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Proceedings of the Institution of Mechanical

http://pad.sagepub.com/content/10/1/348Theonline version of this article can be foundat:

DOI: 10.1243/PIME_AUTO_1956_000_034_02

1956 10: 348Proceedings of the Institution of Mechanical Engineers: Automobile DivisionAlbert G. Fonda

Tyre Tests and Interpretation of Experimental Data

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348

TYRE TESTS

AND

INTERPRETATION

OF

EXPERIMENTAL

DATA

By Albert

G. Fonda,

B.M.E., M.S.*

The test techniques and associated equipment developed for use of the Air Force-Cornell

Tire Tester have permitted road tests yielding unique data on the cornering charaaer-

istics of pneumatic tyres. Account is given of tests performed for the Dunlop Tire and

Rubber Corporation, involving variations of inflation pressure (18 to 45 lb. per sq. in.),

camber ( 30 deg.), and steer (f30 deg.) ; hese angular ranges are unprecedented. The

tyres were nominally 5~00,6.00, and 7.00by 16 section, of normal construction but smooth

and round to eliminate effects deriving from tread pattern.

The ensuing data analysis was based upon familiarity with aircraft derivative notation,

the advantages of which are described, and upon simple tyre theory, which

is

outlined in

an

appendix. The outstanding conclusions, from a practical standpoint, are (1) that

camber thrust strongly affects the static stability

of

the typical automobile;

(2)

that the

motor cycle operates with negligible slip angle below 35-deg. tilt, whereas above 35-deg.

tilt

appreciable slip angle must be developed; 3)

that

a plot of pneumatic trail against

side force has great value because of its linearity and ready significance; and

(4)

that tyre

theory should be utilized to permit rational, concise interpretations of empirical data.

INTRODUCTION

THE ir Forcecornell Tire Tester has been in use since

May 1955 as a tool of research in the cornering character-

istics of pneumatic tyres. The research

has

found its

impetus in the relative exhaustion of less po we rl l methods

of improving the design of not only tyres, but also the

vehicles on which they are used, including aeroplanes when

moving on the ground as well as automobiles.

This

paper

relates the experience of the Cornell Aeronautical Labor-

atory (C.A.L.) in utilizing

this

flat-road tyre tester, describes

certain of the experimental data so obtained, and pursues

an analysis of these data to show their utility.

Notation

C

F

K

L

Half-contact-length

of

tyre.

M

P Tyre inflation pressure.

S

aFy/ac(;C1at front of vehicle, C at rear.

Force component (with subscript) from ground on

tyre.

Lateral stiffness per unit cross-section.

Length of free circumference of tyre.

Moment component (with subscript) from ground

on tyre.

Circumferential distance around tyre equator.

X

Y,Z

Stability axes (or, with subscripts, other axes).

x,y,z

Distance components (or, as subscripts, directions).

a S-P

slip angle of test tyre.

Trail angle of

i th

wheel relative to truck.

Steer angle of test wheel relative to truck.

P

S

U Relaxation length (stiffness parameter).

Camber angle of test tyre.

I I Absolute value; amplitude.

For a further description of the stability axes and of the

notation, reference may be made to Appendix

VI

of Paper

111.

TYRE

PARAMETERS

Every invention passes through three stages: the first,

wherein requirements are approximately satisfied by in-

vention; the second, in which endurance is developed to

make the invention practical; and the third, wherein

research and analysis fully develop the possibilities

of

the

invention. Th e first and second stages have been essentially

completed for the pneumatic tyre, but the third is still very

much under way. The activity of C.A.L. lies in this stage

of research and analysis, the stage wherein the parameters

of tyre behaviour are defined, evaluated, and intelligently

modified.

TheMS. f this paper was received at the Institution on 30th August

1956. Cornering Properties

Project Engineer, Mi lita ry Tire Research, Vehicle Dynamics

Department, Cbrnell Aeronautical Lab orato ry, Inc., Buffalo,

New

York,

United States

of

America.

The basic

f u n d o n s

of tyres fall into three classifications

ride, propulsion and braking, and cornering.

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3/20

T Y R E T E S T S A N D I N T E R P R E T A T I O N

OF

E X P E R I M E N T A L D A T A

349

Tyre-cornering properties express those mechanical

characteristics of tyres giving guidance of the vehicle upon

its path. Principal of these is the relation of side force Fy

to slip angle

a,

he lateral angle of attack of the tyre on the

road. However, to be more general, there are a number of

dependent variables (drag, side force, overturning moment,

aligning torque, static deflexion, circumferential creep, etc.)

that are functions of a large number of independent

variables (load,

braking

moment, slip angle, camber angle,

ida tio n pressure, rim size, cord angle, etc.).

This complex of functional relationships

can

be expressed

as follows

:

F,,

Fyy ,, M,,

etc. =

f

(Fx,

My

,

4, P,

rim, etc.1

.

(59)

where a real advantage of this presentation is the possibility,

obtained from concise notation, of expanding the relation

into a detailed description of the relationships upon which

data are needed. This process of expansion may use partial-

derivative notation to isolate the various relationships.

When applied to equation (59) without regard to the actual

phenomena, derivative notation gives

:

aF,

aFy

aFy

Fy

= /~+q5--kg-+Fz--+etc., a ap aF, . (60)

where each partial derivative is the rate of change of the

dependent variable Fy with one independent variable,

regardless of its variations with other variables. In many

instances, of course, a variable is determined as dependent

or independent merely according to the observers point

of view or the particular conditions of an experiment.

Anassumption implied bythe formof equation (60) is that

each partial derivative is a constant, regardless of the value

of any independent variable. Since, for instance, aFylacx= 0

at and only at F, = 0,

this

assumption is obviously in-

appropriate.

A

rearrangement, based on understanding of

the particular phenomena, may be made of equation (60).

We may assume a set of standard conditions a = 0, q = 0,

p = po O, F, = F,o O, etc., and then evaluate the rates

of change of Fy (etc.) for variations from these conditions.

Then, equation (60) assumes the more appropriate form

This equation shows a series of tyre-behaviour para-

meters

(Coy

aC/ap,

azFYja+ap

etc.), each of which is a

suitable subject for empirical research. By elaboration upon

equation (61) (that is, by specifying the etc. in terms such

as construction effects or friction effects), a multitude

of such derivatives are imaginable. From

this

long list of

unknowns must be chosen those of which the evaluation is

economically justifiable, and of these, a portion must be

scheduled into a programme which does not continue

indefinitely. One such programme, and its results, is

discussed in

this

paper.

Six

ForceMoment

Components

Any solid or elastic body may be restrained by a set of three

forces at, and three moments about, some one point of the

body. The Air Force-Cornell Tire Tester

is

a complete

and versatile facility by virtue of the fact that it measures all

six of these components under realistic conditions of

operation. However, the action exerted upon the tyre by the

ground (or on

any

body by any external medium) involves,

in general, not six but nine quantities. This occurs because,

for three forces lying

in

mutually perpendicular planes,

there are six variables of position (that is, lever arms), two

for each force. Thus, in general,

rill,

=YZFx -ZyFy

. .

. (62a)

My --x,F,+z , . . . (62b)

M, =X~F~-Y,F, . . . (62~)

It is evident by inspection that each moment vector has

two additive components, only the sum of which can be

measured in terms of the restraining moments applied to

the body.

If the axis system is carefully chosen, however, the lever

arms may be made distinguishable, for under certain

conditions one may be known, or if unknown, may be

assumed either minor or constant. Thus, for the stability

axes

of

the tyre, the six lever arms above become :

Lateral offset of load (function of Fy and 4).

z

zy Rolling height of tyre.

x , Longitudinal offset of load (function of rolling

resistance).

z,

Rolling height of tyre.

xy Pneumatic trail.

yx

Lateral offset of drag (function of Fy nd 4).

