The intent of this presentation is to show that a vehicle designed in true accordance with the balanced viewpoint of a professional mass properties engineer may not only demonstrate superior acceleration, braking, and handling, but superior ride, stability, fuel economy, and safety as well. If a design begins with the first principles of how mass properties affect automotive performance in all its aspects , and is optimized accordingly in an integrated manner, then the resulting advanced automotive design may truly “go where none have gone before”.
1. Brian Paul Wiegand, PE
74TH SAWE International Conference on Mass Properties Engineering
Alexandria, VA, 18-22 May 2015
2. …USUALLY BEAR THE STAMP OF A GREAT
INDIVIDUAL:
H ENRY ROYCE – QUALITY
PAUL JARAY – AERODYNAMICS
ENZO FERRARI – ENGINE
POWEL CROSLEY – COST
PRESTON TUCKER – SAFETY
ALEC ISSIGONIS – SMALL SIZE
COLIN CHAPMAN – MASS PROPERTIES
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3. THE LOTUS ENGINEERING COMPANY WAS
FOUNDED BY CHAPMAN ON 1 JANUARY 1952
WITH VIRUALLY NO CAPITAL. ENGINES,
GUAGES, TRANSMISSIONS, DIFFERENTIALS,
AND MOST OTHER COMPONENTS WERE
PURCHASED. THE ONLY WAY THAT LOTUS
VEHICLES COULD BE DIFFERENTIATTED
FROM OTHER VEHICLES AND GAIN A
COMPETITIVE EDGE WAS THROUGH MASS
PROPERTIES, AND IN PARTICULAR THE
RUTHLESS PURSUIT OF MINIMUM WEIGHT.
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4. …IN LACK OF RELIABILITY AND IN INJURY
& DEATH. CHAPMAN OPTIMIZED MASS
PROPERTIES, BUT DID NOT DO SO IN THE
WAY A PROFESSIONAL MASS PROPERTIES
ENGINEER WOULD HAVE. HE WOULD
OVERRIDE THE JUDGEMENT OF HIS STRESS
ENGINEERS AND REDUCE THE WEIGHT OF
STRUCTURE AND SUSPENSION IN LOTUS
RACE CARS TO THE POINT THAT FAILURE
IN USE WAS INEVITABLE.
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5. …AND RE-ENGINEERING EVERTHING
UPWARD FROM THOSE PRINCIPLES TO
ACHIEVE TOTALLY NEW AND SUPERIOR
DESIGNS. ACTUALLY, NOTHING COULD
HAVE BEEN FURTHER FROM THE
TRUTH…
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6. “Colin was extremely sharp, clever and quick-
witted, and very charismatic, but not a really
great engineer or designer. He had a few
principles which he pursued to great effect,
such as light weight…but he never had a really
close grasp of fundamental principles. Perhaps
he might have had if he had more time to learn.
But in his hectic and unscrupulous life it was
quicker to rely on other people to whom he
gave minimum credit.”
Charles Bulmer
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7. …WHAT WOULD BE THE RESULT
IF SOMEONE WERE TO RETURN
TO FIRST PRINCIPLES AND
DESIGN AN AUTOMOBILE
FROM A PROFESSIONAL MASS
PROPERTIES ENGINEER’S
VIEWPOINT ?!?
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9. …INCLUDE THE CONCEPT OF “EFFECTIVE
MASS”:
F = me a
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10. TEXT
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Wt = Weight of the vehicle (lb).
g = Gravitational constant, “g” = 32.174 ft/s2.
I1 = Rotational inertia about front axle line (lb-ft2).
I2 = Rotational inertia about the crankshaft axis (lb-ft2).
I3 = Rotational inertia about transmission 3rd motion axis
(lb-ft2).
I4 = Rotational inertia about rear axle line (lb-ft2).
TR = Transmission gear ratio (dimensionless).
AR = Axle gear ratio (dimensionless).
RD = Dynamic rolling radius at drive wheels (ft).
