) We have, for the application of the formulas derived from all this, the principle that H, g, and γ should use the values they have in the lower layers of the atmosphere, even if should become large (and similarly for β, etc.). Simply stated: Q m u s t i n i t i a l l y b e a c c u r a t e . Our most important task is to calculate the performance; i.e., we want to and from and . Now at high velocities is calculate approximately proportional to 1/c. Because c can only be defined at present to an , along with accuracy of ± 7 to 8%, a similar margin has to be assumed for another uncertainty of 1 to 2% contributed by β. Over all, we can currently to an accuracy of 1/10. Improvement is needed in our knowledge of determine the respective formula values, particularly the exhaust velocity. Assuming exact formula values could be determined through experiment, we could attain considerable accuracy through indirect calculation using formulas (7) through (10). Namely, with the help of dm (8) and ds (10), we could introduce a correction if c depended only very little on L and . First of all we would have1) to express we would have to formulate the term ∙

= =

=

1)

in (3).

∙

∙

=

∙

. This is approximately: [from (8)]

∙ 2

∙

∙ 2∙

∙

∙

somehow as a function of . Then

∙

∙ ∙ . 2

∙

[from (10)]

§ 3. Relationships between Time, Mass, Force, Distance, Air Pressure

23

(3) could then be expressed in the form*: ∙

∙

2

(18)

=0

2

From this we could then determine , and with this value calculate, t, m, s and P. (Admittedly, I personally would calculate the most favorable velocity for my machines in a different way, because the above method would only be practical if: 1 .† 7000

We could then express β and g as functions of s more accurately (this would be especially easy for the case where c is independent of P), and then determine the other parameters with more accuracy. The second approximation of the formulas would certainly come close to a few thousandths of the true value. For a third approximation, it would be recommended to divide the increase of into small segments and to compute each segment using the formulas of the second approximation. Thus we could use exact mean values for β, c, g, s, etc., and possibly afterward make a few more numerical approximations for the respective (cf. segment. We would also have to apply corrections for the fact that p. 11). At this point, I should also mention that I calculated the performance of my machines by other methods. These methods have the advantage over using formulas (7) through (10) because: 1. they account directly for the dependence of the exhaust velocity on the required thrust (i.e.,

c c ) and are applicable to every ; P P

2. if greater accuracy was required, they would attain this goal more quickly; 3.

m0 m1

appears as the independent variable; 4. they are applicable for every velocity,

not only for . But these methods do not lead to such intuitive formulas. We will now derive a similar formula for β. We have:

  0  e



s  s0 H

  v0 v   0  e c   

2 gH   v0  c   v  2 gH c 

H ' H  21 g 2   H   c 

   

    

[from (10a)]. Because H is nearly equal to H', and, as we have seen, it is of little consequence if we use an incorrect value for β,   0  e

v0 v c

2 gH   v0  c   v  2 gH c 

    

H  21 g 2  c  

(11) 2 gH

v v v H   c  2  1  g 2  ln ln 0  0 c  c  v  2 gH  0

* †

c

TransNB: This equation is either numbered incorrectly or numbered out of sequence. TransNB: Original text is missing this closing “)” from the sentence.

(11a)

24

Part I Principle of Operation and Performance

§ 4. Propulsion Apparatus and Jet Velocity

Fd

Fm

As fuel I use liquid oxygen and a combustible liquid; for the upper rocket (cf. p. 17) liquid hydrogen, for the lower a mixture of water and alcohol. The liquids are carried in separate tanks. The oxygen is vaporized just before combustion and heated to 700°C. The fuel is injected in a finely dispersed state into the hot stream of oxygen. Fig. 4 shows a cross section of the Z Z propulsion apparatus design (see also the E two plates at the end of the book). d Z is the sprayer. Here the oxygen flows through 3 to 5 cm diameter tubes E. Externally these tubes are surrounded by the fuel, which is under 3 to 4 Atm* higher pressure. The walls of the tubes d are provided with preferably very small Fig. 4. Fig. 4a. and equally sized holes. Fig. 4a shows a ten-fold magnification of a portion of a tube wall in a cross section dd and from the fuel side. The oven† o is located beneath the sprayer. Here the most intensive combustion takes place. Then follows a constriction, the throat Fm. This seems to me to be necessary in order to provide a certain degree of buildup in the oven. I thereby achieve: 1. a longer retention of the fuel in the oven; 2. a greater pressure (i.e., a higher oxygen density); 3. a higher temperature; all in all, therefore, more thorough combustion. At Fm a nozzle is attached. It is constructed in the manner of Laval‡ nozzles and widens to Fd at the exit. I describe the details later (p. 49 ff.). The outflow of gases through funnel-shaped nozzles has in recent times been extensively investigated. I can presume that these things are well known, and can keep it brief here: The jet velocity of gases from such wide nozzles (Fd = 705 cm2) has not yet been measured directly. Based on the trend shown by previous experiments, (and in agreement with theoretical considerations), one can assume the following: The more perfect the shape of the nozzle, the greater the density of the gases; and the wider the nozzle, the less the interfering effects (friction, etc.), and the jet velocity approaches ever closer to the value that has been already calculated during the past century on the basis of thermodynamic considerations.

*

TransNB: 1 Atm = 1 atm at 760 mm Hg. TransNB: Oberth uses several terms for “combustion chamber” including “oven” as he does here. His terms have been translated to their closest English equivalent. The same is true for the “Jet Velocity” in the chapter title. See the Translation Notes for additional explanation. ‡ TransNB: More commonly known as the “de Laval nozzle” named after Swedish inventor Gustaf de Laval who invented it in 1888 for use on steam turbines. †

§ 4. Propulsion Apparatus and Jet Velocity

25

Zeuner (Turbinen, p. 261 ff.)* provides a clear derivation of jet theory. For my rocket the conditions approach his formulas closely, so that I can use them as the basis for my discussion. According to Zeuner (Turbinen) (155), at every point in the nozzle: x 1    px  x  c  2  9.81  p0  V0  1      p0   x 1  

(12)

as long as p  β. Here I define: specific heat of the outflowing gases at x is the ratio: constant pressure specific heat of the outflowing gases at constant volume is the (absolute) pressure in the oven in kg/m2 is the (absolute) pressure of the outflowing gases at the point being investigated, also in kg/m2 c is the jet velocity at this point is the exit pressure V0 is the volume in m3 of 1 kg of the exhaust gases at the conditions prevailing in the oven. Because the temperature in the combustion chamber must not exceed a certain maximum value, is only dependent on the composition of the gas. Regarding and , it has to be noted that according to Zeuner, if p > β, at every point the relationship between the nozzle cross section Fp and the pressure p is given by the formula:

=

1 ∙ 1

2

1

(13)

From this we can see: p F The ratio d is constant (in reality, only approximately) if (as in Fig. 4) d p0 Fm and ϰ (i.e., the composition of the gas) are constant. According to (12) only p p depends on d for a given gas at a given temperature. If d is constant, then the p0 p0 exhaust velocity will also be (almost) constant and independent of the internal pressure. Nevertheless, the thrust P increases here with increasing , because with increasing , increases and thus the density, and also for a given c and F, the mass of the expelled gas. The above formulas are approximations. First of all, they ignore friction and vortex formation; but even for an ideal gas they would only be correct if the exit pressure is equal to the air pressure, i.e., if = β. *

TransNB: Vorlesungen über Theorie der Turbinen (1899) by Gustav Zeuner (German physicist and engineer).

26

Part I. Principle of Operation and Performance

P r o o f : According to the reaction law the following is valid exactly: =

∙

=

∙

∙

and ( is the absolute temperature in the combustion According to (13), if chamber) and also were constant, then so would be the specific volume Vd of the exhaust gases at the exit. According to (12), the exhaust velocity c, the mass c F expelled in one second d d , and its momentum: Vd ∙

∙

would also be constant. Furthermore, according to (12) and (13),   p  dF would also be constant, and the thrust in vacuum would be greater by   F than in a space with air pressure β. The same momentum of the exhaust gas would thus be opposed by an unequal impulse on the rocket—which is inconsistent with Newton’s third principle (the theorem of the conservation of the center of gravity). In reality, the situation is such that: 1) as β decreases there is a partial separation of the gas stream from the wall of the nozzle; in the process apparently p and consequently also   p  dF become smaller; 2) thereby, the gas in the nozzle, starting at Fm, must experience stronger acceleration (c increases). 3) Finally, somewhat more gas also flows through Fm. With the alcohol rocket (A.R.) Model B, which I will describe later, c increases from lift-off theoretically by 6 to 7%. The smallest value that c can assume, according to my estimation, lies between 1530 and 1700 m/sec. (This uncertainty is thus greater than the entire range through which c can vary! It is so large because so far I could only calculate the sprayer theoretically and was not yet in the position to investigate its principle of operation experimentally.) F If P (and with it ) becomes so small that it would follow from the ratio d Fm per (13) < β, then c rapidly decreases, and that is very undesirable. If I denote = as the overpressure, then: 1 ∙ 1

ü

2

ü

1

§ 4. Propulsion Apparatus and Jet Velocity

27

Fd F (opt) lies very close to d (min) Fm Fm (for the A.R. Model B, for example, the optimum is only about 1.9% greater). p On the other hand, according to (12) it is desirable that d be as small as p0 Fd as large as possible. For technical reasons, ü (and with it possible, and thus Fm ) rapidly reaches an upper limit, and with a varying we must build our rocket p with regard to the largest value of d . In this way, first c would generally be p0 reduced. A further drawback would be that fluctuates, thus being generally smaller than it could be, given the strength of the nozzle. That would incur the following additional disadvantage: The temperature in the combustion chamber must not rise above a certain maximum value. I can achieve this for a hydrogen rocket (H.R.) if I let more hydrogen flow in than is necessary for the compound H2O. In order to be vaporized and brought up to the temperature in the combustion chamber, this hydrogen absorbs heat. Nevertheless, the outflowing gas becomes specifically lighter and c larger.

If we strive for a compromise, at least

N o t e : In order to understand this, one should consider that the dissociation of water vapor, which otherwise begins at 1500º C, also binds much heat without the gas becoming lighter to the same extent as through the generous addition of hydrogen. (By the way, it is also important for the sheet metal walls of the oven to not come in contact with highly dissociated water vapor, but rather with undissociated and greatly reducing gas.)

For the alcohol rocket, I allow more water to flow in for o e o similar reasons. The higher the pressure, under which the gases are, the more they are heated up by the same chemical process. (It is the same as if you let the process take place in rarefied gas and afterward heated it up by compression.) Therefore, if is large, I can allow more hydrogen or water vapor to flow out. Because they are relatively lighter, ∙ , and consequently c, increases. The following device would perhaps be suitable for making independent of the thrust P. One could (cf. Fig. 5) extend the Fig. 5. nozzle at F with a longer cylindrical or slightly convergent section and insert a regulator pin e (similar to that in the Pelton water turbine) from the combustion chamber into the nozzle as needed. [The previously mentioned Model B, however, does not need this regulator pin because the required thrust is almost constant for the A.R. The hydrogen rocket (H.R.) cannot maintain the velocity at all for technical reasons (which, incidentally, is not much of a disadvantage, as will be shown on p. 57). Here the thrust is completely constant, and and c are actually to be set constant.]

28

Part I. Principle of Operation and Performance

For the A.R., the size of the exit

is determined at the point where P/β is x 1

p x smallest. The exhaust gas, at pressure β and absolute temperature Td  T0  d   p0  should fill the volume c  Fd in one second. The amount of heat that is generated by oxidation is equal to the amount of heat that the coolant and the combustion products must absorb, if one can disregard the heat that the oven emits to the environment. Thermochemical tables give the heat of combustion mostly for the case where the combustion takes place at a pressure of 1 Atm and all involved materials are brought to +15° C. So we must calculate as follows: The amount of heat that is provided by oxidation is equal to the amount of heat necessary to bring the fuel and oxygen to 15° C plus the amount of heat needed to bring the combustion products to the reduced temperature in keeping with the Poisson formula for 1 Atm. We calculate the reduced temperature separately for the diatomic and triatomic gases.

=

1 Atm

where ϰ is to be set equal to 1.406 for the first case and to 1.30 for the second are absolute temperatures. From this is calculated. In the case, and and preceding approach, the ratio between fuel and oxygen is determined by the chemical relationships. Thus, for example, 46 g ethyl alcohol binds with 96 g oxygen, or 8 g oxygen with 1 g hydrogen. So if we have computed we can use this formula to determine the ratio between the fuel and coolant. In order to vaporize H kilograms of liquid hydrogen at -253° C and bring it to the reduced absolute temperature , one must supply ∙ 3.400

12 Kal.

(if

lies far above the boiling point). One obtains this value as follows: Let be the temperature at which the specific heat of the gas at 1 Atm pressure, , becomes constant. Now one can determine the amount of heat necessary to bring 1 kg from the boiling point to . Let this be . From to , 1 kg absorbs the heat: = ∙ so in total, =

∙

Q2  T2  12 , therefore 1 kg cp hydrogen absorbs: 3.400 (T1 + 12) Kal.* H kg absorbs H times as much heat. Now for hydrogen,

*

= 3.400 Kal/kg and

TransNB: Due to a typesetting error, the original German text had “3400” (i.e, the decimal point was missing).

§ 5. The Free Flight of the Rocket

29

In order to vaporize S kg liquid oxygen at -183° C and bring it to an absolute temperature of ° one needs ∙ 0.218 ∙

144 Kal.

If one uses liquid air instead of oxygen, the nitrogen that it contains acts as coolant. N kg liquid nitrogen at -195.7º C requires: ∙ 0.244 ∙

121 Kal.

to be heated to at atmospheric pressure. It would take us too far afield to go into further particulars of the calculations here. Whoever wishes to check the details will find the missing data best in the physical-chemical tables of Landolt and Börnstein.* If one knows the composition of the gas and , then one can easily calculate ∙ . Before the application of formulas (12) and (13), ϰ must be computed one more time for all of the exhaust gas. For the A. R., almost only triatomic gases are expelled; here ϰ = 1.30. For the H.R., water vapor and hydrogen are expelled. Here ϰ decreases with increasing water vapor content. We have: Weight of oxygen__ = 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Weight of hydrogen x = 1.400 1.398 1.396 1.394 1.393 1.391 1.389 1.388 1.386 1.385 1.384 1.383

§ 5. The Free Flight of the Rocket If the fuel is exhausted, or if the propulsion ceases for any other reason, then the rocket continues to fly with a velocity that results from and a tangential is therefore the velocity w (due to Earth’s rotation and the wind speed). movement with respect to a coordinate system with a fixed direction and the center of Earth in a permanent location. The common ballistic formulas are not suitable for the trajectory of the rocket, is in the order of 1–10 km/sec. At such velocities one must because first, already take into account that Earth’s gravitational force decreases with altitude and also does not stay parallel to itself (thus is not oriented to an infinitely distant point). Second, air resistance is much less of a factor than for projectiles. This further simplifies the calculation. E f f e c t o f D r a g : Let be the velocity with respect to the surrounding air at the instant the propulsion ceases, the drag, and the air pressure at this point. After seconds, let be the velocity, the drag, and the air pressure. Then: vd t v2  v2  L2  L1 22  2  L1 22  e H v1 1 v1 *

TransNB: First published in 1883 by physicist Hans Landolt and chemist Richard Börnstein. An updated version is still being published as of 2013.

30

Part I. Principle of Operation and Performance

Considering that varies only slightly, as long as we are faced with noticeable drag, we can also write: ;

∙



The retardation due to drag is: ∙

∙



∙ 1

The total retardation: ∙

If

∙

(14)

is the most favorable velocity at point

then (cf. p. 16): L/m1 = g, and

· g. If the velocity (

so the total retardation is equal to

) stayed below

(cf.

p. 27), then the total retardation due to drag would be correspondingly smaller, namely:  L' H L1 vn2 H L1  vn  d t ~        m1 vn m1 v12 v1 m1  v1  t2 vn times as large. v1 For g = 9.6 m/sec2 and = 1000 m/sec, and the corresponding other values, we would obtain, for example:

so only

∙

73 m/sec

(exact value, is 69 m/sec. The difference is so small in part because various errors that we made compensate for one another.) L' = 10,000 m/sec; 1 = 3 m/sec2 (here s and hence the For h2 m1 dh hydrogen content of the air, is greater, and consequently, so is H) h h1 the total retardation amounts to 2.2 m/sec; an insignificant amount. h1 g0 Energy, Altitude and Velocity: In order to lift a body Earth from an altitude h above the center of Earth to an altitude h + dh r=h0 within Earth’s gravitational field (no matter in which trajectory) r2 the work required is: d A  m1  g  d h  m1  g0  2  d h . In order to Fig. 6. h lift the body from h1 to h2, the energy needed is: =

=

∙

∙

1

1

(15)

§ 5. The Free Flight of the Rocket

31

If the body has overcome its climb at the expense of its velocity, i.e., its kinetic energy, then: 1 = ∙ 2 regardless of the direction of and . From these two formulas it follows: 1 1 1 1 =2∙ ∙ ∙ =2 ∙ (16) Of course, this formula only applies as long as one can neglect the influence of other celestial bodies. to the surface of Earth (for my rocket, v1 is the If v11) is not perpendicular _ resultant of the vertical v1 and the horizontal w), the body describes a conic section: an ellipse for < 2  g1  h1 , a parabola for = 2  g1  h1 , and a hyperbola for > 2  g1  h1 . If we imagine the body and Earth’s center being connected by a straight line, then this sweeps equal areas in equal time intervals (Kepler’s Second Law). is the velocity at the highest point of the trajectory If and if dt is a certain (infinitesimal) time interval, then:

D II

DI a

Fig. 7.

∆ =∆

The sides in ∆I are: ∙ ; ; ∙ sin (α is the angle that forms with the horizontal). If I denote half of the sum of the sides as S, and S reduced to one side as Sa, Sb, or Sc, then as is well-known:  I  S  Sa  Sb  Sc 1 1   2h1  v1 s in   1  d t     2h1  v1 1  si n   d t   2 2

 

1 1  v1  dt  v1  dt  si n      v1  dt  v1dt  s i n   2 2

or, because the terms containing dt disappear leaving only those without dt: 2

dt 1  I  h12   v1  dt  1  sin 2   v1  h1  cos   2 2 

1)





Latin letters denote the scalar quantities of a velocity; German [Old English] letters denote the velocity as a vector.

