Racing Chassis and Suspension Design: PT-90 0768011205, 9780768011203

Table of contents :
Preface
About the Editor
Table of Contents
Chapter 1—Racing Tires
Understanding Race Tires (983028) • Chuck Hallum
How to Work Race Tires on NASCAR Ovals (2000-01-3571) • Chuck Hallum
Tire Model and Vehicle Handling (885009) • P. Ratti
The Magic of the Drag Tire (942484) • Chuck Hallum
An Efficient Method for Treating Race Tire Force-Moment Data (942536) • Hugo S. Radt, Jr.
Chapter 2—Suspension Design
Effects of Suspension Geometry and Stiffness Asymmetries n Wheel Loads During Steady Cornering for a Winston Cup Car (962531) • Kent A. Day and E. H. Law
The Effects of Local Spring Perch Flexibility on Suspension Geometry of a Winston Cup Race Car (983032) • Lonny L. Thompson, Gregory P. Herrick and E. Harry Law
The Effects of Chassis Flexibility on Roll Stiffness of a Winston Cup Race Car (983051) • Lonny L. Thompson, Pipasu H. Soni, Srikanth Raju and E. Harry Law
The Effect of Chassis Stiffness on Race Car Handling Balance (2000-01-3554) • Andrew Deakin, David Crolla, Juan Pablo Ramirez and Ray Hanley
Design of a Single Seater Racing Car Suspension System (983020) • Andrew Deakin, Andrew Shovlin, Peter Brooks and David Crolla
Design of a Winston Cup Chassis for Torsional Stiffness (983053) • Lonny L. Thompson, Srikanth Rajuand E. Harry Law
An Investigation into the Effects of Suspension Tuning on the Cornering of a Winston Cup Race Car (2000-01-3569) • Robert W Haubenreich and E. Harry Law
Modeling Steady-State Suspension Kinematics and Vehicle Dynamics of Road Racing Cars. Part II: Examples (942506) • Thomas C. Crahan
Modeling Steady-State Suspension Kinematics and Vehicle Dynamics of Road Racing Cars. Part 1: Theory & Methodology (942505) • Thomas C. Crahan
Suspension System Testing and Tuning with the Use of a Four-Post Rig (983023) • Danilo Cambiaghi, Marco Gadola and David Vetturi
Balanced Suspension (2000-01-3572) • Erik Zapletal
Objective Ride and Handling Goals for the 1997 Chevrolet Corvette (970091) • Joseph P. Ryan, Steven P. Fuja and Henry A. Schmid
Synthesis of Chassis Parameters for Ride and Handling on the 1997 Chevrolet Corvette (970097) • Steven P. Fuja, Henry A. Schmid and Joseph P. Ryan
Ride and Handling Development of the 1997 Chevrolet Corvette (970098) • Michael W Neal and Mary A. Dona
Chapter 3—Design: Aerodynamics and Use of FEA
Aerodynamic Design Considerations of a Formula 1 Racing Car (980399) • Ben Agathangelou and Mike Gascoyne
Applications of Finite Element Analysis in the Design of the Mazda RX-792P GTP Race Car (942526) • John Crawford and Lee Dykstra
Aerodynamics of Race Cars in Drafting and Passing Situations (710213) • G. F. Romberg, F. Chianese, Jr.and R. G. Lajoie
Aerodynamic Development of a Successful NASCAR Winston Cup Race Car (942521) • Terrance D. Laise and Kevin S. Bayless
The Effect of Deck Spoilers and Two-Car Interference on the Body Pressures of Race Cars (942520) • Louis T. Duncan
Aerodynamic Development of the Charger Daytona for Stock Car Competition (700036) • R. P. Marcell and G. F. Romberg
Use of Genetic Algorithms as an Innovative Tool for Race Car Design (2003-01-1327) • Francesco Castellani and Giordano Franceschini
High-Lift Wing Design for Race-Car Applications (951976) • Joseph Katz
The Aerodynamic Optimization of a SuccessfulI MSA GT Race Car (962518) • Dwight M. Woodbridge and R. Brian Miller

Citation preview

RACING CHASSIS AND SUSPENSION DESIGN

Other SAE books of interest:

Chassis Design - Principles and Analysis (Order No. R-206) Edited by William F. Milliken and Douglas L. Milliken

Hands-On Race Car Engineer (Order No. R-323) Edited by John H. Glimmerveen

Race Car Vehicle Dynamics (Order No. R-146) Edited by William F. Milliken and Douglas L. Milliken

Race Car Engineering & Mechanics (Order No. R-308) Edited by Paul Van Valkenburgh

To order these books, contact SAE Customer Service [email protected]; or visit our Web site at store.sae.org

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Racing Chassis and Suspension Design PT-90

Edited by Carroll Smith

Published by Society of Automotive Engineers, Inc. 400 Commonwealth Drive Warrendale, PA 15096-0001 U.S.A. Phone: (724) 776-4841 Fax: (724) 776-5760 www.sae.org June 2004

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. For permission and licensing requests contact: SAE Permissions 400 Commonwealth Drive Warrendale, PA 15096-0001-USA Email: [email protected] Fax: 724-772-4028 Tel: 724-772-4891

All SAE papers, standards, and selected books are abstracted and indexed in the Global Mobility Database.

For multiple print copies contact: SAE Customer Service Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-1615 Email: [email protected]

ISBN 0-7680-1120-5 Library of Congress Catalog Card Number: 2004103715 SAE/PT-90 Copyright © 2004 SAE International

Positions and opinions advanced in this publication are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions. Printed in USA

Preface By Carroll Smith

Little more than a decade ago, the only motor race that attracted measurable interest in the American engineering community was the Indianapolis SOD-almost anyone would at least recognize the name of the current Indy winner. Even Ford and Carroll Shelby's historic wins at the 24 hours of Le Mans in 1966 and 1977 were not recognized as the giant step forward in wheeled vehicle dynamics that they represented. There were valid reasons for this. While both Grand Prix and sports car racing in Europe were highly technical exercises in advanced engineering, heavily supported by the OEM manufacturers, racing was largely a shade tree endeavor in the United States. Until the mid-1970s, with the exception of the few individuals assigned by Ford, GM, and Chrysler to their stock car racing programs, there were few engineers and little engineering going on in American racing. Very few racing teams carried engineers on their payrolls, even as consultants. Stock cars were almost literally that-stock bodies on crude tube frames with almost stock suspensions. Indy and Indy car racing were dominated by English cars-Lotus, Lola, March, and Reynard. Yes, there were bright spots-Bob Riley did design A.J. Foyt's Indy-winning Coyote cars, and David Bruns did design the all-conquering ADF Formula Ford. But the only consistently successful Indy cars designed by U.S. engineers were Dan Gurney's Eagles designed by Roman Slobidiskj. (The early Eagles were designed by Englishmen Len Terry and Tony Southgate; Jim Hall's Indianapolis-winning car was designed by Englishman John Barnard, and Vel's/Parnelli Jones' home-built cars were designed by Barnard and Maurice Phillipe.) Even the Ford and Offenhauser engines that had dominated Indianapolis car racing were outmoded by Cosworth (badged as Ford), llmor (badged as Chevrolet), and later, Honda and Toyota. Things have gotten better. Successful IMSA GTP cars have been designed by Bob Riley, Trevor Harris of Nissan, and designers at Toyota. Bruns designed the outstanding series of Swift Formula Fords, Formula Atlantic, and Indy cars, but basically the design and construction of professional racing cars remains a non-U.S. endeavor. In the new millennium, due almost entirely to ever-increasing television coverage, the lunatic fringe industry in which I spent my working life has become a major spectator sport in the United States. The OEMs have learned that what wins on Sunday sells on Monday. The increasing complexity of the cars and the increased levels of competitiveness have translated into meaningful developments in open-wheeled and stock-bodied racing cars, while the quantum leap in sponsorship and the potential financial rewards of success have enabled racing teams to recruit talented young engineers. Today, there is not a successful team in CART (Championship Auto Racing Teams), the IRL (Indy Racing League), or NASCAR that does not employ at least a few engineers. At the same time, the (supposed) historic relationship between the OEMs and racing has changed. Few, if any, innovations pass from racing to the OEMs. The age of electronic controls has reversed the flow of technology. What we in racing consider to be sophisticated engine control units are actually "de-complicated" adaptations of OEM systems. We have borrowed simulation packages and the four-post shaker rig (and

v

added three more posts) to aid in sorting out our suspensions and adapting the setups to different courses. Even our onboard data-gathering and telemetry systems are developments of hard and soft from the OEM proving grounds. While the domination of open-wheeled race car chassis and engines continues to be non-United States, the development processes-at least with regard to chassis, suspension, and aerodynamics-are largely United States-based. The most popular and fastest-growing segment of the sport-stock car racing-is entirely American and heavily supported by the Big Three OEMs. A generation of young engineers, within both the OEMs and the race teams, has been educated in advanced vehicle dynamics at high force levels. These young people have largely come from the annual SAE student design competitions-an accomplishment of which we can all be proud. The design of racing chassis, car suspension systems, and aerodynamics is a highly technical discipline with very little codified technical history or information. Regrettable as this may be, the reasons are simple: •

Racing car designers and development engineers (seldom the same people) have always worked to stringent time pressures and deadlines. The bottom line is, "The race starts on Sunday at 1:00 p.m. If you're there, fine. If you're not there, the race starts on Sunday at 1:00 p.m." The engineers do not have time to write.

•

Even if they did have time, they would not typically be inclined to do so, at least until they retired. The laws of physics governing the behavior of wheeled vehicles are immutable. While there are no real "tricks" in the design of racing cars, applications of those laws are closely guarded. Wandering around the pits of a Formula One race with a camera is a good way to achieve instant unpopularity.

•

If and when a professional racing car designer decides to write something technical, it is unlikely to appear in the form of an SAE paper. When one has spent a lifetime gathering knowledge, one sells it to the highest bidder-a magazine publishing house. The designers have no need of the prestige accorded to the authors of SAE papers.

There are few exceptions to this rule, and we, the readers, have reason to be grateful to Lee Dyksa, Mike Gascoyne, B.P. O'Rourke, and Peter Wright, whose papers are included in this collection. This leaves the OEM engineers who are assigned to racing programs, and the academics. There is a world of knowledge and experience in the OEMs, but it is mainly concerned with engines and drivetrains. In fact, there is a wealth of published information on racing engines, most of it contained in PT-53, Design of Racing and HighPerformance Engines, and PT-1 00, Design of Racing and High-Performance Engines1998-2003, both published by SAE. However, the chassis and suspension design of pure racing cars has been "farmed out" to independent specialist designers or firms since the early 1970s. The well-known law of "publish or perish" ensures that there is no shortage of SAE papers dealing with the chassis and particularly the suspension of the racing cars,

vi

written by academics. Unfortunately, few of them have "been there and done that," and I found that most of what I read (in my opinion-and I am the editor) is of dubious practical value. There are exceptions, of course, and some of them are included in this book. The students who design, build, and develop the Formula SAE racing cars are less reticent about their designs-and perhaps more eager for the peer recognition that comes with publishing. It is easy to say that these are not "real racing cars," whatever that means. (My personal definition of a racing car is anything into which you bolt a racing driver.) I submit that, even though speeds are deliberately limited to 6Q-70 mph by course design, with power-to-weight ratios in the 9:1 range and very sophisticated suspension systems, these are indeed real racing cars, and much of what these young people have to say deserves to be studied. In my decade as the head design judge of the Formula SAE competitions, I have learned more from the kids than they have learned from me. Fortunately, there are seminal books on the technology of motor racing and the design of racing cars. Everyone interested in the design of racing cars should start by reading (in alphabetical order by author): • • • • • • •

Racing and Sports Car Chassis Design, by Michael Costin and David Phipps New Directions in Race Car Aerodynamics, by Joseph Katz Race Car Vehicle Dynamics, by William F. Milliken and Douglas L. Milliken Time to Win and Drive to Win, by Carroll Smith Competition Car Suspension, by Alan Staniforth Race Car Engineering and Mechanics, by Paul Van Valkenburgh Formula I Technology, by Peter Wright

Most are available from the SAE Bookstore (www.sae.org/bookstore). This book, Racing Chassis and Suspension Design, is broken into three chapters: Chapter 1-Racing Tires Chapter 2-Suspension Design Chapter 3-Design: Aerodynamics and Use of FEA Chapter 1 deals with tires, which connect the racing car to the track surface by only the footprints of its four tires. Through these tenuous surfaces are transmitted all of the accelerations and thrusts that propel the car, decelerate it, and change its direction. The driver's control inputs are also transmitted through the tires to the surface. Through the tires, the driver receives most of the sensory information, which allows the driver to maintain or regain control of the race car at high force levels. Therefore, any discussion of vehicle dynamics must begin with a basic understanding of the dynamics of the pneumatic tire, especially the racing tire. Unfortunately, this information is hard to come by, partially because the subject is imperfectly understood and partially because the tire companies guard their information closely. Most of the information that is available in print is concerned with only the linear area of the tire performance, which is of little interest to the racer.

vii

Chapter 2 on suspension design is an introduction to a complex and fascinating subject. There is a body of thought that holds that the suspension of a modern racing car is relatively unimportant due to the predominance of aerodynamic generated grip. This theory ignores two simple facts: 1.

The speed at the apex of the average racing corner is less than 80 mph, a speed where aerodynamic download is secondary to mechanical grip.

2.

The grip generated by aerodynamic download is additive to mechanical grip. The basis of cornering power and vehicle balance is a linear car with good mechanical grip. Good mechanical grip is generated by, among other things, good suspension kinematics.

While most racing car designers agree on the aims and parameters of suspension design, there is considerable difference of opinion when it comes to details. One can start an argument in any design studio about the importance of roll center envelopes, mass centroid axes, anti-dive, or anti-squat geometry; it is all a matter of weighting the necessary compromises. Eric Broadley, the founding father of Lola Cars, once told me, "Because we are all afraid to expose our ignorance," many successful designers do not write about the subject. Chapter 3 deals with the design of the racing chassis and how aerodynamics affects it. There are three key areas of racing car performance: tires, engines, and aerodynamics. The racing team and the designer have little or no control over the engine or the tires, so they must concentrate their resources on aerodynamics to gain a competitive advantage. I suggest that there are two additional categories over which the designers do have control: suspension kinematics, and driver education. A number of aerodynamic considerations and compromises are involved in the design of a modern open-wheel racing car. A front wing is of critical importance in the design because it has influence over the aerodynamic performance of the underbody and its interaction with the tire wake. The increasing use of computational fluid dynamics (CFD) also brings in the challenges of correlating wind-tunnel data and CFD with on-track performance.

Editorial note: Carroll Smith passed away before he could complete this, his last SAE book. The SAE Publishing Technology Editor put the finishing touches on the book so that it could be published in honor of the service Carroll Smith made to SAE. The following page is an obituary to a great author and racing devotee.

viii

Carroll Smith

1932-2003 Carroll Smith was born on April 3, 1932, and spent his childhood in Oswego, New York. After graduating from the University of Rochester, where he had the good fortune to meet his future wife Jane, he earned his wings and distinguished himself as a pilot in the U.S. Navy. The best laid plans were cast aside when the racing bug bit, and Carroll spent the next seven years driving Formula and sports cars throughout Europe, with considerable talent and success. Following the birth of his daughter Dana, responsibility overcame valor, and Carroll returned to the United States, where he helped change racing history as team manager of Carroll Shelby's Le Mans conquering GT-40 effort. Carroll continued his run of engineering success, assisting champions in series including Formula 5000, Trans-Am, Formula Atlantic, The Tasman Series, Australian Touring Cars, Formula Super-Vee, Formula 2, IMSA, and SCORE off-road racing. Drivers to benefit from his engineering included Mario Andretti, Chris Amon, Denny Hulme, Dan Gurney, A.J. Foyt, Jackie lckx, Steve Millen, Alan Moffat, Danny Ongais, Sam Posey, Bobby Rahal, Peter Revson, and his own son Christopher, the 1992 Toyota Atlantic Champion. Perhaps Carroll's greatest talents and certainly his most enduring contributions were those of an author with a remarkable library of books, beginning with Prepare to Win in 1975, a treatise on the proper preparation of racing cars. Tune to Win, which describes vehicle dynamics and chassis setup, followed in 1978. Engineer to Win, 1984, was more scientific, and Nuts, Bolts, and Fasteners (Screw to Win), 1990, is the definitive book on racing hardware. Drive to Win appeared in 1990 and examined the interaction of driver, engineer, and team. Engineer in Your Pocket, 1998, is a composite of race car handling cause and effect. Each is remarkable for the content as well as the distinctively readable, intelligent, and entertaining writing style that characterizes the warmth and passion that Carroll brought to his everyday life. In the closing years of his life, Carroll spent much of his time, enthusiasm, and energy involving himself with the Formula SAE competition, overseeing and mentoring the efforts of young and aspiring engineers worldwide as they prepared themselves for their own place in the history of the sport that he loved so dearly. Today, the SAE Mentor's Cup bears both his name and his spirit. Carroll Smith died peacefully at his ranch in Northern California on May 16, 2003, following a brief illness. Without a doubt, his legacy and essence will continue through his many friendships and the lives he touched throughout his 71 years.

Christopher Smith January 2004

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TABLE OF CONTENTS

Preface .••••...••••...•••....•••....•••....••••....•••...••••....•••...••••....•••....••••...••••....•••....•••....•••....••••. v About the Editor .••••...••••....•••....••••....••....••••....•••...••••....•••....•••....••••...••••....•••...••••....•• ix

Chapter 1 -Racing Tires Understanding Race Tires (983028) ..•••....••••....•••....•••....•••....•••....••••...••••....••••..••••....••• 3 Chuck Hallum

How to Work Race Tires on NASCAR Ovals (2000-01-3571) ....................................... 15 Chuck Hallum

Tire Model and Vehicle Handling (885009) •••....••••...•••...•••....••••...••••...••••....••••....••....••• 27 P. Ratti

The Magic of the Drag Tire (942484) ..•••....••••....•••....•••....•••....•••....••••...••••....••••...•••....• 37 Chuck Hallum

An Efficient Method for Treating Race Tire Force-Moment Data (942536) ..••••...••••...••••...••••...••••....•••...•••••....••••...•••....••••...••••...••• 45 Hugo S. Radt, Jr.

Chapter 2 - Suspension Design Effects of Suspension Geometry and Stiffness Asymmetries n Wheel Loads During Steady Cornering for a Winston Cup Car (962531) •....•••....•••....••••....•••...••••....•••....•••....•••....••• 59 Kent A. Day and E. H. Law

The Effects of Local Spring Perch Flexibility on Suspension Geometry of a Winston Cup Race Car (983032) •••...••••....••....••••....•••...••••....•••...••••....•••...•••••....••••...•••....••••...••••...••• 77 Lonny L. Thompson, Gregory P. Herrick and E. Harry Law

The Effects of Chassis Flexibility on Roll Stiffness of a Winston Cup Race Car (983051) •••....••••...•••....••••...••••...••••...••••....•••....••••...••••...••• 93 Lonny L. Thompson, Pipasu H. Soni, Srikanth Raju and E. Harry Law

The Effect of Chassis Stiffness on Race Car Handling Balance (2000-01-3554) •...••••....••••..••••....••••..••••....••••...••••...••••....•••...••••....• 107 Andrew Deakin, David Crolla, Juan Pablo Ramirez and Ray Hanley

Design of a Single Seater Racing Car Suspension System (983020) ....••••...••••..••••...••••...••••....•••...•••••....••••...•••....••••...••••...• 115 Andrew Deakin, Andrew Shovlin, Peter Brooks and David Crolla

Design of a Winston Cup Chassis for Torsional Stiffness (983053) •••...••••....•••..••••....•••...••••....••••...••••...••••...••••....•••...••••....• 121 Lonny L. Thompson, Srikanth Raju and E. Harry Law

An Investigation into the Effects of Suspension Tuning on the Cornering of a Winston Cup Race Car (2000-01-3569) ....••••...••••..•••....••••....•••....••••...••••...••••...••••...••••....•••...••••....• 135 Robert W Haubenreich and E. Harry Law

Modeling Steady-State Suspension Kinematics and Vehicle Dynamics of Road Racing Cars. Part II: Examples (942506) ••....••••....•••..•••....••••....•••....•••....••••...•••....••••...•••....••••....•••....••••...• 147 Thomas C. Crahan

Modeling Steady-State Suspension Kinematics and Vehicle Dynamics of Road Racing Cars. Part 1: Theory & Methodology (942505) •••...••••....••••.••••...••••....•••....••••....•••...••••....•••...••••....• 169 Thomas C. Crahan

Suspension System Testing and Tuning with the Use of a Four-Post Rig (983023) •••....••••...•••....••••...••••...••••...••••...••••....•••...••••....• 203 Danilo Cambiaghi, Marco Gadola and David Vetturi

Balanced Suspension (2000-01-3572) •....•••....••••..••••....••••...••••...••••...••••....•••...••••....• 207 Erik Zap/eta/

Objective Ride and Handling Goals for the 1997 Chevrolet Corvette (970091) •....•••....••••..••••....••••...••••...••••...••••....•••...••••....• 219 Joseph P. Ryan, Steven P. Fuja and Henry A. Schmid

Synthesis of Chassis Parameters for Ride and Handling on the 1997 Chevrolet Corvette (970097) ..•••....••••...••••....•••....••••....••••..••••....••••...•••... 231 Steven P. Fuja, Henry A. Schmid and Joseph P. Ryan Ride and Handling Development of the 1997 Chevrolet Corvette (970098) •••...••••....•••..••••....•••...••••....••••...••••...••••...••••....•••...••••....• 241 Michael W Neal and Mary A. Dona

Chapter 3- Design: Aerodynamics and Use of FEA Aerodynamic Design Considerations of a Formula 1 Racing Car (980399) .••••....••••...••••....•••....•••....•••....••••..••••....••••...••••....•••... 253 Ben Agathangelou and Mike Gascoyne

Applications of Finite Element Analysis in the Design of the Mazda RX-792P GTP Race Car (942526) •....••••...••••...••••...••••...••••....•••...••••....• 259 John Crawford and Lee Dykstra

Aerodynamics of Race Cars in Drafting and Passing Situations (71 0213) •••...••••....•••..••••....•••...••••....••••...••••...••••...••••....•••...••••....• 267 G. F. Romberg, F. Chianese, Jr. and R. G. Lajoie

Aerodynamic Development of a Successful NASCAR Winston Cup Race Car (942521 ) •••....••••...•••....•••....••••...•••....••••...•••....••••....•••....••••...• 275 Terrance D. Laise and Kevin S. Bayless

The Effect of Deck Spoilers and Two-Car Interference on the Body Pressures of Race Cars (942520) •••....••••...••••.•••••....••••...•••....••••...••••...• 285 Louis T. Duncan

Aerodynamic Development of the Charger Daytona for Stock Car Competition (700036) ..•••....••••....•••....•••....•••....•••....•••....••••....•••...••••... 301 R. P. Marcell and G. F. Romberg

Use of Genetic Algorithms as an Innovative Tool for Race Car Design (2003-01-1327) •...••••....••••..••••....••••..••••....••••...••••...••••....•••...••••....• 313 Francesco Castellani and Giordano Franceschini

High-Lift Wing Design for Race-Car Applications (951976) ...••••....••••..••••....••••...•••... 319 Joseph Katz

The Aerodynamic Optimization of a Successful IMSA GT Race Car (962518) •••...••••....•••..••••....•••...••••....••••...••••...••••...••••....•••...••••....• 327 Dwight M. Woodbridge and R. Brian Miller

CHAPTER 1 RACING TIRES

983028

Understanding Race Tires Chuck Hallum Hallum Racing Enterprises Copyright© 1998 Society of Automotive Engineers, Inc.

ABSTRACT

APPROACH

A simple tire tread model predicts numerous tire performance characteristics. The macro behavior of the rubber gripping the road under vertical load and horizontal force is hypothesized and used to model heat generation in the contact patch. Contact patch heating explains trends of tire performance with slip, pressure, load, camber, tread thickness, and several rubber characteristics. A pressure supported radial wound toroid tire body model is used to evaluate tire deflection, spring rate, and tread momentum loss variation with speed and load. Tire deflection and momentum loss changes with speed together with slip losses can be used to optimize high speed tire performance. New insight to the true effects of camber, tread heating, tread momentum, and surface rubber sliding is presented that is not covered by other works. The new hypothesis of sliding in the contact patch, slip and re-grip, may lead to new understanding of other tire phenomena.

Specific macro model schematics of the contact patch are presented for various operating conditions of a racing tire .. Summary charts of data for sets of model conditions then show tire performance trends. Variables included are load, pressure, slip (lateral, longitudinal, and combined), camber, and speed. The HRE model only considers tread deformation. The tread rubber is more elastic, deformable, or flexible than the carcass and belt. Maximum aligning torque is in the 1 to 3 degrees slip angle for race tires (3 to 5 degrees for passenger car tires). There is some carcass and belt twist. At high side force aligning torque reduces and there is less carcass and belt twisting. The primary tire deformation at high side force is lateral. The theoretical slip could be corrected. The correction is a function of aligning torque with the maximum correction occurring in the 1 to 3 degree slip angle range.

INTRODUCTION

CONTACT PATCH SLIP MODEL- Figure 1 shows a tire and the contact patch between the tire and ground. The contact patch length and width are shown. The tire body is a pressurized torroidal structure with a tread belt and radial side wall cords. All of the forces that control a race car are transmitted through four (4) of these contact patches.

The objective of this paper is to present an understandable slip-traction model that represents observed tire performance phenomena. Heat generation during tread particle slip is quantified and used to identify the limiting traction conditions of the tire. Contact patch slip and friction heat input to the tread is not considered by most models. The "classic" tire model does not look right. The "classic" model for high side force does not match simple aligning torque data. The "classic" model also does not lend itself to representing hard longitudinal acceleration or braking with 15% slip within the contact patch. The HRE macro model of the tire contact patch is hypothetical. The macro model is intuitively correct. The "slip and re-grip" concept is proposed when a tread particle has reached the limit of adhesion. Heat generation during sliding explains many performance changes with tire slip, traction force, and adjustments. The model explains effects of camber, tread thickness, tire pressure adjustments, and more.

Figure 1. Tire and Contact Patch

3

The HRE model assumes a particle on the tread surface moves a certain distance (with relation to the belt or carcass) before slipping depending upon the unit vertical load (tire pressure primarily). Figure 2 shows the basic tread surface particle maximum deflection condition at a reference tire pressure. The particle moves the same amount laterally (±), longitudinally (±), or any combination before losing grip. The tread belt is the reference plane. Only race tire "slicks" are considered (no grooves and sipes). The premise of the HRE model is similar to some past models. See[1] 1 Fromm model, page 816, and [6] Dixon model page 90.

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Figure 3. High and Low Slip Schematics

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In reality tread elements next to the sliding particles support and slow the particles so they re-grip the road sooner. The sliding particles also pull the griping particles to initiate their slip sooner. The "realistic" contact patch will have sliding initiate before maximum traction is reached and re-grip occurring before the minimum re-grip of Figure 3, probably somewhere near the middle of the maximum traction and re-g rip points. Analytically the traction and slip dependence of the "ideal" and "realistic" models will be similar.