The recognition of these six moment arms associated with

the three force components may result

in

rational inter-

pretations from studies of otherwise uninterpretable

moment data. The original six measured variables might be

supplemented by measuring, for instance, zy z, (rolling

height) from which may be gained a knowledge of y, and

x, (load offsets). Any such moment-arm analysis could not

be attempted without prior recourse to stability axes with

their inherent applicability to tyre behaviour.

The existence of six momentarms is a logical consequence

of the finite size of the contact area in which distributed

forces occur. This concept suggests another measurement

problem: what are the force distributions (apart from the

magnitude and location of the total force) in the contact

plane and at other boundaries? Even a six-component

facility would need additional equipment to investigate

these problems. Fortunately, this type of problem is the

exception; the general rule (gained from aeronautical

experience) is that the six restraining components should be

measured if a multi-purpose facility is intended.

Optional Algebraic Signs

Even after an axis system has been defined, with its own

positive directions, a question of sign still exists at the point



4/20

350

ALBERT

G .

FONDA

of applying the chosen sign conventions to the measured

quantities. In the case of vectors, the question is whether

an action is measured, or its equal but opposite reaction.

For instance, the vectorsF,, F,,, F, are defined in Paper I11

as those from the ground upon the

tyre,

rather than the

opposite vectors from the tyre upon the ground

f,.,

fy,

f,

according to Paper 111). Fortunately, most investigators

seem to adopt the assumption that the forces from the

ground upon the tyre are measured. Similar agreement does

not exist for angles, notably slip angle

a.

The question in

this case is one of observer location : s the observer on the

wheel looking at the motion axes, or on the motion axes

looking at the wheel? The same lack of agreement exists

between assumptions for aerofoil angle of attack, in flight

and in the wind tunnel, and for basically the same

reasons.

The observer

in

flight is located at the wing, watching the

airstream; the observer outside the wind tunnel is aligned

with the airstream, observing the wing attitude. This

situation corresponds to observers in the car as against those

on the tyre-test truck. The former leads to

a

= 8-S

(where

6 is

thought

of

as a modifier to

a

8)

as used in

Papers I1 and V, while the latter leads to

a

= 8-p (where

/Is thought of as

a

modifier to

ag

), as used in Paper

I11

and the present paper. The difference is irresolvable on any

logical basis, and has never been resolved merely for the

sake of uniformity in the aircraft industry. The convenience

of a definition which pleases the respective types of ob-

server probably justifies the slight confusion in the auto-

motive, as well as the aircraft, industry.

TYRE-TEST PROCEDURES

The

Air

Force-Cornell Tire Tester has been in operation

since October 1954, on a series of programmes preceded

by a period of shakedown and technique development.

The developed techniques fall into three classes, and are

performed in this order for any test programme :calibrating

and zeroing, recording, and data processing. Appendix X

describes the calibrating and zeroing procedures for the

benefit of those who contemplate the construction and use

of similar equipment.

Recording of Test Data

The greater amount of the data obtained with the Air

Force-Cornell Tire Tester are obtained during outdoor

runs, although some indoor data are obtained, including

tyre compliances and contact prints. In the outdoor tests,

records are taken while the chosen tyre is steered under

chosen conditions of speed, load, pressure, camber, and

road condition. For the next run, at least one test condition

is altered. Such runs are continued until the scheduled

series of tests on that tyre is completed. A typical number of

runs per tyre is ten, and these can be completed in one to

two hours. A number

of

mounted tyres can be carried on

the truck, so that a great mass of data can be gathered in a

day of continuous testing. If this potential were to be

continually utilized (as it is for a wind tunnel), several large

teams would be needed, using the test apparatus in turn.

However, the testing techniques, much less the demand for

the data, have not yet reached

this

stage of development,

since, at present, each test programme requires some new

item of equipment (with associated shakedown) to permit

the desired technique.

The technique of greatest merit for steering is to hold

each desired angle for about three seconds and then to

steer rapidly to a new angle. This procedure is continued

progressively to a positive peak, back to zero (with or with-

out pauses), then to a negative peak, and then to zero. The

recorder is runcontinuously, but only the periods of steady-

state operation are subsequently analysed. The record-

reading apparatus permits a visual averaging which

eliminates the higher-frequency variations intentionally

passed by the signal filters.

A previous technique involved steering at an approx-

imately steady rate through the same sequence of angles.

Visual averaging of the resulting slanted traces was

in-

herently less accurate and produced more data scatter. This

condition required, therefore, the reduction of many more

data to permit averaging after plotting. The newer tech-

nique consequently gives a major cost saving.

In developing steering techniques, an appreciable amount

of effort was required for equipment development.

As

an

initial experiment, a hand pump was used to pressurize the

steering actuator, but this method proved too slow and

fatiguing. An electrical pump and accumulator were there-

fore provided; the steer rates now available permit any

desired type of steady-state test, and will also permit (if

controllable) many types of transient input when the

demand arises. The rapid fluid flow also flushes away air

which could previously be removed only by bleeding at

fittings.

At one time a technique was used in which the wheel was

steered while

up,

stopped suddenly at a desired angle,

and

then dropped at known load. The sudden stop would

produce system pressurization to minimize the compliance

of the steering to the side force

as

it developed. However,

the transient of truck yaw produced by the sudden side

force required a long pause at steady steer angle, in order

to yield usable data. Thus, contrary to expectations, na

reduction of tyre wear was achieved by this technique.

In

actual fact, tyre wear under any technique, including the

technique finally adopted, has been much less than ex-

pected. A tread life of

100

to 5,000 miles of test could be

expected, of which only 10 miles is typically used.

Data Processing

Because the use of recording oscillographs is standard

practice at the Laboratory, specialized equipment

is

on hand

for processing this form of data. This processing centres

about IBM* digital computers that use punched cards. The

first set of data cards is produced from the oscillograph

record by means of a combined optical enlarger and card

punch. Averaging is performed by the operator when he

International Business

Machine.



5/20

TYRE TESTS AND INTERPRETATION

OF

EXPERIMENTAL DATA 351

aligns a movable hairline with

the

chosen trace. The digital

computer will then process the cards into printed tabula-

tions involving all force and angle summations, as well as the

calibration and zero factors. If resolution for camber is made,

an intermediate set of cards is punched, sorted in terms of

camber angle, and processed. Finally, the printed tabula-

tions are hand-plotted, although facilities have recently

become available for automatic plotting. At various stages

after development of the record, the data are inspected to

detect errors such as faulty or mis-set instrumentation or

faulty calculation.

The resulting plots, shown in Fig. 58, are point by point

presentations of three forces and two moments

(braking

force being zero to date) against slip angle. Of these, the

side force,

F,,

and its dependent moments,

M,

(overturning)

and

Mz

aligning), vary with

a,

whereas drag F, and load F ,

remain essentially constant. These plots constitute the

basic presentation of

all

cornering-behaviour data ob-

tainedon any programme. This form of the data

is

no longer

characteristicof the tester, but instead is characteristic solely

of tyre behaviour relative to stability axes. From

this

point, further analysis

is

a matter of the interpretation of

pure tyre data and will be discussed subsequently, in terms

of a particular test programme.

DUNLOP-CORNELL TYRE TE ST S

By Spring of 1955, the Air Force-Cornell Tire Tester had

achieved the operational level specified by the Air Force, as

proven by the short sample programme of actual tests

D U N L O P C O R N E L L T Y K E TESTS

6.00

-It

SRT TYRE

5

K

KIM 0 CAMBER 30 LB. PER SQ. IN.

CODE:6

ABC 3

SHEET

I

u

z

a

Fig.

58. Typical Plot o j Dunlop-Cornell Data



6/20

b

Fig.

58. Typical Plot of Dunlop-Cornell Data

which followed the period of technique development,

equipment development, and general shakedown. Th e Air

Force had no immediate plans for testing, but did recognize

the benefits which would accrue from permitting use of the

apparatus

on

programmes for the tyre manufacturers and

the automobile manufacturers. Research upon automotive

tyres would not only specifically improve the apparatus,

but would react favourably upon tyre design in general.

