aircraft nasa data 49x17
TRANSCRIPT
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3 1176 00166 6305
NASA Contractor Report 165720
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NASA-CR-165720
I 9?J / ao.2 f SA COMPARISON OF SOME STATIC AND DYNAMIC G(MECHANICAL PROPERTIES OF 18x5.5 AND49x17 TYPE VII AIRCRAFT TIRES AS MEASUREDBY THREE TEST FACILITIES
Richard N. Dodge and Samuel K. Clark
THE UNIVERSITY OF MICHIGANAnn Arbor, Michigan 48109
Grant NSG-1494July 1981
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Nl\SI\National Aeronautics andSpace Administration
Langley Research CenterHampton, Virginia 23665
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TABLE OF CONTENTSPAGE
SUMMARY 1
INTRODUCTION 3
SYMBOLS 6
TEST FACILITIES AND PROCEDURESNASA FacilityFDL FacilityUniversity of Michigan Facility
RESULTS AND DISCUSSION
Static Test Results
Pure vertical loadingVertical spring rate:Contact patch:
Combined vertical and lateral loadingLateral spring rate:Lateral hysteresis:
Combined vertical and torsional loadingsTorsional spring rate:Torsional hysteresis:
Combined vertical and fore-and-aft loadingsFore-and-aft spring rate:Fore-and-aft hysteresis:
Slow-Rolling Yawed Test Results
Relaxation lengthSteady-state side forceSelf-aligning torque-
Dynamic Test Results
Pure vertical loadingYawed rolling side force-Self-aligning torque under yawed rolling-
CONCLUDING REMARKS
i
A COMPARISON OF
SOME' STATIC AND DYNAMIC MECHANICAL PROPERTIES OF
18X5.5 AND 49Xl7 TYPE' VII AIRCRAFT TIRES
AS MEASURED BY THREE TEST FACILITIES
Richard N. Dodge and Samuel K. ClarkThe University of Michigan
SUMMARY
Mechanical properties of 49xl7 and 18x5.5 type VII aircraft
tires were measured during static, slow rolling, and high-speed
tests, and comparisons were made between data as acquired on in-
door drum dynamometers and on an outdoor test track. In addi-
tion, mechanical properties were also obtained from scale model
tires and compared with corresponding properties fro~ full-size
tires. While the tests covered a wide range of tire properties,
results seem to indicate that speed effects are not large, scale
models may be used for obtaining some but not all tire proper-
ties, and that predictive equations developed in NASA TR R-64
are still useful in estimating most mechanical properties.
, of
•
INTRODUCTION
To analyze adequately the takeoff, landing and taxi
characteristics of modern day air~raft, it is essential that
landing gear designers have accurate data available on many
tire mechanical properties. The measurement of these mechani
cal properties, however, is an expensive and lengthy process
since aircraft tires are usually heavily loaded and operate of
high speeds, thus requiring large and costly test equipment to
simulate their operating conditions. Only two such facilities
exist in the United States for the controlled study of such
tire characteristics at realistic speeds and operating condi
tions: the Landing Loads and Traction Facility at the NASA
Langley Research Center, and the Flight Dynamics Laboratory
under the Air Force Wright Aeronautical Laboratories at Wright
Patterson Air Force Base (FDL).
At the present time, aircraft landing gear designers are
forced to rely on very limited aircraft tire mechanical property
data furnished by tire or component manufacturers or by the
government laboratories of NASA and the Air Force. Extensive
use is still being made of NASA Technical Report R-64, "Mechanical
Properties of Aircraft Tires" reference 1, which summarizes
the state of knowledge concerning mechanical characteristics
of such tires as it existed about 20 years ago, and based almost
entirely upon static or very slow rolling data. Almost nothing
is currently available which describes the influence of speed
on such tire characteristics.
3
4
Recognizing the lack of such data, aircraft industry
representatives have for some years ureed a coherent program
for assessing the influence of speed and other dynamic
characteristics on aircraft tire mechanical properties, and,
further, have urged programs designed to assess the continuing
validity of NASA TR R-64 in light of more modern aircraft tire
designs. These efforts became focused in the industry committee
which is primarily active in this area - the SAE Committee A5.
Under the sponsorship of this committee, a program was originated
jointly by the Landing Dynamics Office at NASA-Langley and
the Flight Dynamics Laboratory at Wright Patterson Air Force
Base. These two groups agreed to a co-operative test program
generated jointly by them in conjunction with the SAE A5
committee, and The University of Michigan agreed to conduct a
modest scale-model tire measurement program to determine the
adequacy of scale model techniques in assessing speed and
dynamic effects on aircraft tire mechanical properties.
Two Type VII, modern aircraft tire designs were chosen for
this program: size 49xl7 in a 26-ply rating and size 18x5.5 in
a 14-ply rating. The test plan originally prepared to meet the
needs of the program is given in Appendix B, and it basically
involves evaluating the usual vertical, lateral, fore-and-aft
and torsional static characteristics of both tire sizes, to
gether with me~surements of slow rolling relaxation length, cor
nering force, and self aligning torque. In addition, and most
important, dynamic vertical load deflection, vertical hysteresis,
cornering force and self aligning ~orque ,measurements were to be
carried out on both tire sizes over a speed range to 100 knots.
Each of these properties has important uses in analyzing
operating characteristics of the runway-tire-1anding gear
interaction in modern aircraft. For example, the vertical
load deflection characteristics directly affect landing gear
strut design, while lateral and torsional characteristics of
the tires are directly related to cornering and yaw response
and are thus important to shimmy analysis.. Tire fore-and-aft
elastic properties affect anti-skid and braking design, and
are therefore important in their own right.
The program was initiated in 1975 with the acquisition of
the tires through the Aeronautical Systems Division, Wright
Patterson Air Force Base and tests were conducted independently
by both NASA-Langley and the Flight Dynamics Laboratory. In 1978,
NASA initiated a Research Grant with the University of Michigan
to conduct an analysis of the obtained data and to examine
various methods for the transformation of the data from the
static to the dynamic case. The purpose of this report is to
present the results of that effort.
5
SYMBOLS
Values are given in both SI and U.S. Customary Units.
The measurements were made in U.S. Customary Units,
Ci Constants relating model spring constants to prototype
D - Outside diameter of free tire
E·h - Tire membrane stiffness
Fx
Fy
Fz
h
K
KAL
YMz
N
Po
Q
v
ax
ay
az
n
ny
~
'6
- Fore-and-aft force (ground force parallel to directionof motion)
- Lateral force (perpendicular to direction of motion)
- Vertical force
- Half-length of the tire-ground contact area (footprint)
- Spring constant
- Lateral spring constant
- Yawed-rolling - relaxation length
Turning or twisting moment about a vertical axis throughthe wheel center
- Cornering power
- Inflation pressure at zero vertical load (gage)
- Dimensionless force ratio used in relating model forcesto prototype forces
- Horizontal rolling speed
- Fore-and-aft deflection
- Lateral deflection
- Vertical deflection
- Dimensionless deflection ratio used in relating modeldeflections to prototype deflections
- Lateral hysteresis parameter
- Yaw angle
TEST FACILITIES AND PROCEDURES
The tires used in this program were 49x17, 26 ply-rating
and 18x5.5, 14 ply-rating, Type VII aircraft tires which were
selected in quantities of 5 each from Air Force inventory,
chosen from the same manufacturer and with closely spaced
serial numbers and dates of manufacture. Each of the tires
was subjected to three break-in taxi runs of two miles at rated
pressure and load. The scale model tires used in this study
were designed and built by the University of Michigan which
had experience (reference 2) in the modeling of aircraft tires.
The scale models were constructed to a 12:1 ratio for the
49x17 tire and to a 4:1 ratio for the 18x5.5 tire. Table 1
provides a summary of pertinent geometric properties of the
full-size tires and their corresponding scaled models.
The test plan for each tire is outlined in Appendix B. This
plan was used by each facility, although it was not possible for
each organization to measure all properties identified in the
plan.
NASA Facility.
NASA used the same basic test equipment to determine most
of the tire static vertical, lateral, and fore-and-aft stiffness
characteristics. This equipment consisted of a bearing plate
upon which the test tire rested under a vertical load, and the
instrumentation necessary to monitor the various tire loadings
and displacements. Tire loadings included the vertical load,
which was controlled by the test carriage hydraulic system,
and either the lateral or fore-and-aft load which was applied
to the bearing plate by means of a hydraulic piston. The
7
8
magnitude of the vertical load was measured by load cells
under the bearing plate, whereas other loads were measured
by a load cell located between the hydraulic piston and a
rigid backstop. The displacements were measured with dial
gages and motion transducers.
The dynamic tire data obtained by NASA came from tests
conducted on the Langley aircraft landing loads and traction
facility. A description of this facility can be found in
numerous NASA publications, of which reference 3 is a good
example. Both test carriages were employed in this program.
The large carriage with'a speed potential of 110 knots served
as the test bed for the 49x17 tire and the small carriage
capable of speeds to 120 knots was used in testing the smaller
tire. The runway surface for both tires was dry concrete.
The slow-rolling, quasi-static NASA data were obtained with
the same facility used to acquire the dynamic data except
instead of being propelled by the water jet the carriages were
towed over the test section by a tug.
FDL Facility
The Flight Dynamics Laboratory static and slow-rolling
quasi-static tests were performed on the flat surface Tire
Force Machine (TFM). The basic features of this machine
include a tire/wheel assembly housed in a frame containing
six load cells through which the loads are applied and the
resultant tire forces and moments are reacted, a twenty-foot
flat movable test bed, and a computer-controlled automatic data
logging system.
•
The dynamic data were obtained from the computer-controlled,
120-inch dynamometer test apparatus. The major features of this
apparatus are a test carriage which supports the tire and is
positioned by a servo-controlled hydraulic system, a 120-inch
diameter dynamometer wheel, and a complete process control
system which provides automatic sequencing and control of the
test dynamometer and receives, processes, displays and records
all test data.
A more complete description of these two test systems can
be found in references 4 and 5.
University of Michigan Facility
Static tire data at the University of Michigan were.
obtained primarily from tests conducted on its small scale
static test machine. This machine consists of a rigid bearing
plate mounted on ball bearings, a hinged dead-weight arm and
yoke for applying vertical loads to the test tire mounted in the
yoke, a screw drive and load transducer system for applying
and measuring lateral and fore-and-aft loads to the bearing
plate, and dial gages and variable transformers for measuring
displacements. A more complete description of this apparatus
is given in reference 6.
The slow-rolling quasi-static, yawed tests were conducted
on a 30-inch diameter cast iron road wheel discussed in reference
2. This apparatus consists primarily of a driven roadwheel,
a hinged arm equipped with a tire yoke, and transducers to
monitor lateral force and self~aligning torque.
Dynamic data were obtained from tests conducted on the
University of Michigan 40-inch diameter inside-outside road-
9
wheel. This apparatus consists of a driven cantilevered
roadwheel with apparatus similar to that on the smaller wheel.
All tests described in this report were obtained on the out
side surface of this wheel.
10
RESULTS" AND DISCUSSION
Since the participants in this test prog~am used different
equipment in making their measurements, it was necessary to
convert most of the raw data to some common format. This con
version was done, and to some extent it masked individual dif
ferences in measuring techniques, as, for example, curved steel
drums as opposed to flat concrete surfaces. However such a
presentation does allow direct comparison of results between
different test facilities.
Several pertinent tire mechanical properties were calcu
lated in terms of parameters defined in" reference I and these
are presented, where possible, to illustrate any changes asso
ciated with the newer type VII tires.
STATIC TEST RESULTS
Pure Vertical Loading - The load-deflection curves presented
in figure I for the 49xl7 tire and in figure 2 for the 18x5.5.
tire include the four vertical loading conditions. As is com
monly observed, a hysteresis loop in the vertical load deflec
tion curve is obtained but the load deflection relationship is
nearly linear for increasing load except for relatively low
values of the load.
While there is some variation in the data obtained between
the participants as noted in figures 1 and 2, no consistent dif
ference of any magnitude was observed between vertical load de
,flection data taken at different test facilities.
11
12
The scale model data seems to be within the same general
range of variation as the full size data.
Vertical Spring Rate: . Vertical spring rates were obtained for
each of the test conditions defined in figures 1 and 2 by
measuring the slope of the load-deflection curve extending from
its maximum to a point midway between the loading and unloading
portion of the curve, at one half the maximum tire deflection ,
as illustrated in figure 3. These vertical spring rates are
summarized in figure 4. Again the single dashed lines represent
spring rates calculated in the same fashion from the load
deflection curves predicted by the empirical formula of NASA
TR R-64, equation (23).
Contact Patch: Dimensions of the contact patch were obtained
for all static vertical loadings by inking or chalking foot
prints of the tires at each of the prescribed test conditions.
A summary of the measured contact patch lengths for both tire
sizes is presented in figure 5. The measurements agree well
among the three test facilities, and the contact patch lengths
calculated from equation (5) in NASA TR R-64 are also given.
These computed patch lengths seem to be in good agreement with
the measurements.
In general, as is evidenced from figures 1-5, measurements
representing vertical response of the tire under static loading
seem to be in good agreement from both full size test facilities
as well as from the scale model tire. In addition, formulas
derived earlier from NASA TR R-64 seem to be in good agreement
for all vertical stiffness characteristics with measurements
made on these more modern Type VII aircraft tires.