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Figure 2. Particle Adhesion Circle

CONTACT PATCH TREAD HEATING -The sliding conditions of the HRE tire model allows calculation of contact patch frictional heating. It is well known that sliding with friction generates heat. Figure 4 shows an expanded schematic of a contact patch with 7% slip, a high side force slip condition. During each slip step heat is generated. The heat generated is proportional to the integral of the friction force during slip times the velocity while the particle is slipping. The exact values of the maximum grip and re-grip do not change the hypothesis trends, comparisons, or results.

Upon losing grip the HRE model proposes that the surface particle begins to slip toward its initial unloaded position. Friction force reduces during sliding because the particle has some velocity. At some point as particle deflection reduces and return force reduces the friction force again is great enough for the particle to re-g rips the road. Figure 3 shows two conditions of side slip and regrip, high slip and low slip. In the "ideal" conditions of Figure 3 the traction conditions are uniform and a complete lateral and radial plane of independent tread particles slip together and are not restrained by surrounding particles. In this case the particles reach the maximum friction condition before losing grip. In Figure 3 the particles slide and are assumed to re-g rip at 50% maximum deflection. Sakai data in [1 0] has a side force to slip shape similar to the 50% sliding condition.

In the "realistic" contact patch the slip to re-grip distance is much shorter because surrounding particles pull or support any individual particle. A "realistic" schematic is shown in Figure 5. A reasonable assumption of sliding friction during slip to re-grip is that the force is proportional to the particle average slip deflection in Figure 5. The final slip from the plateau deflection (about % maximum grip deflection) to zero generates less heat than the slip to re-grip region because of lower sliding friction force (proportional to the lower particle deflection). Many

1. Numbers in [ ] refer to references at end of text

4

ity). Average particle deflection times contact patch area and rubber constants is side force. Side force is based on average deflection and accounts for the lower deflection of the trailing edge slip. The friction heat energy in HP can be represented by:

models neglect the trailing edge slip as contact pressure is reduced.

---....--

rr. ILl', NAICM Z7Xt1, 2101 LIF LOAD

0 = F5 (area)*Sa*C1 Horsepower

Where Q is heat energy generated, F5 (area) is the particle deflection area (the side force area of Figure 5 for example), Sa is the actual side slip, and C 1 is a constant that includes rubber characteristics, velocity, and all conversion factors. The heat energy is generated by the intermittent sliding of the rubber in the contact patch over the ground surface. The heat energy, Q, is for reference only. This heat energy is equivalent to a H P loss due to frictional losses. Only a fraction of this energy heats the tire.

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(Eq. 1)

Peter Wright [13] presents data showing HP loss to generate side force is proportional to slip. The loss is the tire side force vector in the direction of travel when there is slip. What is shown here is that the drag force is equivalent to the contact patch heat generation.

.......

CCIItACT PATCII LI!IIGI1C.-

Figure 4. "Ideal" Lateral Slip Schematic, 40 psi Figure 4 and Figure 5 for the "idealized" and "realistic" schematics look considerably different but the side force area and actual slip are almost the same. Realistic, Figure 5, type schematics are used for all side force analysis that follows. The tread rubber is assumed to be at some reference operating temperature.

TIRE-CARCASS BODY MODEL -In conjunction with the contact patch model there is a tire body model. The tire body model is a circumferential belt and radial tension cord toroid that is pressure supported as shown in Figure 1. The belt is assumed stiff laterally (width) and in circumferential tension, and flexible in the radial direction. The tread-belt can bend radially (at the front and back of the contact patch) and compress.

------

,...._.,NAICMZ7Xt1, ...... LOAD

The tread belt deflects under static load until the contact patch area times pressure equals the load. At this condition (P*A = Fv) two additional things occur: 1) summation of the radial cord tension supports the vertical axle load, and 2) belt tension at the leading and trailing edge of the contact patch supports the load. The HRE belt-carcass model is similar to others. Reference[1], pages 237 to 247, presents and discusses a flexible membrane tire model. The HRE model analytical contact patch length and deflection with load results are the same as Reference [1], pages 730-731. The tire static deflection with load for the simplified model is known to be in error [1 ]. At low to normal load the model predicts lower deflection. At high load the predicted deflection is about correct. The carcass-belt model allows calculation and prediction of trends of tire deflection and spring rate to be made.

The Figure 5 slip schematic shape is similar to that of Dixon [6], page 90. But the HRE model hypothesizes a slip to re-grip phenomena, recognizes trailing edge slip, and estimates heating. The average force in the sliding region of the HRE model is below the maximum grip capability of the rubber. The average deflection force in the sliding region is dependent on the ground surface, rubber characteristics, temperature, tire pressure and numerous other factors.

The tire body model also is used to determine the contact angle of the tread with the ground at the leading edge of the patch. Vertical tread momentum is lost at the leading edge of the contact patch. Figure 6 is a schematic of tread belt deflection and the belt contact angle with the ground.

The heat energy is proportional to the average sliding force (average surface particle deflection of Figure 5) times the sliding velocity (actual slip times wheel veloc-

5

Vv = 220*Sin(9.7) =37ft/sec

UNBALANCED CENTRIFUGAL FORCE

(Eq. 7)

So the loss of energy (HP) is, HPv = 380*37/550 = 25.6 HP

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(Eq. 8)

One tire with a deflection of 0.193 inches at a speed of 150 MPH has a theoretical momentum energy loss of over 25 HP. This is a significant amount of energy.

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\d NASCAR TIRE 27 X 11 -------------

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TIRE SPRING RATE CHANGE WITH SPEED- At speed the vertical momentum loss also affects the tire deflection and ride height (axle height). In the example above the load on the road is approximately 2380 lbf (the P*A term, 2000, plus the vertical momentum force, 380). The static tire load at the same deflection is 2000 lbf. Tire spring rate is higher at speed.

VERTICAl /1\380 LBF at IMPACT I \150 MPH FORCE I

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The tire deflection for the 2380 lbf ground load tire at 220 ft/sec is, dR = 13.5*(1-Cos(9.7)) = 0.193 in Figure 6. Tread Momentum Schematic

At static conditions the contact patch length of a 2380 lbf load at 40 psi is,

Loss of tread momentum has several effects: 1) a loss of energy, 2) increased ground load at the front of the contact patch, and 3) an imbalance of tread centrifugal forces. The energy loss is a portion of rolling resistance. Increased ground load at the front of the contact patch results in negative aligning moments at high slip angles, see Dixon [6] page 122. Radial force imbalance leads to a change in tire spring rate with ground velocity. Spring rate and energy changes with speed are calculated using an assumed tread-belt density.

L=2380/(40*11)=5.41 in

= Arcsin(4.55/27) = 9.69 degrees

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= Arcsin(5.41/27) = 11.56 degrees

(Eq. 11)

and the static tire deflection is, dR = 13.5*(1-Cos(11.56)) = 0.274 in

(Eq. 12)

At a speed of 150 MPH the tire deflection reduces 0.081 inches from the static conditions to 0.193 inches. "Average" static tire spring rate with 2380 lbf load is 8696 lbf/in (2380/.274), which increases to 12,332 lbf/in (2380/.193) at 150 MPH. Not all of the vertical impact force calculated is lost to the ground. Some energy goes into side wall and tread bending and is partially recovered. The actual tire spring rate may not change the theoretical amount. Theoretical tire deflection is below actual, so the theoretical tread impact angles are low affording some unknown compensation.

(Eq. 2)

and is shown in Figure 6. The tread weight using an average density of 0.045 lb!in 3 is, (Eq. 3)

ANALYSIS AND DISCUSSION

One foot of tread weighs about ((10.5*12)/(27*n)) 1.5 Ibm. At 150 MPH (220 ft/sec) the tread mass rate is, Mdot = (1.5/g)*220 = 10.26 lbf-sec/ft

(Eq. 10)

the contact angle is,

TREAD MOMENTUM AND ENERGY LOSS- Tread momentum of race tires at speed is huge. The tread impact force, vertical force imbalance, and energy loss are significant. In the Figure 5 case the contact patch length is 4.55 inches and the impact angle is, ~

(Eq. 9)

The basic concepts of the HRE tire model have now been introduced. Trends of tire performance now can be calculated and application examples discussed.

(Eq. 4)

and tread momentum is, M = 10.26*220 = 2257 lbf

SLIP I PRESSURE EFFECTS ON SIDE FORCE AND HEATING - Figure 4 represents 7% slip on a NASCAR tire at 40 psi and a 2000 lb load. For purposes of this paper a NASCAR tire is 27 inches in diameter with a tread width of 11 inches and a tread thickness of 14 inch. With 40 psi tire (and contact) pressure a surface particle is assumed to grip the ground to a maximum deflection of 0.1 inch. The area under the particle path vs tread length and actual slip in Figure 4 are noted in the sub-title. The area is proportional to side force and actual slip ratio

(Eq. 5)

If the "stream" of tread were stopped continuously the force would be over 2200 lbf. The tread impact angle with the ground is 9.7 degrees, and the vertical momentum change, vertical impact force, is, Mv = 2257*Sin(9.7) = 380 lbf

(Eq. 6)

this force is lost. The tread is impacting the ground at a velocity of, 6

times the reference velocity is sliding speed. The product of area and actual slip is the heat factor.

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Note that slip to re-grip takes some time (distance) to occur. This time or distance changes the amount of slip that occurs within the contact patch length for a given slip angle or steer angle, a. The return speed is a function of nominal grip conditions and deflection force of the rubber. The return path and return angle, ~. are ground velocity dependent. For higher speed of the carcass belt reference plane more contact patch length is required to regrip. For the Figure 4 speed conditions actual slip of the assumed model is given by,

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(Eq. 13)

SA= S/(1 +Kv*S) = S/(1 +S)

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where Kv is 1.0 at the calculation reference speed.

Figure 8. Side Force and Heating vs SlipSummary, 20001bfLoad

If contact pressure increases the surface particle deflects farther before slipping. The maximum grip deflection is assumed proportional to tire pressure. Figure 7 shows the "idealized" slip schematic for a NASCAR tire with 2000 Ibm load, 7% slip, and 44 psi tire pressure. The maximum particle deflection is 0.11 inches (0.1 *44/40). The integrated area and total actual slip are noted. The equivalent side force (area under the slip curve) has decreased. In order to get back to the same side force as the 40 psi tire the slip of the 44 psi tire must be increased to about 8%.

------

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An important trend is that as slip increases side force increase drops off while contact patch heating continues to increase at the same rate. At about 6% to 7% slip contact patch heating is going to cause rubber grip and modulus to drop off. At some HF value side force will decrease because the rubber is overheating. If a heat factor (HF) of 0.016 units is assumed critical (where the rubber loses grip and side force decreases) two observations can be made. First, at the specified HF the side force of a lower pressure tire is above the side force of a higher pressure tire. Second, with higher pressure a higher slip is required to reach that same HF for peak force.

... i

Examples - NASCAR teams often put 1 psi more pressure in the outside rear tire during a pit stop to "loosen" the car up. The usual explanation of benefits is that the right rear spring rate is increased giving an increase in right rear load, and a similar load increase to the left front. The outside rear tire should get hotter. But you never hear what really happens. Figure 8 shows that if tire pressure is higher the slip angle must increase to get to the same HF and side force reduces. The higher slip angle forces the inside rear tire to work harder. With the increased outside tire pressure the inside tire will work harder and get hotter. The net side force is reduced some so that end of the car is "looser''. Any load increase to the left front tire makes it works harder, getting hotter, and also turns the car better. Both inside tires work harder (get hotter). If right rear "wedge" or spring rate was increased the outside rear tire would get hotter and the inside rear cooler.

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Figure 7. Lateral Slip Schematic, 44 psi Side force and actual slip for tire pressures of 36 psi, 40 psi, and 44 psi with slip of 1% to 12% can now be calculated. Figure 8 presents the Side Force and Heat Factor summary for a NASCAR tire with 2000 lbf load. A number of trends are evident. Side force with lower tire pressure is higher for any given slip. The side force asymptotic value is the same for all pressures. At a given slip ratio, or percent slip, the lower pressure tires have greater heating.

If the outside front pressure is increased a similar thing happens. The right front will have to slip more to get to the same temperature and grip may be down a little. But with the steering wheel turned further the inside tire is at a higher slip angle working harder. Increasing outside front pressure is similar to putting more Ackerman in the front end.

In Figure 8 the heating coordinate is F5 (area)*Sa and is called the heat factor (HF). The constant, C 1 , in equation (1) is the same for all figures at the reference velocity in this paper and HF is proportional to contact patch heat generation.

7

In both above instances increasing the outside tire pressure, or decreasing the inside pressure, forces the inside tire(s) to work harder. The inside tire temperature(s) will increase. If only one outside wheel spring rate increased the outside tire would relatively get hotter and the inside tire may cool. Spring rate and pressure-slip give opposite tire temperature effects.

RELATNE ALIGNING TORQUE vs SUP ... ····-···-······-········T···· 1.1.

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LOAD EFFECTS ON SIDE FORCE AND HEATING Figure 9 presents the Side Force and Heating Summary of for a NASCAR tire with 1500 lbf load. The curves look very similar to those of Figure 8. The rubber compound is assumed the same as in Figure 8 so the tire should operate at about the same heat factor.

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Figure 10. Aligning Torque Summary

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A higher force at the front of the contact patch occurs at speed if tread momentum is included. The forward force increases significantly as speed increases. The tread momentum force is what causes the aligning torque to go negative at higher speed and large slip angles, see [6] pg. 122. Factors of what percentage of the theoretical tread momentum vertical force actually get to the ground have not been determined.

TOP VIEW

--•

•

Figure 9. Side Force and Heating vs SlipSummary, 1500 lbf Load To get the same operating temperature (HF) the more lightly loaded tire must operate at a higher slip. Excess Ackerman may be desirable on the front end on oval cars to get the more lightly loaded tire to work more. Decreasing inside tire pressure is another way to get more "effective" toe out on an oval. In NASCAR a softer rubber compound is used on inside tires. With lower modulus rubber excess Ackerman or even lower pressure is required to work the inside tire to the same temperature (HF).

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ALIGNING TORQUE- Results of the calculation of contact patch aligning torque (area moment proportional to force torque) at 2000 lbf load and three pressures is given in Figure 10. The shapes of the curves and location of maximum values are as expected. The curves are similar to those in Dixon [6]. The curves are shown to illustrate trends and for comparison to other work. As expected lower pressure results in higher moment values at lower slip.

Figure 11 . Tire Camber Schematic CAMBER EFFECTS- The HRE model shows the true influence of camber on tire performance. Figure 11 shows a schematic of a rolling tire with camber. The ground forces the tread rubber in contact with the ground to follow a straight path. However the belt and carcass "want" to follow a different path. If this is a left side tire with negative camber the surface particles are pulled to

8

the right compared to the belt path. If the wheel is turned to the right some camber force already exists in addition to the slip force. When the tread surface particle reaches maximum grip deflection it still loses grip and slides. The asymptotic tire side force with or without a small amount of camber is the same.

110% THICKER TREAD PERFORMANCE, SAME Fa

Figure 12 shows how side force of a tire with negative camber at 40 psi and 2000 lbf load compares to the force of the zero camber condition of Figure 8. The force starts higher (the amount due to camber) and will blend into the zero camber curve at high slip. The side force with camber is above the no camber curve at all times. But the heat generation (HF) versus slip with and without camber are almost identical. Fe&HF,•PII. -LIFLCWI

Figure 13. Thick & Thin Tread Slip Schematics When right and left side tread thickness is different other things can happen. Assume that the car was set up to get the same tire temperatures on both sides. When going around a corner at the proper slip angle for the thin tire the thick tire is not producing it's share of side force. If the tread is 50% thicker the side force is about 67% (1/1.5) of the thinner tread. By increasing slip 50%, the thick tire can produce the expected side force. The high slip eventually overheats the thicker tire. With the higher slip the thin tire is slipping too much and it overheats as well. The thin tire will also be overheating slightly when the thick tread is at the reference HF. If the inside tire was running cooler than the outside tire these statements are not correct.

Figure 12. Side Force With Camber vs Slip

Assume now that there is thinner rubber on one circumferential strip of the tread, "crowning" for example. When the tire is operating at the slip to get the thicker rubber to the right HF, the thin rubber is overheating. That strip can overheat and blister.

The fascinating thing about camber force (alone) is that the surface particle strikes and leaves the ground at the same point (see camber schematic). There is no slip. Without slip there is no contact patch heating. Camber side force is generated with no contact patch frictional heat, only internal damping heat. Camber force is almost FREE of heat generation.

EFFECTS OF TREAD MOMENTUM- Tread momentum and vertical impact force at one speed was calculated earlier. The solid curve in Figure 14 shows how tread vertical impact force varies with speed if the impact angle is 9.7 degrees, the Figure 5 deflection conditions. The 11 inch wide by 14 inch thick tread energy loss in HP is the dotted curve in Figure 14. The energy loss is simply vertical impact force times vertical impact velocity times a conversion factor. This energy loss is one part of tire rolling resistance.

RUBBER THICKNESS EFFECTS -A new hypothesis of tread heating caused by tread rubber thickness is permitted by the HRE tire model. Figure 13 presents slip schematics for two rubber thickness treads. One is the Figure 5 tread and the second is for a tread with 50% more thickness. Note that the 50% thicker tread must deflect 50% further to get to the same grip with the same pressure. The actual slip of the thicker tread is 50% more to get to the same side force. The thicker tread has more heating because the rubber particles slide 50% further, or 50% higher average velocity, to get the same side force.

There is no question that the full impact force is not transmitted to the ground. Bending and flexing in the tire absorb some force and energy. The theoretical deflection model is known to underestimate the actual deflection. With higher actual deflection the impact angle, actual vertical force, and velocity may approach the theoretical values.

The thicker tread does have more internal damping heating. But race tires operate at relatively high slip and speed so the contact patch frictional heating is much greater than internal damping. The (50%) thicker tire will be at the proper surface temperature with about 82% side force capability (F5 *Sa = 0.82*[1.5*0.82] = 1.01) when at equilibrium temperature conditions.

The loss of the impact force at the front of the tread contact patch causes a disparity of tread centrifugal forces. The tread must be pulled off the ground and vertical energy applied to impart the correct vertical velocity. The

9

_""'"'_ ..__ _

theoretical energy is just what was lost. Over the top of the tread between ± 9.7 degrees of vertical twice that force is acting, see Figure 14. At the Figure 5 conditions the impact force was 380 lbf increasing the vertical load to the ground to 2380 lbf if the impact angle remained constant. But there is now a 380 lbf centrifugal upward force that is not balanced by a downward radial cord tension force. The axle will move up until the ground load is equal to the axle load. Tire deflection reduces with speed. Tire spring rate effectively increases with speed.

AVI!IYIIEliU.KIIa-. wi.CIAD

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Figure 15. Tire Spring Rate & Deflection vs Load and Speed

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ACCELERATION AND BRAKING SLIP- It is difficult to draw a slip schematic with pure acceleration or braking so combined side and longitudinal slip schematics are presented. Figure 16 shows two "ideal" slip schematics at low speed. The upper schematic is a small side slip with hard braking slip, and the lower schematic is small side slip with hard acceleration slip. It can be seen that a surface particle still deflects to the maximum grip amount, the larger circles, before slipping and re-gripping, the small circles. In the acceleration example the tire belt is being pulled to the rear so the longitudinal tread surface particle deflection is forward (compared to the belt reference) and the "sliding" is toward the rear.

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Figure 14. Tread Momentum & Energy Losses To calculate the associated static spring rate the quick way around all this is to say the axle load was 2380 lbf statically. At speed (150 MPH) the axle load is reduced by the tread centrifugal unbalance and the ground P*A force increases by the (same) tread impact load of 380 lbf to give a ground force equal to axle load.

ROLLING DIRECTION

Figure 15 shows how the theoretical average tire spring rate changes with axle load for three (3) different speeds. The spring rate varies with load due to change of the impact angle of the tread, hence the vertical impact force and force imbalance. Theoretical average spring rates are higher than measured as discussed above, and in [1]. However the trend of the spring rate change with speed and load can be visualized.

BRAKING

....~~~-CONTACT PATCH LENGTH -----11,._.-~1

One interesting observation is that the average spring rate, Ks , from zero to loaded deflection is double the instantaneous spring rate, ks , for small load changes about the operating point. This seems to be true at all loads and speeds in Figure 15. Tire spring rates published in tire pamphlets (by Goodyear and Firestone) are believed to be "instantaneous" spring rates. Neither tire company would divulge details of how "tire spring rates" were measured, who knows why? How can those numbers be used if you do not know what they mean? The model also predicts high instantaneous spring rates.

ACCELERATION {WITH SOME SIDE SLIP) Figure 16. Longitudinal Slip Schematics A point of interest here is that when there is a small fixed side slip angle and hard braking the amplitude of the side deflection increases beyond the side slip only condition. Traction circle data show this identical trend, see Milliken & Milliken [1 0] page 58. Under acceleration the side force deflection reduces because the rubber contacts the ground for less distance before slipping.

10

IMPORTANCE OF RUBBER PARAMETERS- To illustrate how three parameters affect tire heating several different tires producing the same side force are evaluated.

Slip and heat losses are inversely proportional to the modulus change, a direct relationship. Tire T4 with a 10% reduction of grip requires a calculation of slip required to get the same side force, or integrated deflection area. A 10% reduction of grip reduces maximum dY to 0.09 and slip average deflection to 0.0675 inches. For a slip ratio of 1/6 (16.67%) it takes 0.405 inches to reach sliding deflection, there is a 0.0675 length at the trailing edge to drop off, and there is 4.073 inches (4.5455-.405-.0675) at the sliding deflection. The side force area is 0.291 square inches, the desired area. For tire T4 with a 10% reduction in grip the actual slip is 0.143 and the heat loss estimate is:

1. The Reference - Tire (T1) has grip G 1, thickness H1, and modulus M1. 2. Thicker Tread -Tire (T2) has grip G1, thickness H2 (=1.5*H1), and modulus M1. 3. Variable Modulus (lbf/in) -Tire (T3) has grip G1, thickness H1, modulus M3 (=1.2*M1 ); Tire (T3a) has modulus M3a (=0.9*M1) 4. Variable Grip- Tire (T4) has grip G4 (=0.9*G1 ), thickness H1, and modulus M1; Tire (T4a) with grip G4a (=1.1 *G1 ).

04 = 1500*(150*0.143)*(88/60)/550 = 85.7 Horsepower (Eq. 18)

All tires are operating at a load of 2000 lb, tire pressure of 40 psi, a velocity of 150 MPH, and at the reference temperature. The reference tire, T1, is assumed to operate at 6% slip and produce a side force of 1500 lbf.

WHOA!! A 10% grip reduction increases slip and losses by a factor of 2.5. Race tires always work at slip angles near the maximum side force limit and a reduction of grip causes big changes, and probably tire over heating .

Tire T1 with the given conditions takes 1.25 inches (.075/ .06) to reach the sliding deflection, takes 0.075 inches at the trailing edge to drop off, and is at sliding deflection for 3.2205 inches (4.5455-1.25-.075). The Fs area is 0.291 square inches and actual slip is assumed to be 0.0566 (S/(1 +S)). The slip heating loss is,

The last example, Tire T4a, has a 10% grip increase. Slip reduces to 4.23% to get the same side force area, and actual slip is 0.0406. The heat loss estimate is: 04a = 1500*150*0.0406)*(88/60)/550 = 24.35 Horsepower (Eq. 19)

01 = 1500*(150*0.0566)*(88/60)/550 = 34.0 Horsepower (Eq. 14)

A 10% grip increase causes a 28% reduction in slip HP loss compared to tire T1. Example results would change if the original reference tire was operating at a different slip ratio or conditions. Examples T4 and T4a show that grip is very critical.

This is the Reference tire's slip heating loss. Tire T2 surface particles deflect 50% more so the actual slip is 50% more to get the same side force. A slip ratio of 9.3% gives an actual slip of 0.0849 (which is 1.5*0.0566) and the slip heating loss is, 02 = 1500*(150*0.0849)*(88/60)/550 = 51.0 Horsepower (Eq. 15) A 50% increase as expected. Actual slip and heat losses are directly proportional to the tread thickness change. The 02 loss heats the tread (equally as fast as a thinner tread), and once operating temperatures are reached continues to heat the thicker tread causing it to overheat. Basically heat loss is only from the tread surface and the thicker tread only has an insignificant amount more tread area (heat loss area). Tire T3 has a modulus increase of 20% so the deflection to the same grip (for the same side force) is down 16.67% (1/1.2). Slip to get the same side force is 4.95%. Actual slip on T3 is 0.0472 (0.0566/1.2), and slip loss is,

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Figure 17. Speed Affects Actual Slip

03 = 1500*(150*0.0472)*(88/60)/550 = 28.2 Horsepower (Eq. 16)

SPEED EFFECTS ON SLIP- Speed affects the actual slip of a working tire. All figures presented to this point are for some "reference" speed. The slip to re-grip takes a certain time. At the reference speed it took the distance "s", depicted in Figure 4. At twice the reference speed the slip motion takes about the same time and twice the distance along the patch length as shown in Figure 17. The contact patch length is traversed in half the time. Speed increase reduces actual slip in the contact patch at the

If the modulus decreases 10% the deflection to the same grip is up 11%, or 0.11 inches. Actual slip on Tire T3a for the same force is 0.0629 (0.0566/.9). The slip HP loss of tire T3a is: 03a = 1500*(150*0.0629)*(88/60)/550 = 37.7 Horsepower (Eq. 17)

11

same slip angle. Note that no corrections for patch length (tire spring rate) with speed were made. With spring rate change corrections contact patch length and actual slip reduces even farther.

Tire cooling (right front for sure on short tracks) in NASCAR should be considered. Numerous times on short tracks a car has messed up the right front in a wreck, and then gone faster. (Harry, "Mr. September'', Gant hit the wall while going for the lead late in a short track race . . . went a lap down . . . got the lap back and won one of his five win streak. Dale Earnhardt and Darrell Waltrip, and others, had similar things happen ... but did not win the race.) NASCAR teams can obviously cool a tire more efficiently than wrecking the car.

The HRE model predicts that speed changes the actual slip to slip angle relationship. Tangent of the slip angle is the slip ratio at low speed. It is beyond the scope of this paper to develop the Actual Slip to Slip Angle relationship with speed. TIRE TEMPERATURE- The tire bulk operating temperature (maximum) for race tires is in the 200 to 230 degrees F range. What is the contact patch rubber temperature? Rubber is being torn off the tread surface in the contact patch. Tread surface temperature 90 degrees before contacting the ground (front) for a hard working tire is over 300 degrees F. Verbal communication indicates surface temperatures of over 500 degrees F have been measured within a few inches of the contact patch trailing edge (Ref. [1], page 401, shows this is possible). By the time the rubber gets to the front, surface temperature is about 300 degrees F. Surface temperature reduces during rotation due to conduction into the tread and convection to the air flowing past the tire. When the front tires are straight, with no slip, heat from the tread is conducted to the ground cooling the tire in the contact patch.

OPTIMIZING TIRE PERFORMANCE- The tools to assist in optimizing tire performance are given in above sections. Vertical momentum losses can be calculated for the corners and straights of an oval. Slip losses for the corners also can be calculated. Side forces required to achieve cornering acceleration can be determined (normal test data) and estimates for longitudinal slip made. Total energy loss of the tires for a lap can now be calculated. Changes to tire pressure, steering geometry, toe, corner loads, etc. can be made and the losses recalculated. If the same traction forces (side or combined side and longitudinal) can be maintained with lower energy losses the car should go faster.