The first such sponsor, the Dunlop Tire and Rubber

Corporation of America, proposed an imaginative series of

tests of interest to them and to their parent company in

England. The objective was to determine, over wide ranges,

the effects of predominant vehicle-operating variables and

of tyre-size variables, in such a manner that the basic role

of the tyre would be emphasized, to indicate criteria in the

choice of a tyre for a given vehicle.

The variables chosen were steer angle (f30 deg.),

camber angle

(f30

deg.), and inflation pressure (18 to

45

lb. per sq. in.). The ranges were intentionally wide (f30

deg. being unprecedented) to guarantee recognition of

weak

trends and explore the boundaries of operation. Tyre size

varied from a nominal

5.00

o a nominal 7.00 on a 16-inch

rim. Conventional carcass construction was used, but all

tread was omitted. This gave a smooth, round, treadless

tyre (SRTT, Fig.59)intended as a simplifiedmechanism for

basic investigation. Load variations were omitted because

(1) only a vehicle applying the rated load of

925

lb. to each

tyre was to be considered; 2) the cancellation

of

load-

increase effects by load-decrease effects, both due

to

load

transfer, was recognized; and (3) the omission helped to

hold the programme to a tractable size.

This problem of reasonable programme size occurs every



7/20


OF

EXPERIMENTAL DATA 353

Fig. 59.

Dunlop

Smooth, Round, Treadless Tyres

to be large; the programme is a 'family tree' with each

generation a type of variable; he potentialnumber of tests is

extreme. The solutionis to prune the tree vigorously

until

it has a practical size and meaningful shape. The traditional

method of testing, resulting from extreme pruning, is to

change only one variable at a time from some standard

condition, on the theory that such effects can then be

superimposed. This method does drastically reduce the

programme, but in many instances cannot be justified.

C.A.L. has developed some special techniques for 'rationally

random' pruning, when needed.

The compromise reached in the DunlopCornell pro-

gramme (Fig. 60) resulted in a total of thirty-eight

different configurations, as actually run. These consisted

of

thirty-four configurations obtained by means of the three

main variables, plus one for wet road (additional pressures

were planned), plus one repeat runper tyre (after comple-

tion of all other runs to detect any wear effects. Fewer

pressures and cambers were used for the 5.00 and

7-00

sizes

than for the

6.00

size. Four alternative seauences of steer

angle were used and three consecutive samples of each

tyre

size,

in

each instance to minimize effects

of

tyre wear.

Experience now indicates that tyre wear

is

less critical than

expected, so that better continuity of testing

can

be

provided. These tests were performed in May and June

of 1955.

t i me

a

tyre-test programme is planned, the present one

not

excepted. The problem occurs because the number

of

possible configurations is roughly the number of values

of

each independent variable (other than

a)

aised to the power

of the number of variables. Each of these numbers tends

HOT

PRESSURE, CAMBER, SLIP ANGLE,

LB. PER SQ. IN.

DEG. DEG.

D (REPEAT)

18

SECTION

ROAD

7.00 DRY

18

30 0

>

CONSTRUCTION TREAD RIM LOAD C

STANDARD NONE

5K-16 925

LB.

/(4)SETTINGS

WET 38

0

.

33

A

B

C

D

25

::

SETTINGS

0

5-00 DRY 28

0, 0

REPEAT

LIFT-STEER-DROP

TECHNIQUE

13

Fig.

60.

Dunlop-Come11 Ty re Test Programme

A & 4 '

C 2 S , 20, 30

SAMPLE 2

D

&3 ,

8, 15'

SAMPLE

3



8/20

354

ALBERT G.

FONDA

CONVENTIONAL ANALYSIS OF THE DA TA

The Dunlop-Cornell tyre tests resultedin thirty-eight pairs

of basic data plots, one pair of which has been shown (Fig.

58 .

This form of thedata is farfrom being readilyinterpret-

able, since the effect of any variable, except slip angle,

can

be detected only by comparison between similar curves of

which the differences are not obvious. Analysis should be

performed which will reduce the basic data plots to under-

standable commentary

on

ty re

behaviour.

This

commentary

should have utility for both tyre design and vehicle design.

For

both these purposes, the form of the data will steadily

gain utility

as it approaches the form needed for equations

of

vehicle motion.

Midway in

this

process is a significant transition form:

graphic cross-plots of the slopes, peaks, intercepts, etc. of the

basic data plots, against some independent variable. Each

such crossplot thus reveals the effects of one such variable.

Cross-plots as such are a conventional tool, but their full

potentialities are often not utilized. The fairing of lines to

fit data

on

a cross-plot

can

give a true improvement of testing

accuracy, as extraneous effects tend to be thus faired out.

These lines, if straight or nearly straight, may then be

mathematically expressed as slopes and intercepts. For

Dunlop, a ull cross-plot analysis

was

made of the thirty-

eight plots of side force (F,) against slip angle

a),

eginning

with the fitting of smooth curves to the data, followed by

evaluation and tabulation of the slopes, intercepts, positive

peaks

and negative peaks of these curves. From this tabula-

tion, all the cross-plots (Figs.

61

through 65) were made.

PRESSURE-LB. PER

SQ. IN.

5.W TYRES 6130 TYRES

7.00

TYRES

Fig; 61. Cornering Stiffness

against Pressure

fm

ach tyre

size)

The slopeaFy/aa, or cornering stilness, is plotted against

pressure for each tyre size (Fig. 61) and superimposed for all

three sizes (Fig. 62). Evidently, tyre size has little effect on

this result, since

al l

three sizes show a stiffness of 115 lb. per

deg. at

25

lb. per sq. in. and substantially equal variations

with pressure (3-3b./deg. per lb./sq. in.). The standard

pressures had been chosen for equal tyre deflections, being

28 lb. per sq. in. for the 5.00,25 lb. per sq. in. for the 6.00,

and 23 lb. per

sq.

in. for the 7.00 sizes. These data thus

indicate that the smal l tyre could be operated under-

inflated o improve its ride and still obtain the same cornering

stiffness as a larger size. The data above 30 lb. per sq. in.

for the 6.00 tyre show a cross-plot slope gradually decreasing

to about 1 lb./deg. per lb./sq. in. at

45

lb. per

s q . in.

Thus,

in terms of cornering stiffness, the effectiveness

of

increased

pressure decreases as the pressure increases.

I60

OO 20 40

60

P R E S S U R E - L B . P E R

SQ. IN.

Fig.

62.

Cornering Stiffness against

Pressure

5.00-16 6.00-16

+

7.00-16

Similar plots of cornering stiffness against camber were

made, but, contrary to curves appearing in the literature

(BulP), no definite trends appeared. On the other hand,

camber does definitely affect the Fy

ersus

01 intercept. This

camber thrust plottedagainst camber angle (Fig. 63) shows

a surprisingly constant slope to 30 deg. for

all

tyre sizes.

The result may be compared with the traditional ap-

proximation Fy= W tan 4 which, only by coincidence, also

expresses the condition of tilt equilibrium for the motor

cycle. A tangent 4 function is not straight, but curves

upward until, at 30 deg., its slope

has

increased by 34 per

cent and its height by 10per cent. The observed slopes (Fig.

63) were 20,16, and

17.5

lb. per deg. at the nominal 925-1b.

load, as compared with an initial slope

of

16-1 b. per deg.

for a function of

925

tah

4.

Therefore, as

an

approximation,

the tangent

4

function varies from excellent to poor, de-

pending on the tyre and the camber angle. A later dis-

cussion will show the significanceof this distinction with

regard to the motor cycle.

Average peak side force plotted against pressure (Fig.

64)

indicates that values on the order of the tyre load are easily

attained, and in fact, exceed it. This fact indicates that

despite the seemingly adverse conditions, friction coeffi-

cients are attained on the road equal to those attained in the



9/20

T Y R E

TESTS AND

INTERPRETATION

OF

EXPERIMENTAL DATA

355

5M) TYRES

+-DEGREES

o 30 ib. per sq. in.

