Automotive Mass Properties Estimation
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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).
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Automotive Mass Properties Estimation
- 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
- 7. 69TH Annual International Conference of the Society of Allied Weight Engineers, Inc. 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:
- 8. 69TH Annual International Conference of the Society of Allied Weight Engineers, Inc. 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 9
- 10. 69TH Annual International Conference of the Society of Allied Weight Engineers, Inc. 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 69th Annual International Conference of the SAWE 14
- 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% (!). 69th Annual International Conference of the SAWE 15
- 16. 69th Annual International Conference of the SAWE 16
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- 18. 69th Annual International Conference of the SAWE 18
- 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. 69th Annual International Conference of the SAWE 19
- 20. 69th Annual International Conference of the SAWE 20
- 21. 69th Annual International Conference of the SAWE 21
Editor's Notes
- AUTOMOTIVE MASS PROPERTIES ESTIMATION
- WHY AUTOMOTIVE MASS PROPERTIES? WELL, AS THE VU-GRAPH SAYS, IT’S A MATTER OF PERSONAL INTEREST…………..SAWE PAPER, JOURNAL ARTICLE, SAE MEMBER, SEMINAR, PUBLICATIONS, PERSONAL LIBRARY, TECH PAPERS AND, OF COURSE, MASS PROPERTIES HAS GREAT SIGNIFICANCE FOR AUTOMOTIVE PERFORMANCE….FUEL ECONOMY, EMISSIONS, RIDE, SAFETY, ACCELERATION, BRAKING, MANEUVER, WHICH IS PRETTY MUCH THE SAME FOR ALL VEHICLES... AND LAST, BUT NOT LEAST, WRITING A PAPER ON THIS SUBJECT SEEMED TO BE A GOOD WAY TO HELP EXPAND THE SCOPE OF OUR SOCIETY. I UNDERSTAND THAT AS A SOCIETY WE ARE INTERESTED IN BECOMING MORE INCLUSIVE, EXPANDING OUR MEMBERSHIP BASE, AND THIS IS MY SMALL WAY OF CONTRIBUTING TO THAT GOAL. THERE ARE ONLY ABOUT 40 PAPERS IN THE SAWE CATEGORY 31.0, AND NONE OF THOSE ADDRESS THE ESTIMATION OF AUTOMOTIVE MASS PROPERTIES FROM A TOP DOWN PARAMETRIC APPROACH. THE VAST MAJORITY OF OUR PAPERS AND JOURNAL TOPICS, ETC., CONCERN AEROSPACE AND MARITIME MATTERS…….
- AND THERE IS ANOTHER REASON FOR DOING THIS, AND THAT IS I THINK THAT A COMPREHENSIVE AUTOMOTIVE MASS PROPERTIES ESTIMATION METHODOLOGY WOULD HAVE A CERTAIN USEFULNESS. I IMAGINE THAT THE BIG ESTABLISHED AUTOMOTIVE MANUFACTURERS HAVE THEIR OWN MEANS OF ESTIMATING AUTOMOTIVE MASS PROPERTIES, WHICH THEY APPARENTLY ARE NOT SHARING, BUT THERE ARE INDEPENDENT DESIGNERS, RESEARCHERS, SIMULATION PROGRAMMERS, AND ACCIDENT INVESTIGATORS.
- TO START THE QUEST FOR A AUTOMOTIVE MASS PROPERTIES ESTIMATION METHODOLOGY I BEGAN WITH A LITERATURE SEARCH TO SEE WHAT WAS ALREADY AVAILABLE, WHICH I INTENDED TO BUILD UPON. WHAT I FOUND WAS THAT THERE REALLY ISN’T VERY MUCH, AT LEAST BY WAY OF A COMPREHENSIVE, RELIABLE, ACCURATE METHODOLOGY. THERE ARE BITS AND PIECES OF WHAT COULD BECOME SUCH A METHODOLOGY IF DEVELOPED AND COMBINED APPROPRIATELY, AND I INCORPORATED WHAT I FOUND THAT WAS USEFUL INTO MY PAPER, WITH PROPER ATTRIBUTION, AS WE SHALL SEE. THE SORT OF LITERATURE I WENT THROUGH IS LISTED IN THE VU-GRAPH. THE BOOKS CAME MAINLY OUT OF MY OWN PERSONAL LIBRARY, AND THE MAGAZINE ARTICLES WERE MAINLY ONES THAT I HAD COLLECTED OVER MANY YEARS. TECHNICAL PAPERS, HOWEVER, CAME FROM A NUMBER OF INTERNET SOURCES BUT MAINLY FROM THE SAE. YOU WOULD THINK THAT THE SAE WOULD HAVE A GREAT MANY PAPERS ON THIS SUBJECT, SO MANY AS TO RENDER THE CREATION OF A PAPER LIKE MINE REDUNDANT, BUT YOU WOULD BE WRONG. THERE IS ONLY A HANDFUL OF PAPERS THAT ATTEMPT A PARAMETRIC ESTIMATION OF AUTOMOTIVE MASS PROPERTIES, AND THOSE PAPERS TEND TO BE AS INCOMPLETE AND UNRELIABLE AS ANY OTHER PUBLICALLY AVAILABLE SOURCE, AS I’LL ILLUSTRATE A LITTLE IN THE COURSE OF THIS PRESENTATION AND AS DISCUSSED AT LENGTH IN MY PAPER.
