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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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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
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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.
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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
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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
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TYRE TESTS AND INTERPRETATION
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
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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
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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
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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.)
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TYRE TESTS AND INTERPRETATION
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.
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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
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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
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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 :
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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
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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
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TYRE TESTS AND INTERPRETATION
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.
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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 & °. (&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.
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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
-
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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.
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