Mass properties have a profound effect on automotive fuel economy, emissions, safety, ride, acceleration , braking, and maneuver . Because of this fact, it is important to have a reliable and comprehensive methodology for the estimation of key mass property parameters in the conceptual design stage. Also, such a methodology would be important for researchers investigating aspects of automotive dynamics, for programmers creating realistic automotive simulations, and for investigators studying the dynamics of automotive crash scenarios . There is a scarcity of published information of sufficient accuracy and/or completeness so as to constitute a viable methodology. Published automotive mass property estimation methods seem to be available only in a non-comprehensive fashion through a variety of scattered sources. It is the intent of this paper to systematize the information drawn from published sources and, with the employment of techniques based on those used in the aerospace industry, to augment and improve upon the published information so as to develop a basis for a comprehensive automotive mass properties estimation methodology. Note the use of the word “basis”; it is not to be imagined that this paper will represent the “last word” in automotive mass properties estimation. What is presented herein is intended to provide a possible overall framework for, and an initial “first cut” at, the development of a comprehensive methodology. Automotive design practitioners working within the established industry may have a far more potent estimation methodology available to them, but in the form of proprietary techniques that they are not at liberty to divulge. Yet even such automotive industry insiders may find an independently derived methodology interesting, and perhaps even useful for comparison with in-house procedures. However, it is the independent designer or researcher that is most likely to find this paper to be of great value, and it is the purpose of this paper to aid such independent efforts through promoting the development of a publicly accessible methodology. To that end this paper presents the development of a preliminary “top-down” methodology which requires as input only those most basic and common overall parameters as would be available in the earliest of design stages or, for existing designs, from the commonly available literature. This includes such parameters as vehicle dimensions, applicable general legal specification or regulation, general vehicle configuration and category, type of suspension, and level of technology (which is generally time dependent). The desired output consists of the curb weight/c.g. coordinates/inertias, the unsprung weight/c.g. coordinates/inertias, the sprung weight/c.g. coordinates/inertias, and the sprung weight roll moment of inertia (i.e., a rotational inertia about an essentially longitudinal axis, the location of which is determined by the suspension geometry).

1. Brian Paul Wiegand, PE
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010

2.  PERSONAL INTEREST
• WROTE SAWE PAPER, JOURNAL ARTICLE
• SAE MEMBER, SEMINAR, PUBLICATIONS
• PERSONAL LIBRARY, TECH PAPERS
 SIGNIFICANCE
• FUEL ECONOMY, EMISSIONS, SAFETY, RIDE
• ACCELERATION, BRAKING, MANEUVER
 EXPAND SAWE SCOPE
• AEROSPACE MASS PROPERTIES
• MARITIME MASS PROPERTIES
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010 2

3.  INDEPENDENT DESIGNERS
 SMALL, START-UP COMPANIES: APTERA MOTORS, MILNER MOTORS, FISKER
AUTOMOTIVE, PANOZ AUTOMOTIVE DEVELOPMENT COMPANY, FUTURE VEHICLE
TECHNOLOGIES, VECTOR MOTORS, TESLA MOTORS, ETC.
 KIT CAR, HOT ROD, CUSTOM CAR INDUSTRY: FIBERFAB US, FOOSH DESIGN,
ROSSION AUTOMOTIVE, ETC.
 DESIGN CONSULTANTS: ENGINEERING DESIGN CONSULTANTS LTD, GORDON
MURRAY DESIGN LTD, TECHNICAL ENGINEERING CONSULTANTS INC, ETC.
 RESEARCHERS
 ALLEN, ROSENTHAL,& SZOSTAK; “STEADY STATE AND TRANSIENT ANALYSIS OF
GROUND VEHICLE HANDLING”, 1987.
 LARRABEE & HAWKS, “THE CALCULATED EFFECT OF CROSS-WIND GRADIENTS ON
THE DISTURBANCE OF AUTOMOTIVE VEHICLES”, 1969.
 SIMULATION PROGRAMMERS
 REALISTIC COMPUTER GAMING: GRAND THEFT AUTO, ROBOT AUTO RACING
SIMULATOR (RARS), GRAND PRIX LEGENDS, ETC.
 VIRTUAL REALITY: VRDS (VIRTUAL REALITY DRIVING SIMULATOR) TO ASSESS BRAIN
INJURY, PREVENT ALCOHOL ABUSE, DRIVER’S EDUCATION, ETC.
 MOVIE SCENES: CARS (PIXAR, DISNEY), SPEED RACER (WARNER BROS), THE DARK
KNIGHT (WARNER, LEGENDARY PICTURES), ETC.
 ACCIDENT INVESTIGATORS
 ACCIDENT RESEARCH ENGINEERS INC, CRASH DATA SERVICES LLC, BISON
FORENSIC ENGINEERS, ETC.
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010 3

