SUGGESTED RESEARCH STUDIES ON THE

RATIONAL DESIGN AND SPECIFICATION OF ~,10TORCYCLE

Transportation Safety Department

Calspan Corporation

85-662

lbe infoimation in this note is ~irected at the recipient; Calspan requests that it not be transmjttcd to others.

September 1975 Revised October 1975 INTRODUCTION

Over the past several years, Calspan Corporation's efforts on two­ wheel vehicles have included both analytical and experimental studies and have dealt with a variety of design and performance questions. One of the aspects of special interest has been that of requirements - the subj ect of this note.

Calspan's activities in the analysis and evaluation of single track vehicles began in 1969 with the development, internally, of an eight-degree­

of-freedom mathematical model of dynamics. This model has j over the ensuing years, been expanded and used for developing computer simulations for both and motorcycles.

Our first externally sponsored \\fork in two-wheeled vehicles was for the National Commission on Product Safety. The purpose of this study was to identify and measure the critical design parameters associated with motions in the vertica 1 plane and the handling qualities of bicycles (Ref. 1).

Early in 1971 Calspan performed iL first study for the Sc}Hvj nn Bi cycle Company. This program was concerned wi th the further developlaent of Cal span 's two-wheeled vehicle simulation and the use of the s.Lmulation in determining the influence of design parameters on bicycle stability and control (Refs. 2 and 3).

Whil e this work was going on we carried out a second program for the government - in this case for the Bm'eau of Product S lfety of FDA/HEW. The progralll was concerned \vi th the safety performance of tricycles and mini­ bikes (Ref. 4).

Our first externally sponsored work on motorcycles was performed for the Ilarley-Davi,1son Motor Company. In this progl'aJll a sophisticated computer simulation for motorcycle dynamics was developed from the earlier internally supported work. The simulation \'::15 used to investig:1te the influence of several motorcycle characteristics on weave instability at high speed (Ref. 5).

1 This initial effort for Harley-Davidson has been follmved by several others. \Ve performed a study during the fall of 1973 of the weave phenomenon

as it applied to a particular prototype design. The next grol~ of studies performed for Harley-Davidson included performance tests of tires on our advanced Tire Research Facility, (TIRF) , full-scale validation testing of the FLH 1200 motorcycle and continued computer simulation studies. Recently we have conducted an additional tire test program for H-D and are currently doing another weave phenomenon investig<:tion on the computer (Refs. 6, 7 and 8).

As in the case of our motorcycle work our bicycle work for Schwinn continued after the initial 1971 program. A second major study was completed in 1973. The study involved experimental \.;ork, analytical effort, and computer simulation. It was during this pTogram that initial effort was put into developing simplified linear theory tools for two-wheeled vehicle analysis (Ref. 9).

Also completed in 1973 was a comparative evaluation of the Schwinn Continental and Continental-based Sprint bicycles" Our 1!1ost recent program with Schwinn included the simulation of a transient handling task, paramf)ter variation studies, testing and an investigation of bicycle flame flexibility (Refs. ]0 through 13).

In all of the above work Cal span's computer simulations of bicycl e and motorcycle r.ynamics have figU1'ed prominer:.tly. Relevant material on these and other (lspects of Calspan' s two-wheeled vehicle work can be found in three Cal span publications in the open literature (Refs. 14-16).

Most recently, we have completed a study of motorcycle response characteristics and handling qual i ties for the NHTSA in conj unction with its general program for improving the accident avoidcll1ce capabiJ i ties of these vehi cles. 11Lis work involved both simuJation and full-scale experimental approaches, the measurement of motorcycle physical characteristics and tire perfornwncc data, and the analysis of machine-rider interactions. The outputs of this study are .. to a large degree, the background for the new research \vhich is suggested here (Ref. 17). 2 Throughout these studies, thE: need for tire performance data and for a clear lmderstanding of the comp 1 ex interactions of the tire and machine parameters has been evident. The purpose of this note is to describe some of the information which has been accumulated and to outline new work which is needed to provide a rational basis for design and selection of motorcycle tires. TECHNICAL DISCUSSION

As indicated in the Introduction, Calspan Corporation has conducted several research programs in recent years involving acquisition of motorcycle tire performance data. The resul ts of this work have led to the identification of certain desirable characteristics in tires and the recognition of areas where more information is needed in order to assure good matching of tire­ motorcycle characteristics. Through the next few pages, examples of available information are presented. These are followed by discussions of pertinent tire characteris ti cs and their influence on motorcycl e sys tern des ign and performmlce.