32

Part I. Principle of Operation and Performance

For ∆II the sides are: ∆

=

∙

;

1 ∙ 2 2

;

. Therefore, 1 ∙ ∙ 2 2

∙ =

1 ∙ ∙ 2

∙

∙

∙

1 2

∙

2

Because ∆I = ∆II, then also ∙

∙ cos =

=

∙ 1

∙ ∙ cos

and when substituted in (16): ∙ 1

cos

=2∙

∙

1

1

In the case of the ellipse, this equation has two roots because there are two points (namely the highest and the lowest), at which the elliptical trajectory is horizontal. The expression for the highest point (thus for the ascent height of the rocket) is: ∙ 2 cos = ∙ (17) 2 For my rocket v is perpendicular to the surface of Earth and thus also to w. Therefore v12  v12  w2 , v1  cos   w . The expression for the height of ascent is thus: =

∙

∙

2

∙

(17a)

2 P l a c e o f D e s c e n t : Although my rocket appears to ascend vertically, it does not fall back to the same place from which it lifted off. First, it is influenced by laterally moving air layers (the horizontal component of their movement is nearly equal to the lateral movement of the higher air layers). N Second, a deviation comes about for cosmic reasons. Due to the rotation of Earth, the rocket moves under a W O great circle drawn around the celestial sphere as observed from the intersection of the plumb line with S Earth’s axis. Initially, this circle runs exactly from west Fig. 8. Fig. 9. to east, but later deviates toward the equator, unless the launch site itself lies on the equator (cf. Fig. 8). Furthermore, the angular velocity of the rocket referenced to the center of Earth is less than the angular velocity of the point on the surface of Earth over which the rocket is currently located. This causes a deviation to the west. In Fig. 9, the arrow connects the geographical points over which the rocket flies. This curve can be easily calculated. Thereby, recovery can be facilitated.

§ 6. Andruck

33

§ 6. Andruck* I believe that the following physical observations will make certain phenomena connected with the ascent of our apparatus easier to grasp and will simplify the subsequent discussion. If a motor car is braked while traveling at full speed, all its occupants and, indeed, each part of their bodies proportional to its mass are driven forward. If the car is quickly set in motion, they are pushed backward. Removing all support from a body (or a system of bodies) on Earth, it falls with an acceleration of 9.81 m/sec2. If it is prevented from falling by an externally applied force (the support), then the body experiences certain tensile and compressive forces: the body is subjected to an Andruck acting against the support. Definition: A b o d y s u b j e c t e d t o a n A n d r u c k t h e r e f o r e m e a n s : on every minute particle of mass of the body a force is acting that does not come from the adjacent molecules, which for all particles is in the same direction and which is proportional to their mass, and would seek to impart the same acceleration to each particle. However, the body is prevented by the support from following this force. We want to consider here only bodies that are large in comparison with the effective radius of the molecular forces, but insignificantly small compared to the major celestial bodies. (Although phenomena of adhesion, capillarity, etc., on one hand, and tidal phenomena and the like on the other, could also be dealt with under the point of view of Andruck.) Because all motion is relative, Andruck occurs whenever all molecules of a body are subjected to a given acceleration but the body is kept at rest (Andruck due to gravity) and also when the molecules seek to remain at rest but the body is accelerated (Andruck due to inertia). In this case, the term “support” is to be interpreted broadly. Every force that holds the body can count as a support if it does not itself seek to impart the same acceleration to every mass particle. Accordingly, a book that is lying on a table is supported just as well as is a hanging lamp; liquid in a container is supported, likewise a floating object. The paper scraps clinging to electrically charged sealing wax are also supported, as are iron filings clinging to a magnet. This is because electrical or magnetic forces of attraction would not impart the same acceleration to every molecule (as would the gravitational force). However, not supported by our definition is, for example, a cyclist in an interrupted loop (cf. Fig. 10). It is true that this performer cannot fall in the sense of Earth's Fig. 10. gravitational pull, because that is * TransNB: Literally “contact pressure” but Oberth uses it to mean various things, such as pressure force, gravitational acceleration (g forces), impact pressure, etc. It has units of m/sec2. Because there is no single-word English equivalent, it has been left as Andruck in this translation.

34

Part I. Principle of Operation and Performance

prevented by centrifugal force. But the centrifugal force itself acts on every particle in the same accelerating manner; gravity and centrifugal force are in equilibrium in every atom,* and the body moves (apart from air resistance) the same way as each atom would move if it were free to move. Therefore, the motion of the body does not cause any tensile or compressive forces to act between the individual atoms. The body is not subjected to any Andruck at all. If it were “supported,” however, there would have to be Andruck acting against this support, which could only result from tensile and compressive forces among the individual molecules. This Andruck has the dimensions of an acceleration (so in the technical system of measurement, m/sec2) and is similarly a vector. Its physical effect depends only on its absolute magnitude, the nature of the influenced body, and the type of support, but not on the originating mass-force. Examples for Andruck a) A n d r u c k d u e t o G r a v i t y : The Andruck that is experienced by all motionless bodies located on Earth (better: non-accelerated bodies), is due mainly to the gravitational pull of Earth (9.80 to 9.83 m/sec2). To be added to this are the Andruck due to the rotation of Earth and the Andruck caused by tidal motion. On Mars, the Andruck amounts to only 3.7 m/sec2 because of the lesser mass and gravitational pull of Mars. On the bright surface of the Sun it would be 271 m/sec2. b) A n d r u c k d u e t o I n e r t i a : (cf. the example of the motor car). A solid body is subjected to very high Andruck for a short time in an impact. If, for example, an ivory billiard ball falls from a height of 20 cm onto a marble slab, it arrives there with a velocity of about 2 m/sec. This velocity is stopped abruptly by the impact, and the stopping distance certainly does not exceed 1 mm for any part of the ball. The average Andruck (a) during the impact we determine from the following formulas (s is braking distance, t is duration of the impact, is velocity prior to the impact): 1 = ∙ ; = ∙ ; = ⁄ ; = ⁄2 ; = ⁄2 . 2 In our case, the average value of the Andruck would thus be: = 4⁄0.002 = 2000 m/sec

The maximum value is even greater. We see other examples of Andruck due to inertia in circular motion. There we can observe especially well the vector addition of the gravitational and centrifugal pressures. c) T h e A b s e n c e o f A n d r u c k we can observe on Earth only if the inertia of a body is in equilibrium with its mass, i.e., if the body can freely follow the pull of gravity as with unsupported (thrown or falling) bodies. And even here, the Andruck is actually only completely missing if the body is not moving, which *

TransNB: Oberth interchangeably uses “molecule,” “mass particle,” and “atom” in this narrative about Andruck. We are using the literal translations.

§ 6. Andruck

35

can only be for an instant (because a moving body is indeed supported by air resistance). In general, the absence of Andruck is naturally more common. Whether be it because no external forces generating Andruck are acting on the system (as is true for the entire cosmos), or be it because the various attractive forces, which act on the system from outside, cancel one another (that might be pretty much the case, for instance, for the fixed stars in the interior of the Milky Way system). Or, finally, be it because the body can freely follow every gravitational pull (stars at the edge of the Milky Way, planets, etc.). The absence of Andruck is thus characterized by the fact that no external natural forces seek to displace the parts of the system with respect to one another. Movable parts therefore arrange themselves in accordance with the forces inherent in the system. For example, if I jump into water from a sufficient height while holding a bottle of mercury in my hand, the mercury forms a sphere in the center of the bottle and touches the side of the bottle at only one point (cf. Fig. 11). (In order to compensate for air resistance, I initially hold the bottle slightly above Fig. 11. Fig. 12. my head and then move it downward with increasing acceleration. Often one must also move it somewhat laterally.) Wetting liquids (e.g., water), on the other hand, try to climb up the walls and force the air into the center of the bottle (Fig. 12). (Incidentally, this experiment succeeds only if the walls of the bottle are moist, otherwise the water does not have sufficient time to rise.) If pebbles lie on the bottom of the bottle, they will be drawn up into the water, and so on. If we can neglect the forces that originate from within the system, then all freely moving parts of a system remain in the same position relative to one another or continue against one another with the same uniform motion. If I hold a stone in my hand during the jump described above, I can let it go and it will remain in the same position relative to my body. If I bump it, then it moves uniformly away as seen by me. Its cross-sectional load must be equal to that of my body because of air resistance, so it has to be quite large. T h e S t a t e o f t h e A n d r u c k is characterized by the fact that every part of the system wants to move in the vertical direction as far as possible. The force that is exerted is equal to the product of its mass and the Andruck. E x a m p l e s : A plumb precisely shows the direction of the Andruck. The strength with which it pulls on the line is directly proportional to the Andruck. Andruck, therefore, can be measured by the pull that a specific weight exerts on an elastic spring. Liquids seek to move as far as possible in the plumb-line direction. If they are prevented from that because they are in a container, then they seek to burst this container. (Lateral pressure. The lateral pressure is also proportional to the Andruck, that is, for example, considered in the calculation of the strength of the side walls of my rocket.) Liquids contained in tall, slim containers will seek to buckle them (cf. Fig. 13).

36

Part I. Principle of Operation and Performance

(If the container is hermetically sealed, one can prevent this, among other things, by pressure filling, in other words, by making the internal pressure higher than the external pressure.) Particles of a different density suspended in water precipitate out against the molecular forces, ceteris paribus proceeding more quickly with greater Andruck. For example, through gravitational Andruck, milk is skimmed in 24 hours, but the same process is accomplished in a milk centrifuge in 5 to 6 minutes. In boiling liquids, the greater the Andruck, the faster the gas bubbles rise, but the liquid particles carried up fall back faster into the liquid and therefore do not splash up as high, etc. Fig. 13. In short, all phenomena that we observe under the influence of Earth’s gravity, occur more intensely the greater the Andruck, and the forces causing them are proportional to the Andruck.

§ 7. Discussion. Results of Our Investigations Thus Far As we saw on page 19 ff., more accurate approximations can be calculated for the propulsion formulas with the help of minor corrections obtained from the values of the first approximation. Because the corrections are so small that they do not change the essence of the subject, we can use these formulas in association with the jet and thrust formulas in order to discuss the performance and operation of rockets. We conclude from this: 1. If a given rocket is to penetrate through a given thin layer of air and thereby obtain a given impulse, then there is a specific velocity ( ) at which fuel loss is at a minimum. But is not yet the most favorable velocity as such, this ( ) remains smaller than by a minute amount. This, however, does not interest us further here. 2. From formula (18) (p. 23) we see that is very strongly influenced if the jet velocity c depends on the required thrust P. Formulas (4) ff., are only applicable for constant c. 3. We can write the formula (4): ∙

:

∙

1

=



.

§ 7. Discussion. Results of Our Investigations Thus Far

For

> 460 m/sec, γ becomes constant,

equal to zero;

37

∙

= 0 and

constant. Now, all apparatuses being considered, especially their nose

∙

cones, are similar to one another, so γ is the same for all. m  g is the weight of the m g rocket, so is the cross-sectional load. We can say: F The most favorable velocity for s and ds is only affected by the ratio of the cross-sectional load to the air density (where weight, cross section, cross-sectional load, and air density can be arbitrary). 4. From (7b):

2 ln

=

ln

2

it follows, because g and H can be considered constant, (

) depends on c, m0 also depends only and , so for a given c and it depends only on . m1 on for a given c and ; likewise for b, ⁄ , , ⁄ , etc. [cf. also (8a), (9a), (10a), (11)]. If we calculate a table that contains as argument and the listed parameters as functions, then this table applies to all rockets with and c, and c come about, i.e., regardless of how large the weight, regardless of how the cross section or the air density is in each, or what the temperature or the composition of the exhaust gas is, or how large the values of ⁄ , , etc., are in each. Furthermore, the differential equations do not yet contain , , etc. For the integration we could proceed using any other value of instead of , let us say m . Then we would obtain the formulas for , , ln a , etc. But mb b

b

a

a

c

c

according to the rules of integration,  dx   dx   dx , i.e., the table, is valid anyway for all rockets and any fuel as long as the velocity is and the exhaust velocity is c: If the initial velocity is and the final velocity , then the time is ⁄ . The fuel loss follows from ln = = ln

⁄

ln

, the altitude from

=

, etc.

The term b (7c), is not affected at all by this calculation because the acceleration is already the derivative of the velocity with respect to time.

38

Part I. Principle of Operation and Performance

I have included a table that specifies the values for c = 1400 m/sec and H = 7200 m. b 500 600 700 800 900 1000 1200 1400 1500 1700 2000 2200 2400 2600 3000 3400 3800 4000 m/sec

0.0 7.3 11.9 16.1 21.5 21.5 25.2 27.7 29.0 31.2 33.6 35.0 35.9 36.5 38.2 39.3 40.3 40.7 sec

11.7 17.0 23.3 30.1 37.8 40.0 64.1 84.3 95.0 117.1 153.7 179.5 206.0 234.0 291.5 351.0 414.0 447.0 m/sec2

log 0.0000 0.0754 0.134 0.191 0.240 0.286 0.371 0.448 0.486 0.560 0.625 0.735 0.808 0.872 1.006 1.138 1.267 1.330

1.000 1.190 1.362 1.552 1.738 1.931 2.349 2.803 3.062 3.631 4.217 5.434 6.427 7.446 10.139 13.74 18.49 21.38

31.4 30.9 31.4 31.4 33.0 34.1 35.6 37.0 37.2 37.8 41.2 36.7 35.1 34.1 29.9 26.9 23.4 21.8 m/sec2

If for a rocket with c = 1400 m/sec e.g., = 800 m/sec and = 3000 m/sec m ma and we wish to know how large log is, then we must look up log (500) and mb m(800) log

m( 500 )

and subtract the first from the second; it is log

ma = 0.815, so mb

m(3000 ) ⁄ = 6.5. The propulsion would take 38.2 - 16.1 = 22.1 sec, and so on. 5. If I place several rockets, as was noted on p. 17, one above the other, and as Fig. 15 shows in cross section, then the computation would become very simple if c is equal for all rockets, if (M1+mo+…) = ⋯ and if the apparatus would also actually maintain this velocity. In this case, we could readily use our table. We could also m simply use an ideal 0 so that: m1 m0 M0  m0   m0   (cf. p. 17)   m1 M1  m0   m1   m Here one can immediately see that 0 and thus can m1 become arbitrarily large. For staging, it would be desirable that each Fig. 15. rocket is larger than all those located above it combined; otherwise the ancillary equipment, which would be required for staging, would

§ 7. Discussion. Results of Our Investigations Thus Far

39

be too heavy. For example, each rocket must have its own propulsion apparatus, among other things. Even for the case that is not maintained, one can see the benefit of staging if one considers that not so much dead weight is dragged along. Of course ⁄ can be arbitrarily large here, too. M    0 m0 It should be taken into consideration, however, that 0 and that  1 m1 v v this expression increases with respect to 1 0 like an exponential curve. If not c even the most favorable velocity can be maintained, the loss of mass is naturally even greater and we soon come to quite impossible numbers. So there is a limit for , after all. 6. From (8a): 2 ∙

= ∙ ln

it follows that: The propulsion velocity becomes larger, the larger c, ⁄ and the smaller become (variations of g count for little in this ⁄ becomes” naturally means, for a given m0, simply context). “The larger “the smaller m1 becomes.” ⁄ is approximately inversely proportional to 7. At high velocities, ln ⁄ the exhaust velocity c. Because here ln is also large, it is usually much ⁄ . more advantageous if we can increase c rather than N o t e : There is a simple criterion for determining whether a device that increases the mass of the empty rocket but also increases c, increases the power for ascent. be the mass of the full rocket and the mass of the empty rocket. Let μ be the mass Let of the device that shall increase the jet velocity; let C be the higher and c the lower exhaust velocity. I denote the ideal propulsion in case C as * (cf. (19), p. 18), and that for c as . Now if . (The change in ∫ Q · dt plays no role here.)

∙ ln : ln If

ln

=

ln

∶ =

then:

∙ ln

ln log log

∙ : ln log log

ln

:;

8. The firmness of my apparatus is primarily based on its internal overpressure, similar to the firmness of a tightly filled balloon. I started out for its calculation with the formulas, which have been developed theoretically for pressure filling, and tested my computations experimentally. For this I pulled small canvas sacks of a particular shape over thin rubber bladders and then tested the whole on the apparatus shown in Fig. 16. A is a 1 cm diameter glass tube, which simultaneously served as a manometer. B is a funnel, C a ruler that hangs *

D

. B

K

A J

G F E

A

H

Fig. 16.

TransNB: This “x” was not a subscript in the original book due to a typesetting error.

C

40

Part I. Principle of Operation and Performance

vertically from a thread D and indicates the water level. E is a cork stopper with a hole bored through it. F is the small sack. The rim of E is lubricated with tallow or vaseline; F is inverted and filled with water. E is then inserted into F and tied. Next, one turns the entire arrangement and compresses E so that A becomes filled with water. Then one pours enough water through B that the entire thing gets the necessary tension. H is a glass tube with a squeezable hose through which one can release water from F or blow in air. G is a piece of dried clay, which is shaped to fit the tip of F. On that, a board I is glued, on which additional weights K can be placed. Regarding the ratio between the contents and the mass of the fuel tanks, the following applies for tight pressurized filling: If for similar shapes the homologous lengths increased by factor a, then the surface will increase by a factor of a2 and the volume by a factor of a3. At constant internal overpressure of a vessel, the homologous tensile stresses also increase by factor a, so the wall must also be a times thicker (if one disregards the fact that thin sheet metal is comparatively slightly tighter than thick). The wall of the large vessel weighs, therefore, a3 times as much. Thus, the ratio between the contents and weight of the wall does not change. If the interior overpressure increases by a factor of p, the homologous tensile stresses, and thus also the weight of the wall, also increase by a factor of p. The ratio between volume and the weight of the wall will then be p times smaller. Because the walls of the liquid tanks constitute a considerable part of m1 (cf. p. 50 and 56), it is desirable here that the internal overpressure not be too high. 9. The lateral pressure of the liquids is proportional to the Andruck (cf. p. 36). Therefore, for high accelerations the walls of the liquid tanks would have to be very thick at least at the bottom, and one would have to take care that the situation shown in Fig. 13 does not occur. In this way m1 would now be large. For this reason the performance of a rocket can sometimes be increased if remains lower than , so that b and a become smaller (this is actually the case for the H. R.). 10. From (13) we deduce: For a given chemical composition of the outflowing p F p gases, the ratio d is determined by d . Furthermore, if d is to decrease, then p0 Fm p0 Fd must increase. Fm p 11. From (12) it follows: For a given d and ϰ, the exhaust velocity increases p0 as ∙ increases. ∙ is independent of and is larger when the natural specific weight of the outflowing gas is small and its temperature is high. Hydrogen is ejected the fastest of all. F p 12. From (13) it follows: With increasing ϰ, d must become smaller or d Fm p0 larger. If different mixtures of di- and triatomic gases flow through the same nozzle, all under the same internal pressure (cf. p. 29), then decreases with increasing ϰ.