Combined Vertical and Lateral Loadings - When a stationary
vertically loaded tire is subjected to a lateral load per
pendicular to the wheel plane the tire experiences a corres
ponding lateral deformation, a vertical sinking and a lateral
shifting of the vertical force-resultant location. As the
lateral load is cycled from zero to a maximum, back through
zero to a minimum and returns to zero, a hysteretic load
deflection loop is generated. Such loops are illustrated in
figures 6 and 7 for the two test tires in question. Since it
has been observed that the nature of these loops is dependent
on the maximum amplitude of the applied lateral load', all test
data were obtained at lateral loads equal to 30% of the vertical
load so the comparisons between different test facilities could
be made.
Again, figures 6 and 7 show that both full-scale sets of
measurements and the model tire measurements seem to agree
quite well.
Lateral Spring Rate: Because of runway roughness, friction effects,
and data recording differences it was often necessary to smooth
the raw data obtained from these lateral load deflection curves.
Such smoothed data were used to determine lateral spring rates
and hysteretic effects described as follows.
Lateral spring rates were measured for all test conditions
by measuring the slope of the line joining the end points of the
load-deflection loop. A summary of these lateral spring rates
is shown in figure 8~ Again there is reasonably good agreement
between spring rates obtained from full scale and model tires,
and once more the formulation described in equation (33) of
TR R-64 agrees well with measurements.
13
Lateral Hysteresis: The static lateral hysteresis can be
obtained from the lateral load-deflection curves of figures 6
and 7 which indicate the energy dissipated during the loading
and unloading cycle. This energy loss is believed to be pri-
marily due to hysteretic effects in the tire materials. A
measure of this hysteretic loss is the ratio of the area of the
hysteresis loop to the total energy input to the tire during
the loading cycle, measured by the two triangular areas under
the load-deflection curve. This ratio, denoted by n , is used toy
describe the lateral hysteresis ratio of the tires and is similar
in concept to tan 8 of a viscoelastic material. Curves of this
damping ratio are plotted against vertical load in figure 9.
Agreement seems to be good between the full scale and model tires
for the 49x17 size, but for the 18x5.5 size the scale model
version seems to exhibit somewhat more hysteresis than its full
size counterparts.
Again, although not to the same degree as for vertical loads,
measurements representing lateral response of the tires under
static loading are similar from all three test facilities, in-
eluding scale modeling.
Combined Vertical and Torsional Loadings - As the twisting moment
is cycled a torque versus angle-of-twist curve is generated
which produces a loop caused by hysteretic loss in the tire ma-
terial. Such measurements on full size tires are difficult to
make since equipment is not commonly available for producing a
torque large enough for the high loads commonly encountered in
aircraft tires. However, the University of Michigan scale model
tires can be loaded in torsion with relatively small loads, and
the results from tests on such scale tires are shown in figure 10.
14
Torsional Spring Rate: It is difficult to assess the validity
of the data presented in figure 10 since there are no full
size tests with which to compare. However, torsional spring
rates can be obtained from the slope of the line joining the
end points of load-deflection loops. The results from such
measurements are given in figure 11. These data may be compared
with values predicted by equations (44) in reference 1, and
there is general agreement between the two.
Torsional Hysteresis: As was the case with static lateral
deformation, torsional loss co~fficients can be calculated from
loops generated in load-deflection curves, such as those of
figure 10. As was done in the lateral case, loss coefficients
were obtained by using the ratio of the loop area to the triangu~ar
areas representing energy input to the tire during .deformation.
These loss coefficients are shown for the 49x17 tire in figure
12 as taken from scale model data and are of approximately the
same magnitude as those found for the lateral tests. This
similarity should be anticipated since tWisting motion is
essentially lateral motion of a non-uniform distribution.
Combined Vertical and Fore-and-Aft Loadings - When a stationary
vertically loaded tire is subjected to a fore-and-aft load the
tire experiences a corresponding fore-and-aft deformation, a
vertical sinking and a fore-and-a£t shifting of the vertical
force resultant. As this fore-and-aft load is cycled back and
forth, a load-deflection curve is generated fo~ming a closed
loop which is attributed to hysteretic characteristics of the
15
tire material. These fore-and-aft load tests are difficult to
perform because they require the measurement of the relatively
small deformation under large loads. Orily the Flight Dynamics
Laboratory has equipment at this time suitable for such measure
ments, and data from the 49x17 tire are presented in figure 13
and data from the 18x5.5 tire are presented in figure 14. Since
fore-and-aft deflection curves are dependent on the maximum
amplitude of the applied fore-and-aft force, all test data was
taken at ± 15% of the vertical load carried by the tire.
It would seem logical to attempt to use small scale tire
models for the generation of fore-and-aft stiffness character
istics since the loads involved should be considerably less
than those needed for the full size tires. However, measure
ments on such models suffer from two difficulties:
(a) Full size tires may be expected to exhibit a certain
amount of slip and realignment in the contact patch area,
which may not apply to small scale models, particularly in the
presence of the large loads induced in the full size tires.
(b) The model scaling laws for the small size tires are
somewhat different for fore-and-aft motion than for the other
types of loadings and displacements since fore-and-aft dis
placements of a tire are highly dependent upon carcass and tread
material stiffness.
Because of the difficult nature of the measurements here
some of the data were smoothed prior to being included in the
plots shown in figures 13 and 14. "
16
Fore-and-Aft Spring Rate: Fore-and-aft spring rates were
measured for each test condition. These rates were again
determined by measuring the slope of the line joining the end
points of the fore-and-aft load deflection loop. A summary
of these spring rates is shown in figure 15.
Fore-and-Aft Hysteresis: A loss coefficient can be measured
for the fore-and-aft load deflection loops, similar in definition
to the loss coefficients obtained for lateral and torsional
loadings. This coefficient was computed from the ratio of the
area under the loop to the area representing energy input to
the tire during the loading cycle. Such data on loss coeffi
cients is given in figure 16. Note that these coefficients
do not vary significantly with vertical load and exhibit values
of the same general magnitude as lateral and torsional hysteresis
coefficients.
17
18
SLOW-ROLLING YAWED TEST RESULTS
The three mechanical tire characteristics reported in
this section all occur when a tire is yawed with respect to
its direction of motion and then slowly rolled straight ahead
with the yaw angle ~ held constant. When rolling commences,
the tire builds up a lateral force perpendicular to the wheel
plane which exponentially approaches a steady-state value.
The rapidity with which this force builds up is characteristic
of the tire and is called the yawed rolling relaxation length
when it is measured as a distance traversed by the axle. After
steady state conditions are reached the lateral force and self
aligning torque, defined as the moment about the vertical
steer axis of the wheel center, act on the axle and in turn
on the vehicle. These quantities are also functions of the yaw
angle of the tire.
Relaxation Length - It is common for tests of yawed rolling
relaxation lengths of tires to produce results with consider
able scatter and the data collected from this study proved to
be no exception. Figures 17a and 17c illustrat~ composite
plots of the results from the three test programs reported here.
This is not unlike data reported from other sources.
String theory, reference 7, implies that for constant inflation
pressure the major parameter affecting relaxation length is
vertical load or tire deflection. Because of this, the relax-
ation lengths at different yaw angles but at the same load were
averaged, and these values are plotted as a function of the load
in summary plots given in figures 17b and 17d. They show that
the three sets of tests, two full size and one scale model,
•
y~eld similar average values for the relaxation lengths for
both tires, with some variation on the 18x5.5 tire. Predic-
tions made from equation (64) in reference 1 are also given
in these figures, and agree surprisingly well with the measure-
ments reported .
One reason for the apparent wide scatter in relaxation
lengths is found by examining the nature of such measurements.
Figure 18 is a plot of side force versus distance traveled at
fixed yawed angle. The force builds up from zero to a steady
state value in a nearly exponential manner. Relaxation length
is defined as the distance traveled for the side force to
build to (I-lie) of its steady state value. In figure 18 it
can be seen that the determination of the steady state value
requires a certain amount of judgment because of circumferential
irregularities in the tire side force. Obviously this choice
can influence the relaxation length considerably.
Steady State Side Force - Tire steady state side force increases
with increasing yaw angle for fixed vertical load in a relatively
linear fashion for the relatively small yaw angles specified
in this test plan. This force will eventually approach asymp~
totically a maximum value controlled in part by the coefficient
of friction between the tire and runway surface. Figures 19
and 20 show that the three different sets of tests produced
comparable values for side force under most of the test conditions
used. The scale model conversion factors used here are the same
as used for the static vertical load-deflection data.
The interaction of side force and yaw angle on vertical
load can be observed somewhat more clearly in carpet plots
19
conventionally used for displaying such data. Carpet plots
for the side force on both test tires are given in figures 21
and 22. From these it is seen that the increase of side force
with yaw angle is strong, as is expected, but also that for
fixed yaw angle the side force remains relatively constant for
increasing load except at angles above 6°. Care should be
taken in comparing data between different laboratories since the
results are dependent on the friction surfaces used.
The slope of the cornering force versus yaw angle curves at
0 0 yaw is defined as tire cornering power, and is a measure of
tire lateral or steering stiffness. Data on this is presented
in figure 23 for both tire sizes tested, and predictions from
equations (83) in reference I are also given.
Self-Aligning Torque - The measurement of self-aligning torque
against yaw angle is more difficult than the measurement of
side force, since the quantities measured are smaller and can
depend on tire force irregularities. Self-aligning torque data
for the 49xl7 and 18x5.5 tires are given in figures 24 and 25.
In figure 24 it should be noted that the maximum self-aligning
torque is reached at a yaw angle less than 9° on the full sized
tires, while the scale tires exhibit increasing values of self
aligning torque up to the maximum yaw angle. The higher torque
noted for the scaled tires is attributed to the higher friction
coefficient available by virture of the lower tire contact
pressures.
Carpet plots of self-aligning torque, yaw angle and vertical
load can be constructed as done previously for side force
values. These are shown for the two test tires in figures 26
20
•
and 27. In general these show that at fixed yaw angle the
self-aligning torque increases with increasing tire load.
21
DYNAMIC TEST RESULTS
Pure Vertical Loading - A thorough study of the vertical load
deflection characteristics of the two tire sizes used in this
program was conducted at various surface speeds according to
the test plan in Appendix B. Basically the test plan called
for vertical load-deflection curves at 5, 50, 75, and 100 knots,
with maximum vertical loads of 50%, 75%, 100%, and 125% of
rated loads, all at rated inflation pressure. Typical curves
from such tests are shown in figure 28. Again, as might be
expected from quite different t~st facilities, the participants
produced load-deflection curves having slightly different
characteristics. For example, the NASA landing loads track
produces load-deflection curves somewhat sensitive to runway
roughness, which is to be expected. On the other hand, data
taken on smooth cylindrical drums such as obtained from the
Flight Dynamics Laboratory and from the University of Michigan
scale model studies are smoother but less realistic since they
include the effects of drum curvature.
Vertical spring rates were calculated for each of the
forward speed test conditions in the same manner as were the
static spring rates. Summaries of these spring rates are given
in figures 29 and 30. In general there appears to be little
influence of speed on vertical spring rate of a free rolling
tire.
It has been observed in other test programs, (see 7.2.2
of reference 8), that the hysteresis loop in the vertical load
deflection curve of a rolling tire is much smaller, or even
vanishes altogether, as compared with the size of the hysteresis
22
in a stationary tire under a vertical load. This negligible
hysteresis implies that the effective damping of the vertical
motion produced by the rolling tire is negligible when compared
with the damping experienced by the stationary tire. This
phenomenon is illustrated in figure 31 where various load
deflection curves have been plotted for the University of
Michigan scale model tire under a variety of speeds. Their data
merely confirm a phenomenon which has been observed in other
test programs.
Yawed Rolling Side Force - When a wheel is yawed with respect
to its direction of motion and then rolled forward with a yaw
angle held constant a side force perpendicular to the wheel
plane is generated. This side force comes from the elastic
deformation of the tire carcass caused by friction forces in the
contact patch. These forces were measured by each of the three
participants in this test program under a variety of test condi
tions. Summaries of these results are given in figures 32 and
33. While there is some scatter in the data, in general a
conclusion seems to be that there is little influence of speed
on side force for either of these tires up to a speed of 100
knots.
The interaction of side force, speed, and yaw angle at a
fixed load may be seen more clearly from carpet plots such as
those presented in figures 34 and 35. From these it is clear
that side force depends primarily upon yaw angle as would be
expected.
23
24
Table 2 shows the results of computations of cornering
power using data from slow rolling tests, and the formulation
for cornering powe~ equation (83) reference 1. It is compared
with measured data taken at 50 knots to determine if slows~eed
mechanical properties can be used to calculate cornering power
at higher velocities. Note that agreement is not particularly
bad.
Figure 36 is a plot of data taken from the last column of
Table 2, illustrating cornering power versus vertical load at
a speed of 50 knots. This figure is similar to figure 23 and
shows that the calculated values of cornering power at 50 knots
do not agree quite as well with the experiment as those values
done under slow rolling conditions.
Self-Aligning Torque Under Yawed Rolling - When a tire is yawed
with respect to its direction of motion by an angle and then
rolled straight ahead with the yaw angle held constant, a self
aligning torque is generated by the interaction of the tire and
the contact surface. This torque may be visualized as a moment
about a vertical axis through the wheel center. Values for this
self-aligning torque were measured by each of the facilities
involved in this program and for the various test conditions
described in the original test plan.
Data for the variation of self-aligning torque with speed
for various yaw angles is presented in figures 37 and 38. As
previously discussed, this type of measurement is difficult to
carry out, even under slow rolling conditions. Under dynamic
conditions it is doubly difficult since self-aligning torque
is quite sensitive to surface irregularities and tire construction.
For that reason it is difficult to achieve good correlation between
measurements made at different locations, and it is also difficult
to assess the value of scale modeling here. The only general
trend that can be drawn from this data is that there is a slight
decrease in self-aligning torque as the speed of the tire increases.
