REPORT 1248

AN EXPERIMENTAL STUDY OF APPLIED GROUND LOADS IN LANDING ‘By BENJAMINMILWITZKY,DEAN C. LINDQUIST,and DmTER hl. POTTER

SUMMARY

An experimental kv&igation haa‘been made of & appliedground loads and the coewt of friction betweenthe tire andthe ground during tlw wheel spin-up prows in impacts of asmall landing geur under comkolkd conditions on a concretelanding strip in the Lungky impact basin. The bti instig-ation included thrtx mujor phuws: impacts withforward epeedat horizontal.?velocities up to approxim.alely86 feet per second,impactsw“thforward speedand rever8ewheelrotationto simu-kd.ehorizontalvelocitiesup to about273feet per second, d spk-updrop te8tsfor comparison with t& other W. In addition tothe basic inmstigd.on, supplementary tests were made toewluate the drag-loadai’kviating e#eci%of preroi%.ti~ the wheelbefore impact 80 as to reduce the relative mlocity between thetire and the ground.

In the presentation of the Tesuh, an aitempt ha been madeto +nterprett)k experinwnlal da.i!aso as to obtuin some irwi@into the phymkal plwnomena involved in the wheel spin-upprocess. From this study it appear8 thai the condi.tti of con-tact between the tire and the ground, and cmequently them~itude oj the coejlcient of friction, vary greatly during &course of an impact and wn”thdi$erent impact conditiom. Thecalm of the coe@ient of jriction appears to be appreciablyinfluenced lqI a numbm of factors, such m the in+w!antaneousA%ding velociiy, the slip ratio, the vertical load, % e$ects oftire healing produced by the 8kidd@ procem, and the e$eck ofcontamination of the ground surface by abradedredder. Somequantitativeindicu4ion8of these e$ecti were obtuimd from theexperiment datu but the nature of the tests did not pmnitcomplete separation of all individual e~ects.

The investigation of the e~ects of wheel prerotdon indicatathat th~ means cm be wed to obtain appreciable reductions inthe maximum drag loads; however,at rery highforuzzrd epeeds,became the spin-up drag Lm.&may be of the 8ame order m, oreven .?4?8sthan, the drag I?oad.scaused by other d.wigncondtli.o?w,the practicul adcan~es of prerotathn could be greatly Tedd.

INTRODUCTION

In recent years the problems associated with ground-impact loads during landing, particularly wheel spin-up dragloads, have assumed increased importance in the design ofairplanes. Although spin-up drag loads may lead to criticaldesign conditions for such airplane structural components asthe landing gem, drag bracing, parts of the wing, enginemounts and nacelles, the a,fterfuselage,tail booms, and even

tail surface+ comprehensive reliable information on the mag-nitude and variation of the drag load is meager, and mistingdata are often in conflict.

The spin-up drag-loads problem may be logically resolvedinto two basic aspects, namely, (a) the e.sternalapplied loads,which are the forces developed between tie tire and the run-way during the wheel spin-up process in landing, and (b) thedynamic loads induced in the landing gear and various otherparts of the airplane structure by the applied loads. Theapplied loads serve as the forcing function which, in con-junction with the mass and flexibility characteristics of theairplane, governs the dynamic response of the structure and,thus, the loads and stressesdeveloped in the airframe.

At the present time a number of dynamic-analysis methodsexist which, -ivMe not perfect and often laborious, permitreasonable accuracy in the calculation of the dynamicresponse if the forcing function is known. In the case ofwheel spin-up drag loads, one of the main problems is theinability to predict accurately the applied drag-load timehistory, because of lack of suf6cient information regardingthe mechanics of the wheel spin-up process, particularly thecoefficient of friction between the tire and the ground, and itsvariation during the impact. The present investigation hastherefore been undertaken primarily to study the appliedground loads in landing and the physical phenomena involvedin the wheel spin-up process, with special attention to themagnitude and variation of the actual coefficients of frictionbetween the tire and the ground.

In the past, attempts to investigate systematically theapplied ground loads by means of flight tests have generallybeen impeded by difficulties introduced by the relativelylarge amount of scatter normally found in flight-test data as aresult of the nnmerouauncontrolled and generally unmeasuredvariables involved and, probably most important, by thefact that such data are usually obtained with stxain gageslocated somewhere in the landing-gear structure, which,nuder dynamic-loading conditions, give a measure of the100al strain or respo~e rather than of the applied groundloads. Furthermore, such landing-gear strain-gage installa-tions are usually inherently subject to large errors due to theeffects of interaction between different components of loadand moment, as well as to hysteresis effects. In the case ofspin-up drop teds in a jig, even though more satisfactoryinstrumentation is feasible, the results are also subject toquestion because of the artificial conditions which mistbetween the tire and the ground in such tests.

1SnpotscdMond@ands NAOATN S24,“An EspwfmmtalInvestigationofWhwlSpfn-UpDregMad&’by BanjnmlnMikvhky, DeonO.Lindq@ andD@xteThf. Pottar,1964.. . 1155

1156 REPORT 1248—NATIONAL ADVE30RY COMMJZTEE FOR AERONAUIHCS

In an attempt to minimize the aforementioned di.iiicuhies,special instrumentation was developed for measuring theapplied ground loads, m well as various other pertinentquantities involved in landing impact, and tests were madewith a small landing gear under relatively md.1-ccmtrolledconditions on a concrete landing strip installed in the Lang-ley impact bash The basic investigation included threemajor phases. linpacts with forward speed were made atfour vertical velocities between 3 and 10 feet per second overn range of horizontal velocitie9 up to the maximum speed ofthe impact-basin carriage, approximately S? feet per second.In an effort to extend the horizontal-velocity range of theinvestigation, forward-peed tests were made in combinationwith reverse rotation of the landing wheel prior to impact;in this manner horizontal velocities up to 273 feet per secondwere simulated. Also, stationary drop tests with reversewheel rotation were made for comparison with the othertrots. In addition to the basic investigation, supplementarytests were made to evaluate the eiTectsof prerotating thewheeJ before impact so as to reduce the relative horizontalveloci~ between the tire surface and the runway, and thusthe amount of impulse required to spin up the wheel.

This report presents an analysis of the applied groundloads measured in the aforaumutioned tests as -wellas a studyof the cmiiicient of Hlction during the period of wheelspin-up. Along with the presentation of the quantitativeresults, an attempt is made to interpret the experimentaldata so as to obtain an undemtamling of the physicalphenomena involved in the tire skidding process and thevarious factors which influence the ccetlicient of friction.Since these interpretations are based on measurements ofthe applied loads and the motions of the wheel and landinggem, rather than on detailed observations in the ground-contact region, they must be regarded more as inferencesthan as established facts, at least until such time as moredetailed studies of the mechanism of the skidding processcan be made.

a.a~aHaaNaaHZapz

F4a

FN~

FnzF,CFAT

F.,

F=,

Fv=gKL

SYMBOLS

acceleration of axle parallel to shock-strut axis, ft/secahorizontal acceleration of axle, ft/sec~acceleration of axle normal to shock-strut axis, ft/se&horizontal acceleration of ground platform, ft/seczvertical acceleration of ground platform, ft/secaforce on axle dynamometer parallel to shock-strut

axis, lbforce on axle dynamometer normal to shock-strut.

axis, lbhorizontal force on ground dynamometer, lbverticaI force on ground dynamometer, lbtotal force, parallel to shock-strut axis, between tire

and ground, lbtotal force, normal to shock-strut axis, between tire

and ground, lbtotal horizontal (drag) force between tire and ground,

lbtotal vertical force between tire and ground, lbgravitational constant, 32.2 ft/se&lift factor, ratio of lift force to total dropping weight

mg mass of ground platform, slugsmw mass between axle dynamometer and ground, SluewP coef6cient of friction, FHT/FvTrd deflected radius of tire, ftr= effective rolling radius of tire, ftR free radius of tire, ft8 shock-strut stroke parallel to strut axis, fts slip ratiot time aftercontact, secVGk horizontal velocity of axle, fpsVm horizontal velocity of carriage in tests with reverse

wheeI rotation, fpsv=, horizontal velocity in forward-speed tests, fpsV=,, simulated horizontal velocity in tests with reverse

wheel rotation, fpsVskfd instantaneous apparmt skidding velocity, fpsV.. vertical veloci@ at instant of initial contact, fpsx~le horizontal displacement of axle, ftZu upper-mass vertical displacement, ft8 tire deflection? ftv angle of inclination between shock-strut axis and

verticaIo wheel angular displacement, radiansSubscripts :av averagemax mtiumo at initial contact8U at spin-up

A dot over a symbol indicates differentiation with respectto time.

APPARATUSEQUIPMENT

The impactibasin equipment consists primarily of a car-riage which is catapulted down a horizontal track and whichincorporates a dropping mechanism for controlling the de-scent of the test specimen with a predetermined verticalvelocity and simulated wing lift while the carriage is movinghorizontaUy. (See refs. 1 and 2.) A schematic view of thecarriage equipped for landing-gear testing is shown in figuro 1.For testing landing gears with forward speed a removwblereinforced+oncrete landing strip was installed in the @pactbasin, as shown in figure 2. The concrete surfaco of t~o

I L-5959G.

FIGUREI.-schematic view of impaot-basin carriage and landing gear.

AN EXPER135NTAL STUDY OF APPLIED GROUND LOADS IN LANDING 1157

~If3Wrm2.—vkw of concretelauding strip installed in Langley impactbasin.

landing strip had a lightly broomed finish in the transvemedirection.

Tlm maximum horizontal velocity of the impact-basincnrriage is about 87 feet per second and the maximumdropping weight is 2,500 pounds. In order ta simulate thewing lift forces which support an airplane during landing,the cmriage incorporates rLpneumatic cylinder and camsystem which is designed to apply any desired upward forceto the chopping mass during an impact. In the present

~

23 !!!lEat-

1

I

investigation all tests were made with a dropping weightof 2,500 pounds and a simulated wing-lift force of the samemagnitude.

LANDING GEAR

The landing gear used in the present investigation is nmain undercarriage unit designed for the T-o and SNTJtrainer airplanes, which have a gross weight of about 5,oOOpounds. The landing gear is of the usual cantilever constric-tion and incorporates a conventional type of oleo-pneunmticshock strut with metering pin and snubber valve. The wheelis fitted with a 27-inchdiameter smooth-contour (type I)tire having a nonskid tread, inflated to a pressure of 32pounds per square inch. The brake assembly for the wheelwas not installed. The original half-fork yoke was replacedby a more rigid tubular member connecting the shock strutwith a specially designed strnin-gage dynamometer formeasuring the forces applied to the axle.

The landing gear was inclined forward at an angle of 15°with respect to the vertical, representing an airplane attitudeapproximately half way between the level and three-pointlanding conditions.

INSTRUMENTATION

A varie~ of time-history instrumentation was employedin the tests. In order to minimize dynamic-response errors,high-frequency instrumentation was used where feasible.The installation of the test insbmrnentation is schematicallyillustrated in @we 3. Photographs of the landing gear andinstrumentation are shown in figures 4 and 5.

r’6

mA

.;; .--

1.

2.3.4.5.6.7.8.9.10.Il.12I3.[4.15.-16.17.18.

:.

Lift rods

Loading weightsUpper-mass vertkol accelerometerAxte atial accelerometerAxle dynamometerStrain-gage beamsAxle normal accelerometer, outerAxle normal accelerometer, innerWheel angular accelerometerWI angular-velw”ty generatorWheel angular-displacement pickup

Ground platform, concreteGround dynamometerGround-platform horizontal accelerometerGround-platform va”col acixkrumeterUpper-mass displacement didw”re cableStrut-stroke slidewireTire-deflection slidewire

Note: 12,13,14,15, and 18 used ininstrument-evaluation drop tests Ionly.

FIWRE 3.-Sohematio view of landing gear and instrumentation.413072—67—78

— .—

1158 REPORT 1248—NA’HONAL ADVISORY COWKtWl?ED FOR AERONAUTICS

FIGURE4.—Front view of landing gear and inatrumentation.

A specially designed two-component dynamometer, in-stdied between the axle and the fork of the landing gear,was used to measure the forces applied at the axle. Thisaxle dynamometer, which has wire resistance strain-gagemembers, measured the axial (parallel to the axis of theshock strut) and normal (perpendicular to the strut axis inthe plane of the wheel) forces transnu‘tted from the axleto the fork of the landing gear, from which the verticrd andhorizontal forces at the axle could be determined. The axledynamometer was designed to measure axial forces up to10,000 pounds and normal forces up to 5,000 pounds andhad natural frequencies, with wheel assembly attached, of403 cps and 220 cps in the axial and normal directions,respectively.

The forces at the axle are, of course, not the same as theforces betwem the tire and the ground, the ditlerencesbeing the inertia reactions of the mass between the dynsmom-oter and the ground which result from the accelerationsof this mass during an impact. In order to determine theseinertia forces, accelerometers were mounted on the landing-gear fork and on the dynamometer so as to measure the axialand normal components of the acceleration of the mass

acting at the tie. The vertical and horizontal ground forcoswere then determined from the axle-dynamometer and asle-accelerometer measurements. Because of twist of thelanding gear due to drag loads, it was neceswy to employtwo accelerometers, laterally displaced from one anothor,to determine the normal acceleration of the center of grrwiLyof the mass between the dynamometer rmcl tho ground.Them accelerometers are referred to as inner and oulornormal accelerometers and their measurements nro desig-nated as ah?=,and aN. .. respectively. (S00 fig. 3.)

In order to evaluate the accuracy of the applied groundforces determined from the axle-dymunomotcr nnd rmlo-acceleration measurements under dynamic conditions, Lspecial series of instrument-evaluation drop tests, withreverse wheel rotation to produce drag loads, was made inwhich the total vertical and horizontal grouncl forces dotw-mirmdfrom the landing-gear instrumentation wero comparedwith data obtained simultaneously from a ground dynamom-eter equipped with acceleromc+ters. Tho ground accelwom-etem -w-oreused to determine the inertia reactions of theground platform, which were added to tho forces measuredby the ground-dymunometer strain gages, in order toobtain the total applied forces between tho tiro and theground platform. These comparisons (see, for ONUXIP1Ofig. 6) indicated good agreement between the applied grounclforces determined from the two sets of instrumentation and

FIGURE5.—Rear view of landing gear and instrumentation.

AN EXPERIMENT AL STUDY OF APPLIED GROUND LOADS ~ LANDING 1159

.81-

— Axle measurements——Ground measurements

\

of a strain-gage beam placed between the dropping massand the rods through which the lift force is transmitted.An accelerometer for measuring the vertical acceleration ofthe upper mas (the mass above the shock strut) duringimpwt was included in the test instrumentatiorifor compari-son purposes.