§ 7. Discussion. Results of Our Investigations Thus Far

41

pd . is p0 indeed given by β for the A. R. and by P for the H. R. and should not be too small. must not be allowed to be too large, otherwise the metal parts and thus would become too large. Refer to 6 and 7 on this. 14. From 6 and from (19) (p. 18) it follows: For a given m = ∙ ln 0 , decreases. From increases as m1 , decreases as the table it follows: For a given increases [one can recognize that this is generally true if one and in (7a) introduces a new value, such as n, for by and then differentiates with replaces   t1  t0  2 gH respect to while observing that . It is < 0]. c v0

13. From (12) it follows: c increases the more we can decrease

t1

In order to keep the loss of propulsion

Q

 m  dt  2 g   t

1

 t0  from

t0

becoming too large, must not be too small. According to 3, is is small (more details on this in 15), or B) if the large: A) if cross-sectional load is large. This is large a) if the rocket is long, or b) if its specific weight is large. a) If we choose to make the rocket long, we must take care that it is not bent by the drag L. We can achieve this: Fig. 17. α) By letting the gas flow out the top and letting the fuel tanks hang down in the middle like a tail (cf. Fig. 17). This design, however, would have several disadvantages. β) If, however, we want the exhaust gas to exit at the bottom (cf. Plate I and Figs 4, 18, and 19), then we must understand that the thrust P would be applied somewhat above the P combustion chamber. The components of the internal stress of the tanks keep one another in equilibrium, so we can consider these tanks as a closed system. Now, pressures p  dF (cf. Fig. 18) act on this system. We can find their P0 P0 point of application if we imagine a level plane drawn through the combustion chamber and draw lines upward w Fm w parallel to the axis. Where these first intersect with metal we have the point at which the metal transfers the load to the outer surface. We can therefore consider the pressures Fig. 18. ∙ as if they would act in the same plane as the sprayer and to its sides. Now, the wall of the nozzle between Fm and Fd is subjected to an upward pressure, but this is obviously less than the pressure acting downward on the torus W.

42

Part I. Principle of Operation and Performance

Now the point of attack for the drag L is at the nose, the resistance to acceleration –(R+G) at the center of gravity, the force P below. Moreover, if there is the slightest lateral rotation, drag would have the undesirable side effect of immediately making the rocket seek –L the horizontal, thereby causing a continual lurching motion. One can only remedy this by mounting appropriate tail fins w. –(R + G) These in turn seek to hold the tail end L P firm while the drag bends the front end, so that the resulting forces continuously strive to buckle the rocket as shown in G w w Fig. 20. In order to prevent this, in keeping with 8 above, a long thin P rocket should either have very great Fig. 20. Fig. 19. , overpressure, which would increase or the rocket should be reinforced by pieces of metal, which in our case would certainly make too large. If m0 we want to keep large here, we have no other choice than m1 to design the rocket with a large diameter, and a correspondingly large mass, so that P* can become smaller. , it is b) At low velocities, that is at high air density and large m0 and at the expense of c. In my apparatus, desirable, therefore, to increase m1 for example, the lower rocket is filled with alcohol and liquid oxygen, and the upper with liquid oxygen and liquid hydrogen. For the A.R. c is naturally much less than for the H.R. (1530 to 1700 m/sec compared to 3800 to 4200 m/sec). But the specific weight of the fuel load is eight times greater. If I wanted to substitute the A.R. in Model B with a single hydrogen rocket, this would hardly be possible. (More details on this in 16). If I wanted to utilize two hydrogen rockets instead of the A.R., the entire apparatus would be about five times as long, therefore about 125 times as voluminous and 18 times as heavy. 15. If we make the external air density n times smaller, in other words, if we lift the rocket up high enough before launch, we thus achieve the following advantages: a) is larger, or if does not change, then the cross-sectional load is n times less and so there is a decrease in mass and fuel consumption on the order of n3. (Model B is designed so that it can be launched at an altitude of 5500 m above sea level).† The apparatus is first raised to this heightperhaps on a cable hanging between two airships (cf. Fig. 21). Should it launch from sea level, where β is twice as large, it would then have to be twice as long and eight times as large and heavy. * †

TransNB: This P was erroneously a p in the original German text. TransNB: This closing ")" was missing in the original German text.

§ 7. Discussion. Results of Our Investigations Thus Far

43

b) Because the drag per unit area of the cross section is n times smaller, then, according to 8 and with similar shape, the internal pressure of the tanks needs to be only 1/n as great, Fig. 21. and is thus proportionately smaller. If we have no reason to reduce the internal pressure, then we can make the rocket more slender and save fuel. c) If the outflowing gas at Fd were in both cases of equal temperature and composition and if it would flow at velocity c, then the ratio between the largest cross section F and the exit cross section Fd would not change (cf. p. 28). In particular, F is now n2 times smaller. c should remain constant, β and are n times smaller, therefore, the specific volume of the exhaust gas is n times larger, dm is n3 times smaller and the absolute volume n3/n times smaller. Fd should dt therefore also be n2 times smaller (just like F). Now, however, in reality, for the same

,

0 p0

is n times smaller, likewise for

pd (opt.) (because P/β remains constant), therefore c increases according to (12) p0 and Fd must decrease. — If T0 remains the same in both cases, then the absolute temperature and the specific volume of the exhaust gas are less in the second case F F ; d therefore has to be even smaller. — d would be larger by a factor of F Fm F F F according to 10, so m  d . The term d would definitely become smaller. F F Fm This has an advantage: the fuels remain longer in the oven, which can be shorter (in the absolute sense). p If one wanted to give up the advantage of making d smaller, would p0 decrease and so would the weight of the propulsion apparatus. Admittedly, c would then also be somewhat smaller, because less coolant would be required for a given T (cf. p. 27). There is an optimum between both approaches that can be found with the help of criterion 7. 16. Now I want to suggest, if only roughly, why the hydrogen rocket proves to be superior if the air density is very low. m a) We saw that 0 becomes larger the smaller β0 becomes. If we denote br as m1 the weight of the fuels and that of the empty rocket, then approximately br k  , where k is a proportionality factor. Now for an alcohol rocket the fuel m1  0

44

Part I. Principle of Operation and Performance

load has a specific weight that is q times heavier. If I use capital letters for the A.R. and lowercase letters for the H.R., based on what was said in 8, I can write: =

∙

Furthermore, from (8a), (3) and 14 in thin air: ~

and from (19): =

∙ ln

=

= ∙ ln 1

If

∙ ln 1

=

∙ ln 1

∙

.

, then: ∙ ln 1

∙ ln 1

∙ ln 1

∙

∙

ln 1

c/C is a given number. In this case, therefore, the hydrogen rocket achieves a higher velocity by ejecting all of the fuel. In order to discuss this formula, we note br : that, for s m a l l m1 ln 1 ln 1

Now because q >

~

c , alcohol loading is advisable. C

Furthermore, ln 1 ln 1

ln 1 ln 1

ln

=1

ln ln 1

§ 7. Discussion. Results of Our Investigations Thus Far

45

br br ) increases from 0 to  if increases. m1 m1 br , i.e., with The entire expression approaches the value of 1 with increasing m1 c decreasing β0, and therefore must become even smaller than > 1. Naturally, C  br  ln 1  q m1   this applies all the more to the smaller expression ; for this reason,  br  ln 1  m1   therefore, the hydrogen rocket is recommended more and more the smaller β0 becomes. b) Because of the low specific weight of the fuel load of the H.R., the lateral pressure is low. This is an important advantage because it means that the acceleration can be greater (cf. 9) and the propulsion of shorter duration (cf. 6). = , then . This relationship causes the following: If the c) If rocket, for example, is to carry recording instruments of a certain weight, but on the other hand is to be carried aloft by another rocket and therefore should not be too heavy, a hydrogen loading is preferable, even if an alcohol rocket of equal empty weight would perform even better. In Model B if we were to replace the H.R. with an alcohol rocket that has the same volume, this could indeed perform somewhat better. But for the same total performance, the new apparatus would have to be at least five times as heavy as Model B, and for every kilogram of hydrogen, we save about 200 kg of alcohol and 420 kg of oxygen. d) Finally, the behavior of metals at the temperature of liquid hydrogen should be considered. They all become hard and brittle. If I place a cube with side lengths of 2 cm on a table and lay centered across it a 50 cm long and 1 cm thick glass rod and then try to bend both ends down far enough to touch the table (cf. Fig. 22), then the glass rod will break. With a glass fiber of 0.1 mm diameter (obtained by Fig. 22. rapidly stretching molten glass), the attempt readily succeeds. Now for the rocket, bending always will occur due to the changing drag, internal pressure, etc. Theoretically, this could be avoided almost completely by the correct calculation of the material strength at each point, but in technical realization certain imperfections would remain. The principal bending modes are in a certain ratio to the overall size of the apparatus, so for brittle material, the thinner the walls, the less dangerous the bending. If the material is protected from fracturing, then the low temperature can also m provide an advantage: the tensile strength and thus 0 increases significantly. m1

Here ln is a constant, and ln (1 +

46

Part I. Principle of Operation and Performance

17. If the rocket were not exposed to gravity and air resistance, then it stands m entirely within our discretion to choose as large a ratio 0 as we want. The less m1 the air pressure and gravity, the better the rocket is able to perform, so the rocket is the apparatus of choice for entering into planetary space. 18. From formulas (16) and (17) it follows: The height of ascent does not depend on the mass and the nature of a body, but only on its velocity . In (17) and (17a) the denominator interests us. It means that the height of ascent is only final, i.e., the body can only then fall back to Earth, if < 2  g1  h1 . The parabolic velocity 2  g1  h1 , amounts to, for example, about 11,160 m/sec at 70 km above the equator. 19. (16), (17) and (17a) also imply that for my rocket, in addition to h and the full velocity the geographic latitude of the launch site plays a role. It also plays was the most favorable velocity at h or whether it a (small) role whether should have been greater. 20. We can now investigate further which ascent angle, i.e., which direction of v1, is the most favorable for the rocket. v1 is the resultant of v1 and w. The rocket is as large as possible. reaches its highest point [according to (16)] if is then a minimum if the ellipse is as elongated as possible (Kepler’s Second Law), i.e., if v1 is perpendicular, but is a maximum (because of Earth’s rotation), if v1 is horizontal and oriented toward the east. The optimum would be a certain inclination to the east (α). At low velocities it would be small, but considerable at higher ones (because here the ellipse is in any event elongated). At the parabolic velocity, v1 would have to lie horizontally to the east. We could find the angle α if we calculate in (17) using the law of cosines and somehow find the optimum. Now it should be noted in regard to Model B: α) This inclination to the east would require rather complicated precision instruments and their weight alone could easily increase the mass of the smallest m rocket (for it would have to carry them), and thus decrease ln 0 , so that the m1 height of ascent would not experience any increase. β) If we wanted to let the rocket first climb above the atmosphere and only then give it a lateral thrust, we would lose 1 to 2 km/sec performance in exchange for, in the best case, not quite 470 m/sec. If we wanted to let the rocket fly up at an angle from the start, it would have to fight against air resistance for too long. That would slow down a small apparatus, whose velocity reaches close to (such as, for example, Model B), 34 times more than would be gained in propulsion. γ) Finally, we also do not want to make the first apparatus too complicated, in order not to leave the success of the first attempts too much to chance. If ever the ascent conditions should be better investigated, and, furthermore, if rockets were large enough so that the weight of the guidance equipment no longer plays a significant role, and if for some reason the velocity should remain well below , then an inclination to the east should certainly be sought. Especially if, perhaps, not a high altitude but a high horizontal velocity is desired instead.

§ 7. Discussion. Results of Our Investigations Thus Far

47

21. It would perhaps be good to summarize the limiting assumptions we have made. The derived theory applies of course only to the case where 1. c is constant; 2. the rocket travels at a velocity at which the drag is equal to gravity and the drag coefficient is constant; 3. the rocket ascends vertically; 4. liquid fuel is used, and, finally, 5. the rocket gets its strength mainly through pressure filling. We could make these limiting assumptions because these requirements are all met by Model B1). Of course, from our formulas many rather interesting things can be deduced. But now I want to conclude this theoretical treatise and just briefly repeat the principal requirements at which we have arrived because of our formulas: a) Highest possible cross-sectional load, b) Highest possible launch location, c) Thinnest possible walls, fewest possible metal parts, the greatest possible m value for 0 , internal pressure not too high, especially not in the tanks, avoidance m1 of impulsive accelerations, d) Combination of several rockets, e) The jet velocity as high as possible and the highest possible temperature in the combustion chamber, use of specifically light propellant gases, small value for pd , kept as constant as possible, p0 f) Small apparatuses should ascend vertically, g) The velocity must be adjustable; the most favorable velocity must be maintained as exactly as possible, and many others. These requirements frequently conflict with one another. It is a matter of design to find the optimum between all.

1)

N o t e : Just as this theory provides a good framework for more general considerations, so one can also expand the results of this discussion for other cases.

Part II

Description of Model B: Discussion of Technical Implementation (Reference Plate I and II at the end of the book)

§ 8. Introductory Remarks In order to show that apparatuses of the aforementioned type are possible, it will be most appropriate to describe such an apparatus. As I already said at the start, I will not go into details; I would even say that the description that I bring to you here is for the purpose of demonstration. It is intended to show as clearly as possible how the derived principles can be put into practice. In reality, I would deviate in several points from the construction described here. It would not be possible for me within the scope of this book to justify the deviations. In my drawings I have also only indicated what is essential. I simply drew a longitudinal section through both rockets as seen from the cut surface, and two cross sections. The horizontal dash-dot lines (•••) between the longitudinal and cross sections, which are marked with Greek letters, indicate where the cross section lies. I have drawn in black ink what belongs to the A.R., in red ink what belongs to the H.R. The purpose of Model B is to investigate the height, composition and temperature of Earth’s atmosphere, to determine the curve for γ more precisely, and to confirm and improve our calculations of c, T, p, etc. (especially for the H.R.). As previously mentioned, the actual apparatus consists of the A.R. and the H.R. It is 5 meters long, 55.6 cm wide and weighs 544 kg; 6.9 kg of that comes from the H.R. In addition, there is an auxiliary rocket (cf. p. 61). Regarding the construction, it needs to be said that I consider the materials question not yet definitively solved here. Although construction is feasible in the indicated manner, significant improvements could probably still be achieved. The material is subjected here mainly to tensile stress. For the A.R., I have considered an aluminum alloy that has a specific weight of 3.0 g/cm3 and a tensile strength of 30 to 32 kg per mm2. Because the stress lasts only ½ minute (cf. the table in § 7.4) and there are only thin parts throughout, a load of 20 kg ⁄ per mm2 could be used. —I would get exactly the same ratio (with a

§ 9. The Alcohol Rocket

49

different thickness of the solid parts) if I had based my calculations on some other material, of which a wire of 1 mm2 cross section could likewise be loaded with 6.7 cubic decimeters of the same substance (cf. § 7.8). If it could carry ⁄ would become smaller and larger. If it could withstand more, then ⁄ would have to be smaller. less, then The interior of the oxygen tank should be lined with an alloy of copper and lead, which would contract to the same extent as the aluminum alloy when cooled to -170° to -180° C. At those points where the partition between parts of very different temperatures abuts the outer surface, it would have to carry thermal insulation for some distance. In fact, if the transition from warm to cold parts occurred over too short a distance, then certain undue tensile stresses (e.g., such as those resulting in the breaking of glasses that one suddenly fills with something hot) would endanger the apparatus.—The metal parts that come into contact with the flame would have to be of pure copper. For the walls of the sprayer, pure silver lining would be less costly than copper for frequent launchings. Because it, in fact, is not attacked by flame and oxygen, it could be used more often, and possibly even transferred from an old to a new apparatus. Then the awkward work of the drilling of pores would have to be undertaken only once. The question of material is particularly difficult for the H.R. Pure lead still seems to me the best solution, which at this temperature becomes similar to good steel. Copper or very soft iron are also likely to prove their worth.—But in order to find the best, very thorough work is still necessary. For the material of the H.R. I have also assumed that a wire of 1 mm2 cross section could be loaded with 6.7 cubic decimeters of the same material.

§ 9. The Alcohol Rocket General: = 7700 m (the apparatus is lifted by balloons to 5500 m, (cf. Fig. 21))*, and the auxiliary rocket needs 2200 m to achieve velocity . 16.5 kg/cm3 < p0  20 kg/cm3. Fuels: 341.5 kg water, to which 45.8 kg alcohol is mixed; 1.67 kg rectified alcohol; 98.8 kg liquid oxygen or the equivalent quantity of nitrogenous liquid air. In this case it needs (cf. p. 29) less water. 1700º C < T0 < 1750º C ~ ~0.39 kg/cm2 Nozzle ratios: ⁄ = 0.329; ⁄ = 5.86; ⁄ = √5.86 = 2.42 = 29.9⁄2.42 = 12.35 cm = 55.6√0.329 = 29.9 cm; Exhaust velocity: According to § 4, (12) we would find c to be somewhat higher than 1800 m/sec. But because of manufacturing imperfections, c is *

TransNB: The second “)” is missing from the original book.

50

Part II. Description of Model B: Discussion of Technical Implementation

probably reduced to somewhat more than 1600 m/sec. In order to find a lower limit for performance, I initially set c equal to 1400 m/sec, although in reality c, and thus performance, is certainly greater. Largest diameter of the rocket: 55.6 cm. The alcohol-water tank is under an overpressure of 3 Atm as is the space dedicated to the H.R. The oxygen tank is under a pressure of + 1.5 Atm. As liquid is withdrawn, the pressure is maintained by vaporization of a portion of the liquid. Wall thickness of the propulsion apparatus: 2.35 mm. The wall thickness of the oxygen chamber: 2.8 mm. The propulsion apparatus weighs 16.2 kg, the oxygen tank 10 kg, the pumps 8 kg, and the fins 4 kg. The nose, etc., (wall thickness about 0.4 mm) weigh 6 kg, the sprayer 3 kg. All other parts combined weigh 4 kg. M1 + m0 = 56.2 kg* M0 + m0  544  9.7 M1 + m0 56.2

However, we will set this ratio equal only to 9. The cross-sectional load of the fully fueled rocket: 0.225 kg/cm2 = 500 m/sec;

= 2800 m/sec to 2900 m/sec.