A somewhat more comprehensive illustration of self-aligning
torque versus speed and yaw angle at fixed vertical load is
given in figures 39 and 40. These semi-carpet plots illustrate
somewhat more clearly the slightly decreasing nature of self
aligning torque with speed. They also clearly illustrate the
non-linear relationship between self-aligning torque and yaw
angle for constant speed and vertical load.
Overall there seems to be considerable variations between
values of self-aligning torque measured under runway and drum
conditions, again possibly due to two reasons:
(a). The influence of runway or drum surface friction
effects on self-aligning torque. Obviously a concrete runway
and a steel drum present widely different friction limits to the
tire contact patch.
(b). The curvature effect of the drum on self-aligning
torque can be significant.
Overall it appears that while correlation is difficult to
obtain between drum and runway tests, speed does not signifi
cantly affect the maximum value of self-aligning torque
obtained, although the angle at which the maximum occurs is not
the same for each test facility.
25
26
CONCLUDING REMARKS
There were several objectives to this study, but
the major ODes are as follows: a) Determine the relationship
between tire mechanical properties obtained statically, quasi
statically and dynamically, b) Examine differences in measured
tire properties between data taken on runway surfaces and on
dynamometer drums, c) Evaluate the role of scale modeling in
determining mechanical properties of aircraft tires, and d)
Explore the application of empirical formulas derived in TR
R-64 to more modern Type VII aircraft tires.
As has been observed before, it was found in the series
of tests that the hysteresis characteristics of a rolling tire
were negligible compared to the hysteresis found infue stationary
tire, both under conditions of vertical oscillation.
Most of the effects measured in this study showed little
or no change with speed up to about 100 knots. For example,
vertical spring rate of the tires did not change significantly
nor did side forces generated due to rolling at a yaw angle.
However there seems to be less consistency to self-aligning
torque data. In some cases it appe~red to be rather independent
of speed, while in other cases it showed some variation with
speed, usually decreasing as the speed became higher. The nature
of this particular relationship is dependent on the magnitude
of the yaw angle.
The level of agreement between test facilities was good
for static mechanical properties, since both facilities used
flat surfaces for such measurements. Measurements made dynamic
ally showed less agreement, probably because the curvature effects
associated with the steel dynamometer drums may have caused
some differences in properties, particularly self-aligning,
torque. Generally agreement was good for side force and self-
aligning torque for small yaw angles, but measurements tended.
to differ at larger yaw angles as curvature effects became more
pronounced.
Scale modeling of tire mechanical properties has generally
proved to be satisfactory for obtaining large quantities of data
at low cost. For example, static vertical load-deflection
curves from model tires agree well with full size tire data, and
lead consequently to good agreement for spring rates and contact
patch lengths. Similarily lateral load-deflection characteris-
tics agree well between scale models and the full size tires,
although hysteresis effects are not quite as closely modeled as
the stiffness properties.
Scale modeling does not seem to be adequate for fore-and-
aft stiffness measurements since the scaling laws involving
translation from small models to full size tires are quite
different for this property than for the other properties.
Fore-and-aft characteristics depend almost entirely on the elas-
tic stiffness of the tire carcass, while for vertical and lateral
properties the inflation characteristics are dominant.
Scale modeling of both slow rolling and dynamic effects
seems also to be quite good. Side force and self-aligning
torque both seem to agree well at relatively small yaw angles
but not at larger yaw angles. Similarily, speed effects seem
to agree quite well between model and full size tires.
27
28
In summary it appears that scale modeling of aircraft
tire mechanical properties is warranted, provided that care
is taken to use it judiciously in those areas where it has
proven to be successful.
Finally, it is encouraging to note the good agreement
between the formulations developed in NASATR R-64 some years
ago to the tire mechanical properties measured on these more
modern Type VII aircraft tires. Load-deflection curves and
vertical spring rates are well represented, as are contact
patch lengths, lateral spring rates, and relaxation lengths.
Predictions of fore~and-aft spring rates, slow rolling cornering
power and cornering power at high speeds can not be confirmed
as well because of variations in measured data. However, due
to the relatively speed insensitive nature of mechanical
properties measured here, it may be concluded that the data from
TR R-64 probably apply equally well to dynamic tire characteris
tics as to slow speed characteristics. This is one of the
major conclusions of this work.
REFERENCES
1. Smiley, Robert F. and Walter B. Horne, "Mechanical Propertiesof Pneumatic Tires With Special References to Modern Aircraft Tires", NASA TR R-64, National Aeronautics and SpaceAdministration, Washington D.C., 1960.
2. Clark, S.K., R. N. Dodge, J. I. Lackey, and G. H. Nybakken,"The Structural Modeling of Aircraft Tires", AIAA PaperNo. 71-346, AIAA, N.Y., 1971.
3. Tanner, John A., "Fore-and-Aft Elastic Response of 34x9.9,Type VII, 14 Ply-Rating Aircraft Tires of Bias-Ply, BiasBelted, and Radial Design", ANSA TN D-7449, NationalAeronautics and Space Administration, Washington D.C., 1974 ..
4. Hampton, James R., "Aircraft Tire Mechanical Property Testing",Paper presented at 4th Symposium on Nondestructive Testingof Tires, 23-25 May 1978, Sponsored by Army Materials andMechanics Research Center.
5. "Air Force Flight Dynamics Laboratory Landing Gear TestFacility Wright-Patterson Air Force Base", Brochure prepared'by the Mechanical Branch Air Force Flight Dynamics Laboratory1977.
6. Dodge, R. N., R. B. Larson, S. K. Clark, and G. H. Nybakken,"Testing Techniques for Determining Static MechanicalProperties of Pneumatic Tires", NASA CR-2412, NationalAeronautics and Space Administration, Washington D.C.,June 1974.
7. Von Schlippe, B., and Dietrich, R., "Zur Mechanik of Luftreifens" (The Mechanics of Pneumatic Tires.) JunkersFlugzeug-und Motorenwerke, A-G. (Desau). (Translationavailable from ASTIA as ATI 105296)
8. Clark, S. K., "Mechanics of Pneumatic Tires", NationalBureau of Standards Monograph 122, National Bureau of Standards, Washington, D.C., 1971.
29
Appendix A
The basic concept used in modeling mechanical properties
of aircraft tires is shown in figure A-I. After considerable
experimentation it has been verified that most tire elastic
stiffnesses are linearly proportional to inflation pressure.
This conclusion holds for vertical stiffness, lateral stiffness,
fore-and-aft stiffness and torsional stiffness.
Notice in figure A-I that the intercept is not zero at zero
inflation pressure, but rather some positive value. This
observation gives rise to the concept that a typical tire stiff
ness value may be expressed analytically as shown in equation (A-I),
(A-I)
30
where K represents a typical tire spring rate, the product "Eh"
represents tire membrane stiffness, which for the same cord angle
between model and prototype may be expressed approximately as the
number of plies times the end count times the cord modulus. PO
is the inflation pressure and D is the tire diameter, used here
as a characteristic length. CI and C2 are constants which must
be determined from experiment. In equation (A-I), the influence
of the tire carcass is expressed by the product CIEh. The
influence of the inflation pressure in the tire is given by the
term C2POD. In the formulation CI and C2 are constants for
each tire and for each different stiffness property under considera-
tion.
In view of the fact that equation (A-I) represents the spring
rate, then the load carried by the tire may be represented in
equation (A-2) as derived directly from equation (A-I) where F
is equal to a typical tire force.
... •
(A-2)
In Eq. (A-2), the tire diameter D has been inserted in the deno-
minator of each side of the equation, so as to retain a dimension
oless tire deflection (D)'
Practically we know that a non-linear load deflection
curve is formed when either a model tire or a full size tire is
cyclically loaded. If such a curve could be reduced to dimen-
sionless form then it should be the same for both model and
prototype. Alternately if one could determine the dimensionless
load deflection curve for the mode, then it could be used to
predict the full size load deflection curve. This process uses
Eq. (A-2) as its basis, since it is a dimensionless load-deflection
relation.
We may achieve this by reducing the load-deflection loop on
the model to dimensionless form and then reevaluating it back
up to the true dimensions of the full size tire. This may be
done in the three steps illustrated in figure (A-2)., where the
variables used are the dimensionless force and the dimensionless
deflection as given by Eq. (A-3).
'IT = FjD = (A-3)
owhere g is the general functional form and D is a dimensionless
variable.
In figure (A-2a) the model force-deflection curve is shown
as originally taken on the model tire. This may be reduced to
a dimensionless form by scale change as given by figure (A-2b),
using the variables as given in Eq. (A-3). These may then be
31
32
expanded to the full size tire by the relations between the
diameter of the full size tire and model, and between the
products Eh and POD of the full size tire and model. This is
illustrated in Figure (A-2c) . In practice this is nothing more
than a scale change of the original load deflection curve taken
on the model tire. This concept is simply that if one reduces
the load deflection curve of either the model tire or the full
size tire to a dimensionless form, then those two curves should
be identical if scale modeling has been done properly.
It is necessary to devise a means for determining the
constants CI and C2 which appear in Eqs. (A-I), (A-2), and (A-3).
This may be done by constructing the scale model of the tire and
measuring the appropriate spring rate as a function of inflation
pressure as shown in figure (A-I). By taking a series of
measured spring rates at different inflation pressures, this curve
can be produced for anyone of the tire stiffness properties.
For example, figure (A-3) shows actual data for the 49xl7 model tire
for the vertical spring rate as a function of inflation pressure
for three different model tires. One can see the excellent
linearity obtained from this data.
In figure (A-3) it is seen that the three different scale
models have a very linear relationship between vertical spring
rate and inflation pressure, so that the constant CI may be
determined from the intercept of the line with the ordinate,
while the constant C2 is determined from the slope of the line.
From figure (A-3) and Table lone can calculate the
coef~lcients required to convert model static vertical load
deflection data to full size data fdr -the 4HxT7 tire. First,
the end count and ply thickness were the same for the full
size tires and models used in this study. Thus the "Eh" was
directly proportional to the number of plies. Therefore:
where C1Eh = 28.22 and C2D = 5.457 but "Eh" = ,2 and D = 4,
Fm
= 1.3645.457
4
Q =
thus: Cl = 28.22 = 14.11 and C22 =
Referring to figure (A-2b) and (A-2c) :
F = DpQ[C1Eh + C2DPO]p p Dm[C1Eh + C2DPO]m
where subscript m refers to the model and p refers to the full
size. Substituting:
F =P
Using data from Table 1 and assuming C1Eh and C2D are the same
for model and prototype:
F = {48P 4
[14.11(26) + 1.364(170)(48)]}F
[28.22 + 5.457(50)] m
F = 458 FP m
This implies that to convert a vertical force on the 49x17 model
tire to full size, the model value must be multiplied by 458.
Similar coefficients were obtained for the other static elastic
properties of each tire size.
The deflection coefficient was simply the scale factor:
0p = 4: om = 120m for 49x17
33
Table A-I presents a complete tabulation of all conversion
factors used in this report.
Table A-I - Conversion Factors Used in Converting UM Model
Data to Full Size Data - Dimensionless
._~---
PO PoTIRE Full Size Model Fz Fy Fx Mz Oz Oy Ox
1482 kPa 103.4 99.2 120 - - 4 4 4kPa
18x5.5 (15 psi)-
(215 psi) 344.8 51.6 53.5 - - 4 4 4kPa
(50 psi)
1172 kPa 137.9 1005 1005 557 5880 12 12 12 IkPa(20 psi) I49x17 (170 psi) 344.8 458 458
I119 4077 12 12 12
kPa(50 psi) I
I
Fz = vertical load 8 = vertical deflectionz
F = lateral load ° = lateral deflectiony y
F = fore-aft load ° = fore-aft deflectionx x
M = self aligning torquez
34
Appendix B
The details of the test plan used to produce the data
in this report are listed below:
I. Static Mechanical Properties (each loading at 4 tire locations,90° apart)
A. Vertical Load
1. Vertical load deflection as per SAE AIR 1380,wherethe vertical loads are to be 50, 75, 100 and 125percent of the tire rated load; the inflation pressure prior to loading is to be maintained at therated value.
2. Contact patch lengths measured under each of thevertical loads.
B. Lateral Load (Maximum lateral loads limited to ±30% ofthe vertical loads
1. Lateral load-deflection under each vertical load asper SAE AIR 1380
2. Lateral hysteresis for all tests in B-1.
3. Center of pressure shift as per SAE AIR 1380 forall tests in B-1.
C. Torsional Load (Maximum torsional loading limited to±80% of linearity)
1. Torsional load-deflection curves for all verticalloads.
2. Torsional hysteresis for all tests in C-l.
D. Fore-and-aft Load (maximum fore-and-aft loads limitedto ±15% of the vertical load.
1. Fore-and-aft load deflection curves for all vertical,loads.
2. Fore-and-aft relaxation length for all tests in D-l.
3. Fore-and-aft hysteresis measurements for all testsin D-l.
4. Fore-and-aft center of pressure shift for all tests inD-l.
35
36
II. Quasi-Static SloW-Rolling Yawed Mechanical Properties(All tests at rated inflation pressure).
A. Cornering Force - Fully developed cornering force atslip angels of 1,3,6, and 9 degrees at the four verticalloadings.
B. Self-Aligning Torque - Fully developed self-aligningtorque at slip angles of 1,3,6, and 9 degrees at thefour vertical loadings.
C. Lateral Relaxation Length - As determined by transientyawed rolling tests under the four test vertical loadsand slip angles of 1,3,6, and 9 degrees.