I I 1 I I I I J4

2

t

I ( I [ I I I 1 Io .04 .c% .12 J6

llme atter cnntact, W

lWuRD &-Comparison of axle and ground mxurements of appliedforces in a typical instrument-evaluation tes5. Vvo= 7.64 feet persacond; VH,O= 10& 6 feet per second.

gave added confidence in the &e measurements, which werethen used as a basis for the main part of the teat program.

The vertical velocity at the instant of initial groundcontact ma determined from the output of an elementalelectromagnetic generator. The horizontal veloci~ of tiecarriage in the forward+peed tests was determined fromhorizontal-displacement measurements obtained by meansof o photoelectric cell mounted on the carriage and light-bmm interrupters fixed at one-foot intervals along the track.

The lift force acting on the dropping maw was preset andits time history duriog the @pact was measured by means.,

A two-phase induction drag-cup generator was used formeasuring the angular velocity of the wheel. The angulardisplacement of the wheel was detemoined by means of asegmented ring mounted on the wheel. Brushes wereattached to the axle so that electrical contact was made andbroken 30 times during each revolution of the wheel. Thissegmented ring was also used for calibrating the angukw-velocity generator. I?or evaluation purposes, an angularaccelerometer was installed on the wheel.

The vertical displacement of the upper mass and theshock-strut stroke were measured by means of variable-resisttmceslide-wirepotentiometers, positively driven in bothdirections. In order to increase the sensitivity of the upper-mass-displacement measurements, a series of separate slidewires W& arranged in such a m“anneras to p~oduce full-scale record deflections for each ten inches of mass displace-ment. Measurements of the tire deflection during impactwere obtained from the diilerence between the Valu-wof theupper-mass displacement and the vertical component ofthe shock-strut stroke. In order to evaluate the accuracy ofthe measurements obtfiined by this method, a stationqslide wire was used to measure directly the tire deflection inthe special series of instrument-eval~ation drop t,ests; thedata obtnined by the two methods were found to be in goodagreement.

The more important characteristics of the individualinstruments used in the tests are given in table I, page 34.On the basis of these characteristics, the mtium errorsin the derived measurements are believed to be within thefollowing limits :

Total horizontalforce on tire, F=,, lbAd? ~-8--.. _L_____________________ 4S?86&wndmmrm@________________________ +,%?s6

Totu.Jverticalforce on tire, Fv,, lbAxle m~____________________________ kwo&mtim~m~--- Al______”_” ___________ 4+?10

Tire dqlectti, 6, fi____________________________ 50.03& ?i.o?+zon.td W?rXi@, v=l.,.fl/8&_______________ &6Carriagehorizontal veik%y, V& ft/~ec____________ &l.3

It should be noted that the foregoing values apply to themaximnm values of the measured quantities; that is, avertical load of about 9,oOOpounds, a drag load of 4,5oopounds, a tire deflection of 0.35 foot, and tie and horizontalvelocities of 86 feet per second. When the measured quan-tities are smtdler than these mtium values, the errorsare, in general, proportionately reduced.

The electrical outputs from all the insbmments wererecorded on a 36-channel oscillograph equipped with atimer which produced timing lima on the record at intervalsof 0.01 second. A typical oscillograph, record is shown,reduced, in @me 7.

—.. _____ —

1160 REPORT 1248—NATTONAL ADVISORY COMIUTTEE FOR AJ3RONAUTICS

FmuEE7.—OscilIograph record for typical forward-speed Wt. VVO=9.68 feet pm second; V’0=S4.1 foot por second.

EQUATIONSUSEDFOR DERIVEDQUANTITIES

In view of the fact that it was not feasible to meesurecertain desired quantities directly (for example, the totalvertical and horizontal forces between the tire and theground), it was necessary to deduce these quantities hornother closely related measurements. The equations usedfor this purpose are discussed in this section.

AI?PLIEOFORCESFROMAXLEMEASUREMENTS

The applied ground form were obtained by addition ofthe forces acting on the de and the inertia reactions due tothe acwil&ations of the mass between the axle dynrunometerand the ground. ~orn fig&e 8 it can be seen that. . .

FH,~FN~ cos p+F~, sin p

~==FA, COS q—&, SiIl(fF }(1)

whereFAT=F4a+m&4a

FN,=FN~+m~N~

and mmis the mw (3.58 slugs) between the axle dynamom-eter and the g&mnd. @ fig. 8, the inertia or rewrsedeffective forcca m~b and m~y. are indicated by meansof dashed vectors.)

The forces .l?A=and ~’= were meaSureddirectiy by the tiedynamometer. The &al acceleration a~= was obtained by

means of a single accelerometer located on the modificcl yokoof the landing gear. (See fig. 3.) Since the yoke and axle-were very rigid in the direction parallel to the shock-strutaxis, the axial acceleration of the yoke was msnmed oqurtlto the axial acceleration of the center of gravity of thomesa between the de dynamometer and the ground. Onthe other hand, normal forces produced some twisting of thelanding gear in the plane perpendicular to the shock-strutaxis. I?or this reason it was necessa~ to use two acceler-ometers (seefig. 3) and linear extrapolation to determino ticnormal accele~ation at the center of gravity of the mawbetween the axle dynamometer and the ground.

In order to illustrate the generil characteristics of theforce measurements, time histories of the upplied grouncl-force components FAT, FNT,FVF, and F=*, aa well as timehistories of the tie forces F~= and FN~and the inerth reactions mwda and m.a~~, horn which the previously mentioned ap@ed ground forces were calculated, are shown kfigures 9 (a) to 9 (c) for a typical forward-speed teat.

l?rom the horizontal and vertical components of th[applied ground force, the time histories of the coefficient ofriction, defined as

F‘T

~=lq=@

were determined. (See fig. 9 (d).) As used herok the h“coefficient of friction” signifies the value of the ratio of t,h

AN EXPFEU3H3NTAL STUDY OF APPLIED GROUND LOADS IN LANDINQ 1161

‘i

i\

1

\

F

II

\

Forces on axle dynamometerT

FNO

U#o For ward

Fafces an wheel

fivT

Forces on ground dynamometerFHr I

Amg o J mg %g

%47

r I FHqC7v I F%9

///fl////I// //, ///, ///, ,//1

l?murm8.—Diagramof forcesandreactions.

instantaneous applied drag force to the applied verticalforce, as actually measured, and not necemarily the max-imum value of this ratio that can be attained under givenconditions of contact between the tire and the ground.This distinction ie necessary because, under certain con-ditions (small slip), the drag force is governed by thecircumferential distortion of the tire rather than by the lirnibing friction between the tire and the ground, asis discussed inn mbsequent section.

APPLIED FORCRS FROM GROUND MEASUREMEN~

(INSTRUMENT-EVALUATION TR9TS)

b previously mentioned, a ground dynamometer equippedwith accelerometers was used in a special series of drop testsas an additional means of determining the applied groundloads for comparison with the values obtained from the axleinstrumentation. The total applied ground loads weredetermined from the sum of the forces in the grounddyna-momoter strain-gage membens and the inertia reactions dueto the acceleration of the’ ground-platform mass m. (7.51slugs). As can be seen from figure 8,

mlFvT=Fvz+mga~x

xhere FEZ and FVZ were determined directly from theyotiddynamometer strain-gage measurements and aH~and

zv~were obbined from accelerometers attached to the groundplatform, as shown in figure 3. (In fig. 8, the inertia forcesn+H~ and m~vg are indicated by dashed vectors.)

APPARRNT SRIDDING VELOCITY

For use in studying the variation of the coefficient ofFrictionduring the spin-up process, the apparent skiddingvelocity V,zti was detmuined. The apparent skiddingveloci~ is defied as the difference between the actualtranslational veloci@- of the axle and the translationalvelocity which would exist if the wheel were rolling freelywith the same angular velocity. Since the axle veloci~ for~ freely rolling wheel can be expressed as the product of thesflective rolling radius of the tire r. and the wheel angularvelocity d, the apparent skidding velocity during spin-up maybe written as

v,k,d=v~l,-r$ (3)

It should be noted that the apparent skidding velocity is notneccamrily the same as the actual sliding velocity betweenthe tire and the ground, which may vary from point to pointin the ground-contact area. The term “apparent” is used inrecognition of the fact that equation (3) neglects the effectsof the circumferential and radial distortions of the tire which,under the action of drag loads, modify the tangential veloci-ties of the tread in the ground-contact region and therebyalter the actual local sliding velocities somewhat in com-parison with the values which would apply for a circum-ferentially riggd wheel.

Since the applied loads during an impact cause a fore-and-aft oscillation of the landing gear, the de velocity is not thesame as the carriage velocity. Therefore, in these tests thedifference between the axle velocity and the initial cmriagevelocity was determined by integration of the horizontal ‘component of the axle acceleration, and the axle velocity wascalculated horn the expression

Jt

V&=V=O- a=~dt0

where aH~was determined from the normal and axial accel-eration components of the de by means of the geometricrelationship (see fig. 8):

aHa=a.v=cos p+a.4~ sin P

The instantaneous value of the effective rolling radius of thotire was determined by means of the relationship (seeappendix A’):

rB ~–~

ro—

sin- 1r

1–$

1

(4)

8- R——

3 J

REPORT 1248—NA~oN& ADVISORY

6x Id

4 -

n

a-0

0 L.” ‘- -.

l(o) I I I I I 1 I I

6X 103

l(c) I I I I I I I I

L

3x 103

–3t

J (b) I I 1 I I I I \

60 r

(e) I I 1 I I I I Io .04 08 J2 .t6

llme after contoct, sec

FIGURE 9.—Time bistmies of basio data and derived quantities from carriage instrumentation in a typical forward-speed test. VVO=’7.6 foot porsecond; VHO=44 feet per second.

AN EXPERIMENT AL STUDY OF APPLIED GROUND LOADS IN LANDING 1163

where R is the free radius of the tire, rd is the geometric de-flected radius, and 8 is the vertical deflection of the tire, asdetermined from the measurements of the upper-maw verti-cal displacement ZUand the shock-strut axial stroke .s bymeans of the geometrical relationship

6=2.—8 Cos p

I?or illustrative purposes, time histories of the quantitie9involved in the calculation of the apparent skidding velocityme shown for rLtypical forward test iDfigures 9 (e) and 9 (f).

RESULTSAND DISCUSS1ONGENERAL CHARACTERISTICSOF A TYPICALIMPACT

In order to obtain an overall physical picture of the impactprocess during a landing with forward speed, it may behelpful, before proceeding to the main results of this investi-gation, to consider briefly, with the aid of figures 8 and 9,tlm manner in which the various forces are developed sub-sequent to ground contact and their effects on the motionsof the wheel and landing gear, particularly the processwhereby the conditions of contact between the tire and theground are progressively changed from full skidding at theinstant of initial centact to free rolling following the com-pletion of spin-up.

At the instant of initial ground contact the dropping masshas essentially constrmt vertical and horizontal velocitycomponents. The mechanically simulated wing-lift forceis appro.xinmtely equal to the dropping weight so that thelift factor K~ remains close to 1.0 throughout the impact(fig. 9(d)). Following ground contact, the deflections ofthe tire and the shock strut produce a vertical ground forcel’VT (fig. 9(c)), governed by the vertical velocity and thetim and shock-strut characteristics, which acts to dissipatathe vertical momentum of the dropping mass. In thepresence of this vertical force, the relative horizontal velocitybchveen the tire rmd the ground, or skidding veloci~, givesrise to a frictional or horizontal drag force F’= (fig. 9(c)).The moment produced by this drag force, acting throughthe deflected radius rd of the tire (fig. 9 (e)), plus a smallmoment due to the longitudinal offset of the vertical forcefrom the center of the wheel, causes an anguhw accelerationof the wheel and an increase in the angular velocity 8 withtime @g. 9 [e)), which, in turn, serves to decrease the skiddingvelocity with time (fig. 9 (f)).

Since the coefficient of friction p during the spin-up process(fig. 9 (d)) is generally larger than the tangent of the angle wbetween the landing-gem axis and the vertical axis, the re-sultant force on the landing gear has a rearward-acting com-ponent in the direction perpendicular to the landing-gear~ti (nornd force ~N~ in fig. 9 (b)). Bemuse the landinggear has fle.sibility in bending, this normal force produces arearward acceleration aNaof the axle, perpendicular to thelanding gem ask (fig. 9 (b)). The axle also experiences anacceleration a~=parallel to the landing gear axis (~ 9 (a))m rLresult of the compression of the shock strut and the tire.Since the resultant of these accelerations has a reamvard-ncting horizontal component, the horizontal velocity of theaxle Vul, is somewhat reduced in comparison to the velocity

of the carriage VH (fig. 9 (f)), which tends to decrease theskidding velocity slightly. During this phase of the impactthe axle may experience appreciable rearward deflections.An additional increment in rearward motion of the axle isprovided by the kinematic displacement due to the telescop-ing (shor@ing) of the inclined shock strut during the impact.

The’ ~rocess of tire skidding continues, with decreasingskidding veloci~ (fig. 9 (f)) as the angular velocity of thewheel d is increased (@g. 9 (e)), until tie angular impulsebecomw equal to the change in angular momentum requiredto bring the wheel up to ground-rolling speed. The decreasein the skidding velocity with time is accompanied by anincrease in the coeilicient of tiction (fig. 9(d)). As thecondition of free rolling is approached, the coeilicient offriction passes through its maximum value, at some finitevalue of the apparent skidding veloci~, and then rapidlydrops to near zero as the final stage of the transitionfrom skidding to free rolling is completed.

This sudden decrease of the coefficient of fkiction causesthe drag force to drop abruptly, with the following conse-quences. The landing gear, which had previously been de-flected toward the rear by the drag force, now acceleratesforward under the i.niluenceof the internal elastic forces andthe vertical load, the horizontal velocity of the tie becominglarger than the carriage velocity. The landing gear pas&sthrough its undeilected position, attains large forwafd deflec-tions, then again reverses its direction of motion relative tothe carriage. The ensuing damped fore-and-aft oscillation,which occurs at about 11 cycles per second, is associated withthe natural frequency of the landing gear in bend@, includ-ing the effects of the equivalent mass of the rolling wheel.

Following the sudden drop-off of the drag force, a similartype of elastic springback and resulting torsional or circumf-erential oscillation, at a natural frequency of about 55 cyclesper second, takes place in the tire which, because of its tor-sional flexibility, had been circumferentially distorted by thedrag-load moment. This circumferential springback impartsa positive increment to the angular veloci@ of the wheel, sothat it becomes larger than the angdar velocity of the tiretread. The use of this larger wheel angular velocity inequation (3) leads to the calculation of negative values forthe apparent skidding velocity V,kti (fig. 9 (f)) immediatelyfollowing the decay of the drag force (fig. 9 (c)), even thoughthe actual average skidding velocity between the tire andthe ground during this period may be nominally zero or evenslightly positive.

