THE UN IV ER SIT Y OF MI CHI GAN COLLEGE OF ENGINEERING Department of Engineering Mechanics Department of Mechanical Engineering Tire and Suspension Systems Research Group Technical Report Noo 10 STRUCTURAL MODELING OF AIRCRAFT TIRES so K. Cyrk Ro No -dge J. Io Lackey.G. HI Nybakken ORA Project 05608 supported by: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GRANT NOo NGL 23-00501.0 WASHINGTON, D C o administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR May 1970

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TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS iv NOMENCLATURE vi I INTRODUCTION 1 II. SUMMARY OF RESULTS 3 IIIo THEORY OF MODELING A. Modeling of Tire Mechanical Properties 4 B. Modeling of Tire Stress Levels 10 C. Modeling of Tire Equilibrium Temperature 14 IV. MECHANICAL PROPERTIES OF MODEL AND PROTOTYPE TIRES 17 V. MEASUREMENT OF TIRE MECHANICAL PROPERTIES 29 VI. REFERENCES 35 VIIo ACKNOWLEDGMENTS 36 APPENDIX 1: METHODS FOR INTERPOLATING FORE-AFT TIRE STIFFNESS 37 APPENDIX 2: MODEL TIRE CONSTRUCTION AND DEVELOPMENT 40 General Comments 40 Scale Modeling of 40 x 12 Tire 42 Tire Development 55 DISTRIBUJ1TION LIST 60 iii

LIST OF ILLUSTRATIONS Table Page I. Tire Operating Conditions 24 II. Fore-and-aft Stiffness Data 38 III. Specification Sheet for Tire A-14 45 IV. Properties of Typical Model Tires 57 Figure 1. Tire geometry and nomenclature. 4 2. Tire co-ordinate directions. 17 3. Vertical load-vertical deflection data for model and prototype tires. 25 4. Lateral load-lateral deflection data for model and prototype tires. 26 5. Fore-aft load-deflection data for model and prototype tires. 27 6. Twisting moment-rotation data for model and prototype tires. 28 7. Vertical load-vertical deflection test for model tire. 29 8. Fore-aft load-deflection test for model tire. 30 9. Close-up of fore-aft test showing brake. 30 10. Lateral load-lateral deflection test for model tire. 31 11. Twisting moment-rotation test for model tire. 31 12. Loom for stringing tire cord. 41 13. Mold inserts and holder. 41 14. Unmounted model tire, rim and spanner for dis-assembly. 43 15. Mold and tire cross-section for model of 40 x 12 tire. 43 iv

LIST OF ILLUSTRATIONS (Concluded) Figure Page 16. First step in rubberizing the tire cord. 47 17. Completing the rubberized fabric. 48 18. Finished fabric cut to a bias angle. 48 19. Mandrel for laying up the tire. 49 20. Rubber liner on building drum. 49 21. First ply of fabric on building drum. 50 22. Ply 2 and tread on building drum. 30 23. Rolling on the tread cover. 51 24. Completed green tire and mold inserts. 51 25. Bladder inserted in green tire. 52 26. Bladder and green tire inserted into one half the mold. 52 27. Mold assembly with green tire just visible, prior to lifting. 54 28. Completed tire A-6 after removal from mold and trimming. 54 29. Tire A-6 mounted on rim. 55 30~ Comparison of model tires static load-deflection at 12.5 psi inflation. 58

NOMENCLATURE English Letters C - Couple or moment c - specific heat of tire material p D - tire nominal diameter E - tire carcass modulus of elasticity in the plant of the shell F - force on tire h - heat transfer coefficient between tire and surrounding air K - thermal conductivity of tire material k - radius of gyration of tire about its axis of rotation 0 klk2 *k kl0 - numerical exponents k,k,k - tire elastic stiffnesses, or spring rates L - length M - mass p0 - tire inflation pressure T - time V - wheel forward velocity w - tire section width Greek Letters -; - tire deflection 0 - temperature - tire relaxation length vi

NOMENCLATURE (Concluded) - Poisson's ratio of tire materials n - dimensionless factors P - tire material density a - tire stress - angle of rotation of tire about a vertical, or steer, axis Subscripts m - model p - prototype x,y,z - co-ordinate directions according to Figure 2. vii