CONCLUSIONS

The tread surface is the primary means of cooling the tire. Wider, high performance, tires increased the tread width and cooling area. Contact area for wide and narrow tires at the same pressure is similar. Additional cooling area improves tire performance. Performance data correlates better with tread surface area than width.

The HRE macro model of the contact patch presents a different perspective of how the tire works. The slip to regrip feature of the HRE model shows enough detail that first order sliding losses in the contact patch can be calculated. A portion of this energy goes into heating the tread. Contact patch heat generation is proportional to the actual slip ratio times side force (or traction force) times speed. Heating continues to increase at a high rate even when side, or traction, force starts to level out.

On Fuel drag cars tire surface temperature is over 600 degrees during the "burn ouf'. Within seconds of stopping and starting to back up to the start line the tire surface temperature is back to ambient. When the car begins accelerating tire surface temperature 90 degrees (angle) before ground contact increases to about 390 degrees F within a couple of revolutions. Tread surface temperature (at the 90 degree before impact position) stays near 400 degree F through the run. Over 5 G's acceleration is now maintained on Top Fuel cars for several seconds.

The HRE model gives a new understanding of camber benefits. Camber force is provided without slip and contact patch heat generation. The only heating is from internal damping. For race tires camber force is almost "free" of heating. Do not put in excess camber which reduces outside edge patch length in the corners. Thick tread heating in the past has been attributed to internal damping of a greater amount of rubber. The HRE tire model shows that a 50% thicker tread generates 50% more contact patch friction heat to produce the same side force. With the same heat loss area, tread surface area, thicker tread tires will overheat because of the increased contact patch heat generation.

Tire surface temperature is very critical. In NASCAR a 1 psi change of tire pressure can make an observable difference in car performance. In Figure 8 for a tire at 40 psi operating at 0.016 HF 1 psi is a 2.5% pressure change. At a constant HF the 1 psi change would translate to about 0.06% slip, which is about a 1% change. The pressure change converts to about 0.0002 HF if slip is held constant, about a 1.3% change in HF. So a few percent reduction of HF or slip would result in an observable tire and car performance increase due to tire temperature reduction.

Sample calculations of tires with variable rubber mechanical characteristics illustrates the effects of those parameters. Grip is by far the most important parameter evaluated. Work is currently underway to evaluate thermal characteristic affects on tire performance.

12

NOMENCLATURE

The comparisons of tire performance using the HRE macro model and observed performance shows the soundness of the approach. Some predicted effects of speed are unsubstantiated. Believing that slip and re-grip occurs, and slip is the primary mode of heat input to the tire may lead to other more significant conclusions.

A: Area, in 2 d: Tread (and belt) thickness, in. dR: Tire deflection, in. D: Diameter, in. F: Side, Acceleration, Braking, Load, or Vertical force, lbf g: Gravitational constant, 32.17 (lbm-ft)l(lbf-sec2 ) HP: Horsepower, 550 lbf-ft/sec = 1 HP ks: Instantaneous spring rate, lbflin K 5 : Average spring rate, lbflin Kv: Velocity correction, Slip Constant L: Contact patch length, in. M: Modulus of tread, lbflin Mdot= Mass Rate of tread, (lbm/g)lsec(WhtD) *VI g M: Momentum, M * 11V MPH: Miles per hour, 1 MPH= 1.467 fVsec Q: Heat energy, HP R: Tire Radius, in. s: Particle slip to re-grip motion, in. S: Slip, or Slip Ratio, at zero velocity S: Tan a SA: Slip, actual, at speed, SA: S I (1+(Kv * S)) T: Temperature, degree F V: Velocity, fVsec w: Width of tread, in. W: Weight of tread, Ibm dY: Surface particle deflection, in. to maximum grip. function of rubber, unit load, etc. a.: Slip angle, degrees, or wheel angle p: Tread impact angle, degrees p: Tread (and belt) density, lbm/in 3 1t: Pi, radiansl180 degree, (3.14159)

Understanding how the tire works gives the car and tire engineer more knowledge to get optimum performance out of ALL tires. Tire performance can be optimized using heat energy and momentum loss trends with pressure, slip, load, etc. that are presented. Various forms of racing are interested in different things. Even the tire companies may benefit from the new viewpoint of this work.

REFERENCES 1. Mechanics of Pneumatic Tires, U.S. Dept. of Commerce, National Bureau of Standards, Nov. 1971, S.K. Clark Editor. 2. Vehicle Dynamics Terminology, SAE J670e, Society of Automotive Engineers, Inc., Warrendale, PA, July 1976. 3. Tires and Handling, SAE Inc. PT-59, 1996, Edited by Ellis Johnson. 4. BFG Team T/A News, Tech Topics, Volume 13, Issue 2. 5. Aird, Forbes, Aerodynamics for Racing and Performance Cars, HPBooks, 1997. 6. Dixon, John C., Tires. Suspension. and Handling, 2nd edition, SAE Inc., 1996. 7. Gillespie, T.D., Fundamentals of Vehicle Dynamics, SAE Inc., 1992. 8. Hallum, Chuck, The Magic of the Drag Tire, S.A.E. Paper 942484, Presented at SAE MSEC 1994. 9. Haney, Paul and Braun, Jeff, Inside Racing Technology. TV Motorsports, 1995. 10. Milliken, W.F. and Milliken, D.L., Race Car Vehicle Dynamics, SAE Inc., 1995. 11. Sakai, H., The Dynamic Properties of Tires, Bulletin, JSAE No. 3, p70-71, 1971, also, International Journal of Vehicle Design, Vol. 2, No. 1, 1981 , and Vol. 3, No. 3, 1982. 12. Tremayne, David, The Science of Speed, Patrick Stephens Limited, 1997. 13. Wright, Peter, Formula 1 Tyres, Race Car Engineering Vol. 7 No 6, 1996.

SUBSCRIPTS

a: Acceleration A: Actual b: Braking

c:

Camber

1: Load

s:

Side

v: Vertical V: Velocity dot: Rate, sec- 1 Wheel heading is the Reference direction Tread belt is Reference surface

13

2000-01-3571

HOWTOWORK RACE TIRES On NASCAR Ovals Chuck Hallum Hallum Racing enterprises Copyright © 2000 Society of Automotive Engineers, Inc.

working tire contact patch (CP} length is about 5 inches. With 7% slip a tread particle would have to. move 0.35 inches .over the CP length. The surface rubber particle moves about 0.1 inch before slipping so the particle is slipping over more than half the CP length. At high side force values restoring torque is low and there is very little correction for steer to tread CP angle.

ABSTRACT

Working NASCAR tires correctly will help a team qualify well and have a chance to win on Sunday. Aerodynamics, engines, and shocks are not the only things. Tire usage dictates suspension geometry, springs, weight jacking, and shock choices. Tire slip losses in corners are huge, over 100 HP in qualifying trim and over 150 HP in race trim. Proper tire usage reduces drag HP for qualifying and controls right side tire heating in race trim. Tire slip loss heats the tread rubber and is the primary factor limiting car performance on short tracks. Evaluation of several adjustments on tire and car cornering performance is determined using the Hallum Contact Patch Model presented in SAE 983028 Understanding Race Tires. One psi of tire pressure is significant to car performance. Tire and car performance changes with toe, Ackerman, camber, aerodynamic force, load jacking, and weight, are compared to the performance change with tire pressure. The Hallum Model considers heating so dynamic tire performance phenomena can be evaluated.

The 7% slip gives about a 7% drag vector of the side force. If the tire side forces produce a car lateral acceleration of 1.5 "g" the tire drag is about 0.1 05 "g" (0.07*1.5}. For a 3600 Ibm car that's 378 lbf. At 150 mph that converts to 151.2 HP (378*150*88/(60*550)}. That's a substantial retarding force AND heat generation energy. The 7% slip is a 4-degree slip angle.

DIRECTION OF TRAVEL

I

SLIPANG~ I

INTRODUCTION

The tire performance objective on short tracks is to get as much side force as possible for the least slip loss. In qualifying slip loss heat generation on an individual tire is not much of an issue because the tires are cold and can absorb considerable heat before the tread surface temperature is too high. But tire drag losses are important in qualifying so the total slip loss must be low. During the race the outside tires have to be kept below some critical temperature or heating rate to survive. Inside tires must be worked harder. At the selected right side tire heat rate total losses must be minimized to go faster than other teams. What generates most of the performance? Simple slip friction culprit. A rubber particle on the tread may move 0.1 inch before

DRAG FORCE

Figure 1

Traction Force Vector Schematic

Slip generated heat is equivalent to the tire side force Drag Vector shown in Figure 1 times velocity. The tire performance model (see Appendix for a review of the Hallum Slip Model} presented in SAE 983028,

heat that limits tire during cornering is the surface of a race tire it loses grip. A typical 15

Understanding Race Tire§111 , defined the term Heat Factor (HF). HF is equivalent to the tire drag vector force. HF times velocity is proportional to heat generation in the CP during cornering. At a limiting HF the side force area (F.) is calculated and is equivalent to cornering performance of a baseline condition. Then individual variable changes are made and a new cornering F. performance determined using the same model. If F•• at the same HF, is higher cornering performance is improved.

at the CP is equivalent to the side force Drag Vector energy. Tire drag slows the car just like aerodynamic drag. The slip energy heats the tire and track surface. This loss and heating is controlled in different ways for qualifying and racing.

DIRECTION

SIDEVIE'A'

~ _...j 1---

Pressure is used as the reference change because many people have an idea of that performance increment for Winston Cup cars. Performance shift with Ackerman (toe), camber, aerodynamic force, load jacking, and weight shift are compared to the performance change with tire pressure adjustment. Analysis explains the effect of increasing, or decreasing, tire pressure by 1 psi on one tire. The related car performance change is larger than might be expected. "Wedge" (a spring adjustment) or "jacking" (a track bar adjustment) changes to affect car performance the same as a 1 psi change in tire pressure is determined and both are rather large. These adjustments are used in different circumstances. A very small change in toe is equivalent to a 1-psi change in tire pressure so alignment is critical. The comparative effects of camber, aero force, and weight are also discussed.