FORWARD-SPEED TESTW

Time histories of applied loads,—Figure 10 shows severaltypical time histories of the applied vertical and horizontalground loads and the coefficient of friction, as measured inimpacts with forward speed. The data presmted are for anaverage initial vertical velocity of about 7.5 feet per secondand horizontal velocities up to approximately 83 feet persecond. (For clarity, time histories from only a few repre-sentative tes.ta,selected fmm a more extensive twt proemm,are shown in figure 10. Figure 11 summarizes the mostimportant data from the complete series of forward-speedtests.) A number of basic eilects can be seen from figure10. As the forward speed is increased, since the impulse

——

1164 “ REPORT 124&NATIONa

8XI03

ADVIBORY CO~ FOR AERONAUTIC

Vjfo, Vvo,

fps fps

6 - —.— I9.3 7.61—--— 43.6 7.6I—-–— 65.8 7.54—— 83.4 7.52

4 -

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I I I I I 1 I I I I I I r I I I I Io .02 .04 .06 .08 .10 J2 .14 .16 .18

Time Ofter Coil!oct, S90

FICNJRE10.—Time hiatmies of applied loads and coefficient of friction in typical forward-speed teds. Vvo I=7’.5f3feetpersecond.

am

All EXPDRIMENTAI, STUDY OF APPLIED GROUND LOADS IN LK@$Dll?G 1165

8 Id

1

Vvow, fPs

A 9.600 7.55

6 m 5.730 3.00

g

-S4 -

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.04 -

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Horizcmtol velocity, fps

FIGURD Il.-summary of applied loads in forward-spsd task.

required to bring the wheel up to ground-rolling speed isincreased, the wheel skids for a longer time. Because thevertical load increases with time du&g the period of wheelskidding, as the skidding process is prolonged, there is anincrease in the magnitude of the vertical load which exists atthe time of spin-up and, therefore, an increase in the maxi-mum drag load with increasingforward speed. (The general-ity of this result is, of course, restricted to the range of for-ward speeds where spin-up rmdthe maximum drag load occurboforo the maximum vertical load is reached, which wasthe situation in them tests.) This effeot of the forwardspeed on the maximum drag load can also be seen from

4131372—G7-74

3:005.737.559.60

(f) ,

iigure 11 (a); the vertical load at the time of spin-up isshown in iigure 11 (b).

In these forward-speed tests the wheel turned throughonly a fractional part of a revolution during the skiddingprocess, the angular &placement at the instant of maximumdrag load, at the highest horizontal velocity investigated,being less than 100° at a vertical velocity of 3 feet persecond, and even smaller at the higher vertical velocities.

As can be seen from @ure 10, two types of superimposedoscillations are evident in the drag load subsequent to spin-up.The high-frequenoy oscillations,at about 55 cycles per second,are due to the torsional vibrations of the wheel and tire

1166 REPORT 1248—N’A!IToNAL ADVISORY COMMF17CEDFOR AERONAUTICS

assembly which are initiated by the circumferential spring-back of the tire at the end of the spin-up process, as pre-viously mentioned. The low-frequency oscillations, atabout 11 cycles per second, result from the alternatingangular accelerations which are imparted to the rollingwheel by the fore-and-aft oscillations of the landing gearrecited by the drop-off of the ~~ load, also previouslydiscwwd.

In the case of the impact with zero horizontal velocity, thesmall negative or forward-acting drag load is attributed tothe kinematic displacement of the axle to the rear, whichresults from the telescoping (shortening) of the inclinedshock strut. A forward-acting horizontal force is necessagto produce the angular acceleration of the rolling wheelrequired by the rearward acceleration of the axle; an addi-tional increment in negative drag load during this periodis produced by the rolling resistmce of the wheel.

As can be seen from figures 10 and 11 (c), the magnitudeof the maximum vertical load varied appreciably over therango of horizontal V-eloci@ cm-end by the tests, even whenthe vert.icrd velocity was essentially constant As thehorizontal velocity was increased tim zero, the maximumvertical load fit decreased, then increased, so that at thehighest forward speeds the maximum vertical loads wereconsiderably higher than at zero horizontal veloci6y. Thesevariations of the vertical load are caused prim&ily bydi.llermces in the internal friction forces within the shockstrut which result from the fore-and-aft bending of the land-ing gear during the impact. The (equivalent static) forceswhich cause this bending Wer from the applied groundforces by an amount equal to the inertia reactions of themasses between the shock strut and the ground. In otherwords, the bending moments responsible for the increasedshock-strut friction are those =ociated with the instan-taneous bending deflection, or dynmnic response, of thelanding gear, rather than those due directly to the appliedground loads. Thus, the effects of strut friction on thevertical load under dift’erent impact conditions can be m-plnined by consideration of the bending response of thelanding genr:

In an impact with zero horizontal velocity, the resultantforce is essentially vertical, so that a bending moment. tend-ing to deflect the landing gear forward is present throughoutthe entire impact. By the time the maximum vertical loadis reached, this forward deflection has become appreciable sothat substantial strut friction forces &t which cause themaximum vertical load to be greater than the value whichwould be obtained if bending moments were not present.

In impacts with iinite horizontal velocity, on the otherhand, the bending moments on the landing gear changesign during the impact. As a result, the landing gear isfirst deflected toward the rear, attains a maximum rearwarddeflection shortly after the maximum drag load is reached,then springsforward, passesthrough zero deflection, reaches amaximum forward deflection, and oscillates with decayingamplitude. The effect of strut friction on the maximumvertical load depends largely on the magnitude of thebending deflection at the instant when the maximum verti-cal load is reached. This, in turn, depends on the shape ofthe drag-load time history and the value of the mminmm

drag load, the amount of time elapsing between tho occur-rence of the mminmn drag load and the masimun ver~icalload, and the natural frequency of the landing gear.

For example, when the forward speed is small, because thetime to spin up is short, the maximum rermmrd clefloctionis small and occurs early in the impact, considerably beforethe maximum verticaJ load is reached. Thus, the landinggear is already in the process of fore-and-aft oscillation whenthe maximum vertical load is reached, the bending deflec-tions at this instant being either positive or negdive,depending on the factors previously mentioned. The mini-mum effect of strut friction, and thus the smallest value ofthe maximum vertical load, is obtained for the conditionwhere the landing gear passes through zero deflection at theinstant of mtium verticrd load. In theso tests, thissituation occurs at a horizontal velocity of approximateely20 feet per second. (See @g. 11 (c).) At lower horizontalvelocities the landing gear has larger forward deflections atthe instant of maximum vertical load since it has been subjectto a forward acceleration for a longer time. At higlmrhorizontal velocities, because the time to spin up is increased,the maximum rearward deflection increases and occurs at nlater time after contact; as a result, the amount of rmr-ward deflection, and thus the magnitude of the strut frictionforces, at the time of mtium vertical load increases withincreasing forward speed (for the range of conditions wherethe maximum drag load occurs before the max&mm vor~icalload). Since the maximum rearward deflection occursafter the maximum drag load is reached, the effect of strutfriction on the mtium vertical load can be very large,even though the applied (ground) drag loacl has rdrmdydropped to low values at the instant of maximum vertical load.This situation exists at the highest forward speeds for whichdata are shown in figures 10 and 11. Of course, if thaw woreno strut friction, the vertical loacl would be almost inclo-pendent of the forward speed and the drag 10MI; in this CMO,the only eiTectof the drag load would arise from the rehwtively small component parallel to the axis of the shock strut,which would tend to increase the rate of closure of the strutsomewhat and thereby cause a slight increase in the rmirdforce produced in the strut.

Coefficient of friotion.-Figure 10 also shows the variationof the instantaneous value of the coefficient of friction (as clo-fined previously) between the tire and the ground during thospin-up process. As can be seen, the coefficient, of frictionin each test started out at an intermediate value imme-diately after initial contact, increased steadil~ with time,attained a mtium value just before the mrmimum drugload was reached (at a fite value of the apparent skidclingveloci~), then dropped very rapidly toward zero as thotransition from skidding to rolling was completeel.

The variations of the coefficient of friction during nnygiven impact and from one set of conditions to another cmbe explained qualitatively by consideration of several effectswhich appear to iniluemm the characteristics of the centactbetween the tire and the ground; namely, the phenomenoncalled “slip,” the effects of changes in the instantaneousvalue of the skidding velocity, the effects of variations inthe vertical load, and the effects of heating of tlm tire run-ning surface produced by the skidcling process.

AN EXI?ERIMEWM.L STUDY OF APPIJDD GROUNLILOADSIN fJANDING 1167

Some insight into these effects can be obtained from theresults of previous investigations of the braking of the rollingwhcela of automobiles. (See, for example, ref. 3.) In thecase of a rolling wheel, if a braking torque is applied, thermgular velocity is reduced, even though the horizontalvelocity of the axle maybe held constant. This reduction inangular velocity under the action of a torque gives rise to theconcept of slip. (The tam “slip” may be somewhat mis-leding since, at low values of torque, the reduction in angularvelocity occurs almost exclusively as a result of the circum-ferential and radial distortions produced in the tire by thetangential forces developed between the tire and the ground,rather than through actual sliding of the tire contact surfaceover the ground.) The ratio of the change in angular veloci~of the wheel under torque to the angular veloci~ of the freely-rolling wheel for the same axle velocity is called the slipratio. As is discussed in append& A, the slip ratio mayalso be e.spressed m the ratio of the apparent skiddingvelocity of the tire to the horizontal velocity of the axle.

The relationship between the slip and the horizontdforcedeveloped between the tire and the ground can be easilyunderstood if one &at considers the situation which existswhen sm elemental block of rubber, in contact with theground, is subjected to an increasing horizontal force in thepresence of a vertical force. As the horizontal force isapplied, at fimt, because of the interlochg or adhesivenature of the contact between the block and the ground,no appreciable relative motion takes place between the con-tacting surfaces and an opposing equal tangential force isdeveloped in the contact region. Under the action of theseforces, however, cmelastic deformation of the block in bend-ing and shear occurs, essentially proportional to the hori-zontal force. Because of this elastic deformation, a relativemotion is produced between the top of the block and thesurface in contact with the ground, even though no actualsliding motion exists in the ground-contact area. Thisrelative motion between the top and bottom of the block isrumlogousto the relative circumferential motion between thebead and the tread which is the basis of deformation slip intlm case of the tire. As the horizontal force is increased, apoint is reached where the tangential stxessbetween the tireand the ground reaches the limiting value which can bemaintained by the interlocking or adhesive forces. byfurther incrense in the applied horizontal force causes theblock to slide relative to the ground. Following the onsetof sliding, since the interlocking bond between the contactingsurfaces has been broken, the tangential force immediatelybecomes appreciably smaller than its value at the instant ofincipient sliding and continues to decrease with furtherincrease in the velocity of sliding.

The variation of the tangential force developed when arolling wheel is subjected to a braking torque can be visual-ized if each section of the tire in contact with the groundisassumed to behave in more or less the same way as the ele-mental block just discussed. In the case of the tire, of course,the situation is much more complicated; since the effectivestiffness and the distortions of the casing differ considerablyfrom point to point, the distributions of the vertical groundpressure and the tangential stresses vary appreciably overthe contact area.

At low values of torque, that is, at small slip ratios, thetangential stresses are mostly below the level at which localsliding occurs, so that the contact between the tire and theground is basically of an interlocking or adheaive nature.In this region finite slip is due prhimrily to elastic deforma-tion of the tire, sinm little or no actual sliding occurs be-tween the tire contact area and the ground; as a result, inthis region the slip is essentially proportional to the torque.As the torque is increased, the deformations and the tan-gential stressesbecome larger, so that the slip and the totalhorizontal force increase. With further increase in torque,an increasingly greater part of the ground-contact areareaches the limiting stress level that can be maintained byadhesion, so that more and more points in the contact areabegin to slide. As soon as a given tire element begins toslide the tangential force which can be developed by thatelement is considerably reduced, and a transfer of tangentialstress takes place to load up elements which have not yetbegun to slide. As a result, as more and more elementsbegin h slide, a point is reached where the total horizontalforce begins to decrease with further increase in braketorque. From the foregoing considerations it is clear that,after the horizontal ground force has reached its maximumvalue, the process is unstable with further increase in braketorque. Since the ground force becomes increasinglyinsticient to balance the brake torque, the wheel rapidlydecelerates to zero angular velocity (slip ratio equal to 1.0)and locks. At this point, full skidding, at a velocity equalto the axle velocity, exists over the entire ground-contactarea.

As a result of the physical process just described, the dragforce (and, therefore, the ratio of the drag force to the verti-cal force) for a braked wheel increases rapidly with slipratio, reachw a maximum at a relatively low value of theslip ratio (the so-called “point of impending skidding”), anddecreases with further imzreasein slip ratio until the locked-wheel condition is reached at a slip ratio of 1.0, as may beseen from figure 12, which is taken horn reference 3.

In the literature on tire friction the ratio of the horizontalform to the vertical force is generally referred to as thecoefficient of friction. It should be recognized that thisusage is not strictly correct over the entire range of slip

12

ir

Forward speed,krnnv

1.0 ——— —— —____ _ ___6:7

* ------ ----+

. ---- ]5---- ----j .8

-- ---- - -v-.% 5(-J

—. -.~.

% .6 ~.

E.g

‘4~.

3

.2

I/1 I I 1 I I I I I I I

o .10 .20 .30 .40 .50 .60 .70 .80 .90 LOOSlip ratio, S

FIcwmm12.—Variatlon of coefficient of friotion with slip ratio. Brak-ing tests on ckv conorete (from ref. 3).

1168 REPORT 124~NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

ratio, inasmuch as at slip ratios below the “point of impend-ing skidding” tho horizontal force developed depends solelyon the resisting torque or, what amounts to the same thing,on the deformation of the tire and not on the ground frictionsince, in this region, the horizontal force is l&s than thelimiting value which can be tiaintained by friction betweenthe tire and th~ ground. For slip ratios above the “point ofimpending skidding,” on the other hand, the horizontalforce developed is the maximum value which can be main-tained by tilction under the particular conditions of contactinvolved,’ so that in this range the ratio of the dmg force tothe vertical force is more properly termed the coefficient oftilction of the tire. The friction at the “point of impendingskidding” is analogous to, though not identical with, theclassical “static friction, whereas the friction for the locked-wheel condition corresponds to what is commonly calledkinetic or sliding friction. Between these two limits the&lction appears to involve both types in combination.