Cross-sectional load at the end: 0.0232 kg/cm2. The combustion duration amounts to 36 to 40 seconds; during the first 15 to 20 seconds, is precisely maintained, but later the apparatus stays below this ≤ 20 Atm. From this it follows (for c = 1400 m/sec): value in such a way that P/M0 = 34 m/sec. The mass expelled in one second is: 12.01 kg/sec

13.21 kg/sec

Combustion occurs in the following manner (cf. drawing No. 2): Tubes C, which are 2.5 cm wide at the bottom and 3.6 cm wide at the top, do not quite reach the ceiling of space A. Between these tubes there is rectified alcohol, which is brought to a boil by the pump, which I indicated with mn, pumping hot oxygencontaining gas into a suitable network of tubes. This gas rises through the alcohol in fine bubbles. The alcohol vapor escapes through tubes C. Into them, cone-like tubes D, with holes bored through the wall, extend from the oxygen chamber, as I have indicated on p. 24. The pressure in A is somewhat above Atm, and in the oxygen chamber it is + 1.5 Atm, so that the oxygen is injected as a fine spray. These tubes have an ignition device G at their ends so that the mixture ignites. Because much more oxygen is injected than is required for combustion, we obtain a gas that contains 95% oxygen and at 20 Atm has a temperature of about 700° C. Tubes C continue into space B (E). Here they are surrounded from outside by alcohol-water, which is forced through narrow pores in thin streams and burned there. *

TransNB: This value (56.2 kg) should be the sum of the components in the previous paragraph (51.2 kg) plus the weight of the H.R. (6.9 kg from p. 48). That totals to 58.1 kg.

§ 9. The Alcohol Rocket

51

D e s c r i p t i o n o f t h e A l c o h o l R o c k e t 1) : The nose cone a forms a separate part of the apparatus. It is fitted over both rockets like a hat and held in place by elastic springs (dynamometers b, b'). It consists of two symmetrical parts; when the fuels are expended, the connections between these parts, the nose and the dynamometers, are loosened and the two halves fall apart as soon as the H.R. begins to function. That appears complicated, but as a matter of fact, it is quite simple. However, I want to still keep the details to myself. Inside there are air-filled cavities (c) that are intended to prevent the nose cone Fig. 23. Fig. 24. from sinking should it fall into water. Because the air in front of the nose at 2000 to 3000 m/sec is strongly heated, space c must also have some simple means of cooling (something like a fan) (not shown). Its work is facilitated by the fact that the internal air cavities are in contact with justvaporized hydrogen, which rises out of the H.R. from the nozzle of the H.R., flows around the thin wall d and finds its way to the outside via some kind of relief valve at K. The space that is to receive the H.R. has a diameter of 30 cm, while the diameter of the H.R. itself is only 25 cm, so that all around it a 2.5 cm wide space remains, which is filled with hydrogen gas and again subdivided by d. The air cavities would connect exactly with the nose of the H.R. if it were not 1 cm lower. Pads ( f ) are necessary because at its low temperature, the H.R. would fragment at the slightest shock. Naturally, space between the pads must remain free for the escaping hydrogen vapor. e is the container for the alcohol-water. Located therein is a float g, whose purpose we will talk about later. The pressure in e amounts to 3 Atm, which is maintained by pumps mn pumping into the double floor h hot gas, which rises upward from here through numerous small openings. The pressure is regulated automatically. If it should become too high, a relief valve allows gas to flow out through K. The alcohol-water mixture flows alternately through valves y and tubes o into chambers and , which both have a second exit to K at the top, and finally a third at the bottom to tube k, which is connected to the sprayer Z. These chambers also have a double floor i. Gas coming from mn likewise rises through its pores. These chambers , function as pumps. The valves open and close in such a manner that one chamber is always refilled from e, while the other, under 20 to 23 Atm pressure, pumps the alcohol-water to the sprayer. (Prior to launch, both chambers are of course filled in order to increase the fuel load of the apparatus.) Because the pressure varies considerably in , and because the lowest pressure is not sufficient for the strength of the apparatus, and also because of the peculiar shape of these chambers, they must be rigid, in contrast to the rest of the rocket, so they must get their strength through metal parts. The oxygen tank s is 1)

Cf. Plate I.

52

Part II. Description of Model B: Discussion of Technical Implementation

under a pressure of 18 to 21 Atm. The pressure in space A is lower by 1 Atm. Nevertheless, the separating wall between the two must be straight and thin; hence it is supported by wires q, which hang on the stiffeners of p. The upper surface of the oxygen tank is in the form of an elongated horizontal ellipsoid. thus extends farther Because the cross section of the rocket is circular, space down into the oxygen tank at two opposite points; at these two points are located to the sprayer. The liquid the valves , which bring the diluted alcohol from in accumulates in the center at k.—The oxygen must be kept at a pressure of 21 Atm by vaporization. It vaporizes: 1. because the much hotter space A is located under it. But this alone is not sufficient, it needs in addition 2. hot gas blown through the pumps mn in the manner indicated. This hot gas contains water vapor that on this occasion forms ice crystals, which float atop the oxygen and therefore .—The oxygen do not harm the pores of the sprayer, but do somewhat increase tank also contains a float device g, which above all things has the task to keep the fuel consumption in step with the oxygen consumption. Through the interaction of the floats in the alcohol and oxygen tanks, the relief valve of the oxygen tank in addition to the vaporization of the oxygen is controlled electrically. (It is also located at K.) If the oxygen level drops too slowly, the pressure in the oxygen tank grows, whereby more oxygen squirts into the sprayer. The walls of the oxygen tank must be 2.8 to 3 mm thick. Expansion chamber W is connected to the diluted alcohol in the sprayer via tube k. It is there: 1. to fill the whole space between the tubes E with the diluted alcohol, and 2. to maintain the pressure at a certain level. Both could not be achieved by , alone. The pressure in W is also maintained by having pumps mn pump in hot gas. In addition, it contains a float g, which above all regulates the function of pumps , . W is located under the nozzle of the H.R. and must therefore be protected against heat emission. W is egg-shaped. Between W and there is a space I where the instruments, which regulate and record the functioning of the A.R., are placed to protect them likewise from heat fluctuations. In addition, an electric direct current source, kept as constant as e1 possible, and a small e4 m6 dynamo should be placed m8 m2 there. m4 n Pumps mn function as e2 m1 to K follows (cf. Fig. 25): A m7 small piston pump m9 e3 m1 pumps alcohol alternately m e7 3 m5 and into both vessels e8 , and continuously into vessel n. Vessels , pump Fig. 25. oxygen into n (similar to , for the alcohol). Pieces of sodium are located on the bottom of , . When valves , or, respectively, , are open, oxygen flows in and lifts the pieces of sodium. When both vessels or are filled, then these valves are or . Due to the presence of closed and alcohol flows over the oxygen through the sodium, vigorous combustion immediately begins, whereby the oxygen content

§ 9. The Alcohol Rocket

53

is driven into n via or .* In n, alcohol and oxygen are suitably mixed. Sodium is also located there, and thereby all the alcohol and oxygen are vaporized and hot gas, highly enriched with oxygen, flows through tubes . n is lined internally with there are fireproof material and surrounded externally by liquid oxygen. In valves that regulate the amount of gas flowing to h or i. The rate of function of can also be regulated. N o t e : I cannot say for certain whether the use of sodium will fulfill its purpose, for I have not yet conducted such an experiment. If not, pumps m could also function such that a mixture of oxygen and alcohol vapor is brought to explosion over the liquid oxygen, perhaps by an electric spark. An electric spark would also suffice to ignite a good mixture in n. But once combustion is underway there, certainly it all burns until there is nothing more to burn. This is confirmed by anyone who has ever dipped a smoldering wood chip into liquid air.

Oven O (cf. also Plate II) has no direct contact with the outer surface, but rather there is a thin wall t in front of it, which is connected to the outer surface by metal struts (not shown) and in this way kept in the correct position. Liquid that flows from the sprayer vaporizes between t and the wall and thus protects the oven wall from burning. The vapor escapes between the sprayer and the outer surface at L into the oven. Inside the oven it remains close to the walls, so with high vaporization the walls themselves are again isolated from hot gas. So that not too much liquid vaporizes and the wall t does not start burning from the top, a thermoelement is located at T1, which causes more liquid to flow if the temperature here gets too high. The space between t and the outer surface is wider at some places. Here the liquid flows down and here also is a float that inhibits the flow of liquid in case the liquid rises too high, thus preventing overflow of the liquid into the oven.—The space between the outer surface and and divided again surface t passes through a wall u, which is somewhat below into two parts, Q and R. When the fuel is exhausted, first the liquid in R, and then

t Fig. 26.

Fig. 28.

Fig. 27. L

A

K L‘

t b

K

J

Fig. 29.

* †

Fig. 30.

†

TransNB: The “l” appears like “e” in Fig. 25 because it its written as a script “l” TransNB: Fig. 30 is not mentioned in the original German text.

54

Part II. Description of Model B: Discussion of Technical Implementation

that in Q, is vaporized by hot gases from mn. Through this arrangement is much less than it would be if the oven and nozzle were lined with fireproof material, and that is (according to § 7.6), an important advantage. Also, it is possible to allow the gases to flow past metal, which retards them less than something like asbestos or fireclay. The nozzle of the A.R. is either simple and circular, as has been indicated on the plan, or is divided into seven or more parts (cf. Fig. 26), which originate at the common oven. The first is preferred for small apparatuses (such as Model B), the latter for larger ones (cf. Fig. 53). Fins w are only alluded to in the plan. There is a total of four systems of two fins each, which are joined to each other by transverse walls. They are fastened to the propulsion apparatus. The ends can be rotated around the axis X. During ascent the fins are folded down and thus achieve stabilization and also control, because they can be moved from I (see below). During descent they fold backward and thus support the apparatus (cf. Fig. 27). In this way a parachute is unnecessary. The fins, including accessories, weigh 4 kg. After being dropped off, the alcohol-water tank can be filled with air. First, with open valves, air must flow through so that the tank is dried and cleaned. During the subsequent filling, due care must be exercised. Air should first be streamed through the oxygen tank in a tube so that it is suitably cooled. Otherwise, an explosion could occur due to the compression heat with high hydrogen content. In this way the rocket is capable of bringing down air samples. The time for filling should correspond to a mark on the recording strip (cf. p. 55). It is also perhaps worth mentioning how I imagine finding the descended parts of the rocket. The launch site should be selected so that the auxiliary rocket and the A.R. fall into water and the H.R. into an inhabited area. In the outer wall there are circular hatches, the rims of which are seated in the outer wall, as shown in Fig. 28. Behind these is a vessel containing a balloon b (cf. Fig. 29) hanging from a rolled-up cord s. Because the vessel is under an internal pressure of 9 to 10 Atm, the balloon is fairly compressed, but when free it becomes 10 times as large. Now the hatches rotate at hinge A; on the opposite side they are soldered between L and L'. Moreover, they are sealed airtight. Behind the soldering there is an acid in space K, which is divided into chambers by cross walls. This acid eats the solder, whereby after a few g1 M H K hours the doors snap open, because the internal R pressure is so great, whereupon the balloon is freed. g3 From the landing site of the A.R. one can infer the R motion of the upper layers of air, and from that, the landing site of the H.R. g1 g2 M The following c o n t r o l d e v i c e s a n d p r e c i s i o n i n s t r u m e n t s are located in the A.R.: 1. An efficient and constant direct current g4 electrical p o w e r s o u r c e . 2. A g y r o s c o p e in the following mounting: the Fig. 31. gyroscope K turns in a horizontal evacuated casing H, which can rotate around axis . On rotation about

§ 9. The Alcohol Rocket

55

this axis an electrical current is generated; and are suspended in a ring, which itself can rotate around axis and generates an electrical signal when in an inclined position. These currents affect the position of the fins, at the same time recording how much the steering mechanism was used. M is an electric motor that spins the gyroscope. 3. A c c e l e r a t i o n i n d i c a t o r s are recommended, one for smaller and one for larger accelerations. They consist essentially of a weight on an elastic spring, recording contact pressure and therefore acceleration, and generating electrical currents proportional to the acceleration. From the acceleration one can draw conclusions about the velocity and from this velocity about the altitude if the acceleration is recorded on time-marked paper strips. The gravitational force changes with altitude. If one has a first approximation of the altitude, then from that you can correct1) the acceleration and subsequently more accurately determine velocity, altitude, and so forth. The acceleration indicators must function very accurately. Fortunately, they can be tested both before and after flight with high precision on a centrifuge. They hang down from a gyroscope on an appropriate vertical guide such as shown in Fig. 31* (but not from the gyroscope itself). 4. The f l o a t s , which record the alcohol and oxygen levels, also generate electrical currents that in part regulate the ratio between alcohol and oxygen and in part are used for the apparatus described under 8 (cf. p. 56). 5. Manometers are used to record the various internal pressures. One must be located under the nose cone. 6. It is also desirable to have aneroid barometers located at neutral places on the outer surface or on the fins, where they generate electrical currents corresponding to external pressure. They need not and cannot be especially accurate. The best mounting locations can be tested by using a model of the rocket shape in a centrifuge or, better still, in a steady stream of air. Should these barometers be too unreliable, they can be replaced by the following apparatus: a type of planimeter (it can also be an electric current z meter) determines the velocity from the data produced by the acceleration indicators, and a second one determines b the altitude. Its indicator consists of a roller z (cf. Fig. 32) r r r under which a sheet metal strip b is pulled on the rollers r. The lower edge of b is horizontal, the upper is cut so that, by advancing, a rheostat generates currents, which Fig. 32.

are proportional to = ∙ . It is not difficult to also record these currents, and it is good if we get a clear picture of the functioning of all devices. 7. The internal pressure that attempts to blow away the nose cone is, of course, greater than the resistance of the outer air L. Springs b are therefore under tension. This tension generates electrical currents and is recorded. If the currents of 5, 6, and 7 are added in a suitable way, they give an indication of the drag L. 1) *

namely, by taking into account the change in g. TransNB: This figure number is incorrect in the original book. It was listed as Fig. 7.

56

Part II. Description of Model B: Discussion of Technical Implementation

8. These currents and those corresponding to fuel levels act on electromagnets suitably mounted on the ends of a balance beam (naturally, the same polarities are located opposite to each other). By its position, this increases or decreases the functioning of pumps mn and thereby the acceleration. Because in the vicinity of Earth, weight is a linear function of the fuel level, and furthermore, because is maintained if L = G (cf. p. 16), this apparatus ensures that is maintained. 9. Several t h e r m o g r a p h s (preferably thermoelements are included in the A.R.); one is located in front of the nose to record the compression heat of the air. 10. The e j e c t i o n d e v i c e should also be mentioned here.

§ 10. The Hydrogen Rocket A. General : For the A.R., the acceleration is somewhat less at the end than it would be according to . As a result, the altitude at which the A.R. reaches its terminal velocity is somewhat higher than the altitude we calculated with Formula (10a). (I estimate the altitude as 3 to 6 km higher.) ─ Advantages: 1. for the A.R., becomes constant; and 2. for the H.R., the cross-sectional load can be smaller.— and ( ) depend on the actual value of c. For For equipping the A.R., c = 1400 m/sec, we find β1 = 8.82 kg/m2. This would correspond to an altitude of approximately 56.2 km above sea level. is 3 Atm. Fuel: 1.36 kg hydrogen, 1.94 kg oxygen; T0 = 1700º C. Nozzle Ratio: = (because ); x = 1.388. ⁄ = 10.95; ⁄ d = 25 cm; = 7.55 cm; = 3.31. Exhaust Velocity: We would find that c = 4400 m/sec. For the same reason as with the A.R., I underestimate c here: c = 3400 m/sec. Above, the hydrogen is at an overpressure of 0.12 Atm (initially, the H.R. would naturally be bent by the drag if it were not placed within the A.R.) During operation of the H.R., the ground pressure of the hydrogen during the first second amounts to 0.11 Atm, later slightly less. The hydrogen tank must therefore withstand an overpressure of 0.24 Atm. Its wall thickness would only need to be 0.0144 mm. Therefore 1 sqm would weigh 34.2 g. Weight of the hydrogen tank and the nose: 33 g. Oven and sprayer: length 1.05 m; internal pressure 3 Atm; weight 0.466 kg. Instruments: 1.5 kg. Pumps, oxygen ring and reinforcements: 0.5 kg. Nozzle and its outer surface: 0.3 kg. Fins: 0.3 kg. Parachute: 0.5 kg. m1 = 3.60 kg; m0 = 6.90 kg; fuel: 3.30 kg m0 m m = 1.915; log 0 = 0.2825; ln 0 = 0.650; m1 m1 m1 vx  3400  0.650  2210 m/sec

§ 10. The Hydrogen Rocket

57

Acceleration during the first second: 200 m/sec = 0.406 kg/sec 3400 m/sec Because the internal pressure and the exit pressure remain constant, this number also remains constant. 3.30 kg Burn duration: = 8.15 seconds. 0.406 kg/sec = 200 m/sec ;

∙

= 6.9 kg ∙

= 64.3 m/sec; ∙

∙

∙

= 7 m/sec;

= 5210

71.3 = 5139 m/sec

With this initial velocity, the rocket would reach an altitude of about 1960 km. Exit Pressure: = 0.0196 Atm, from which the nozzle ratio is computed, best from the formula: because = 3 Atm. (One finds =

Here: = ∙

;

=

∙

.

N o t e : A: is the total volume of the gas ejected during one second.

Description of the H.R. (cf. Plate I) The nose cone a is constructed similar to that of the A.R. It snaps apart during descent, whereby the parachute, which is located below the nose in space f, can deploy. Incidentally, the nose cone remains attached to the H.R. The interior of the nose cone is lined with porous linen material, behind which water flows down. This water is located at c and is injected through a tube by pump e into the nose cone, where it flows Fig. 33. down the walls. During descent, the parachute should not offer to the air crosswise surfaces, but instead length-wise surfaces with a slight tilt (cf. Fig. 33) so that they are not heated by the air stream, but still brake1) the fall quite well because of the relatively high viscosity of thin air (cf. Gaede’s molecular air pump) and the low empty weight of the H.R. Where the parachute offers a surface perpendicular to the air stream, it must be effectively cooled, possibly by having small pieces of ice between the layers of material of which it is made.

1)

Incidentally the parachute will brake only secondarily.