D. Lateral Center of Pressure Shift - as per SAE AIR 1380for all tests in II-A.
III. Dynamic Mechanical Properties (All tests at rated inflationpressure).
A. Vertical Load
1. Load-deflection curves up to the four test verticalloadings at speeds of 5, 50, 75, and 100 knots.
2. Hysteresis loss for all tests in A-I.
B. Cornering Force - Cornering force versus slip angleat 5, 50, 75, and 100 knots, at the four test verticalloadings for slip angles of 1,3,6, and 9 degrees.
C. Self-Aligning Torque - Self-aligning torque versusslip angle at 5,50,75, and 100 knots at the four testvertical loadings for slip angles of 1,3,6 and 9 degrees.
TABLE 1 - GEOMETRIC PROPERTIES OF THE TEST TIRES
GeomAtrie Property
Ply Rating
Max. Outside Dia.
Min. Outside Dia.
~,rax. Width
Min. Width
Shoulder Diameter
Shoulder Width
T.Ileight
Maximum Load
Hated Inflation(unload)
Rated Inflation(load)
Aspect Ratio
Loaded Radius'at Rated Conditions
Flange Diameter
Rim Diameter
19x17 18x5.5
Full Size Model Full Size Model
26 2 14 4
125.17 em 10.16 em 46.23 em 11.43 em(49.28 in. ) (4.00 in. ) (18.20 in. ) (4.50 in. )
119.84 em 43.18 em(47.18 in. ) (17.00 in. )
43.76 em 3.61 em 14.94 em 3.43 em(17.23 in. ) (1. 42 in.) (5.88 in.) (1.35 in.)
39.45 em 13.16 em(15.53 in. ) (5.18 in. )
109.22 em 41.15 em(43.00 in. ) (16.20 in.)
36.83 em 12.70 em(14.50 in.) (5.00 in. )
907 N 69 N(204 1bs) (15.50 1bs)
176.1 kN 378 N 27.6 kN 506 N(39600 1bs) (85 Ibs) (6200 1bs) (113.7 1bs.)
1172 kPa 345 kPa 1482 kPa 345 kPa(170 psi) (50 psi) (215 psi) (50 psi)
1220 kPa 1544 kPa(177 psi) (224 psi)
0.84 0.87
51.31 em 19.05 em(20 .. 20 in. ) (7.50 in. )
56.69 em 4.98 em 24.76 em 6.25 em(23.50 in. ) (1.96 in. ) (9.75 in. ) (2.46 in. )
50.80 em 20.32 ern(20.00 in.) (8.00 in. )
37
w00
Table 2 - Measured and Calculated Values of Cornering Power
N = 'IT180 (Ly + h)kA kNjdeg (lbjdeg)
dF Ly h k' Calculated N Measured NTire and Facility Fz 1jJ=0 1\
d1jJ' Njdeg cm cm Njcm kNjdeg 50 knotskN Measured N (lbjdeg) (in) (in) (lbjin) (lbjdeg) kNjdeg(lb) (lb/deg)
49x17 26 PR 200.2 11100 58.4 27.99 8835 13.33 11.68Po = 1172 kPa (45000) (2500) (23.0) (11. 02) (5045) (2996) (2625)
(170 psi) 176.1 11100 66.0 26.42 9110 14.70 14.22(39600) (2500) (26.0) (10.40) (5202) (3305) (3196)
NASA132.1 9880 55.6 23.39 9519 13.13 12.93
(29700) (2222) (21. 9) (9.21) (5436) (2952) (2908)
88.1 10500 51.3 19.86 10582 13.14 12.15(19800) (2352) (20.2) (7.82) (6043) (2955) (2732)
..._- .... ~ .._, ......_...-.' ~ -~,,~._.
220.2 8150 59.7 30.43 6584 10.35 7.17(49500) (1833) (23.5) (11. 98) (3760) (2328) (1612)
176.1 8900 62.2 2731 6975 10.90 7.53(39600) (2000) (24.5) (10.75) (3983) (2450) (1693)
FDL 132.1 9200 61.5 24.00 7343 10.96 7.38(29700) (2069) (24.2) (9.45) (4193) (2463) (1660)
88.1 9880 54.6 19.94 7646 9.95 5.82(19800) (2222) (21. 5) (7.85) (4366) (2237) (1308)
.i
:
• • • •
Table 2 - Measured and Calculated Values of Cornering Power
N = 1~0 (Ly + h)kA kN/deg (lb/deg)
•
dF Ly h k A Calculated N Measured NTire and Facility Fz dljJ' ljJ=O N/deg cm cm N/cm kN/deg 50 knots
kN Measured N (lb/deg) (in) (in) (lb/in) (lb/deg) kN/deg(lb) (lb/deg)
221.5 10400 57.2 31.55 6355 9.84 -(49800) (2333) (22.5 (12.42) (3629) (2212)
170.8 11100 53.3 28.50 7260 10.69 8.93(38400) (2500) (21. 0 (11.22) (4146) (2403) (2007)
UM127.2 11600 42.7 2393 8619 10.02 10.31
(28600) (2609) (16.8 (9.42) (4922) (2252) (2319)
86.3 11700 30.2 20.12 9807 8.62 7.54(19400) (2631) (11. 9 (7.92) (5600) (1937) (1695)
18x5.5 14PR 34.5 1454 15.5 10.01 4164 1. 85 -
Po = 1482 kPa (7750) (327) (6.1 (3.94) (2378) (417)- ;0
(215 psi) .•..
27.6 1481 9.6 9.27 4254 1.40 -(6200) (333) (3.8 (3.65) (2429) (316)
20.7 1632 11.2 8.30 4662 1. 58 -NASA (4650) (367) (4.4 (3.27) (2662) (356)
13.8 1690 7.9 7.06 4536 1.18 -(3100) (380) (3.1 (2.78) (2590) (266)
!iI
II
Iw .l..O
Table 2 - Maasurad and Calculated Values of Cornoring Power
N = 7T180 (Ly + 11)1\:>.. l\:N/dcg (lb/dcg)
dF Ly h k/,. Calculated N Measured NTire and Facility Fz . d\p' \jJ=0 Njdeg cm cm N/cm kN/deg 50 knots
kN Measured N (lb/deg) (in) (in) (lb/in) (lb/deg) kN/deg(Ib) (Ibjdeg)
34.5 16C1 39.6 10.03 3269 2.83 -(7750) (360) (15.6) (3.95) (1867) (637)
27.6 1512 36.8 9.40 3380 2.73 -(6200) (340) (14.5) (3.70) (1930) (613)
FDL 20.7 1512 31. 0 8.00 3515 2.39 -(4650) (340) (12.2) (3.15) (2007) (538)
13.8 1156 22.9 6.60 3818 1. 96 -(3100) (260) (9.0) (2.60) (2180) (441)
34.5 1619 20.8 10.41 3889 2.21 -(7750) (364) (8.2) (4.10) (2221) (477)
27.6 1779 18.0 9.04 4371 2.06 -(6200) (400) (7.1) (3.56) (2496) (464)
UM20.7 1690 15.7 7.52 4805 1.95 -
(4650) (380) (6.2) (2.96) (2744) (439)
13.8 1468 13.7 6.05 5380 1.85 -(3100) (330) " (5.4) (2.38) (3072) (417)
I • • •". " -" ..
60
180
200
220
S
40
10
30 :D
825 g
o«20 g
...J«u
15 f=0::W>
35
j,
il///jr
! ,f/41//" ,,!
,.~''I/
,rr///"'it!' -- NASA
.:',/ ---- FDL//']//1 --- UM
:.' _.- Eq. (23), ref. 1
{"20 / L._.. I I I I
/ 1.0 2.0 3.0 4.0 S.O (in)
o -L.._~_..L---_---.J
o 20 4.0 6.0 8.0 10.0 12.0VERTICAL DEFLECTION (em)
40
140-
160
180
~ 120
o«g 100
...J;J 80f=0::
~ 60
j / j1/ ,f
il" l 45
1// :/ ~X//// 4011./, ,/
'(,//,/ - 35
i', I/ l'/ ~ 30:0/i l/ 8
/;// - 25 ~~: g,j! 20 ~
/1// <t/7 -- NASA t5 gI·:·," ---- FDL w/4 --- lH.1 ~ 10 >401-':/ ---Eq.(23J,rrfl I
I'i' i2°
1
" l(~ I ~ -j 5/;1;0 2.0- 30 4.0 5.0 (In.l '
OlL...4_ ..l-._-.l---L-..-L-_~- __-"--_.. ----'o 20 4.0 6.0 8.0 100 120
VERTICAL DEFLECTION (r.rnl
~ :::rg 120...J
...J:3 100f=n::~ 80
(a) (F) = 125% Rated Loadz max
(b) (F) = 100% Rated Loadz max·
20 :eooo
IS;:;o«g
10...J«ui=
5 crw>
25
-- NASA---- FDL--- UM_.- Eq. (23), ref. 1
o 2.0 40 60 8.0 100 12.0VERTICAL DE>"LECTION (em)
/L:·,I
"I ",,,,~'/"
! ItII ~,
40 /.~ill
201/,.
- /l,JL--l I I I/110 20 30 40 SO(in)
o '
~ loot~ 80o«o...J 60...J«ui=0::W>
140
r
' -!30
120 11/ I
II' ~-25 _//,./ . £'J
Z 100 I,/;/ c-oX ',,, --120 is
[
:f i ~
~ :: ),::/" - NASA -(15 S« 'I ---- FDL I
u /i ---UM 1104~40' ..J -·-Eq(23),refl : ~
> t //15 ~20 ./t~ I ..1--. -' '
(,~~O_._3~__'l ~ .}~~~~lJo 20 40 60 80 tOO 120
VERTICAL DeFlECTIUN :em.\
(c) (F) = 75% Rated Loadz max(d) (F) = 50% Rated Loadz max
Figure 1 - Composite Static Vertical Load-Deflection Curves (49x17,26 PR, Type VII Tire; Inflation Pressure=117~ kPa (170psi); Rated Load=176.1 kN.(39600 1b)) 41
35f- -j8000
(a) (F) = 125% Rated Loadz max
25 --NASA-- .-- FDL----UM 5000
~ 20--- Eq. (23', ref 4
vi
0 4000 ~<l: 00.J 15 <l:
...J 3000 g<l: ...JU <l:f- lO u0:: 2000 ~w> w
>5 1000
1.2 (in.!-L.
24 3.2DEFLECTION (em.)
(b) (Fz)max = 100% Rated Load
6000
7000
2000
vi.c
5000 -=o<Io
4000 ...J...J<l:U
3000 i=0::W>
10001.4 (in)1.21.00.6 0.8
0.8 1.6 2.4 32 4.0VERTICAL DEFLECTION (em)
--NASA----- FDL---- UM--- Eq. (23), ref. 1
30
z 25
=0<l:
200.J
.J<l:u 15i=0::W>
10
5
...~4000~3000~
o-1
2000 <iui=0::
1000 ~
o.Slin,)
--NASA----- FDL----UM--- Eq. (23) , ref. 1
~2+; t5~<l:
9...J 10<l:Uf=t5 5>
5000
1000
--NASA----- FDL----UM--- Eq. (23), ref. t
20
0J><~/0.400"""'...c,;t--,---,--~-~-"----, 0 ~ ~~
0.8 1.6 2.4 0 0.8 1.6 2.4VERTICAL DEFLECTION (em.) VERTICAL DEFLECTION (em.)
(F) = 75% Rated Load (d) (F ). = 50% Rated Loadz max .z maxComposit"e·'Static Vertical Load-Deflection Curves, (18X5:1r;14 PR,Type VII Tire;Inflation Pressure=1482 kPa (215 psi); Rated Load=27,6 kN (6200 Ib))
z~15o<l:
: 10<l:U;::t5 5>
(c)
Figure 2 -
, • A
at
Kz=Slope of thisline
og-.J-.J«·urc::w>
•
(8z)max 8z(VerticalDeflection)
Figure 3 - Graphical illustration of det~rmination of kz
43
24 14,000 12 7,0000 0
_.I!--iJ 0 00
~ /~, 0 12;000SIO
6,000~E 20u /0 0 .5"- x ,~ "- x _,- cr -x "-Z x "- z ?- xo x .ci.>l: X
10,000 ~ ~ 5,000=w 16 x wa w
~w t:i t:i~ 0:: o NASA 0::0:: o NASA a,ooo rr: 4,000<.9<.9 <.9 o FDLz o FDLl?
~6z
12 z0: 0: x UM 0:0- x UM a.. a..(/) 6,000 0- (/) '---Eq.(23), ref. I 3,000 (/)(f)-1 ---Eq. (23), ref. I -.J -1 -1<l: a <r 54
<l:u U uf= 4,000 i= f= 2.000~0: rr: 0::w w w w> > > >
4 2,000 2 1,00030 40 2,000 3,000 4,000 5,000 6,000 7,000
0(IOOOlbs.)
0 05
Obs.)