In addition to the effects of slip ratio previously discussed,it is also evident from figure 12 that the magnitude of theforward speed has an appreciable influence on the value ofthe coefficient of friction. This influence can be seen evenmore clearly from figge 13, also taken from reference 3,which shows the effects of the forward speed on the coefE-cient of tilction at slip ratios in the primarily adh~ive andsliding regions. (Fiige 13 appears to be a cross plot of thedata from the same series of tests on which fig. 12 is based.The curves labeled “adhesive tilction” and “sliding friction”correspond with the data for “impending skidding” and slipratio of 1.0, respectively, in fig. 12.)

1.2r1.0 -

Adhesive tiCtiWI

:8.- 0.Y 0* 0% .6 -

E~

$.4 -v

2

tI I I t 1 1 ! I

o 10 20 30 40 .50 60 70 80Forword speed, krn/hr

)?IGDEE13.—Effect of forward speed on ooefficient”of friction. Brakingtests on dry concrete (from ref. 3).

The effects of the forward speed on the coefficient of fric-tion arise primarily through changes in the magnitude of thelocn.1skidding velocities in the regions of sliding in the ground-contact area. At a given slipratio, an increase in the forwardspeed cauies an essentially proportional increase in the skid-ding velocities at points in the ground-contact area wheresliding already @ts. Also, because of inertia and hysteresistiects associatedwith the rate of deformation of tire elementspnssing through the ground-contact area, which tend to re-

duce the effectiveness of the mechanical interlocking betwcmthe tread and the ground, an increase in the forward speedtends to reduce “thelevel of tangential stress at which slidingbegins, so that a greater proportion of the contact area is ina state of sliding. As a result of the foregoing effeck and thofact that the local coefficient of friction at any point withinthe ground-contact areawhere sliding exists decreaseswith in-creasingskiddingvelocity, it follows that, for slipratios beyondthe “point of impending skidding,” where a large part of tlmcontact area is in a state of sliding, an increase in the formmdspeed cau.w an appreciable decrease in the overall coefficientof friction for the tire as a whole. Also, since an increase inforward speed tends h accelerate the transition from adhesionto sliding, as previously noted, the value of the slip ratio atwhich the masimum overall coefficient of friction occurs issomewhat decreased at the higher forward speeds. On t,hoother hand, at low slip ratios, below the value at which tlmmtium overall coeilicient of friction appears, sinco tlmhorizontal force is developed primarily through dlmsiveground contact and tire deformation, a change in horizon talvelocity has relatively little effect on the overall coefficientof friction.

In the preceding discussion the influence of the slip ratioon the coefficient of friction has been considered as a pri-marily mechanical effect. On the other hand, from observa-tion of tires subjected to drag loads, it would appear thfitanother aspect should be considered; namely, the offocts ofheating of the tire tread surface which results from tho worlcdone in sliding. It is lmown (see, for example, ref. 4) thotthe coefficient of friction of tire tread rubber on concretodecreases markedly with increasing temperature. On thobasis of elementary considerations, it is shown in appendisB that the sliding work per unit of tire area in contact withthe ground, which may be taken as a qualitative inde.. of thoheat concentration in the tire ground-contact arm, dependsto a great extent on the slip ratio, as well as on othor fnctora,such as the vertical load, the tire pressure, and tho codiicim tof friction; the greatest heating effect, everything else beingequal, occurring at a slip ratio of 1.0. These considerationssuggest that at least part of the eifect of slip ratio is a heatingeffect. This aspect is fiscussed in more detail subsequentlyin connection with the forward-speed tests with revermwheel rotation.

The concepts just discussed permit some interpretation ofthe variations of the coefficient of friction in the tests of Lhopresent investigation. In the forward-speed tests (fig. 10)the process is reversed from that in braking; that is, the proc-essbegins, at the instant of initial contact, when the tire is notrotating, so that the slipratio is equal to 1,0 and full skidding,at a velocity equal to the horizontal velocity of the ah,exists over the entire ground-contact area of the tire, just asin the case of the locked wheel in the braking process. Forthis condition, because of the high skidding velocity, theabsence of any adhesive contact, and the large heat concm-tration per unit of tire contact area, the coefficient of frictionimmediately following ground contact is comparatively low;in fact, lower than at any other stage of the skidding process.As the wheel begins to rotate imder the influence of tlmmoment produced by the drag load, the angular velocity in-creases so that the slip ratio and the local skidding volocitios

AN EXPERIMENTAL STUDY OF APPLJED GROUND LOADS IN LANDING 1169

in the ground-contact area are reduced; also, the rate ofintroduction of fresh tire-tread area into the ground-contactregion is increased so that the heat generated per unit timeby the skidding is distributed over a larger tin+tread area.As a result of the combination of the foregoing effects, thecoefficient of friction increaseswith time from its initial value.As the.angular velocity approaches the value for free rolling,an increasingly greater part of the ground~ontact area passesfrom sliding to adhesive contact. The mtium value of theoverall coefficient of friction is reached when virtually all ofthe tire contact area has attained a state of adhesive contactand the tangential stresses due to tire distortion reach theirhighest values, With further increase in the angular velocityof the wheel, the deformations of the tire and the slip arisingtherefrom are rapidly reduced, so that the tangential stresses,and thus the total drag force and the overall coeflkient offriction, drop to near zero as the fial stage of the transitionfrom slid~ to rolling is completed.

From the foregoing discussion it appears that the variationof the coefficient of friction in an impact with forward speedcan be esplained, at least qualitatively, by consideration oftlm dfects of slip ratio, skidding velocity, and heating of thetire surface. The effect of the skidding velocity is particu-larly evident at the begipning of me spin-up process wherethe slip ratio is the same for all tests and the skidding velocityis equal to the horizontal velocity; it can be seen from figure] O that, in gemmnl,the coefficient of fiction decreases pro-gressively with increasingskidding velocity. A slight, thoughsystematic, decrease in the maximum value of the coefficientof friction with increasing forward speed is also evident.This latter result may be largely due to inertia and hysteresiseffects, previously mentioned, which tend to reduce theeffectiveness of the interloclmg contact at low slip ratioscorresponding to the “point of impending skidding.”

Effeot of verti~al velocity,-The effects on the appliedlords caused by changes in the vertical velocity at contactme summarized in figure 11. The usual, not quite linear,increase in the mtium vertical load with vertical velocityis evident (fig. 11 (c)). It can also be seen that the effects offorward speed on the vertical load were less pronounced atthe lowest vertical velocity. This result appears due tnthe fact that the strut friction is appreciably reduced at lowverticnl velocity since the bending moments on the gear,and thus the bending deflections, are smaller. Also, thetire can compensate more readily for the effects of strutfriction, that is, reduced shock-strut travel, by deflectingsomewhat more, with relatively little increase in verticalforce, since the slope of the tire force-deflection curve iscomparatively flat at small deflections.

As would be expected, the maximum drag load at anygiven horizontal velocity increased with the vertical velocity(fig, 11 (a)). Since an iucrase in vertical velocity resultedin an increased rate of rise of the vertical load, and since the~mount of impulse required for wheel spin-up is essentiallyconstant for any given horizontal velocity, the time to spinup decreased with increasing verticil velocity (@. 11 (d)).Even though the time to spin up was reduced, this effectwas offset by the higher rate of rise of the vertical load, whichcaused tho verticnl load at the time of syiu-up to be increased

with increasing vertical velocity (@g. 11 (b)), so that themaximum drag load increased with vertical velocity. Also,because of the higher rate of rise of the vertical load, the rateof increase of the masimum drag load with horizontal ve-locity was greatest at the high vertical velocities (& 11 (a)).In the tests at a vertical velocity of 3 feet per second, rela-tively little increase in the masimum drag load with hori-zontal velocity is noted at speeds above about 40 feet persecond. This result occurs because the characteristics ofthe landing gear are such that, at low vertical velocity, thevertical load is essentially constant over a large part of theimpact time; thus the vertical load which exists at the timeof spin-up is essentially unchanged with variations in thetime to spin up. As a result, changes in time to spin up,within this essentially constant vertical-load region, produceonly small differences in the maximum drag load.

Figure 11 (e) shows how the ratio of the maximum dragload to the maximum vertical load varies with the verticaland horizontal velocities. The highest values of the dragload relative to the vertical load, of course, were obtainedat the high horizontal velocities where spin-up occurs whenthe vertical load is near its mtium value. As can be seen,a large reduction in load ratio, most pronounced at lowhorizontal velocities, occurred as the vertical veloci@ wasincreased. This reduction results from the decreased timeto spin up at the higher vertical velocities, previouslydiscussed. At a given horizontal velocity, since the dragimpulse required for spin-up is essentially constsmt, whereasthe total vertical impulse increases directly with the verticalvelocity, it follows that the ratio of the vertical load at thetime of spin-up to the maximum vertical load will be.reducedwith increasing vertical velocity, so that the ratio of themmimum drag load to the maximum vertical load conse-quently is also decreased with increasing vertical velocity.

Figure 11 (e) also shows that the curves for the differentvertical velocities tend to converge at the higher horizontalvelocities. This result is explained by the fact that, at thehigher horizontal velocities, spin-up occurs when the verticalload is near its mtium value, as previously indicated, sothat the ratio of the maximum drag load to the masimumvertical load approaches the value of the coefficient of frictionat the time of spin-up. When the maximum drag load coin-cides exactly in time tith the m~um vertical load, theratio of these t+o loads is the coefficient of friction at thetime of spin-uP. Since the time to spin up decreases withincreasing vertical velocity, the horizontal velocity at whichFH~~ti/FVT&GP.uincxeases~with increasing vertical veloc-

ity. For horizontal velocities beyond this value, becausespin-up occurs subsequent to the peak vertical load, theratio FHT-IFv,.= .should decrease with further”increase in

horizontal velocity. As a result of the foregoing considera-tions, the curves of F=,-/FVT_ for, different vertical

velocities have to cross one another somewhere in the horizon-tal-velocity r@on beyond ~e range of these forwmd-speedtests. The vertical spread of the c~es in figure 11 (e)at the highest ‘horizontal velocities shown may thus beattributed to two eihcts due to ‘changes ih the verticalvelocity; namely, ditlerenceg in the value of the horizontal

1170 REPORT 1248—NA!ITONAL

velocity at which FHr_/FvT=e=Pm and differences

ADWSORY COMMITTEE

inthe

value of the coefficient of friction at the time of spin-up.The latter effect is indicated in figure 11 (f), which shows

the ratio of the m&mum drag load to the vertical load atthe same instant, that is, the coefficient of fiction at thetime of maximum dxag load. As can be seen, there wassome decrease in the coeilicient of friction with increasingvertical docity. Several factors apparently combine toproduce this result. With iucrensing vertical velocity, sincethe rate of rise of the verticnl load is increased, the rate ofrise of the drag load is increased. Consequentlyj the amountof angular displacement of the wheel between the instantof contact and full spin-up is decremed. Thus, more skiddingenergy is transferred to the tire per unit time and this energyis distributed over a smaller area of the tire periphery, sothat the concentration of heat and, thus, the temperatureof the tire tread surface are increased. In addition, highertangential stresses are produced in the tire contact area asa result of the larger vertical deflections of the tire, so thatthe remaining amount of tangential stress available for theproduction of drag load in the interlocking contact regime isreduced. Also, the vertical ground pressures are increasedrmd the rates of loading are higher. Each of the foregoingeffects tends to cause a reduction in the coefficient of frictionm the vertical velocity is increased.

FORWAED4PRED TESTS WITH REVERSE WHEEL ROTATION

Time histories of applied loads.—Jn order to obtain anindication of the characteristics of the applied loads for therange of forward speeds beyond the maximum velocity ofthe impachbasiu carriage, forward-speed tests were madewith reveme rotation of the landing wheel. In these teststhe carriage horizontal velocity was approximately 86 feetper second and the landing wheel was spun up backwardbefore impact so as to produce relative velocities betweenthe tire and the landing strip at the instant of contact up toabout 273 feet per second. Figure 14 shows a number oftypical time histories from such tests at an average verticalvelocity of about 7.5 feet per second, and also includ~ data(solid-line curve) horn one test with no reverse wheel iotation.For clarity, the rwults of only a few selected tests are .@ownin figure 14. The maximum values of the applied verticaland drag loads for the complete series of forward-speed testswith reve~e wheel rotation are shown in figure 15. Alsoshown in figure 15, fbr comparison, are the results obtainedin the forward-speed testswithout reverse rot@ion previouslydiscussed.(longdash curv6s).

Before these results are considered in detail, it should bepointed out that the use of reverse wheel rotation in combinwtion wkh forward speed does not yield complete simulationof actual impacts at high forwald speeds. For example,even though the relative veloci~ between the tire peripheryimd the ground is made the same at the instant of contact,the slip ratios during the first part of the spin-up process inthe reverwrotation tests are, of counse, higher than in cor-responding true forward-speed impacts, the amount depend-ing on the difference between the si.ndated horizontal veloc-ity and the speed of the carriage. Thus, for the highestsixmdated horizontal velocity in these tests (273 fps), theinitial slip ratio is about 3.2; whereas, in an actuaj forward-

speed impact

FOR AERONAUTICS

the initial slip ratio would be 1.0. As a result,the variations of the slip r~tio during the spin-up process arediflerent in th=e tests than in true forward-speed impncts.Also, because of the higher slip ratios during the first partof the spin-up process, the amount of rubber removed fromthe tire per unit time by the skidding process is distributedalong a shorter length of ground travel than in an acLualforward-speed impact, so that the concentration of abrndedrubber in the ground-contact area is greater in them tcsis.The differences in the slip ratio also influence the amount oftire periphery coming in contact with the ground and theheating of the tire during the spin-up process. All of t,hoforegoing dif&ences, which are, of course, greatest at t,hohighest simulated horizontal velocities (highest initial slipratios), influence the coefficient of friction and the appliedloads. IYeverthelese, the results obtained, although notcompletely realistic, do serve to indicate, at least qualit-atively,the manner in which the applied loads w-odd vmyif the forward speed were increased to high values. With t,hoforegoing restrictions, the results presented in figure 14may be considered to be a continuation of those shown infigure 10.

As in the case of the forward-speed tests previously dis-cussed, an increase in the relative velocity betwe,en the tiroand the ground at the instant of initial contact (simulatedhorizontal veloci~) causes the duration of the skiddingprocess to be increased, so that a longer time is required forthe completion of spin-up. At the lower simulated hori-zontal velocities, where spin-up occurs before the maximumvertical load is reached, the maximum drag lend increnmswith increasing simulated horizontal velocity, just ns in thoforward-speed tests and for the same reasons prmiouslydiscussed.