I. INTRODUCTION The measurement of mechanical properties of aircraft tires is an expensive and lengthy process. Aircraft tires normally tend to be rather heavily loaded as compared with conventional automobile and truck tires, and to be run at quite high speeds, so that equipment to simulate field operating conditions is large and expensive. Only one major facility exists in the United States for the controlled study of aircraft tire characteristics under landing conditions. This is the well known Landing Loads Simulator track at NASA, Langley Field, Virginia. Considerable interest exists in obtaining dynamic or transient properties of aircraft tires for use in shimmy analysis work. A number of recent experiences with shimmy analysis followed by actual landing gear experience lead one to believe that current shimmy theories, using static mechanical properties of aircraft tires, are not now capable of clearly defining the shimmy characteristics of an aircraft landing gear system. There seems to be no obvious flaw in the theoretical formulation of shimmy calculations. One possible short-coming lies in the use of the elastic properties of tires as determined by static tests. If such properties could be determined under dynamic conditions, the values might be different enough so that better agreement between shimmy theory and experience would ensue. Such data is difficult to obtain on full size tires, again due to the size and complexity of the equipment needed to produce the appropriate operating conditions for the tires. Additional problems occur from time to time in aircraft tire operations which most conveniently could be solved by tests involving specific conditions.

Such tests may be difficult and expensive due to limited facilities, due to size and complexity of the equipment needed at these facilities, or due to safety considerations. For these reasons, it was felt desirable to review the possibility of structural modeling of aircraft tires, with the general thought that if such models could be developed, then they could be used to predict the effect of dynamic factors upon static mechanical tire data by reproducing the actual operating conditions of the aircraft tire. Such simulation, done on a small scale, should be much easier and more economical to carry out than actual full scale measurements. It would appear that the ability to produce a scale model aircraft tire which is capable of quantitative interpretation would be a valuable contribution to aircraft preliminary design, as well as to many practical operating problems.

II. SUMMARY OF RESULTS A research program has investigated the problem of producing small scale models of aircraft tires. It has been shown that such a scaling can be obtained in theory for the mechanical properties of aircraft tires, both static and dynamic, as well as for the overall or macroscopic stress state of such tires but not for their detailed or microscopic stress state. The question of thermal modeling is still unresolved but theoretical indications are that tire temperature distributions will not.be similar or analogous between model and prototype. Experiments have been conducted on a small scale model of a 40 x 12, 14 PR, Type VII aircraft tire, with a scaling factor of 8.65. Agreement is excellent between the basic static tire mechanical characteristics in model and prototype, referred to a dimensionless basis. The structural modeling concept discussed in this report is believed to be exact for mechanical properties of an aircraft tire, including static, rolling and transient conditions.

III. THEORY OF MODELING The theory of tire modeling may be divided into three separate categories or sets of modeling requirements, involving tire mechanical properties, tire stresses and tire temperatures. These will be discussed separately. A. MODELING OF TIRE MECHANICAL PROPERTIES The first, and least restrictive case, is modeling of tire mechanical properties, which is the primary concern of this report. For that purpose, consider the tire mechanical properties, both static and dynamic, to be defined by the following engineering variables, as illustrated in Figure 1. p,E,Po Figure 1. Tire geometry and nomenclature. where F = load on the -tire C = moment on the tire D = tire diameter, a characteristic length* E = Young's modulus for the tire material = Poisson's ratio for the tire material Any characteristic length is satisfactory, but tire diameter is a readily available measure of size. 1,

P = tire inflation pressure 0 6 = tire deflection p = tire material density k = radius of gyration of tire and wheel 0o It should be noted that the tire carcass properties are represented as single quantities E and j, although in actuality they are distributions of elastic properties throughout the carcass. This dimensionless distribution must be maintained in the model tire exactly as in the full size tire in order for modeling to be exact. This is a requirement which is analogous to the need for geometric similarity between model and prototype, a well known and universally accepted condition. Several obvious dimensionless variables may be identified by inspection. These are 1 = complete geometric similarity between model and prototype, including the dimensionless distribution of elastic properties between model and prototype for the tire carcass. I =H b/D k P 3 D 4 E FD 6