To date, some 30 motorcycle tires have been tested on Calspan' s Tire Research Facility (TIRF) to obtain a variety of performance data. Since the purposes of all of the tests were not necessarily the same, complete information for comparison purposes is not available at this time, but the ranges of design parameters and operating conditions are sufficient to ill us trate trends and indicate nominal performance characteristics. The tire design parameters covered arc:

Diameter (inches): 16 to 21 Width (inches): 2.75t05 Tread: ribbed, universal, trials Manuf3 cturer: 5

Operating conditions covered are:

Inflation pressure (psi): 16 to 31

Speed (mph): U!J to 90 mph (most tests were performed at 30- 35 mph) Normal load (lbs.): 125 to 700 Surface condition: dry (limited wet surface clata are also available) angle range (deg.): + 1 to - 8 Inclination angle rango (deg.): up to 50

4 The primary performance measurements which were made are the three forces (, side force and normal load) and the three moments (overturning moment, moment, and aligning tcrque) in the standard SAE tire coordinate system. In addition, measurements of and radial and lateral force runout were made in some cases. The basic measurements were then used for computing the performance chayacteristics of interest - cornering sti ffness (CI,'IJ, stiffness (C"() , and , for instance.

In the applications to date, we have had no occasion to analyze these data in the broad sense of an evaluation of the motorcycle tire state-of-the­ art. For the purposes of this note, however, we have made some preliminary checks to determine ranges and trends of performance characteristics. These I show values of cornering s tiffnc coeffi ci ent (CoJ ranging from .11 to .33 lbs/deg/lb and of camber thrust fficient (C~) from .006 to .025 10s/ deg/ lb.

L Values of pncull1Cltic trail range a ' lhtle as .4 inches up to nearly 2.0 inches. Relaxation lengths fro o 8 inches have bpen measured. Other

interesting relationships are sl d in the following figures.

figure 1 shows a typical motorcyc] e tiTe I.;:npet plot as obtained on Calspan's Tire Research Facility (TlRF). In this case, the test variables of interest are s lip angle (0<.), inclination angle (0), and total side force (F ) - all measured at a constant value of normal force (F ). These data may y z' I be transformed into values for cornering stiffness coefficient (Co(, equal to

I F /cI./F computed about the'J( =~=o point) and camber t.hrust coefficient (C y, y z " equal to F /t{ F computed about the·j( =¥=O point). For the data shown, these Y . z ; ; computed values are Co(.= .18 and Clf' .0155 with dimensions of lb/dcg/lb.

Figure 2 shows distributions of '(he side force performance coefficients for the three t.ypes, inJependent of tire size. The coefficients, however, do reflect nominally rated load and recommended inflation pressure conditions (based on the motorcycle manufacturer's recommendations). TIle high I CO<., values for the ribbed-type tire shovm are typical for lightly loaded front I tires on small machines. Note the apparlmtly low value of C b'for the t1'ials-

5 -----r-----r------+------l----

FIGURE 1. TYPICAL ~IOTOP.CYCLE TIEL CARPET PLOT r-r ------'T- ·~- ~}'l~-o/~'~;- -y~---- -]----:-]- --'--1

. f::. ~ .N< ()I ...,...... ·0 i ~ 'i q' 0 q.. . o. I ! ' I (" I" . r-.. r . . I r-~l -, .I' --n-- 'I""'-~'- ---:+-1:' -·--J'---····~-·-·-·-rli ;:i 'r!! .. I !. , ' I ,.-, .-< I . ! II j I : I I :2 . I t: ~ ~!>-< I' I I JI: I I .-< cj i" I I :3 j I ~§~ .. ------1- ---.... ---+.~.-.-- -. --t--+·~-··---· .. j--··-.. -----.... -~-----... ---- ~·-·"-:--.--H g~' j •. \ iii' ~ .. 'I OJ' :1 I I I ~ g . 11" . I ; 1 . !