For the higher simulated horizontal velocities, spin-upoccurs after the mtium vertical load is renched. In thisregion, since the vertical load is decreasing with time, thovertical load which exists at the time of spin-up is reducedas the duration of skidding is increased; as a result, the dragload at the time of spin-up decreases with increasing simu-lated horizontal velocity, since the coefficient of friction dthe instant of spin-up is more or less the same for all testsin this series. In figure 14, the drag-load time historios forthe higher velocities are seen to exhibit two peaks; tho firstoccurring when the vertical load is at u maximum, thesecond at the time of spin-up, when the coefficient of frictionis at a maximum. Because the coefficient of friction was somuch larger at the time of spin-up, when the skiddingvelocities and the slip ratios were small, than at tho timo ofmaximum vertical load, when the slip ratios and the skiddingvelocities were larger, the maximum drag lend in theso testsalways occured at the time of spin-up, rather than at thetime of mmimum vertical, load. Consequently, tho mrwti-mum @ag load reached its highest value for the concliLionwhere the completion of spin-up coincided with the occur-rence of thp maximum vertical load and decreased with fur-ther “increasein simulated horizontal velocity. I?iguro 16shows that the maximum drag load reached its highest valueat a s“&ulatad horizontal velocity of about 112 feet porsecond and dropped to about 60 percent of this value at thehigher test VOIOCitieS.-Although the maximum drng load

~’ KKPERJMENTAL

103

.

STUDY OF APPL~D GROUND LOADS IN iL4NDllTG

n‘H~OI v%,

fps fps86.0 7.46

—.— 13S.6 7.30173.4 7.30

––-––– 2025 7.50—— 2438 7.51—— 273.3 7.53

OAt 8=0

❑ At I rswolutiwof wheel

1 I 1 I I t I I I t I I I I I Io .02 .04 .06 .08 .10 .12 .[4 .16 .[8

Time after contoct, set . . ,

F[aurm 14.—Time histories of applied loads and coefficient of friotion in typical forward-speedvrheel rotation. Vvoa =7.44 feet per second; Vtia =s5.5 feet per seoond.

. .

tests with reverse

1171

1172 REPORT 124*NA~ONAL ADW80RY COMbD?FTEE FOR AERONAUTICS

Q

34 - ug

/“

2 -/ —— Forword-spssd tests, “V. 8 7.55 fps

/’

w

-/~_} Rwrse-rotofh t@S; ~. . 7.45f~S; &w=86.1 fps

%

I I I I I I I I I I I I I Io 40 80 la 160 200 240 280

Initiol Iuxizontol velccity, ~. W ~ , f Ps%

FImnm 15.—Comparison of mminmm applied loads in fomvard-speed tests with reverse wheel rotation and loads in true forward-speed tests.

always occurred at the time of spin-up in these teats, it ap-pears that, if the horizontal velocity were high enough,spin-up would be delayed until the vertical load was smallenough that the drag load would be smaller at the time ofspin-up than at the time of maximum vertical load, eventhough the coefficient of friction were larger at the time ofspin-up.

In these tests, as in the forward-speed tests, circumfer-ential springback of the tire and bending springback of thelanding gear occurred following the drop-off of the drag load;the ensuing torsional oscillations of the wheel and fore-and-aft bending oscillations of the landing gear resulted in theoscillations evident in the drag-load time histories of &we14 subsequent to the time of spin-up.

The effects of the drag load on the vertical load were aswould be expected from the previous discussion of theforward-speed tats. For those conditions where spin-upoccurred just before the maximum vertical load was reached(for example, at horizontal velocities of 86.o and 124.9 fpsin @. 14), the large dynamic bending deflection of thelanding gear at the time of maximum vertical load resultedin large shock-strut friction forces which greaily increasedthe maximum vertical load. At higher simulated horizontalvelocities, because the coefficient of friction decreased, theshapes of the dr~-load time histories were greatly changedso that the drag impulse at the instant of maximum verticalload was reduced. As a result, the bending defections atthe time of maximum vertical load, and consequently thestrut friction forces, were smaller so that the mtiumvertical loads were considerably reduced at the higherhorizontal velocities. Even in these cases, however, thebending response of the landing gear resulted in a momentaryrise of the vertical load slightly after the maximum dragload occurred, when the bending deflection reached itsmaximum value, as can be seen horn the individual timehistoriw in iigu.re14.

The overall variation of the mdmum vertical load withsimulated horizontal velocity is shown in figure 15. Thehighest valuea of the mtium vertical load occurred at a

o

simulated horizontal velocity of about 112 feet per mcond.In this region, because of the irregularities in the verticrd-load time history, mused by the sudden changes in the shock-strut-ofice area remdting from the metering-pin displace-ment, the exact phasing between the drag load and thevertical load appeara to be critical. As a result, relativelysmall differences in the initial conditions or in the time tospin up caused fairly large differences in both the maximumvertical and maximum drag loads, aa can be seen from tlmsolid and short-dash curves in figure 16.

Coefficient of friction,-The variations of the coeilicient offriction during the spin-up process in these tests were con-siderably ditlerent from those in the forward-speed tests.As can be seen from figure 14, the coefficient of friction in thereverae-rotation tests started out at relatively high (forthe high skidding velocities involved) values at the beginningof each impact, decreased with time, then increased until omtium value was reached just prior to the completionof spin-up. The later phases of the time histories are similarin appearance to those obtained in the forward-speed tests.As an aid in interpreting these variations, the points atwhich reversal of the wheel rotation takes place (0=0) moshown. At these points the slip ratio is, of course, equal to1.0. Also shown, for the two highest speed tests, me thopoints at which the wheel rotation passed through a completorevolution: At the lower speeds the wheel angular displace-ment w-= always less than a full revolution.

As previously noted, the values of the coefficient of frictionat the beghming of the impacts were relatively high, eventhough the skidding velocities were large. This result isapparently due to the very high slip ratios during the iimtpart of the skidding process. At these high slip ratios,because the large angular velocity of the wheel contributesa major part of the total skidding velocity, the rate of intro-duction of tire-tread area is relatively large compared withthe rate at which work is done in skidding; thus, the skiddingenergy is distributed over a larger area of the tire runningsurface so that heating of the tire surface is reduced, (Seoappendix B.) As a result, the transition which the ground-

AN -EKPE RThD3NTAL STUDY OF APPLIED GROUND LOADS IN I.ANDING 1173

contact surface of the tire undergow from its initially coldcondition to the higher temperatures characteristic of normaloperation requires an appreciable length of time in thereverse-rotation tests. In an actual forward~peed impact,on the other hand, since the wheel would be turning slowlyduring the early part of the spin-up process, the skiddingenergy would be much more highly concentrated in the tiresurface, the transition from cold to hot rubber would begreatly accelerated, and the coefficients of friction duringthis stage of the impact would be much lower.

The variation of the coefficient of friction during theremainder of the spin-up process in the reverse-rotationtests apperua to be governed primarily by the combinedeffects of the slip ratio and skidding veloci@, both of whichdecrease with time, as well as by changes in the verticalload, As was previously indicated, a reduction in theskidding velocity tends to increase the coefficient of fiction.On the other hand, because of the effecb of tire heating, areduction in the slip ratio tends h decrease the coefficientof friction for slip ratios greater than 1.0 and tends toincrease the coefficient of friction for slip ratios less than1,0, as is indicated in appendix B. As a result of the com-bination of the foregoing effects, the coethcient of frictiontit decreasca with time, reachea a minimum value at aslip ratio greater than 1.0, then increasea until a maximumwdue is reached at very small slip ratios, where local slidingin the ground-contact area is transformed into adhesivecontact just prior to the completion of spin-up. Theprocess during the interval between a slip ratio of 1.0 and

03

———

full spin-up appears to be very similar to the complete spin-up process in the forward-speed tests previously discussed,except for differences in the magnitude of the vertical loadduring thiEperiod and possibIe effects of the residual elevatedtemperature of the tire resulting horn the previous skidding.

The time histories of the coefficient of friction for thehigher simulated horizontal velocities in figure 14 indicatea momentary peak during the early stages of the spin-upprocess. These peaks do not appear to be directly connectedwith the rotation of the -wheel through one revolution andtheir cause is not evident.

k addition to the effects of the slip ratio and the skiddingvelocity, variations in the vertical load on the tire appear tohave an influence on the coefficient of friction. Some in-dications of the effect of the vertical load may be obtainedfrom the valuw of the coeiiicient of friction at the pointswhere #=0. At these points the slip ratio is equal to 1.0and the skidding velocities are more or less the same for alltests in this series. Therefore, difbrences in the coefficients ,of friction at these points may be indicative of the eilect ofvertical load. This effect is discussed in a subsequentsection.

From the foregoing discussion it appears that, because ofthe artificially high slip ratios, the variationa of the coei%-cient of friction in the reverse rotation tests may differ ap-preciably from those which would be obtained in a trueforward-speed impact. In particular, it would appear thatthe co@cients of friction at the beginning of the spin-upprocess would be considerably lower in an actual forward-

V% ,(w

Typs of test fps

Forward speed 7.55

Reverss ratotion 7.45

_.. -+nvelwe of wtical-bad time histmks---,---- for “all tesfs

,/

-.

Y I I I I I I 1 I Jo .02 .04 .06 .08 .10 .12 .14 .16 .18

Time afler contact, sec

FImmEJ16.—Composite of applied-load time histories in forward-speed tests and fomvard+ped tests with roverss wheel rotation (V~a=S6.1feet per second).

1174 REIPOET 124%NATIONAL ADVISORY COMM3TTDE FOR AERONAUTICS

speed impact since the initial slip ratio would be equal tf1.0, which, for the same skidding velocity, would result hgreater heating of the tire. Similarly, it would be expecttxthat these differences would also have some effect on tlmshape of the drag-load time histories and on the time hspill up.

An overall illustrative picture of the load variations in th~forward-speed teats and in the forward~peed tests with reveme wheel rotation (complete series of tests) is shown irfigure 16. In this figure the shaded area indicates the en.velope of the vertical-load time histories for all tests. Th(boundaries of the drag load are indicated by means o~short segments of the drag-load time-history curves in th(vicini~ of spin-up.

SPIN-UP DROP TES19

Spin-up drop tests, either in a jig with a single landing gemor with a complete airplane, are widely used in the develop-

, ment and proof testing of landing gears and the airplanestructure. In order to evaluate the validity of this methodof simulating landing impacts, a series of spin-up drop test9with the carriage tied was made for comparison with thetrue forward-speed tests and the forward-speed tests withreverse wheel rotation previously discussed. A few typicaltime histories of the applied loads and the coefficient offriction from such tests are shown in &ore 17. The maxi-mum values of the vertical and drag loads are shown asfunctions of the simulated horizontal velocity and are com-pnred with the results of the other tests in iigure 18. Com-parisons of two tidividual spin-up drop-test time historieswith time histories obtained in the other types of tests forcorresponding impact conditions are shown in iigu.re19.

As can be seen from figure 18 and horn comparisons offigures 17 and 10, for low simulated horizontal velocitiw, theapplied lords and the coefficients of friction in the spin-updrop tests were higher than in the forward-speed tests.However, for simulated horizontal velocities above about60 feet per second the loads in the spin-up drop tests wereappreciably smaller than in the other types of tests.

In tbe spin-up drop tests, of come, the slip ratio is in-finite throughout the impact, and the angular displacementof the wheel during the skidding process is much larger thanin a forward-speed impact. Since, for any given value ofthe skidding velocity, the rata of introduction of tire-surfacearea into the ground-contact region is much greater in aspin-up drop test than in a forward-speed impact, the con-centration of skidding energy in the tire surfaca is grestlyreduced, so that there is less heating of the tire. This effecttends to make the coe.flicientsof fiction for a given skiddingvelocity in the spin-up drop tests larger than in the forward-speed tests. On the other hand, the spin-up drop teatsinvolve an element which tends to reduce the coefficient offriction; namely, the contamination of the ground beneaththe tire by particles of rubber which are removed from thetire by the skidding process and tend to act as a lubricant in ,the ground-contact area. In an impact with forward speed,this abraded rubber is distributed over an appreciable lengthalong the ground, so that its eilect is relatively small. In adrop test, on the other hand, these particles of rubber ac-cumulate in one spot on the ground. For the drop tests.at

1ct1{t

low simulated horizontal velocities this effect is negligible be-cause very little rubbar is removed from the tire, simm thototal amount of work done in akidding is small. With in-creasing simulated horizontal velocity, howevar, more anclmore rubber is removed horn the tire and the thiclmcss of thoaccumulated deposit becomes huge enough to cause markedreductions in the coefficient of friction throughout most of theskidding process. At the highest simulated velocities, pos-sibly because the abraded rubber is in a gummy or ovenmolten state, ,the coefficients of friction, and cmsequontlythe drag loads, are reduced to very small values, as can boseen from the time histories in @e 17.

The total accumulation of abraded rubber during a givcmimpact is, of course, grmtest at the end of the skiddingprocess. Consequently, at the higher simulated horizontalvelocities, ‘the coefficient of friction does not increase as thoskidding velocity is reduced, even as the wheel comes to rest,in contrast to the results from the other types of trots wherethe coefEcient of friction increased considerably as the skid-ding velocity decreased. As a result, in the spin-up dropteststhe maximum drag loads for the higher velocities donot occur at the end of the skidding process, ns in the othertypes of twts, but rather at the time of maximum verticalload.

At the lower simulated horizontal velocities, whero thoeffects of the abraded rubber are unimportant, the reducedheating of the tire surface, previoudy mentioned, results insomewhat higher coefficients of friction in tho drop teststhan in the forward-speed tests, the greatest diibmnces beingin the maximum values of the coefficient of friction. Thesed.iilerencesin the maximum values may result from the factthat the nature of the contact between the tire and” thoground as the skidding velocity is reduced to zero is difForontin the two types of tests. In the spin-up drop teats thotransition is from a state of skidding to a stato of rest;whereas, in the forward-speed teats, the transition is from astate of skidding to a state of rolling. In the drop tests, thomtium value of the codlicient of friction probably corre-sponds to a condition where the entire area of the tire touch-ing the ground is in a state of adhesive contact. In thoforward-speed tests, on the other hand, this condition isnever completely reached since, even for the limiting cam ofa freely rolling tire, local sliding exists over some parts of tlmcontact area. Furthermore, in the wise of the roIIing tire,the effectiveness of the mechanical interlocking between thetire and the ground in the regions of adhesion is probablyreduced somewhat because of inertia and hysteresis effectsassociated with the deformations of the tire during rolling,which tend to hinder the tire from conforming to the irrogu-laritieain the surface of the ground.