OCLTA

SLIP SCHEMATIC

HIGH SLIP

LOW SLIP

r· -·· ·- ·-l I

SLIP MIIGL[

L

I NORMAL HARD

~~~~~~

__ j

'SLIP

~70.:

or

II'ACE:

CA9 91DE FOReE

Figure 3 Contact Patch Slip Schematics The slip deflection in Figure 3 is for an individual particle. When individual particles are connected the maximum slip deflection decreases as shown in the appendix. The realistic deflection-slip model is almost identical to that of Dixon121 • The Hallum model says there are a large number of small slips occurring at the observed maximum deflection (and that deflection is not the maximum friction value). The heat generated by these slips is used to predict performance changes and limits of the tire.

Figure 2

Camber force has no slip so there is no slip heating in the CP associated with camber force. Camber force is free (of CP heating). In racecar tires this is true to at least 5 degrees of camber. Figure 4 is a schematic of a tire circumferential section with camber. As the tire rolls the tread rubber contacts the ground and follows a straight line path to where it lifts off the ground. The carcass however wants to follow a path closer to the inclined free carcass periphery. If viewed from above (vertical to ground) there is an area between the· two paths. That area is equivalent to a side force (area) defined as camber force. There is no slip.

Tire and Contact Patch

BACKGROUND The tread contact patch (CP) is shown in Figure 2 and Figure 3. Figure 2 includes a depiction of the carcass and Figure 3 shows the macro schematic of slip within the CP. Each slip of a tread surface rubber particle generates heat. In normal race tires the heat generated 1

The loss components of the total energy loss of working tires are:

Bracketed numbers are listed references

16

There are three ways to look at the effects of the changes to be discussed. The three ways are:

1.

SLIP FRICTION loss at the CP interface due to the traction vector and sliding 2. TREAD MOMENTUM loss at the front of the CP, impact momentum that is not used 3. CARCASS and TREAD Internal Friction losses due to strains within the tire 4. SURFACE HYSTERESIS losses due to road surface indentations

1. Hold the steer angle or slip constant. Holding slip constant and comparing F. /Wt, or just F., tells how steering feel will be affected at initial turn in or for short-term side force requirements. Looking at HF tells whether that F. can be held through the turn or whether it will change. 2. Keep F. constant. Holding F. constant and comparing HF shows if grip will improve (HF down) during cornering or grip will go away (HF up). 3. Keep HF constant. Keeping HF constant and comparing F. /Wt, or F., gives a better idea of the steady state performance change to expect.

Only Slip Friction is analyzed for short track application. · The Tread Momentum term is much smaller (about an order of magnitude) than the Slip Friction term on short tracks. The "other'' energy losses are not discussed because they are smaller in relation to the losses that are discussed. The first two losses, Slip Friction and Tread Momentum, are mechanical losses and are the more significant losses in race tires. The last two losses, Internal Friction and Surface Hysteresis, are internal and are dependent upon tire construction and properties. A race team tire engineer has some control over the first two losses and very little control over the last two.

Tire performance Method 2 is the most useful. The HF change shows if the tire will run cooler or hotter. HF changes more than F. because of the slope difference and is more obvious. EFFECT OF 1 PSI Side force (F.) and heat factor (HF) versus Percent Slip for 2250 lbf Load and 1000 lbf Load are given in Figure 5 and Figure 6 respectively. Curves for tire pressures 4 psi above and below the operating pressure are shown in the figures. These curves allow visualization of an HF change equivalent to 1 psi. The driver can definitely "feel" car handling change related to a 1-psi change. HF changes cause an outside tire to ''go away" (overheat), or cool and gain grip. Figure 5 for the 2250 lbf load is presented first because a Reference HF must be selected that limits tire performance. The outside tire has a higher load with higher pressure and reaches the limiting tire temperature first. The HF limit is in the "knee" of the F. curve. A value of about HF = 0.014 is a reasonable assumption for calculations. In Figure 5 the selected limiting operating condition is HF = 0.014163 units at 2250 lbf load, 44 psi, and 4.8% slip. Choice of this operating point is explained later. At these conditions the side force area is F.= 0.30922 in2 •

TOP VIEW TREAD FORCED PATH ~

Figure 4

Tire Camber Schematic

PARAMETER EFFECT ON TIRE PERFORMANCE Tires in NASCAR racing are heavily loaded and tire heating is more significant than in other forms of racing. Car adjustment parameters for NASCAR tires are compared on the basis of slip losses and slip generated heat. The analysis presented is applicable to short tracks where rolling resistance is less important. If the car can run faster in the corners lap. time will reduce. Baseline cornering loads are assumed to be 1000 lbf on the inside tire and 2250 lbf on the outside tire. These loads represent nominal cornering conditions at short and intermediate NASCAR WC ovals and include banking "g" loads, typical load transfer, and aero loads at a reference speed. Front and rear loads are assumed the same. Operating tire pressures are assumed to be 36 psi on inside tires and 44 psi on the outside tires.

A key observation about Figure 5, and the other tire performance figures, is that near the limiting operating condition F. is rising slowly and HF is steadily increasing. Around 5% slip the slope ratio of HF to F. is about 5:1. Lots of heat is generated for little F. gain. If tire pressure is reduced to 40 psi and the car is run at the same speed with the SAME tire load the same side force MUST be produced, F.= C, to turn the car. For F.= 0.30922 in2, P =40 psi, and Load= 2250 lbf, Slip and HF at the new condition areS= 3.93% and HF = 0.011705 units. For the 4-psi pressure reduction HF reduced 0.00246 units. For a 1-psi reduction HF drops 0.00061 units (a 4.3% reduction) at the same speed. A 4.3% reduction in HF is significant.

17

handling is based on how all four tires work together to turn or accelerate the car. Other tires dilute the affect of one tire.

2250 LBF LOAD; 44, 48, 52 PSIG

o.35 0.30

-/) v 'J.V

0.15

,//

0.10

)

o.05 0.

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~~

o.25 o.20

,..._ /_'. VV'

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v

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-~

v

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- -- ~

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_v

0.025

v· ~

0.020 0.015

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3

t; if

Camber force (area) is added to the slip area in the CP, but slip is not increased. Figure 7 shows F. and HF for a tire with 2250 lbf load, 40 psi and 44 psi with 0 degrees camber, and 44 psi and 4 degrees negative camber. F. area with negative camber increases significantly for no increase in heating compared to the 44-psi curve. At the reference condition of 4.8% slip, zero camber, and 44 psi the side force and heat factor are F. = 0.30922 in2 and HF = 0.014163 units. The 4-degree negative camber curve shows that F. = 0.31461 in2 at the same HF and same 4.8% slip (remember camber doesn't affect slip and HF).

i

0.005

""" 2

EFFECT OF NEGATIVE CAMBER

~

4

5

6

7

8

0.000

Pa:ICB'fl' SIDE SLIP -· Fs44 - o tF 44

-+ Fs52 --t> HF 52

---Fs48 -a- tF 48

Fs & HF vs. SLIP

FIGURE 5

2250 LBF LOAD, 40 & 44 PSI

At the same HF the side force increases to F.= .31912 in2 with a 4-psi decrease, a 3.2% F. gain. For a 1-psi reduction F. goes up 0.8%. Change in F•• with HF = C, is a much smaller percentage than the HF change above because the slope of the HF curve is much higher than the F. curve in Figure 5. The F. gain gives us a little better idea of the potential performance or velocity gain. Required F. goes up with the square of the velocity. Car speed cannot quite increase this much because HF must be multiplied by velocity again to get energy. Energy is the ter~ that really must be held constant. An approximation of the velocity gain is the cube root of the F. gain. For this example cornering velocity might increase 0.27% (1.0027"3=1.008).

0.35

0.30 o.25 0. 20

_,d ~

...

o.10 jl 05 0. r, 0....... 0

-

FIGURE 7

-

.--

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v

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1

2

3

4

5

6

7

8

FIGURES

---Fs36 -a- tF 36

2

v

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6

7

8

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0.005 4

~

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9

i

0.000 10

Fs ·4,44 tF ·4,44

- .. Fs 0,40 - G HF 0,40

-+ Fs 0,44 HF 0,44

Fs & HF, 0 DEG & ·4 DEG CAMBER

The 4 degrees of negative camber gives a 1.7% F. gain for the same heating at reference conditions. A 1-psi pressure decrease at zero camber gives a 0.8% F• increase at the same HF, so 4 degrees of negative camber is equivalent to about a 2-psi pressure decrease. So, 2-degrees of negative camber is equivalent to a 1-psi tire pressure decrease.

....(,)~ if

i

EFFECT OF LOAD

Pa:tCBfl' SLIP -• Fs32 - o tF 32

~

~

_v

/

Pa:ICB'fl' SIDE SLIP

1000 LBF LOAD; 32, 36, 40 PSIG 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000

v

1

vi 0.030

.V

l'

0. 15

0.035

-

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'~

-

0.16 o.14 i--:::: ~ 0.12 - / ..--_.) 0.10 / .,::.-::; ..:::::-'/ o.08 -// 0 ~ 0.06 ~v 0.04 :.-1~/ ;1 0.02 V" 0. vv• /~ ~

~~

To evaluate load effects on the outside tire, cornering load is increased to 2300 lbf. Figure 8 shows F. and HF for 2250 lbf Load and 40 psi and 44 psi as well as 2300 lbf Load and 44 psi. The effect of the 50-lbf increase can be compared to the effect of a pressure change at different slip ratios. Figure 9 shows F. and HF for 1000 lbf Load and 36 psi and 32 psi as well as 1050 lbf Load and 36 psi.

-+ Fs40 --t> HF 40

Fs & HF vs. SLIP

If tire pressure is changed on the inside tires similar F. and HF shifts occur. But left side tire HF values are not critical. Inside tire performance is not about to "go away" when the nominal HF is below 0.01 units. Tire performance limits are right side tire dependent but left side tires can "load" or "unload" right side tires. Car

Load can be either mass or force. A 50 Ibm (mass, or lead weight) can be added to the load on a tire, or a 50 lbf (aerodynamic load with no mass) applied to a tire. 18

effect of adding 50-lbf force, a 5% change, is to increase F. 7%. The side force increases more than the weight, but again HF also increases. At constant HF both Wt and F. increase by 5%. If aerodynamics cause the load increase the F. increase is equivalent to reducing tire pressure 3.1 psi and a 1-psi decrease is equivalent to 16-lbf aero force at the 1000 lbf conditions.

Side force area calculated based on load does not know the difference. Analysis of cornering "g's" takes into account the difference. For example the Reference conditions are a total front load of 3250 lbf, but the front mass is about 1800 Ibm. The difference being "g" and aerodynamic forces. 2250-2300 LBF LOAD; 40 & 44 PSIG

1050 LBF-36PSI & 1000 LBF-32136PSI

o.35

0.035

0.30

0.030

-~ ~

0.25 /

0.20

/-"

-~

0.1o

.v II

0.05

J

0.15

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lZ'" ~

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3

~

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5

6

7

8

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0.12

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0.

PERCENT SIDE SLIP -.- Fs44,2300 -a- Fll40,2250 -+-e- HF44,2300 -o- HF40,2250 +

FIGURE 8

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et!f.

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4

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Pa:ICENT SIDE SLIP -a- Fs32, 1K -+- Fs36, 1K

Fs44,2250 HF44,2250

-.- F836,1050 -e- HF36,1050

Fs & HF vs. SLIP

FIGURE9

Aerodynamic load on one tire is evaluated first to show effects of load on side force. Figure 8 shows the outside tire performance for Baseline and 50 lbf added. In the region of 4.8% slip it can be seen that the effect of adding 50 lbf is about equivalent to reducing pressure 2.5 psi with no weight or mass change. Detailed calculations show that 50 lbf is equivalent to 2.54 psi tire pressure reduction when keeping HF constant. Figure 8 shows the equivalency factor is about the same no matter if HF or F. is held constant. A 1-psi decrease in pressure is equivalent to an aerodynamic force of about 20 lbf.

-B-

HF32, 1K

+

HF36, 1K

Fs & HF vs. SLIP

Performance at 1000 lbf load is reasonably important because this condition is near corner entry conditions, on both front tires, before load transfer and "g" conditions change. If aerodynamic load comes up 5% the car will turn in better. If weight is added the car will still turn in better, but the tire will soon overheat unless load is taken off the outside tire. Load can be taken off one tire by proper use of springs, stabilizer bars, or track bar adjustment. Additional evaluation of weight effect on tire performance is given in the Appendix. The Hallum macro-slip model predicts F. increases more than load during dynamic conditions. However the improvement in F. cannot be maintained because the tire will overheat after some number of revolutions.

Let's look at adding 50 Ibm of weight to achieve the F. increase and evaluate the effects at fixed slip, constant FjWt, and constant HF. Assuming that the original load was due to 2250 Ibm weight, the 50 Ibm weight increase is 2.22%. At fixed slip' F. increases to 0.31774 in2 , a 2.76% gain, but HF increases. At constant HF the F. area increase is 2.22% (0.31609 in2 at 4.69% slip compared to 0.30922 in2 at 4.8% slip). Constant HF is the constant FjLoad condition and same corner speed.

EFFECT OF PARAMETERS ON CAR PERFORMANCE

Inside and outside tires are connected and generally point in the same direction. The analysis above varied the slip percentage to match HF or F. on one tire. HF or F. match on two connected tires (right and left) is not probable so car performance results are slightly different than shown above.

Steering ''feel" is a little better with the added weight and turn in slightly better. Once into the corner steering angle should be reduced to keep HF the same. Car velocity in the corner is identical at the same HF with the added weight. With banking "g" load a 50 Ibm can give an 80-lbf load change (see Table 6 next section) and corner speed can increase slightly.

CAR PERFORMANCE, TOE EFFECT A typical NASCAR front end set up is assumed initially and then changes made to observe performance changes. A typical front steer cornering condition is 2250 lbf, 44 psi, and 5% slip on the right front (RF); and 1000 lbf, 36 psi and 4.5% slip on the left front (LF). These are set up numbers for "uncompensated" front steer cars I

Figure 9 shows inside tire performance for 1000 lbf load and for 50 lbf added. The effect of 50 lbf on the results is larger at the lower load conditions as one might expect. At a constant 4.8% slip, 1000 lbf load, and 36-psi the

19

have seen on set up sheets. This is called 1OOA, negative Ackerman (inside tire slip angle 10% less than theoretical). Crew chiefs add static AND bump toe out to compensate for toe in at steer angles, see reference [3].

fraction of total F•. R Side HF increases 0.0004 units and the R side tire still overheats when L side tire pressure is increased. Tire loads were kept the same in Table 2. Is this disguising something?

At the above front-end "typical" condition the tire side forces and heat factors are derived from Figures 5 and 6 and are shown as the first set of numbers in Table 1. At this reference condition the RF tire is assumed to be running above its HF limit (want correct Ackerman to be Baseline). For proper Ackerman the slip percentage (angle) of both right and left tires is the same. calculation results of the slip percentage to get the same side force area, as the typical set up, is the second number set in Table 1. The slip is 4.8% to get the same F,. With the same F. corner speed is the same and the R front HF has reduced 5% or 0.00075 HF units. The 4.8% slip on both tires is the BASELINE condition.

CAR PERFORMANCE, LOAD SHIFT DUE TO 1 PSI Some people claim 1-psi changes load a huge amount. Tire, s,pring rate increases about 50 lbf/in but there is a spring hooked up to that wheel. A 1 psi increase (44 psi to 45: p13i) with a 2250-lbf load increases axle height about 0.01 inches (see Appendix). If the wheel mechanical spring rate is 1000 lbf/in (high, gives high load shift, and· all wheels the same) load increases is about 10 lbf. Load now redistributes. Assume the right rear (RR) pressure was increased 1 psi. The rear weight did not incn:»ase so the rear wheel loads become RR +5 lbf and LR -5 :lbf for a 10-lbf differential on the rear. Since the ch.sis is rocked over a little the LF has +51bf and the RF -5 lbf. There is no weight shift right to left or front to rear. For a 1 psi RR pressure increase the front tire loads shift as noted. Load shifts for a LR pressure increase are the opposite.

With excess Ackerman the L.F. slip is 1.1 times that of the R.F. The third set of numbers in Table 1 is for the excess Ackerman condition. The R.F. HF has reduced more, another 0.00067 HF units, giving a cooler running RF tire than the Baseline, correct Ackerman condition. Note the excess Ackerman condition has total HF lower than with proper Ackerman. CAR PERFORMANCE, PRESSURE EFFECT Front end and rear end tires are assumed to have the same weights and loads. Table 2 shows Baseline correct Ackerman conditions as the first set of numbers. The second set of numbers is for increasing the outside tire pressure 1 psi and changing steer slip percent to achieve the same total F, to corner at the same speed. The RF tire HF goes up 0.0003 units (...2%) indicating that the RF tire will overheat. Note that the steer angle had to increase ·and the LF tire F. is higher. Based on single tire information we expected a bigger HF change (double). The real HF change the driver "feels" is closer to the aHF = 0.0003 unit shift.

Table 3 shows the Reference side forces and heat factors with the second number set for a 5 lbf force load shift to the right. In Table 3 pressure is not Increased so the changes due to load shift can be evaluated independently. For the S~lbf shift the R side HF increased o.ooo04 units. The HF increase is an order of magnitude smaller than the shift for 1 psi (and no load shift). The driver may not even "feel" this load shift. A crew chief told me his driver could "feel" a 15-lbf load change. The 15-lbf load change would triple HF shift giving a change closer to a 1-psi pressure ch~nge that we·know drivers can ''feel". ·

Now let's increase the inside tire pressure by 1 psi rather than the outside tire. The third set of numbers in Table 2 show conditions to .get the same total F,. The steer angle percent changes a little, but the big thing is the inside tire F. decreased, forcing the R side tire to take on a larger 20

Looking at a 5-lbf load shift to the L side, the third set of numbers in Table 3, it is seen that R side HF does decrease. But again the decrease in smaller than perceptible to the driver. Car performance change is small for the 5-lbm shift of a 1-psi tire pressure change.

If 50-lbf load at the rear were shifted to the left the third set of numbers would occur at the rear. With RR running cooler the car would tend to understeer. Then there is the front load shift that tends to overheat the RF tire. The car may really push. Load jacking, or wedge, affects both ends of the car.

CAR PERFORMANCE, 1 PSI & 5 LBF CHANGE TA8LE5 IWi IOH1'.1ACKINGorLOADSHFT

Table 4 shows how front or rear overall capability changes when 1-psi is added to either to RR or LR (change is the same for RF or LF) tire. In this table the load shift associated with the pressure increase is included. The first set of numbers is for the Baseline condition for reference.

WH · lbl

RFor RE 2250 LF or Lfl. · 1000 101118

44

4.8 0.309:!2

36

4.8 0.12012

44

4.8 0.31774 4.8 0.11219 0.42993

0.005138 0.019891

4.8 0.80070 -..:t_

.•

0 ;z; -0.1

r---;_ ~

...

-

I

-0.2 I

-0.3

0

2

3

s

4 NORMALIZED SLIP ANGLE

111

LOAD, N: 806

•

•

6008

+ 8000

FIGURE 11

6

,.

2406 _

7

4010 MAGIC FORMUlA FIT

NORMAliZED SELF ALIGNING TORQUE

54

8

9

0

-2

~

\

z

~

-4

z

...__ ..._

~

~

at.;g ()

0"

" ::1"

"'~

i

...

..

....._

'-

-6

-8

-10 0

2

6

4

8

10

12

14

SLIP ANGLE, DEG •

+

LOAD: 806 N

,.

2406 N

4010 N

FIGURE 12 RECONSTRUCTED LATERAL FORCE- LOW LOADS

0

-2

z

~

tll

z

-4

at.;g

~ ~

" " 9

()

~

~ .

'~

!2 ~

.

~

-6

-8

~

r----~

I

-10

2

0

6

4

10

8

12

SLIP ANGLE, DEG •

LOAD: 4010 N (DATA)

+

6008 N (DATA)

,.

8011 N (DATA)

FIGURE 13 RECONSTRUCTED LATERAL FORCE- HIGH LOADS

55

14

300

200 :::1! I

z

ttl'

;:J

?1 ~

0

100

~ ~

0

~

tlJ VI

0

~

~

~ ~ ....._

.

-100 0

4

2

•

LOAD: 806 N

6 8 SLIP ANGLE, DEG •

2406 N

10 "'

12

4010N

FIGURE 14 RECONSTRUCTED SELF ALIGNING TORQUE- LOW LOADS

200 :::1! I

z

ttl' ;:J

0

g 0

100

25

z0

~

~

VI

0

-100 L-----~------~-------L-------L------~--~--~----~ 4 0 2 6 8 10 12 14 SLIP ANGLE, DEG •

LOAD: 4010 N

•

6008 N

"'

8011N

FIGURE 15 RECONSTRUCTED SELF AUGNING TORQUE- HIGH LOADS

56

CHAPTER 2 SUSPENSION DESIGN

962531

Effects of Suspension Geometry and Stiffness Asymmetries on Wheel Loads During Steady Cornering for a Winston Cup Car Kent A. Day and E. H. Law Clemson Univ.

Copyright 1996 Society of Automotive Engineers, Inc.

tools predict the normal loads and tire camber for Winston Cup cars running on banked tracks. If tire force data are available. these tools can also predict the side slip angle of the car. the front wheel steer angle. and the level of understeer. This is particularly useful in evaluating different setups for "tight" or "loose" handling. Provisions are included in the model for evaluating the effects on tire load and camber of asymmetries commonly designed into this type of race car. These asymmetries include spring split {different rate springs on the left and right sides). offset center of gravity. unequal lengths of the right and left side upper and lower control arms. etc. For certain suspension configurations both the lateral and vertical position of the front roll center varies significantly with body roll angle and vertical displacement (or bounce) - and hence \\'ith lateral acceleration and track bank angle. The lateral position of the rear roll center is not very sensitive to body roll and bounce: however. the vertical position can change. These effects together \'r'ith the changes in tire camber and steer angle v.ith body roll and bounce are included in the model. The modeling tools developed and described below require measurement of the chassis and suspension components as well as the rates of the suspension springs and anti-roll bars. The software and measurement techniques are completely integrated. This allOl'i"S the user of the model to perform "what if' analyses by changing the suspension components. suspension attachment points. and/or the spring and anti-roll bar rates. The user can then analyze the resulting kinematics and wheel loads. If tire force and moment data are available. the model l'.'ill also calculate tlte steady state side slip angle of the vehicle and predict the level of understeer. Two cars \\ill be studied to illustrate the application of these techniques. These are a standard Hopkins "left tum" car and a modified version of the standard car in which the suspension geometry has been altered to provide better control of the front roll center. The cars \\ill be analyzed in steady state cornering (no longitudinal acceleration) on a 24 deg banked track. typical to speedways at Charlotte. NC and Atlanta. GA. For each of the two cars. the effects on tire normal loads and tire orientation (camber and steer angle) l'.ill be investigated as the follo'\\1.ng parameters are varied:

ABSTRACT Tuning a race car for good handling requires accurate prediction of the tire normal loads and tire orientation as specified by steer and camber angles. This paper describes the development and examples of the application of computer models which have been developed to predict suspension geometry characteristics and wheel loads for Winston Cup cars running on banked tracks. Example cases are presented illustrating the effects of roll center movement, front spring split (different rates right to left). and cross weight percentage {wedge). INTRODUCTION The highly competitive nature of NASCAR's (National Association of Stock Car Auto Racing) Winston Cup Series along l'.'i.th its limitations on testing (seven tests are allowed per year) and over 30 races per year at 18 different tracks provides a need for efficient computational tools which can predict the handling characteristics of a given chassis setup (i.e .. specification of suspension geometry. spring and antiroll bar stiffnesses. and shock absorber configuration). These tools can then aid in tuning the car for improved handling performance. In this series. teams are allowed as little as two hours of practice to set up the car prior to qualifYing. During this practice. the use of data acquisition equipment is prohibited. Despite the fact that two races are held at most of the tracks each year. the setup for a car to be used on a given track often varies for the two dates for many reasons. These can include climatic differences. tire differences. and changing requirements for the car issued by the regulating body. Since the lateral force between the road and the tire is strongly dependent on the orientation of the tire (camber and steer angles) as well as the vertical load on the tire. suspension tuning of a car for good handling requires a thorough understanding of suspension geometry or kinematics and proper management of the tire normal loads. Chassis measurement techniques and accompanying computational tools developed for suspension analysis and tuning of Winston Cup cars are described in this paper. These

59

A steady state load model of a typical Winston Cup car configuration was developed which uses information from the kinematic model as input to predict the tire normal loads. The model has seven degrees of freedom. These are: (1-3) vertical pitch. and roll displacements of the sprung mass. and (4-7) vertical displacement of each of the four wheels. The steady state load model requires that the user input the e>..1ernal inertial and aerodynamic forces and moments acting on the vehicle. This is accomplished by specifying the

were set to keep the solution algorithm from considering physically. unrealistic conditions. ~b and ~ are vectors that specifY lower and upper bounds on the acceptable solution. Aerodynamic data should be configured in a lookup table that lists the aerodynamic force and moment coefficients as a function of the car attitude and orientation relative to the track. The lookup table is accessed during the iterative solution of the nonlinear algebraic equilibrium equations. The final solution will include the actual aerodynamic forces specific to the final orientation and attitude of the car. Aerod~'namic loading is not considered in the examples presented below as appropriate data were not available for the vehicles being considered. The model calculates the tire loads acting on the vehicle required to maintain static equilibrium on a cwve of specified radius and bank angle at a specified speed. These include: ( 12) the "front axle" and "rear axle" lateral forces exerted on the car by the track. and (3-6) the vertical load exerted on each tire by the track. As mentioned above, the kinematic and static load models represent a typical Winston Cup car configuration. The physical features of the models include double A-arm front suspensions and a solid rear axle \\'ith long trailing anns typically referred to as "truck arms". The rear axle is typically set up with camber and toe. A Panhard or track bar is used as a lateral locating device for the rear suspension. Anti-roll bars can be used for both the front and rear suspensions. All four of the upper spring perches are adjustable for "wedge" allowing change ofthe static wheel loads. VALIDATION OF THE STEADY STATE LOAD MODEL - To assess the accuracy of the model. a car with known geometry and spring rates was tested on a static test rig. In this test, the chassis of the vehicle was held fixed and displacements were input to the tires at the contact patch. Wheel loads and tire camber were measured. Two types of tests were performed: (1} a ride test and (2) a roll test. For the ride test. all four wheels received simultaneous displacement inputs at the contact patch of +I· 1.5 in about a nominal condition of 1 in rebound for the front suspensions and 2 in rebound for the rear suspension. A complete hysteresis loop was performed. In the roll test chassis roll was simulated by inputting displacements of equal magnitude but opposite sign to the left and right side contact patches. Roll motion was simulated over a range of +!- 2 deg. As with the ride test a complete hysteresis loop v..'as generated.

centripetal acceleration of the ''ehicle, the track bank angle.

Hysteresis in the system is primarily a result of friction in the

and the aerodynamic down force and pitching moment acting at the sprung mass center of gravity. The conditions for static equilibrium of the car result in a set of nonlinear algebraic equations of the form:

suspension pivots. The results ofthe validation test are shown in Figures 13. All of the plots show the change in the response parameter relative to the initial start condition (1 in rebound in front 2 in rebound in the rear). Figures 1 (a) and (b) show measured and model predictions of tire camber angle for the left and right front wheels respectively. As can be seen, the largest error is on the order of 0.3 deg. This error is of the magnitude ex-pected considering the accuracy of the present methods for measuring the suspension points and components. Measured and predicted values of tire vertical loads are shown in Figure 2 for the ride test. Hysteresis in the measured data has been removed by averaging. As can be

(a) roll center location and its dependence on chassis roll angle and vertical deflection. (b) front spring split and (c) wedge or cross weight. CHASSIS GEOMETRY MEASUREMENT

The modeling and computational tools developed for predicting wheel loads. tire camber and steer are integrated with a detailed procedure for measuring and analyzing the chassis and suspension geometry. The kinematics and steady state tire load models require detailed information describing the geometry of the chassis and suspension components. The car can typically be measured in one day by two people. The coordinates (x.y,z) of 48 chassis and suspension points are measured relative to a level surface plate. The front suspension components are measured off the car on a fixture designed by Ford Motorsports called the "Spindle Indexing Fil!.ture" or SIF. The SIF allows the spindle geometry (in particular. the location of the upper and lower ball joint centers) to be accurately measured. To accurately predict the tire nonnal loads, the rates of the suspension springs must also be measured along with the torsional stiffness of any anti-roll bars. SUSPENSION GEOMETRY ANALYSIS AND MODEL

To calculate changes in wheel camber, steer. and other kinematic parameters such as roll center location as a function of chassis position, a complete 3-D kinematic model of the entire car was developed. The model uses specifically formatted data acquired from measuring the car. making it easy to study the effects of different suspension components and changes in suspension attachment points. STEADY STATE LOAD MODEL

EW=Q

(1}

These are solved using a sequential quadratic programming technique as implemented in MATLAB [ 1]. In solving the equations. constraints on the solution of the form:

{2)

60

measurements of the car and subsequent processing by the kinematic analysis model). As mentioned above. two cars will be used as examples of the analysis procedures developed in this project. These are a standard Hopkins "left turn" car and a modified version of the standard car in which the suspension geometry has been altered to provide better control of the movement of the front roU center. Table 1 sununarizes the nominal setup parameters common to both

seen. the model agrees well with the predicted results. The maximum error in wheel load prediction is about 3%. Results of the roll test are shown in Figure 3 for all four wheel positions. Again. excellent agreement exists between the model and the measured values with a maximum error of approximately 1%. It should be noted that for the rear suspension. the auxiliary roll stiffness of the rear axle/truck ann assembly had to be determined and input to the model. The structure of the rear suspension is such that roll resistance is produced by bending and misting of the trailing arms independent of the suspension springs. Determination of this auxiliary roll stiffness was accomplished by calculation of the rear roll stiffness due to the suspension springs and comparison of this value \\ith the measured rear roll stiffness which included contributions from the suspension springs and the auxiliary roll stiffness. For the test car, the rear roll stiffness v.--as calculated as 295 ft-lb/deg and the measured "total" rear roll stiffness was 407 ft-lb/deg. This implies an auxiliary rear roll stiffness of 112 ft-lb/deg.

cars. Table L Static Setup Parameters. Parameter Front Toe (dee:) Rear Toe {deg) Front Caster (deg) Front Tire Camber (deg) Rear Tire Camber (deg) Front Chassis Heiibt (in} Rear Chassis Heiibt (in) Tire Stiffness (lb/in) Front Anti-Roll Bar Dia. (in) Rear Anti-Roll Bar Dia. (in) Front Spring Rate (lb/in) Rear Sprin_g Rate (lb/in) Wheel Loads, Front (lb} Wheel Loads, Rear {lb)

CALCULATION OF SIDESLIP AND FRONT STEER ANGLE The ability of a tire to generate a lateral force (at a given slip or steer angle) is strongly dependent on the normal load between the tire and the road and the tire camber angle. Both of these are outputs of the steady state load model. The amount of load transferred from the inside tires to the outside during cornering is a function of the height of the center of gra,.ity (CG) and distance from left to right wheel centers (track). The amount of load transfer for the front and rear tires is governed by the roll stiffness of the front and rear suspensions as well as the roll center locations of each. Generally speaking, load transfer decreases the lateral force capability of a pair of tires for a given slip angle (however, there are tires for which this effect can be very small). Typically. the total roll stiffness would be selected on the basis of the permissible amount of body roll. The roll stiffness distribution (percentage front to rear) would then be chosen to provide acceptable handling attributes (understeer, oversteer, side slip angle} for the operating environment of the vehicle. To illustrate the calculation of steady state handling parameters, an example will be given using some race car tire data. To predict the handling characteristics, representative tire force and moment data is required. Typically, tire lateral force is given for a range of slip angles, camber angles. tire pressure and normal loads. Tire aligning moments will not be considered as their effect on vehicle handling is negligible. Sample tire data is shown in Figure 4 for one camber angle, one tire pressure and a range of normal loads. A variety of mathematical techniques have been developed for efficient handling of these data [2,3]. However, for this simple example, linear interpolation will be used and camber effects \\ill be neglected (i.e .. the camber will assumed to be zero for all wheels). The process begins by using the steady state load model to predict the tire normal loads and per axle lateral forces (assuming that kinematic data has already been obtained from

Left

0 0 +5.5 +3.5 +1.5 6 6.75 2500 1.125 0 1200 350 936 864

Right 0 0 +5.5 -3.5 -L5 7 7.75 3500 1.125 0 2000 375 841 759

For the standard car, the following tire normal leads were obtained for the condition of traversing a 24 deg banked tum with a centripetal acceleration of 1.4 g's: Left Front: 827lb, Right Front: 1804 lb. Left Rear: 952lb. Right Rear: 1460 lb.

The per axle lateral forces were 1547 lb for the front and 1418 lb for the rear. Having the normal loads for each wheel and per axle lateral loads. the corresponding slip or steer angles can be obtained by interpolation in the tabulated tire data which lists lateral force versus slip angle for a range of normal loads. It is important to note that if tire camber data were available. a second interpolation for camber would be required. The procedure for the rear axle is as follo\\"S. (1) A table or curve of lateral tire force versus slip or steer angle is constructed for both left and right wheels for the particular normal load for each wheel. This is done by interpolation over normal load. (2} As the steer angle of the left wheel with respect to the right is known and is due to the relative toe (which is known for the roll and bounce displacement calculated by the steady state load model). the lateral forces of left and right wheels may be added to give the axle force as a function of either the right wheel slip angle. the left wheel slip angle. or the average slip angle, a,.. Thus a curve or table of axle lateral force versus any of these three slip angles may be constructed. Since the total rear axle lateral force is known from the steady state model, the corresponding a,. can

61

be found by interpolation in the table. sideslip angle is then given by:

J3 =

1~ R" -a.