- SO, THE LITERATURE SEARCH TURNED UP SOME USEFUL THINGS, BUT NO EXISTING COMPREHENSIVE ESTIMATION METHODOLOGY. THERE WERE ATTEMPTS TO DEVELOP METHODS FOR ESTIMATION OF CERTAIN AUTOMOTIVE MASS PROPERTIES, BUT THE RESULTS WERE USUALLY NOT SATISFACTORY, AT LEAST NOT BY THE STANDARDS THAT WE WOULD APPLY. MOST OF THE DIFFICULTY SEEMED TO STEM FROM THE FACT THAT THE AVAILABILITY OF APPROPRIATE AUTOMOTIVE DATA FOR THE DEVELOPMENT OF SUCH A METHODOLOGY WAS VERY LIMITED. THIS NEED FOR DATA MAY HAVE BEEN THE REASON BEHIND THE DEFICIENTCIES OBSERVED OF EXISTING ATTEMPTS: IT MAY BE WHY DATA WAS NOT NORMALIZED FOR VEHICLE TYPE, CONFIGURATION, WEIGHT CONDITION, APPLICABLE SPEC/REGULATION, OR LEVEL OF TECHNOLOGY; AND WHY THE EQUATIONS RESULTING FROM REGRESSION ANALYSIS WERE OFTEN FORCED TO GO THROUGH THE “0,0” POINT. IT WAS A MATTER OF DESPERATION FOR DATA, AND THE RESULTANT FEELING SEEMED TO BE THAT ANY DATA IS GOOD; JUST THROW IT ALL IN TOGETHER AND THE VARIETY WILL MAKE THE RESULTING ESTIMATION ROUTINE MORE ROBUST. AND “0,0” WAS ONE MORE DATA POINT……….. THEN THERE ARE SOME OTHER MISCONCEPTIONS. THERE SEEMED TO BE A CERTAIN DISPAIR ON THE PART OF SOME AUTHORS THAT CERTAIN MASS PROPERTIES COULD BE ESTIMATED WITH ANY DEGREE OF ACCURACY REGARDLESS OF AMOUNT OF DATA AVAILABLE. THE PROBLEM SEEMED TO BE THAT PARAMETERS LIKE WHEELBASE, HEIGHT, WIDTH, TRACK, ETC., WERE EXTERNAL MEASUREMENTS; BUT MASS PROPERTIES LIKE THE CENTER OF GRAVITY AND INERTIAS WERE DETERMINED BY THE INTERNAL ARRANGEMENT OF THE COMPONENT MASSES. OF COURSE, NORMALIZING THE DATA SO THAT IT CONFORMS TO A SPECIFIC AUTOMOTIVE PARADIGM: PASSENGER CAR, FWD, FRONT ENGINE, US SPEC, CURB WEIGHT CONDITION, ETC. IN THAT WAY THE INTERNAL ARRANGEMENT OF THE COMPONENT MASSES IS ACCOUNTED FOR, ALTHOUGH IN A GENERAL WAY. THEN THE MEASURED EXTERNAL PARAMETERS CAN PROVIDE CLUES AS TO THE SPECIFIC MASS PROPERTY VALUES……….. IN SHORT, WHAT’S OUT THERE BY WAY OF AUTOMOTIVE MASS PROPERTIES ESTIMATION WOULD BE A LOT BETTER IF IT HAD BEEN DONE BY WEIGHT ENGINEERS, NOT PEOPLE FROM OTHER DISCIPLINES TRYING TO DO A MASS PROPERTIES TASK.