11. A REDUCTION OF “I1” AND “I4”:
1) REDUCES WEIGHT MASS
2) REDUCES EFFECTIVE MASS
3) REDUCES UNSPRUNG MASS
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12. ONE FOURTH THE WEIGHT:
Whalf / Wfull = ( π R2 t / 4) / π R2 t = ¼
ONE SIXTEENTH THE ROTATIONAL INERTIA:
Ihalf / Ifull = ( π R4 t / 32) / ( π R4 t / 2) = 1/16
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WEIGHT OF TIRES, WHEELS, ETC. IS NOW:
8W8 / 4W4 = (8 π R2 t / 4) / 4 π R2 t = 1/2
AND THE ROTATIONAL INERTIA IS NOW:
8I8 / 4I4 = (8 π R4 t / 32) / (4 π R4 t / 2) = 1/8
16. REEVES OCTOAUTIO – 1911
PANZERSPAHWAGEN – 1942
PAT CLANCY SPECIAL – 1948
AVS SHADOW – 1970
ELF TYRRELL P34 – 1975
MARCH 2-4-0 – 1976
WILLIAMS FW08B – 1982
COVINI C6W – 2004
KEIO UNIVERSITY ELIICA - 2004
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23. PERFORMANCE COMPARISON OF:
BASELINE VEHICLE – KNOWN ENTITY
WITH:
“ADVANCED CONCEPT” – DEVELOPED
FROM BASELINE
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24. TRIED TO AVOID ANY CHANGES NOT ESSENTIAL TO
TRANSITION FROM 4 FULL SIZE TIRES TO 8 HALF
SIZE TIRES.
HOWEVER:
1) HAD TO REDUCE SPRING STIFFNESS BY HALF AND
RESIZE SUSPENSION, 1 INCH LOWER.
2) HAD TO KEEP FULL SIZE BRAKES AND INCREASED
NUMBER TO EIGHT & MOVED INBOARD.
3) HAD TO MAKE BOTH REAR AXLES DRIVE (“LIVE”)
AXLES.
4) HAD TO CHANGE ORIENTATION OF ENGINE
FROM LONGITUDINAL TO TRANSVERSE.
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25. 1) WEIGHT: -0.3% 2) EFFECTIVE WEIGHT: -1.5%
3) ROLL RESIST: -55.1% 4) LOAD CAP: -17.7%
5) TRACTION: +5.1%
6) AERO DRAG: -14.6% 7) AERO LIFT: +15.0%
8) HYDROPLANING: Vc : -14.5%, Ls: -51.6%
9) TIRE LIFE: -49.8% 10) STANDING WAVE: -9.4%
11) SSF (OVERTURN RESISTENCE): +13.9%
12) ROLL GAIN: -8.9% 13) LAT ACCEL: +44.1%
14) DIRECTIONAL STABILITY: Kus = 6.85 vs. 0.20 deg, Vchar
= 32.6 vs. 188.3 mph, SM = 0.09 vs. 0.02
15) TRANSIENT RESPONSE: DIY = 0.74 vs. 0.75, AYR/ω =
1.185 vs. 1.003 16) ROAD SHOCK: -49.3%
17) ROAD CONTACT: BUMP -6.0%, DIP +34.6%
20) GYROSCOPIC REACTIONS: -80.5% front, -64.0% rear
21) FUEL ECONOMY: HIGHWAY +6.3% / CITY +3.3%
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31. 1) PRODUCIBILITY
a) TIRE PROCUREMENT
2) MARKETIBILITY
a) STYLING
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32. FIVE MINUTES ARE ALLOCATED FOR
ASKING QUESTIONS OF THE AUTHOR
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Alexandria, VA, 18-22 May 2015 32
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Lastly, it should be noted that the “advanced concept” as presented
herein does not represent the pinnacle of achievement, and would
seem even more compelling when subjected to further development.