C.I

.-' Ci -~ "\ I III ~ ~!- --~~~---.- -I-<~~\ ~:;< ·--·---1----- I ~. ------1

, . 1 I' I . i . ". ! ~~ i "--"'~---~/''''-~-10;_''-'~_-''_''_'~' __ +''_ -",,",,---,"' __ "';>'~" .. -"'... '".i-"'- ...... ;;:~-~,.~~_,...... ;.._~~:~ ...,.::::>:.- __ !~ __ ~ _____ .______~ r: i 'j: I I 1 f: I--'-----L-- In I Ih I

E~ I ..... ____ ...1, __ ._ ._ .. '. (-.) !. I . '. :2 ~: I .1 ---t-e:--I

@l ·1--" :~- ... . . I . " ·I.!.... ~ I ~: f----O·~··--~-o -':'-Et ~/()--. -- --1-"'0 -----:l:...... --.-~.-· --l-'--'-' ---. ~ ---.. -. i ,.... :::::: I j .... -.... -.- .. ~-i-l- t • • y ...... • -"'-t-----'\

0, ~ g ~ g 5{ J t . C' ('I '1 ~J 0 11 I I I I . I L. __ ~ __ ... _.____ .~I __ ._ .~ __ :~L __ ._.~ ~. ___ .. j ~~'I~ o~:w~~ .~J/:~~ ______.l~_· .. _~._' L._ ..J 7 type tires (admittedly, only a small sampl e) and the close grouping of the value for this coefficient for ribbed tires near the theoretical value of the tangent of one degree (.0175). The significance of this value can be seen in the following.

It can be shown that to a first approximation the sideslip angle of the motorcycle body (i.e. frame) is given by:

b + (I + Gi) R 1::"~Wr:z..ll- C"'R

where: f-> body s lip angle, radians b c.g. to rear axle, ft. R := radius of turn, ft. A~::: lateral acceleration, g WR. :::. rear axle weight, Ibs. Coc:.p,.:= TOelr tire cornering stiffness, #/rad (negat:i ve)

Gr := a gyroscopic effect, dimensionless CCSR. = rear tire camber stiffness, #/ra<1 CPiZ:= rider lean angle, rad e := rider] ean gain, dimensionless

If rider lean is set to zero and the small gyroscopic term, G, i~: C~e ignored (it is of the order of . OS) it can be seen that when WR. := 1 thb is independent of Ay and takes on a constant positive value, '"R. 'Dlis in turr. means that the machine lloses out of the turn at all speeds. This arises from the fact that camber thrust provides all of the rear tire side force - no tire slip angle is needed.

. C,!'i:?. SlT1CC W 1S the camhcr thrust coefficient in il/rad/# the equivalent ~ critical value in degree wlits is 1/57.3 = .0175.

8 (\f < 0 1'- ,; 0 z 11) n '

The above consideration is one of several that can be examined by use of generalized steady-state expressions for other parameters than ~ i.e. - steer angle, roll angle, rider input torque, and rider lean.

Figures 3 and 4 show pTcliminary examples of some design and operational propert ies/performance interactions for motorcycle tires that are obtainable from currently available data. Figure 3, showing the effect of tire pressure on the side force coefficients, indicates little effect of this variable on the ( . . h ). I Cti parameter CWltlnn t e test l'anse but substantJ_al decrease in the C ~ coefficient with increasing pressure for the test load of 300 lbs. This suggests that over­ inflation of motorcycle tires can seriously decrease camocr thrust and, in turn, require some,vhat higher slip anBlcs (and, therefore, sideslip and/or steer angles) in ordel' to olnain suffid ent side force for a given cornering acceler­ ation.

Figure 4 shows similar side force data as a function of tire section width for 18 inch diameter ti res (of eli fferent manufacturer for ribbed and I universal tread patterns). Here, the C~ parameter is relatively unaffected i while the Co(. characteristic decreases as width increases. It should be recognized, however, that the normal loads on the tires as tested have also been increased foy the greater widths. A plot of cornering stiffness, i.e. C~, defined as d l~/J.:( ~=O (the non-normalized C(j. parameter) would sh~'h' a slightly increasing trend with section width.