2. The length of the upper section of the spindle, from the axle center to the upper ball joint was lengthened by 1 in. 3. The right upper A-arm attachment points were moved 0.25 in inward towards the vehicle centerline and 0.25 in downward. The ann was resized from an original length of 7.875 in to 8.1875 in. 4. The lower arms were rotated 4 deg downward about a longitudinal axis passing through the lower ball joint center. This resulted in lowering the lower arm attachment points by 0.75 in for the front pivot and 0.45 in for the rear pivots. Figure 5 shows the change in the lateral and vertical position of the front roll center for both cars over a range of centripetal accelerations on the 24 deg bank. For the turn radius used in the simulation {1025 ft), -2 g's of centripetal acceleration corresponds to approximately 175 mph. Positive values of lateral position are to the right of the vehicle centerline as determined by the center of the main frame rails. As can be seen. the modified design considerably reduces front roll center movement in both the lateral and vertical directions. The roll center of the modified car never moves more than 3.5 in to the right of centerline whereas that of the standard car moves to the right front contact patch approximately 30 in to the right of centerline. The change in height of the roll center also is significantly less for the modified car. decreasing from its initial height by only 0.2 inches. The front roll center height for the standard car decreases rapidly to ground level as the roll center passes through the right front contact patch. Figure 6 shows the location of the rear roll center for both cars. The rear suspensions for both cars are identical. As can be seen. the differences between the two cars are not significant. The small differences seen are due to small changes in roll stiffness caused by the different front suspension geometry which in tutn causes the vehicle to stabilize at slightly different attitudes for a given centripetal acceleration. These will be discussed in the following section. Figures 7 and 8 show the camber and steer response of all four wheels. For the simulation. the steering system was not moved, hence the changes in steer shown in Figure 8 are due to vertical displacement roll. and pitch of the chassis. As can be seen. the modified design does not significantly alter the wheel orientation from that of the standard car. The maximum difference in camber is approximately 0.2 deg and much less for steer angle at 0.02 deg.

(3) The vehicle

(3)

where 13 is the sideslip angle. h is the distance from the rear axle to the CG of the complete car. and ex,. is the average slip angle for the rear axle. The term R * is given by:

(4) where R is the radius of the turn measured parallel to the horizontal and ~ is the track bank angle. The steer angle for the front axle is then obtained in a manner similar to that followed for the rear axle. The relative steer angles of the left and right wheels are related by relative toe and anv Ackermann effect designed into the steering system. C~mpliances in the steering system are considered negligible for a properly designed steering linkage. Once the curve or table of lateral force versus slip angle (right, left, or average) is obtained for the front axle with the appropriate normal loads for right and left wheels. the slip angle for the knO\m lateral force can be determined. The average steer angle. 8. for the front wheels is then: (5)

where 11 is the distance from the front axle to the CG of the complete car and a.r is the average slip angle for the front wheels. Vehicle side slip and the front tire steer angles are two of many parameters that can be used to study the steady state handling characteristics of race cars (3). The front tire steer angles. when compared to the neutral steer angle give an assessment of understeer/oversteer beha\'ior. Larger front steer angles than the neutral steer angle indicate understeer whereas smaller front steer angles (than the neutral steer angle) indicate oversteer. The side slip angle of the car may also have a significant influence on the driver's perception of the handling. EXAMPLE CASES

EFFECTS OF ROLL CENTER MOVEMENT ON ROLL STIFFNESS - As \\'a& shown in the previous section. the roll center movement of the standard car is substantially different from tlmt of the modified car. To assess how this affects the tire normal loads. simulations were run for both of the cars over a range of centripetal accelerations vaJ)ing from -1.0 to -2.0 g's {left turn} on a 24 deg banked track. For all cases examined in this paper. aerodynamic loading was not considered since no data were available for this purpose. Figure 9 shows all four tire loads for both cars over the full acceleration range. As can be seen, the two cars have practically identical tire loads, indicating that the variation in roll center movement seen v.ith the two cars has a minimal effect. The maximum difference seen in wheel loads is approximately 8 lbs occuning equally at the front and rear

KINEMATIC COMPARISONS -Example suspension responses calculated \vith the model are shown in Figures 5 to 8 for t11e standard and modified cars being studied. The primary objective in the design of the modified car was to limit the movement of the front roll center both laterally and vertically while not severely affecting other suspension responses such as tire camber or steer. To convert the standard car to the modified car. the following changes were made. I. The left upper A-arm pickup points were moved outward from the centerline by 0.5 in and lowered vertically 0. 75 in. The upper arm was resized from its original length of8.875 to 9.375 in to maintain the same static camber.

62

As the amount of spring split decreases. the load transfer at the front decreases while the load transfer at the rear increases. This is due to changes in the roll stiffness distribution ·with the different setups. Table 4 summarizes the variation in roll stiffness for the three cases showing that the essentially constant rear roll stiffness becomes a greater percentage of the total stiffness with decreasing split. In general, this would be viewed as a "loosening" effect assuming that roll steer effects do not become significant due to larger roll angles caused by the lower total stiffness. Figure 11 illustrates the effect of front spring split on the attitude of the chassis. Due to the decrease in roll stiffness with decreasing spring split, about 0.3 deg more roll can be seen for the 1600/1600 case as compared to the 1200/2000 case. A very small effect can also be seen in the chassis pitch angle. For Figure 11 (b), a smaller negative pitch angle (more nose up) corresponds to the rear of the car being lower. For the small difference seen, the rear spoiler would be approximately 0.14 in lower for the 1200/2000 case as compared to the case "'ith no spring split.

tires. This observation is further explained by comparison of the roll stiffness distribution of the two cars. Table 2 summarizes the roll stiffness for the two cars. As can be seen. the standard car has a slightly greater total roll stiffness than the modified car by about 40 ft-lb/deg. The majority of this difference does appear to occur at the front of the car. However. its magnitude is small and only results in a 0.2% difference in the roll stiffness distribution. Table 2. Comparison of Roll Stiffness and Stiffness Distribution. Parameter Front Roll Stiffness (ft-Ib/deg) Rear Roll Stiffness (ft-lb/deg) Total Roll Stiffness (ft-lb/deg) Front/Total Stiffness (%) Rear!Iotal Stiffness

Standard Car 1705

Modified Car 1667

269

267

1974

1934

86.4

86.2

13.6

13.8

Table 4. Comparison of Roll Stiffness and Stiffness Distribution.

(%)

Parameter Front Roll Stiffness (ft-lb/deg) Rear Roll Stiffness (ft-lb/deg) Total Roll Stiffness (ft-1b/deg) Front/Total Stiffness (%) Rear!Iotal Stiffness

The load curves in Figure 9 illustrate unique behavior particular to cars cornering on banked tracks. As the car travels at higher rates of speed on the banked track, the load supported by the front and rear axles increases. This results in increasing load on the right side tires (with increased centripetal acceleration) at a greater rate than the left side tires are losing load. For the left rear tire, the increase in vertical loading dominates the lateral load transfer at the rear axle resulting in a slight increase in tire load with centripetal acceleration. This is a consequence of the particularly small rear roll stiffness. Also note that there is a difference in the slopes of the curves for the front and rear tires. More load transfer occurs for the front tires as the roll stiffness distribution is strongly biased to the front end of the car. EFFECTS OF FRONT SPRING SPLIT - The different front spring splits were evaluated using the model for the standard and modified cars. Very little difference was noted between the two cars. Therefore. only results from the standard car will be presented. These are illustrated in Table 3. The basic idea was to change the amount of spring split while maintaining the same vertical stiffness. Plots of the tire loads are given in Figures 10 (a) and 10 (b) for the front and rear, respectively. As can be seen there is little difference in the tire loads, a maximum of8lb for thel400/1800 case and a maximum of 17 lb for the 160011600 case. The differences are essentially the same in magnitude for all four tires. Table 3. Spring Rates Used to Study Spring Split Left Front Spring (lb/in) 1200 1400 1600

1200/ 2000 1705

1400/ 1800 1608

1600/ 1600 1482

269

271

271

1974

1879

1753

86.4

85.6

84.5

13.6

14.4

15.5

(%) EFFECTS OF VARYING CROSS WEIGHT PERCENT AGE - As was previously mentioned, the static load distribution of a Winston Cup Car can be modified by moving the upper spring perches (i.e .. adjusting the wedge) for any of the four suspension springs. Cross weight is expressed as the percentage of weight on the right front and left rear tires. Table 5 summarizes the distributions simulated with the model. For all but the last condition, the static weight on both of the left side tires is 1800 lb and the static weight on the right side tires is 1600 lb. These are the maximum allowed left side weight and minimum allowed right side weight, respectively. For all of the cases the percentage of total weight on the front tires (nose weight) is constant at 52.3 %. Simulation results are presented in Figure 12. It can be seen that cross weight percentage can be used to offset the resulting load transfer. Changing the percentage cross weight has the effect of reducing the load transfer at one end of the car and increasing it at the other end. For the first four cases studied, a decrease in cross weight percentage results in less load transfer for the front tires and more load transfer for the rear tires. This bas the effect of increasing cornering power

Right Front Spring (lb/in) 2000 1800 1600

63

the chassis attitude which could possibly influence the chassis aerodynamics.

at the front of the car and reducing it at the rear resulting in less understeer (looser) as the percentage is decreased. The last case (50%) which has equal left and right side weights is clearly at a disadvantage to the other cases. Significantly higher load transfer occurs at both the front and rear of the car as compared to the other cases. Comparison to the case of 50.1% cross weight and unequal left and right side weights. the 50% case shows 200 lb more of load transfer at the front and 150 lb more of load transfer at the rear. This would require the tires to run at higher slip angles to match the performance of the other cases.

4.

Table 5. Cross Weight Percentage and Static Wheel Loads Cross Weight (%)

50.1 49 48 47 50

LF

RF

Tire (lb) 936 955.5 972.5 989.5 888.5

Tire (lb) 841 821.5 804.5 787.5 888.5

LR Tire (lb) 864 844.5 827.5 810.5 811.5

Changes in static cross weight (wedge) performed

while maintaining the same left and right weight percentages as well as the front to rear percentages can be used to effectively to reduce the lateral load transfer at one end of the car while increasing it at the other. For the cross weight percentages studied. load transfer at the front of the car was reduced while it was increased at the rear which should act to loosen the car. The effect of wedge is linear across the entire range of centripetal accelerations. indicating that it can be treated as a -static" offset to the case of no wedge (equal right and left tire loads at the front and rear of the car). 5. While the effects of roll center movement and changes in spring split were shown to result in only small differences in tire normal loads (and therefore lateral load transfer) these small variations may make the difference between a tight or loose race car undergoing limit handling. Further testing is required to detennine a driver's sensitivity to the above changes.

RR Tire (lb) 759 778.5 795.5 812.5 811.5

REFERENCES

SUMMARY AND CONCLUSIONS

I.

Integrated modeling and computational procedures for assessing suspension geometry and prediction of tire nonnal loads have been demonstrated. The effects of movement of the front roll center. front spring split and wedge have been investigated for standard and modifie-d Winston Cup cars. For the modified car. the suspension geometry was changed to limit the movement of the front roll center. The cars were analyzed in steady state cornering on a 24 deg banked track over a range of centripetal accelerations from -1.0 to -2.0 g's. The turn radius was constant for all of the simulations at I 025 ft. This resulted in a maximum cornering speed of approximately 175 mph. Aerodynamic loading of the chassis was not considered as data was not presently available. For the cases examined. the follo\\ing conclusions may be drawn. I. The suspension geometry of the standard car was successfully modified to limit the movement of the front roll center without significantly changing the camber and steer response of the front wheels. 1. Simulations of both the standard and modified cars showed a minimal {8 lbs maximwn difference) effect on the tire nonnalloads. The small differences in front roll stiffness (about 2'X.l indicate that the front roll stiffness is primarily a runction of the spring rates and the spring locations. This is beneficial from a chassis tuning point of view. as no compensation due to roll center movement is necessary to keep a relatively constant roll stiffness. 3. Changing the front spring split also had a relatively small effect on the tire nonnal loads. the maximum difference being approximately 17 lbs for all four wheel positions. A 13 percent reduction in the front roll stiffness was seen as the spring split was varied from 800 lb/in to 0 lb/in. In general. the reduction in front roll stiffuess would tend to loosen the car (less understeer). Spring split did have a small effect on

2.

3.

64

Anon.. Optimization Toolbox Users· Guide. The Mathworks. Inc .. Natick MA 1994. Radl H. S .. and DA Glemming. "Normalization of Tire Force and Moment Data." Tire Science and Technology. TSTCA. VoL 21. No.2. pp. 91-II9. April-June. 1993. Milliken. William F .. and Milliken. Douglas L.. Race Car Vehicle Ih-namics. SAE. Warrendale. PA 1995.

3

.........__ 2.5 C>

2

~~ "(

Q)

"0 L..

1.5

~

Q)

.c

E

1

LL

0.5

ro 0

~

~

~

_J

0

~

-0.5 -o -1 .5

-1

.........

~

~e~s a e red'

-0.5

-1

0

0.5

1.5

1

Ride (in)

Rebound

Jounce (a)

-0.5 -1 ~

C>

-1.5

.............

4~

'i ~

Q)

"0

-2

~

Q)

.c -2.5 E ro

0

~

-3

~

LL

0::

-3.5 -4 -4.5

-o -5 -1 .5

~e~s a e

~

'

~red' -0.5

-1

0 Ride (in)

0.5

~J~ .....

""'

.......

1

Rebound

Jounet:

(b)

Figure 1. Ride Test, Measured vs. Predicted Tire Wheel Camber.

65

1.5

2200

2200

2000 800 600

v

400 200 000 8()'1

/

L

v

v

/

v

1800

@:1600

~ 1200

F

LL

0::1000

600

600

I~ ~~~ed

400

-1.5

..().5

-1

0 Ride On)

Jounce

0.5

/

vL

~.5

1.5

v

/

I~ ~~e:

I>: lol

.... ....

• • • • · RearSprings.

.00

~

• • • • · Rear Anti-Roll Bars

IOl ~

"'z

.00

• • • • · Rear Springs.

~

• " • " · Rear Anti-Roll Bars

~ -100.00

~ -100.00

g

...0

-200.00

-200.00 -1.5

-1.0

-.5

.0

.5

LATERAL ACCELERATION (g's)

FIGURE 2-lOC

1.0

1.5

-1.5

-1.0

-.5

.0

.5

1.0

1.5

LATERAL ACCELERATION (g's)

FIGURE 2-lOD

F. FORD #1 LATERAL LOAD TRANSFER DUE TO SPRINGS & ANTI-ROLL BARS F. FORD #2 LATERAL LOAD TRANSFER DUE TO SPRINGS & ANTI-ROLL BARS

Tire Load Vs. RoD Angle

Tire Load Vs. RoD Angle

"'- -"' '

-:;-

a:g

5

= ~

""

lol ~

p

2000.00 1900.00 1800.00 1700.00 1600.00 1500.00 1400.00 1300.00 1200.00 1100.00 1000.00 900.00 800.00 700.00 600.00 500.00 400.00 300.00 200.00 100.00 .00

I•

Accel. Parameters

ROLLANGLE(degrees)

-

..... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

-

oo

0

~

'

- -

N

'>

>

~

>

>>>

>>>

>

>

>

>>

>>>

>

>>

>


>

~

Changing the slope of the

Raise Y2 & Y3 equally

>

>>

>>




>


small change

> large change

> very large change

1) A large increase in the static roll center height 2) An increase in the drop of the roll center during bump 3) A very small decrease in the rise of the roll center during droop 4) A large reduction in lateral movement of the roll center away from the centerline during roll 5) A large drop of the roll center as it moves away from the centerline during roll 6) Very large increases in camber angle during both bump and droop 7) A large reduction in camber angle during left & right roll

Note: These observations are highly dependent on the link lengths and angular relationships which existed in the baseline design. Therefore, they may not represent the results which may be produced by similar modifications on another design. Use the above trends as a general guide during the optimization process and note any deviations.

IV VEHICLE DYNAMICS

4.20 CHANGES IN ATTITUDE- Large forces are generated when the sprung and unsprung masses are accelerated. These masses are accelerated vertically during bump and droop, laterally during cornering, and longitudinally during braking or acceleration. These accelerations cause changes in vehicle attitude and load transfer. Lateral acceleration during cornering causes the vehicle to roll and possibly yaw. Longitudinal acceleration during acceleration or braking causes the vehicle to pitch. Vertical acceleration during bump or droop may also cause the vehicle to pitch.

The motive forces which a tire can generate depend to a certain extent on the vertical load which is forcing the bond with the road surface. Controlling the levels of this load within the optimum levels of the tire design and the fluctuations of this load during transient motions of the vehicle is accomplished both by smooth driving techniques and proper suspension design. 4.10 MASS PROPERTIES - Many factors are involved in the transfer of load within an accelerating vehicle. The first obviously is mass. The more the vehicle weighs, the more load will be transferred for any given acceleration. Mass in a vehicle is categorized into two types, sprung and unsprung. Sprung mass is the mass of the vehicle which is supported by the suspension springs, and unsprung mass is all other mass such as wheels and tires.

4.30 LOAD TRANSFER - Tire load is increased or decreased (transferred) when the sprung and unsprung masses are acted upon by these external accelerations. Load is transferred from the inside (unladen) to the outside (laden) tires during cornering; from the front to the rear during acceleration, and from the rear to the front during braking. Tire load is increased during bump, and decreased during droop. The analysis becomes more complex when these accelerations are combined. For example, load is transferred to the outside front tire during turn entry when the brakes are applied. Managing these load transfers is of great importance if the vehicle is to be controllable and stable. The linearity of the transfer curves can be as important as the total load transferred. The worst thing for the driver to experience is a significant non linearity in load transfer and adhesion at a time when he or she is not expecting it.

4.11 Center of Gravity - The frrst characteristic of mass is its center of gravity. The e.g. is the point in three dimensional space from which the vehicle can be suspended and maintain equilibrium. All accelerative forces (not tire or "link" forces which act on the roll center) act on the vehicle through this point. Therefore, the lower the center of gravity, the less load will be transferred either longitudinally from rear to front when braking, or laterally from side to side when cornering. Related to the center of gravity, is the mass centroid axis. This is the e.g. of each section of the vehicle if the vehicle were to be divided up into sections along the longitudinal axis (as seen in Figure 4-1).

4.31 Lateral Load Transfer Due to Sprung MassSprung mass load transfer can be analyzed by the following two mechanisms (seen in Figure 4.2): A) The frrst mechanism of sprung mass lateral load transfer is the mean rollover moment which the sprung mass produces about the mean roll center when laterally accelerated. The mean rollover moment is made up of the three components discussed in section 3.13.

4.12 Moments of Inertia - The second characteristic of mass is its distribution away from the e.g. Any mass distributed away from the e.g. creates a moment of inertia. These moments exist in the planes of roll (longitudinal), yaw (vertical), and pitch (lateral). The greater the mass is located away from the e.g., the more acceleration will affect load transfers in any of these planes.

B) The second mechanism is the non-rollover moment which the sprung mass produces about the ground plane when laterally accelerated. This torque can only be calculated once the sprung mass is transferred (along with the accompanying mean rollover moment) to the mean point on the center-line at the same height as the mean roll center. Note: this is simply a matter of transferring a force and mass to a different point in space by applying the required torque about the new location.

Mass Centroid Mass Centroid Axis Roll

FIGURE 4-1

The sprung mass and mean rollover moment is then distributed from this location to the point on the centerline at the respective front and rear roll center heights as a product of the front/rear roll resistance ratio. Once these are distributed, the contribution of this second mechanism can be quantified for the front and rear suspensions.

MASS CENTROID AXIS RELATIVE TO ROLL CENTER AXIS

176

Roll Angle I

,+, - - 1

1---\ Gy

Static C.G.

'+'

Dynamic C.G.

I

Gy

Left

Right

~prung

Mass

Unsprung Mass I

Gx

Yrm

Static Roll Center

I

rGy

GX

\

I 1

Dynamic Roll Center

Ycg

Yus

Yus

~------------X1--------------I~------------X1--------------I

FtR

Ftl Left Tire Reaction Force

Right Tire Reaction Farce

FIGURE4-2 LATERAL LOAD TRANSFER PARAMETERS B) In vehicles which do not have an equal static weight distribution front to rear, the e.g. is located either forward or rearward of the longitudinal center of the vehicle. When this type of vehicle is vertically accelerated, additional pitching moments are generated about the longitudinal center of the vehicle. For example, in vehicles with a rear weight bias, downward acceleration in bump will cause load to transfer to the rear, and viceversa.

4.32 Lateral Load Transfer Due to Unsprung Mass - Load is transferred by the unsprung mass through the following two mechanisms (seen in Figure 4.2): A) The first mechanism of unsprung mass lateral load transfer is due to the moment which the unsprung mass produces about the ground. When laterally accelerated, the unsprung mass acts on the moment arm formed between the unsprung e.g. and the ground.

V SUSPENSION DESIGN RECOMMENDATIONS

B) The second mechanism is due to the camber change of the tire/wheel assembly. As the tire rolls, the e.g. moves laterally away from the contact patch center of pressure. This lateral displacement forms a moment arm. The unsprung mass produces an additional moment about this arm when vertically accelerated. Due to the small angles of camber seen in road racing however, this contribution to load transfer is typically ignored.

The following is a list of design recommendations listed in order of priority, which should provide a good starting point in the modeling/design of an unequal length control arm suspension. 1) Use the longest lower control link possible to minimize camber change. 2) A low roll center should used be to reduce jacking and camber change. This will also provide the driver with a linear feeling of load transfer while minimizing the chance of traction loss. Static roll centers are usually placed near ground level.

4.33 Longitudinal Load Transfer Due to Sprung Mass - Load is transferred longitudinally when pitching moments are generated about the longitudinal center of the vehicle. This pitching moment can be created when braking & accelerating, and during bump & droop.

3) Reduce roll center motion during roll. This will reduce the contribution that the lateral displacement makes to rollover moment. It will also help maintain a constant relationship with the mass centroid axis.

A) During braking or acceleration, the longitudinal acceleration acts on the sprung & unsprung masses to create a pitching moment about the ground plane. This pitching moment transfers load from one end of the vehicle to the other.

4) Front camber change during roll should have a slight negative slope. This assures adequate contact patch area and camber thrust. This also reduces understeer of the front laden tire during tum entry.

177

5)

Minimize toe change during bump (bump steer).

6)

The roll axis should have a similar slope to the mass centroid axis. This will provide linear diagonal load transfer during cornering.

7)

Minimize track width change during ride and roll changes.

8)

The motion ratio should be kept near 1.0 to improve damper/spring efficiency.

This is a steady-state model which ignores time based factors such as: damping, rates of change and response. The intent of this model is to provide the reader with simple nondifferential mathematical equations in the hope that these can be used for an understanding of the basic principles of motion and load transfer. A more extensive model would consider the effects of time and the third plane of action. This type of model was considered overly complex for the basic understanding this text attempts to provide.

9) Use linear rising wheel rates (greater than 15% rising rate usually requires an inboard suspension design).

These equations cover suspension motions in two dimensions (vertical and lateral), due to bump, droop and roll. Effects of caster, and other longitudinal geometrical constraints are not considered. These effects however can easily be added. Load transfer in two planes (lateral and longitudinal), due to bump, droop, roll and pitch is covered along with tire load changes due to bump and droop. Load transfer due to yaw is also not covered.

10) Minimize scrub radius. SAl angles up to 10 degrees are common.

11) Be careful when using anti-dive geometry due to its effects on caster during travel. VI DEVELOPING A MATHEMATICAL MODEL Considering the complex constraints and the number of variables under consideration, suspensions can be effectively modeled only on computers. This section describes the process of developing a simple two dimensional steady-state kinematic and dynamic model for an unequal length four bar link suspension system commonly found in competition vehicles.

6.10 2D STEADY-STATE KINEMATIC MODELING EQUATIONS - The 2D Kinematic Model Diagram seen in Figure 6-1 will be used to develop the equations which model the kinematic motions of the suspension. The kinematic modeling variables in this diagram are defined using the equations on the following pages.

+Y Dynamic Centerline

--i f----

Static Centerline

Dynamic Roll Center

Pas. Camber Angle

Left Susp. Instantaneous Center

X6

~~--~~l_~L_--~L_L_Li_L_Li__ _~4-L_l__ _~--~~==========~--·

-·X Note: 1) All horizontai dimensions are specified WRT the static centerline (- to the left, + to the right) 2) Ail (static) vertical dimensions within the chassis should be measured WRT the chassis bottom .3) All (static) vertical dimensions not directly attached to the chassis should be measured WRT the ground All (dynamic) vertical dimensions are calculated WRT the ground ~) The sprung mass rotates about point "X" on the centerline ot the mean dynamic roli center height

!)

FIGURE 6-l 2D KINEMATIC MODELING PARAMETERS

178

NOTE: Unless otherwise stated, left and right versions of the following equations are equivalent once the subscripts are changed from left to right. The following equations ignore tire compliance.

(EQ 6-4)

XIL &XIR= 1/2 the absolute value of the track width

(EQ 6-5)

(EQ 6-1)

where 11 8

11

is wheel camber.

X 2 &I;= Lower inner pick up point (left shown, right is similar)

(EQ 6-1A)

~=Average

(EQ 6-6) (EQ 6-7)

of the left & right absolute track widths where~~~

(EQ 6-2)

is the roll angle of the sprung mass.

X 3&J;= Upper inner pick up point (left shown, right similar)

where 11 x' II and II y' II are the static values of each dimension, 11 XL 11 & 11 X R II are the left and right values of each dimension respectively. ~f=

11

(EQ 6-8) (EQ 6-9)

Front ground clearance (rear is similar)

Y. -Y.

The equations for the upper & lower inner pick up points consider the fact that the vehicle rolls about a point on the centerline at the mean dynamic roll center height.

, {ay -1g)M.,.+LT -Fif

I f - If

S;

Z

2K MR 2 4 .if

+( ( sinxL ;sinxR )-sinx')

IS

(EQ 6-3)

r:Z +(x; -lx~lt

X4 &~= 11

~R

11

Lower hub carrier pick up point

("~L

11

is shown,

is similar)

In this equation, 11 GY 11 is the vertical acceleration in G's 11 , 11 lg 11 is the acceleration due to gravity in 11 G's 11 , 11 M •f II is the front sprung mass, 11 Fif 11 is the front jacking force,

11

II

LT, II is the longitudinal load transfer,

spring rate, and

11

MR,1

11

11

K.rr

11

is the front

is the front motion ratio for the

springs. The third term in the ride height equation is the reduction in ride height due to the drop of the lower kingpin ball joint as the wheel changes camber. The chassis drops by the same amount as the drop in the lower ball joint in suspensions supported by springs which act on the lower control arm. Note: The third term in this equation should be changed to account for the drop in the upper kingpin ball joint in suspensions which are sprung by the upper control arm. Rear ground clearance is calculated in the same manner.

(when vehicle is not airborne)

~L =r: +{sinxL -sinx')

r;z +(x; -lx~Lit

(EQ 6-llA)

+~-k+DJ (when vehicle becomes airborne) In equations 6-10 & 6-1 I, II L111 is the lower control arm length, and 11 D111 11 is the maximum suspension droop. The second term in the equations for 11 ~ 11 is the change in the height of the lower kingpin ball joint due to changes in wheel camber.

x' & X= The static and instantaneous angle which the imaginary line between the lower kingpin ball joint and the center of the tire contact patch makes with the ground is found by (EQ 6-4) & (EQ 6-5):

179

X 5& Ys = Upper hub carrier pick up point (" YsL" is shown, "YsR" is similar)

SA/= Static Steering Axis Inclination

, (x' -x')

SA I =arctan

11

(EQ 6-12A)

fs' 2 +(x;-lx~LI) 2

, 5R

(EQ 6-19)

8 11= Wheel camber

,

(X

,

(X R

(EQ 6-13)

eL =SA I

(EQ 6-14)

8R =SA! -arctan

(when vehicle is not airborne)

YsL =Ys'+(sim:L -sine')

4 R,

Ys-~

(EQ 6-12)

+arctan

4L -XSL )

(EQ 6-20)

YsL -~L

-XSR ) YsR-~R 4

(EQ 6-20A)

Scrub = Scrub Radius (left shown, right is similar)

(EQ 6-14A)

+J'i-(J'i'+DJ X 7 &J;= Instantaneous Center (left shown, right is similar)

(when vehicle becomes airborne)

~L -X -J;L

In equations 6-12 & 6-14, "L11 11 is the upper control arm length, and 11 Hhc 11 is the hub carrier height. The second term in the equations for 11 Ys 11 is the change in the height of the upper kingpin ball joint due to changes in wheel camber.

( f.2L -X2L ( X

))-(r.

3L

-X ( 3L

fsL -.J;L ))

X -X

(EQ 6-22)

e' &e= The static and instantaneous angle which the imaginary line between the upper kingpin ball joint and the center of the tire contact patch makes with the ground is found by (EQ 6-15) & (EQ 6-16):

(EQ 6-23)

The location of the instantaneous center (see Figure 3-1) is calculated by finding the intersection of the upper and lower control arm extensions. This intersection is found by setting the equation (Y =mX +b) for the upper & lower control arms equal to each other. X 8&Yg= Roll Center

X 6 = Hub carrier offset (left shown, right is similar)

(EQ 6-17) (EQ 6-25) ~=Spindle

height where 11 Xn &J;L 11 & 11 X 1R&Y.,R" are the left and right values respectively. (when vehicle is not airborne) The location of the roll center (see Figure 3-1) is calculated by finding the intersection of the vectors ·which connect the instantaneous centers with their respective tire contact patches. This intersection is found using the same methods used in EQ 6-22 & 6-23.

(EQ 6-l8A) (when vehicle becomes airborne)

180

X 9 &Yg= Upper Outboard Spring/Damper pick up point (left shown, right is similar)

(EQ 6-26) (EQ 6-27) X10 &~ 0 =

Lower Outboard Spring/Damper or push-rod pick

where "~" is the offset of the upper pull-rod pick up from the upper kingpin pick up point. Note: this formula also assumes that the upper pull-rod pick up point is in-line with the upper control arm.

up point

~L

f.;L)) X 10L =X2 L- ( L1 -S0 ) co{ arctan ( -(X (EQ 6-28) L -X2L) 4

Y.;R-~R -X

X !OR =X2R +(LI -S() )co{arctan( X

4R

)]

~ 2 &~ 2 =Push or Pull-rod bell-crank pivot point (used only in inboard suspensions discussed later) (left shown, right is similar)

(EQ 6-28A)

2R

(EQ 6-35) (EQ 6-36)

· ( ~ 011 = ~R + ( L1 -S0 ) sm

arctan (

f.;R -_

~R

The inboard spring mounting point "~ 4 &~ 4 " used in inboard suspensions can be calculated by using (EQ 6-35 )]

(EQ 6-29A)

&36) and substituting "X;4 &~~" for "X;2 &~~.

x4n x2R

6.20 2D DYNAMIC MODELING EQUATIONS

where "s()" is the offset of the lower spring/damper or pushrod pick up from the lower kingpin pick up point. Note: this formula assumes that the lower spring/damper or push-rod pick up point is in-line with the lower control arm.

6.21 Lateral Load Transfer - Figure 4-2 describes the nomenclature which will be used to develop this model. The process of calculating the lateral load transfer consists ofthe following five steps:

s;L &s,L =

Static & instantaneous length of Outboard Spring/Damper unit (left shown, right is similar)

Step #1 - The first step is to calculate the mean rollover moment of the sprung mass. This moment has three components (described in section 3.13). The rollover moment is calculated using the e.g height, and the mean values of roll center height and track width. These mean values are defined by the longitudinal location of the e.g. along the vehicle's centerline (seen in Figure 6-2).

(EQ 6-30)

(EQ 6-31)

o.. = Spring Deflection o. .=S,-s; 1

The height of the center of gravity can be calculated using (EQ 6-37):

(EQ 6-32)

~ 1& ~ 1=

Upper Pull-rod pick up point (only used on pull-rod suspension types discussed later)

y

(~.grA)+(~.g.fB)

e.g.

A+B

(EQ 6-37)

where "Yc.g.j " & "Yc.gr " are the front and rear e.g. heights · respectively.

(EQ 6-33)

The mean roll center Yg 111 can then be calculated using (EQ 6-38): (EQ 6-33A)

Yo = (YgrA)+(YgfB) 8m

181

A+B

(EQ 6-38)

Mean Roll Center

Mass Centroid

FIGURE6-2 MEAN LOCATION OF ROLL CENTER

The mean 1/2 track X 1m is found using EQ (6-39):

_LM =O=F;LXl,.-F;RXl,.- MPx Fhu

Xrm

4 , _ __ _ _ _ _

1-1

X1m

.:xsm

I

------------~~------------X1m--~------~·

Note: 1) All values are given at the mean location 2) The Mean Rollover Moment is the result of the accelerated Sprung Mass at the e.g. acting over the Roll Moment Arm (Yrm, Xrm) and The Jacking force acting over X8

FIGURE 6-3 MEAN ROLLOVER MOMENT DIAGRAM

182

Step #2 - The second step is to calculate the mean sprung mass load transferred from the inner two tires to the outer two tires using the known mean rollover moment. This is accomplished by simultaneously solving for the left and right tire reaction forces F,L and F,R using (EQ 6-42) and (EQ 6-43); and summing vertical forces to zero: MsGy = F,L + F,R.

Step #3 - The front and rear load transfers due to the roll moment can now be calculated as a product of the mean load transfer (step #2) and the ratio of front to rear roll resistance. (EQ 6-44) cannot be used to directly calculate the front or rear load transfer due to the roll moment because the roll resistance of each suspension determines the percent of the mean roll moment that is distributed to the each end of the vehicle. This only applies for a torsionally stiff chassis. The front LI;_1 and rear LI;_r load transfers are then calculated by

MG 2

FtL =_!___I_

M,,(~.g.- Yg

111 ){

equations (EQ 6-45) and (EQ 6-46) respectively.

(EQ 6-42)

Gx +GY tan)+F1,X8111

L~f =( ~ )(F,L ;F,R}

+----~--------~------~---

2XIm

=[RR~J[M.,(oJ~.g. -YgJ+GY tan(~.g. -Y8m))+FJ X ml RRI 2XIm

MsGy

1

F,R=-2(EQ 6-43)

Ms( ~.g.- Yg,J( Gx +GY tan)- Fj,X8111

8

(EQ 6-45)

2Xlm The resulting sprung mass load transferred from the unladen to laden tires due to the mean rollover moment is therefore defined by (EQ 6-44):

LT. = lm

F -F tL tR 2

M_,( Gx(~.g.- Yg

111

(EQ 6-46)

)+Gy tan(~.g. -Yg,))+ F1,X8n,

RRf , RRr and RR, are defined as the front, rear and

2Xu"

total roll resistance of the vehicle (see EQ 6-65). The resulting front rollover moment diagram is shown in Fig. 6-4.

(EQ 6-44) Roll Angle

--- Gx

\

Gy

\

Left ' Unsprung Mass \ \

1"'"..0~--Gx

\ ......

---

Static Centerline

I I 1 I

o;,,,;~::::,~:o~~~: tGy G x Rollover Moment

Frant Sprung Mass located on the Centerline at F-ront DRC height with Yu accompanying Rollover Moment

Center Yu

I

f------------- X1f --------------r~----------- X1f - - - - - - - - - - - - - !

Ftl

FtR Right Tire Reaction Force

Left Tire Reaction Force

Note: 1) All values are given for the front suspension 2) The Rollover Moment is distributed to the front suspension based on the front/total roll resistance ratio

FIGURE 6-4 DISTRIBUTED (FRONT) ROLLOVER MOMENT DIAGRAM 183

Step #4 - The fourth step is to calculate the sprung mass load transfer due to the non-rollover moment. This moment is created when the sprung mass at each end of the vehicle is laterally accelerated over the moment arm formed between the roll center and ground. Note: The sprung mass of the respective suspension and the accompanying rollover moment are now located at the point on the vehicle center-line at the height of their respective roll center. We have already calculated the load transfer due to the rollover moment and are now only concerned with the effects which the sprung mass (which has been transferred to the point on the center-line at the roll center height) has on the load transfer(described in section 4.3l.B).

The moment equation (front suspension shown) of the unsprung mass about the ground is calculated using (EQ 652) (CW=+):

The moment equation (front shown) of the sprung mass about the ground is calculated by (EQ 6-47) (CW=+):

(EQ 6-53)

(EQ 6-52) The third component of the tire reaction forces F; 3 L and F; 3R are then solved simultaneously by summing vertical forces equal to zero: M111 GY = F; 3L + F; 3R. The vertical force (for the front suspension) on the left and right tires from the unsprung mass is defined by (EQ 6-53) and (EQ 6-54):