25

lb. per sq. in.

+ 20 lb. per sq.

in.

6.00

TYRES

Fig.

63.

Camber Thrust against Camber Angle

7.00

TYRES

PRESSURE-LB. PER

SQ. IN.

5.00 TYRES

PRESSURE-LB. PER SQ.

IN.

6.00 TYRES

a

I,200

1,000

925

800

a

I

600

Y

9

;;

400

200

0

10

20

30 40 50

INFLATION

PRESSURE-LB. PER

SQ. IN.

b

Fig,

64 .

Peak

Side

Force against Pressure

PRESSURE-LB. PER

SQ. IN.

7.00

TYRES



10/20

356

ALBERT

G .

FONDA

I F S lMOTOR CYCLE I.F.S. IMOTOR CYCLE

I.F.S.

IMOTOR CYCLE

*

I

-20 -10 0 10 20 -20 -10 0 10 20

20 -10

0

10 20

F,

J

DEG.

-

-

IF,

'

EG.

-l DEG.

I51

I

5

7.00 TYRES.00 TYRES 6.00 TYRES

Fig. 65. Peak Side Force against Camber

laboratory (1121.0). The effect of pressure is to increase

peak side force at the rate of about

10

lb. per lb./sq. in. in

the range of standard inflation 5 5 b. per sq. in. Increases

of tyre size in

this

pressure range (Fig. 64b) cause increases

of peak side force. As the pressure rises beyond 30 lb. per

sq. in. for the 6.00 tyre, the peak force drops and then

rises again. The isolated test on a wet road showsp = 0.63

at 38 lb. per sq. in. for the 6.00 tyre. Lack

of

time and lack

of

suitable weather precluded further wet-road tests.

The effectof camber on peak side force is shown (Fig. 65)

by plotting the peaks against a special parameter Fy4/lFy1.

This parameter has the magnitude of 4, but the sign of

Fy , nd is positive for a motor cycle rounding either a

right- or

a

left-hand curve. The typical independent front

suspension, on the other hand, has negative 4 due to the

body roll for positive

Fy

and

vice

versa

so

that

Fy+

is

always negative. The positive cross-plot slopes

2.0,2.7,

and

2.5 lb. per deg.) indicate that camber of the motor cycle type

w i l l increase the peak side force available from a tyre.

Parallelogram suspension will, on the other hand, decrease

available peak side force. This effect is strongest, the data

shows, for the smallest tyre. The implications of these

camber effects for both the motor cycle and the automobile

will be presented in a later section.

A summary of the various cross-plot slopes may be

concisely presented, Table

6,

by the use of derivative

notation. Values of derivatives could be similarly quoted in

handbooks if such notation were used, just as rated load,

dimensions, and rolling radius are now quoted. Load effects

could be expressed by additional derivatives, such as

a2Fy/aFzaa hich is, numerically, the slope of the popular

Fy

ersus

Fz curve for a = 1 deg. Th e aeronautical designer

uses such listings of derivativevalues, from wind-tunnel tests,

to choose among aerofoil sections. The automotive designer

could do likewise if such tyre data were available. Further-

more, judgements could be formed of desirable values, and

these could be specified as tyre design objectives. These

criteria might well vary from make to make of car,

so

that a

tyre design could be optimized for a particular car

or

type of

car. These comments are made in recognition of the fact

that presentation of data is an inescapable problem when

tyre tests are made, and that a standard means of presenta-

tion is as desirable as a standard notation.

In the case of aligning-torque data, there are to date

even fewer standardized presentations than for side-force

data. The practice of plotting side force against aligning

torque was introduced by Gough115 and thoroughly

discussed by him ; ts many advantages do not need to be

repeated at this time. C.A.L. has plotted a portion of the

Dunlop-Cornell tyre data on similar co-ordinates (Fig. 66) .

This plot shows, for comparison, two similar tyres drum

tested by Dunlop of England (Goughl15.

118).

The data

fall mainly in the fourth (and second) quadrants, because

Table 6. Tyre Derivatives for Three Tyre Sections

Tyreseaion I

5.00

6.00 1

7-00 Units

a = Of3 deg.

115

115 lb. per deg.

p

= 251b.per 15 I I

F z= 925 lb.

aa

a

=Of3 deg. 3.3 2 9

3-1

lb./deg. per

p = Std. f 1b.

lb./sq.

in.

,

p = Std. f 5 b. 10 10 12.5 Ib./deg. per

= 0

per sq.

m.1 1

lb./sq.

in.

p =

Std.

2

for 2.7 2 5 lb. per deg.

TY)PCak

a

4 =

Of30deg. 7for

Largest values underlined

;note lack

of consistency.)



11/20


OF

EXPERIMENTA L DATA

357

M , is mainly negative for positive

F

.By placing side force

on the abscissa, the major convexity

is

up and down, rather

than lateral, and the plot becomes a 90-deg. rotation of

Gough's choice.

Y

0 200 400 600 800

SIDE FORCE FY-LB.

Fig. 66.

Comparative M , against Fy

Plots

7.60-15

1,000 Ib. load

24 lb. per sq. in. inflation

From Gough-Fig.

10

(Ref. 118).

8

wt. (896 lb.) load

24 lb. per sq.

in.

inflation

From Gough-Fig. 6 (Ref.

115)

7.00-16 Treadless on

5 K

rim

925 lb. load

23-25 lb. per

sq.

in.

inflation (hot)

From Dunlop-Come11 Tests ,

June 1955.

6.40-15 on 44

Rim

Such data have, it is believed, never been presented

for slip angles beyond about 10 deg.

As

shown, a minor

lateral convexity occurs, because of (1) the reduction of

side force after its peak, combined with

(2)

the correspond-

ing positive increase of aligning torque. Neither quantity

varies rapidly with slip angle in this region, so that, on the

M, versus

F,,

co-ordinates, these slip angles are quite

closely spaced.

This

plot of Dunlop-Cornell data shows

stronger aligning torque and less slip angle for a given side

force than the English data, in the region from

0

to 8 deg. of

slip angle. This must be the result of

(1)

drum-to-highway

difference,

(2)

tread-to-treadless difference, or

3)

con-

struction-and-diameter difference, in order of decreasing

likelihood. More data are needed to distinguish further

among these possibilities. Only a limited amount of data

were analysed in this manner, with the objective of showing

the shape of the curve for extreme slip angles. However,

such comparisons constitute definite progress toward a final

understanding of the relationship between the drum test

and the more valid, but more difficult, highway test.

UNCONVENTIONAL ANALYSIS OF THE DATA

After the M, versus

Fy

plot for the 0 to 30 deg. slip-angle

range was inspected, it seemed that, despite the interesting

shape of the curve, it was too confusing a curve; to be

more precise, it was too curved.

It

is the nature of

any

phenomenon that once functions of the data are found that

give a straight-line data plot, these fmctions, be they simple

or complex, very probably have true relevance to the nature

of the phenomenon and are, in any case,

of

great utility.

Therefore, it is valid to plot and replot data until a straight

line is formed, so that an empirical relation (form mx+b on

those co-ordinates) can be fitted. This gave justification

for

continued analysis involving unconventional co-ordinates

.

However, such trial plots are preferably not made at

random, but with some intuition and understanding of the

problem. There were many clues available in the case of

these tyre data. Aligning torque can be regarded as an input

applied by the driver

(via

the steering wheel) to the tyres,

whereby the tyres produce the side force on the vehicle a d

on the driver. Thus, in the sense of servo mechanics, the

input M , and the output F,, are coupled by the transfer

function

F y / M z

(output against input). In the kinematic

sense,

M J F ,

is a force-ratio mechanical advantage of the

driver over the lateral acceleration force. In equation (62c),

we noted M ,

= xyFy-y,F,;

since

y ,

and F, should both be

small, M , / F y ~ x y , hich is also significant. Finally, Gough

had already shown lines of constant M,/Fy, pneumatic

trail (Fig. 67), on his Fy against M , plots. These reasons

led to the trial of a plot of pneumatic trail ( t ) against side

force

(Fy),

which is an innovation, so far as is known.