The “distributed traction” characteristic of the “advanced concept”
lends itself naturally to take best advantage of the benefits of
“distributed drive” as proposed by Hao, Chen, and Wang in their
paper, and as demonstrated by Keio University with their Eliica. That
the automobile of the future will have complete electronic control over
braking, drive, roll, pitch, ride, and stability seems certain, and the
mass properties driven configuration of the “advanced concept”
represents a complementary means to physically employ that new
technology to greatest advantage. Many have gone a part of the way to
this goal, but at present it still remains a place “where none have gone
before.”
FURTHER DEVELOPMENT ?
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“…friction would be off the chart when the thing turns......or tries to! And the weight of four more tires, wheels and related suspension and
steering bits would so negatively impact fuel economy that it would more than offset the reduction in rolling resistance. "Rolling resistance"
is just one small variable in the overall “…friction would be off the chart when the thing
turns......or tries to! And the weight of four more tires, wheels and related
suspension and steering bits would so negatively impact fuel economy that it
would more than offset the reduction in rolling resistance. "Rolling resistance"
is just one small variable in the overall efficiency equation...”
Bob Lutz...”
[1] 14 June 2014
[1] Robert Anthony Lutz (1932- ) has served as Executive Vice President for BMW, Executive Vice President of Ford Motor Company,
Head of Chrysler Global Product Development, and Vice Chairman of Global Product Development at GM. He retired from GM on 2 May
2010, and now heads his own consulting firm. In an E-mail exchange this author made reference to the advantages of the “advanced
concept”, and thereby received the comment as quoted.
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“…friction would be off the chart when the thing turns......or tries to! And the weight of four more tires, wheels and related suspension and
steering bits would so negatively impact fuel economy that it would more than offset the reduction in rolling resistance. "Rolling resistance"
is
The Edsel may have failed for insubstantial reasons, but reasons which
are significant in the marketplace. For the “advanced concept” to be
marketable reasons of that type have to be addressed. As noted in
Chapter 2, simply mating conventional automotive architecture with such
small wheels (not to mention an unusual number of them to boot) results
in an appearance certain to found “silly” and reminiscent of a “kiddie
car” or “small trailer”. Present day styling trends emphasize large wheels
and tires, even to the point of decreasing performance, as demonstrated
by the Car and Driver “plus-sizing” study. The styling has to be of “an all
new car design” paradigm in accord with the all new configuration
paradigm, and it has to appeal to the emotions; an emotional commitment
generally has to precede (or supersede) the rational for mass appeal to be
attained.
Editor's Notes
MASS PROPERTIES & ADVANCED AUTOMOTIVE DESIGN
Charles Bulmer (1922-2012) was a great British automotive journalist and one-time editor of The Motor, a contemporary of Colin Chapman.
There is the familiar “weight mass” (W/g), but an automobile has components that get accelerated not just translationally but rotationally as well. The effect is that of extra mass, all that stuff in the second term after “W/g”.
You’ve all heard the expression “to kill two birds with one stone” which is intended to be representative of the height of efficiency. Well, as mass properties engineers we can frequently improve on that. In the automotive case…
Using the formulae from the SAWE Weight Engineer’s Handbook for a right circular cylinder…
Using the TRA formulae (standard and proposed) from The Pneumatic Tire by Gent and Walter (standard formula shown)…
Where:
Lcap = Tire load capacity at pressure “Pi” (lb).
K = Tire service factor (Ktruck&bus = 1.00, Kpassenger car = 1.10).
Pi = Tire inflation pressure (psi).
S = Tire section width "adjusted" for equivalent circular periphery (in).
DR = Nominal wheel rim diameter (in).
The red replaces the yellow (lose the spare tire). The small size tires are pushed out to the edges of the body envelope; if kept within the original wheelbase then “pitch stability” becomes a problem. The smaller tires, lack of overhang, etc., allows for at least a one inch reduction from the original ride height of 7.125 inches. This is essentially the ADVANCED CONCEPT…
So in effect we took two steps forward, and one step back…but we still have a significant reductions in weight and effective mass!
“Historical vectors” are previous vehicle designs that embodied some aspect of the proposed advanced design, but were incomplete. However, some of my claimed benefits of the advanced design were demonstrated….