58

Part II. Description of Model B: Discussion of Technical Implementation

The letters on the plan Plate I correspond to those of the A.R. Here the oxygen is enclosed in a circular ring in which it is brought to vaporization, whereupon it flows through tubes E. It is under a pressure of 3.1 Atm. The hydrogen is brought to a pressure of about 5 Atm by pumps , and surrounds tubes E from outside. The empty space inside the oxygen ring, from which the oxygen tubes branch out, serves here as the expansion chamber.—As in the case of the alcohol tank, the hydrogen tank can also take air samples here, provided: 1. that there is air or some other gas (coronium?) there, and 2. that this gas can be stored in a container, which one can P1 dispute on the grounds of atomic theory. In S i S pumps are tubes that carry the hot , a a y gases (i) embedded in some kind of filter S, Fig. 34. which nearly reaches the top. Reason: the hot gases contain water which, on contact with the hydrogen, immediately precipitates. Because ice is heavier than liquid hydrogen, these ice crystals would sink to the bottom and plug the pores of the sprayer if they were not held back by the filter. Also for this reason the drainage for the pump space lies somewhat higher than the a‘ a‘ lowest point of , , so in this way is never empty and collects ice crystals that are in the hydrogen despite all precautions (cf. Fig. 34). Liquid hydrogen surrounds the oven and nozzle. Fins w are in the tangential plane of the wall. They can slide up and down Fig. 35. the wall and are held there by hinges a and a' (cf. Fig. 35). Because they are level with the stream of exhaust gas, they can 1. also steer effectively in thin air, 2. accommodate the H.R. better within the A.R., 3. be located in the space between the outer air and the exhaust gases where they least hinder the motion of the rocket. In their design, it is important to pay attention that the separation occurs while the A.R. is still working. Otherwise an upward pressure would result. On the plan, pumps mn are partially omitted because they would otherwise obscure the drawing. ____________ The precision instruments of the H.R.: 1. An e l e c t r i c b a t t e r y . 2. S t e e r i n g g y r o s c o p e as in the A.R., only correspondingly smaller and lighter. 3. Likewise, an a c c e l e r a t i o n i n d i c a t o r . 4. Devices to indicate f u e l l e v e l s . They only have significance here as recording devices because the H.R. gets velocity control only by: 5. M a n o m e t e r s . The instruments listed under 6 for the A.R. can be omitted here.

§ 11. Measurements with Model B

7. However, the pressure experienced detected and recorded by s p r i n g s b. The instrument listed under 8 for the velocity is not maintained. 9. Thermographs, etc. 10. On the H.R. is a similar mechanism A.R. However, it is not triggered here by during descent.

59

by the nose, as with the A.R., is A.R. is not included here because for releasing its nose cone as on the a float, but only by a chronometer

§ 11. Measurements with Model B The following measurements can be performed with Model B: From the acceleration and the time we can deduce the velocity and the altitude. Likewise, taking into account landing location, the velocity can be deduced from the delay and elapsed time. Observation of the rocket during ascent by telescope should also not be excluded. The descent of the H.R. happens relatively slowly at low altitude, so that we thereby can directly measure air pressure and temperature. On the other hand, we can also calculate air pressure from the drag of the air against the nose of the A.R., and we indeed obtain this from the recordings (cf. p. 55) of 7. By comparison of both values we obtain the drag coefficient. By extrapolation of γ for the H.R., we find from the drag that it experiences, the density of the upper layers of air (the air samples should be taken into account). In a thin atmosphere that contains much hydrogen, combustion can occur at the nose cone due to the heating and compression of the air. The air density could thereby appear to be nine times greater than it actually is. [As we have seen (p. 22), this, by the way, barely changes the performance of the rocket.] From the decrease in drag at altitude, we can deduce more accurately the specific weight of the air. From this and from the various air samples, conclusions as to air pressure and temperature are also possible. During descent, the thermometers measure correctly; the thermometer data are a check for the above results. The piston strokes of the pumps are counted during the sampling of air. From this and from the manometer, conclusions on the air pressure are again possible. Because all these items mutually support and complement one another, they can be subsequently determined quite well by way of indirect calculations. In the process, it seems to me to be an especially fortunate circumstance that we measure directly exactly those that particularly interest us in building rockets. Of course, liquid fuel levels, interior pressure, temperatures, etc., are also recorded during ascent. It appears to me to be especially advantageous that one can find the jet velocity c from the fuel consumption and acceleration, augmented by gravity and drag, and that further, from the interior pressure and the acceleration, one can construct what might be called an apparent ratio K' p between d , which for the building of rockets, is more important than the p0

60

Part II. Description of Model B: Discussion of Technical Implementation

pd . One can also obtain this, of course, if one compares the composition, p0 temperature and overpressure of the ejection gases with c, taking into account friction, etc. From the difference between the calculated and the actual landing site, one can determine the movement of the upper air layers, provided that steering control is accurate. This can be tested beforehand by placing a model with a carefully adjusted gyroscope subtly supported in a steady air flow (cf. Fig. 36). actual

§ 12. About the Technical Devices 1. P r e l i m i n a r y T e s t s : Before building Model B, above all things the functioning of the sprayer and the nozzles should be investigated experimentally. Initially some experiments on spraying of liquids through fine openings would have to be done. There are questions concerning the best internal pressure, amount of out-streaming liquid, ejection velocity, and droplet size of the f m d

S

d c

R

m

d b

R rocket model f coil spring for balancing the front part d thin steel rods S support that takes m recording apparatus the place of P

Fig. 36.

c d

Fig. 37.

vaporized liquid when it enters the rapidly moving gas stream. That could, for example, be measured by forcing the liquid through a small metal plate b perforated with fine openings against a narrow tape that is moving rapidly and pushed sideways, that is from c to d, past the metal plate, and then afterward counting the droplets on it. The other experiments could be done at lowest cost near water with an appropriate gradient. A further experiment might consist of capturing the gas, which is being ejected from a model of the oven, directly over streaming water (cf. Fig. 38), and examining it for the content of unburned materials. A similar experiment would be to measure the temperature in the oven in order to determine the degree of combustion. For this, the diameter of the sprayer tubes, the pressure and the temperature of the oven, etc., could be varied. Thereafter would come the tests with nozzle models. The test nozzles can be significantly smaller than the nozzle of Model B, because one can draw conclusions on Model B from the data

§ 12. About the Technical Devices

61

for various sizes. The experimental setup could be as follows (cf. Fig. 39): gas flows into the receptacle of a large water-air pump; water flows in at A and drops here through a O C sieve in fine streams into funnel B. At D there is an opening in A into which the nozzle model C is inserted so that it is sealed airtight but easily movable. Here, the exhaust gas is A A correspondingly cooled so that less would have to be taken D away. With the alcohol nozzle especially, we have the situation where the exhaust gas is almost completely absorbed Z by the cold water. During the b O first tests, the nozzles must be protected from heat transfer; we can later use walls with cooling. Z Zerstäuber O Ofen b Brause These tests would also be of value * because one could possibly use Fig. 38. the results to build very efficient aircraft turbines. However, they do not need to use large resources. We will obtain accurate data, after all, following the first ascent from the records of a rocket that is equipped with the instruments described under 1 to 8. We also measure the substances that are supplied to the firebox, in Fig. 39. addition to measuring , , 1) etc., so that we can also indirectly determine c. In this experiment we further learn: a) how much heat is transferred through the walls of the nozzle and oven into the liquid between the casing and the combustion chamber, and b) which nozzle shape and pressure ratios are the most favorable. Finally, we can also experiment with the regulator pin described on p. 27. In addition, there should be experiments to test out pumps p and mn, and finally testing all recording and control devices. 2. T h e A u x i l i a r y R o c k e t : In order to give the apparatus an initial velocity of 500 m/sec, there are only two means: a) one fires it from a cannon; b) one lets it attain this velocity under its own power. For a) one advantage of my apparatus is that the walls are thin and therefore is small (compared to previous rockets). However, if we want to shoot it from a cannon, the metal parts would have to be strong due to the extremely high Andruck, and we would lose said advantage. Therefore, it is good if it starts with lower acceleration, that is, with rocket propulsion. However, the acceleration should not be too low in this case, otherwise the apparatus would have to struggle too long against gravity. Also here, for rocket conditions, the initial acceleration at least must be large. The best / ratio while keeping close ratio during launch would compare with the best / to 2.6:1. Naturally, p would also fluctuate by the same amount, whereby according to 7 and 13 the fuels would not be used efficiently. One can remedy this: a) by nozzles with regulator pins (cf. p. 27), or b) by placing the A.R. on top of still Z

1) *

In addition to thrust P, perhaps by having the nozzle push upward against an elastic spring. TransNB: Key for Fig. 38: Z = sprayer; O = oven; b = spray.

62

Part II. Description of Model B: Discussion of Technical Implementation

another alcohol rocket with a wider nozzle and a higher thrust. The latter is preferable for Model B. I do not need to say much about this auxiliary rocket here. If the A.R. of Model B is feasible, then the auxiliary rocket is certainly feasible. Reference Fig. 40 for its design. It has a 1 m diameter, reaches up to about the pump area of the A.R. and has four slots for the fins of the A.R. The oxygen is located in tank a, which fits into the nozzle of the A.R. Its design is as simple as possible after the pattern of what was said in § 12.12. Completely filled, the auxiliary rocket weighs 220 kg and works for 8 seconds; the acceleration that it imparts to the A.R. is initially Fig. 40. 100 m/sec2, which later becomes somewhat less due to increasing drag. Perhaps also worth mentioning are bands of metal strips, which are placed around the outside of the alcohol tank of the A.R. and consist of four pieces held together by hooks b and are discarded together with the auxiliary rocket (Fig. 41). 3. I n t e r n a l P r e s s u r e i n t h e O v e n a n d C o m b u s t i o n : Liquid will probably be swept along out from the combustion chamber of Model B, thereby p reducing c. This drawback becomes smaller with increasing p, because a) d p0 increases according to formula (14), thereby the movement of gas is less for the , is same size firebox. The velocity, with which the gas streams through and , and becomes substantially (almost) independent of smaller with increasing . In the process, small liquid droplets vaporize better because they remain longer in the combustion b b chamber; b) they also vaporize better because dense gas releases b b they do not need to more heat than thin gas; c) because at high b b absorb as much heat in order to evaporate; d) the same amount of liquid carried along impairs the exhaust velocity c less at higher w w w because the difference between the specific internal pressures weight of the liquid and that of the gas decreases, i.e., the gas with a velocity , which is only dependent streams through on ∙ . Apparently, first a liquid droplet of a certain size hinders a stream of denser gas less than a stream of thin gas, and Fig. 41. second, it is thereby carried along more rapidly. If we could to the highest critical pressure of the mixture, then increase only the temperature and composition of the substance streaming through would be of interest to us, and the question of whether it is liquid or gaseous, would be irrelevant.

§ 12. About the Technical Devices

63

4. T h e S p r a y e r Z would be lighter if one could fill the alcohol-water mixture into hanging cone-like tubes (as with the oxygen in Model B). However, I do not believe the combustion would be as thorough in this way. 5. I m p o r t a n c e o f P u m p s , : The pressure should be high in the combustion chamber because of what was said in § 12.3 and § 7.13, but from § 7.8, low pressure should prevail in the fuel tanks. The importance of the pumps , lies in the fact that they reconcile these requirements. The importance of the pumps grows with the size of the apparatus: large apparatuses have in themselves the necessary cross-sectional load, hence we can build them to be wider. Thereby the internal pressure in the fuel tanks becomes lower, which is necessary from § 7.8, 9, to keep them rigid. For apparatuses with cross-sectional loading more than 1.1 kg/cm2, however, it is also important that is high, and all the more so the larger the cross-sectional load. For the hydrogen rockets the pumps lose their importance if the weight of the carried instruments is large in comparison to the weight of the fuel tanks. In the H.R. Model B, for example, I have drawn them only for the sake of principle; they increase the propulsion by not even 400 m/sec. If the weight of the instruments is relatively low, then the pumps are especially effective in hydrogen rockets. Incidentally, I consider the pressure chamber pumps , as a quite favorable technical solution for this problem. Piston pumps could never accomplish this task. p m 6. Another reason why 0 (or, if we prefer, 0 ) can be larger for large m1 pd rockets is the following: in rockets of this type we can divide the nozzles, indeed into 7 or 19 or more parts (cf. Fig. 26). Thereby the combined system of oven, nozzle and pumps is not higher than for small apparatuses. But here it is less m important, because its relationship to the fuel level is less. (It is for the ratio 0 m1 the same as if we would have succeeded in shortening the oven, nozzle, and pumps in Model B). In apparatuses of this type, of which more will be said in the third part, the H.R. is not placed inside the A.R., but instead sits on top of it (cf. Fig. 53). The upper wall of the A.R. therefore has extensions that fit into the nozzle of the H.R. Possibly during ascent a special nose cone can be placed over the H.R., which increases its strength in the lower air layers, and is then dropped off together with the A.R. In this case, chamber I would be better located above the H.R., directly below the parachute. The reason why it was located so low in Model B was primarily to prevent bending of the hydrogen tank due to the influence of acceleration. That reason disappears here. The role of the auxiliary rocket is taken over here by regulator pins. 7. We then come to giant rockets when an object of a certain greater weight is m to be carried aloft. 0 must indeed have a definite minimum value; now if is m1 large, then must necessarily also be large. Such a large rocket has, a) because of its high cross-sectional load, already at the beginning a very high most favorable velocity, which it perhaps cannot reach throughout its entire flight; b)

64

Part II. Description of Model B: Discussion of Technical Implementation

here the internal tank pressure is relatively low; and c) of the A.R. for = is here already close to one atmosphere, if not higher. But a), b), c) were, according to § 7.15, the main reasons for an elevated launching site; i.e., for this rocket it is not so important that the Fig. 42. launching site is high. It launches comfortably from the ocean surface. If the tanks are pressure filled with air, they can well withstand the pounding of the waves. Then the rocket lies flat on the water, sinking rearward a little deeper, thus making it easy to be taken into tow by a ship, which at the same time would also have to carry well-insulated containers for the liquid gases that Fig. 43 would only have to be used for fueling immediately before launch. When filled, the rocket would assume a vertical position in the water, so it is ready for launch. So that there is no ice attached to the H.R., it is surrounded with a shell of paper, which would not stick to it and be pulled apart at the moment of launch. 8. W h e n f i l l i n g the H.R. necessary caution must always be exercised. The hydrogen tank must first be brought to an internal overpressure, which is related to that to which it will be exposed later at the same ratio its current elasticity modulus relates to that at the temperature of liquid hydrogen. Then it must be cooled down by pumping in more and more freshly vaporized hydrogen. Only when it is approximately at the temperature of the liquid hydrogen may it be added. 9. S t a r t i n g U p M o d e l B : 15 seconds prior to launch, the small pump is set in motion; 5 seconds before launch the dynamo must be started. Lift-off occurs as soon as the oxygen-alcohol mixture in A and B has caught fire, which is achieved by ignition elements G. 10. Of course, the H.R. p u m p s mn do not operate with sodium, but with an electrical spark. 11. A l t i t u d e o f A s c e n t : 2  g1  h1 equals for = r + 70 km: 11,160 = r + 140 km: 11,106 m/sec. For altitudes between 70 and 140 km, m/sec; for one finds the parabolic velocity by interpolation. From the foregoing one can see that it is possible to reach this velocity. If, for example, the A.R. gives to the H.R. a performance of 3000 m/sec (however, a large alcohol rocket gives to the H.R. a performance of more than 4000 m/sec) and if c = 3400 m/sec for the H.R. (in reality, however, the exhaust velocity may amount to 4300 m/sec), then for the H.R.: ln

=

11,000 3000 = 2.542; 3400

= 12.72;

a value which can be exceeded by an additional division.* So my apparatuses could very probably attain cosmic velocity.

*

TransNB: staging.

§ 12. About the Technical Devices

65

12. S i m p l i f i c a t i o n s : Model B is more complex than it should be in order to meet the requirements posed on p. 48, 2nd paragraph and discussed in the previous chapter. I described such a complicated machine because I wanted to show what types of technical devices are conceivable in order to increase the performance of such an apparatus. This is in fact good for a better understanding of Part III. At an altitude of 300 km one can hardly still talk of Earth’s atmosphere; anyhow at 500 or 1000 km, nothing significantly different will be found than at 300 km. An undivided* alcohol rocket could already reach this altitude, especially when one considers that c is actually greater (undivided rockets fueled with methyl alcohol would moreover have a somewhat higher performance than the A.R. of Model B, whose performance is calculated for ethyl alcohol). We could also save having the auxiliary rocket and the regulator pins. If is maintained, then the curve showing / as a function of s for = 500, = 7000, c = 1700 is as follows:

m/m 2

P/m

0

40 30 20 10

s=

5

10

15

20

25

30 km

Fig. 44.

Now if I let the rocket start entirely under its own power, then it first must attain the most favorable velocity. In this case, initially the acceleration, and so also the thrust and thus p, must naturally be greater. If I later let the rocket remain at somewhat less than , the curve for P and thus is as follows: P/m

0

s

Fig. 45.

whereby the auxiliary rocket is in fact superfluous. (Of course the propulsion lasts for 18 seconds, that is 10 seconds longer than with the use of an auxiliary rocket, and the performance is less by about 76 m/sec and in addition, of course, by ). Furthermore, we could significantly simplify the oven if we would place less value on a high final velocity. We could place the oven directly next to the outer surface and simply cover this with asbestos, which we moisten prior to launch. A further simplification would be to line the nozzle with a material that could resist the flame for ¾ minute. If one wanted to use rigid instead of swiveling fins, then a parachute would be necessary, and the performance would be reduced by a further 100 to 200 m/sec. Nevertheless, an apparatus with all these simplifications would still reach an altitude of more than 250 km. Admittedly such an apparatus can give us no *

TransNB: single-stage.