The remaining terms may be written in a general functional relation using a typical dependent property, the relaxation length X of the tire. One may express this as a function of the pertinent engineering variables remaining as (D) = f(F, V, Po, D, p) (1) The method used to obtain the dimensionless variables from a relationship such as Eq. (1) will be taken from Langhaar [1], and will not be derived here. Using Langhaar's notation, the dimensional matrix for the pertinent engineering variables is given by Eq. (2): F V p D p M 1 0 1 0 1 (2) L 1 1 -1 1 -3 T -2 -1 -2 0 0 Let the functional relationship between the relaxation length and the other variables be of the form k k k4 k) () f(F1V 2 p D 4 p5) (3) = 0 Then the exponents are related through the expressions k1+k + k = 0 k1 + k2 - k3 + k4 - 3k = 0 (4) -2k -k -2k = 0

In Eq. (4), the unknown exponents k3, k4, k5 may be expressed in terms of kl and k2 in the form k = -k -k = -k +k +-k k 5 1 3 1 1 2 2 2 2 k4 = - 2k1 k = - k — k 3 1 2 2 The dimensionless terms governing the relaxation length may now be expressed as a, dimensionless matrix of coefficients: kl k k k4 k 11 1 0 -1 -2 0'_1~7~~~ I 1 0 ~~~~(6) 118 0 1 -1/2 0 1/2 From this, one obtains two additional 11 terms which must be held constant in order that the model and prototype are identical: p= D Y ) 118 p uo (7)4 Of these terms, H18 is the ratio of tire velocity to a characteristic wave velocity, and is similar in concept to a Mach number. 11 is, however, the important scaling parameter since it relates the tire inflation pressure p, tire diameter D and the force acting on the tire between model and prototype. In view of the fact that complete geometric similarity is an additional requirement, 7~~~~~~~~~tr

then any appropriate tire section width, tire diameter, or tire section height could be used in place of the diameter D in 117 so long as the dimensional character of that term remains the same. The Russian R. K. Gordon [2] has arrived at 1 by a somewhat different line of reasoning. A short discussion of the scaling parameter 11 is in order. If the inflation pressures for model and prototype are known, and if the relative sizes of model and prototype are known, then the appropriate forces between model and prototype may be determined by the fact that "7 must be equal for model and prototype in a given test situation. The scale ratio or model diameter D is at the choice of the experimenter. The pressure p must, however, be determined in conjunction with the required equality for H4. This latter term demands that the Fatio of inflation pressure of the model tire to its modulus of elasticity must be identical to that ratio in the full size prototype. Under those conditions, it may be seen that one may construct the small size model of a large aircraft tire using a purposely lower modulus of elasticity in the small model. This will allow a lower inflation pressure p, since in the model the ratio (Po/E) must remain the same as in the prototype. This further means that in evaluating the dimensionless term H8' the influence of velocity of travel will be amplified in the model. For example, if in the model it is possible to use a low modulus of elasticity and a relatively low pressure, reference to Eq. (7) shows that the model velocity can be made significantly higher. This is seen by equating H8 for the model and prototype, and solving for the model velocity. This gives v = E)(m (8)

where the subscripts m and p refer to model and prototype, respectively. If the material densities of the prototype and model are essentially the same, Eq. (8) shows that the model velocity V needed to obtain an equivalent prototype velocity V may be substantially less than the prototype velocity by the ratio of the square root of the model tire modulus to the prototype modulus. Methods of controlling tire modulus are available and may be used to advantage here. In effect, high speed tire testing on the model can be conducted at relatively low speeds. In general, this dimensional analysis shows that a typical tire response quantity, relaxation length X, is related to the dimensionless 1 terms through the relationship D= ( 1' 2'H8) <9) If the dimensionless relaxation length A/D is to be the same in both model and prototype, then each of the terms H1 through II8 must be the same in model and prototype. As discussed, this can be achieved by the use of geometric similarity, by the use of the same materials, but with the degree of freedom that the model tire modulus may be substantially reduced over that of the prototype provided that the modulus distribution is analogous or geometrically similar in both caseso This will allow all n terms to remain the same and will allow enhancement of velocity effects, which is desirable for high speed tire testing. In effect, H4 = po/E represents the primary independent variable of this analysis, since the modulus of elasticity of the tire carcass materials represents one distinct input decision. The second basiCd variable is 12 = 6/D,