Reeves Octoauto was designed to reduce the load on the short-lived (1000 mile life) and fragile early tires. It did that, but also displayed a very smooth ride for the time. However, the car was extremely expensive and both tires and roads were improving rapidly… It had a weight of about 6,500 lb (2,943 kg) and a length overall of 240 in (6096 mm).
Protection acquired by light armor and high speed over rough ground.
Advanced Vehicle Systems (Don Nichols) entry (designed by Trevor Harris) for Can-Am racing series: 10” wheels in front and 12” wheels rear. Tires were made by Firestone and supposedly would have been able to withstand theoretical 250 mph top speed; driver George Follmer actually reached 190 mph, 20 mph faster than competition. Cooling and suspension problems prevented success.
Designer Derek Gardiner created this Formula 1 racer with four 10” front wheels and two conventional size wheels rear. First season out was very successful*, but Goodyear would not continue development of a unique tire size used by only one racing team. Initial success (2nd & 3rd overall for the season!) was attributed to better aerodynamics and reduction in effective & unsprung masses.
*Down in power with respect to much of the competition (the Ferraris reportedly had about 40 hp/30 kW more) the P34 seemed to have an advantage on the more twisty circuits. In 1976 a long series of successes ( 2nd & 3rd at Monaco GP, 1st & 2nd at Swedish GP, 2nd at Watkins Glen, 2nd at Japanese GP) culminated in the P34 placing second and third overall for the season!
Ferruccio Covini has produced a limited number of these unusual high-speed sports cars. The vehicle has “superior safety in the advent of a tire blow-out at speed, greater braking power, reduced unsprung weight, and less risk of hydroplaning”. Improved directional stability and aerodynamics are also claimed. Highly customized examples can be purchased today for undisclosed sum.
Developed by Prof. Hiroshi Shimizu of Keio University, the 5-passenger ELIICA (Electric Lithium-Ion Car) is intended to demonstrate the potential of electric cars. It uses eight wheels of conventional P188/55R16 size, probably to cope with the high performance and curb weight of over 5,300 lb (2,400 kg), of which about 1,500 lb (680 kg) is batteries. It has been clocked 0-62.1 mph (100 kph) @ 4.11 seconds with a top speed of 118.1 mph (190 kph). The use of full size tires and hub motors all around results in a higher unsprung mass than need be, but the ride is very smooth.
Not a real “validation” of the concept, that would involve building a “proof of concept” prototype and testing it. This sort of relativistic theoretical comparison doesn’t prove the validity of the concept but does lend it some plausibility. The baseline vehicle: 1958 Jaguar XK150S was chosen due to the amount of known data at hand. The use of a more modern vehicle would have presented problems in obtaining data and wouldn’t add much to an analysis based on relative changes of an “adv concept” w.r.t. the baseline.
MADE GREAT EFFORT TO KEEP SUCH CHANGES TO A MINIMUM, BUT THESE UNAVOIDABLE CHANGES OCCURRED AS PART OF A NATRAL DESIGN EVOLUTION.
Weight accounting that reflected those necessary changes is recorded in Appendix B of the paper. Roll resistance based on Prof. Clark’s equation on pg. 54 of paper. Load capacity was determined by the TRA formula already introduced. Traction was base on change in tire-to-road contact area. Aero drag chg is based on various sources; aero lift chg based on a paper by Prof. Mitra (see pg. 56-58 of paper). Hydroplane critical velocity based on equation by Koutný and equation by Horne & Joyner; squeegee length based on Metz & Meyers study. Tire life was determined per equation from The Pneumatic Tire.“Standing Wave” critical velocity calculated via McGivern/Shirk equation and Krylov/Gilbert equation. SSF is a standard equation found in a multitude of sources. Roll gain was determined by recourse to standard formulae for roll resistance. Lateral acceleration methodology is given in paper pages 108-111. Directional stability determined per the standard equations from a number of sources. Transient response was determined mainly from References 91, 4, 53. Road shock and contact determined by methodology of Colin Campbell . Gyroscopic reactions determined by standard formula. Fuel economy see pages 161-166.