These preliminary plots arc presented merely to illustrate the type of information which can be.: obtained from aVclilable data. Many other combin­ ations of parameters arc possihle.: ,md useful and one of the steps which is recommended later jn this note for further research treats the analysis of our avajlable tire performance data in a Illore cO:-:1prchensive study than was possible ill this initial examination. 10 1' :. '~TL~CIf1-rr;:-=.i-J±.i:-~:.~.·7lf: I ~: -I~; i L-ll.~1;! :-I~~_Ttu~;~T;_:2~~_~-; . ~ ~; __ .-==_:J ~- i--L-L'j--' ,I .-1-1 ~-i -: ! 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'v:> iL_.I::;~::i ~J T3~.:rd,}I • -W -:; il 1\11 ;':'JI> ,';',:;.", o. :: L '31 % ff 20LO S,7' H':;'r-.-o.! ~~HJ, G.1 0' X 0' ~"~i~. It is important that the role of tire cornering stiffness (C",J ]n motorcycle 1 ateral- directional control be understood before examining require-· ments for suitable tire combinations. For most machines, well over one-half the required side force for cornering is obtained from camber thrust. In fact, on some machines, the s ide force clue to inclination angle (as achieved by the motorcycle in satisfying the roll fIloment balance requirement in a steady-state turn) may be more than sufficient* for maintaining the turn and Hould have to be reduced by the development of slip angles producing forces in the opposite direction. III general, for rec:.soll8bly designed machines under normal operating conditiolls, the camber thrust developed by the tires will be quite close to that required for cornering so that only very small slip' angles (less than one degree) are needed to trim to the desired operating conditions. On this basis, high val ues of cornering stiffness for motorcycle tires, unlike those for automobiles, are of reduced significance and, similarly, high peak normalized side force performance values (due to slip angle and for dry conditions) provide no sub·­ stantive advantages.

One of the most iJ~ortant aspects of motorcycle behavior is the

V3riation in tLe illter<~'.:tions of the tire performance characteristics on the different machines. These variat LOllS occur primarily because of the influence of the tire caml1er thrust on the requirements for the development of tire slip angles to achieve lateral-directional force and moment balance. When the camber thrust from the tires is sufficient to meet s:'de force requirements in cornering, the tire is not required to opera te at any s lip angle. When the camber thrus t is not sufficient, the additional force must be supplied by tire slip angle; when the camber thrust is mere than enough, slip angles must be develo]1cd whjch actually reduce the side force to the desired level. This can be demonstrated by the following silIllJ)ified analysis.

*Tll(;-cYlt]cal---valuc discus~;ed earlier is the "just enough" condition.

12 When a motorcycle is in dynamic equilibriwll in a turn, the resultant roll and yaw moments and side force must be zero---the sum of the tire forces must equal the centrifugal force; the yawing moments due to these forces at the front and rear tires about the system e.g. must balance; and the roll moment due to centrifugal force must be equalized by the moment produced by banking the vehicle in a turn. As a first approximation:

Fy = O·, May = Fyf + Fyr (a)

~Iz 0; a Fyf = b Fyr (b)

Mx = 0; May h cos ~rJ= lVh sin cp ( c)

where: M = mass of rider-motorcycle system ay = lateral acceleration

Pyf front ~leel side force Fyr rear wheel side force a -- horizontal distance beth'ccn front wheel contact point and system center of gravity b = horizontal distance betlveen r0ar wheel contact point and system center of gravity h height of system center of gravity above the growld plane

~ bank angle (roll angle) of the system with respect to vertical W rjder-motorcyclc system weight; Mg.

The values of Pyf Dnd Fyr arc functions of the tire performance characteristics and slip and inclination angJes. Again, represented in a simplified manner -

CL R + ~) + C~R cp

where:

c~ =: cornering stiffness, Ibs/deg C;s-= camber stiffness, Ibs/deg f3 = sideslip angle, deg

13 ~ = steer angle, deg

~ rake angle, deg R turn radius, ft. a.... ( ~.I- R. - ~ ~ Q) =; 0<;:, front wheel s lip angle (f3- ~) '" cx'R.' rear wheel s lip angle

If the side force requirem(mts are exceeded by the swn of only C ~ F"and C ¥R. with concurrent satisfaction of the roll moment equation (which can be simplified to Ay = g tanc.p) , the front and rear slip angles must be such that forces opposing thos e due to inclination angle are developed. In effect, /3 will be small (and in some cases, as shown earlier, the vehicle may be "nosed out" of the turn--even at high speed) and ~ is utilized primarily as a triil device (as contrasted to its use as the primary control mechanism in automobiles) to satis fy the yaw moment balance.