I I

200

0

a i

1

-200

z

I

2

J

- 00

-

600

The result (Fig. 68) is shown, in this case, on an outline

of the actual contact area of the tyre tested. This display is

appropriate, because t

versus Fy

shows the position in the

contact area of the side force, against its own magnitude.



12/20

358

A L B E R T G. FONDA

OUTLINE OF ACTUAL

PRINT

KINGPIN

OF TYRE

AS

TESTED

MECHANICAL LCAToN

Fig.

68.

Pneumatic Trail Against Side Force

Thus, the plot has very real physical significance in terms

lof conditions in the contact area. The kingpin location can

be spotted on this plot to show mechanical and total trail.

Another graphic advantage is the great compaction of data

in the skid region, from

10

deg. to 30 deg., into the near

vicinity

of the friction

limit

and zero trail. This compaction

is quite appropriate because slip angle is of little importance

to tyre behaviour in the skid region. The equispacing of

t ra i l

values desirably avoids the expansion of small values,

which was observed (Fig. 67) at these large side forces.

On he other hand, perhaps too much attention is called to

t at

s m a l l

values of Fy. Since it is difficult to measure t from

M , and Fy when both are s m a l l ,

it

may, by the same token,

be unimportant to the driver

;

his possibility requires

further investigation.

But the most significant fact, by far, is the close approxi-

mation to linearity exhibited by this t versus Fy plot. It

appears that we have found-much more easily than would

have been expected-a set of co-ordinates upon which

aligning-torque data become linear. This linearity allows

fitting of a straight line of the form t = i+ lFyI(at /aFy)

where

t i

is the intercept and at/aFy is the slope. The advan-

tage is that only

two

parameters need now be specified as a

replacement for the whole complexM , versus Fy curve. Two

such functions were tried as approximations to the original

data curve,namely

(a)

t = -256+O.OO3l1Fyl, which was a

fit to the steeper slope appearing from 1 deg. to 4 deg., and

(b) t =

-2-38+040251Fyl,

which was a fit to the data from

5

deg. to 11 deg. For

all

three curves

M , versus

F,

was

tabulated, then plotted (Fig. 69) against

a;

he latter

required use of a correspondingF. versus

CL

curve.

Evidently a) is a poor appromation beyond 4 deg.,

whereas (b)

is

good below 5 deg. (in fact excellent below

3 deg.), and is thus a valid means of calculating M , from Fy

in the region

a

= f 1 deg. Since the approximationFy=

aaF,/aa can be applied up to 6 or 8 deg., the whole normal

operating range for both M, and Fy is covered by only three

tyre

parameters: ti, at/aF,, and aFy/aa. These can also

I - -DE GR E E S

Fig. 69. Side

Force

and Aligning Torque Against

Slip

Angle

a) t = -2~56+0.0031F

b) t

=

-2.38+0.0025Fy

( c ) Curved t versus

Fy

be expressed as (aM,/aF,), a2M,/aFY2, and

aFy /aa; a

fully force-moment derivative form of notation thus ap-

pears. These moment derivatives could be added to the

list which was proposed for inclusion in reference hand-

books.

Pressure, load, and tyre construction would, of course,

affect

the values of these derivatives. Some pressure effects

were revealed (Fig. 70) when actual data values o f t against

Fy were plotted for four of the thirty-eight configurations

tested. Before these plots were made,

Mz

against

F,

was

plotted for the

a

=

f 5

deg. range and a straight line was

fitted; its slope gave an approximation

of

to shown by

broken lines, whereas its negligible intercept indicated little

error, at Fy =

0,

in the averageM, . Th e increased values of

trail with decreasing inflation pressure evidently occur

because of the greater contact length at lower pressure. Th e

cross-plot would certainly reveal a derivative such as i3to/ap.

However, there comes a point at which purely empirical

investigations reach a point of diminishing returns, because

of excessive complexity. A proper application of tyre-

behaviour theory should greatly

simpllfy

such a situation by

revealing broader significances hidden in limited empirical

data.

The present problem can be approached by the method of

non-dimensionalization, namely of the

t

versus Fy curve,

since we know that a reduction in the total number of

variables affecting the curve can thereby be obtained. Side

force, F,, can obviously be non-dimensionalized

by

the

divisor F, (normal load), and gives a cornering coefficient

Fy/Fz (Goughl15) on the abscissa, with the value Fy[F,= p

corresponding to

peak

side force. The divisor for t should

have length units; for instance, as Gough suggests, the root



13/20

T Y R E T E S T S A N D I N T E R P R E T A T I O N

O F

E X P E R I ME N T A L D A T A

359

Fj -LB.

U

0

z.

I

-

-2

-3

I

0

z

_I

I

-2

-3

-1.000

-800

- 600

-400 -200

0 200

400 600

81x)

1,000

F - L B .

b

High pressure

:

Standardpressure : Low pressure: Standardpressure :

(30

lb.

per

sq.

in.) 7A3

(30

lb.

per

sq.

in.)

7B3

(28 lb. per sq. in.) 7C3

Do (25 lb. per sq. in.) 7A7

(25

lb.

per

sq.

in.)

7B7

+

(23 Ib. per sq. in.) 7C, 07

DQ (18

lb.

per sq. in 7A14

(18

lb.

per sq.

in.)

7B14

w (18 Ib. per

sq.

in) 7C14

Da

(25

lb.

per

sq.

in.) 7A7'

(25

lb.

per

sq.

in.)

7B7'

+ (23 lb. per sq.

in.)

7C7'

Fig. 70. Pneumatic TraiI Against Side Force for Various Pressures

of the product of tyre diameter and tyre deflexion. There is

more basis in theory, however, for the divisor

t,,

the value

of pneumatic trail calculated from a theory such as that

theory

given in Appendix XI. This value is obtained by

dividing

the expression for

M,,

equation (73), by that for

Fy, quation

(74),

giving

:

1 - N.

0 2

3

4 5 6

Fig. 7 1 . Calculated Pneumatic Trail Against Half-contact

Length

in

which 1 is the half-contact length and u s the relaxation

length, a stiffness parameter of the tyre. This expression

may be plotted as values of t, against 1for various values of

u (Fig. 71).

The stiffness parameter u may be evaluated in a number

of

ways (Appendix XI); or present purposes, the easiest

method was to evaluate the standing lateral stiffness

aFy/ay

and to divide this into the cornering stiffness, giving

the

sum l + u . Tyre contact prints were made to give

measurement of1; the resulting valuesoft, shown in Fig.

71

were in fair agreement with corresponding values of to.

(The largest uncertainty was because of hysteresis in Fy

against y.) In the resulting plot of t / t , against

Fy/Fz

Fig.

72), the value of

t / t ,

at

Fy =

0 would be +

1.0,

if the theory

0 0.2 0.4 0.6 0.8 1.0

1.2

IFylIFz

Fig.

72.

Ratio t / t, Against Ratio Fy/F z



14/20

360

ALBERT G.

FONDA

were complete in all respects. The theory used predicts a

constant trail, regardless of F y ; the observed reduction of

trail with Fy s a function of tyre-to-road slippage, not

considered in this theory. This decrease is therefore an

empirical function of the tyre-road friction coefficientp.

Therefore, the non-dimensional plot

( t / t , )

against

(Fy/F,) consists of a family of curves for various values of p

and p only, at least for normal ranges of pressure, load, and

even tyre construction. This plot promises, therefore, to

give a master curve which is valid for a great variety of

operating conditions for various tyres. Then by making

simple, cheap, non-rolling tests upon tyres, that is, lab-

oratory tests, values

of

I and

u

for various conditions

could be determined. These would become the handbook

values from which, by use of the master curve, M , versus

Fy

could be found for given

p

and

F,.