Acceleration analysis was carried out via the computer simulation automotive acceleration program developed as the basis of this authors 1984 paper “Mass Properties and Automotive Longitudinal Acceleration”. As the “Advanced Design” evolved a new acceleration run was carried for each step in that evolution. Run #1 represents the baseline acceleration as per the tire methodology used in 1984. Run #1a was a revision of Run #1 using the revised tire methodology of 2015 in order to eliminate any changes of baseline to advanced concept due to methodology variation. The change in acceleration performance from Run #1a to Run #9 is what we are concerned with here. Run #4 simply represents the ideal change in weight mass and effective mass without consideration of any of the attendant consequent effects, which means this is still four full-size wheels & tires (Runs #2 and #3 are 1984 Baseline runs not relevant here). Run #5 represents only the mass effect of change to eight half-radius wheels & tires but nothing else; still not realistic. Run #6 represents the effect of a realistic evaluation of the traction available with eight little tires and only the rear axle driven; must convert and take weight penalty of rear two axles driven to get sufficient traction; Ground clearance, VCG, HOL are changed appropriately. Run #7 include the new drag & lift coefficients, frontal area reduction, rolling resistance reduction. Run #8 included suspension weight penalties, steering weight penalties, and I/B full-size brake weight penalties. Run #9 involved the weight penalties for engine orientation change from longitudinal to transverse orientation.
The braking simulation computer program is new and was written for this paper; the program validation and listing are given in the Appendices. For braking comparison only two runs, a baseline (Accel Run #1a configuration) run and an advanced concept (Accel Run #9 configuration) run, were made.
An attempt was made to determine the three major vibration transmissibility functions per the equations of Prof. Gillespie (Ref. [28]) as presented in my paper “Mass Properties and Automotive Vertical Acceleration” of 2011. However, apparently there are typos in Gillespie’s book for those equations (one of which I was able to identify previously). As for the unknown typos, requests to Prof. Gillespie and other academics went unanswered. So I used the two vibration transmissibility equations as formulated by a Prof. Dukkipati (Ref. [22]) which worked perfectly, giving the results shown. The top set of plots represent the ROAD-to-SPRUNG MASS VIBRATION TRANSMISSIBILITY, and the INTERNAL-to-SPRUNG MASS VIBRATION TRANSMISSIBILITY for the front suspensions with and without anti-roll bar. The bottom plot represents the same transmissibility factors as determined for the rear axles. The UNSPRUNG MASS-to-SPRUNG MASS TRANSMISSIBILITY is the one transmissibility type that is missing as Prof. Dukkipati does not present an equation for that one. RESULTS: The Advanced Concept generally represents much less transmissibility at the sprung mass resonance frequency for both transmissibility types, but for internal vibration transmissibility seems somewhat higher in the roughly 5 to 10 CPS range.
The principle ride mode frequencies and nodes were also determined as presented in my paper “Mass Properties and Automotive Vertical Acceleration” of 2011. The Baseline vehicle has principal mode ride frequencies of 1.46 CPS and 1.16 CPS about node points #1 (pitch) and #2 (bounce). The Adv Concept (in Equivalent Conventional Form) has principal mode ride frequencies of 1.62 CPS and 1.11 CPS about node points X1 (pitch) and X2 (bounce). Both vehicles have rather harsh pitch motions (ideally should be less than 1.3 CPS) as a result of the Baseline vehicle being rather stiffly sprung (old sports car suspension philosophy).
Besides restoring the longitudinal weight distribution and improving “weight transfer” and roll resistance in a turn, the change in engine orientation/location as shown also allows for better front structure energy absorption design for crash safety.
When Pierre Jules Boulanger was designing the 1948 Citroen 2CV he had no problem getting whatever size tire he needed as the whole project was being worked at the direction of parent company Michelin. Alex Issigonis had a bigger problem getting the 8” tires as originally conceived for the original 1959 “Mini” (Austin 7 / Morris Mini Minor) from Dunlop, so he had to settle for 10” wheels. Styling is subjective, but all important if public acceptance is desired…