which defines a length scaling. From this, it may be concluded that tire mechanical properties may be readily modeled between full size tire and small scale tire provided that one learns how to use tire materials in such a way that the distribution of carcass stiffness or elastic constants is the same between model and prototype, and that preferably the absolute level of the elastic constants be significantly reduced in the model compared to the prototype, without changing the relative or dimensionless distribution. B. MODELING OF TIRE STRESS LEVELS A second level of sophistication in tire modeling theory may be brought about by attempting to model the internal stress state between small scale model and prototype, in addition to the appropriate mechanical properties. Let us in this case imagine that the tire stress state is governed by the same engineering variables as shown in Figure 1, where all symbols are the same as before except for the stress level a. It is recognized from the previous dimensional analysis that six dimensionless products must be automatically satisfied by any model. These are HI = complete geometric similarity, including distribution of elastic constants (10) 2 (11) I = k /D (12) 3_ 0(13) 4 E 1 10

= (Poisson's ratio) (14) H6 = FD/C (15) Assuming these to be true, the stress state in the moving tire may now be expressed in the general functional form = f(P, D, V, F, p) (16) p The right-hand side of Eq. (16) is identical to that of Eq. (1), so that the dimensionless quantities governing this are identical to those previously gotten in Eq. (7), i.e. 7 F (17) POD 18 E (18) Now one may write = o 1' 2' ( 12-18) (19) Equation (19) shows that if one wishes to maintain the same stress level in model and prototype, then all terms 1, H8 must be held identical, and in addition the inflation pressure p must be the same in both model and 0 full size tire. Since po must be constant, then from H4 (Eq. (13)) it is seen that modulus of elasticity E of both model and full size tire must also be the same~ In effect, this forces one to use the same materials for the model as the full size tire. 11

The rules for one form of modeling a full size tire to small scale can now be seen by a study of Eqs. (10) through (19). For example, the requirement of complete geometric similarity again means that the small scale tire should be geometrically proportional in all respects to the original tire. Since it is necessary to use the same inflation pressure in the small scale tire as in the full size tire, Eq. (13) requires that the modulus of elasticity E remain the same in the model as in the prototype. Then the stress level expressed in Eq. (19) will remain the same between the small scale and full size tire. Equation (11) shows that the dimensionless deflection of the tire should be the same on the model as on the full size tire. Equation (14) shows that the Poisson's ratio of the material used to make the model tire should be the same as that of the full sized tire, and.this will of course be automatically satisfied if the same materials are used. In addition, the distribution of cord angles and materials should be identical between model and prototype. Equation (17) shows that under these conditions, the load applied to the model tire should be in the ratio of the square of the scale factor. For example, if the model tire is one fifth of the size of the full tire, then a load equal to one twentyfifth of the full scale load should be applied to the model tire. Finally, Eq. (18) shows that the model tire should be run at the same surface speed as the full size tire, since both the material density p and the Young's modulus E of the material will be the same in both model and full size tire. If all of these conditions are met, then Eq. (19) predicts that the overall or macroscopic stress state in the model tire will be the same as in the full size tire. 12

It should be noted that this set of requirements is somewhat stricter and more confining than the previous set which dealt with mechanical properties of the tire alone. Here, the pressure is specified as is the modulus of elasticity of the model tire material. This was not the case in the previous analysis describing only mechanical properties, where it was possible to reduce modulus and pressure simultaneously and still retain dimensional similarity. This simply means that in the previous case, the stress levels in the model tire were not equal to those in the prototype. Here, where equal stress levels are desired, the additional restrictions of pressure and modulus equality are necessary. In order that this situation be understood more clearly, it should be mentioned that in a practical sense it is essentially impossible to insure that a textile-cord structure be made in small scale that is identical in all respects to a similar structure in large size. Textile cords are manufactured only in discrete sizes and in general cannot be scaled downward arbitrarily. The details of aircraft tire construction are sometimes so numerous as to render the construction of a completely similar small model almost impossible, even though the overall, macroscopic constants of the tire carcass material may be successfully modeled. For these reasons it is very probable that such effects as durability and failure will be very difficult to assess on a scale model with any significant scale ratio simply due to the basic unavailability of the proper materials, and the great difficulty of producing a completely geometrically similar structure. Put in other terms, the detailed construction cannot be modeled practically, so that the microscopic or local stress state will not be equal between model and prototype. 13