Because the coefficients of friction in the spin-up droptests were so much lower throughout most of the horizontal-velocity range, the drag loads in these tastawere considerablysmaller than those in the other types of tests for tho range ofhorizontalvelocity of practical interest (fig. 18). As a directmsequence of the decreased drag load, the bending deOoc-ions of the landing gear were reduced, so that the vertioalDadsin the drop tests did not exhibit the large increases dueo shock-strut friction, which were indicated in both the truo

AN EXP13_IW%L STUDY OF APPLIED GROUND LOADS IN LANDING

bjf , v%,‘o

fp fps

—.— 25.2 7.24——— 650 7.76—---— 124.9 7.61------- 2227 7.50—— 233.3 7.58

—— __

“~L\\ > --=1===-==-=--~- ->. <.——-———-‘l __

0 I I I I I I I I I

I I I I I I I I I I I I I I I I I 10 .02 .04 .06 .08 .10 .12 .14 .16 .18

Time after ccmloct, sec

1175

FI~URE 17.—Time histories of applied loads and coefficient of friction in typical spin-up drop tests. V~=O; VVo@=7.54 feet per second.

-—. —— —.. .— _— .

1176 REPORT 124%NATIONAL ADVISORY COMWTTE E FOR AERONAUIMCS

~y , fxo— Fwd-sRfkd teds 725

8X 10s— — Rwerse-mtatian tssfs, VCtiw= 86.1 fps 7.45

:x-n-up drew tests, %==0 7.55

6

__

o -=.+.

E.

Z4%rm

~\$

‘-w-----’

____

2 -\

\&/

.— ~-o-d++

I I I I I I I I I Io 40 so [20 160 200 240 280

Mid hmizmtalvekity, VHOor ~ , fpsso

Fmmm 18.—Wmparieon of maximum applied loade in fomvard+d tests, formrckped teds with reveree rotation, and spin-up drop tests,

v&? v%, :’103

fps fps

Fwward-speed test 7.65 74.9——— —sppn-:~ drop test 7.?6 75.2

A“-.

Fvr \

I I I I I I I I -t

I 1 I I I I f I Io 02 04 06 .08 Jo .12 .14 .16 .;8 (

Vvo, VH.,

fps fps

Rmrs.e-mtatiw test 7.50 202.5Va,.85.6 fps

———– SP$-:~ dmp ts& 7.48 202.0

m

I I I I I I t I t

I I I I I ! I I JD? .04 K 08 .10 .12 .14 .16 ,18

Time after contact, sec

FIGURE19.-Compariaon of time hiatoriee of applied loada and coeffioienta of fiction in spin-up drop tests and in correspondhg forward-spoodteats and forward-epeed tests with reverse w-heelrotation.

AZV E=13RIMJ2NT AL STUDY OF APPLIED GROUND LOADS IN LANDING 1177

forward-speed tests and the forwardapeed tests with reversewheel rotation. These differences areparticuhwly striking inthe range of horizontal velocity where spin-up in the othertests occurs when the vertical load is near its maximum value.

Figure 19 shows direct comparisons of two typical drop-test time histories with the results of the other typ& of tests.The figure on the left is for a horizontal velocity of about 75foot per second nhd indicates relatively good agreement.The figure on the right, form horizontal velocity of about 202feet per second, is typical of the results for the higher horizon-tal velocities rmd clearly indicates the greatly reduced dragloads in the drop tests, particularly in the later stages of theskidding process where the accumulation of abraded rubber inthe ground-contact region becomes very large.

l?rom the foregoing results it is evident that spin-up droptests yield uhconsetiative 10MIsfor the range of horizontalvelocities of practical interest iii airplane design. It thusnppeara that data obtained from such tests should not beused without qualification as a basis for design or for dy-nnmic nnalysesof landing loads. The foregoing comparisonsrdso indicate why some airplane manufacturers (see, for ex-ample, ref. 5) have resorted to the use of artificial groundsurfaces in drop tests, such as grids of various types, in orderto obtain coefficients of friction high enough to satisfy theANC-2 ground-lends design requirement of P=o.55.

VARIATION OF:COEFFICIENT OF FRICTION

As was previously indicated in the discussion of the timehistories of the applied loads for the three types of testsconsidered, the coefficient of friction during the wheel spin-upprocess vnried over a wide range of values during any givenimpact; furthermore, considerably di.tlerentvariations werefound under different impact conditions. Some of the factorscontributing to the variation of the cmdlicient of friction,such as the effects of slip ratio, skidding velocity, heating ofthe tire surface, contamination of the ground-contact areaby nbraded rubber, and the effects of changes in the verticalload, were briefly discussed. In this section, the variation oftlm coefficient of friction is considered somewhat morequnntitntively; unfortunntelyj however, because of the natureof the tests, it was not generally possible to separate com-pletely the effects of all the various factors which influencethe cocilicient of friction.

Etleot of skidding velocity.-l?igure 20 shows the variwtions of the coeiiicient of friction with the instantaneousvalue of the npparent skidding velocity in several typicalimpacts for each of the three types of tests considered.These results, of course, include the effects of variations inthe slip ratio rmd in the vertical load during the spin-upprocess, as well as the effects of tire heating. In these graphsthe progress of the spin-up process is from right to left, thehighest skidding velocity for each curve corresponding to thevalue just after initinl contact, and zero skidding velocityindicating complete spin-up.

(n) l?orward-speed tests:Figure 20 (a) shows the variation of the coefEcient of fric-

tion with the apparent skidding velocity in several typicalforward-speed impacts. The right-hand extremi~ of eachcurve corresponds to a slip ratio of approximately 1.0, theslip rntio in ench teat decreasing as the skidding velocity is

reduced. As can be seen, the coaflicient of friction rangedfrom minimum values of about 0.56 to 0.60, at the beginningof the impacts at the higher forward speeds in this series oftests, to mtium values betweau about 0.76 and 0.90 atlow values of the apparent skidding velocity (just prior tothe completion of spin-up), the highest values of the coefE-cient of friction occurring in the lowest speed impacts.

The fact that the maximum values of the coefficient offriction, which are associated with the interlocking type ofcontact between the tire and the ground, appear to decreasewith increasing forwaxd speed may be due to the inertia andhysteresis effects connected with the rolling deformations ofthe tire, which tend to hinder the tire from conforming per-fectly with the irregularities in the ground and thus tend toreduce the effectiveness of the interlocking bond.

It should be noted that the decrease in the indicatedcoefficients of friction as the apparent skidding velocityapproaches zero is caused by the relaxation of the circum-ferential distortion of the tire as the spin-up process is com-pleted, which was previously discussed. Because of thisrelaxation of the strains in the tire the tangential stressesinthe ground-contact area, and thus thedrag loads, arereduced,so that the indicated values of the coefficient of friction aredecreased. These values of the tangential stresses and theindicated coeiiicients of friction therefore do not correspondto the maximum values which can be maintained by theconditions of contact between the tire and the ground at lowskidding velo~ities; such valuw should be at least as high asthe maximum values (at the “point of impending skidding”)shown.

In figure 20 (a) the circular symbols indicate the occur-rence of the maximum drag load. Site, in these tests, thevertical load was in the process of increasing when themaximum coefficient of friction was reached, the drag loadcontinued to increase and reached its maximum value afterthe coefficient of friction had already dropped somewhatfrom its maximum value.

The curves shown i.Qfigure 20 (a) indicate that, in general,the coefficient of friction decreases with increasing skiddingvelocity, the differences between the individual curves beingdue primarily to differences in the slip ratios at any givenskidding veloci~, differences in the heating of the tirerunning surface which result from the diflerent relationshipsbetween the slip ratio and the skidding veloci~ in the indi-vidual tests at the various initial horizontal velocities, anddifferences in the vertical load at any given skidding velocity.The effects of slip ratio and vertical load is considered furtherin a subsequent section.

(b) Forward-speed tests with reverse wheel rotation:Figure 20 (b) shows the variations of the coefficient of

friction with the apparent skidding velocity in several typicalforwmd-speed tests with reverse wheel rotation. The right-hand extremities of these curves, of course, correspond toslip ratios greater than 1.0, the highest value being about3.2 for a simulakd horizontal velocity of 273.3 feet persecond. The range of skidding velocity where a slip ratioequal to 1.0 occum is indicated by the shaded band. (Thisband has a finite width because the carriage horizontalvelocities were not exactly the same in all tests.)

REPORT 124& -NATTONATJADV180RY CO~ FOR AERONAUTICS

‘Ho, Wo,

fps fps

vi% = 7.56 tps

—.— 19.3 7.61.— --— 43.6 7.6 I—. --— 65.8 7.54— — 83.4 .7.52

(o)o I I I I I I I I I I I f 1 I

v“=n, V5,

I .0

r *-.

f pi fps

—-— 124.9 7.46—--— 138.6 7.30—---— 173.4 7.30-––––--2325 7.50——— 243.8 7.5 I_.—.—

/

—-—-— -273.3 7:53

1., / 0 ‘t ‘HT___ ,/

1.0 ~

J

,,

l\

;\.U

F‘ ‘~ ./—=——’—h’ >

.6 ““ ‘\-.~ “\

.

?’,

,—- .—.

\

fp: fps

—.— 25.2 7.24—--— 65.0 7.76—---— 124.9 7.61–––––––iii? 7:50——233.3 7.58

0 At FH /

- b/

/“ Y“—————————————’‘—4-

/“”.+

[

/—-–-”—’’—————._——->~ —-———~ —— ——— _ —---”-.—. — —

/4-/

.2 :’ Vw=o

Vvow = 7.54 fps

(c). -.,

I I I T I I I I 1 I I I I I

o m 40 60 80 100&? Skkwyiwy, ‘~i, fps

180 200 2-20 240 260 280

(a) Fonvarckpeed teats.(b) Forward-meed tests with reverse wheel rotation.(CjSph-up&p tats.

F1~URE20.—Variation of coefficient of friction with skidding velooity for typioal fomvard~ed tests, fomvard-speed tests with mVOrSOwhdrotation, and spin-up drop tests.

,. .,7:.( .,

AN D2iT’ER~NTAL STUDY OF APPLIED GROUND LOADS IN LANDING 1179

It can be seen that in these teste the coefficient of fictionstarts out at vnluea fairly high as compared with the generaltrend of the data. As was previously discussed, these rela-tively high initial vfdues of the coefficient of fiction appearto bo largely due to the arti.ticiallyhigh slip ratios during thefirst part of the spin-up process, which result in reduced heat-ing of the tire.during this period. (Some discussion of therelationship between slip ratio and heating is given in ap-pendk B.) These resultssuggest that, in the reveme-rotationtests, because -of the high slip ratios during the early stagesof the skidding process, the transition of the running surfaceof the tire from its ‘initial cold condition at the instant ofcontact to the higher t-pera.ture representatives of normalspin-up conditions takes place rather slowly. As a result,the coefficient of friction has fairly high values (correspondingto values for cold rubber at high sliding velocities) at thebeginning of the skidding process, then gradusll~decreaseaas tho reverse rotational velocity of the tire and the associatedslip ratio am reduced and the energy concentration in thetire surface and, consequently, the temperature are increased.This effect is illustrated schematically in figure 21. In trueforward-speed impacts, on the other hand, since tbe skiddingprocess begins at a slip ratio of 1.0 where the energy concen-tration in t.lmtire is large, this transition occurs ahnost in-stmtancously, and the cold-rubber values of the coefficientof friction are not perceived. As a result, the initial portionsof the curves for the reveme-rotation teats appear to have nopractical significance as far as true forward-speed impactsare concerned. Nevertheless, the general trend of the curvesprovides at least an indication of the variation of the coeffi-cient of friction with skidding velocity.

It will be noted from figure 20 (b) that, with the exceptionof the artificial initial parts of each curve, the basic trend ofthe data for the entire range of skidding velocity falls withina fairly well clebed and relatively narrow band. The bandfor the complete series of forward~peed tests with revemewheel rotation, a total of 14 runs covering a range of simu-lated horizontal velocity from 97 to 273 feet per second, isinrlicrded by the shaded region in figure 21. The basic trend

1.0r

shown, of course, includes the effects of differences in the slipratio, which in these tests varied directly with the skiddingvelocity (since the carriage velocity was essentially constant)”and, therefore, could not be separated from the effect-sof theskidding veloci@. The spread in tie curves within the band(see fig. 20 (b)) appears to be largely due to the effects ofdifferences in the vertical load, which will be discussed later.

The overall trend of the data indicates a variation of thecoetlicient of friction from low values between 0.26 and Q.40at an apparent skidding velocity of 260 feet per second tomaximum valuea between 0.70 and 0.85 at an apparent skid-ding veloci~ of 17 feet per second. As in the case of thetrue forward~peed teatspreviously discussed, the decrease inthe indicated values of the coeilicient of friction as the ap-parent skidding veloci~ approaches zero is due to the relaxa-tion of the tire circumferential distortion and therefore doesnot represent the variation of the limiting values of the co-efficient of friction at low skidding velocities.

(c) spin-up drop tests:Figure 20 (c) shows the variation of the coefficient of fric-

tion with the skidding velocity for a number of typical spin-updrop tests. As can be seen, these tests yielded very highcoefficients of friction when the initial simulated horizontalvelocity was low, and very small coeilicients of friction, evenat low skidding velocities, when the simulated horizontalvelocity was large.

The high values at low simulated horizontal velocities werepreviously attributed to the reduced heating of the tire result-ing from the high slipratios. The particularly high maximumvalues of the coefficient of friction at low shrndated hori-zontal velocity may be due to the fact that a more perfectinterlocking contact between the tire and the ground is possi-ble in the drop tests, where the wheel comes to rest, than inthe forward-speed -tests,where the wheel comes up to groundrolling speed, as previously discussed. (The indication of afinite skidding velocity corresponding to the maximum valueof the coefficient of friction is associated with the circumfer-ential distortion of the tire and does not represent the actualrelative velocity between the tire and the ground in thisregion.)

‘———~

.8 -* ‘ II

‘----.5 /-’’’--—---,______<old=6 / ~’-Transltian~.

-/~--—___(hqh slip ratio)

z /7z.~ .4 - I111111111

llllllllllllmiilllllllllllllllllllllllllmllllllllllllll

/

c‘5.8 111111111111111111:::::~cd

,2 -

I I 1 1 I I I I I I I I I Io 40 80 120 [60 2W 240 280

Apparent skidding velocity, V&, fps

Figure 21.-Schemntic representation of variation of coefficient of friction with skidding velocity in forward-speed te-stswith reverse reheel rotation.