- So, I wanted to do something comprehensive, meaning……. And I wanted it to be top-down, meaning I wanted estimation routines requiring high-level parametric input: length, width, height, wheelbase, track as would be available early on in the design stage or as would be available from the common literature for existing vehicles….. To do this I would do a proper regression analysis: using most appropriate model(s), floating intercept, normalized database(s), and rational determination of satisfactoriness……. All I needed was adequate data. Well, the NHTSA, as a result of the decades old debate on roll-over safety, began collecting vehicle track and C.G. Height data for the calculation of vehicle Static Stability Factors (SSFs = T/2Hcg), and that grew to include all the top level parameters and mass properties. The VIPMD has about 500 data items………. Integrated with the results of my analysis would be those useful results of the literature search: Campbell & Basso………………. Colin Campbell is an engineer and the noted author of many books on automotive engineering. G.L. Basso is someone about whom a good deal less is known; he is a researcher who has written or co-written a number of technical papers for the Canadian government: “Functional Derivation of Vehicle Parameters for Dynamic Studies”, National Research Council of Canada, 1974.
- Now, the way the resultant total mass estimation methodology of my paper works is illustrated by this vu-graph. The mass properties for the total vehicle: weight, cg, inertias, and products are estimated per the regression analysis formulae I developed plus Basso’s equations (for the products). Then the unsprung vehicle mass properties are estimated via Colin Campbell’s method. Finally, the sprung vehicle mass properties result from the application of the normal weight accounting equations to subtract the unsprung mass properties from the total vehicle mass properties…..
- Then the only thing left to do to make this methodology truly comprehensive in determining all the high-level vehicle mass properties is to determine the sprung mass inertia about the roll axis as shown…. Roll axis at distance “d” from, and some at some angle “phi” with respect to, the longitudinal reference axis.
- Now, just to give you an idea of what some the estimation routines look like, we include this vu-graph. This is just a sample, the paper literally has dozens of ways to calculate many specific mass properties, depending on what parameter input is available. Note we have one of G.L. Basso’s contributions at the end there…..
- Speaking of Basso’s contributions, here is essentially Colin Campbell’s contribution to this methodology: the estimation of the unsprung mass properties……. The ‘94 Ford Taurus is used as an example because the unsprung mass of this vehicle was determined empirically by two different methods, and then painstakingly calculated by yours truly; the results are all so close…If there are any questions about this later I have a considerable number of back-up vu-graphs…. Anyway, as you can see the unsprung weight is determined by taking an appropriate coefficient for the type of suspension contemplated, multiplying by the vehicle (curb) weight, and adding in the weight of a set of wheels and tires. The weight of the wheels and tires may be approximated by finding something similar to what is wanted from the wheel and tire weight tables included in the paper, or very often the exact weight can be found for the specific items from an internet data search. Once the unsprung weight is determined the other unsprung mass properties can be estimated via some simple calculations as illustrated in my paper…..
- Plot of vertical cg variation for 10 Front Engine, RWD, US spec, 1985-1995 passenger cars Jaroslav Taborek, Mechanics of Vehicles, Cleveland, OH; Machine Design, 1957. Eq. 5.7 Allen, Rosenthal, and Szostak, “Steady State and Transient Analysis of Ground Vehicle Handling”, Automotive Crash Avoidance Research, Warrendale, PA; SAE SP-699, 1987. Eq. 5.8 Study of relative stability of various automotive configurations during cornering while undergoing acceleration or braking, Needed estimates of: Zcg, Ixxs, Izzs, Irolls to conduct dynamic simulations; backed by the NHTSA and the SAE and STILL HAD TO DEVELOP ESTMATION ROUTINES using an 18 vehicle database varying from: 1956 to 1980, economy car to motorhome, FWD to RWD to AWD. Wiegand, 1 parameter (Hoa) linear regression analysis equation. Eq. 5.10 6 parameter (Wb, Tf, Tr, Loa, Hoa, Woa) linear multi-regression analysis equation. Eq. 5.13
- There are literally dozens of “conclusions” of various degree of significance in Chapter 10 of the paper, but this is essentially the conclusion from the 35,000 foot level, so to speak….