In the event that such tire stress comparisons are desired, it should again be emphasized that the modulus of elasticity, or elastic constants, of the model and full size tire must be held the same, that the inflation pressure of the model must be identical to that of the prototype, and that the surface speeds must also be equal between the two. Under these conditions, forces proportional to the square of the scale factor arise between model and prototype, as indicated by Eq. (17), while the overall or macroscopic internal stress state of the model tire is the same as the full size tire. C. MODELING OF TIRE EQUILIBRIUM TEMPERATURE Now consider the somewhat more complex case of including in the analysis the quantities which determine the equilibrium temperature of the running tire. In order to do this, we adopt Eq. (20) as a basic statement of functional dependence. KGp 5 = f(p, D, V, F, p, cp, K, h) (20) pV D where the new symbols are as follows: K = thermal conductivity of tire material $ = temperature c = specific heat of tire material p h = heat transfer coefficient between tire and atmosphere. The particular form of the left-hand side of Eq. (20) is chosen so as to represent temperature in a dimensionless fashion. Other representations are possible, but do not lead to anything different. The dimensional matrix involving these 14

variables is shown in the table below, where temperature 0 is taken as a basic physical variable. F V p D p c K h o p M 1 0 1 0 1 0 1 1 L 1 1 -1 1 -3 2 1 O (21) T -2 -1 -2 0 0 -2 -3 -3 89 10 0 0 0 0 -1 -1 -1 A dimensional analysis of these variables leads to the following dimensionless characteristics which must be equal between model and prototype, over and above those given by Eqs. (10 through (19), previously derived: K 17 (22) L7 =-~Dh 81 v= p c (23) 8 V-P-cP Of these two dimensionless quantities, Eq. (23) will be automatically satisfied provided that the conditions described in the previous dimensionless analysis are fulfilled, that is, the velocity of running and density of the tire material are the same between model and prototype. The heat transfer coefficient h and the material specific heat c will be approximately the same in the full size tire as in the model, so that Eq. (23) will be automatically the same for both model and prototype. However, 1 very probably will not be equal between model and prototype, since the heat transfer coefficient h and thermal conductivity K of both model and full size tires will be approximately the same, while the characteristic 15

length D will vary as the scale factor. Based on this, Eq. (20) may be rewritten as V2 c f(l12' 2' 13' 4' 5'8) (64) p From this, it may be seen that the temperature 0 of the model tire will be the same as that of the prototype provided that the velocity of travel and the specific heat of the tire material are the same as in the full size tire, and in addition that all of the dimensionless factors H1 through H8 are held constant between the scale model and the full size tire. As was just discussed, it is possible to do this with the exception of the single dimensionless factor 1. Its influence on the equilibrium temperature is not known but may be substantial, since in effect it represents the ratio between the volume of the tire which generates heat due to hysteresis loss, and the convective heat transfer surface area of the tire. It is possible under particularly fortuitous conditions that a good approximation of the full size equilibrium temperature may be obtained from a model tire, but it appears that no guarantee of this exists. Therefore, it is concluded that in general thermal modeling of aircraft tire temperature rise may not be possible without extensive experimentation and the development of suitable scaling factors based on experimental data.

IV. MECHANICAL PROPERTIES OF MODEL AND PROTOTYPE TIRES From the discussion in the previous section, it is seen that the structural modeling of an aircraft tire can only be assured if the pertinent dimensionless variables are the same for both model and prototype. In general this means that such quantities must be measured for both tires and compared. In this work, the method used to do this relies on the measurement of several force-deflection relationships in the model, followed by comparison with known full-size tire data, for these same properties. In accordance with the previous section, all models are geometrically similar dimensionally and are approximately scaled in their cord end-count, although the individual cord size has not been so scaled. To facilitate an understanding of the various loading situations used in this report, a co-ordinate system as shown in Figure 2 has been chosen. (Rtotation about z-axis) |Y(( o(Fore-') / (Vertical) Figure 2. Tire co-ordinate directions. 17