———-——

1180 REPORT 1248—NATIONAL ADVISORY COMMITTE E FOR AERONAUTICS

With increasing simulated horizontal veloci@-, abradedrubber accumulates in the ground-oontact region until the

“deposit beccmea large enough to cause marked reductions inthe coefhient of friction, also previously discussed. At thehigher simulated horizontal velocities, because of the largeaccumulation of abraded rubber, much of which is in a moltensemi-fluid state, the codlicient of fiction drops to low valuesimmediately after cmtact and do~ not increase as the skid-ding velocity decreases, even as the wheel comes to rest, sothat the entire skidding process takeaplace at small values ofthe coeilicient of friction. These remiks are, of course, radi-cally diilerent than those obtained in the other types of testsand me responsible for the much smaller drag loads in thespin-up drop tests at the higher simulated horizontalvelocities.

(d) Comparison of cmfticients of friction in the three typesof twts :

The variations of the coefficient of friction in the threetypes of tests me compared in figure 22. The band shown forthe forward-speed tests with reverse wheel rotation is thesame M the basic trend previously presented in figure 21. Itcan be seen that the values of the coefllcient of friction indi-cated by the basic trend in the reverse-rotation tests appearto be somewhat lower than in the true forward-speed tests.A possible explanation for this result is afforded by the fol-lowing considerations. In the forward-speed tests with re-verse rotation, for the range of skidding velocities greaterthan the carriage velocity, the slip ratios are greater than 1.0and increase with skidding velocity up to a mtium valueof 3.2 at a skidding veloci~ of 273feet per second. Since theslip ratio repreaentathe ratio of an increment in skidding dis-tance to a corresponding incremmt in ground travel, theconcentration of abraded rubber in the ground-contact areaincreases with increasing slip ratio. As a result, at skiddingvelocities higher than the carriage velocity in the reverse-rotation tests.,the concentration of abraded rubber is some-what greater than in a true forward-speed test, though smaller

than in a spin-up drop test, and the coefficients of friction amtherefore somewhat lower than might be expected from truoforward-speed tests for the same skidding velocities.

For skidding velocities less than the carriage velocity,the coefficients of fiction are also somewhat smaller in therevers~rotation teats than in the true forward-speed teats,even though the slip ratios in this region are smaller than 1.0.In the reverse-rotation tests the direction of the rotation ofthe wheel changes when the slip ratio becomw equal to 1.0,so that, for slip ratios less than 1.0, part of the surfoce of thotire coming into contact with the ground has been in contaotwith the ground previously, when the slip ratio was greaterthan 1.0, and is therefore at a higher temperature. In thoforward-speed tests, on the other hand, this situation doesnot exist; since no change in the direction of rotation of thewheel occurs and the wheel does not turn through o fullrevolutiorr during the spin-up process, the regions of tho tireentering the ground-contact area have not been in contactwith the ground previously, so that the surface of tho tiroentering the ground-contact area is cold. When the initialslip ratio in the revers~rotation tests is only slightly greaterthan 1.0, however, the angular displacement of the tire priorto reversal of its rotation is small enough that in the very losts~ga of the &dding proc~, when the skidding vdooitybecomes small, cold rubber, which has not previously beenin contact with the ground enters the ground-contact meo.In these cases, the coefficients of friction are appro.xinmtelythe same as in the forward-speed tests.

Figure 22 also shows, as previously discussed, that spin-updrop tests yield unrealistic values of the coefficient of fric-tion throughout the range of simulated horizontal velocitiesof practical interat. Because the coe5cients of friction amso low, the loads developed in the drop tests are gmierdlyunconservative. These results indicate that spin-up droptests, at least onto rLconcrete ground surface, are not at allrepresentative of actual landings with forward speed onconcrete runways.

Vjf , fps

‘“0 r~..:5.2

~ Rword-speed testsI!lllllllll!!llllRmwse-mtotion t=ts

V=W=8ELI fps

— Drop tests

.8*e-Q,-2 .6*

%

g ,4

5 11111111111v

t

/.2

v“ =7.5 fpsOm

I I I I I I I I I I I I I I Io 40 80 120 160 200 240 280

Apporent skiddirq velocity, ~~(~, fps

FIcmmE 22.–-Comparison of variations of coefficient of friction with skidding velocity in fomvard-speed tests, forward-speed teats with roversowheel rotition, and spiu-up drop teats.

AN DXPJ3RR15NTAII 8Y!UDY OF APPLD3D GROUND LOADS IN LANDING 1181

1,0r

.4

.2

I

—.-—43.6 7.6 I—--—65.8 7.54 v% =7.57 fps

w——83.4 7.52

o (o) I I 1 1 I 1 I I I I o t I t 1 1 1 I )

.8

1“-

-— ___ =Z’,l-l/;.*. -——

‘-’*=1.

–—’~=_-_~_,_

,6%sOJ Vvo,

fps fpsf

.41

—— 124S 7.46—— 138.6 7.30 Km, = 85.5 fps ‘N%?d

“.

—— I73.4 7.30 - ‘</-----—202.5 7.50

.2 - ——243.8 7.5 I ‘%.”~7.44 fps~

--—-—- 273.3 7.53 IO ~f fHTmOx

(b)I

( ! I I I I 1 1 1 1 I I 1 1 I 1 I 1 I 1 1 Io .1 .2 .3 .4 .5 .6 .7 .8 .9 Lo 20 3.0 4.0

Slip rotio, S

(a) Forward~peed tests.(b) Forward+peed teata with reverse -wheelrotation.

Framm 23.—Variation of ooeffkient of friotion with slip ratio in typical forwwrd~d tests and forward-speed tests with reverse wheel rotntion.

EIYeotof slip ratio.—Figures 23 (a) and 23 (b)show thevariations of the coefficient of friction with the slip ratio inthe. forward-speed tests and the forward-speed tests withreverse wheel rotation, respectively. These results, of course,include the ofFectsof variations in the skidding velocity andin the vertical load, as well as the effects of tire heating.

In the forward-speed tests (fig. 23(a)) the slip ratio isequal to 1.0 at the instant of initial contact, the skiddingvelocity at this instant being equal to the forward speed.Tho instantaneous skidding veloci@, of course, decreases astlm slip ratio becomes smaller during the spin-up proccas.Tho main interpretation which can be drawn from thisfigure. is that, for any given slip ratio, there is a generaldecrease in the coefficient of friction with increasing skiddingvelocity, the largest effect of variations in the skidding ve-locity appcming at low skidding velocities. The limitationsof the data prevent separating the e.f?ectsof skidding veloc-ity and vertical load from those due to variations in the slipratio.

Tho coefficients of friction in the forward-speed tests withrcwelaewheel rotation are plotted against slip ratio in figure23(b),the scale for slip ratios greater than 1.0 being cnm-pressed. Since the actual horizontal velocities were approxi-

mately the same in all tests, the slip ratios are directly pro-portional to the skidding velocities and these effects canagain not be separated. This figure is therefore essentiallythe same as figure 20(b).Since,for any given slip ratio,the skidding velocity is the same for all tests, the verticalspread of the curves must be due to some other variablefactor such as the vertical load. This effect is considerednext.

Effect of vertioal load.—As previously noted, in theforward-speed tests with reverse rotation, since the horizon-tal velocities were essentially tie same for all test9, difler-encea in the coefficiaut of friction at any given slip ratio orskidding velocity must be due to some other variable facto=,such as the instantaneous vertical load. These differencesin the vertical load appear because the time at which agiven skidding velocity or slip ratio is reached in any par-ticular test is a variable depending on the magnitude of theinitial simulated horizontal velocity.

Some indication of the effect of the vertical load on thecoefficient of friction is given in iigure 24where the coeiii-cienta of friction at slip ratios of 1.0 and 0.15, correspondingto skidding velocities of about 84 and 13 feet per second,respectively, are plotted against the vertical load at the same

1182 REPORT 1248—NA~oNAL ADVISORY COMMI?I’IZIE FOR, ARRONAUTTCS

I .0

[

S=Q15( v!= 13fps)

o 0.8 -

AO* S=I.O 08MO

( V&@ 84 fPS) f% ~oo~

$’~ .6 -,,/-

.— ___ _

00 0z . 0

~ .4 -g

o PrirK to orIe rewlution%

}Reverse- mtotion ts&s

8❑ Subsequent to cme revolution

.2 -A hnvord-speti te5t5

I I ( I I I Io I 2 3 4. 5 6X103

tnstontoneous vertknl Iood, Ffi, lb

J?mmm 2+L-Effeut of vertkal losd on coefficient of &lotion.

instrmt. The data shown were obtained from the completeseries of forward~peed tests with reverse wheel rotation.Also shown are corresponding test points from three trueforward-speed tests at approximately the same carriage ve-locity as in the reverse-rotation tests. The test points forrLslip ratio of 1.0 generally exhibit relatively little scatter.Most of the test points in figure 24 correspond to a timewhen the tire had rotated through only a tiction of a revo-lution. The square symbols represent test points whichoccur shortly after the tire has completed one full revolu-tion; that these values of the coe.flicientof fiction are some-what lower than the general trend of the data for a slipratio of 1.0 may be due to the higher temperature of thesurface of the tire remaining hm its prewious passagethrough the ground-contact area. This effect is not evidentfor the slip ratio of 0.15, possibly becnuse a greater time haebeen available to permit cooling of the part of the tire incontact with the ground when this slip ratio occurs.

The overall trend of the data in figure 24 indicates thatthe coefficient of iiiction generally decreases appreciablywith increasing vertical load, the data for a slip ratio of 1.0suggesting that the coefficient of friction reaches a maximumvalue at a finite verticnl load, in the neighborhood of 1,000pounds in these tests. A similar decrease in the coefficientof friction with vertical load is imlhted, though not soclearly because of the greater scatter, by the data for a slipratio of 0.15. The effect of the vertical load on the coefE-cient of ftiction appears to be more pronounced at high slipratios, where full skidding exists, than at very small slipratios, where an appreciable part of the ground-contactregion is in a state of interlocking or adheaive contact. Thegeneral level of the coefficient of friction was, of course,considerably higher in the iuterlocking-cent act region, aswas discussed previously.

EFFECTS OF PREROTATTON

Although prerotation of the landing wheels of an airplanebefore impact to decrease the relative velocity between thetire and the ground has often been suggested as a means forreducing spin-up drag loads, one of the main reasons thatprerotation has not come into wider use is a general beliefthat the reductions in drag load would be very small unless

the prerotation speed is matched almost exactly with thoground-rolling speed, a requirement which may be rothordiilicult to achieve in practice. In order to obtain quanti-tative information regarding the effect% of prerotation onwheel spin-up drag loads, a series of forward-speed testswith varying degrees of prerotation was included in the over-all investigation of applied ground loads. All tests woremade at a carriage horizontal veloci~ of about 86 feet persecond.

Figure 25 shows the manner in which different amounts ofprerotation, ranging horn no prerotation up to 94 percent, orahnost complete prerotation, affect the applied lode on thelanding gear for impacts at a vertical velocity of about 9.4feet per second. (The percentage prerotation is baeed onthe ratio of the peripheral velocity of the unreflected tire atthe instant of contact to the horizontal velocity at contact,)These results show that, as would be expected, increasing the

10;103

al /f/

w~t Knr,g8 fps fps

s ----- 9.41 84.7.@

6—-— 9.40 85.3

E

— 9.4 I 85.5

34

E

P2 -

&l_/J__ .—

0 .04 .08 .12 .16Time offer wntoct, sec

l?munn 25.-Effect of prerotation on time histories of appllod loads.VW=P=85.2 feet per second.

amount of prerotation decreasea the time to spin up andreduces the maximum drag load, with a consequent reductionin the vertical load. The influence of the drag load on thevertical load was similar to that discussed previously in con-nection with the other tests.

In figure 26, the maximum vertical loads and the maximumdrag loads from tests at three vertical velocities are plottedagainst the percentage prerotation. The ratios of themaximum loads with prerotation to the maximum lordswithout prerotation are shown in figure 27. The effect ofprerotation in reducing the drag load is evident. It can alsobe seen that prerotation produced a larger percentage reduc-tion in drag load at the higher vertical velocities, where theneed for reduction is greatest.

In figure 26 it will be noted that the drag load is not equcdto exactly zero at 100-percent prerotation, even though theperipheral veloci~ of the unreflected tire at the instant ofcontact k equal to the horizontal ground speed. The reasonfor this result is that the rolling radius of the wheel becomessmaller as the tire compresses under the vertical lorLclduringthe impact; consequently, the angular velocity of the wheelmust iucreaeaif the peripheral velocity of the tire is to remainequal to the horizontal velocity. To produce the necessaryangular acceleration of the wheel requires a finite drug force,

AN E~ERJMENTAL STUDY OF APPLIZiO GROUND LOADS IN LANDING 1183

10%103

14.

,..,’.,

. . . ;,!

{>0 0

0v v-

2 -

0 I I 1. 1 1 J

6%103

fps

0 9.5

4❑ 7.503.2

g

-} 2, ,

I&

o

-2 ~ I I I I I 120 40 60 so 100 I20

Prerotatim, percent

l?IcWmE 2&-Effeot of prerotation on uxirnum applied loads.v ~a=&L5 feet per second.

as is indicatecl by the curves for 100-percent prerotation.On the other lmnd, rLslight amount of excessive prerotationinitially produces a small negative drag load, followed by apositivo drag load which arises for the same reason as at100-percent prerotation. (See, for exnmple, data for 116-pcrceut prerotrdion in @. 26.) Because of this variation inrolling radius, it appears impossible to obtain exactly zerodrag load throughout an impact.

With regard to the practical usefulness of prerotation, itshould be noted that in many cases there maybe no pmticu-lnr need to reduce the spin-up drag load to levels below thoseest~blished by other design loading conditions, since thehmclinggenr must be strong enough to withstand these otherloads. I’or example, the design requirement for brakedrolling nmounts to 2,400pounds for the configuration tested.As can be seen from figure 26, for the horizontal velocityof these tests nnd a vertical velocity of 9.5feet per second,the drng load can be reduced from about 4,4oOpounds to2,400pounds (a 45-percent reduction) by use of a prerotationof 60 percent. This result indicates that, for the range ofconditions covered in these teats, partial prerotation can beemployed to produce useful reductions in the spin-up dragIond.

-—_

Lf,o, fps

9.47––––– ;;:——

,,?.,,

I I I I I

Frerototiq percent

Figure 27.—Ratica of maximum applied loade with prerotation tonmsimum applied loads without prerotation, as functions of percent-

~m=8&5 feet per second.age prerotation. V

Figures 26 and 27 also show the effect of prerotation on them-um verticnl loads. It can be seen that incensing thepercentage prerotation also leads to a reduction in verticrdload, through reduction of the bending moments acting onthe landing gear, as previously disc~d. In these tests theminimum vertical load occurred at a prerotation of about80 to 85 percant, where the minimum strut bending responseoccurred at the time of mtium vertical load.