Further laboratory

measurements of the second basic stiffness parameter,

K

(Appendix XI), would allow prediction of the

Fy

versus

a

behaviour, at least in the linear region.

It

would seem

profitable, therefore, to place hture emphasis on the use of

tyre theory to interpret tyre data, rather than to rely

entirely upon the empirical approach, since

it

is possible

thereby to reveal the hidden significances of empirical data.

UTILITARIAN SIGNIFICANCE

General

Philosophy

Th e ultimate goal of human research is human benefit; the

research is conducted on the assumption that, by studying

and understanding a phenomenon, ways can be found to

make better use of that phenomenon. To study implies the

collection of empirical data, whereas to understand

specifies that theory be devised whereby such data may be

thereafter predicted. Such predictions of complex phe-

nomena necessarily proceed, ultimately, from observations

of simple phenomena. The merit of the entire process lies

in the probability that the ultimate goal can be more

economically achieved by simple observation plus theory,

than by complex observation. In many instances, it is only

after considerable research that specific, rather than general,

objectives can be stated; this accomplishment is another

advantage of the method.

To apply this philosophy to vehicle dynamics, we may

note that the complex phenomenon of vehicle behaviour is

observed every day by the millions of people who drive and

ride in our various forms of transportation. This mass of

observation, however, produces little analytical criticism of

vehicle behaviour

.

Even a trained, professional driver-critic

is hampered by the confusion of data in any single driving

test, and by the great difficulty of altering the conditions of

test. The trial-and-error construction of prototypes for this

purpose is expensive in the case of the automobile, pro-

hibitively so in the case of the aeroplane. The alternative to

this procedure is to replace the vehicle, for example the

automobile, by the more economical simulator. This may

be an analogue computer constructed on the basis of a

theory of automobile behaviour, or even a mathematical

computing process in which the theoretical equations are

utilized. This simulator must be provided with data

regarding the vehicle constants, the tyre behaviour, and the

disturbing inputs (including those

of

the driver). The

resulting calculated behaviour must be judged good or bad,

according to the same subjective criteria the driver-critic

would utilize. Ultimately, such a simulator can become not

merely an automobile simulator but a tyre, car, and driver

simulator. To attain this level, the automobile simulator

should be expanded at one end to include tyre theory, so

that laboratory data (for example,

1 u,

and I-) ay be used

instead of road behaviour data; and expanded at the other

end to include driver behaviour, both as an element in the

control loop and as

an

excellence meter incorporating

subjective-opinion criteria.

Tyre-behaviour data are obviously indispensable to the

accomplishment of this goal. Like

any

link in any chain, the

question is not whether it is needed, but of how difficult it

is to forge this l ink to the required minimum strength.

It

seems apparent that tyre-behaviour data are at present one

of the weakest links in the vehicle-dynamics chain.

It

seems

furthermore that the most profitable approach will be found

in the verification and use of tyre-behaviour theory allowing

complex predictions from simple observations.

Specific Applications

Utilization of the data on tyre behaviour obtained on the

Dunlop programme may be demonstrated in two examples,

both showing the effect of camber, for the automobile in one

case and the motor cycle in the other. The latter will be a

unique study permitted by the unique data. The former

will demonstrate the utility of derivative notation.

It is known to many that the adoption of independent front

suspension (I.F.S.) in lieu of a solid axle not only avoids the

problem of shimmy, but also increases the static margin of

the car by moving the neutral steer point aft a good

6

inches.

This increase occurs because, with I.F.S., the wheels are

maintained approximately parallel with the body and thus

produce camber thrust which reduces the side force at a

given slip angle. This effective reduction of front cornering

stiffness can be calculated from two tyre derivatives and the

vehicle derivative d+ldFy, the rate of (front) wheel camber

with side-force-per-wheel. For a typical American sedan,

d41dFy

is

-0.009

deg. per Ib. which signifies

-1

deg. of

camber per

111

Ib.

of

side force. The pertinent equations,

assuming constant pressure and constant average load, are

:

aFy aFy

Fy

=

a- C-

a

a

for the tyre, and

d 4

4 = F

Fy

for the automobile.

Substitution of the second into the first, differentiation,

and rearrangement gives :



15/20

TYRE

TESTS

AND INTERPRETATION OF EXPERIMENTAL DATA

36 1

2 4 6 8 10 I2 14 15

SLIP

ANGLE,

a -DEGREES

Fig. 73. Side Force Against Slip Angle fm Various Camber

Angles

Substituting previously quoted values for the tyre

derivatives gives :

d F = - -

115

du 17

- 9.5 lb. per deg.

l+m

This value is the effective front cornering stiffness with

I.F.S. The loss of

15-5

b. per deg. compared with a solid

front axle is a

14

per cent reduction of the effective

CI (dFY/dw),,and a 7 per cent increase of the effective

.ooo

800

m

600

ir

L

Y

Y

9

UJ

400

G

200

C

C 2 / C l + C 2 . This increase equals a 9-in. rearward re-

location of the neutral steer point. Thus,

I.F.S.

camber

thrust (a type of roll steer) is revealed as the predominant

contributor to the understeer of modern automobiles.

Designers may well consider variations of the tyre para-

meter aF,/a+ as opposed to variations of the vehicle

parameterd +/d F y .The effectof independent rear suspension

upon neutral steer point (Bastow59) should also be recog-

nized.

Whereas, for the automobile, slip angle is primary and

camber angle is secondary, the roles are (as recognized by

Wilson-Jones'87) reversed for the motor cycle. This fact

may be demonstrated by a plot of side force against slip

angle for various camber angles (Fig. 73), based on Dunlop-

Cornell data, but somewhat idealized. The dotted line for

I.F.S.

demonstrates the above-calculated reduction of slope,

and extends the trend to peak side force. Th e nearly vertical

line for motor cycle behaviour demonstrates the minor im-

portance of slip angle in the normal operating region, that

is up to 35 deg. tilt (ay

=

0.70g). Beyond this point,

appreciable slip angle is required, rising to about 4 deg. at

48

deg.

tilt,

the motor cycle's potential limit. The same

conclusions can be drawn more accurately from a plot of side

force against camber angle for various slip angles (Fig. 74).

Th e motor cycle, when in equilibrium in tilt, must operate

along the line F,,=W tan

.

Although the tyre data are only

approximate aboveFy = 700 lb. or 4 = 30 deg., it is evident

that the potential limit is approximately

4

= 48 deg. with

a = 4

deg. This rather amazing potential

(a , ,=

1-15g) is

LIMIT

OF

DATA

-I

0

0 10 20

30 40 50

CAMBER ANGLE, 4

-

EG.

Fig. 7 4 . Side Force Against Camber Angle for Various Slip Angles



16/20

362 ALBERT G . FONDA4

not realizable for the American touring motor cycle because

its crash bar will rub on the ground at about 35 deg. or 40

deg. of tilt. The resulting transfer of load to a metal surface

reduces the side force and causes a skid-out, and also

reduces the righting moment due to side force. This reduc-

tion will probably exceed the increase due to load transfer;

the net excess overturning moment introduces a spill as

well as a skid.

A competition motor cycle uses no crash bar and has a

raised foot-rest and a raised silencer or none at all. The

steady tilt angle of the motor cycle, when operated

by

a

master rider over a smooth, lugh-fiiction surface,can indeed

approach 50deg., with cornering speeds well in excess 5 to

10 per cent) of those for automobiles on the same course.

Under less ideal conditions, one vehicle or the other may

hold the advantage; the differences are complexly de-

pendent upon course layout and surface condition

versus

accelerating and handling abilities. A critical factor for the

motor cycle is road roughness, since

it

causes reduction

of

load and, hence, of side force and righting moment. The

excess overturning moment will then induce a falling

motion which is combated by the natural free-control

stability (Wilson-Jonesl87) of the cycle and by the drivers

reactions. There will be, for instance, increased steer angle,

hence, increased slip angle and perhaps increased side force.