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Part II. Description of Model B: Discussion of Technical Implementation

information about the movement of upper layers of air, for the time during which it has the tangential movement of the upper layers of air is relatively too short compared to the time during which it has the lateral movement of lower air layers. If we wanted to do without measuring the drag that the nose experiences (should the apparatus thus conduct purely meteorological investigations, Model B investigates simultaneously the resistance factor and the ejection of gases), then a further simplification would consist of holding constant using a manometer. However, would first have to be theoretically calculated as accurately as possible. We could also do without pumps , and the pressure vessel if we held the alcohol-water tank at the same pressure as there is between the sprayer tubes. For that, its walls would naturally have to be thick. We would also still have an advantage, namely, that the shape of the rocket could be slimmer. So with the same fuel consumption, the cross-sectional load could be greater, or at the same crosssectional load, fuel consumption would be less.—Also, if this simplification were carried out, then = 1200 m/sec and the rocket would reach (adding ) somewhere above 100 km altitude. Now it would need nothing more for its ascent than pumps mn; the sprayer Z; an alcohol tank with double floor h; a manometer, which regulates the flow of the heating gases; a safety valve; and an oxygen tank with the same accessories. Added to this would be a steering gyroscope, the previously somewhat moistened parachute, and the ejection mechanism. No cooling of the nose would be necessary in this case. The duration of ascent and descent for this apparatus would be not quite six minutes. It would move away at the most 10 km from the launch site, thus would be easy to find particularly as one would know approximately in which direction one would have to search. We could therefore also do without any locating aids. We could also obtain a comparatively simple vehicle, which would have the same performance (but with six times greater fuel usage) as Model B (but which, because it is larger, could be launched from a height of 2 to 3 km) by stacking three such simple rockets one atop the other; the lowest an alcohol-water rocket; in the middle, a rocket in which liquid methane gas serves as fuel and with water as coolant; and on top a hydrogen rocket. ____________ As essentially new, compared to previous rockets, I consider: 1. T h e u s e o f l i q u i d f u e l s in place of the explosive materials previously used. Advantages: a) The velocity can be regulated. m b) 0 is larger. m1 c) The exhaust velocity is increased (especially for the H.R.); first, because lighter gases are expelled, and second, because with suitable nozzles the propulsive force of the fuels is better utilized.

§ 12. About the Technical Devices

67

d) The operation is less dangerous. 2. T h e s t a g i n g o f r o c k e t s . Advantages: a) Less dead mass is carried, b) The individual rockets can be built differently according to their different purposes. 3. I consider as my invention: the velocity regulator; the ejection mechanism; the pumping chambers; vaporization by injection of fine liquid bubbles. Finally, formulas (3) through (11) appear to be new: the same for the study of natural phenomena from the standpoint of Andruck.

____________

Part III

Purpose and Prospects I have already discussed the purpose of Model B (p. 59 ff.). The apparatuses described on p. 63 ff. can now be built so powerful that they are able to carry a person aloft. However, one would first have to ascertain experimentally how much Andruck a human being can withstand without harm. Namely, if the velocity during the thrust period is much less than then every second that the propulsion takes to attain that is longer than necessary consumes almost 10 m/sec of so we want the acceleration to be as high as possible. Of course, this also increases the Andruck.—Now how much Andruck can a human being withstand?

§ 13. Physical Effects of Abnormal Andruck on Humans E x a m p l e s : I know of a case in which a fireman jumped from a height of 25 m, landing without injury in a prone position onto a rescue net that depressed to a depth of 1 m. The Andruck that he had to endure at impact was certainly more than 240 m/sec2. But this case was probably an exception. With a jump from a height of 8 m in an upright posture into a body of water, the Andruck increases to more than 40 m/sec2. The Andruck of this jump would probably never harm a healthy person. However, in headfirst dives from this height, blood rushes to the head and faintness, even apoplexy, has been observed, although here the braking distance is greater (outstretching of the arms, impact toward the rear). So a human can tolerate greater Andruck in a direction from the head to the feet than in the opposite direction—The human body tolerates the greatest Andruck in the transverse or sagittal direction. Because the tensile and compression stresses are lowest in this orientation for a given Andruck, nature gave it the greatest Andruck resistance in this direction. Nature might also just as well have saved material and perhaps allowed the connective tissue to be weaker in this direction. The latter probably did not occur for practical reasons. It happens so often that we slip sideways and fall such that we would not be able to survive if we were to suffer internal injuries every time, as would be caused by excessively high Andruck. And the Andruck is high in such cases because the braking distance is usually short.—Well-known is the headfirst dive backwards into water.

§ 13. Physical Effects of Abnormal Andruck on Humans

69

The diver is positioned with back to the water and falls backwards, while initially keeping his feet on the diving board. The result is a rotational movement, which should be exactly timed so that the diver enters the water head-first. If the feet leave the diving board too soon, the diver strikes the water flat on his back (cf. Fig. 46). If the board is 2 meters above the water, the skin has to withstand an Andruck of 200 m/sec2 (due to the hardness of the water surface*) and also turns bright red. The back muscles and kidneys are subjected to Andruck up to 160 m/sec2, the rest of the body up to 80 m/sec2, and head and legs up to 70 m/sec2. If the diver is careful and extends his arms far enough to the rear so that the lumbar region is spared impact with the water surface, then the kidneys will only be subjected to an Andruck of no more than 80 Fig. 46. m/sec2 and the diver will have no bodily harm other than a red back.—I once slipped while jumping into water from a height of 6 meters and fell on my side. I did not experience the least harm from the Andruck. So it seems that the human body can, in mechanical terms, tolerate an Andruck up to 60 m/sec2 in the head-to-foot direction, and 80 to 90 m/sec2 in the transverse direction. Now the question is whether this Andruck can be tolerated during a long period of time, i.e., at least 200 to 600 seconds. One could argue as follows: If I tie a cord to a dynamometer and give it a short, sharp tug so that the indicator shows 100 g, then I can say that the cord withstands a pull of 100 g continuously, and can certainly continuously withstand a pull of more than 80 g. If, however, in place of a wool or cotton cord I use a strand of pitch twisted at 25 to 30° C, then although it withstands an instantaneous strain of 100 g, it can no longer be said that it can continuously bear even 10 g. In fact, even the smallest continuous load, perhaps just even its own weight, will cause it to steadily become longer and thinner until it eventually breaks.—There are also intermediate stages. For example, if a tube made of strong paper is filled with pitch, we have a structure that will not break under low continuous tension and can intermittently withstand very high tension, provided it has time to regain its original shape. However, if the tension is continuous, resistance decreases significantly. Similarly, one could say that our body is likewise a system composed of plastic and rigid substances, and that some of our organs, (e.g., liver, kidneys, and spleen) have about the strength of pitch at 30° C. But this argument is not valid. The fluid substances of our bodies have nowhere near the viscosity of pitch at 25°. (Except perhaps the gelatin contained in the bones and fasciae, but it is precisely these structures that best withstand continuous tension and pressure; one can assure oneself thereof: 1. by putting a load on them; or 2. by testing suitably loaded bones and fasciae in a centrifuge.). The momentary strength of the above-mentioned pitch tube is due solely to the viscosity of the pitch. The fluid and pulpy components of our bodies could certainly not be *

TransNB: i.e., due to incompressibility of the water.

70

Part III. Purpose and Prospects

expected to resist deformation any more than would a sausage filling. Therefore, at least 19 20 of the strength of our bodies depends on materials that behave as the wool thread mentioned above. The following case was observed during the war: A pilot flew at a speed of about 216 km/hr that equals 60 m/sec, four times around in a spiral with a diameter of at most 140 m. He was therefore subjected to an Andruck of 51.5 m/sec2 for more than 29 seconds without suffering any injury. This example naturally supports my postulation that humans can withstand this Andruck for 200 to 400 seconds (though without Fig. 47. complete confirmation). The absence of Andruck can do us no physical harm. The mere fact that all important life processes are possible in either a standing or prone position proves that we are not dependent on Andruck coming from any particular direction (as are parts of certain geotropic plants).

§ 14. Psychological Effects of Abnormal Andruck Conditions Our organ for sensing Andruck is the vestibule of the inner ear.* There, floating in the center of the ear fluid and held in place by sensitive, elastic bristles, is a calcareous granule, which presses against some of the bristles whenever Andruck is exerted, thereby indicating its magnitude and direction (with respect to the head). This organ is complemented by the three semicircular canals of the inner ear, which indicate the spatial movement of the head, in addition to general body sensations, particularly those coming from the muscles, joints, senses of touch and pressure, also by our eyes, and by our judgment about our position, orientation, and movement. The interactions of these components, i.e., the connections of all these various impressions, are only based in a small part on conscious thought, individual learning, or Fig. 48. training. For the most part, it is based on inherited instincts, which explains the speed of response, reliability, and naturalness of this organ, as long as the movements are of an order of magnitude that we ourselves can produce by our own muscle power. And it also explains its striking failure with movements of other orders of magnitude. Two examples for that: Let us imagine a swing carousel. The diameter at the top is 8 m; the seats are suspended 2 m from the top. Even when it turns rapidly, such as going once around in 6.5 sec, the riders’ sense of balance is not in the least disturbed *

TransNB: i.e., the vestibular system.

§ 14. Psychological Effects of Abnormal Andruck Conditions

71

(provided they do not become dizzy—more on that later). At T = 6.5 sec* the seats swing outward by 1.15 m, so the radius of the circle of curvature is 5.15 m. The velocity is 5.1 m/sec, the centrifugal acceleration 5 m/sec2. The resulting Andruck amounts to 11 m/sec2 and is inclined 26.6º from the vertical. Despite this considerable inclination from the vertical, to which our bodies and the seats are also subjected, we can, with our eyes closed, hold a rod parallel to the surface of Earth; at least the average of various rod positions shows no systematic error. On the other hand, if a pilot (Fig. 49) flies at 190 km per hour on a curve of 520 m radius of curvature, the Andruck he experiences is composed of the same components and thus has the same direction and magnitude. But the pilot no longer has the feeling that the ground is fixed; rather, he has the impression that his perpendicular is inclined about 10º from the vertical and that the ground is 16º

A

A

Fig. 49.

Fig. 50.

Fig. 51.

higher and is turning around the axis of his path A. He does not feel dizzy so long as he does not think about his position.—The pilot, about whom I spoke on p. 70, had an impression similar to that in Fig. 51. He also was not dizzy, but did feel as if he were “curiously thin and heavy.” It seemed to him that his velocity was “actually not really so large,” a sign that time seemed to be passing slower than normal for him.—One can observe a similar though significantly smaller inclination tilt of telegraph poles when viewing them through the window of a fast-moving train. Because of the close connection of the various components, the psychological effects of the same Andruck vary in different situations. The Andruck due to circular motion is the least unpleasant. Horizontal acceleration is more unpleasant, and slight upward acceleration is even worse (e.g., elevators, bow of a ship in heavy seas). However, rapid upward acceleration is not unpleasant to the same degree. If an elevator descending at 1 m/sec brakes in a distance of 20 cm, then for 2 5 sec, a = 2.5 + g m/sec2; this would be much more unpleasant than if for 2 5 sec a = 25 + g m/sec2† (such as when jumping into water). (An analogy would be ticklishness. A gentle touch tickles more than a rough one.) It further seems to make a big difference whether we are already aware of being in motion, or at least prepared for the onset of Andruck. Further, it contributes a lot to the psychological effect on whether we feel we are in control of the acceleration, or * †

TransNB: T here means the time for the carousel to do one revolution. TransNB: The squared symbol was missing in the original German book.

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Part III. Purpose and Prospects

even better, whether we can convince ourselves that we want the movement in question. I think that a voluntary jump into water (especially if we jump in an erect position and bend the knees slightly, giving us the subconscious impression that we are jumping down onto something) has an entirely different effect psychologically than does an involuntary fall. Incidentally, it seems only those Andrucke* are apt to have such varying effects that result from forces of a magnitude similar to what we can normally generate under favorable conditions by mere muscular strength without artificial aids. On the other hand, strong, persistent, and uniform Andruck seems to have the same psychological effect regardless of its origin: one loses a sense of the location of the ground and displaces the vertical in the plumb direction (almost reached in Fig. 51). One loses track of one’s actual executed movement. Curves become underestimated and time seems to elapse more slowly (cf. also p. 74). The stronger and more persistent the Andruck, the more the pleasant or unpleasant side effects mentioned fade. Feelings of dizziness are basically quite different. There is only one thing common to all types: a mistrust of our vestibular system and our locomotive system, and a desire to hold onto something or to prostrate ourselves as low as possible. We become dizzy when our vestibular system does not work normally for some reason, that is: 1. When the ear fluid is in motion instead of at rest (such as when we rapidly, turn, swing, etc.) or when our inner ear is adversely affected by illness (e.g., Ménière's disease) and we have not yet become accustomed to the new condition (the way deaf-mutes can accustom themselves to the loss of their static organ); 2. If the extraordinarily complicated interaction of sensory impressions is disrupted because the relevant sections of the brain are not functioning normally (e.g., due to blood congestion, lack of blood, fever, or due to poisoning with something like alcohol or nicotine); or because certain obsessive ideas prevent the normal flow of associations (fear of heights, stage fright, agoraphobia, etc.); 3. When the individual components of our sensory system contradict one another, so that it appears insufficient. Fortunately, in this case, dizziness almost only occurs with intensive thinking about our situation. For example, pilots only become dizzy in curves if they think about how the ground is moving; 4. If we distrust our vestibular system or our capabilities, such as when we tell ourselves that we are not up to the task before us. (Hence the old rule: Do not reflect when roofing, mountain climbing, or flying!)—If our vestibular system functions normally, we can endure the most fantastic sensory illusions without dizziness (cf. Fig. 51). Uniform Andruck itself causes no dizziness. The underlying causes of s e a s i c k n e s s have not yet been explained. But it is definitely not caused by “a mild brain concussion” (in other words, by a mechanical injury due to abnormal Andruck), as is stated in some medical books, because, 1. we have seen that the brain can withstand much worse shocks than those resulting from heavy seas; 2. adults become seasick more readily than children (e.g., who would want to be rocked for hours in a cradle?!), but genuine brain concussions have been shown to occur at a lower Andruck in children than *

TransNB: Plural of Andruck.

§ 14. Psychological Effects of Abnormal Andruck Conditions

73

in adults; 3. seasickness quickly ceases once one has firm ground under their feet again, but a brain concussion, which led to just as threatening symptoms, can last for hours, days, or even months; 4. seasickness can be caused and sometimes temporarily cured by suggestion during hypnosis, but a brain concussion cannot. It appears that seasickness is due to irritation of the parasympathetic nervous system. Interestingly enough, there seems to be no way to make adults dizzy for longer than ½ hour without them becoming seasick afterward. It is all the same whether the dizziness is caused by rotation, swinging, blood congestion or lack of blood, brain concussion (hence the aforementioned fallacy), nicotine or something else; if the sensation of dizziness lasts long enough, then seasickness also follows. Conversely, seasickness can apparently occur without having been preceded by dizziness, (of course, once it occurs, nausea and vomiting are always associated with dizziness because the normal sequence of sensory associations is disrupted). In my rocket, abnormal Andruck will certainly not produce dizziness. But whether the observer will become seasick later is another question. I personally do not think so. I believe that seasickness is caused more by repeated up-and-down motion. No matter how abnormal, a constant Andruck, for example, when a ship goes over only a single huge wave during an entire voyage, seasickness would not occur. Certainly, the connection between our consciousness and our static organ (by which I mean, as already mentioned, the calcareous granules in the vestibule of the inner ear) is interrupted during sleep. If not, for example, it would not be possible for us to have other experiences in our dreams than only those when in a prone position. Normally, our judgment functions must first fall asleep and, only later, the sensory nerve ganglia. Otherwise, one experiences the familiar dream, shortly before the onset of sleep, that one is falling.* One can also evoke this impression by hypnosis or autosuggestion (the details of which I cannot elaborate here.) Once the static organ has been put to a deep enough sleep, the first fright no longer acts as a waking impulse, and one can afterward observe the psychological effects of the lack of Andruck. There are also alkaloids that dull the equilibrium organ, e.g., scopolamine from 0.002 (!) g upward, but unfortunately, even this small dose is dangerous. Incidentally, scopolamine alone is not enough to simulate a lack of Andruck; the general muscular and joint sensations must still be suppressed (possibly by alcohol), in addition to the skin sensitivity (by possibly putting oneself in water or by rubbing one’s skin at the points of support with anesthetizing substances [cocaine]).—The notorious witch salve of the Middle Ages also had, among others, the effect of numbing the feeling of Andruck.—Certain bromine compounds also affect the static organ in this sense, but interfere with the psychological side effects of the lack of Andruck.—Likewise the static organ can be irritated by electrical shocks; we believe we are falling toward the cathode. If one compares the sensations thus formed with those one has when jumping or falling down from a high place, then one gets an idea of the psychological effect of the absence of Andruck, which is certainly true initially. There remains considerable uncertainty about the later stages, because they cannot be verified by the jump. *

TransNB: This may be the source of the English expression “to fall asleep.”

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Part III. Purpose and Prospects

Absence of Andruck in the first one-fifth of a second produces fright. This fright is reduced: 1. the more often we have experienced a lack of Andruck; 2. the better we were prepared for its occurrence. If the feeling of Andruck is not suddenly extinguished, as when jumping or under hypnosis, but gradually, as in the application of poisons, then this fright fails to appear at all. The fright is followed by an odd pulling sensation in the vicinity of the esophagus, which—after about ½ minute—gradually disappears again. Likewise during the first second, the brain and sensory organs start to function with extraordinary intensity, the receptivity for sensory or tactile impressions increases, the brain functions amazingly fast, and thoughts and decisions are directed to concrete things, dispassionately and logically. Time seems to extend. The first two minutes seem as long as four hours, but one still has some feeling for how much time has actually elapsed. So that goes hand in hand with an unusual insensitivity to pain and feelings of displeasure, which extends beyond the state of the absence of Andruck, provided it does not last too long. This may also be the reason why a jump into water is experienced as a pleasure and not a torture. Actually, neither the bastinado that one receives when jumping feet first into water, nor the rush of blood to the head when headfirst, is a pleasure. One’s upward-downward orientation remains intact, although it may not necessarily be correct if the eyes are closed. The heart beats faster than normal. All these symptoms may be explained teleologically. In nature, Andruck is missing if we fall down from somewhere, and then everything depends on not feeling sorry for ourselves, making clear and precise observations, and grasping every opportunity to rescue ourselves. Later these phenomena diminish. The heart, evidently fatigued, beats slower than normal; the brain also functions slower; sensitivity to pinpricks, touch, and pinches increases, but not so much as normal. Only the strange freedom from feelings of displeasure seems to persist unabated as long as the feeling of Andruck is missing. Seasickness has never been observed, also not afterward. Incidentally, a need for sleep soon occurs; dreams are usually pleasant. All of these phenomena decrease significantly when the specific experiment is repeated. Every pilot, for example, will agree that the tight feeling in his chest and stomach during his first rapid dive was much greater than during later ones. It is on the whole the question of how many of the observed symptoms are actually the result of the absence of Andruck. They are indeed the kind that occurs in general with excitement about an unusual situation. The absence of Andruck, once it is no longer an unusual condition for us, possibly would have no psychological effect at all. If a deaf-mute, whose static organ has been destroyed, closes his eyes under water, he no longer knows where up or down is, and initially becomes fearful. If he repeats this test often enough (in the process taking advantage of an air hose in his mouth), then every trace of anxiety eventually disappears. By the way, one never observes the mentioned symptoms as clearly as they had to be described here, for the sake of brevity, because all the means mentioned have strong psychological side effects. It would be quite possible that the absence of Andruck has other, even quite unpleasant, effects. Nevertheless, in this case

§ 14. Psychological Effects of Abnormal Andruck Conditions

75

there would also be no obstacle to launching a human in a rocket, because first, the connection between Andruck sensitivity and consciousness can be interrupted, and second, because the psychological effects of abnormal Andruck conditions can probably be remedied by acclimatization. So the first flight need only go to an altitude of about 50 to 200 km (descent time 100 to 200 seconds). In doing this, if the absence of Andruck* is tolerated well, subsequent ascents can go higher. Otherwise, we would first try the aids mentioned. So much for low Andruck. Our robustness with respect to high Andruck would have to be determined experimentally even prior to the construction of the apparatus. For this we could use a large carousel (Fig. 52). An elongated metal arm B, B' rotates around an axle A and is supported by wheels C, which run in a channel D. At the end of B', a cabin F hangs from hinge E'. F does not touch the ground and is fitted with wheels in front and skids at the rear so that it quickly comes to a stop if B' breaks. At the end of B' a balancing weight F' is suspended at E. The entire apparatus should operate as smoothly as possible; at c should be elastic springs, which are not too strong (even better, air-filled chambers L) to absorb vibration. The oscillation period of this spring device should be at least one second. The test subject has his seat in F; from here also the speed of the cabin is regulated. Naturally the speed of the rotation is precisely recorded. Because F travels in F‘

E

B

A c

c

B‘

E‘ F

D D

B B L C D

D F‘

B

A

F

D

F

B‘

D D

D

Fig. 52.

trench G† and is surrounded all around by piled-up dirt, the experiment is not dangerous. Because of the slow start, the size of the circle of curvature (the radius of curvature should not be less than 60 m) and the smooth movement, the test subject will sense that the Andruck is exerted nearly vertically, and so we have a means to observe the psychological in addition to physiological effects of high Andruck. I should also mention here that the rocket that we are discussing does not even ascend exactly vertically (cf. I, § 7.20 γ). The aforementioned carousel could also be used directly for training. So much for the effects of abnormal Andruck. I have written at length about these effects because most readers probably have no clear picture of them. I also * †

TransNB: i.e., weightlessness. TransNB: The indicator G is missing from the figure in the original German book.