50 100 150 200 250 10 15 20 25 30 35°MAXIMUM VERTICAL LOAD (kN) MAXIMUM VERTICAL LOAD (kN)
(a) 49 x 17 P = 1172 kPa (b) 18 x 5.5 P = 1482 kPa0 (170 psi) 0 (215 psi)
Figure 4 - Static Vertical Spring Rate VB Maximum Vertical Load
•
922
° NASA /: 8o FDL 20
x UM /' cP_.- Eq. (5), ref. 1 18
~, x 7
26\6x
/' xO60
~~24 6
22 E 14/ ~
-/0 u c
- 50 20 -: I5~
E ./X8c I- 12 x I
~ 18 :.:: t9 I-Z t9
I40 A 16 ~ ~ 10 4~
I- 0 NASAt9 /
, t9 ...J
z 14 z I 0 FDLw w u 8 UM
I...J 12 ...J
x3~30 l-
I 100 0: - - Eq. (5), ref. 1 0:u 6~
I-
~ 20 80: 2
6 4
10 I I I I I 4 I
10 20 30 40 50 2 3000 5000 7000VERTICAL LOAD (1000 Ibs,) 2 VERTICAL LOAD (Ibs)
00 0 050 100 150 200 250 \0 15 20 25 30
VERTICAL LOAD (kN) VERTICAL LOAD (kN)
(a) 49 x 17 P = 1172 kPa (b) 18 x 5.5 P = 1482 kPa0 (170 psi)
0 (215 psi)
Figure 5 - Patch Length vs Vertical Load
( a) F z'" 222.4 kN
(50000lbs.)
- NASAi="z= 176.\ kN(39600Ibs)
----- FDLFz=176.1 kN(39600Ibs)
---UMFz =187.8kN(42210 Ibs)
'3 -6 ·4 .;:/ ~(2 4 6 8'-10 LATERAL-20 DEFLECTION (em)
, .
, , / -30,'.
/. -40
I -50
(b) F :::0 177.9 kNz (40000 lbs.)
2 4 6 8-10 LATERAL-20 DEFLECTION (em)
-30
-40
-50
LATERAL50 LOAD (kN)
40
I I ,
-8 -6 -4 -2 ;;
'/",'j!'
-- NASAFz= 89.0 kN(20000Ibs)
-. -- FDLi="z= 881 kN(\9800Ibs.l 30
-'-LIM 20Fz=939 kN(21100Ibs) 10
//'
/
LATERAL50 LOAD (kN)
40
30
20
10
././/
-- NASAFz = \32. t ktJ(29700Ibs)
----- FDLFz=132.1 kN(29700Ibs)
---UMFz =141.4kN131ROO Ibsl
;----+---+----+~'"'_M'---i--+---+-----'-8 -6 -4 -2 " 2 4 6 8
- to LATERAI__20 DEFLECTION (em)
-30
-40
-50
(c) F z '" 133.4 kN(30000lbs.) ( d) F
z'" 89.0 kN
(20000lbs.)
Figure 6 - Composi te Static Lateral Load-DeflectionCurves (49x17, 26 PR Tire; InflationPressure=1172 kPa (170 psi); MaximumLateral Load'" '± 30% of Vertical Load).
46
10
LATERALLOAD (kN)
1"/,, ,, ,
1.0 2.0 3.0LATERALDEFLECTION (em)
-6
-10
-4
-8
8
6
4
10
LATERALLOAD (kN)
-3.0 -2.0
--NASAFz=27.1 kN
(6100Ibs.)
----- FDLF =27.6kNz (6200Ibs)
---- UMFz =28.0 kN
(62981bs.l
-6
-10
-8
,/// 2.0 3.0, LATERAL-~, DEFLECTION (em)
6
4
-3.0 -2.0
--NASAF =35.1 kN 8z (79001bs.l .
----- FDLFz=34.5kN
(7750Ibs)
----UMFz=34.6 kN
(7786Ibs)
(a) Fz ~ 34.2 kN(7700lbs.)
(b) F ~ 27.6 kNz (6200 lbs.)
--NASAFz=208kN
(46701bsJ----- FDL
F =20.7kNz (46501~J
----UMF =20.8kNz (46781bsJ
-3.0 -2.0
10 LATERALLOAD (kN)
8
6
4
1.0 2.0 30LATERAL
-2 DEFLECTION (em)
-4
-6
-8
101LATERAL__ NASA LOAD (k N)
F : 13.3kN 8
------ FZD~2990Ibs) 6 fFz : 13.8kN
(3100Ibs.l
1/.
---- UM 4 /'>,1Fz =13.8 kN /1.
; 3098Ibs.) " /2 1/.,'
:/j/t---+----t.- I I I I J IJ-I I I I I j
-3.0 20 -10 l~t/ \:'~TER~~ 3.0
/~~: -2 DEFLECTION (em)
:' / t- 4I.v
-6
L8
(c) F ~ 20.5 kNz (4600lbs.)
(d) F ~ 13.8 kNz (3100 lbs.)
Figure 7 - Composite Static Lateral Load Deflection Curves(18x5.5, 14 PR Tire; Inflation Pressure=1482 kPa(215 psi); Maximum Lateral Load ~ ± 30% ofVertical Load))
47
7
o
I
3000
0 x
------ 0----. 0---- x 0 2500-----0 x c"-
0 2000~0
0
:i
'S0rI
-::-45(t: :
~ 4Off-·oX~ 35
~ 3.0w~
~ 2.5 f500 0::
0:: 0 NASA ~~ 2.0 - 0 FDL ~<1. x UM 1000 (f)
ffi 15[-- -- Eq (33), ret. I I <if- I I 0::
:s 10f2600~-h--ttr;OO- 6doo ~ 5003
o:r I VERTICAl LOA~:~_~O10 1:> ~O 2S 0
VERTICAL LOAD (kN))
c5000.;::
.ri
I~7000
- 6000
o x
xo
oo
x___ 0 0
~ 0---8w~0::
~ 6z0:: 5a...(f)
--J<!0::W
~.J
11
E 10u"- 9zoX
(a) 49x17 26 PH P =1172 kPao (170 psi)
(b) 18x5.5 14 PR P =1482 kPao (215 psi)
Figure 8 - Static Lateral Spring Rate vs Vertical Load
>- 70~
t-="x
o NASA Z
a FDL w 60 -
x UM, u x
lJ... xlJ...w .50 x
0U aen(j) 40w acr:
a x W ax f- a0 a en 30 0 00 0 >- .0
0 I 0
35
o NASAa FDLx UM
f5 2025 30VERTICAL LOAD (kN)
I I I
2000' 4000 6000VERTICAL LOAD (Ib.)
:;j 20cr:w!:i-1 .10 -
30 40VERTICAL LOAD (1000 Ibs.)
I I
125 150 f75 200VERTICAL LOAD (kN)
:100
>-~.60
t-="zwU .50i:i:lJ...W8 ~o
en xenw.30cr:wf-enr .20I-l<{ 0
ffi .10
!:i-l
(a) 49 x 17 26 PR Po= 1172 kPa
(170 psi)(b) 18 x 5.5 14 PR Po
= 1482 kPa(215 psi)
Figure 9 - static Lateral Hysteresis Coefficient vs Vertical Load
CJlo
5684 112ANGLE OF TWIST(deg)
200
+300I;-400j
nJISTI~3
MO),1ENT (kNcm)
100
200
300
-112 -84 - 5656 .84 1.12 140ANGLE OF TWIST (degl
200
300
400
200-
300
-140112 -84 -.56
(a) F =228.0 kNz (51250 lbs.)
(b) F =182.4 kNz (41000 lbs.)
to Full
I
.56 .84ANGLE OF TWIST (deg.)
50
IIIsot TWISTiNG
. : MOMENT (kN em)
100+
100
1150I
(d) F =91. 2 kNz (20500 lbs.)
Angle of Twist - UM Model
-.84 -.56.56 .84ANGLE OF TWIST (degJ
TWISTINGMOMENT (kN em)
100
2001II
(c) F =137.9 kNz (31000 lbs.)
10-Static Twisting Moment About Vertical Axis vsSize 49x17, 26 PR Tire; P o=1172 kPa (170 psi)
Figure
..320
I
'60
-..S 0"
• Q)~"O
w~a::
20,000 ~a::a..(f)
-'«zo(f)a::
15,000 ~
x 25,000/
/
x UM--- Eq. (44), ref.'
x
/
x
200
~ 240a::<.9za::a..(f)
-l«2o(f)0::ol-
280-E .uO"• Q)
2"0.,:,t;.---
/
10,00048,000
200
30,000 (Ibs,) 40,000
120 140 160 180VERTICAL LOAD (kN)
'20 20,000
'00
..
Fig. 11 - Static Torsional Spring Rate vs .Vertical LoadUM Model to Full Size 49 x 17, 26 PR Tire;P
o=1172 kPa (170 psi)
51
-
-x
.60~
-I-~ .50~u1..1..1..1..~ ~O~u(f)
~ .30-a:::wI-~ .20~:c...Jc::{z .10-,o(f)
a:::g 0-
20,000I
x
I
~o,ooo (I bs. )
x
I40,000
I
x
I
48,000I
100 125 150 175VERTICAL LOAD (kN)
200
Fig. 12 - Static Torsional Hysteresis Coefficient vs Vertical LoadUM Model to Full Size 49 x 17, 26 PP. Tire; P =1172 kPa(170 psi) a
..
0-<rZo~...J-
t ,f<r ,,//o ,,/
20 z //15
<r //w //0::: /' /
10 °LL ," ,, ,5
", ,//, ,/,
35
30
25
----- FDLFz=176.1 kN
(39600lbsJ
,"
35
30
25
20
15
10
----- FDLFZ=220.2 kN
(49500Ibs.l
20
25
30
35
-3.0 -20 -\.O //" /' 5
I I
/1 /' 10, ,/,' 15
I ,-I I
1 ,
I "I ,I ,
" "1 '
I "I ,I,'
I,
i'
1.0 2.0 3.0
FORE-AND-AFTDEFLECTION (emJ
-3.0 -2.0 -1.0," ,/ / 5" /I I
/ ,/ 10, I, ,
" / 15"/'// 20
1/IIt 25
30
35
1.0 2.0 3.0
FORE-AND-AFTDEFLECTION (em.}
(a) (b)
35 0-<rZ
----- FDL 30 g~
Fz=132.lkN t-
(29700Ibs,) 25 ~I
20 0z "<r "15 I //w '10::: I I
10 f2 /~//' ,1
, I
5 //, "
51.0 2.0 3.0 \
FORE-AND-AFT10 DEFLECTION (em,)
15
20
25
30
----- FDL 30Fz=88.1 kN
( 19800lbs i 2520
15
10
5
-30 -2.0 -1.0 //, ,",,'
/,'"n
"",
1.0 2.0 3.0
FORE-AND-AFTDEFLECTION (emJ
5
10
15
20
25
30
35
-3.0
Figure 13 - Composite Static Fore-and-Aft Load-Deflection Curves(49x17, 26 PR Tire; Inflation Pressure=1172 kPa (170psi); Maximum Fore-and-Aft Load ~ ± 15% of VerticalLoad)
(c) (d)
..."
.a· .•
53
4500
~ 4000 /1g3500 / /-' I /I-- 3000 / /~ 2500 I /
~ 2000 / /<[ I IW1500 I I0:: / Ie 100~ /
/ II /
IiI •
/ ).' I
/ I
/ !/ i" ;I .
iI
iI
i!
/I
I/
I/
/
I\
4500t
~ 4000..o .g 3500 t...J I
t 3000 T /<[ 2500 - I6 /~ 2000~' I, I
li! 1500 VolJ... 1000/
II
//
-O.R -0.6 -04 / /
/ // /
/ // I
/ /I /
I // /
/ // /
/ II/ /
/ // /
/ /I /
I /I /
I /I /
I /I /1/
02-500
-1000
-1500
-2000
-2500
-3000
-3500
-4000
-4500
-0.8 -0.6 -0.4 / // I
/ // // /
/ // /
/ // /
/ // /
I /I ;/
, I
/ /~, /
i/V
0.2 0.4 06 0,8-500 FORE-AND-AFT-fOOO DEFLECTION (em)
-1500
-2000
-2500
-3000
-3500
-4000
-4500
(a) F =34.5 kNz (7750 Ibs.)
(b) F =27.6 kNz (6200 lbs.)
i -2000
f-<:50GI!-3000
,-2500
0.4 0.6FORE-AND-AFTDEFLECTION (em)
i4000ez !
- 3500+o I
g3000~ /1...J /{I- 2500 I /u- I /!2000 / /
<[2 1500 II III
ll!1000 / /
e 50~ /
-08 -0.6 -04 -O,~/ I 012 07 0'6 -O~q'
I I - 500 FORE -,1ND :,c"/ / 1- '000 DEF'.EeTIO', '0'"" /. / ,,-1500I .
/ /
,1///1//,
1/
~CJ<[
~ 2500t A
~20001 //QI500 //
~ 1000 /1/W / In:: Io /lJ.. / /
.--. - +----+-~_t.'_-(16 -04 -02/ I 0.2
/:, j- 500, ~()OO
. 150('
-2000
(c)
. '350C
f-4000
F =20.7 kNz (4650 Ibs.)
(d) F =13.8 kNz (3100 lbs.)
54
Figure 14 - Composite Static Fore-and-Aft Load-Deflection Curves(18x5.5, 14 PH Tire; Inflation Pressure=1482 kP~ (215psi); Maximum Fore-and-Aft Load ~ ± 15% Vertical Load)
32 x
0L..--L.----l.---L---...L----.L----l0100 125 150 175 200
VERTICAL LOAD (kN)
(a) 49 x 17
)(
------~----.----
o FDL--- Eq (47). ref 1.
ooo
- 6000 ~c".d
___~--- 5000'::::'...__- W
.- I-.___ <t
_____--- _ 4000 0::
<.?Zo -
- 3000 g:(/)
llL.
- 2000 <tI
oZ
~-.l-.----L--4-0..L10-0--..L--6-0..L~-0---L---- 11000 <[-VERTICAL LOAD (Ibs.) ~o
~-_...l---I-_-..l.I----.L-I----lI---.lJI lL.15 20 25 30 5
VERTICAL LOAD (kN.)