However, at a tilt angle of say 40 to 45 deg., the recovery

tendency wi l l not be sufficient, and consequently, a sudden

spill will occur.

It

is interesting to debate the effect of, for

instance, centre-of-gravity height, which in the steady

state is irrelevant. Investigations at C.A.L. are in progress

to obtain tyre data from normal motor cycle tyres, with their

differences of construction, to compare with data on the

Dunlop SRTT.

CONCLUSION

Recent, Current, and Future Tyre Tests

The

Air

Force-Cornell Tire Tester has been utilized since

the Dunlop tests for various programmes of cornering-

behaviour tyre tests. That is, various independent variables

such as pressure, load, camber, and construction have been

investigated to discover their effects upon the tyre force-and-

moment versus slip-angle behaviour. I n these cases, the

results are still under study and have not yet been reported.

Such tests do, however, constitute the major field of suit-

ability of this research device, and the number of con-

ceivable research problems (even among the above-quoted

variables) is virtually unlimited. It is becoming evident

that this vast programme must be guided according to

the suggestion of Hadeke1105 (Appendix XI) and others,

namely, that the empirical data should be analysed on a

basis of tyre theory. Thus, the whole programme is en-

compassed by and implicit in the problem of developing

and verifying tyre theory. T he major use of the Air Force-

Cornell tester, both current and future, therefore lies in the

gradual solution of this problem.

In research involving tyre noise, the analytical method

immelately becomes highly complex and the empirical

method may be used exclusively. By noise is meant, first,

audible noise (including squeal) and, second, tyre-behaviour

noise. Appreciable attention has been given to audible noise

recorded on magnetic tape and studied, in some cases, by

spectral analysis. The ease and precision of controlling the

test variables is a functional advantage, opposed by the

undesirably high ambient noise level of the truck. Study of

the transient variations of inflation pressure may be of value,

and methods for doing

so

are at hand. The second type of

noise, tyre-behaviour noise, has been only cursorily eval-

uated to date. By use of the two-axis recorder, continuous

(intinite-number-of-point) plots have been obtained of

side force against slip angle and aligning torque against

side force (Fig. 75). The force and moment signals were

lightly filtered, sufficient only largely to eliminate recorder

overshoot. These records reveal that the side force is slightly

noisy, and low-speed tests have indicated that this results

mainly from irregularity of pressure distribution and carcass

stiffness in the contact area, rather than from inertia-

induced load variations. The much greater noisiness of the

torque would be, understandably, explained by the same

phenomena. This high noise level explains the difficulty

experienced in obtaining consistent torque data. In either

case, any apparent average behaviour differences (attributed

to other variables) may be questioned when they approx-

imate or are smaller than this behaviour noise. Indeed, the

apparent close repeatability of the cornering

stiffness

(137

and

138

Ib. per deg. in Fig.

75)

cannot be maintained on the

average, although no rigorous tests for repeatability have

been made.

With regard to the future, the possibilities in testing may

be expressed in terms of possible modifications of the

equipment, some probable and some improbable. The most

improbable is the extension of tyre-behaviour data in

dry

sand (Kerrllg), because the present device does not have

the ideal

functions

for this type of test, nor could it main-

tain those it does have under sandy conditions.A possibility

is the testing of motor cycle tyres at 30 deg. to 50 deg. of

camber; most likely

this

test would involve no changes to

the tester, but would rather involve provision of a ditch to

accommodate the lowered load cell, while testing a t low

speed.

A series of major modifications actually under way are

those for the Tire Dynamics Investigations being sponsored

by the Air Force (MRB, ARL, Wright AFB), which will

furnish data on both transient and steady-state tyre be-

haviour. These data are needed for continued analysis of the

serious military problem of aircraft nosegear shimmy. For

this

programme, instrumentation modifications will include

new strain-gauge circuits by which each bridge gives a total

force or moment, rather than a component axle-tip force;

and will include accelerometers by which any hub-and

wheel inertia effects are removed from the side force and

load signals. Equipment modifications include a steering

servo-mechanism for pulse or sinusoidal inputs, a brake

installation, and a dual-wheel installation. The complexity

of this programme is a natural consequence of the desire to

predict prototype behaviour, rather than to chance a



17/20


OF

EXPERIMENTAL DATA

3 6 3

(a)

Side force against slip angle.

( b ) Aligning torque against side force.

Fig. 75.

Data of

Two-axis

Recoroh

prototype disaster. The resulting enlargement of the

capabilities of the tester will be of importance also to non-

military

interests.

The brake installation, for instance, will be important

for tests of tyre

braking

behaviour without slip angle and,

even more significantly, cornering behaviour with braking.

The effect of propulsive torque on cornering behaviour

should also, eventually, be investigated;

it

is just possible

that the

Air

Forces dual-wheel installation will permlt one

wheel to supply the other with power. With the brake

installation, the peak braking force

as

well as the peak side

force (and transitions thereto) may be investigated with

respect t o road materials and surface treatments. The 111

range of tyre behaviour m a y also be correlated, by means of

tyre theory, with friction studieson he contacting materials.

Effects of road roughness might be investigated, prefer-

ably at low speeds to eliminate suspension effects.

On

the

other hand,

an

oscillating test load might be applied to

duplicate, on smooth roads, rough-road and suspension

effects. Additional sensing elements might be added to

detect the steady and/or transient force distributions, as

well as the force-moment totals.

A

related investigation

would be the construction of an i n s m e n t e d wheel

or

suspension to allow force-moment measurements

of

tyres

on he car; slip-angle measurements would be required in

addition.



18/20

364 ALBERT

G .

FONDA

Speed effects might be investigated either in the zero-to-

critical range where they are minor, or in the critical range,

where the internal masses and dampings of the tyre are

excited with sufFicient rapidity to be influential. (Another

type of speed effect involves the 6lm break-through time on

wet roads). If necessary, the top speed of the truck could be

raised (for instance, by Jato units, with a tail fmfor stability)

or

the truck could be replaced by a high-speed bus,

wingless aeroplane, or rocket sled. The attractive alternative

of

the moving road also provides the usual advantages of an

indoor installation. The expense of such approaches

suggests substitution, if possible, of prediction theory

verified from data obtained at lover speeds, or on drums,

and then converted. The present test device was designed

for

the possibility of

drum

testing, with or without the

presence of the truck.

It is evident that the possibilities for empirical research

upon the pneumatic tyre are many and varied, and that

much future research effort upon these problems is justified

for the sake of improvements

in

vehicular transportation.

ACKNOWLEDGEMENTS

The sponsors of the research described are the Mechanical

Branch,

Aircraft

Laboratory, Wright Air Development

Center, U.S.A.F., which made possible the creation of the

apparatus

;

he Mechanics Research Branch, Aeronautical

Research Laboratory, Wright Air Development Center,

U.S.A.F., which is sponsoring tyre dynamics investi-

gations; the Dunlop Tire and Rubber Company of

America, whose programme of testing and analysis

supplied most of the presented data; and Cornell Aero-

nautical Laboratory, which made possible additional tests

and analysis, as well as most of the time for the writing

and presentation

of this

paper.

APPENDIX X

C A L I B R A T I N G AND Z E R O I N G

This description of pre-test procedures is given to convey certain

semi-routine, but practical, information of value to those who

contemplate the construction and use of similar equipment, and

is omitted from the main text only for its lack of general engineering

interest.

The oscillograph is a recorder which photographically plots

continuous histories (traces) of a number of points of light, of

which each maintains a position varying with an instrumented

force, moment, or position. Calibration consists of determining

each such rate of variation, or the slope of the output against input

plot, while zeroing consists of determining each trace position for

zero input, or the intercept of that plot. The

two

operations are

performed separately because a number of factors can affect the

zero, which is easily checked, whereas the calibration is inherently

stable and not easily checked.