There are several aspects of tire performance which have been recognized wi th regaTd to their relationship to automobile handling but \dlich appear to be of greater consequence to the motorcycle. These include:

1. Tire dynamics - as measured by the response time for the buildup of side force following the imposition of a change in operating condition. It is u.c;ually characteri zed by an equivalent distance of traveJ termed relaxation length.

2. Tire/wheel nonuniformity - variations in side force as a function of tire (wheel) ciTcumferential position. These produce fluctuating disturbance

inputs which may excite resonant motion~ ,)f the vehicle. In particular, free control osciJlations of the assembly may be initiated from this source.

3. Camber thrust coefficient - because the motorcycle derives a large portion of its side force from camber thrust, information on this parameter is required up to large angles - in the range of 40-50 degrees.

Possible discontinuities or abrupt changes 111 value are significant.

14 4. Slip angle/inclin3tion angle relationships - the fixed steer lateral-directional control characteristics of motorcycles are significantly influenced by the parameters C'F and CrR and their difference. In fact, this ColI' Co(; effect (\\'hich js equivalent to the roll-camber steer effect in automobiles) is the principal und_ersteer term for motorcycles (which tend to be oversteer on the basis of weight distribution and cornering stiffness values alone). Thus, apparently small variations in the values of the individual coefficients may result in substantial change in the val ue of the term, Ca'R , and - C~R

thereby change the under/over steer characteristics of the machine. This can

be ShOlYn \\'i th an example taken fro]11 the work reported in Ref. 17. The under­ steer factor, K, is desc:ribed by the eX1Jression:

ho C 5"iZ. = + (! 1- q) K [~ C,1....(z" Co C.:(F J where: h static margin 0 C a combined tire performance parameter 0 G gyrosocpic effect

C == tire cornering sti ffness Cd..'"J~ , elK tire camber thrust stiffness CX· F' C~R

Values for the first term weTe computed for several motorcycles to be in the range of -.01 to -.03 (the negative sign indicates oversteering). Values for the second Lcrm ranged from +.01 to +,08, indicating the aOility to affect the steer charactcristic:s of the motorcycle signj ficantly by proper selection of tire coefficients.

15 SUGGESTED STUDIES

In the previous discussion, we have described some of the problems associated with the selection of motorcycle tires to assure good stability and control characteristics of the machine throughout its operating envelope and ",e have indicated the type or information which is available for theiT solution. The following brief descriptions outline sever,)] study tasks which a:re aimed at acquiring additional perspective.

1. Tire Data Analyses.

Extend the preliminary cmalyses described in this note, using currently avajlable data, to define trends and values for interactions of tire design ancl operational variables. Emphasize the evaluation of camber thrust

characteristics and analyze the s~nsitivity of motorcycle response parameters to changes in these characteristics at front allcl rear. Among the specific topics to be covered \'JOuld be the effects of high rear camber thrust c:apabili ties on steering requirements, influences of tire parameters on wobble stability,

and variation of pneumatic trail itS a function of slip ctngle magnitude.

2. Tire Performance Parameter Variation Study.

The objective of this ,vork ,,",ould be to examine in some detail the effects of changes in tire characteristics on the values of performance parameters and stability indices for a single motorcycle design. The approach would utilize the Calspan two wheel vehicle clynamics simulation program supported by constant coefficient analyses. Reasonable ranges in such tire fa,::tors as C"", Ct , pneumatic trai], relaxation length, and load and their combinations (as functions of fTont or ) location) ,-;ould be investigated to determine sensitivity of the machine's responses to these changes. The output of the study 'VDuld be the identificatiol1 of cri tical factors and the defini tion of allowable vari:ltiollS in these factors which would limit changes in the response ch3racteristics to some selected value.