(b) 18 x 5.5
E~ 10 I-
Z..:<:
W 8>--~n::<.?z 0>--0::0..(/)
I- 41-lL.<:(
I
0Z<:( 21- I
I 2000wn::0
0 1lL.
5 10
x
15000 '"2,.D
5000 ~olL.
, w~0::
<.?Z
10000 ~0...enllL.<t.o
o Z<t
I
o
40000LOAD (Ibs.)
o
30000VERTICAL
x
o FDLx UM
---Eq. (47), ref. 1I4
~24<:r0:
<.9Z 200::'0..(J)
I- 16lL.<:(
I
oz<t 12
I
wgs 0
lL. 8
E~ 28z::;..
Figu~e,15 - Static Fore-and-Aft Spring Rate vs Vertical Load.
l-I- .50zz w 0w uu 50 x LL .40li.... x LL 0li... W 0 0w 0
8 40 x u .30(j)
x (j)
U'5 (j)
w wffi .30 0 ~ .20I- 0
0 I-(j)(j) >->-
I.20 o FDL I .10l-I- x UM LL DFDLli... <t« II
.10 0 00Z z« I I I <t
I 30000 40000 50000 I 4000 6000w W0::: VERTICAL LOAD (Ibs,) 0::: VERTICAL LOAD (Ibs,)f2 f2
100 125 150 175 200 5 15 20 25 30 35VERTICAL LOAD (kN) VERTICAL LOAD (kN)
(a) 49 x 17, 26 PR rl'ire; P·' = 1172 kPa (b) 18 x 5.5, 14 PR Tire; P = 1482 kPa0 (170 psi) 0j.' (215 PiSi)
Figure 16 -.Static Fore-and-Aft Hysteresis Coefficient vs Vertical Load
80'-
I,
oOx
(II
~\__i200
ooo
° I\;ASAo FDLx UM
_.- Eq (64), ref 1
70 l,
- 20~
~\
'Of-~,o<-I_---' ----', -
tOO 150
VERTICAL LOAD :~N~
I ~ C' .-9---x--., 50!... 0 /~
~ ~ / x,(lOr- .u l..~ Ix <ollx<"!,
EEOL
()
') 1° NASA "go FDLo 3° NASA • 1° UMI) 6° NASA • 3° LJ~'"
/::; go NASA • 6° UM I'!l 1° FDL .. 9° UMr.1 3" FDL --1':'1(>;4), ref t
~ 6° FDL _..-JIL- --=-=I--::- __I150 200
VERTICAL LOAD, kNtno
IQ("'l_
II 0
7:', ~
(a) 49 x 17, 26 pn Tire;Po=1172 kPa (170 psi)=
(b) 49 x 17, 26 PR Tire;Average Values P=1172kPa (170 psi) 0
x
oo
--Q ---
I
II
I,I
-L-~_~25 -'0 35
LOAD '~:'\JI
°°
401
1 0 NASAo FDL
)6! x UM
t: )?I --- Eq (64), ref 1
c; ~ c
~ ::o
;~; 2U l
i-; t6~,- I~. '2~'
8~'
4r-o~1_---:":::--_:"=1_
5 10 15 20VERTICAL
•
o
c
8o
o
---'__~_.......l-'__ -l hJ10 ,~ 20 25 30 ~s
VERT'CAL LOAD (kNl
(c) 18 x 5.5, 14 PR Tire;P =1482 kPa (215 psi)o
(d) 18 x 5.5, 14 PP. Tire;Average Values P =1482'kPa(215 psi) 0
Figure 17 - Yawed-Rolling Relaxation Length vs Vertical Load
f)7
-------------------------~-~-------------
CJl00
25,000
-.220,000
-w~ 15,000oLL
~ 10,000(f)
5,000
1-- ~ =C' (1 - - ). o's e
NASA Towed Cornering49 x 17 26 PR Po= 170 psiRun #6 l/J =9 0
Vertical Load =45,000 Ibs.
20 40 60 80 100 120Ly DISTANCE TRAVELED (in.)
Figure 18 - Illustration of Determining Yawed-RollingRelaxation Length, Ly
r0 i
,l
I ~18000I
o NASA~18000flO~ x st o FDL 0
o NASA, o FDL 1;0000
x UM
1'6000I
x UM 0
70L 700
II
roo ll4000,h()'
~ 6lI 0
z l 12000 ~ l'2000 ~~ 50 SOt-w I 0 WU 0
1'0000~ ~ 40~urr. 10000 gs.
0'I.. lI()l u..
~Ito~
w0 8000 e
i.'i I (J) (J)
30 0301 0
I16000 x 6000
"0
20~, I
20
,ofn -i 4000 0 4000
12000 10 20000 Q1
x·
OL ~_L .1.---'--__ '- _ _.L.--l~-':"""_ ...i- _I 0 .L ___-,- ,__ .~____
0 2 4 6 8 10 0 2 4 6 8 10YAW ANGLE (deg l YAW ANGLE (deq)
(a) F ~ 218.0 kN (b) F ~ 173.5 kNz(49000 Ibs. ) z
(39000 Ibs.)
80, l1HOOC
, o NASA 0 1160007()l n FDLI , UM
n I0
:1400C'60r
z i'20,lO-",-'< n- 50- -:0
L..' WuJ\OOO·J1E0::
0 I 0ti- 110, 11.
lu LL0 jsooo~iii
30 l 1\
6'jOOI,
20~
" 4000
o
o
o
o
o
o
o NASAo FDLx UM
o
(d) Fz
l,sooo1'6000
~'4000 .
~'2000 1;i ~
. ~10000 ciI 0
t:~looo.l2000
o0L-L-:2'--J'---J.4~- , 8 10 - ~
YAW ANGLE (deg)
~ 89.0 kN(200001bs.)
10
20
2000
I \ ~.-L.-...l.- 16 8 10
ANGLE (deg)
~ 133.4 kN(30000 Ibs.)
. .L_. ~_l
2 4YAW
)Lo
Figure 19 - Slow-Rolling Side Force vs Yaw Angle(49x17, 26 PR Tire; P =1172 kPa (170psi)) a
59
400
2400
2800
800
3200
~2000~
j 1600 ~, w1200 9
(/)
I10
o
D
oD
~ 27.6 kN(62001bs.)
(b) Fz
. [14,000,
l-I
12,OOOr
~i
_10,OOOiz '
~ 8000~o 'LL r~ 6000~U1 r
4000~ ~L 0 NASAI D 0 FDL
2000
f: x UM
°OL-~-2 --- 4 6 8YAW ANGLE (deg.l
,0.D
2400
2800
2000
D
-1600 ~
un::o
1200 LLwo(f)
~~ ,:,~~C~J:::oO'---'---'2--L 4 5 8 10
YAW ANGLE (deg)
(a) F ~ 34.5 kNz (77501bs.)
12,000
10,000
Il~ 80001.oJ "Un::2 6000lei0
(f) 'l0000
"0
2000D
2000~ :L
QG ....1.-_-L-.-i..-~._ ...... _.l...--I-'---'----'::-'o Z 4 6 8 10
YAW ANGLE (deg.l
800
14,OOOr
12,OOO~~
IO,OOO~
- t~ 8000,
~ 60aaflLi rG
U"l4000I
D
ox
D
o
x
D
o NASAa FDLx UM
- 3200
2800
- 2400
2000
- 1600 ;::;urro
1200 LL
wo(f)
400
z ::':::[
tj 8000n::oLL
~ 6000(f)
4000
2000~ ~
~ 0
°ole
x
x
0
D
0
D
\l D NASAa FDL
~
x UM
_._._....1- .!. .._l_--.l.-.. .l---,<',---l,---l'=--_"-""'2 4 6 8 10
YAW ANGLE (deg.)
2800
2400
2000.:1
w1600 g
e1200 ~
(/)
800
400
~ 20.7 kN(46501bs.)
13.8 kN(31001bs.)
Figure 20 - Slow-Rolling Side Force vs Yaw Angle(18x5.5, 14 PR Tire; Po=1482 kPa (215psi))
60
20
61
\I
'd '""""s::'""""ro'M
(fJ
'do.ro00..:It'-
r-!r-! "'-'roC) ro
'r-! P-i~.l4J-4Q)C\j
>1:'-r-!
{fJr-!~
o
20
20
24
Vi16 :e
oo
12 9wua::
8 ewo
4 (f)
vi'6 :8.oo
o12~
wua::
8 ewo
4U)
16.2oo
12gwu
8 ~lJ..
Wo
4 U)
Ol---~..L----l--L-~-::L-~---------; 0200 150 100 50VERTICAL LOAD (kNl
l-5..L0,-..-4...J.0;::-----:;3"'::::0-~2:=::0::;---_io----··------J
VERTiCAL LOAD (\000 Ibs.l
(a) NASA
80
w~40o
~20~ 20••
~1°=0/
o 2~0 150 100 50V~TICAL LOAD (kNl
50 40 30 20 40VERTICAL LOAD (1000 Ibs.l
(b) FDL
'::[~60~w .
~40r-
~ I9 201(f) I
LI
oL' _~::::2±::::zj:::::z~! ____I 0200 150 100 50
I I VE~TICALILOA~ __ L __
50 40 30 20 10VERTICAL LOAD (1000 Ibs.l
(c) UM Model to Full Size.
2 60oX
80
w~ 40olJ..
we 20(f)
~
(1),...;b.Os::
c:t:;::ro~
~
C\l
(1)~
~b.O
'..-i~
"d,......,s::,......,ro ....'Owro c.o I!')I-=l,...;r-l~
ro'-'U'..-i ro+JP-.~~(1):>C\J
co(J)'<;ji~r-l
II(1) 0UP;~o .~
~(1)
~(1)'r-i
"dE-<'..-iUHX::
P-.b.OS::'<;ji
•..-i ,...;r-lr-l ~
OlDp::.II!');::x000
r-l r-l(1),-,
3600
3200
2800 ~.,;
2400 ~
2000~
1600 ~lJ..
1200 wa
800 ifJ
400
3600
3200
2800
2400.2
2000~u
1600 g§1200~
800 ~
400
3600
3200
2800~
2400~2000w
u1600 ~
1200 ~a
800 V)
400
7750 6200 4650 3100VERTICAL FORCE (Ibs,)
(b) FDL
I I I ! I ._ I
7750 6200 4650 3100VERTICAL FORCE (lbsJ
(a) NASA
2
0'36 30 24 18 12VERTICAL FORCE (kN)
18
16
14
~12z::::'10w~8olJ..6w94(f)
18
16
t4
2 12-'"~IO
w~8ou.. 6w~4
2
o I I .v: I J< I Vi; 1.1...---, 30 24 18 12
VERTICAL FORCE (kl'J)-'--_-J.1_ ... ~l._____ __ ~--J
7750 6200 4650 3100VERTICAL FORCE (Ibs)
(c) UM Model to Full Size
18
16
14
~t2z~10w~8e6w9 4(f)
201, /, /, 6 /C'-~~ I I
62
3500
700
500 g~.D.3
4000:W~o
300 Q..
<.9Z
2008Sz0:o
100 u
600
·0x
* Using measured values of Conlaet Palet>Lenglh. Relaxalion Lenglh and Laleral SpringRale as in equalion (83). ref.1
I I
2000 3000 4000 5000 6000 7000 JVERTICAL LOAD (Ibs.l
__...l..- _ ..-1- ' I '-
5 10 15 20 25 30 35VERTICAL LOAD (k Nl
- NASA Calculated*o NASA Measured Slow-Roiling
---FDL Calculated*3000 0 FDL Measured Slow-Rolling
----UM Calculated It
x UM Measured Slow-Rolling _--------,,-
",",,',",'"
",",
",
""," --------cf __-------0' 2500(1)
"0"
z.2000
0:W~0 1500Q..
l?Z-0:
1000wZ0:0u
500
2500 ~........D
3000
0:.2000 lu
~oQ..
I ~l1500 ~
0:WZ0:
1000 8
o
xx
It Using measured values of ConIact PalchLenglh, Relaxation Lenglh and Laleral SpringRale as in equalion (83). ref. t
! 5002Fio·-z'0 ~O 4'0 50 IL._~E~~IC~L LOAID(10~~s.l I
00 50 100 15C 200 250·-l 0VERTICAL LOAD ( kNl
8L *(-- NASA Calculated: 0 NASA Measured Slow-Rolling---- FDL Calculated*
6 0 FDL Measured Slow-Rolling- --- UM Co Iculated *
x UM Measured Slow-Rolling
14
0:W~oQ..
l?Z0:WZ0:ou 4
_120'(1)
"0.......
~10
(a) 49 x 17 26 PR = 1172 kPa(170 psi)
(b) 18 x 5.5 14 PR Po
= 1482 kPa(215 psi)
Figure 23 - Cornering Power vs Vertical Load Slow-Rolling - Comparison of MeasuredValues and Those Calculated From Eq. (83), ref. 1.
mw
64
1200
t
9000 1200 9000
1100 o NASA8000 1100 -
8000o FDL
1000 x UM 1000r: n 7000 __
E o NASA 7000u'JOO u 900 o FDL -?:
0.n Z ..n.'< 0
6000~.'< x UM
6000~loJ 800 w 800::> :J :::> :::>0 p 0 o.n:: 700 n: n: 700-
5000 gs.a - 5000 ~ 0l- f- a x f-.e:> 600 I') e:> 600 - a
e:>?: " Z z4000~". a - 4000;;; z
'--~ 500 0e:> 500 e:> • e:>:J :J :J :J-1
13000:
<l400
II 03000 "7-, 400 0'--'- '--'- '--'--, .J -' -'W I,' LoJ WIf)
:::L_ 12000If) (f) 300 - a
2000 if)
20al 0
100- 0<j,ono 100010'0 -
a --'-- ---L .L ,I . 0 a 0
0 2 4 6 8 10 a 2 4 6 8 10YAW ANGLE (r1P~.l YAW ANGLE (deg.l
( a) F ~ 218.0 kN (b) F ~ 173.5 kNz (49000 lbs.) z (39000 lbs.)