(EQ 6-47)

F

13R

The second component of the tire reaction forces F; 2 L and F;2 R are then solved simultaneously by summing vertical forces equal to zero: M.!fGy =F12 L +F; 2R. The vertical

=

MG uf y 2

(EQ 6-54)

Therefore, the unsprung mass load transferred from the unladen to laden tires is defined for the front and rear by (EQ 6-55 and (EQ 6-56):

force (for the front suspension) on the left and right tires from the non-roll moment is given by (EQ 6-48) and (EQ 6-49):

F;3L- F;3R

=-M_,_if_G_Y +-M_.if~·_G_xY.:_8~f ' 2£ 2 2XIf

F

(EQ 6-55)

2

(EQ 6-48) (EQ 6-56) (EQ 6-49) The total lateral load transferred due to lateral and vertical accelerations for the front and rear suspensions is then found by (EQ 6-57) and (EQ 6-58)

Therefore, the sprung mass load transferred from the unladen to laden tires due to the non-roll moment is defined for the front and rear by (EQ 6-50) and (EQ 6-51 ):

F12L -F12R

(EQ 6-50)

LT. = F12L -Ft2R

(EQ 6-51)

L rr

_ ~2!-

2r

2

2

+ M_ifGxYg.f + M,!fGxY,if 2X11

Step #5 - The final step in calculating the lateral load transfer is to determine the unsprung mass load transfer. This load transfer is generated when the unsprung mass is accelerated over the moment arm formed between the e.g. of the unsprung mass (~) and the ground. Note: the moment arm created by increasing camber angle will be ignored here. The equations are similar to those of the non-rollover moment sprung mass transfer.

2X1.f (EQ 6-57)

+ M.,rGxYgr + MurGxY,1r 2X1r

2X1r

(EQ6-58)

184

6.22 Roll Resistance - The roll moment generated when the sprung mass is laterally accelerated must be resisted to maintain stability. This resisting couple (as seen in Figure 6-5) is generated through the tire contact patches by the springs and anti-roll bars. These tire forces form a couple around the vehicle center-line which limits the roll angle for a given lateral acceleration. Roll resistance and its distribution therefore affects the entire suspension design. For example, the load transferred from the inner rear tire to the outer front tire at tum entry has a large effect on the acceptable levels of camber and roll center movements. The suspension design process requires both experience and many iterations of the model to obtain the required balance.

&

and

where the front wheel rate in roll is defined (using the average of the left & right motion ratios) by (EQ 6-63): (EQ 6-63) In (EQ 6-63) the wheel rate is defined as a function of square of the motion ratio, because the spring and wheel rates must be converted to forces using their respective deflections before their moments can be balanced. This can be easily understood by performing a moment balance on a balance beam or "see-saw" which has an asymmetrical pivot point; using rates and deflections instead of forces.

F;11

The front roll resistance couple is then defined by (EQ 6-64) as a function of the spring and anti-roll bar rates "K_1 " & "Kr~f " and their respective (left & right average)

(EQ 6-60)

F;s +sin~(x11 +tan~(~1 - Ysr ))K"fL

motion rations "MR1 " & "MRrlif ", where the springs and

F;ll = F,,,.- 0 wfll Kwjll =

are the instantaneous left and right front

(EQ 6-62)

F;L = F;s + Ou:P" KufL =

are the left and right front wheel deflections, and

wheel rates. Through substitution, the roll resistance couple for the front suspension then becomes (EQ 6-62):

(EQ 6-59)

F;L

"o wfll "

"KwfL " & "K"fll "

Using Figure 6-5, the roll resistance couple RRC1 (front suspension shown) is found to be (EQ 6-59):

where the left and right total tire reaction forces are calculated using (EQ 6-60) and (EQ 6-61):

"F;s" is the static tire reaction force for one side, "o wfL "

where

anti-roll bars act in parallel:

(EQ 6-61)

F;s -sin~(X11 -tan~(~/- Yg1 ))Kwfll

Roll Angle

-- Stotic Centerline

I (

I

---Gx1 (

\

\

\

\

Roll Resistance Couple

Distributed Frant Rollover Moment

Dynamic Roll Center

----

FtLZ*Ul

r

FtR

Ftl

Right Tire Reaction Force --·

Left Tire Reaction Force

FIGURE 6-5 ROLL RESISTANCE COUPLE

185

Equation 6-64 is exact at any roll angle. At small angles, we can simplify this equation by assuming that sin~rad~~rad where "~rad" is a small roll angle in radians. This simplification essentially linearizes the roll resistance couple by removing the "sin" dependency, therefore producing a constant value for all angles. This assumption is only reasonably accurate for small roll angles. For small roll angles then, the simplified version of (EQ 6-64) can be converted from "lbinfrad" to "lbinfdeg" by multiplying by "n/180 ". The front roll resistance per degree can now be closely approximated (for small roll angles only) using (EQ 6-65): 27tX1/(Ks1 MR/ +K,b1 MR,b/) !bin

180

deg

In EQ 6-67 ' "Fif " & "Ftr " are defmed as the additional front and rear tire reaction forces due to load transfer, "Gz" & "Gy" are the longitudinal and vertical accelerations in "G's", "lg" is the acceleration due to gravity in "G's" ' "Muf " &" Mur " are the front and rear unsprung masses, and

"~if

" & " ~~r" are the front and rear unsprung

mass e.g. heights. The front and rear tire reaction forces are then solved simultaneously by summing vertical forces equal to zero: Ftf + F,r = ( GY -lg)( Ms + M,if + MJ. The front and rear tire

forces are defined by (EQ 6-68) and (EQ 6-69): (EQ 6-65)

,w:,(G.~.g. -(Gy -lg)B)+ M,if(G.J;if -(Gy -lg)(A+B))+ MIIPZJ;Ir A+B

The resulting vehicle roll angle when laterally accelerated is then defined by (EQ 6-66) (CW=+):

~=-[

Ms( Gx(~.g.- Yg,.)+Gy tan~(J~.g.- Y81,))+ F1X 8 ] RR1 jdeg+RR,jdeg

(EQ 6-68)

F•

=~g

~,(Gz~g +(Gy -lg)A)+ M11,(G.~" +(Gy -Ig)(A+B))+M,1 G.J-;1

=----------------------------------------A+B (EQ 6-69)

(EQ 6-66) The longitudinal load transfer from the front to the rear is calculated by (EQ 6-70):

6.23 Longitudinal Load Transfer - Load is transferred longitudinally during braking & acceleration and in bump & droop. Pitching moments about the ground plane are created when the sprung and unsprung masses are longitudinally accelerated (seen in Figure 6-6). Pitching moments are also created about the middle of the wheelbase at ground level, when the sprung mass of a vehicle with a forward or rearward weight bias is vertically accelerated.

F -F

LT = ...!!__!!_ z 2

l

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c

Min Steering Sensitivity g/100 deg

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Steering Torque Gradient Ratio

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,........ L_ __________ L_ _

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970097

Synthesis of Chassh; Parameters for Ride and Handling on the 1997 Chevrolet Corvette Steven P. Fuja, Henry A. Schmid, and Joseph P. Ryan General Motors Corp. Copyright 1997 Society of Automotive Engineers, Inc.

ABSTRACT

SUBSYSTEM ATTRIBUTES

This paper describes the performance attributes of the all-new front and rear SLA (short-long arm) suspensions, steering system, and tires of the 1997 Corvette. The process by which these subsystem attributes flowed down from vehicle-level requirements for ride and handling performance is briefly described. Additionally, where applicable, specific subsystem attributes are rationalized back to a corresponding vehicle-level performance requirement. Suspension kinematic and compliance characteristics are described and contrasted to those of the previous generation ( 1984 to 1996 Model Year) Corvette. Both synthesis/analysis activities as well as mule-level vehicle development work are cited for their roles in mapping out specific subsystem attributes and related vehicle performance.

ROLLDOWN PROCESS - The C5's suspension/steering system design and functionality are thE3 result of a structurecj flowdown process dictated by Gemeral Motors' 4-Phase Vehicle Development Process. This process may be summarized as one in which Voice of the Customer (VOC) inputs flow down to Vehicle Technical Specification (VTS) requirements, which in turn flow down to Subsystem Technical Specification (STS) requirements. See Figure 1. This process is a systems engineering-based method which captures customer inputs and then translates these desires into me•asurable engineering metrics. Competitive vehicles are~ benchmarked for these engineering metrics, and the measured results form om~ set of inputs to the negotiated vehicle-level targets which ultimately become the VTS. (Other inputs to the VTS may include such items as rele~vant C4 historical data, technology rollout considerations, etc.) These vehicle-level specifications are then rolled down to subsystem and component-level specifications which must be satisfied to enable the vehicle level goals to be met.

INTRODUCTION The all-new 1997 Chevrolet Corvette has been internally dubbed "C5", shorthand for 5th Generation Corvette. Likewise, the previous generation Corvette (1984 to 1996 Model Year) is referred to as C4 (4th Generation Corvette). These terms will be used throughout. This paper is one of a set of four SAE papers which discuss the evolution of the C5 Corvette's ride and handling characteristics. Reference [1] is sequentially the first of the four, and describes how vehicle level targets for vehicle dynamics performance were defined. The paper you are now reading is second in the series, and describes how these vehicje targets resulted in specific subsystem attributes for suspensions, tires, and steering system. The third paper in the series (Ref. [2]) describes the execution of the front and rear suspensions in production hardware. The last paper (Ref. [3]) deals with the final development tuning of those suspensions, as well as that of the tires and steering system. Together, the four papers describe the derivation of the C5's vehicle dynamics attributes, from the broadest expression of customer desires and preferences to the specific desi{~n details of the final product to be delivered to those customers.

IC>ther

'

Inputs

-

I

I

Voice of the ~ustomer Other I

L----~~~

I

Vehicle Technical Specification

Subsystem Technical Specification FIG. 1: Requirements Flowdown

231

Inputs

In .the case of the C5 suspensions and steering system, thrs rolldown of vehicle-level requirements to specific suspension/steering system attributes was accomplished by a variety of methods, including extensrve computer simulation, actual hardware builds (mules: alpha, and beta vehicles), and knowledge by recognrzed experts in the field (both inside and outside of General Motors). In systems engineering, equally important to the rolldown process is the process of confirming that subsystem and component goals are met, then reassembling those validated subsystems back into an overall vehicle, and finally checking the performance of the vehicle against the original goals. Again, the C5 team used both analytical models of subsystems as well as subsystem hardware tests to demonstrate capability, the~ assembled these subsystems into more complex vehrcle models or actual vehicles. Objective vehicle testing against VTS metrics completed the systems engineering process. The result is a requirements-driven vehicle system design enabling world-class ride and handling capability.

Saginaw Division), is located forward of wheel center. It shoul~ be noted that Magnasteer™ was considered part of vehrcle program content from the very beginning, and that the front suspension was designed accordingly to complement the Magnasteer™ II system.

SUSPENSION STATIC DESIGN FACTORSNecessary to understanding a suspension's influence on overall vehicle dynamics is a system of describing that suspension's kinematic and compliance characteristics. At GM, these suspension attributes are known as Static Design Factors (SDFs). Over 60 SDFs are defined and are monitored analytically as well as (in some cases) experimentally as a suspension design evolves. As is the case with any complex system, modifications meant to improve one particular suspension attribute may cause degradation in another area. Packaging changes and other considerations will also drive changes which must be quantified, evaluated, and balanced in terms of impact to overall susp1:msion and vehicle performance. This continuous, proac:tive modeling, measuring, and balancing of suspension SDFs is key to arriving at a vehicle which delivers capable, pleasible dynamic performance.

FIG. 2: CS Front Suspension (Alpha Build)

KI.NGPIN GEOMETRY- CS's front-view kingpin geometry IS set up to enhance steering system performance, with the aim of satisfying vehicle-level requirements for improved steering feel and better midrange handling. CS features a relatively short spindle length of 63mm (vs. 93mm in C4), and a relatively upright kingpin (8.8 degrees for CS vs. 16.0 degrees for C4). Since the spindle length acts as a moment arm for both Fore/Aft and Vertical road input, reduction of this length results in lower kingpin moments due to rough road events, thereby reducing the resulting steering system transient forces and enabling better rough road handling. Reduced spindle length also results in a lower camber moment to be reacted by the upper and lower ball joints; these resulting reduced ball joint lateral forces act to reduce kingpin friction and hysteresis, which may further improve steering feel. In the side view, CS features 6.5 degrees of caster angle and 36mm of caster trail. By contrast, the C4 design features 5.9 degrees of caster angle and 45mm of trail, with a 12mm side view spindle offset. The reduction in caster trail was aimed at reduced front cornering compliance to enable a vehicle-level goal of improved yaw damping and better midrange handling. An additional input parameter to the determination of caster geometry, however, was the vehicle-level goal of g?od steering wheel road feel, with a desire for relatively h1gh handwheel torque gradients (steering wheel effort as a function of lateral acceleration). Since the caster trail is the moment arm for steering system loads resulting from lateral acceleration, this desire for high torque gradients is in conflict with reduction in caster trail desired for improved yaw damping. The need for

FRONT SUSPENSION AND STEERING TOPOLOGY - Figure 2 shows an isometric view of the CS front suspension. In the tradition of the earlier generation Corvette, the upper and lower control arms and knuckle are all cast or forged from lightweight aluminum to enable low unsprung mass for good wheel control and impact isolation. Also similar in concept to the previous Corvette is the use of a composite transverse leaf spring and monotube shock absorber. The lower control arms and steering rack mount to a cast aluminum crossmember, which in turn is hard mounted to the frame rails. The crossmember, with its machined interfaces, serves as a precision locating surface for the suspension/steering system components. The upper control arm attaches directly to the hydroformed frame rail. The steering rack, which features Magnasteer™ II (a variable effort steering system developed by GM's Delphi

232

balance between these two conflicting goals was recognized early on, and dmve extensive computer modeling to explore the relationship among front cornering compliance needs, torque gradient needs, and the interaction of the suspension with steering system tuning. Even the earliest Cc, computer simulations and front suspension mules focused on upright kingpin geometry and carefully balanced caster geometry as an enabler of good steering feel. Competitive vehicles were measured for their kingpin geometric features and were also quantified at a vehicle level for their steering feel performance attributes. Specific steering attributes of some of these competitive cars were eventually factored into C5's VTS.

,..... .........,.................-90---"""--"""""""'"'" ___________________, _______ _,.,.......................................................................

' ·,_ eo--,

'

60 ·,.._

50+-,,,

30

t

E 10 .1.. ~ --

:f

~

:t

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i _____ cs!

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-......

-80--

'·,·, ·,

·,.,

.,.,

·, \

-, \

'

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:

FIG. 4: Front Suspension Roll Center Height

Early suspension mules experimented with different camber curve slopes around zero wheel center travel. These cars, with their adjustable levels of roll camber, were subjectively evaluated for such difficult to quantify attributes as rough road wheel kick. Computer simulations both preceded the hardware development as WE~II as tracked it through development-led changes. The resulting camber geometry and roll gain offers good down the road midrange handling without intrusive wheel kic:k, yet enables the high maximum lateral acceleration capability necessary in a Corvette.

i

RIDE QUALITY FEATURES- One message which came through very strongly from the Voice of the CL1stomer was the desire for improved ride quality, particularly in the area c•f impact isolation. Several suspension features were aimed at satisfying this requirement without sacrificing the handling capability necessary in a high-end sports car. The lower control arm is set up as a modified Lshaped arm, rather than an A-arm, featuring a stiff bushing close to wheel center for good lateral stiffness, and a soft "ride" bushing aft of wheel center for reduced fore/aft stiffness. These bushing locations and compliances are careful.ly matched to enable good isolation, yet result in minimal toe change under transient roc:1d inputs, to the benefit of rough road handling. Another ride "enabler" is the transverse fibE~rglass leaf spring. The packaging efficiency of this springing medium allows the shock absorber to be placed further outboard laterally than could be achieved with a conventional coil spring over shock absorber arrangement; the result is a better shock lever arm ratio (1 .:34:1), which enables better wheel damping authority for both isolation and roadholding. A key vehicle-level feature which enables good ridE! performance out of the suspension is the exceptional rigidity of the C5's unique body structure.

' .

~-------------------~.~~--~-----.

i.1o , \

10 -So I

fa fso i-60-'-

'

.... -70 J. I

;

i-C4t

1. . ---···-------...SO-----------------------------------\. . ____ j

\\

Camber, Deg.

·,

Ron Ctr. 1-lt,._mm_,_,'c--',-..-------------------i

,......................,~....--.------..---------...--90-,-.----------..................1

''·,·,·,,,

E

+~ ·,_'-,"

20 ~

CAMBER GEOMETRY - C5's camber geometry is shown relative to that of C4 in Figure 3. C5 has a static negative camber setting to allow enhanced cornering power under maximum lateral acceleration. The slope of the camber curve around the layout design position is less aggressive than that of C4, providing less camber change and tread change for low lateral acceleration road disturbances, improving rough road handling and tracking. Roll center height and roll center height migration as a function of ride travel are similar to the C4 design. See Figure 4. Roll stiffness of the new car is somewhat lower than that of C4; accordingly, roll steer is likewise reduced.

.

.,

'

40

-40--

' ' -,

.

'-.w_._

-80-'-

=----------------------~[__--9Q.._:-------·-----~-j FIG. 3: Front Suspension Camber

Reduction in roll stiffm~ss is part of an overall vehicle level strategy of allowing somewhat more compliance and higher gains, but with greater levels of damping. This approach work:s to the benefit of both ride and handling by better managing tire normal load variations due to road inputs. The occupants' perception of higher gain may be minimal because they are less sensitive to absolute gain (controlled by stiffness) than they are to rate of change (controlled by damping).

233

Body stiffness unparalleled in an open roof production car provides a firm reaction surface so that springs, dampers, and bushings in the suspension can function properly without excessive series compliance. Early mule work also focused on suspension enablers for improved ride quality. Different variants of the leaf spring were tried, as were other springing systems (including a bell crank system with horizontal coil springs over shocks!). Impact harshness considerations were developed in hardware by use of an early mule which had adjustable fore/aft stiffness down to very low levels, as well as adjustable side view geometry; this vehicle was the hardware realization of extensive lumped parameter simulation work which focused on the same attributes.

CS's Magnasteer™ II system is capable of varying handwheel efforts with both vehicle speed and lateral acceleration, enabling a wide tuning range of effort characteristics for varying vehicle regimes (parking lot vs. highway vs. aggressive high lateral acceleration events). This capability was first simulated in the aforementioned steering vehicle models to assess the bandwidth of their effect on customer-perceived attributes; subsequent vehicle development in hardware focused on mapping out performance requirements within this bandwidth to result in a subjectively pleasing package for the customer. The eatrliest Magnasteer™ development work in hardware was actually performed in C4 vehicles. Because CS has different kingpin and steering geometry as well as different tire requirements, the C4 Magnasteer™ E!xperience was not directly applicable to CS. Accordingly, simulation work significantly preceded hardware development work on CS steering performance. Simulation first focused on modeling and understanding the C4 system to serve as a hardware correlation point. A CS model was then developed, and this model was used to set subsystem performance attribute targets which were needed to enable vehicle steering goals as defined in the VTS. When actual CS hardware arrived later in the vehicle program, the CS models were benchmarked against measured vehicle performance, with the result being exceptionally good correlation.

BRAKE STEER CHARACTERISTICS - Front suspension braking performance characteristics were dictated by a philosophy of making the vehicle insensitive or neutral to acceleration/deceleration events. As such, brake steer characteristics for both symmetric and asymmetric events were kept to a minimum by matching carefully balanced control arm bushing compliances with plan view tie rod anglel. These neutral steer characteristics, combined with a wheelbase increase of over 200mm and a slightly positive scrub radius (1 Omm), provide a significantly greater envelope of vehicle capability under braking. Brake performance sensitivity to scrub radius was evaluated in hardware by the use of suspension mules using tire/wheel combinations with several different wheel offsets. The wheel offsets used allowed evaluation of changes to both direction and magnitude of scrub radius. This sensitivity work was augmented and enhanced by computer simulation provided by GM's NAO Brake and Bearing Systems group.

REAR SUSPENSION

STEERING SYSTEM INTERACTIONS- A strong message from the Voice of the Customer was the desire for improved steering feel. As such, the CS steering system and how it interacts with suspension parameters and tire characteristics was the subject of extensive computer simulation before hardware was ever built. The GM NAO Vehicle Handling Lab has developed sophisticated vehicle models capable of simulating the complex nonlinear functions of the steering system. Steering system characteristics such as hydraulic boost, friction, lash, etc. may be modeled based on physical tests at a subsystem and component level. These analytical tools may be used to simulate full vehicle tests which are statistically correlated to customer preferences. Thus, given good vehicle level targets of steering performance, the team could use these analytical tools to synthesize a design capable of meeting these goals be-fore hardware is built. Subsequent hardware build approximates the desired capability, and is available for development engineers to tune to final configuration using both objective and subjective evaluation.

FIG. 5: C5 Rear Suspension (Alpha Build)

TOPOLOGY- Conceptually, the CS rear suspension resembles the CS front suspension and is a significant departure from the C4 rear suspension. Like 234

the CS front, the CS rear is a true SLA suspension with a modified L-shaped lower control arm for decoupled lateral and fore/aft compliance. It uses cast aluminum components and features a transverse fiberglass leaf spring and monotube shock absorbers. See Figure 5. Steel plunging halfshafts with constant velocity joints deliver torque to the 18" tire/wheel combination. As in the case of the CS front suspension (and in contrast to the C4 rear suspension), the lower control arms and tie rods mount to a cast aluminum crossmember with machined interfaces. The upper control arms attach to the hydroformed frame rail. The CS rear suspension's kingpin geometry is conceptually similar to that of the front due to the fact that knuckle castings are identical, front to rear; angular orientation differences enable front to rear caster and kingpin angle differences. By contrast, the C4 rear relies upon a non-plunging halfshaft to act as the upper control arm; as such, the outer Cardan joint of this halfshaft acts as an effective upper ball joint. The C5 geometry, with separate components (plunging halfshaft and true upper control arrn) providing separate functions (torque delivery and suspe~nsion control, respectively) enables the reduced scrub radius and spindle length summarized in Table 1.

SDF Caster Angle

C4

1.2

Even the earliest mules were SLA architecture, with a separate upper control arm to enable the desired camber geometry. Various levels of roll camber were subjectively evaluated for rough road and truck groove performance. Other factors such as tire size, alignment settings, etc. also influence wander behavior, so these considerations had to be kept in mind when making these evaluations. Tl'1e resulting combination of camber geometry and roll gain represent the necessary balance between good down the road performance on less than optimal pavement and the necessary high-g cornering power required.

;-····-·······-----,-~--·-··-·····--·-··---SO..;--·--···-····--·---···-------·---·--··:

'

~"

(degrees)

Scrub Radius (mm)

Spindle Length (mm)

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Camber, deg.

C5

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FIG. 6: Rear Suspension Camber

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123.0

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80

1

60

70 \

TABLE 1: Rear Suspension Kingpin Geometry

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CAMBER GEOMETRY- CS's separate upper control arm also allows a more optimal tuning of its camber geometry. See Figure 6. Note also negative static camber setting for improved maximum lateral cornering power. CS's reduction in camber change as a function of ride travel around zero wheel center travel and reduction in tread deviation with ride travel is considered to be directionaUy correct for improving rough road handling and minimizing truck groove wander. An additional benefit of CS's improved camber geometry is a reduction in roll center height, and an improvement of roll center height change as a function of ride travel; the lower roll center height will n:;sult in less jacking during cornering, and the improved slope will result in the roll center height being fixed to the vehicle during ride/roll events, enabling more predictable roll performance. See Figure 7.

~ 20-

0

:

;: 10 -:_10 •

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-40

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FIG. 7: Rear Suspension Roll Center Height

TOE CHANGE UNDER ACCEL.!DECEL. EVENTS- A further benefit of the CS's upper control arm and the resulting reduced spindle length and scrub radius is their influence on the tractive and braking steer

235

performance of the car. A large reduction in spindle length and scrub radius results in corresponding reductions in kingpin moments due to acceleration/deceleration events. These reduced kingpin moments are then reacted through control arm bushings and a tie rod plan view angle carefully matched to minimize toe change during these events. This is in keeping with the previously stated vehicle-level philosophy of neutral steer characteristics under fore/aft inputs. These suspension features, combined with CS's wheelbase increase, result in clearly superior performance under drop-throttle events. Toe change under accel./decel. conditions was the focus of considerable early mule work. Early analytical work had focused on minimizing these toe changes as a key enabler of achieving the neutral character desired in the car. Early hardware execution, however, pointed out the importance of such subtleties as body and component series compliance, as well as bushing non-linearities. Each of these additional compliances were trac~:ed down in turn and were either minimized or managed through complementary hardware and simulation work. Resulting toe change under freerolling conditions was then predicted analytically as well as measured experimentally on suspension compliance measurement systems such as GM's Vehicle Handling Facility and a similar faGility at Goodyear's Akron Technical Center. The resulting toe change under fore/aft inputs is exceptionally low, resulting in the desired vehicle level performance under accel./decel. events. This careful management of toe change under fore/aft road inputs is also a key enabler of ride isolation improvement. Because steer characteristics are so well controlled, greater compliance can be allowed without sacrificing handling precision, to the benefit of impact harshness.

played a strong role in the determination of opinions on this topic. In the end, the very small amounts of toe-in exhibited by C5 were considered appropriate as an enabler of mid-range responsiveness, as well as being subjectively pleasing to the driver. SIDE-VIEW GEOMETRY- C5 features a relatively long side-view swing arm (2.1 meters) and a somewhat reduce!d side-view swing arm angle (5.2 degrees for C5 vs. 7.8 degrees for C4). This results in the reduced levels of Percent Anti-Squat (PAS) and Percent Anti-Lift (PAL) shown in Figures 8 and 9. Long side-view swing arms with relatively low angle changes as a function of ride travel result from C5's SLA architecture; trailing link suspensions such as C4 usually result in shorter side-view swing arms with more angle change with ride travel.

r....... ····-----SO-,----··-··---,--------·-··-·-·-----·-·-·----·--··--·---·-·-·--·-·--..-· 80

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Il... _____ -9() _ _ _ _ ,_,____ _,_ ' ______________ _

FIG. 8: Rear Suspension Percent Anti-5quat

LATERAL FORCE STEER CHARACTERISTICS - CS's use of a rear-mounted, stiff tie rod (toe link) allows it to toe in slightly under the application of a cornering load. This lateral force steer is in the understeer direction, and thereby reduces rear cornering compliance. This in turn enhances lateral acceleration response time and thereby addresses Voice of the Customer inputs which demand responsiveness in midrange handling events. CS's lateral force understeer is enabled by virtue of the body-side toe link attachment to a rigid crossmember, rather than to a rubber isolated differential (as is the case with the C4 rear suspension). The direction of toe change under the application of lateral load was the focus of considerable debate, test, and simulation work by experts both within and outside of GM during the early phases of the CS vehicle program. All sides agreed that very small, controlled levels of lateral force steer were appropriate for the C5, with the difference of opinion arising in regard to the sign of that toe change (toe in or toe out). Tuning philosophy, subjective preferences, and development heritage

CS is able to reduce PAS and PAL and still retain good pitch control because of its increased wheelbase. Equally important to absolute pitch gain is the driver's perception of pitch under accel./decel. events. In a twoseat car such as the Corvette, the occupants sit closer to the rear axle than would be the case on a car which has a back seat; rear suspension anti features may therefore be more perceptible to occupants than would be the case on other types of vehicles. Earliest mule work focused on very low levels of anti features, with the mule also incorporating the C5's extended wheelbase. Since this earliest mule was deemed too "pitc:hy" under acceleration, subsequent development work focused on a mule with adjustable anti features. This vehicle was used to more precisely map out driver preferences with respect to pitch control. Obviously, spring rate and shock authority also contribute to pitch perception, so tuning considerations had to be kept in mind when making these evaluations.

236

TIRE CONSIDERATIONS EXTENDED MOBILITY TIRES - Standard on the CS is the use of Goodyear Eagle F1 GS Extended Mobility Tires (EMT), otherwise known as "run-flat" tires. These tires offer the capability of driving with zero air pressure; this capability, combined with C5's Tire Pressure Monitor system, obviates the need for a spare tire, benefiting the customer both in terms of increased trunk space and reduced overall vehicle mass. While EMTs. offer obvious benefits to the customer, they also present unique challenges to the suspension design. EMT construction which allows runflat capability also generally results in higher vertical tire spring rates and increased unsprung mass. Both of these characteristics. tend to work against good impact isolation and good wheel control. Fortunately, CS's suspensions were designed with EMTs considered standard equipment from the very beginning, so these tire attributes were recognized and comprehended early in the suspension design. Additionally, C5 benefited from lessons learned on the C4 Corvette, which offered an earlier version of EMT tires with one suspension option package. Accordingly, the CS suspensions were designed to provide relatively low fore/aft stiffness (with corresponding neutral steer characteristics) to minimize impact harshness. Additionally, C5's exceptional body stiffness at local shock/spring/bushing attachment points allow optimal isolator and damper performance to the ibenefit of both isolation and wheel control. Early suspension mules relied upon C4 EMT tires. Since these earlier variants of EMT technology are somewhat stiffer and more massive than those which ultimately were developed for CS, they served to provide a worst case scenario for considerations such as impact harshness, wheel control, and peak jounce bumper loads. Continuously during the course of the vehicle program, development engineers from both GM and Goodyear worked suspension compliances, shock and spring combinations, and tire characteristics in a complementary fashion to arrive at the resulting total C5 package.

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SPRING AND SHOCK CONSIDERATIONSThe rear leaf spring is packaged beneath the lower control arm, suspended by rubber isolated tension links. These links serve to decouple the leaf from the lower control arm in the fore/aft direction, preventing the leaf spring from contributing to fore/aft suspension stiffness, and thereby reducing impact harshness. The choice of a leaf spring for the CS rear suspension was influenced by needs of packaging efficiency. Benefits offered include increased trunk volume as well as enhanced shock lever arm ratio. The decision to mount the spring and shock to the lower control arm (as opposed to mounting directly to the knuckle) was a conscious tradeoff of what would have offered an even greater potential improvement in shock lever arm ratio. Mounting these elements to the lower control arm results in a knuc:kle which is decoupled from the shock and spring transient forces which might result in undesirable toe changes, particularly under rough road events. Additionally, mounting the shock to the lower control arm provides benefit by decoupling fore/aft stiffness from the shock absorber's load path. This reduces series compliance to the damper and thereby enhances shock authority. In suspensions which mount the shock directly to the knuckle, a "bell crank" mechanism can result, whereby reducing the fore/aft stiffness to improve impact harshness can result in more effective compliance acting in series with the shock absorber. This in tum results in diminished capability for wheel control. An early CS candidate rear suspension which featured a multi-link lower control arm exhibited this undesirable coupling in analytical modeling.

LATERAL REQUIREMENTS- Tire characteristics form the basis of front and rear cornering c function properly.

INTRODUCTION

C:HASSISINTERFACE

OVERVIEW- The fifth generation Chevrolet Corvette introduced in 1997 {CS} is a completely new vehicle, featuring significant design changes in areas compared to the fourth generation Chevrolet Corvette of 1984-96 (C4). Four papers have been written that summarize the Systems Engineering approach to the suspension design of the 1997 Chevrolet Corvette. The first paper [Ref. 1] reviews the customer research, Engineering Direction, human factors and analytical evaluation that established the objective Ride and Handling targets for the vehicle. The second paper [Ref. 2] describes the "roll down" of the vehicle level performance targets to specific subsystem attributes and parameters for the suspension, steering, and tires. The third paper [Ref. 3] reviews the hardware that complies with the specifications established in the previous two steps. This paper summarizes the 1inal development tuning of the suspension, steering and tires. Careful execution of the procedures and techniques discussed in this series of papers was critical in producing the highly optimized suspension of the 1997 Chevrolet Corvette and for assurance of high customer satisfaction for ride and handling performance.

STRUCTURAL FOUNDATION- The C5 structure was a clean sheet of paper design [Ref. 4]. The new structure enabled the suspension to be tuned for improved ride and handling by decoupling the structure and suspension dynamically. Control arm bushings, shocks, springs and anti-roll bars were tuned independent of structural interaction, unlike C4, which had to account for structural interaction. C5 structure had four primary design specifications to decouple structure and suspension, as shown in Table 1.

ABSTRACT

Table 1. Body Structure Specifications. Freq Mode

Range (Hz)

Supports

Static Stiffness

0-5

Handling

1st Torsional

5-50

Structural

23 Hz (separation from suspension tramp mode)

