Aircraft NASA Data 49x17

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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

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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

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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.

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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.

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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.

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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.

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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.

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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

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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. "

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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.

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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,

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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

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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

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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

•

"

DO NOT REMOVE SLIP FROM MATERIAL

Delete your name from this slip when returning materialto the library.

NAME MS

/)';.,1

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LABt:-fl-fZ-Y

,

NASA Langley (Rev. May 1988) RIAD N-75