With this co-ordinate system, then, fore-aft, lateral, and vertical forces applied to the tire's contact patch have been denoted by F, Fy, and F, respectively. A similar notation is used for the appropriate deflections, 5x, 6y, and 6. A couple or twisting moment about the z-axis has been termed C, and the z z resultant angle of rotation, r. It is possible to use H71 H6, and H2 to describe basic load-deflection relations in a dimensionless way so as to compare the prototype tire with the model tire. Four basic mechanical properties have been chosen since they can be easily measured: (1) Vertical Load-Vertical Deflection - (F vs. 5 ) z z (2) Lateral Load-Lateral Deflection -- (F vs. 6 ) y y (3) Fore-Aft Load-Fore-Aft Deflection - (F vs. 5 ) x x (4) Twisting Moment-Rotation -- (C vs. z Each of these quantities may be expressed in a dimensionless way using the dimensionless variables I12, II6, and'7: F 6 (1) Vertical Load-Vertical Deflection - ( 2 vs. 2 D p D 0 F 6 (2) Lateral Load-Lateral Deflection (. Yv pD2 D F 6 (5) Fore-Aft Load-Fore-Aft Deflection - ( vs. 2 D 0 oD C (4) Twisting Moment-Rotation _ — (-_ z vs. t). p D 18

Using these dimensionless parameters, comparisons with the prototype can be made to gauge how well the model tire matches it. These four load-deflection relations are extremely important since they span a wide range of tire deformation effects, from that of an inflated membrane to that of an elastic sheet. Some previous analytical and experimental studies by the authors [3], [4], [5] lead us to believe that most tire mechanical properties may be viewed as the sum or interaction of contributions from the inflated nature of the tire, acting as a gas envelope, and from the elastic nature of its carcass. If the four load-deflection relations just listed are the same, on a dimensionless basis, between model and prototype, then it is strong evidence that all tire mechanical properties are adequately modeled. This is because: (1) Vertical load-deflection appears to be primarily an inflation pressure effect for aircraft tires. See Ref. [3]. (2) Lateral load-deflection and twisting moment-rotation appear to be a mixture of both inflation and carcass elasticity effects. See Ref. [4]0 (3) Fore-aft load-deflection appears to be almost entirely a carcass elasticity effect. See Ref. [5]. Since the fore-aft properties depend on carcass elasticity, a measurement of the fore-aft stiffness is in an overall gross sense a measurement of the modulus of elasticity E of the carcass. The importance of this cannot be overemphasized, and it merits some further discussion. Practically speaking, the measurement of the modulus of elasticity E of the tire is extremely difficult, while the measurement of the fore-aft stiffness F k = - is easy. x 6 x 19

Assuming then that k is proportional to E, and having previously recognized P that II = - must be held constant for both the prototype and the model in order 4 E to satisfy Eq. (9), then it is seen that: p0 P E k x Furthermore, it is recognized from 7 that: Fx =F o p o P Thus, (F) (F)( x p _ _ xm ~(po D2( ) (D2 o where the subscripts m and p again refer to model and prototype, respectively. (Po) (x ) P ( ) (k) (D) xp. p This approach is not entirely unreasonable since the fore-aft stiffness of an aircraft tire is known to be relatively independent of inflation pressure at 20 M~~~~~prsuea x p~~~2

or near its operating pressure. This method has been used to calculate the reference inflation pressure of the model tires used in this report, based on the use of Eq. (25) and the measured (kx ) and (kx). Thus, from the start, a nondimensional plot of the fore-aft load-deflection data for the prototype and the model will coincide exactly since the one has been used to define the other, and it only remains to check the other mechanical properties to see if one has attained a successful modeling of the prototype. Unfortunately there is not a large amount of fore-aft stiffness data available in the literature. In this particular effort a 40 x 12 14 PR tire was chosen as the prototype since excellent mechanical property data is available for it from Horne and Smiley [6]. However, its fore-aft stiffness must be estimated by interpolation from other test data. A method for doing this is developed in Appendix 1. It yields a value for this prototype of (kx) = 6800 lb/in This is the fore-aft stiffness value used in Eq. (25) to determine the operating pressure of the model tire. The sequence of measurements on a given model tire is now as follows: (1) The fore-aft stiffness of *the model tire is measured at an inflation pressure and vertical load which are estimated from past experience. This yields (k). x m (2) Using Eq. (25), the proper model inflation pressure (p )m is calculated. (Q) Using 77, from Eq. (7), the proper model vertical load is calculated from 21