4.  BOOKS
 BOSCH AUTOMOTIVE HANDBOOK, MECHANICS OF
VEHICLES, THE AUTOMOTIVE CHASSIS, HANDBOOK OF
VEHICLE DESIGN ANALYSIS, ETC.
 MAGAZINES
 AUTOMOTIVE ENGINEERING (SAE), ROAD & TRACK, THE
AUTOMOBILE, MOTOR TREND, CAR AND DRIVER, ETC.
 PAPERS
 “FUNCTIONAL DERIVATION OF VEHICLE PARAMETERS FOR
DYNAMIC STUDIES”, NATIONAL RESEARCH COUNCIL
CANADA.
 “DEVELOPMENTS IN CENTER OF GRAVITY AND INERTIAL
ESTIMATION AND MEASUREMENT”, SAE.
 “TYPICAL VEHICLE PARAMETERS FOR DYNAMICS STUDIES
REVISED FOR THE 1980’S”, SAE.
 ETC.
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010 4

5.  NO EXISTING COMPREHENSIVE TOP-DOWN
AUTOMOTIVE MASS PROPERTIES ESTIMATION
METHODOLOGY
 AUTOMOTIVE DATA FOR DEVELOPMENT OF
METHODOLOGY VERY LIMITED
 EXISTING METHODOLOGY ANALYSIS DEFICIENT
 DATA NOT NORMALIZED FOR TYPE, CONFIGURATION,
WEIGHT CONDITION, SPEC/REGULATION, LEVEL OF
TECHNOLOGY
 FORCED “0,0” INTERCEPT
 MISCONCEPTIONS
 “THE CENTER OF GRAVITY IS…PROPERTY OF A GIVEN
CAR AND CAN NOT BE READILY ESTIMATED”
 “…NO CORRELATION WITH ANY MEASURED VEHICLE
PROPERTIES THAT WOULD ALLOW…(Pxz)…TO BE
ESTIMATED…”
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010 5

6.  COMPREHENSIVE
 TOTAL VEHICLE WEIGHT, C.G. COORDINATES, INERTIAS, PRODUCTS
 SPRUNG WEIGHT, C.G. COORDINATES, INERTIAS, PRODUCTS
 UNSPRUNG WEIGHT, C.G. COORDINATES, INERTIAS, PRODUCTS
 TOP-DOWN
 HIGH-LEVEL PARAMETER INPUT: VEHICLE LENGTH, WIDTH, HEIGHT,
WHEELBASE, TRACK
 PROPER STATISTICAL ANALYSIS
 APPROPRIATE REGRESSION MODEL: LINEAR MULTI-VARIABLE, POWER MULTI-
VARIABLE, ETC.
 FLOATING INTERCEPT
 NORMALIZED PASSENGER CAR DATABASES: FRONT ENGINE/RWD/1984 U.S.
SPEC SPORT/SPORTY, FRONT ENGINE/FWD/’85-’95 U.S. SPEC SDN/CPE, FRONT
ENGINE/RWD/’76-’88 U.S. SPEC SDN/CPE
 ANALYSIS RESULT SATISFACTORINESS: SAWE CRITERIA (WEIGHT ENGINEER’S
HANDBOOK PAGE 18.9); OTHER STATISTICAL INDICATORS: STANDARD ERROR, P-
TEST, F-TEST, ETC.
 ADEQUATE DATA: NHTSA VIPMD, VARIOUS LITERATURE SOURCES
 COMBINE WITH SELECT LITERATURE SEARCH RESULTS
 UNSPRUNG MASS PROPERTIES (COLIN CAMPBELL, MODIFIED)
 PRODUCT OF INERTIA (G.L. BASSO)
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010 6

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Virginia Beach, VA, 22-26 May 2010 7
USE THE TOP-LEVEL REGRESSION ANALYSIS DERIVED
ESTIMATION ROUTINES TO DETERMINE THE TOTAL VEHICLE
MASS PROPERTIES, AND USE THE MODIFIED COLIN CAMPBELL
METHOD TO DETERMINE THE UNSPRUNG MASS PROPERTIES,
THEN FIND THE SPRUNG MASS PROPERTIES VIA STANDARD
“WEIGHT ACCOUNTING” PROCEDURE:
1995 Chevrolet Lumina:

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Virginia Beach, VA, 22-26 May 2010 8
Iroll = Ixs Cos2ф – 2 Pxzs Sinф Cosф + Izs Sin2ф + Ws d2

9.  Wt = - 15.3678 Loa – 86.3740 Woa – 3101.8312 Hoa + 870.3500 Wb
- 2675.1199 Tf + 4963.0342 Tr + 343.9573 (Eq. 3.11)
 Lcg = 0.7354 Wb + 0.7287 Tf – 1.0662 Tr + 0.0431 Loa – 0.2256 Hoa
- 0.4656 Woa – 0.6321 (Eq. 5.6)
 Hcg = – 0.1956 Wb – 0.1954 Tf + 0.2150 Tr – 0.0335 Loa + 2.1407 Hoa
– 0.1524 Woa – 1.5109 (Eq. 5.13)
 Ix = 355.9595 Wt
0.3340 Hoa
-1.8351 Hcg
4.1633 Tf
-4.2664 Tr
7.7809 Woa
-0.4812
(Eq. 7.37)
 Iy = 0.6722 Wt
0.6639 Wb
8.5279 Loa
0.9883 a-2.6097 Hoa
-14.4677 Hcg
2.0423
(Eq. 7.39)
 Iz = 1305.5048 Wt
-1.1589 Wb
11.1997 Loa
-0.0403 Lcg
-4.8950 Tf
-3.7181 Tr
9.3188
Woa
-5.3959 (Eq. 7.41)
 Pxz = 0.0374 Wt2/3 Wt/g tan 2λ (G. L. Basso) (Eq. 9.2)
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010
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Virginia Beach, VA, 22-26 May 2010 10
1994 Ford Taurus:
Frt: Wusf = (3237.3 x 0.0675 x 0.59) + (2 x 40.37) = 209.7 lb (95.1 kg) / axle Est., vs. 197.1 lb (89.5 kg)/ axle Act.
Rr: Wusr = (3237.3 x 0.0530 x 0.59) + (2 x 40.37) = 182.0 lb (82.5 kg) / axle Est., vs. 195.1 lb (88.5 kg)/ axle Act.
Tire
Weight
Table
Wheel
Weight
Table
APPENDIX D

11. 69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010 11

12.  A BASIS FOR A COMPREHENSIVE TOP-
DOWN ESTIMATION OF AUTOMOTIVE
MASS PROPERTIES HAS BEEN DEVELOPED
AND PRESENTED BUT…
 DUE TO THE INFINITE VARIATION IN
AUTOMOTIVE TYPE, CONFIGURATION,
SPECIFICATION/REGULATION, AND
LEVEL OF TECHNOLOGY THERE IS
INFINITE SCOPE FOR FURTHER
DEVELOPMENT.
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010 12

13. FIVE MINUTES ARE ALLOCATED FOR
ASKING QUESTIONS OF THE AUTHOR
69TH Annual International Conference of the Society of Allied Weight Engineers, Inc.
Virginia Beach, VA, 22-26 May 2010 13

14.  Senior Research Engineer, ICI Ltd
 Senior Project Engineer, Walker Mfg. Co.,
Wisconsin, U.S.A.
 Managing Director, The Sports Car Garage,
Blackburn, Lancaster, U.K.
 Technical Officer, Royal Aircraft Establishment,
Farnborough, U.K.
 Author of Six (6) Books on Automotive
Subjects
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15. The paper “Developments in Vehicle Center of
Gravity and Inertial Estimation and Measurement”
introduced a means by which the total vehicle
unsprung weight may be empirically determined
while the vehicle is on the VIMF (Vehicle Inertia
Measurement Facility) test device. The method was
applied to a 1994 Ford Taurus. In two tests, values
of 150.5 kg (331.8 lb) and 177.4 kg (391.1 lb) were
obtained for the unsprung weight. Then the
Transportation Research Center in East Liberty,
Ohio, tore the Taurus apart and weighed the
unsprung mass (which would seem to require a
good deal of judgment as some components are
only to be considered partially unsprung!);
resulting in a weight of 178 kg (392.4 lb),
suggesting a possible error range for this
measurement method of -18% to -0.3% (!).
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19.  WORKED FOR NATIONAL
AERONAUTICAL ESTABLISHMENT
LABORATORY, NATIONAL RESEARCH
COUNCIL OF CANADA.
 WROTE REPORT LTR-ST-747,
“FUNCTIONAL DERIVATION OF VEHICLE
PARAMETERS FOR DYNAMIC STUDIES”,
1974.
 DERIVED METHODS FOR AUTOMOTIVE
Pxz ESTIMATION.
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