IZOO - 9000 1200 - 9000
1100 - - naao 1100 - 8000
1000 - o NASA 1000 oNASA
E' o FDL - 7000 E o FDL 7000u :JOO -u 900 x UM - x UM -?: f) Z ..n
--" - 6000 0::-'< rOiw 800 UJ W 800
::> :J :::>0 0 0n:: 700 5000 go;
n: 7000 0 5000 2f- f- f-
e:> 600 e:> e:> 600· I e:>z
4000~z
ro~z 7-
500 -~
500 - I') e:>:J :J ::J-''" "7- 3000 ~<l 400 0 3000 400 -
I~ a ,> '--'- '--'--' .; -'
300L -'loJ 0
j "w w
if) 300~ 8 2000 (fl(f)
200~ 0
2000 if)x
ZOO,-a
L-'~" ~J:oo0 8
1000
10:t8 100~x
I I I I 1 1 _L---L-toO o .
0 2 4 6 8 0 2 4 6 8 10YAW ANGLE (deg) YAW ANGLE (deg.)
(e) F ~ 129.0 kN (d) F ~ 89.0 kNz (29000 Ibs.) z (20000 lbs.)
Figure 24 - Slow-Rolling Self-Aligning Torque vs Yaw Angle(49x17, 26 PR Tire; Po = 1172 kPa (170 psi»
500 0
500o NASA 350
o NASA 350x
o FDL o FDL~ 400 x UM 0
300 = E 400 xUM 300':;:.Dz E.w z
x Ww 250 :::> w x 250 :::>:::> a :::> aa? 300 ct: a ct:0 0::: 300 00
~ 200 ~ 0 200 p~ ~ 0
~~
0 z (.:J x ZZ 0 0 z z Z~ 200 x ISO ~
~ 200 150 ~0 0 -.J 0 0 -.J::::i <! 0 0 <!.<!
0 I -.J IlL. <!
100 ~t.I x
100 LL1 I 0 XlL.-I u- 0 ww (j) -I (j)100 w 100 xIf) 0
(j)
50 0 50
0 0 00 a0 2 4 6 8 10YAW ANGLE (deg.l
(a) Fz:::: 34.5 kN (b) F ~ 27.6 kN
(7750 Ibs.) z (6200 Ibs.)
500 500
o NASA 350 o NASA 350
o FDL o FDL
E 400 xUM 300~ E 400 xUM 300;z :e z :9
250~ ww w 250 :::>:::> a :::> ag 300 0::: a300 ct:
0 ct: 00200~ 0 200 ~~ ~.(.:J
~(.:J z (.:J zz z z z~ 200 0 x 150 ~ ~ 200 150 ~0 -.J -.J-.J <! ::::i <!
II I I<! 0 u- <! I.L.0 100 LL1 I
100 LL1lL. 0 lL.-I 0 (j) -.J x (j)w 100 w 100u: 0 x (j) e gx 850 0 50
0 x 0
0
00
0 0 . I I ....L-.I._-l...-.l.-... 02 4 6 8 0 2 4 6 8 10YAW ANGLE (deg,) YAW ANGLE (deg.l
(c) Fz~ 20.7 kN (d) F ~ 13.8 kN
(4650 Ibs.) z (3100 Ibs.)
Figure 25 - Slow-Rolling Self-Aligning Torque vs Yaw Angle(18x5.5, 14 PR Tire; P -, 1482 kPa (215 psi))a
65
66
(a) NASA
(b) FDL
(c) UM Model to Full Size
Figure 26 - Slow-Rolling Self-Aligning Torque vs Vertical Load and
Yaw Angle, ~ (49x17, 26 PR Tire; P ~ 1172 kPa (170 psi))a
. ----- - ----'
(a) NASA
7750 6200 4550 3100VERTICAL LOAD \Ibs.\
(b) FDL
!::~ ~" 400 ~i? 400 / 300 iso "'~- go 0::
",f-_Z" 300r' .-/ -- -- f?0/ 3° ~. 90 200 ~t§ 200 Y_./ o' z:J 0/,1° In , ././- go 100 :s<! 100 - ..-- ln __ ,;;..---' 3° ~- <!..:.. L1 ,- ~;-------- Ll..d 0 1L LL_ . - ~(f) 36 30 24 18 12 (F
VERTICAL LOAe: i:<i~)
__l--.L L-...- ......1.-__
7750 6200 465C' 3100VERTICAL [GAO (Ibs'
(c) UM Model to Full Size
Figure 27 - Slow-Rolling Self-Aligning Torqueand Yaw Angle, ~ (18 x 5.5,14 PRkPa (215 psi))
vs Vertical LoadTire; P ~ 1482
a
67
mco
o<J:g-l<J:U
~ "IilLJ>
o VERTICAL DEFLECTION
o<J:g-l<J:~I1-'cr'~I
Io VERTICAL DEFLECTION
o<J:o-'-l<rv
-i=crw>
VERTICAL DEFLECTION
(a) NASA;49 x 17,26 PR Tirev=50 knots
(b) FDL;49 x 17,26 PR Tirev=50 knots
(c) UM Model; 49 x 17,26 PR Tirev=50 knots
Figure 28 - Typical Vertical Load-Deflection Curves at Non-Zero Speeds
•
I I
40 60 SOSPEED (Knotsl
o -'--~~~=---L.-::~-l..-"L,---l---:L--_-l 0o 20 40 60 SO 100
SPEED (Knots)
.. o
x x
o NASAx UMa FDL
o
o
oo
100
14,000
12,000
c
"- 10,OOO~
wI-
SOOO ri~
Z6000 0:
CL(j)
4000 <i~lcc
2000 ~
o
24~
~ 20t: 16~~n:
~ 120:CL(j)
...J S<!Ui=E5 4>
x xx x ~ x 0
o NASAx UM
o
j14,000
~12'OOO ~
10,000:::::'W
1 ~SOOO a::
~
z6000 g::
(f)
--.J
4000 <5i=a::w
2000 >
~ 222.4 kN(500001bs.)
177.9 kN(400001bs.)
'" 133.4 kN(300001bs.)
~
Z6000 cr
CL(j)
--.J<!Uf=a::w>
4000
114 ,000
i12 ,OOO ~~IO,OOO :e.., w·SOOO ~
a::
oo
x x
o
o NASAx UM
(d) Fz
24 ri
~ 20~;; i-'" I x
16(1.L; xtr I.
i 12~
~ Ji= f-
~ 4r ~ 2000
Ut ~-'--!--J- ---"--,----,-I--'--_.,.LI-----l----.:'l------l 0o 20 40 60 SO 100
SPEED (Knots)
'" 89.0 kN(200001bs.)
o
14,000
12,000 ....,c
"10,000;gloJI<!
SOOO n:~
z6000 it
(f)
...J
4000 <5i=0:w
2000 >
o
ox xx 0
o NASAx LJ M
x x x
_ 24
t220/~ ,-"j 16trcc
~ 12it:n..(j)
--.J 8
l<!ui=cc~ 4
0L~"'--'--:2:'::10-'--4.,.LIO-..l-6'-0-L-S..L0-'--1~0-0
SPEED (Knotsl
Figure 29 - Vertical Spring Rate vs Speed(49x17, 26 pp Tire;P =1172 kPa(170 psi)) 0
'2~7000 'l 7000
60000 6000 ~Bto Bl0
0 00
0~
c:...... x ...... ~ x x x l(
......Z x x x x x
5000 ~ -'" x x x5000~-" x
w 8 0 w w 8 wf- f- f- f-<!
4000~<!
4000 Ci?0:: 0::
t9 6 ~ t9 6 t9Z Z Z z0: o NASA 3000 fi 0:: 3000 g:a... a...Cf) xUM (f) Cf) o NASA
Cf)
.-J 4 ..J ..J4 x UM ..J<! 2000 S <! 2000 (3u ui= f- f-
0:: n:: 0:: 2
~:OO0::
w 2 w w w> 1000 > > >
0 ---'- ! I I --l- 0 00 20 40 60 80 100 0 20 40 60 80 100
SPEED (KNOTS) SPEED (KNOTS)
(a) F ~ 34.5 kN F ~ 27.6z (7750 Ibs.) z (6200 Ibs.)
Figure 30 - Vertical Spring Rate vs SpeedP
o=1482 kPa (215 psi))
o ..L.-...L --:._ .L....L__L ...L-L-.L. 0o 20 40 60 80 100
SPEED (KNOTS)
( d) F ": 13 . 8 kNz (3100 Ibs.)
(18x5.5, 14 PR Tire;
l7000 II o roo6000 ~
~ lOX x ~ x 6000 -0~
)(~x x
...... ...... ......
5000 ~z 0
1 ·-'" 5000 ~
w w 8· '.lJf- f- I-
4000 ;i <! ''<!0:: 4000 a:::
t9 0 f..:J
J3000 ti ~ 6 I Z<'- !0: 3000 iTI 0... 0... (.1..I en ef) o NASA
'f)
_J ..J 4 -J2000 ;5 <! x UM 2000,Ju
f- l- i-0:: 0:: a:
1000 w w 2 1000I.,J
> > >
o
x x
o
(c)
x xx X
o NASAx UM
t2[E to~ x
: 8~t0::
~ 60::a...Cf)
--! 4~
~ i~ 2r
oIL--L---lI_l-...L.!__L.-.LI-L!- _..l..-.L - ~_' 0o 20 40 60 80 100
SPEED (KNOTS)
F ~ 20.7 kN'z (46501bs.)
70
og--.J--.J<{U~0::W>
VERTICAL DEFLECTIONFigure 31 - Vertical Hysteresis Loops at Various Speeds UM Model 49 x 17 26 PH
I a." FDL at 3° YAW ANGLE I Oz NASA ot ZO 'rr-"W ANGLE iI~O~
°6 FDL 01 6 0 YAW ANGLE i °z FOL at ZO YAW t.NGLE i22000°9 ;-DL at go YAW ANGLE - 2200(' 100~ , LIM at ZO YAW ANGLE
I
80 0:'9 Z
~
1'8000 ~Os °9
°9~';~ eoL18000 ~
....,. z "g<.
x I y x9 x9l.l~, I-'og1·1 . °9
. 0 -1'4000 ~UJ °6 ° L, .u EOl °9 °9 u
GOt60g Og 6114000 a::'rr: '9 0 D:: e.g C0 J. _. L.- a "6 x6
x6X6 1 LL.
I.L i LL
ILl ,I:1C10 lLJ lL!
foe °6l.!...i
°6 06 -1'0000 ~la 0 6 °6 or. ~-), ~ 0 40 °3 °3c') \JI
15000
en 0:,> ~ -_J
~.-J -~ 3 "3 I .-1,-'( <! <!
"3 '<3 x3 - ;:;(100 <::....~ 2- ~°3 ° 1-- ~,
20f Q 3 °3 0, CJ t 20 °3 °3 " I .....-n-: ..J 3 1 D: - .J Ci:0 I 0 0 0; ;),I 02 !- 121\:)0 ;,:~ Z '-1 .x 1 x, °1 -i 2000 zi lOx, xl
OL_~L OL-i----.-L,
.L-' ! I _ i _J L .1 .. i_. .;_ .-10 20 40 60 80 100 0 20 40 60 80 iOO
SF-EED (KNOTS) SPC:ED(KN01S)
(a) F ~ 222.4 kN (b) F ~ 177.9 kNz (50000 1bs.) z (40000 1bs.)
.-t,'"
l'8000 fI}
')gJ _., lU
°6114000 ~.o 09, u.
~ lOGOn 6e6 .-
3 ~ ..f)
<i16000°3J 6i
i ()0, ; 2:1CJO z
09
co
Xl'.__ 1 I I
40 60 80SPEED (KNOTS)
I °z NASA at ZO YAW ANGLEI nz FDl at ZO YAW ANGLE
100}- xl UM 01 ZO YAW ANGLEiI.
i "9 x9Z 80~-
~ 133.4 kN(30000 1bs)
(d) Fz ~ 89.0 kN(200001bs.)
Figure 32 - Side Force vs Speed at VariousYaw Angles (49x17, 26 PR Tire; P =1172.kPa(170 psi)) 0
72
oL-"";:;':::-"-"7:'::-'--::!7:':-...L--:::'-=---"-~_---'0o 20 40 60 80 100
SPE.EC (KNOTS)
0' I I L I . ..l..-..o... ~ __.__ -l !)o 20 40 60 6C ,OC"
SPEED (KNOTS,
~ ')00
. wi 1500 e, (f)
i~20do ~
I ~
. -J<[
11000 ~cz
I ,-13000II
~2500 _if,CD...J
c
",
07 NASA at Z· YAW ANGLE14f- x; uM al ZO YAW ANGLE
! 09I °4
'.2r: '9.,
Z 10~6 "6 °6 '6~ "6
~ "6
~ 8~u..
500
J3000
~2500 ~12000 ~i f2
~1,150C ~if,;j
J ~
1
1000
~
°6•
34.5 kN(77501bs.)
27.6 kN(62001bs.)