Vibration

Nodal Lines @ front edge of seat, vehicle centerline

Structural

21 Hz (separation from suspension hop mode)

Vibration

Nodal lines @ front and rear shock towers

1st Bending

DEVELOPMENT PROCESS - CS ride and handling goals specified significantly improved ride, but not at the

Input Mobility

241

5-50

50-800

Noise

Specification 720 N-mm/deg (>10X roll couple distribution)

20 dB separation from mount

STATIC STIFFNESS - The static stiffness specification insured that the torsional stiffness of the structure did not interact with the roll stiffness distribution of the front and rear suspensions. Thus, anti-roll bars and ride springs were very efficient, and did not require oversizing to compensate for torsional deflection of the structure.

C5 ride and handling goals. Jounce bumper development was a major subset of chassis development, because of it's role in managing the highest suspension and structure loads. DEVELOPMENT TIME LINE - The ride and handling process was very iterative and was active over the entire C5 program. Different types of vehicles were used to prove different objectives during that time. Mule vehiciE!S built from C4s were used initially to prove suspension concepts and help set goals and specifications for the C5. Pre-Alpha vehicles were the first chassis built from the ground up and closely represented design intent at that time, except styling. These vehicles were used to prove out structural design and suspension isolation capabilities and helped establish the Alpha and Beta tuning libraries for chassis components. Alpha vehicles were the first completely new vehicles built from the ground up that represented 100% mainstream design. They included functionally correct components in all areas. These vehicles and the previously established tuning libraries were used to establish the preliminary chassis tuning of the complete, design intent vehicle.

STRUCTURAL 1st TORSIONAL MODE -The 1st torsional mode of the structure was decoupled from the suspension by frequency and mode shape. The 23 Hz frequency provided adequate separation from suspension tramp (16Hz), so tramp mode vibrations were not amplified by the structure. By placing the 1st torsional mode nodal line at the front edge of the seat and center line of the ve:hicle, perception of shake was minimized at the seat track and steering wheel. Shock tuning could focus primarily on wheel control without compromise to control structural shake. STRUCTURAL 1st BENDING MODE - Similar to the 1st torsional mode of the structure, the 1st bending mode was decoupled from the suspension by frequency and mode shape. The 21 Hz frequency provided adequate separation from suspension hop (15Hz), so hop mode vibrations were not amplified by the structure. By placing the 1st benaing mode nodal lines at the front and rear shock towers, the structural bending mode was further isolated from road induced excitation. The primary excitation by the suspension for stuctural bending vibrations occurs at the least sensitive area of the structure. As with structural 1st torsion, shock tuning could focus on wheel control without compromises to control structural shakEL

VEHICLE LEVEL

CHASSIS DEVELOPMENT ACTIVITY

MULES

SUSPENSION CONCEPTS

PRE-ALPHA

STEERING

ALPHA

STEERING

RTD

TIRE MOLD SHAPE

INPUT MOBILITY- Specifying 20 dB separation between the suspension isolation components and the attaching structure enabled interior road noise specifications. The mobility specifications insured the effectiveness of each isolator by forcing each to be the weak link in the system. Due largely in part to the comprehensive specifications created for each major subsystem at the beginning of the program, chassis development was able to achieve all the targe:ts for ride, handling, vibration, and noise. Only predetermined tuning elements were adjusted, no suspension or structure revisions or patches were required (for all three levels of suspension).

SHOCK VALVING RTD SHOCK MOUNTS CONTROL ARM BUSHINGS BETA

STEERING TIRE TREAD PATIEHN SHOCK VALVING RTD SPRINGS JOUNCE BUMPERS STAB BARS SHOCK VALVING

CHASSIS COMPONENT DEVELOPMENT

PROTO

TIRE CONSTRUCTION SHOCK VALVING

This section describes the development process for optimizing the individual chassis components of the FE1, FE3, and F45 suspension packages. A minimum amount of effort was required to tune springs and anti-roll bars. Their development was straightforward, and once established, did not have to be revisited at a later date to "fix" subsequent issues. Emphasis was placed on control arm bushing development becausB of their key role in achieving the

RTD STEERING SHOCK MOUNTS ALIGNMENT

Figure 1 . Chassis Development Timelin1e.

242

Beta vehicles were also built from the ground up, with the first production intent components, and were used for the majority of chassis tuning. Prototype vehicles were built with production parts and were used to refine and finalize the tuning process. The timeline in Figure 1 shows the development sequence and the iterative nature of the development of the C5 suspension. CONTROL ARM BUSHINGS - Due to the robustness of the suspensio1 design, only one control arm bushing package was necessary for all suspension levels. The assembly plant was willing to proliferate, but the suspension design did not require it. The C5 uses Short-Long Arm (SLA) suspensions front and rear, as shown in Figures 2 and 3. The control arms were designed as close to an "L" shape as possible, with a stiff "handling" bushing near wheel center and soft "ride" bushing aft of wheel center. The front upper control arm is a symmetric A-arm, due to packaging constraints of the front suspension during full lock steering. The "separation of function" concept for the control arm bushings worked very well in hardware execution. Except for the front upper control arm (which was subject to very tight package constraints), all other control arm bushings were sized sufficiently to accommodate the anticipated rate of each, using a conventional rubber/elastomer bushing. Bushing durability, linear and non-linear rate characteristics, contribution to ride rate, and other factors were considered. Higher cost bushing alternatives (i.e. lubricated journals, voided or non-symmetric, cross-axis ball joints) were considered, but determined to not be necessary with the C5 suspension designs. __,

..

Figure 3. 1997 Chevrolet Corvette Rear Suspension.

Ride Bushings- Reducing the rate of any ride bushing improved impact hardness or reduced interior noise but not have a significant impact on handling. The suspension kinematics were robust to normal changes in bushing rates, compliance SDFs were somewhat decoupled, and primarily, unwanted toe change was nonexistent. The suspension elasto-kinematics were designed for near-zero toe change with fore-aft displacement. Development experience with the ride bushings confirmed that large reductions in rate still did not introduce unwanted toe change. Handling modes such as rough roads, split-coefficient braking, braking-ina-turn, accelerating in a turn, and dropped throttle were not significantly affected, a tremendous advantage for tuning suspension forE~-aft compliance. If the ride bushings were stiffened, there was a negligible improvement in handling, and always a significant degradation to ride quality and interior noise. There was little to be ~1ained from specific bushing packages for each suspension option. Only one control arm bushing configuration was required to obtain the clesired handling characteristics plus refined ride for all three suspension levells.

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Handling Bushings - Increasing the rate of any handling bushing would improve multiple areas of handling but not significantly degrade impact hardness or increase interior noise. Handling bushings were extremely stiff, typically 3 to 6 times higher rate than ride bushings. Analysis Support -A system to objectively quantify the kinematic and compliance characteristics of a suspension is necessary to understand, measure and simulate a suspension's influence on overall vehicle dynamics. At General Motors, these suspension attributes are known as Static Design Factors (SDFs). Over 60 SDFs were defined in analytical models, many are used in handling models and are monitored on the vehicles. As may be the case with any complex system,

I

\ l

Figure 2. 1997 Chevrolet Corvette Front Suspension.

243

modifications that improve one suspension attribute may degrade another [Ref 2]. Chassis Analysis synthesized a set of nominal bushing rates to meet the suspension SDF targets that in turn were synthesized to achieve the handling requirements. Using the nominal bushing rates as a basis, a tuning library of 20% softer and 15% stiffer bushing rates was obtained and subjectively evaluated by Chassis Development. To assist the development process, a bushing rate sensitivity study was run which examined the effect on handling of varying each bushing rate individually or several simultaneously. Eighty-one combinations of nominal, soft, and stiff bushing rates were analyzed for the front and rear suspensions. Seventeen compliance related SDFs were track.ed. An example of the analysis is shown in Figure 4, where 1 of the 17 SDFs (Lateral Force Compliance Steer) is shown for 11 of the 81 bushing combinations.

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Due to the necessarily low aspect ratios of the 'lifting' surfaces and the dominance of tip flows, the flow structures around a racing car are characterised by large areas of vertical, unstable and separated flows. Understanding the interaction of tyre jet vortices

Year

255

produced at varying angles of . slip, with a three dimensional high lift wing in very close ground proximity, is just one example of the enormous challenges faced by the F1 aerodynamicist Even components on the car such as the high 11ft multi element wing& or radiator ducts, of which there Js much available literature, interact so greatly with other areas of the car that it renders these studies of limited value. It should at&o be borne in mind that often the most performant aerodynamic 'package' may sacrifice the inherent performance of one component for the benefit of another in its wake. This consideration often renders accepted aerodynamic logic invalid.

AERODYNAMIC COMPONENTS OF A FORMULA 1 RACING CAR

To attempt to describe in detail the different components that make up a F1 car, and more importantly the flow· around them and interaction between them Is beyond both the scope of this document. Instead, the remainder of this report tries to focus on areas that can be 'isolated', and that present problems of direct interest to the F1 aerodynamicist. As a basic design philosophy, the aerodynamic designer is trying to maximise the downforce and minimise the drag produced by the car, while maintaining a constant aerodynamic bafance over the whole working range of the car. These rather simple ideals prove to be rather Jess simple to obtain in reality.

The wealth of experimental knowledge, an emphasis on relative performance improvement and the complexities of the flows around the generic F1 car, have meant that the pursuit of theoretical understanding of the flow problems faced has been compromised. However, as experimental methodology is honed by all the teams, prospective competitive advantage is minimised and more teams are looking towards numerical methods in order to enhance understanding of the more complex flow structures present around the car. Of all the available solvers. it is the Navier-Stokes solvers which are now most in favour vltth the F1 teams, primarily due to the fact that their increasing commercial availability has led to increasingly available expertise in their use.

FRONT WING The front wing of an F1 car is typically a two element high lift wing with an adjustable flap to vary the downforce obtained from the wing, and f\ence balance the car with different rear wing configurations. The front wing runs in very strong ground effect,. with typical ground clearances ranging from 70 to 100mm. Due to the fact that the rest of the car operates in the wake generated by this wing, and that this wake severely effects in particular the undertray and· dlffuser of the car. It is important to tune the wake profile of the front wing. Experience has shown that the front wing should have a constant distribution of lift across it's chord, and due to tip effects, greater incidence and chord Is required outboard .to · achieve this. Inevitable tip effects are minimised and harnessed by the front wing endplate, Which. can influence large gains at the rear of the car. The lower to the ground, the better the· sealing effect of the front Wing endplates and the more efficient the front wing. HoweVer. the height of the endplates. is governed in the regulations at 50mm above the flat bottom of the car.

As suggested above. of increasing Importance to the F1 aerodynamicist is the understanding of vortex interaction,. and thus methods of control and enhancement. A good example of this is the realisation that the control of the front wing tip vortex/front wheel jet vortex interaction can lead to very large gains in downforce at the rear of the car, to the detriment of front wing performance. With this in mind, it is clear that the ideal numerical solution would capture flow details in all the fluid volume around the car, not only close to the generating surfaces, This requirement precludes most potential flow methods due to their inability to model vortex interaction, and indeed at extremis even the latest Navier-Stokes solvers with current turbulence models, since all stilt faD to adequately predict vortex burst. However, on the acceptance that all currently available codes wilt not fully capture the flow structures present, ·calibrated' cnl•.uo..-.. are becoming great n::lr,~m&>trir: r.nr"nnlimAntir•n the wind tunnel offering valuable insight into the racing car. Current production and detailed too1et111~r with other factors restlicting to mean that the improvements in aerodynamic performance are still a consequence of experimental wind tunnel testing. However, lPU1tatlc>nal techniques are being used more and more in harmony with experimental development to help the aerod\J•narnicl~st inrtnrt"lv~ understanding of the discipline the car.

Due to the presence of the ground, the front wing is very efficient {in racing car terms!). With a Lift/Drag ratio in the range 7 - 9. The of the front wing is strongly dependent on the presence the front A rotating wheel produces strong crosswise flow areas close to the ground in front of the wheel due to a squeezing Or jetting effect ·Vortices are highly influential in understanding the form of front wing wake, and their effect with steering angle of the front wheel. This is still a tittle understood transient aerodynamic effect, which is difficult to reproduce accurately in a wind tunnel test. this reason such a problem may avail itself to more ambitious numerical investigation.

256

The front wing produces 25-30% of the total downforce of the car. The amount of downforce produced is very dependent on the front ground clearance, and it is this fact that produces most of the aerodynamic stability problems. As the front of the car moves lower the front wing produces more downforce due to increased 'ground effect' and more effective sealing of the endplate. This in itself produces a forward shift in balance, but also the increased upwash from the front wing reduces the rear downforce, increasing the ballance shift. Designing a front wing that is both efficient and is not sensitive to ground clearance does greatly improve the driveability and efficiency of a F1 car.

REAR WING A typical rear wing configuration on a current F1 car consists of a two or three plane wing, with the upper element set varying between a low chord single element wing at comparatively low incidence, to a large chord, highly cambered three element wing. The range of available rear wings is so as to allow tuning of downforce levels to particular circuits. The rear wing produces approximately 30-35% of the total downforce of the car, and about 25-30% of the total drag of the car. Optimisation of the individual elements, and the interaction of the lower elements with the diffuser is of critical importance to the aerodynamic design of the car. The addition of the lower elements actually reduces the downforce produced by the total rear wing layout itself, but increases the efficiency of the car by increasing the downforce produced by the undertray and bodywork. Optimisation of rear wings is one of the few areas where the use of isolated numerical studies is applicable, especially for the highly cambered multielement upper wings which run in relatively 'clean' upstream flow conditions.

UNDERTRAY AND BODYWORK From the FIA regulations the floor of a F1 car must occupy two clearly defined planes between the rear edge of the front wheels and the front edge of the rear wheels. The surfaces of the floor in these planes must be flat, rigid, and impervious. Downstream of the front edge of the rear wheel, a diffuser section is used to lower the pressure under the car and thus generate downforce. About 40% of the total downforce of the car is produced by the undertray and bodywork. In general the body of the car can be thought of as a bluff body close to the ground, with a large wake and associated form drag. In general, improving the design of the diffuser and producing lower pressures under the car does not lead to an increase in drag, and so the production of downforce by the body of the car is normally the key to an aerodynamically efficient car.

WHEELS As suggested above, the open wheels of an F1 car cause much of the complexity in the flow around the car. They produce about 40 % of the total drag of the car, and also produce lift which is very difficult to measure experimentally. This can often be a source of confusion in experimental assessment. They further affect the car's aerodynamics by producing strong cross flows in critical areas of the car. Ultimately, a better understanding of the interaction of the flow field around the wheels with the rest of the car, including the effect of steering angles on the flow field, could indicate ways of harnessing these flow characteristics.

Again, the aerodynamic stability characteristics that the diffuser implies on the car are of critical importance in vehicle driveability. Thus stall phenomena should be predictable and tuned to specific requirements, The lower elements of the rear wing can be used as a 'spoiler' to set a base pressure condition and thus control stall characteristics. The diffuser angle can also be used to tune stall characteristics, where a higher angle of the diffuser generally gives more downforce over the prestalled operating range, but causes the diffuser to stall at higher rear ride heights, and vice-versa. The particular diffuser angle chosen is normally a compromise between aerodynamic efficiency and stability.

CONCLUSION It has long been understood that the success of a modern F1 car is heavily dependent on its aerodynamic performance characteristics. This fact can be quantified using various 'in house' simulation tools. Analysis of the progression in aerodynamic performance of Tyrrell racing cars over the past few years suggests that, for periods of stability in regulations, there is a linear rate of increase in downforce. It is clear that regulation changes result in reductions to this trend, but generally the F1 constructor can expect a measurable return to any investments made in the aerodynamic development of the modern F1 car.

Due to the low aspect ratio of the undertray, and also due to the presence of the rear wheels, the flow under the diffuser is characterised by large areas of highly vortical three dimensional flow. In general the full flow in the underbody is little understood, and is very difficult to investigate experimentally. Surface pressure measurements, surface flow visualisation and numerical modelling are possible methods in attempting to understand some of the aspects of this flow.

257

The aerodynamiCs of a modern Formula 1 n.ldf¥g'•·iS a field that has. due to it's complexity, been the realm of the expetim~t: With the· ot\lf'reot,statu&.;of rttJmedca1

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322

Fig. 7 Three-quarter view of the surface panel model of an Indy-car's rear wing (using 1152 panels).

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pressure gradient, allows the development of a laminar boundary layer as long as the pressure decreases. This, of course, can result in a noticeable reduction of the viscous friction drag. The next region, shown in Fig. 10, is the top (called "rooftop") where the pressure variations are small and in full-scale a transition to turbulent flow is expected within the boundary layer (usually near the point of maximum suction). The last part of this diagram consists of a recovery region where the pressure gradient is unfavorable. This is the most sensitive region on the airfoil and its proper shaping can help to delay flow separations. Liebeck, in Ref. 2, proposed a family of such curves based on the Stratford separation criteria, so that if the pressure distribution in the suction side is contained within this diagram (as in Fig. 10), then the flow over this airfoil will stay attached (at a particular Reynolds number). Of course, in practice, the sharp corners in this schematic target distribution must be avoided and the dashed line shows a more practical pressure distribution, not exceeding the boundaries set by the solid line. Fig. 11 demonstrates how the above approach is applied to a two element race car wing (after Ref. 7). In this

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An additional feature observed on such low aspectratio wings is that the strong downwash created by their tip vortices delays severe flow separations and wing stall. This is demonstrated by the quarter-scale experimental results shown in Fig. 9. Of course, the wing was designed to operate at the condition shown in Figs. 7, with its end plate edges being horizontal (corresponding to a = -20 deg, in Fig. 9). Interestingly, when wing angle of attack was increased close to 20 deg. over the design condition (a= -40 deg, in Fig. 9), the isolated wing did not stall!

3.0

2.5

2.0

HIGH-DOWNFORCE RACE-CAR WING DESIGN The previous examples showed the highly three dimensional nature of the flow field, in which race car wings operate. However, when accounting for these effects, the methodology developed for airplane applications can be transferred to the race car wing design discipline. Similar to 'airplane practice', a typical wing design process can start with setting up a target pressure distribution (on the suction side of an airfoil) to meet tasks such as maximum lift over drag. Figure 10 describes schematically the main regions in such a target pressure distribution and Ref. 2 provides information about how to establish those diagrams. Similar target pressure distributions can be developed by using more recent airfoil design methods (e.g. Ref. 4) or by experimental investigations. Typically, near the airfoil's leading edge, the suction builds up and within this region the pressure decreases along the chord. This region, with a favorable

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case the complete geometry of the race car was modeled by a panel code (as in Ref. 6} and the airfoil shape was developed within the calculated three-dimensional flow over the vehicle. Thus, by adopting a target distribution, similar to those proposed in Ref. 2, the new airfoil shape could have been developed. The solid line in Fig. 11 describes the targeted pressure-distribution boundaries originally developed for a single element airfoil. However, in this case of a two element airfoil, larger levels of suction can be maintained near the trailing edge because of the high suction on the following flap's leading edge. Therefore, even if the pressure curve extends outside the boundaries of the target-line near the trailing edge, as shown in this figure, the flow stays attached on the wing (and this was validated by flow visualizations).

Fig. 11 Schematic description of the target pressure distribution on the main element of a rear wing. The centerline pressure distribution was computed by the code of Ref. 6. The geometry of the airfoil is shown by the inset to this figure. (after Ref. 7).

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GURNEY FLAPS

1.50

As a closing example for the use of high-downforce wing technology on race cars a case is presented for the reversal of the 'technology transfer' process. A quite interesting trailing edge device, called 'Gurney flap' (Ref. 2}, is frequently used on race cars, but only recently was applied to airplane wings (Ref. 8). Such a flap is a small plate, mounted at large angles (close to goo) onto a wing's trailing edge, and its height is on the order of a few percents of the wing's chord (usually less than 5%). The effect of the flap on the flow is described in the inset on top of Fig. 12, and flow visualizations indicated that the trailing edge boundary layer on the suction side is reduced as a result of the sharp turn at the trailing edge. Again, for wings that operate near high lift coefficients, this reduces trailing edge separation and increases lift, as shown in Fig. 12 (incidentally, this data is for the rear wing of a 1988 Indy car). The advantage of this simple flap is in its simplicity which can help to trim the aerodynamic loads on a car by just changing the flap size or

324

1.25

1.00 0.75 0.50 0.25

----6--} --o--} --+=::=} --o--

Baseline wing with flaps on trailing edge and side fin Baseline wing with flap on trailing edge Baseline wing

a,deg

Fig. 12 Effect of small goo flaps on the aerodynamics of a small aspect ratio rectangular wing (rea.r wing of a.n 1987 INDY car). Based on 1/4 wind-tunnel test results, presented in SAE Paper 89-0600, Fig. 9.

by removing it. At lower lift coefficient values, when the wing trailing edge boundary layer is thin, the drag will increase and wing lift/drag ratio will be reduced with the addition of this trailing edge flap. The more surprising application of such trailing edge flaps is on the two side fins (or end plates) on a race car's rear wing (shown in Fig. 12). The experimental data clearly indicates that the downforce is increased when mounting these small plates on the trailing edges of the side fins. Their effect is to create an effective camber for the end plates, and the suction side of the plate under the main wing reduces the pressure there (increasing downforce, in the case of an inverted wing). CONCLUSIONS The examples presented demonstrate that a high-lift airfoil developed for airplane application cannot be used automatically for race-car applications. For a successful design, proper computational or experimental tools are required to model the complex, three-dimensional flow field over the complete vehicle. These tools can be used then to provide information on the wing's pressure distribution in its actual position. The airfoil shape and the wing geometry can be developed now by using a 'Target Pressure-Distribution' envelope borrowed from airplane applications. REFERENCES 1. Katz, J., "Race Car Aerodynamics," Robert Bentley Publishing, Cambridge, MA, 1995. 2. Liebeck, R. H., "Design of Subsonic Airfoils for High Lift," J. Aircraft, Vol. 15, No. 9, 1978, pp. 547561. 3. Eppler, R., and Sommers D. M., "A Computer Program for the Design and Analysis of Low-Speed Airfoils," NASA TM 80210, Aug. 1980. 4. Drela, M., and Giles M. B., "ISES: A Two Dimensional Viscous Aerodynamic Design Analysis Code," AIAA Paper No. 87-0424, Jan. 1987. 5. Katz J ., "Aerodynamics of High-Lift, Low AspectRatio Unswept Wings", AIAA J., Vol. 27, No. 8, 1989, pp.l123-1124. 6. Ashby, L. D., Dudley, M.D., Iguchi, S. K., Browne, L., and Katz, J ., "Potential Flow Theory and Operation Guide for the Panel Code PMARC," NASA TM 102851, March 1990. 7. Katz J., and Dykstra, L., "Application of Computational Methods to the Aerodynamic Development of a Prototype Race-Car," SAE Paper 942498, presented at the SAE first Motor Sport Engineering Conference, Dec. 5-8, 1994, Detroit, USA. 8. Ross, J. C., Storms, B. L., and Carrannanto, P. G., "Lift-Enhancing Tabs on Multi-Element Airfoils," AIAA Paper 93-3504, Aug. 1993, Monterey, CA.

325

962518

The Aerodynamic Optimization of a SuccessfuiiMSA GT Race Car Dwight M. Woodbridge and R. Brian Miller General Motors Corp. Copyright 1996 Society of Automotive Engineers, Inc.

ABSTRACT

series. 1995 also marked the debut for the 4 valve Aurora VS engine, along with a significant change in the allowable aerodynamic configuration of the car.

This paper describes the methodology used to achieve optimum aerodynamic performance of the 1992 through 1995 Oldsmobile Cutlass Supreme IMSA GT race car and will demonstrate the continuous improvements successfully used to respond to rule changes and competition.

All development work on the body of the car was carried out at the GM full scale wind tunnel (GMAL) in Warren, MI and validated through vigorous track testing. A Reynolds number of 1()6 was sought in the wind tunnel to simulate average on track conditions. As competitive deficiencies were identified by race teams and as the rules were changed, continued wind tunnel and track testing was necessary to maintain the performance of the car. This continuous development process was key to the success of the Oldsmobile Cutlass Supreme.

The concerted effort by the sanctioning body to limit the aerodynamic performance of IMSA GT race cars for the 1995 season required a rigorous wind tunnel test program backed by track validation to maintain the necessary aerodynamic balance, cooling flows, engine induction flow, and overall competitive parity. The specific modifications that were evaluated to accommodate these rules changes will be detailed in this paper.

COf\.-IPETffiON APPLICATION

Special test methodologies developed to better understand specific aerodynamics questions such as the effects of vehicle attitude, internal cooling flows, underbody treatments, and engine air inlet performance will also be discussed.

The IMSA GT series consists primarily of sprint races lasting approximately one hour and endurance races of three to 24 hours in duration. These races are conducted on dedicated road racing courses and a small number of temporary street circuits in the United States and in Canada. These tracks range from 1.43 miles (2.30 km) to 4.00 miles (6.44 km) in length with an approximate average cornering speed of 80 mph {129 kph) and a maximum speed of over 200 mph (323 kph).

INTRODUCTION The Oldsmobile Cutlass Supreme race car was originally designed for competition in the SCCA Trans-Am racing series. In 1992, the design was modified to allow it to be also eligible for the IMSA GT championship. It was initially powered by a 6.0 litre engine for the endurance races with a 6.5 litre all aluminum V8 being fitted for the GTS sprint season. In GTO trim a 4.5 litre V6 was used. In its first season of IM:SA competition, the Cutlass won four GTS races finishing second in the Manufacturer's championship and also won five times in GTO competition resulting in a Driver's championship. The following year the Oldsmobile Cutlass secured the Manufacturer's championship with six wins in the nine race series. In 1995 the Oldsmobile Cutlass Supreme attained both the Manufacturer's and Driver's championships with six wins. Furthermore, the Cutlass earned all but one pole position in the. eleven race

The International Motor Sports Association {IMSA) has the difficult task of balancing the performance of normal aspiration with turbo charging, various engine displacements, numerous vehicle types, tire sizes. factory teams against independents, and tube frame versus unibody race cars. Along with sliding minimum weight requirements, aerodynamics has become a key area which IMSA uses to equalize the field. As a result of this philosophy, aerodynamic performance can vary greatly between competitors and every effort must be made to ensure that maximum benefits are reaped from the approved race vehicle configuration.

327

VEHICLE DESCRIPTION

Note bow the 1995 season rules change proposal resulted in a further reduction of the total downforce capability of the car (run 1994.2). The specifics of these rules changes and the configurations that were tested relevant to these changes will be detailed in a follov.ing section entitled Effects of Rule Changes.

GT cars are based on the silhouettes of production vehicles. A typical road car has an unacceptable amount of aerodynamic lift for racing applications. This lift reduces the lateral and longitudinal traction capabilities of the tires. There are three areas which are critical for developing downforce to counter this lift. The front undertray, defined as the surface beneath the nose ahead of the front tires, and splitter, defined as the upper surface of the undertray which projects ahead of the valence, are used to produce downforce ahead of the front axle to aid front grip. The length of the splitter ahead of the nose of the car and the shape and angle of the undertray will detennine the downforce capability and stability of the front end. To balance this force on the front of the car, IMSA allowed the use of a wing on the rear deck. The angle of attack, height above the deck. longiru.dinal distance from the rear axle, number, shape, and placement of airfoil sections, aspect ratio, endplate design, and Gurney flap usage are all variables which will affect the level and efficiency of the rear downforce produced. The third area used to generate downforce is the rear undertray. This is the sloped floor behind the rear tires and below the bumper. On a typical GT type of car with a flat bottom between the front and rear axles, a well designed IMSA-spec diffuser develops only a fraction of the overall downforce of the car. However, a poor design or a damaged rear undertray can significantly reduce rear downforce by interfering with the rear wing.

CONTENUOUSDEVELOPMENT

Figure 2: IMSA GTS Oldsmobile Cutlass Supreme installed in the GM wind tunnel

The Oldsmobile Cutlass Supreme debuted in the IMSA GT series in 1992 and still competes today. There were few rules changes in the area of aerodynamics until 1995. The successful performance of the GTS-1 class against the new WSC fonnula prompted IMSA to significantly alter the GTS-1 technical specifications. Figure I shows how the aerodynamic coefficients continued to improve until late 1994.

Since the Cutlass body had previously been developed for the SCCA Trans-Am series, initial efforts were focused on exploiting the differences in rules with IMSA. Particular attention was paid to increasing overall downforce with little regard to drag due to the potent powerplant of the Cutlass. One such area was louvres in the hood which significantly augmented front downforce. In Figure 2 the louvres are the four black rec-

Test

Figure 1: Summary of sprint race trim aerodynamic coefficients

Figure 3: Underhood aerodynamic treatments - radiator outlet ducting indicated by arrows

328

at Laguna Seca in 1994. This piece incorporated a steeply raked mid-section between the front wheels and another two such sections directly ahead of the wheels allowing it to more efficiently evacuate the air from beneath the vehicle. When later tested in the wind tunnel, an increase in front downforce of 10% was seen over the standard tray. Figure 4 shows a schematic of these changes. Figure 5 shows a trace of the underbody pressures along the longitudinal centerline of the car for three different front undertray configurations including the L-aguna unit. Note the added amount of negative pressure at the rear of the Laguna undertray as compared to the other two.

tangles on the hood ahead of the front axle. Figure 3 shows the carbon fiber ducting that connects the radiator to the louvres. By porting the air from both inside the engine bay and that exiting from the radiator through these ducts, the positive pressure below the hood - which generally causes lift - was greatly reduced. When the outlet side of the radiator was connected to the louvres in the hood, front downforce was augmented by 13%. This equates to almost 60 lbf (267 N) of added front downforce at 150 mph (241 kph). In an attempt to produce more front downforce, two additional95 x 7 in (241 x 178 mm) louvered ports were added outboard of the original vents and the original louvres were reduced in size by 33%. This along with nming one third of the porting from underhood and the rest from the radiator outlet produced an additional 15% of front downforce or another 60 lbf {267 N). As mentioned before, the front undertmy is crucial for developing downforce. In IMSA trim, this is a panel beneath the nose that extends from the leading edge of the splitter to the forward-most part of the front wheel assembly and is the full maximum width of the nose. The angle of attack or effective diffusion angle of this surface can greatly alter front downforce. By moving the rear of the undertmy up an additional 1.5 in ( 13 mm) front downforce was increased by almost 30% or over 100 lbf (445 N) at 150 mph. This evidenced itself as a noticab1e amount of pitch and ride height sensitivity on the track. The variability of front downforce with respect to vehicle motions required a chassis set-up that maintained the proper dynamic attitude of the undertmy under heavy braking and cornering. When the trailing edge of this panel was curved further upwards, front downforce dropped by 4%. Rear downforce was also hurt by 1% indicating that the flow downstream of the undertray was possibly turbulent due to separation caused by the added curved piece. A flat undertmy with 1.5 in (38 mm) of rake relative to the chassis was used in the following races.

0-~n 0.25

1

--

...

.0.75

:::r

\

..

~

~ Figure 5: Underbody pressure coefficients from floor strip

This equates to added downforce. The splitter was a key means of creating front downforce on the Cutlass. This is the upper portion of the undertray that extends beyond the valence (see lower left portion of Figure 6). The splitter produces downforce by taking advantage of the positive pressure created as air is displaced by the front of the car. The result of adding an additional 0.75 in (19 rom) of splitter was an increase of 8% in front downforce and a 2% reduction in drag. This put another 30 lbf (133 1\1) on the front tires to aid cornering grip without any aerodynamic drag penalty. This, along with less ride height sensitivity, made the splitter an ideal device

SECTION 1\- 1\