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Part III. Purpose and Prospects

had to show that no insurmountable difficulties result from the effects of unusual Andruck on our bodies. If a human being can withstand an Andruck of, for example, 40 m/sec², then the vertical acceleration could amount to b = (40 - g) ≈ 30 m/sec². If = 9000 m/sec, then the duration of propulsion is 300 sec. In the process, 300

 g  dt  2400 m/sec are lost due to Earth’s gravitational pull and an additional 0

200 m/sec are consumed by drag. If all the thrust is used for acceleration, then the ideal propulsion would have to be 11,600 m/sec. As we have seen, this can be achieved. N o t e : Our knowledge of the physiological and psychological effects of abnormal Andruck conditions is still quite incomplete. I would therefore be truly grateful for any communication in this area1). I merely wanted to prove here that also in this area preparatory work is conceivable.

§ 15. Dangers during Ascent The ascent is far less dangerous than one would first imagine. Let us consider Fig. 53 (cf. addendum). The pilot is located in chamber I, which has aluminum walls that are 1.5 to 2.5 cm thick, and during ascent the windows are covered on the outside with comparable aluminum plates. It seems to me quite out of the question that the cabin could burst. The parachute is located above the cabin. The nose cone can be discarded at any time, whereupon the parachute would open in the air. Only three dangers threaten the pilot during ascent: 1. Failure of the pumps, 2. Failure of the control device, 3. Explosion. Now the apparatus ascends, if possible, over a large body of water (if only because of the discarded A.R.). If the pumps described on p. 63 fail, then the apparatus falls into the water; because it floats, this does not matter.—As for 2: if a) a tail fin breaks, or b) a failure of the control mechanism occurs, then the pilot needs only to shut off the pumps, whereupon the apparatus falls.—As for 3: Four types of explosions can occur: a) an explosion in the combustion chamber or in the pump chamber of the A.R. can only occur at the beginning of the flight. The greater the thrust (P), the more there is to be feared. Because acceleration cannot increase above a certain maximum value, the decreasing mass soon causes P to decrease as well (initially P increases somewhat because of the increasing drag). Now consider Fig. 53. It is unlikely that in such an explosion metal parts would be hurtled in the direction of I. Only an explosion in the uppermost pump chamber could have this effect. But if this case should still occur, the (full) liquid tanks of the A.R. and the H.R. would act as buffers, as 1)

Naturally it would be even better if physiologists and psychologists would take up the subject matter.

§ 15. Dangers during Ascent

77

would the thick-walled pump chambers of the H.R. b) An explosion in the pumping chambers of the H.R. would in and of itself be less severe than in the previous case. The liquid tanks of the H.R. would totally suffice as a buffer. c) d) The explosion of a liquid tank due to overpressure is first of all unlikely, and second, it would hardly have serious consequences for the pilot; not in the case of the A.R., for there the H.R. protects the pilot, and not in the case of the H.R., because its overpressure is too low. Likewise, it would not be bad for the pilot if the H.R. were compressed because of headwind (which can only occur at the beginning). Now in any explosion, liquids would be released, which would probably ignite. But now, I is wrapped on one side by the initially moistened parachute, and on the other side, anyway, there has to be insulation against the extremely cold liquid hydrogen. As long as this does not burn inside the H.R., it protects I very effectively against the fire, but even if it does burn, then the nose along with I is blown off because of the weak walls of the H.R. But even if this* should not occur, then in this case (which is even only possible if liquid oxygen enters the hydrogen area) the hydrogen will be forced out of its container within 2 to 3 seconds and, because of its lower specific weight, will fall behind the moving rocket so that the pilot can emerge from this without detriment. So one sees that, within Earth’s atmosphere, no danger threatens the pilot other than that which could result from excessive Andruck. During the free flight of the rocket, stray meteorites† constitute a certain danger (zodiacal light‡). Fortunately, meteorites are rarer the larger they are. Meteorites large enough to penetrate a 2 cm thick aluminum plate are so infrequent (other than at the time of meteor showers) that in all probability a rocket could fly for more than 100 years before it encounters one. (This can be calculated from the number and luminosity of meteor showers, taking into account the surface area over which they were seen, their velocity, and the gravitational force of Earth.) Furthermore, small holes in the walls of cabin I need not necessarily cost the life of the pilot. The air in I must be renewed continually in any event (possibly by vaporization of liquid oxygen, cf. p. 80). One can easily build the air renewer so that it automatically keeps the air pressure in I at the same level and perhaps alerts the pilot when air is escaping. He can then close the hole by placing a rubber patch over it. The interior air pressure would press it against the hole, sealing it off. In case I comes down in the water, this rubber patch would later need to be somehow attached to the wall. Whether the descent is dangerous, naturally depends primarily on the descent location. Descent into water is perfectly safe. On land, almost everything depends on the parachute. The location of descent can be calculated and, as we shall see, can be influenced by the pilot.

*

TransNB: i.e., the blow away. TransNB: A common mistake. This should be “meteors” if inside atmosphere and “meteoroids” if outside. It only becomes a “meteorite” once it hits Earth’s surface. ‡ TransNB: Oberth seems to have mixed up meteors with zodiacal lights, which are not related to one another. †

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§ 16. Equipment of the Rocket I will say only the basics about the equipment for this rocket. The precision instruments correspond in general to those described on p. 54 ff. For 2: If the apparatus is to have an inclination to the east, then two gyroscopes must be provided, one in the horizontal and one in a vertical plane. Finally, a third gyroscope perpendicular to the other two is desirable in order to control them. For 3: In this case, all three directions of acceleration in space are recorded. The acceleration indicators are of course connected to the gyroscopes. We obtain the three velocity components from the three acceleration components, and from these we obtain the three space coordinates (relative to the Sun or center of Earth) by a kind of clock mechanism connected to planimeters. These planimeters are essentially conical wheels with a sliding axis and constant rotational speed (cf. also p. 55). Simpler yet, these parameters can be integrated from the acceleration data through an electrical current, provided this can be done accurately enough.— Now everywhere the rocket is located, there are certain gravitational accelerations that we must also take into account, if the apparatus is to indicate properly. It is thus necessary that an influence is exerted on the mentioned weights of the acceleration indicator that is proportional to the pertinent gravitational component. This can be achieved approximately by the following apparatus: Let us assume that we have in some way obtained the three space coordinates (x, y, z), referenced to the center of Earth so that we can form x2, y2, and z2. We can do this, for example, if we let sheet metal strips move under a roller in the right proportion to x, y, and z. The lower edge of these strips is straight (cf. Fig. 32), while the upper edge is curved in a certain way so that the movement of the roller represents a certain function of the travel component. Then we mechanically add these effects (x2 + y2 + z2 = h2) and let an equilateral hyperbola corresponding to the total effect run under a roller, that gives the effect  1  g  g 0  r 2   2  . This effect is then to be divided in the ratio of the three h  direction cosines, i.e., in the ratio x : y : z. For example, we can divide a current that is proportional to g (regulated by some kind of balance) into three branches 1 1 1 and switch in resistances proportional to , , that are simply activated by the x y z space components. Thus, the task is already solved, because the three currents can easily exert force effects on the three weights proportional to gx, gy, and gz. Naturally, numerous other solutions are also possible. Of course, this apparatus could only be used in the vicinity of Earth. The apparatus becomes considerably more complicated if changes in the gravity field due to the movement of Earth and remaining celestial bodies need to be added. From Einstein’s General Theory of Relativity and Riemann’s Curvatures Theory, one can conclude that in this case ten different function strips would be necessary.

§ 16. Equipment of the Rocket

L1 d1 G1

Q v L2

G2

d2

Q

Fig. 54.

79

N o t e : The expression “weight on an elastic spring” was actually more of a temporary assumption, an image, to make the description more easily understood. In reality, I would let something like the mass of a column of mercury act against the elasticity* of a closed volume of air. Glass tube G1, which should not be too wide, is sealed airtight inside glass tube G2 and extends completely to the bottom. The two volumes of air L1 and L2 are separated from each other by the mercury Q. The thinly drawn piece of G is amalgamated or gilded. If Andruck increases, then L1 increases and L2 decreases, whereby the wire d1 rises further out of the mercury, thus weakening an electrical current that passes through d1 and d2. v is a valve that pumps air into L2 or removes air if the apparatus does not indicate properly. The damping factor of the oscillation should be 2.1, or else the oscillation period should be very long. The influence of the gravitational components can be brought into account by adding adjustable resistors outside in the current flowing through d1 d2.

Naturally, such an apparatus is controlled in that the pilot can at any time observe the angular diameter of Earth and its position in relation to other celestial bodies and from that determine h and . This does not make the apparatus superfluous: first, because it will be a welcome control for the pilot. Deviations in indicator information will always be present because such a complicated apparatus will never function completely accurately, but these deviations would exhibit a certain trend. Second, the pilot has more time for observations. In any case, the rocket should be equipped so that it functions as automatically as possible. The apparatus described under 8 is not used here, because the most favorable velocity is not maintained. Here the velocity is regulated by a weight, which is suspended from an elastic spring and maintains the Andruck at the same level. If the pilot changes the suspension of this spring (using mercury tubes with the regulating resistances mentioned above), then the acceleration changes. 8a: In this case the hydrogen rocket of course would not have to simply burn out, but rather it can be turned off by the pilot and restarted later. I should also mention the following: if the observer completely shuts off the fuel flow to pumps p1,2 and mn, then free flight occurs and the rocket is not subjected to Andruck. Now, because both liquid oxygen and especially liquid hydrogen wet the walls of the tank, then these liquids collect on the walls and force the vapors to the center (cf. Fig. 12). The valves, which bring the liquid to the pumps, are located fairly close to the bottom (thus at the partition). But they would still be covered with liquid if they extended far into the interior. If these valves are opened, the internal pressure, in the absence of Andruck, also forces out the liquid, not gas. (It is different with the safety valves, but these are now not needed at the moment.) So the rocket can also actually be placed back into operation at any time during free flight in the ether space.† But the Andruck should not act in the direction from the nozzle mouth toward the nose; a rocket in which this is a risk must have special liquid valves for this case.

* †

TransNB: Oberth might mean “compressibility.” TransNB: See TransNB on p. 7 for explanation of ether space.

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It should be noted for No. 10: The nose a can also be discarded here, and the parachute can be opened up far from cabin I of the observer. Because I is connected to the H.R. only by electrical cables, I can also be reeled out to a distance, whereby the view in all directions of space is free (cf. Fig. f 55). Because Andruck is absent, one can easily give things any position in relation to one another. Thus, that a here a is held in the specified position a near I should indicate the following: I the solar constant at the distance of HR w Earth amounts to 2.3 cal/min·cm2* (average of all specified values since w 1900). According to the laws of heat w radiation, a small sphere with a uniform surface floating free in space Fig. 55. is thus hardly heated to more than 240º above absolute zero, because then equilibrium would occur between incoming and outgoing radiated heat. (The fact that the average temperature of Earth amounts to +15º is because it radiates heat.) I can now leave the cabin I bare on one side and paint the other side black. If I is cylindrical and I turn the black side toward the Sun, its temperature rises to 25° C. But at larger distances from the Sun the temperature would be too low. However, I could raise the temperature: a)† if I give I Fig. 56. the shape of a half cylinder (cf. Fig. 56), color the flat surface black and position it perpendicular to the rays of the Sun. However, I would be too heavy, so I chose the approach of concentrating the Sun’s heat on I using the hollow reflective interior of a. N o t e : By this device, with suitable position of I and a, the interior temperature would be kept at a tolerable level from the edge of the Sun’s atmosphere to the asteroid zone.

Prior to descent, I can be reeled back to the H.R. and fastened. The H.R. itself is likewise brighter on one side than on the other. If one turns it with its bright side toward the Sun, the hydrogen will not evaporate. To these apparatuses, which in principle are also available in Model B, some special ones will have to be added. Here I will only mention the air renewer apparatus. Located on the cabin I are two containers with liquid oxygen and nitrogen for the case when I is leaking. They are suitably positioned so that the Sun causes vaporization. But they can also be artificially heated if the air pressure in I drops. On short flights, the used air can be purified with potassium hydroxide. On longer flights it flows through a black tube on the shaded side, where all impurities precipitate out, with only gaseous oxygen and nitrogen remaining. These are then conducted from the tube back to the sunny side, where they are * †

TransNB: The original German incorrectly had a “g” in the units – “gcal/mm”. TransNB: “a)” is superfluous because there is no “b).”

§ 17. Outlook

81

heated and reintroduced into I. In order to clean the tube of precipitated impurities, it is periodically brought to the sunny side, disconnected from I, and opened, whereupon these substances again vaporize and flow out into empty space. Perhaps I should also mention the periscopes (Fig. 53, p. 90, P P), which permit observation of Earth during powered ascent, and finally the apparatuses that serve special purposes during the flight. The cabin I is a little more than 2 m long, with a diameter of 1.20 m. During ascent and descent, the pilot lies in a hammock, which is rolled up in the interim so that there is free room for movement.

§ 17. Outlook With the foregoing, it is well proven that, with the present state of science and technology, it is possible to construct vehicles that can attain cosmic velocity and that it is probably possible for humans to ride in these vehicles. However, I do not want to close this discourse without writing about whether there is any prospect that such apparatuses will ever really be built. I do not want to claim that this will happen within the next 10 years, but I would like to show the uses of these apparatuses and what they would cost, in order to come to a conclusion about whether they will ever be built. Model B, including preliminary tests, would come to 10,000 to 20,000 Marks peacetime currency.* Apart from making measurements as cited in § 11, this model would be of no use. However, the benefit of any scientific discovery cannot be judged in advance. It happens often enough that things that seemingly lie quite out of the way of daily life later achieve the highest practical importance. (I want to remind you here of electricity.) However, if one wishes to obtain money from the general public for some purpose, then one must either be in a position to secure for them a direct tangible benefit or one must at least be able to make the project very popular. With Model B, I can do neither of them adequately. But what of the larger vehicles, which could also carry humans to on high? With the apparatus just described, the following experiments and observations could be carried out first. These experiments can be facilitated by having the observer(s) leave the apparatus in a diving suit and, because there is no Andruck, they can reach any desired point. They merely need to be connected to the apparatus by a line that they could use to pull themselves back. Experiments: a) Experiments that are only possible in a large, airless space. b) During free flight, the apparatus is not exposed to Andruck. Therefore, many physical and physiological experiments can be performed that are impossible on Earth because of gravity.

*

TransNB: This is the German currency that was used after the end of the First World War. In 1924 this was replaced by the Reichsmark.