Calibration is performed before every major programme of

testing, for instance once a month in periods of active test, al though

efforts are now being made to verify and utilize the inherent

calibration stability over even longer periods. The technique of

calibration is to apply known inputs, record the outputs,

and

plot

one against

the

other after developing, reading, and tabulating the

trace-position records. Positions are applied by reference to

protractors or inclinometers. Horizontal forces are applied with a

cable, pulley, and chain hoist from a lift truck and are measured

by a hanging beam balance. Vertical forces are applied by the

tester-loading system against a platform beam balance through an

hydraulic jack. Recently some continuous calibrations have been

made, in which each tester strain-gauge-beam signal was con-

tinuously and immediately plotted against a strain-gauge-proving-

ring signal by means of a 2-axis recorder. Prohibitive time would

have been required to obtain, read, and plot the same information

if

an

oscillograph had been used to record a long succession of

calibration conditions. The mud-shield effect described

in

Paper

I11was recognized only by use of t h i s continuous plotting equip-

ment. T here has been, however, no indication that this shield had

produced any serious effect upon prior test data.

Zeroing is performed at the start of each day of testing and, in

part, at the

start

of each set of runs on a given tyre. First, by using

a jack to support the wheelin mid-air, zero load, drag, and moments

are

applied and a record

is

taken. If a subsequent wheel change

appreciably affects unsprung (by the gauge beams) weight, this

zero is repeated. Second, while the test wheel, as well as the fifth

wheel, is freely trailed, records are made for zero side force and

slip angle. This procedure inherently produces a zero intercept of

the

F,

versus

a

data and is repeated for each tyre to remove any

effects of tyre construction dissymmetry. The balance potentio-

meters (Figs. 43 and 44,Paper 111) are adjusted to give approx-

imately zero bridge unbalance for typical zero inputs, but these

settings are not critical.

Certain zero trace positions are slightly shifted when the wheel

is put into rotation, since a horizontal link load is induced by

bearing-and-seal friction and appears as a drag force and an

aligning torque.

The

link load is evaluated every few months by

replacing the

l i i

with a spring scale, and calculated corrections

are thereafter made. This zero shift is absent when the brake-

torque linkage is fitted.

An

additional set of trace zero shifts does

occur when the wheel is cambered, due to

the

wheel-and-hub

weight, but

this

effect disappears when the data are resolved back

to

uncambered (stability) axes.

Another standard procedure is to set the height of the hinge box

on the bed-plate, in order t o adjust to zero the pitch attitude of the

load cells as influenced by variations of tyre size, load, inflation,

and camber. This procedure avoids the necessity for correcting

X

and Z vectors for pitch attitude,

or

equivalently, avoids mech-

anical trail as measured at the intersection of the Zmeasurement

a x i s

with the ground plane. These bed-plate settings are calculated

beforehand from knowledge of tyre height and variations in height

with pressure, load, and camber, some of which the tyre manu-

facturer can supply, and from knowledge of the truck height

variation with reacted load due

to

its suspension compliance. The

predicted settings are then checked on the road. A setting accuracy

of & &deg. (&A nch mechanical tral is maintained, and does

permit minor variations of load, pressure, and camber without

resetting.

APPENDIX XI

T H E O R Y O F L A T E R A L T Y R E D E F O R M A T IO N

Th is appendix is a recapitulation of the basic tyre theory introduced

by TemplelOs*(40) and von Schlippelol

and

utilized by a number

of subsequent theorists. There is much to indicate, however, that

the majority of the researchers a nd designers

in

the tyre industry

have little appreciation of the theory. Thi s is an unfortunate

circumstance, for the theory is quite simple and quite effective. For

t h i s

reason, a version of the derivation is now presented, based

on the more complete presentation by Hadeke1105 in his monumental

digest

of

present knowledge, but with an emphasis upon the

physical concepts involved.

T h e number following the astensk denotes a reference giveti by

HadekelloJ and i s specified in Append ix X I I of

this

paper.



19/20

T Y R E T E S T S A K D I N T E R P R E T A T I O N

O F

E X P E R I M E N T A L D A T A

365

Both Temple and von Schlippe express the lateral distortion

pattern of a tyre in terms of the shape of its deflected equatorial

line. In the contact area, this line (assuming no slippage) is immobile

relative to the ground, and therefore has the shape of the path of

the wheel, for example, straight for steady slip angle or when

non-rolling. Outside t he contact area, the deflexion (Fig. 76)

decreases toward zero in the manner of a stretched string (repre-

senting the circumferential cords tensioned by inflation) restrained

by lateral springs (representing the lateral component of stiffness).

*CONTACT LENGTH+

EQUATORIAL LINE

.+.

-

s--?

WHEEL CENTRE-LINE

Fig.

76.

Deflected Equatorial Line

This shape is approximated by the exponential relations

- + I

y

= y l e T (65)

for s > (forward of the contact area), and

- L+ / - s )

. . . . . (66)

Y = y z e

for s


20/20

366 A L B E R T G.

FONDA

on

a

in such a manner that y1 = oa and y2 =

o+2Z)a

(Fig.

7 9 ) .

Then substitution into equations

( 7 0 )

and

( 7 1 )

and differentiation

with respect to a gives

( 7 4 )

while d M , / d a remains unchanged from equation

( 73) ,

since the

rolling deformation consists merely of superimposed angular and

lateral deformations due to

Mz

nd

Fy,

espectively. These

deformations are nand

y

=

( u + l ) a ,

where by substituting the latter

into

equation

( 7 2 )

we obtain equation

( 7 4 ) ,

as would be expected.

Modifications to these equations are given by Hadeke1105 (quoting

Templelos* (40), von Schlippe and Dietrichlol, MaierlO5* (361,

Fromm99, Julienlos* (231, and Forsterlos*

(27))

in which various

effecrs are considered, such as beam stiffness of the carcass,

variation of

K

with cross-section shape changed by loading

(Thorsenlo7 and Andrewsll,), slippage in the contact area, longitu-

dinal slip, path curvature (Fig. 52, Paper 111), and so on. These

theories deserve study, development, and application by any

advanced student of tyre behaviour.

These are only second-degree effects, however. The primary

facets of tyre behaviour evolve from the theory and equations

given above. Th e three constants

1

u, and K, being basic, appear

repeatedly in various behaviour equations. Thus, a number of

expressions may be written for

K

and u in terms of empirical

measurements, such as

1

dFy/dy, dy/ds, and many others. These

overlapping solutions permit t he establishment of firm values for

K

and

U

T o quote Hadekel,

this

should be a much more rewarding

task han the oft-repeated (but always inconclusive) mere measure-

ment of particular elasticity characteristics (cornering power,

static elasticity, etc.), firstly, because the two basic parameters

K

and (I completely specify the behaviour of the tyre under both

static and rolling conditions, and secondly, because these para-

meters are more likely to exhibit clear laws ofvariation (with tyre

size, load, and inflation pressure) than other quantities.

APPENDIX XI1

R E F E R E N C E S

All references which are identified by superscript numbers without

parentheses will be found in the master reference list given in

Appendix

I11

of Paper I.

The remaining references, which appear with parentheses, are

from the more exhaustive reference list of Hadekel

(105)

and are

listed below:

105* ( 23) Julien, M. A. 1937 J1. SociCtC des Ingenieurs

de lAutomobile, April, Lenvirage et la Tenue de

Route.

105

( 2 7 ) Forster, B. (Undated) DKF, ZB 22, Versuche

zur

Feststellung des Haftvermogens von Personen-

wagen-Bereifungen.

105* (36) Maier,

E.

1943 LGL Report 169, Zur Frage der

Seitenbeanspruchungen von Flugzeugfahrwerken,

(M.O.S. T I B Library Translation 277 Lateral

Stresses on Aircraft Undercarriages.

105 (40) Unpublished work kindly communicated (to Hadekel)

by Professor G. Temple, F.R.S.

how to read tyre data-proceedings of the institution of mechanical engineers

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