It is of interest to compare the results of the prerotationtestswith those obtained for the sameinitial skidding velocityof the tire in forward-speed tests without prerotation. hthe forward-speed tests without prerotation, of course, theinitial skidding velocity is the same as the horizontal velocityat contact. In figure 28 the mfium vslues of the drag

-- .— - — .—

1184 REPORT 1248—NATIONAL ADVISOEY f201WJTPEE

4 -

g

j3@2

I -

Forword-~ed tests

v 1 t I I I I I I Io 102030405060 70s090

%dding ~kity at ~ntod, v~do, f~

~QWBE 28.-COmpIWk0n Of ~mum @ 10adSb prerotation te@Sand fornmrd+peed tests for equal initial skidding velocities.

load in both types of teds are plotted against the initialskidding velocity. The maximum drag loads with prerota-t,ionare seen to agree closely with the curves for the forward-speed tests without prerotation. It thus appears that theeffect of prerotation on the maximum drag load is essentiallythe same w the effect of reducing the forward speed.

Comparisons of the time histories of the drag load fortests with prerotation and without prerotation am shown infigure 29 for several selected intial skidding velocities and avertical velocity of about 9.5 feet per second. As can beseen, for tests with approximately the same initial skiddingvelocity, the time histories are similar; however, the testswith prerotation indicate a slightly longer time to spin up.

103— Prerdotim tests, Vvom-9.56 fps

----- Fcnvmrd-spwd tests, Vv =940 fpsOm

VmMO, 84.7 fps [Perofo!ion, O%)------ Z-IIY.

/’7/ \

/F \ \65.3--,1

\

/A\\

f/ \ ---64.5 \

// ,/\ (23.4%) \

\ \/ ‘ ./ \ \

i\

I\ I\\

\

\\\

II11.\

\\ \\\\

\\

7 I I 1 1 f

o .01 .02 .03 .04 .05

Time ofter wmtod, sec

fiQURE 2fL—timparieons of drag-load tiie histon- in prerotationtests and fomvard+peed tests for sever@ initial skidding velocities.V- in prerotation tests, approximately 85 feet per second.

FOR AERONAUTIC-S

The same type of agreement was found for impacts at mverticdvelocity of 7.6 feet per second.

In evaluating the eifects of prerotntion, a word of cautionis necessary. The results for the forward-speed tests withand without reversa rotation in figure 15 show that thomtium drag load tit increasea with increasing forwardspeed (iiitial skidding velocity), reachea a peak at about 120feet per second, then decreases with further increase invelocity. In the prerotation tests of the present investiga-tion the carriage horizontal velocity was about 86 feet persecond, well below the value for peak drag load, so that myreduction in skidding velocity obtnined by prerotation, evena small amount of prerotation, caused n decrease in the dragload. On the other hand, for horizontal velocitiw above12o feet per second, an insufficient amount of prerotat.ionmay actually cause an increase in drag load if the skiddingvelocity at contact is reduced to values in the vicinity of thopeak drag load. For example, at a horizontal velocity of 200feet per second, figure 15 indicates n maximum drag 10MIofabout 2,700 pounds. In order to reduce the maximum dragload below this level, the relative skidding velocity wouldhave to be reduced to less than 50 feet per second, that is, bya prerotation of 75 percent or more. Any lesser amount ofprerotation would actually cause the drag load tc bo in-creased. This possibility should always be considered inthe design of prerotation devices when the horizontal veloc-ity is higher than that at which the peak drag load occurs,and care should be taken to insure tlmt suilicient prerotationis produced to yield a relative velocity small enough actuaUyto cause a reduction in drag load. ThB restriction, hovmver,still provides considerable latitude in matching the forwardspeed. On the other hand, for very high forward speeds,the maximum spin-up drag load may be of the same order as,or even less than, the drag load caused by other designconditions, so that the practical advantages of prerohtionwould be greatly reduced. Even in such cases, howovor,prerotation might still be useful m a means of reducingdynamic stresses and consequent fatigue problems in tlmlanding gear and other parts of the airplane structure.

From the results of the many tests which were made in thobasic study of w-heelspin-up drag 10NIs, certain inferencesmay be drawn regarding the probable effects of prwotwtionon tire wear. It would seem that prerotntion should greatlydeme tire wear. On the other hand, no appreciableamount of tire wear was evident in tho impact-basin tests,even though the program involved somo 45o simulated land-ings without prerotation, covering a range of vertical veloci-ties up to 9.6 feet per second and initial skidding velocitiesup to 273 feet per second. The tires on an airplane havingthe same type of landing gear were worn out, however, in asubstantially smaller number of landings under much 10SSsevere impact conditions. Since the onl-Ysource of tire wearin the h-pact-basin tests is the wheel ~pin-up process, themuch larger rate of wear in the flight landings appmrs to betdue ta sources other than wheel spin-up, perhaps brdcingand turning conditions. From these considerations it wouldappear that prerotation should have little effect on tire life.

AN DXTDRIMXNTAL STUDY OF APPLIED QROUND LOADS IN IA.NIXNG 1185

CONCLUDING REMARKS

A study has been made of the applied loads and thecoefficient of friction in impacts of a small landing gear undercontrolled conditions on a concrete landing strip in theLnngley impact basin. The basic investigation includedthree major phases: forward-speed tests at horizontal veloci-ties up to approximately 86 feet per second, forward-speedtests with reverse wheel rotation to simulate horizontalvelocities up to about 273 feet per second, and spin-up droptests for comparison with the other tests. In addition to thebasic investigation, supplementary tests were made to eval-uato the drag-load alleviating effects of prerotating thewheel before impact so as to reduce the relative velocitybetween the tire and the ground.

In the presentation of the results an attempt has beenmade to iDterpret the experimental data so as to obtain someinsight into the physical phenomena involved in the wheelspin-up process. From this study it appears that the condi-tions of contact between the tire and the ground, and conse-quently the magnitude of the coefficient of fiction, vary

greatly during the course of an impact and with differentimpact conditions. The coefficient of friction appears to beappreciably influenced by a number of factors, including theinstamkmeous skidding velocity, the slip ratio, the verticalload, the effects of tire heating produced by the skiddingprocess, and the tiects of contamination of the groundsurface by abraded rubber. Some quantitative indicationsof these effects were obtained from the experimental data butthe nature of the tests did not permit complete separation ofall individual effects.

From the study of the effects of wheel prerotation, itappears that this means may be used to obtain appreciablereductions in the maximum drag loads; however, at very highforward speeds, because the spin-up drag loads may be ofthe same order as, or even less than, the drag loads causedby other design conditions, the practical advantages ofprerotation could be greatly reduced.

LANGLEY aERONAUTICAL LABORATORY,ATATIONALADVISORY Co arbrmxrEDFoR &3 R0NATJTICS,

LANGLEY F~LD, VA., Augu8t 18,1956.

APPENDIX ADEFINITIONS

The purpose of this appendix is to present briefly some ofthe equations used in calculating the relative motions be-tween the wheel and the ground from the measured data.

ROLLINGRADIUSBy analogy with the rolling of a rigid wheel, the effective

radius for the free rolling of a deformable wheel is definedby the equation

G=rJl (Al)where

x, horizontal translation of the axle in rollingO angular displacement of wheel

rolling radiushr’ estimate of the rolling radius may be obtained by

means of a simple geometrical argument, along the samelines as that used by R. C. Whitbread and described in refer-ence 6. The adjacent sketch represents a rolling -wheel offree radius R, deflected by an amount 8=OB; the deflected

Sketoh (a).

radius is rd. Assume that the arc ABC has been compressedso that the mean footprint length is equal to the chord AOC.Assume, also, that no sliding between the tire and theground occurs in rolling. Thus, for an angular displacement

as shown, the axle will be displaced horizontally by an amount

With the foregoing substitutions, equation (Al) gives thefollowing expression for the rolling radius:

(M)

It Cmequation

be readily shown that the right-hand member of(A2) is very closely approximated by the linem

2R+r4 for the practical range of tire deflection,fnnction ~

.SOthat

(A3)

or, since r.j=R— 6,

r,mB—~3

@3a)

where 6 is the tire deflection.llquation (A3a) appears to be substantiated fairly well by

experimental data. (See ref. 6.)

APPARRNT SKIDDING VELOCITY

If skidding exists, the horizontal displacement of tlm deXul, is not equal to the horizontal displacement x~ in froo,rolling. The apparent skidding distance x,~,.jis the diflemncebetween the actual translation of the axle and the tmnslationin free rolling, for the same angular displacement of Lhewheel. Thus,

x*~~=x&~-z~

=zti&-r80 (A4)

Differentiating with respect to time gives the following ex-pression for the apparent skidding velocity:

Vd.= V..–r$ (A6)where

vfi~=$,t,d

v=&=&,

SLIP RATIO

The slip ratio is normally defined as the ratio of the changein the angular velocity of a wheel, under the application oftorque, to the angular velocity of n freely rolling wheel atthe same axle veloci~; that is,

#f-d#f

w-here

4 angular velocity of wheel under torque

#f angular velocity of freely rolling wheel

Multiplying numerator and denominator in equationby re and noting that TJY=V=l, gives

(A6)

(A6)

(A7)

1186

APPENDIX B

TIRE HEATING

A rough evahmtion of the factors which influence theheating of the tire during the skidding prows may beobtained from the following elementary considerations.Assume that the tire is a good insulator, so that the heatproduced by the skidding remains on the surface of the tire;the temperature rise of the surface will then be directiyproportional to the concentration of skidding energy per unitof tiie surface arm. For simplicity assume that l’v~, p,and r, are constant; also, assume line contact betmeen thetire and the ground (rigid tire). Consider the work donein skidding and the area of the tire in contact with theground during an increment in time At, during which thetire rotates through an angle Ad and the axle is dis-placed horizontally through a distance AGZ,; the skiddingdktnnce during this interval is given by (see eq. (A4))

L@tfd=f%xto-rao @l)

The work done in skidding k

A’W=FH#Xtitd

‘/.l~V#$kid

The amount of tire surface making contact with the groundis

‘=6 “Aewhero w is the width of the tire contact area.

(The factor

gis introduced to insure that AA is positive regardless

of the direction of rotation.)

Tho ratio of the incremental work to the incrementalarea is, therefore,

Dividing numerator and denominator of the right-handside.by At-and passing to the limit gives the iutens@ of theskidding energy in the tire surface area making contact withtlm ground:

From the definitions of V,,id and S (eqs. (A5) and (A7))it follows that

(52)

%here, forS<l, 8>0

01,4<0

so that Eis always positive.Equation (132) indicates, in first approximation, how the

energy concentration in the tire surface varies. It is immedi-ately evident that, everything else being equal, the greatestenergy concentration occurs at iS=l, the values at theextremes of the range of S being

6(S.Q—

,(...,::V T——w

Since the coei%cient of fiction decreases with increasingtire-surface temperature, that is, decreases with increasingskidding energy per unit surface area, this simplified argu-ment indicates that, all other factors being the same, thecoefficient of friction should reach its minimum value at aslip ratio S= 1 and increase as iYbecomes either less than orgreater than 1. It also appears that the coefEcient of friction

P.should decrease with increasing values of ~=. These

observations, of course, refer only to the effects of heating.

REFERENCES

1. Batterson,SidneyA.: TheNACAImpactBti and‘iVaterLandingTestof a FloatModelatVariousVelocitiesandIVeights. NACA~P. 795,1!344. (supersedesNACAVCRP163.)

2. Miltitzkyj Benjamin,and Lindquist,Dean C.: Evaluationof theReduced-MassMethod of RepresentingMng-Lift EHectainFree-FallDrop Test of LandingGear. NACA TN 2400,1951.

3. F5mter, B.: Versuohemr Festellungdes Haftverm@ene vonPersonenwagen-l%reifungen.DeutacheKraftfahrtfonohungZb.No. 22, (Berlin),(Undated).

4. Hample,V. G.: FnotionStudyof AiroraftTire Materialon Con-orete. T% No. 25460,BoeingAirplaneCo.,Aug. 11,1950.

6. Drake,D. ‘iv.: FriotionSurfacesforSpin-UpSimulationinLantig-GearDrop Tests. Trans.A.S.M.E., vol. 74, no. 7, Oct. 1952,Pp. 1269-1279.

6. HadekeJR: The MechanicalCharaoterieticsof Pneumatiollres.S &T Memo.No. 5/50,Britiihhfinietry of Supply, TPA 3/TIB,Mar. 1950.

1187

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1188 RDPORT 1248—NATIONAL ADVZSORY COMIWMIEE FOR AERONAUTICS

TABLE I.—CHARACTERISTICSOF TEST INSTRUMENTATION

Instrument G~$m:~ Estfmhcf totalQuantity measured natural fre-quency, cps quenoy, ops maximum error

Aslenormrd force, FNc.-------. -----_ -----. -.---------------, ----------------- *220 800 &90 lb

Axle axial forc.e, Fde---------------------------------------------------------- =403 800 + 240 lb

Axle normal acceleration, inner, a~c{-------------------------------------------- 800 800 + O.8g

Axle normal acceleration, outer, a~-oO------------------------------------------- 800 800 &O. 6g

~de~ala~k=tion, aAa---------------------------------------------------- 140 160 i o. 4g

Gmmdvefical foWFr,---------------------------------------------------- b275 800 + 160 lb

Gmudhotintd for~FHZ -------------------------------------------------- b100+ 800 + 230 lbGround vertical tiemtion, av<----------------------------------------------- 520 800 + o. 2g

Ground horizontalacceleration, aHO-------------------------------------------- 530 800 + o. 2g

Wm@m&pla-ent, 0------------------------------------------------- ------------ 1,650 *10

Wm@mveloci@, 6----------------------------------------------------- ------------ 800 *1. 6 porcontUpper mass displacement, A-------------------------------------------------- Flat response 600 *0. 2 inoh

to 20 OpsShock&rutaxialstroke, 8---------------------------------------------------- Flat response 100 &0.16 inoh

to 20 OpsTire displacement (tied instaUation)------------------------------------------- Flat IWPOIW 100 ztO.16inoll

to 20 OpsVertioal velocity atcontac~ VYo----------------------------------------------- 1, 000+ 800 + 0.1 fps

Wform ------------------------------------------------------------------- ------------ 100 *2peroontC-e hofiontd @lac-ent ---------------------------------------------- 1, 6S0 *O. 1 ftWtio~ph-g ----------------------------------------------------------

----------------_------- ----- +1 porcont

I

● ‘iWthwheel assembly attaohed.b TWth grmmd platform attached.