~~~~~~~~~c

Lr

.0.25

u

In 1994 the undertray was split into three sections: a center piece and two outboard panels that could be adjusted to different angles. Wmd tunnel testing showed that by raising the trailing edge of these two panels from their previous horizontal position, front downforce was increased by 16% or almost 50 lbf (222 N). Further development on the tray led to what was internally known as the 'Laguna' undertray due to its premiere

_.....,.,.........,

'1

---

-----~t,n

SE!;TION C • C

1--i r - - - - - -

"\., . .....,. ...... c:oo.-eosSECT10N8·8

Figure 4: Front undertray modifications

Figure 6: Sideview of engine bay

329

for tuning front downforce. As seen from prior testing at GMAL, the flow of air beneath the vehicle had a significant impact on overall aerodynamic performance. In addition to the front splitter and the front and rear undertrays, air management underneath the car was controlled via engine compartment and rear axle enclosure panels, the flat bottom between the front and rear axles, and the angle of the chassis with respect to the ground. Maintaining proper rake was important as the aerodynamic front normal force ratio. Nr/N, varied from 37.7% @ 0 in rake to 44.0% @ 0.75 in (19 mm) rake. Nr/N is a measure of the amount of front downforce versus total down force. A front normal force ratio greater than the static weight distribution yields an aerodynamic shift towards oversteer with one less than this moving towards understeer. Front downforce increased by 35% or 150 lbf (667 N) by maintaining proper dynamic ride heights. Enclosing the complete bottom of the car improved front down force by 6% or 30 lbf ( 133 N) and rear downforce by 11% or 50 lbf (222 N). This was accomplished by placing a flat plate under the engine and a rear plate under the rear axle compartment opening. The rear undertray was designed as an expansion area to provide a favorable pressure gradient at the rear to help evacuate air from beneath the car. IMSA code required this tray to be a flat surface with no tunnels or concavity. The wind tunnel floor pressure strip was key in the development of the under-

louvres. Raising the front of the trimmed pieces 1.0 in (25 mm) reduced downforce by 3%. The trimmed dive planes in their original location produced a 2% drag penalty that slowed the cars' top speed by 2 mph (3 kph) and were subsequently used only at the slower tracks where the cars were traction limited. In 1993, attention was turned to the rear of the car in an effort to balance out the additional front downforce. Three two element and one single element wing profiles were tested in various configurations and widths. The goal was to optimize downforce, minimize drag, and offer the greatest tuneability for the race teams. In addition, maintaining the suitable front/rear dovnlforce ratio to retain a predictable and proper handling vehicle was an important criterion. The wing was also optimized to reduce rear downforce loss during a yawed state which helps in producing consistent aerodynamic cornering

Figure 8: High aspect ratio rear wing assistance. The first goal was to establish the longitudinal and vertical location of the rear wing. When moved back 2.75 in (70 mm) from the baseline location. rear downforce went up by 15% or 130 lbf (578 N). Drag also went up by 6%, but was found to be acceptable for the amount of down force gained. The efficient greenhouse and high rear deck of the Cutlass led to the conclusion that maximizing the vertical height of the rear wing was preferred. This was confirmed in testing as downforce decreased as the wing was lowered.

Figure 7: Dive plane installed on nose body treatments on the Cutlass. With the louvres, undertray, and splitter tuned for maximum front downforce, small dive planes or winglets were added to the nose. Figure 7 shows one configuration of dive plane that was tested. It was found that these pieces were extremely design and location sensitive. When first placed on the car. front downforce was reduced by 3% and rear was down 2.5%. By trimming the leading edge of the dive planes back I .5 in (38 mm), front downforce was up 7% from baseline. The forward portion of these pieces tenninated 1.0 in (25.4 mm) above the splitter. It was believed that this allowed air flowing along the surface of the splitter to interact v,r:ith the forward kickers on the front wheel wells. This aided in exhausting underhood air out between the bodywork and the tire with an effect similar to the

The IMSA code book specified a maximum wing area of 780 in 2 (5032 cm2) and a maximum width of the rear \\ring at 74.0 in (1879 mm) for GT cars. This allowed the engineers to test a wing at the maximum allowable width and one at a modified aspect ratio to obtain peak efficiency. Figure 8 shows the 74 in wide wing installed on the vehicle in the wind tunnel prior to testing. It was conjectured that a maximum width wing allowed the wing tips to be directly exposed to ground, thus potentially offering more rear downforce through a reduced interaction with the deck. However, test data did not support this theory with a 22% or 204 lbf (907 N) reduction in rear downforce. This study led to the investigation of multiple element

330

Figure 9: Airfoil study for rear wing

Figure 11 : Bi-element Liebeck airfoil based wing

wings of differing profiles. With IMSA initially allowing the use of multi-element rear wings, engineers built several prototypes to test in the wind tunnel. The first wing utilized a standard NACA profile (see Figure 9, profile C & Figure 10). Tills provided a predictable amount of downforce for a given angle of attack, but was limited by severe stall at angles greater than 18°. Subsequently, a two element Liebeck airfoil based wing was tested with excellent results (see Figure 9, profile B & Figure 11). Finally a third wing profile with a much longer chord on the second element was tested (see Figure 9, profile A & Figure 12). These _latter two configuration were capable of sustaining higher angles of attack (o:) before stalling and hence yielded more downforce. The lift sensitivity of the wing assembly to the angle of the secondary element was an ideal way for the teams to adjust rear downforce. These hi-element wings utilized modified Liebeck airfoils with increased camber in an attempt to maximize downforce potential. Four different slot

Figure 12: Bi-element wing with elongated second element

gap geometries wen: tested to determine the optimum settings

along with various rear end plate configurations. An increase in rear downforce by 20% or 150 lbf (667 N) was achieved with only a 7% penalty in drag with the wing fully optimized. The two element rear wing was used from 1992 until 1995 when IMSA mandated a spec rear wing consisting of a single element of Liebeck profile.

EFFECTS OF RULES CHANGES The sanctioning body where the Oldsmobile Cutlass Supreme competes is the International Motor Sports Association (IMSA). This group blends prototype and GT type vehicles into the same races. Considerable aerodynamic freedom was allowed up through the 1994 season at which time the World Sports Car (WSC) class replaced the GT Prototype (GTP) class. The WSC class vehicles were much slower over a given lap due to IMSA's attempt to contain escalating vehicle costs. At the same time, the GT classes were also undergoing restrictions to reduce vehicle speeds so as to ensure that the WSC vehicles maintained a speed advantage. Figure 13 shows how IMSA GT rules changed from 1992 to 1995. IMSA's approach for 1994 was to increase the weight to displacement scale and tn incorporate an air restrictor device for "endurance" races 12 hours or longer. Based on the projected performance of the various allowed configurations, GM Motorsports engineers decided to maintain the same weight and reduce the engine displacement, along with adding the

Figure 10: Wing with standard NACA-type airfoil and enlarged endplates

331

GT Rule I Rule Change

Year 1992

Wheelbase =Production dimension unless specifically approved Maximum width =79 in (2007 mm) Rocker panel width must be within 6 in (152 mm) of production Hood vents: Rear facing louvres on top surface Maximum area =450 in2 (0.29 m2) • Rearwing: Maximum width = 74 in (1880 mm) Maximum area =780 in2 (0.50 m2) Maximum height = Top of roof • Minimum ride height =3 in (76 mm) rocker to ground • Weight scale: 6.0 L =2350 lb (1 066 kg) 6.5 L = 2450 lb (1111 kg)

1993

• Wheelbase= Corresponding production greater than 103 in (2616 mm) can convert to 103 in • Bottom edge of door must not be Ylider than widest part of car

1994

• 55 mm dia. air restrictor required for events of 12 hours of more • Minimum ride height =2.5 in (63.5 mm) • Hood vents must present a solid surface when viewed from above • Weight scale: 5.0 L =2500 lb (1134 kg) 5.5 L = 2600 lb (1179 kg) 6.0 L =2700 lb (1225 kg) 6.5 L =2800 lb (1270 kg)

1995

• • • •

Figure 14: Engine air inlet treatment - circle indicates location of restrictor orifice throughout the season. GT type cars met with considerable race track success in 1994, prompting IMSA to further restrict the GT cars' performance potential in 1995. This was done primarily in the area of aerodynamics. The key elements of the changes included a single element 'specified' rear wing. Figure 10, and no hood louvers or venting of air on the top surface of the vehicle hood. In addition, the center floor area between the leading and trailing edge of the tire was to remain open to minimize the effects of a flat vehicle underside. The focus of the 1995 racing campaign was to optimize the IMSA rear wing and restore as much of the front downforce and radiator cooling flow as possible.

• Hood vents: • Rear wing:

Not allowed Single element Liebeck profile LD104E only Chord length= i0.75 in (273 mm) Maximum width =72 in (1 829 mm) Maximum height = Top of rear window • Weight scale: 5.0 L =2600 lb (1179 kg) 6.0 L =2850 lb (1293 kg) 4.5 L =2600 lb (1179 kg) 4 valve engine

Figure 13: IMSA rules changes required air restrictor. An air restrictor design was sought to maximize engine performance while meeting packaging and serviceability constraints. A diffuser area ratio and included angle were chosen to give the best tradeoff for power and installation space. The nozzle diffuser design selected performed very close to the theoretical pressure drop and recovery predicted. Figure 14 shows this trumpet extending from the restrictor to a flexible, removable couple ahead of the engine airbox. The resulting air inlet restrictor package resulted in less than a I 0% percent power loss when compared to the unrestricted endurance specification engine. The air restrictor design improved power recovery by more than 75 hp (55.9 kW) over the sharp edged orifice. Flow tests showed approximately 80% pressure recovery compared to an unrestricted system. Air inlet location was important to optimize power, and placing the inlet at a high pressure point minimized the impact of the restrictor. The inlet that was inherited from previous SCCA racing incorporated a port at the rear of the hood at the base of the window. Figure 15 shows this cowl inlet with a vertical tab at the rear of the opening in an attempt to augment inlet pressure. While this did help. pressures measured in the intake plenum still showed that at high rpm, the engine was seeing less than atmospheric pressure. This led to testing a forward facing opening placed above the radiator inlet. This intake can be seen at the lower left of Figure 3 between the sets of headlights. A subsequent on-track comparison showed that this inlet increased top speed by 3 mph (5 kph) over the cowl inlet. The restrictor was not required for the 1995 season. However, a less restrictive snorkel induction system with a downward facing inlet was used to help increase available intake plenum pressure

Little room was left for development with the new spec wing. Installing the IMSA specification single element rear wing reduced rear dov,!flforce by 285 lbf (1268 N) or 25% across the entire IX range. As vertical and longitudinal location had been developed, it was simply a matter of establishing the IX characteristics of this v.ring for adjusting the fore-aft aerodynamic balance of the car. It was found that Gurney flaps placed perpendicular to the trailing edge of the wing with varying heights could increase the maximum stall angle of the wing, thus providing more downforce capability. These flaps also proved useful in tuning rear dm.vnforce throughout the IX range. Increasing the flap height by 0.25'' (6.4 mm) produced a dCLRICo ratio of 3.9 versus a 3.5 ratio produced when a was raised by 4°. This meant that the

wing with the larger flap enjoyed 10% less drag while providing

Figure 15: Initial engine air intake at cowl

332

and opened directly into the engine compartment. By relieving underhood pressure, these openings increased radiator air flow by 8% and front dov-mforce by 70 lbf (311 N) or 25%. In addition to the valence cutouts, the front wheel well openings were widened in sideview to allow underhood air to escape behind the front wheels (see Figure 17). This improved front downforce by 60 lbf (267 N) or 18%. These modifications point out the significance of managing the air flow exiting the radiator and ensuring that it is evacuated properly from beneath the hood. The new rules package did not allow a complete recovery of the downforce level of 1994, but the engineers were able to deliver an aerodynamically balanced vehicle to the race teams. DEVELOPMrnNTS~nL\RY

Figure 16: 'Valence breathers'

Figure 18 highlights the incremental coefficients made to the Cutlass throughout its aerodynamic development. The sequence of the chart matches the order that the configurations were discussed above Incremental Coefficients Configuration evaluated Test .:l.Co aCLF .:l.CLR

the same amount of differential downforce. The front end of the vehicle proved to be a challenging area in trying to regain lost downforce. Even though a significant amount of rear downforce was sacrificed with the single element wing and a proportionally smaller amount of front downforce was lost with the removal of the hood louvres and dive planes, the proper front-to-rear balance and adequate radiator cooling flow were still required. IMSA GT rules allowed the engineers to take advantage of the area below the front bumper and ahead of the front wheels. Thus, 6 x 9 in (152 x 229 mm) ports were opened just ahead of the front wheel well openings (see Figure 16). These were internally designated 'valence breathers' and extended from the top of the splitter to the bottom of the bumper

Ducts from mdiator outlet to hood louvres

1992.1

-0.012

Added outboard louvres & duct 113 from underhood

1992.1

0.000

Rear of front undertray moved up 1.5 in

1992.1

Rear of front undertray outboard panels moved up

-0.047

0.006

-0.049

0.013

0.000

0.083

0.039

1994.1

-0.008

-0.038

0.006

Added 0.75 in to front of splitter

1992.1

-o.oo8

-0.024

0.004

Enclosed bottom of car

1992.1

0.009

-0.019

-0.030

Dive planes added to nose

1992.2

0.012

0.006

O.D18

Trimmed front of dive planes back 1.5 in

1992.2

0.010

-0.023

0.010

Raised front of dive planes 1.0 in

1992.2

0.003

0.010

-0.010

Rear wing moved aft 2.75 in

1993.0

0.032

0.030

-0.108

Installed wing at maximum width

1994.2

-0.018

-0.027

0.057

Installed IMSA spec wing

1994.2

-0.060

-0.133

0.226

-o.oss

.().004

Opened valence breathers

1994.2

0.016

I

Figure 18: Incremental changes

IMPROVED TESTING MEmODS BRAKE AND COOLING FLOW ANALYSIS - Cooling ducts on the Oldsmobile Cutlass race car had three primary functions. These were to keep the brakes at an optimal temperature, provide fresh air for the heat exchangers, and to help cool the driver. By optimizing each of these flows, overall aerodynamic performance was enhanced. Thus, a precise way of metering the amount of air flowing through each of these ducts was very

Figure 17: Widened front wheel well openings

333

importaiJt. Highly sensitive rotating vane anemometers were employed for this purpose. A 2 lt 4 grid of 5 in (127 mm) anemometers was placed on the rear of the engine water radiator to measure the rate of flow across the entire exit face. Too liule flow would have resulted in overheating and too much added to the pressure under the hood and could degrade front downforce and increase drag. Two 5 in anemometers were also placed on the transmission and differential coolers at the rear of the car. one per heat exchanger. 1bese coolers were fed by a 5 in duct placed on the right side 'B-pillar' and exhausted through an 80 in 2 (516 cm2} opening at the rear of the car locaterl in the standard license plate area. The vertical placement of the inlet was established using the data gathered by these anemometers. The limitation of these dry bearing anemometers was quickly found when they were installed in the brake ducts. These units subsequently failed due to the high velocities encountered in the duct work, leading to the use of pitot-static probes to measure this flow. Due to the sensitivity of the probes to flow angularity, great care was taken during installation to keep them parallel with the duct and away from sharp bends and data were compared only to runs within the same wind tunnel session. These data were useful in selecting body configurations and inlet locations that provided an adequate amount of cooling flow. Once again, too little air would overheat the brake rotors and calipers, while too much would hurt the overall aerodynamic perfonnance and not allow sufficient heat to build in the rotors. ENGINE AIR INLET ANALYSIS - Competing against the turbo-charged Nissan and Porsche engines, the Oldsmobile V6 and V8 required high engine air inlet pressures to increase their performance potential. A MAP sensor was placed in the cowl inlet to monitor this area. During on-track testing a marked depression below atmospheric pressure was seen in the airbox when the engine was at high rpm and the car was at near terminal velocity. This indicated that more work was necessary to alleviate this problem. To study this phenomenon in the wind tunnel. a dummy engine was built that would allow air to flow through it and out of the standard exhaust system. The valves were removed and a plate was placed over the pistons. While this did not simulate the draw of air by the engine during the intake cycle, it did reduce the amount of air that spilled around the pressurized inlet. UNDERBODY PRESSURE ANALYSIS- As aerodynamic aids became restricted by the sactioning body. attention was turned to optimizing the bottom of the car. IMSA rules required a flat plane between the front and rear wheels no lower than 2.50 in (64 nun} from the ground at static ride height_ This allowed for development of the front and rear undertrays and strategically placed underbody panels. In order to study this in more detail in the wind tunnel, a pressure strip was placed on the floor of the runnel along the longitudinal centerline of the vehicle. This apparatus consisted of 54 static pressure taps drilled into an aluminum strip at 4.0 in (102 mm) increments. Figure 5 shows results from some of the testing conducted with this pressure monitoring device in place.

SUI\.1MARY

The Oldsmobile Cutla~s Supreme race car which had initially been designed for racing within the SCCA Trans-Am series was shown to have been successfully developed for IMSA competition. Full scale, fixed ground plane wind tunnel testing coupled with on-track validation was fundamental to the domination of the Cutlass in GT racing. Furthermore, these tests were crucial in assessing the effects of rules changes months before they were put into effect. Developing legal aerodynamic aids for these cars and having the ability to test them at the track ahead of time gave the Cutlass a much needed aerodynamic competitive advantage. The development process required assessment of not only the aerodynamic forces on the vehicle, but also the internal flows and the pressures beneath the car. The six component force balance at the GM wind tunnel combined with the data control computers provided a great deal of feedback on how changes affected the forces applied through the tires. However, tools such as the underbody pressure strip and anemometers were crucial to developing a robust and efficient package for the endurance races and a stable. high performance vehicle for the sprint races.

ACKNOWLEDGEMENTS The authors would like to acknowledge Alain Clarinval (Brix Motorsports), Lee White (Rocketsports), Max Schenkel (GMAL), Gary Eaker (GMAL), Kevin Bayless (GM Motorsports Technology Group (GM MTG)). Tom Gideon (GM MTG), and Terry Laise (GM MTG) for their part in the development of this vehicle and the test methods described herein.

REFERENCES I.

K.B. Kelly, L.G. Provencher, and F.K. Schenkel, ''The General Motors Engineering Staff Aerodynamics Laboratory- A Full Scale Automotive Wind TunneL" SAE Paper No. 820371, February 1982.

2.

Ira H. Abbott and Albert E. Von Doenhoff, ''Theory of Wing Sections", Dover Publications, Inc., New York, 1959.

3.

Gino Sovran and Edward D. Klomp, "Experimentally Determined Optimum Geometries for Rectilinear Diffusers with Rectangular, Conical or Annular Cross-Section", Elsevier Publishing Co .. New York. 1967.

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