0zNASA al ZO YAW ANGLE"z UM .Jl ZO YAW ANGLE
14i "914i 0z NASA al ZO YAW ANGLE
~3000x9 3000 "z UM al ZO YAW ANGLEI
"9 "9 °9 It2 12
°9 °9 °9 2500 __x9 too~(f)z
°6 CD z x9~ '0 06 "'6 -l ~ to x9x6
159w °6 "6 °6 2000 t3 I..Lc2000~u "6 u 9 x6 0",cr 0:: cr
"6°g °9 0a l, a a 8 "6 LLLLLL. LL °6
w °6 °6 ww1500 i:5 "6 °6 1500 ~0 0
(f)°3
°3,~ <n .6
°3 ...J...J "3 ...J°3 <[<[
x3 ...J <[°3 ° °3"3 <[
::2: "3 3 x3 ::2:::2: x3 1000 2i a: x3 tOOO a:a:4r a
1 Iaa 0 z zz z
~o, 0, 0,0, J500 2 , 0, 0, 0, 15002 x, '"x, "I x, x, x,
I ",oL I__ ...L~ .L.--'-_i I - 0 0 1 , i I I I..---L. ..L-L.. _ _ _ Jo
() 20 40 60 80 100 0 20 40 60 80 100SPEED (KNOTS) SPEED (KNOTS)
(c) Fz
~ 20.7 kN(46501bs.)
13.8 kN(31001bs.)
Figure 33 - Normal Side Force vs Speed at VariousYaw Angles (18x5.5, 14 PR Tire; P =1482kPa (215 psi)) 0
73
r"\r"\•..-100P.
0t-.
SO• ~ r-i(1),-,
70 16 £? ~
260 14 8•..-1 ro
"'"E-tP;
;;:; 50 12 g ~
u10 t! 0::
cc 40 P;C\le cc t-.w 30
se (Dr-i0 6 w C\lr-iu; 20 0 II4 u;
10 02 t-.P;
0 0 r-iX .~
O)r"\
(a)'<:j'i
NASA '-'00..c(l)r-i
r-i0.00s::o<r:o
0E;:'<:j'i
.,; ro'-'so IS~ ~
70 16g :z;
260 14::: "d~
9°:'" s::"'" roO);;:; 50 t2u to t!g; 40 ~t-.cc (])t-.u. sew 30 (])r-i0 6 W P.0u; 20 4 u; rJ) II
10OO~
0 :> ro0
(])~
c.>(b) FDL ~r-i
O'ro~c.>
'r-!(])oj..)
~~'..-1 (])rJ):>
80 -~~~9°:'"
IS
70 - / / /' 16 ~ '<:j'i
'3 60 - /:yr:; 14 8M
;;:; 50- 12g (])
u /~/,/ 10 t! ~
g; 40 ;l/- sg; 0.0u.
77h'~w 30 u. '..-10 6w ~u; 20 - 0
4 V}
10 1''iJ 20 ' - --- 0 •
(c) UM Model to Full Size'
74
2000 .2
500
o
3000go= IJ!
2500
w
1500 ~Li..,W
1000 0(f)
14
12
10
z~ 8wU0::
60<.L
W ,0 4f--(f)
2
00 25 50 75 100
SPEED (Knots)
(a) NASA14
3000
122500
10- ..,9°= IJt
2000 ~z /I
/~ 8 /1
IW
W Uu / if 1500 0::0:: I / 00 6 I / LLl1.. I
16°=1Jt ww 1000 00 4 -- (f)
(f)
2 ·500
0 ------ 005 20 42.5 60SPEED (Knots)
(b) UM Model to Full Size
Figure 35 - Side Force vs Speed and Yaw Angle (18x5.5, 14 PRTire; Vertical Load ~ 27.6 kN (6200 Ibs.);Po=1482 kPa (215 psi»
75
14
*Using measured values of contact patch length,relaxation lengths and lateral spring rate as ihequation (83), ref. f
3500
3000'
..
12 00 --()l
2500 ~Q) ....---- ---0 " ",...------- .........
~10"x ' ..... ,
/ " , ./ " " .0
~ / --0::: x 2000 f5~8 0
~0
0 x 0 0 a..0... x <.9<.9 1500 zz6 -
0:::0::: 0 Ww NASA Calculated * zz 0:::0::: o NASA Measured 50 Knots 1000 0
84 u---- FDL Calculated*
o FDL Measured 50 Knots
2 ----UM Calculated* 500•
x UM Measured 50 Knots
10 20 (1000 Ibs.) 40 500 0
50 100 150 200 250VERTICAL LOAD (kN)
Figure 36 - Cornering power vs Vertical Load76 ..
8000 0 0 t OOO"YAW ANGLE at 1° " YAW ANGLE 011·
0 x YAW ANGLE 01 3°60006000~
xYAW ANGLE 01 3°0 8
:J"0OoYAW ANGLE 01 6° o YAW ANGLE at 6° 4000
o "'5'6000
L4000 oYAW ANGLE 01 go 4000 4000' o YAW ANGLE 01 3°
x x - 2000 4000 20002000 x 2000 - NASA
_ 2000· ~x x NASA _ x
E = 0 0-- 2000,~ I
x~ "z 0 -~ ~ " 0
,20 40 60 80 100 "0 E 20 40 0 60 080 0
~ 8000f 16000 ~EO·· ,
0
j,ooo!z 20 40 60 80 100 - z '-cc <:I <:I 0 ,g ~8 6000 0 a~ 6000 ~ GOOO[FDL -4000'"'19 . a 8 4000 ~
12000 ~~ 4000f xx x x 0:: 8 0 a a § 4000~j2000 ~ 8 4000 cOL 0::
0 ,,,. ~11 8 8 8,,, x x x x . 2000 ~ FOL; 200:[ ~ 2:)00 <'; 2000 -x x x
J19
~z
otzz l') I z19 Z ::::i I t ~..J ::::i 19W 20 40 60 80 '00 w 0 1- 20 40 60 80 100 ::::itf)
8000~6000 tf) 1- 20 40 60 80 100 ::::i u.. <l
<l I"YAW ANGLE r.f \0 u.. ..:. ..J u..
..J W ..J
6000 ~0 0 0 xYAW ANGLE of 3° bJ 6000 ..J if) W0 4000
J4000~ 6000L tf)
a 0 oY~N ANGLE of 6° - 9
~40004000 x x oYAW ANGLE of 9° 4000 x~
8 4000x UM ex2000 x ~
0 . UM 20002000 x a - 20002000 UM 2000 " '"" " " " " 51
" " " "0
0 00 o I i I ! I20 40 60 80 100 20 40 60 80 tOO o 20 40 60 80 100
SPEED (Knots) SPEED (Knols) SPEED (Knols)
(a) F ~ 177.9 kN (b) F ~ 133.4 kN (c) F ~ 89.0 kNz (40000 Ibs.) z (30000 Ibs.) z (20000 Ibs.)
NOTE: NASA vertical load subject to some fluctuation
Figure 37 - Self-Aligning Torque vs Speed at Several Yaw Angles(49x17, 26 PR Tire; P =1172 kPa (170 psi))
o
Figure 37
x 200
250 II ·1600 200
0 0 x 160200 x x x x t20 120
x " 150 150120
0150 00 0 80 x NASA 80 ~
" - 100 100
E 100 " 0 S 80 £ 0 "E - E £i::> xz" NASA w ~ 50 " " NASA 40 ::::. Z " " 60 ;:;:::> 50 a "w - 40 i? w :::>
:::> 50w 0 :::> w 0 x 0:::>
0 0 0 0 :::> 0 lrlr I- lr 0
, lr 0 0 00 0 20 40 60 080 fOO ~
lr 20 l-I- _--l.-L-.J_--L .. -i.-..L-l_l-..1...-....l __.. -
L')I- ~
40 60 80 0
0 z 0 L')L') 20 40 60 80 100 Z L') L')
L')z
z 1609 z z z . 160t§t§200 ,,·"'W ANGLt. of 1o.j 1- z Z
t§200L') " YAW ANGLE at 1°L') :J;,,+ :J :J :J ..
,YAW ANGLE 01 Y -; 120 ~ .. xYAW ANGLE at 3° 120 ';1 .. 0 - 120~o YAW ANGLE at 6° ~ S150r g l.i- ~ 150
0 ..J
~ 0oYAW ANGLE 01 6° ..J -' 0 0 w
oYAW ANGLE at 9° w . 0 YAW ANGLE 01 9' w w If)lOoL: If) 0 If) If) 00 80
tOO 80 100 x . 80UM 0 0 UM
x 0 8 xUM x
50" "40 " x x x 40 0 40
!l 50"
50 x
" " "" " "00 20 40
00
,"°060 80 100 20 40 60 80 tOO 20 40 60 80 100
SPEED (Knots) SPEED (Knots) SPEED (Knots)
(a) Fz~ 27.6 kN (b) F ~ 20.7 kN (c) Fz
~ 13.8 kN(6200 lbs.)
z (4650 lbs.) (3100 lbs.)
Figure 38 - Self-Aligning Torque vs Speed at Several Yaw Angles.(18x5;5, 14 PR Tire; P =1482 kPa (215 psi))
o
•• r
SPEED (Knots)
(a) NASA
(b) FDL
SPEED (Knots -
(c) UM Model to Full Size
80
t.Jt =3° 200~ 250 -z -"-
t.Jt=go .0
~ 200-150 w
a :::>0::: a0 0:::f- 150 0
<.:) 1° 100 f-
Z gO <.:)
- zz 100 -<.:)
Z
-l<.:)
« 50 -lI 50 «
1.LI
-l1.L
W-l
(j) 0w
0 (j)
0 25 50 75 100SPEED (Knots)
(a) NASA
! 250r200
-"-.0
w 150 w:::> 200a :::>0::: t.Jt =6°
a0
0:::
f- 150 0
<.:)100 f-
Z<.9
- Zz 100 -<.:)
Z
-l<.:)
« 50 -l
I 50«
I
1.L 1.L-l -l
..,W W(j) 0
__ ..1.-.___ 0 (j)
~OO
(b) UM Model to Full Size
Figure 40 - Self-Aligning Torque vs Speed, Yaw Angle.(18x5.5, 14 PH Tire; Vertical Load ~ 27.6kN (6200 1bs); P
o=1482 kPa (215 psi))
-
..w~0:C)
Z-0:: _--a..enw0::f-- ~ _
INFLATION PRESSURE, Po
Figure A-I. Tire spring rate vs inflation pressure
81
,.a.
E 'Cr'~ DIMENSIONLESS Q.0 PROTOTYPE
0 ~MODEL ~ +0 N .c:.
Fm....... u LLJLL. + -.A: U
W '"-"- 0U a.-.,..oJ 0
IIII
0 a.LL.
8m?]= (~: )
8 =7] Dp
(0) ( b) (c)
Figures A-2. Typical load-deflection curves.
\ -.'.'82
VERTICAL SPRING RATEVS
INFLATION PRESSURE
SCALE MODEL 49xt7SCALE FACTOR 12: t20 t----_+__
200.----,------r---r-----r-----,---......
~
w~
~ 120t-- -.--+-----. -
t9Z-g: 100t------t--- -t---#--~----l--__~.-._
(J) Kz=28.22+5.457 Po..J ( r2=0.998)5 801------+--~--
~ 60- -- J---1-- J.--~
..j t80
'" o SIN 21160 o SIN 26
c ~ SIN 29.-"(/)
.0 140 _.__..
305 10 15 20 25INFLATION PRESSURE J psi
0~_ __'____...L.._.._ ___1.__~_ ____'L-.-.___...J
o•
Figure A-3. Vertical sp~ing rate vs inflation pressurefor 49 x 17 tire models.
83
T
•
NASA CR-1657204. Title ant Subtitle A COMPARISON OF SOME STATIC AND
DYNAMIC MECHANICAL PROPERTIES OF 18x5.5 AND49xl7 TYPE VII AIRCRAFT TIRES AS MEASUREDBY THREE TEST FACILITIES
1. Report ~ . 2. Government Accession No. 3. Recipient's Catalog No.
5. Report Date
Julv 19816. Performing Organization Code
7. Author(sl
Richard N. Dodge and Samuel K. Clark8. Performing Organization Report No.
11. Contract or Grant No.
14. Sponsoring Agency Code
Contractor Report
t----------------------------~10. Work Unit No.9. Performing Organization Name and Address
The University of MichiganDepartment of Mechanical Engineering
and Applied Mechanics NSG-1494~~A~n~n~A~r~b~o~r2,~M~i=c~h~i~g=an~-4~8~1~0~9~-------- ~ 13. Ty~~ Report andP~i~ Cov~~
12. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWashington, D.C. 20546
15. Supplementary Notes
.Langley Technical Monitor: John L. McCartyFinal Report
16. Abstract Mechanical properties of 49xl7 and 18x5. 5 type VI I aircrafttires were measured during static, slow rolling, and high-speed tests,and comparisons were made between data as acquired on indoor drumdynamometers and on an outdoor test track. In addition, mechanicalproperties were also obtained from scale model tires and comparedwith corresponding properties from full-size tires. While the testscovered a wide range of tire properties, results seem to indicate'that speed effects are not large, scale models may be used for obtaining some but not all tire properties, and that predictive equations developed in NASA TR R-64 are still useful in estimating mostmechanical properties.
17. Key Words (Suggested by Author(sl)
Tires, aircraftLanding gear
18. Distribution Statement
Unclassified - Unlimited
Subject Category 03
19. Security Classif. (of this report)
Unclassified
20. Security Classif. (of this page)
Unclassified
21. No. of Pages
8522. Price
A05
N-305 For sale by the National Technical Information Service, Springfield. Virginia 22161
•
"
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,
NASA Langley (Rev. May 1988) RIAD N-75