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c) In ether space,* telescopes of any size can be used, because the stars do not twinkle. Of benefit to us is also the black color of the sky, in addition to the absence of Andruck and air. A large, moderately shaded, concave mirror made of sheet metal would suffice as a lens. If this was extended on three steel bands to a position a few kilometers from the rocket, then we obtain a telescope that, for most purposes, is a hundred times superior to the best instruments on Earth. (Already with much smaller instruments, questions about whether the planets are inhabited, the question of the trajectories of the larger meteorites† that could endanger voyages to the planets, the most important questions of stellar astronomy, etc., are being answered.) d) Because the sky is completely dark, masking the solar disk suffices for observing the regions in proximity of the Sun at will. e) Certain investigations of radiant energy are not possible on Earth because the atmosphere absorbs shortwave light rays.—We also cannot generate certain wavelengths artificially, but in space they would be easy to extract from the light of blue and ultraviolet stars. Because their wavelengths are equivalent to the size of molecules and atoms, this could easily lead to interesting and far-reaching physical-chemical discoveries. f) We could determine how much radiant energy comes from different regions of the sky. If we protect a body from all large amounts of radiant energy (especially from the rays of the Sun) with shiny metal plates, behind which it is freely suspended, and if we, on the other hand, also ensure that it radiates its own heat out to the colder parts of space, then we could bring its temperature exceptionally close to absolute zero, many thousands of times closer, for example, than the temperature of solid helium. It is not inconceivable that there occur some completely new phenomena (e.g., in the behavior of electrons, etc.). At least it would be worth the effort to conduct this experiment. g) Finally, with an initial velocity of = 11 km/sec, such a rocket could travel around the Moon and investigate its unknown hemisphere.‡ However, I do not believe that the means will ever be found to build such machines just for the sake of these experiments. The construction of such an apparatus would come to over 1 million Marks in peacetime currency. With proper handling, it could fly up to 100 times, but for each flight with an observer, nearly 25,000 kg alcohol, 4000 kg hydrogen and the corresponding amount of oxygen would be required, and, together with the water, it would weigh about 300,000 kg. An apparatus for two observers would have to weigh at least 400,000 kg. If we let such large rockets circle Earth, they would provide a small moon there, so to speak. They would also no longer have to be configured for descent. Traffic between them and Earth could be maintained with smaller apparatuses so that these large rockets (we will call them observation stations) increasingly could be transformed for their intended purpose. If the absence of Andruck for a long duration stay produces ill effects, which I doubt, then two such rockets could be

*

TransNB: See footnote on p. 7 for the explanation of “ether space.” TransNB: See footnote on p. 77. ‡ TransNB: i.e., the far side of the Moon not seen from Earth. †

§ 17. Outlook

83

connected with a cable several kilometers long and rotated around each other.— The purpose of these observation stations would be as follows: 1. With their precise instruments, they could recognize details on Earth and send light signals to Earth with suitable mirrors. They would enable: telegraphic connections for places that are not reached either by cables or electrical waves.* Because they would already notice, in clear skies, a candle at night or the reflection from a pocket mirror by day if they knew where they should look for them, they could especially contribute much to the contact of expeditions with their home countries, of distant colonies with the motherland, to shipping, etc. In this way, because they could observe and photograph unexplored countries and unknown peoples (e.g., Tibet), they could also benefit geography and ethnology. Their strategic value for theaters of war with low average cloud cover is obvious; whether the country to which they belong is itself waging war, or whether war combatants pay a lot for their reports. For small, plane mirrors, and if the station is not too distant, the mirror signal would be observable only in a limited area. The station could detect icebergs and warn ships; either indirectly by reporting the iceberg to a marine observatory, which would then provide a telegraphic notification of its location, or directly, if its mirrors are powerful enough that ships can detect them through mostly foggy air. The Titanic disaster of 1912, for example, could have been prevented in this way. The stations could also contribute a lot to the rescue of castaways, to news services, etc. 2. This station would have some practical use, but the following would be even greater: One could spread out a circular, wire net (Fig. 57) by rotation about its center. In the gaps between the individual wires (shown here exaggerated in size), movable mirrors of light sheet metal could be mounted so that one can move them to any position with respect to the plane of the wire net by electric currents from the station. The entire mirror would gravitate around Earth in a plane perpendicular to the plane of Earth’s orbit and the net would be inclined to the rays of the Sun by 45°. Now by proper positioning of the individual facets, one could

Fig. 57.

*

TransNB: i.e., electromagnetic (radio) waves.

Fig. 58.

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Part III. Purpose and Prospects

concentrate, as needed, all the solar energy reflected by the mirror to single points on Earth, or spread over large stretches of land, or, when one has no more use for it, let it radiate back into space. If, for example, the mirror is 1000 km wide, then the solar image projected by each facet would be 10 km in diameter; if they were all congruent, then the energy would be concentrated on an area of 78 km2. Because the reflecting surface could be as large as desired, colossal effects could be achieved. For example, through such concentrated sunrays it could keep the route to Spitzbergen or to the northern Siberian ports free of ice. If, for example, the mirror only had a diameter of 100 km, it could make broad stretches of land in the north habitable by using diffused light to heat, and in our latitudes it could prevent the feared spring freezes (ice men*) in addition to night frosts in the spring and autumn, thereby saving the fruit and vegetable harvests of entire countries. It is especially significant that the mirror is not fixed over a single point on Earth and could therefore perform all these tasks simultaneously. As to the question of the material for this mirror we must realize that: 1. no oxygen is present in space, 2. it only heats up a little. It will stay even colder if we leave its rear surface rough or color it black. For the material I would propose sodium, which under the conditions in question has a specific weight of 1,† considerable tensile strength, and a silver sheen. It could be carried aloft in large pieces by individual rockets and, once outside the rocket, it could be rolled into sheets or extruded as wire or tape because it would still be at normal temperature. Joining the individual pieces could be performed by people in diving suits, likewise the polishing. If the reflective sheet has a thickness of 0.005 mm‡ and if the mass of the wires, etc., is as large as that of the sheets, then the whole thing would weigh 10 g per square meter, or 100 kg per hectare. With regular trips by rockets to the observation station, the cost of a rocket ascent that can carry up 2000 kg sodium, in addition to the usual load, would be 50,000 to 60,000 M gold standard. So each hectare of mirror comes to 3500 M in all. If we figure that 3 hectares of polar lands could be cultivated due to 1 hectare of mirror surface, then we see that a time could well come when this mirror, and with it the entire enterprise, would be profitable. A mirror 100 km in diameter in this way would come to be about 3 billion Marks, and its construction would require about 15 years if 100,000 kg of sodium were brought up each week. Now because such a mirror could, unfortunately, also have great strategic value (one could use it to explode munitions factories, generate tornadoes and thunderstorms, annihilate marching troops and their supplies, incinerate entire cities, and anyway cause maximum damage), it cannot even be ruled out that one of the civilized nations might begin the implementation of this invention in the foreseeable future, especially because even in peacetime a large part of the invested capital should bear interest. * TransNB: “Eismänner” (“ice men” in English) is a German expression for the last possible cold period with the danger of frost in the middle of May. † TransNB: The specific weight of sodium is 0.97 gm/cm3. ‡ TransNB: Although this incredibly small number seems like an error, it is the correct number when calculated from the data that Oberth provided. Although it is mathematically correct, it is not realistic.

§ 17. Outlook

85

3. I should like to mention one more thing here: The observation station could at the same time be a fueling station, because if the hydrogen and oxygen were protected from the Sun’s rays, they would keep there in a solid state for as long as desired. A rocket, which is refueled there and departs from the observation station, does not suffer air resistance, and only slight deceleration due to p gravitational force. Its acceleration and therefore d could be very small, p0 whereby, from I., § 4, (12) the propulsive force of the fuels is tremendously utilized. If the rocket never has to pass through an atmosphere or be subjected to Andruck, then its shape and strength could also be whatever we desire; b may be arbitrarily small (cf. also I., § 7.15 and 17) and furthermore we could make the m tanks of sodium sheet metal. In the process 0 becomes very large. Furthermore, m1 it does not require a high initial velocity to leave the gravitational field of Earth, because, first of all, Earth’s potential is already less at the observation station and, second, the propulsion of the rocket only has to make up for the difference between the required final velocity and the velocity of the observation station of about 6 km/sec. If, for example, we link a large sphere of sodium sheet metal, which was produced in place and filled with fuel, with a small, strongly built rocket that pushes the fuel sphere ahead of it and is continuously refueled from it, then this results in a very efficient apparatus easily capable of flying to another planetary body. There, the rocket descends to the surface of this planetary body while the fuel sphere orbits around this world and, after ascent, the rocket would reconnect to it so that the apparatus can voyage back again. Visits to foreign planetary bodies would certainly have great scientific value. However, I do not want to address this subject at this point.

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Addendum As this document was going to print, the work of an American scholar, Professor Robert H. Goddard of Clark College in Worcester, Massachusetts, became known to me. The work was published in Washington in 1919 by the renowned Smithsonian Institution under the title: “A Method of Reaching Extreme Altitudes” and it concerns rockets. Prof. Goddard was able to experiment with considerable resources, while I primarily had to attempt a theoretical treatment of the problem. For this reason, our works complement each other. Goddard worked with smokeless nitrocellulose powder. He first investigated the functioning of funnel-shaped nozzles with a divergence of less than 8º and found that this greatly improved the thermal efficiency. He was able to convert up to 64½% of the thermochemical energy into kinetic energy of the exhaust gases (Exp. 51), while so far, in the best common rockets, the efficiency barely exceeds 2%. Goddard further found that efficiency improves if the nozzle is made larger with a similar shape and the same ratio of the amount of powder to nozzle contents. This was naturally to be expected, because, in his experiments, the amount of powder increased by the 3rd power, while the wall surface, and therefore friction, increased only by the square of the linear quantity. After all, especially with the present state of aerodynamics, experimental confirmation of theoretical considerations is absolutely necessary.—The role of friction is surprisingly small, even in small nozzles. The throat of the smaller nozzle was about ½ cm wide; the thermal efficiency in the reported experiments was between 30 and 50%. In a larger apparatus, the nozzle throat was 1 cm wide; here the efficiency lay between 57 and 65%, proof that friction can surely only play a very minimal role here. (In my apparatus, the friction would likely be significantly higher, relatively speaking.) The nozzles that Goddard worked with were meticulously polished, and some were made of the finest steel, others of ordinary iron, but at any rate, of heavy materials. In my apparatuses, on the other hand, the nozzles are made of thin, sheet metal. This will certainly not happen without warping, and a thin layer of ice would accumulate on the nozzle wall of the hydrogen rocket, which would considerably increase the friction. But because the nozzles of my apparatuses are significantly wider, friction will not be greater. The high level of thermal efficiency is remarkable. (The best diesel engines, for example, convert barely 40% of the thermal into mechanical energy, and

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steam engines do not even return 21% of the supplied heat energy as work). Goddard explains the high thermal efficiency by 1. absence of friction, 2. low heat dissipation by conduction (because the explosion takes place very rapidly) and, 3. the high combustion temperature. Based on his sophisticated experiments, Goddard was able to draw conclusions about the exhaust velocity in airless space. He could confirm (as was to be expected according to theory) that the exhaust velocity increases with decreasing ambient air pressure and approaches a maximum value in airless space. Goddard conducted still further experiments on apparatus materials, the shape and length of the nozzle, and so on. He reported on experiments with four different types of powder. He found that the exhaust velocity increases with increasing combustion temperature (which is also natural when the gases have about the same molecular weight). He achieved the highest velocities with the smokeless powder “Infallible,” produced by the Hercules Powder Company (explosion heat 1238.5 cal/g; exhaust velocity up to 2.434 km/sec), and with Du Pont pistol powder No. 3 (972.5 cal/g and 2.290 km/sec). Goddard did not describe any particular apparatus. The principle he suggests is the following: The powder is packed in individual cartridges. The exhaust apparatus is relatively small and is automatically loaded and fired like a machine gun, but at a more rapid rate. The apparatus would basically serve the same purposes as my Model B. It is also (as I must frankly admit), without a doubt, more suitable than an oxygen apparatus. However, Goddard’s principle does not have the development opportunities, which I have discussed in the third part of my document. Goddard also considered the use of hydrogen and oxygen, as is shown in a note (19, p. 66). However, he did not follow up on this; he only noted that the operation of the apparatus would be significantly more difficult. Perhaps he chose the explosive powder rocket because of its ease of applicability. As for the theoretical part of Goddard’s work, his calculations and formulas are easier to understand than mine. But my work may, in general, bring more to this field. Goddard’s formulas and computations are naturally quite similar to mine. In a beautiful way, Goddard calculated the probability of a collision between a rocket and a meteorite.* I would also like to mention that Goddard thought of sending a rocket filled with flash powder to the Moon. On impact the flash powder would ignite, thus making the impact of the apparatus visible to a viewer. Of course, I cannot go into all the details of his paper here, but I can recommend it to all readers who are proficient in English, because the experiments were conducted meticulously, and the document is easy to understand and interestingly written. One will readily see that I proceeded independently of Goddard by comparing our publications with each other. Incidentally, I can prove through witnesses that *

TransNB: See note on p. 77. Goddard in his paper (Appendix G, p. 63) erroneously called them “meteors” instead of “meteroids.” Oberth mistranslated “meteors” to “meteorites” here.

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my work goes back to 1907. My first complete plan dates from 1909. It concerned an apparatus that would be capable of carrying several people aloft. The propelling apparatus was supplied with moistened gun cotton like a machine gun. The gas would stream out laterally at the top. The form of the nozzles was still quite imperfect. They looked like the water nozzles of Pelton turbines and, like those, also had regulator pins, which worked automatically to prevent excessive Andruck. The ordnance was stored in chambers with thin, moistened walls, which would be discarded when empty. The entire thing is reminiscent of Fig. 17 (p. 41). Despite its imperfections, an apparatus of this type would be capable of ascending. At that time, I already knew about the physical phenomena of Andruck, the formula (19) on p. 18, in addition to (1)–(5), and the relationships discussed in § 7) 1–3, 5–7, 17 and 18. In 1912, I drafted the first plan of an oxygen-hydrogen rocket. In 1918, I performed calculations on a small model in which the exhaust gases streamed out the bottom and the first stage was an alcohol rocket. I established formulas 6–11 in the summer of 1920 as I attempted to develop a complete rocket theory. I calculated the plan for Model B during the composition of this work in the winter of 1921/22 in order to demonstrate the implementation of my theory in practice, likewise quite independently of Goddard. Further details would probably be of no interest here.

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P: Periscopes m, n: Pumps for heating gases Red relates to the Hydrogen Rocket, black to the Alcohol Rocket.

Addendum

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92 Addendum

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v E

o2

p2

t

d

β

Addendum 93

94

Addendum

q

n m2

q

S

m1 l8

l1 A

m1

h

D c c G

k

D c A c h h G

D c

h

G

A D c k

G

L L

T2

E

E

E

E

T1 O T1

Sprayer Scale 8 : 10

Postscript Pp. 48/49: The container for the liquid oxygen should be constructed of copper sheet, the hydrogen rocket should mainly be constructed of lead. With respect to the fuel, it can be said, in general, that the temperature of the out-flowing gas can be considerably hotter than I initially assumed. So one could take the fuel ratio (cf. § 4) to be significantly more favorable than I stated. On p. 57: My comments concerning the parachute have been criticized the most. I would say to that: This is first of all not a core issue. One could also build apparatuses that reduce some of their speed while still outside Earth’s atmosphere through reaction m0 would have to be 20 to 40 times larger, i.e., if the force. Only then m1 apparatuses are to carry the same payload, they have to be 20 to 40 times as big and heavy before ascent. Here I now have a means of making the apparatuses lighter and cheaper. I called this thing a “parachute”* because I just could not think of a better word. But I said at the same time in the footnote on p. 58 that the braking function of this “parachute” is only secondary. In fact, the empty sheet metal hull of a small apparatus would already be slowed down sufficiently by simple air drag; and for a manned apparatus, the braking force of the parachute alone would not be sufficient for a successful landing anyway. It could reduce the descent speed of large rockets only to 80 m/sec at most, so, before landing, the remaining speed would have to be slowed by reaction force. (However, there is a difference between whether I slow the apparatus down 11 kg/sec by reaction force and hence have to make the apparatus 20 to 40 times larger and heavier, or slow it down only 80 m/sec using a parachute and thus use an apparatus 1.02 times as large and heavy, than if I had no reaction force at all for braking). The details given for the parachute on p. 58 are partially incorrect. It cannot offer any longitudinal surfaces to the airflow; on the contrary, this must be avoided where possible if the spacecraft is to enter Earth’s atmosphere with cosmic velocity, as they would absorb a large amount of heat due to friction with the air (as do meteorites) and thereby consume too much cooling water. Also airplane-like wings seem to me to be out of place for such a vehicle.

*

TransNB: In German “Fallschirm,” which literally means “fall screen.”

96

Postscript

The counter flow of air here has to be opposed by concave surfaces if possible. Best would be an approximately annular parachute, as drawn by Mr. Valier in his book, Der Vorstoß in den Weltenraum.* (The figure below shows a cross section of an apparatus with such a parachute in deployed state. The dashed lines are intended to illustrate the movement of the air.)

As aerodynamics teaches, the air in the hollow space of the nozzle and in the parachute moves very little and is, apart from initial heating by compression, also heated very little, and the main part of the initial kinetic energy of the apparatus is used for the formation of air vortices. If I make the parachute as airtight as possible and cool the inside with ice (water cannot exist at the prevailing low atmospheric pressure), then the resulting vapor can only escape through the hollow side. It thus forms, together with the low air movement in the hollow space, the best thermal insulation. The same applies to the nozzle if I let the vapors of the cooling substance flow out through the nozzle. So this way we need a minimum amount of cooling water or ice. It is, for example, almost impossible to ignite a model of my parachute from the concave side using a (turbulence free) gas burner. Of course a manned rocket should not hit Earth perpendicularly, because the braking distance would be too short. But because a manned rocket has a lateral movement anyway, especially if it is launched at an angle, which would be best, it approaches Earth on some curve of second order, which one can easily influence so that its near-Earth point falls in the upper layers of air. Even if the layer within which the parachute can work is assumed to be only 7 km thick (above that the air is too thin, and below that the strong deceleration endangers the safety of the travelers), and even if the rocket approaches Earth on a parabolic trajectory, the braking distance, or more precisely, the distance traveled in the assumed layer, is more than 800 km. *

TransNB: In English: The Advance into Space published in 1924 by Austrian-born Max Valier with the assistance of Oberth. It is a less technical version of the subject matter of Oberth’s book meant for the general populace.

Postscript

97

Proof: Polar equation of the parabola: =

1

cos

; cos

=

1

(ϱ: radius vector, φ: deviation, h: thickness of the applicable air layer for the braking trajectory, r: Earth radius, p: parabola parameter) = For ϱ = r we get cos For ϱ = r + h: cos

=

2

= 1; = 0.

1=

1

1=

2

1 7 1 6370 2 ∙ 1 0.0011

1 = 0.9978

= ± 3.8º Braking path: s  2    r  840 km.

On the entire path, however, we only need to accomplish enough to ensure that the parabolic velocity is transferred into an elliptical velocity. Then the rocket would pass through the same location in the atmosphere during its second close approach to Earth, thus extending the braking path because the ellipse would fit a circular trajectory even more closely, etc. But the near-Earth point would not be shifted much closer toward Earth. This would continue until the circular velocity is reached. Then the braking path would become infinite, so to speak, and the spaceship would descend in a sufficiently long spiral.—Moreover, we have the possibility of pulling the parachute cords up or down, thus orienting the parachute at an angle to the direction of flight and generating an upward or downward force, allowing us to maintain a suitable height for longer periods of time.

98

Postscript

P. 59 to 61: What was said about the preliminary tests is obsolete. As Dr. Hoefft,* Vienna, showed, fins are dispensable for hydrogen rockets of manned apparatuses. As a result of the low acceleration, they first begin to function in airless space, so lurching due to air resistance disappears. The control can be accomplished more purposefully if the regulation pins on the different sides are inserted to different degrees, rather than having fins on different sides press to different degrees on the exhaust stream.

___________

*

TransNB: Franz von Hoefft was an Austrian engineer who founded the first space-related society in western Europe, Gesellschaft für Höhen-forschung (Scientific Society for High Altitude Research), in 1926, shortly after this 2nd edition of Oberth’s book was published.