(po) (D2) (F ) (F) om m z m z p (po)p 02 ( p (4) The fore-aft stiffness is again measured using the new (po)m and (F ). Due to the very weak dependence of (kx) on these quantities, this one cycle of correction is usually sufficient to give an accurate (kx)m x m (5) Equation (25) is again used to calculate (k) (D) xm p ( om (k) (D) po( x p m (6) Equation (7) is again used to obtain the model vertical load corresponding to any prototype vertical load (p ) (D) (F) (F) o ( z m (Fz) p (p 2) (7) Lateral stiffness of the model is measured at the rated model pressure and vertical load. This gives (F ) and (6). A dimensionym ym less plot of these is prepared and compared with a similar dimensionless plot for the prototype. The ordinate of such a plot is (F /P D2) while the abscissa is (y /D). (8) Vertical stiffness of the model is measured at the rated model pressure. Again a similar dimensionless plot may be used to compare model and prototype data. In this case, the ordinate is (Fz/PoD2) while the absicssa is (6 /D). 22

(9) Twisting stiffness is measured at the rated pressure and vertical load for the model. The dimensionless plot comparing model and prototype data combines the properties of 7 and H8 to use as ordinate (C /P D3) and as abscissa the rotation angle i. (10) Correspondence of tire mechanical property data between model and prototype in steps 7, 8, and 9 is taken as indicative of satisfactory tire static modeling. It is worth noting at this point that all data given for the model tires in this report are for exercised tires. It was discovered very early in the project that the mechanical properties of the tires were noticeably affected and then appeared to become stable, after they had been exercised for a period of time on a small road wheel. These changes were most pronounced at low inflation pressures, as one would expect. Consequently, every tire was "run in" for three or four hours at fairly moderate conditions, which were scaled equivalents of about 60 mph speed, 6000 lb vertical load, and 60 psi inflation pressure. Summaries of the comparisons of several model tires, specially constructed to scale the 40 x 12 14 PR prototype, are shown in Figures 3 through 6. Table I lists the operating conditions for each of the models as well as for the prototype. The vertical load F shown in the table was that used when obtaining twist, fore-aft, and lateral data. 23

TABLE I TIRE OPERATING CONDITIONS p F 0o z D w* Tire (psi) (lb) (in.) (in.) 40 x 12 - 14 PR Type VII 95 14500 39. 3 12. 12 Prototype Model A-18 25 48.2 4.57 1.67 (2 Ply, 840/2 Nylon, 10 EPI) 48.2 4.57 1.67 Model A-15 23 482 66 (2 Ply, 840/2 Nylon, 10 EPI) Model A-14 19 38.2 4..58 1.64 (2 Ply, 840/2 Nylon, 10 EPI) Model A-13 20 38.2 4.56 1.62 (2 Ply, 840/2 Nylon, 10 EPI) w = Section Width 24

' I. I I.22 * PROTOTYPE 40x12-14 PR TYPE E - 0 MODEL A-18.20 E MODEL A-15.18 A MODEL A-14.16 V MODEL A-13.14 0 Fx.12PoD2 2.10.06 _.04.02 0.01.02.03.04.05.06.07.08.09.10.11 sz /D Figure 3. Vertical load-vertical deflection data for model and prototype tires. 25

.022.020.018 0 A O.016.014 Po D2.012_.010 1 PROTOTYPE 40 x 12 -4 PR.008 TYPE MODEL A- 18.006 0 MODEL A-15.004 [] _ MODEL A-14 MODEL A- 13.002 0 0.005.010.015.020.025.030.035.040.045 8y /D Figure 4. Lateral load-lateral deflection data for model and prototype tires. 26

.020 - PROTOTYPE 40x 12-14 PR TYPE l (CALCULATED 0 MODEL A-18.018 D MODEL A-15.016, MODEL A- 14 _ " 1_ ___ V MODEL A-13.012 PoD2 C 010.008 _/i.006.004 0.001.002.003.004.005.006.007.008.009.010 x /D Figure 5. Fore-aft load-deflection data for model and prototype tires. 27

* PROTOTYPE 40 x12-14 PR TYPE VE |.006 0 MODEL A-18 O MODEL A-15 V A MODEL A-14.005 V MODEL A-13. |.| A lZI I dVo cz Po D3.003.002.001 00 1~ 20 30 40 50 60 Figure 6. Twisting moment-rotation data for model and prototype tires. 28

V. MEASUREMENT OF TIRE MECHANICAL PROPERTIES All data recorded in this report was collected on what will hereafter be referred to as the Static Testing Device. This device was designed so that the model tire could be tested to obtain ea ch of the four basic mechanical spring constants previously mentioned in this report, vertical load-deflection, lateral load-deflection, fore-aft load-deflection, and twisting moment-rotation. Construction of the device is very simple, consisting of a wooden base, two steel loading plates, a tubular steel 900-elbow arm,a rotating yoke, a, steel point hinge, and a counterweight. Figures 7 through 11 show different views of a model tire under test in it.. The bottom steel loading plate was attached to Figure 7. Vertical load-vertical deflection test for model tire. 29