] 6 3. Supplementary Tire Test Program

As noted previously, currently available tire data spans a wide range of design, operating conditions, and performance characteristics but, since the data were acquired on several diversified programs, coverage is incomplete with respect to some factors. For example, only a few trials-type tires have been tested and relaxation length data are not available on most of the tested tires. This work would be aimed at testing a nwnber of tires judiciously selected to provide data to fill in gaps in current information so as to enhance the quality of observed performance trends and interactions. A relatively modest J)l'ogram is suggested for an initial effort - perhaps 20 configurations - with the recognition that more crnnplex interactions (the effect: of the different types of wear, \\'11ich occur at the front and rear locations, on the performance parameters, for exanple) could be investigated at a later time. lest results would be applied in association \\'ith current data to eval uato influences on the performan ce of motoreycl es.

17 REFERENCES

1. Rice, R. S. and Roland, R. D., "An Evaluation of the Performance and Handling QUD.li ties of Bicycles," Calspan Report No. VJ-2888-K, April 1970.

2. Roland, R. D. and Massing, D. E., "A Digital Computer Simulation of Bicycle Dynami cs, i! Calspan Report No. YA- 3063-K-l, June 1971.

3. Roland, R. D. and Lynch, J. P., "Bicycle Dynamics - Tire Characteristics and Rider Modeling,!' Calspan Report No. YA-3063- K-2, March 1972.

4. Rice, R. S. and Rolalld, R. D., "An Evaluation of the Safety Performance of Tricycles and Minibikes," Calspan Report No. ZN- S144-K-I, November 1972.

S. Roland, R. D., Kunkd, Dennis T., "Motorcycle Dynamics - The Effects of Design on HIgh Speed Weave," Calspan Report No. ZN-S2S9-K-I, ~lay 19i3.

6. Roland, R. D., "Performance Tests of Harley-Davidson Electra­ Glide fLH-1200 l'>!otorcycle Tires," Calspan Report No. ZN-S438- V-I, June 1974.

7. Davis, J. A., "Full-Scale Valiriation Testing of the Harlcy­ Davidson Electra-GU de FLH-1200 ~lotorcvcle," Calspan Report No. ZN-S472-V-l, July 1974.

8. Roland, R. D., "Performance Tests of S.00-16 Motorcycle Tires," Calspan Report No. ZM-SS97-V-l. October 1974.

9. Roland, R. D. and Rjce, R. S., "Bicycle Dynilmics, Rider Guidance Modeling and Dj sturbance Response," Calspan Report No. ZS-SIS7-K-l, April 1973.

10. Kunkel, D. T. and Roland, R. D., "A Comparative EVClluiltion of the Sch\~inn Continental and Continental-based Sprint Bicycles," Calspan Report No. ZN-536l-K, August 1973.

11. Rice, R. S., "Bicycle Dynamics - Sinplified Steady-State Response Ch:lracteristics and StabiUty Indices," Calspan Report No. ZN-S43l-\,-1, JlllC 1974.

12. Davis, J. A. and Cassidy, R. J., ff'Dl e Effect of Frame Properties on Bicycle Efficiency," CaJspan Report No. ZN-S431-V-2, November 1974.

18 REFERENCES (contd)

13. Davis, J. A., "Bicycle Tire Testing - Effects of Inflation Pressure and Low Coefficient Surfaces," Cal span Report No. ZN-5431-V-3, May 1975.

14. Roland, R. D., "Computer Simulation of Bicycle Dynamics," Symposi urn on Mechanics and Sport, Appl led ~lechanics Divis ion, 'IlIe American Society of Mechanical Engineers, New York, November 11-15, 1973.

15. Lynch, J. P. and Roland, R. D., "Computer Animation of Bicycle Simulation," 1972 FA.ll Joint Computer Conference - American Federation of Information Processing Societies - Anaheim, CA, December 5- 7, 1972.

16. Roland, R. D., "Simulation Study of Motorcycle Stability at High Speed," Paper ~o. 730.20, pTesented at tile Second Inter­ national Congress on Automotive Safety, San Francisco, CA, July 16-18, 1973.

17. Rice, R. S., Davis, J. A., and Kunkel, D. T., "Accident Avoid:mce Capabilities of Motorcycles," CClJspan Report No. ZN-557J-V, JWle 1975, Vol. I - Final Report - Technical; Vol. II - Final Report - Appendices.

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