Figure 8.Fore-aft load-deflection test for model tire. ii x/4<;~i-:;:rij~-'::~::~:~~~jp;~'~,:.g Figure 8. Floreaft load dflectio test fhori modkelir 30~~~~~~~~~,

i iiiiiii~~~~~~iiiiii~~~~ii~~~i~~i!~iiii~~~~iiiiiiii~~~~~~iiii~!i~~~~iiiiiiiiii!11!iiiiiii:::_iijii~iijiiiil - F:i:~igure 10.:L a t e r a l loa teral deflection test for modetire~. Fiigure 11o Twisti n g m o m e nt-rotation te istformode.l tire i'iiiii':(ir:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...............:~ii~~~~~~~~iii~~~~~~ F~~~F~~~ib~~~~~ g~~~~ i~~~~~iIE'i~~~~~~~~~iB ~ ~ ~ ~ j~~~~iifi ~ ~ ~ ~.................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:::,-i:i:i:;::_-~: _ —:-:_-:ii':i::.............. ~ ~ ~ ~ ~ ii................ 7. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~............ —;i''.' -:: —:::;: -:~ ii ~:: i~~~i~i'li":a~~~iiii~i i-i_:iiiiii~i"!:i~i~i.......................::::i:a~~."~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~M Figure 11. Twisting moment-rotation test for model tire.sibiities! 3L~~~~~~~M

the wooden base, and the top loading plate had three.437 in. dia. bearing balls sandwiched between it and the bottom plate. The top plate had a high friction surface bonded to it with contact cement so that tire slippage was held to a minimum during loading. The tires were inflated through a small hole along the axis of the axle, opening into the interior of the rim with oil seals inserted within to maintain pressure. The pressure was regulated by a general purpose low-pressure regulator, which was monitored periodically so that proper pressure was maintained. Inflation pressures could be held to within + 1/2 psi. with this regulator. It is important to have close pressure control in these experiments due to the large scale ratio, in this case 8.65. Experimental reproducability was good for vertical load-deflection where, on the average, data could be reproduced to within + 3%. For twisting momentrotation, data variation was as high as + 8%, and for lateral and fore-aft experiments, it was as high as + 10%.;To compensate for this, the tires were tested a minimum of three times and also rotated to a new position before each run. This amount of variation in properties is not particularly large, since studies on full size tires indicate a similar set of variations. As a matter of record, all the deflection data collected was taken at "apparent equilibrium"; i.e., when all creep had ceased. The first measurement on a model tire was that of its basic fore-aft spring rate, as previously discussed. This was generally done at a relatively high pressure (e.g., 20-25 psi). Then after obtaining (k, Eq. (25) was used to calculate the reference pressure for the model tire:

(k) (D) (p) xm ___P (25) om (k )p (D) (Po)p Using the appropriate values for each of the variables the prototype, Eqo (25) becomes: x m (39.3)(95) (n (I(j(in[2 ((lb)('() m (D)m 6800 (b$i~<) (k<) (k x)m (Po)m = 549 (D) psi (25a) m(D) Using this calculated reference pressure, one may use 7 = ( ) to calp0 culate the proper vertical load that should be used for the model tire to simulate the 14,500 lb rated load of the 40 x 12 prototype. This gives 2 14500 lb or (F )m (Po) (D ) lb or z 0 m m (95)(39.3)2 (F) =.0989 (p) (D)m lb (26) For example, tire A-14 had a fore-aft stiffness (k ) = 160 lb/in. From Eqs. (25a) and (26), one would find that the reference pressure and vertical load should be: (Po)m -~ 19 psi (F) 39o 8 lb z m With these new parameters, a second fore-aft measurement would be made to verify 33

that the correct (k ) had been determined. When this had been done, then the x m other mechanical properties were measured and compared with the prototype.. It is worth listing some of the principles and techniques used in measuring the various mechanical properties: (1) All loads applied to the contact patch in the xy-plane were applied away from the hinge of the static testing device to keep side movement of the hinge-arm to a minimum. (2) The model tire was always relieved of vertical and side loads, i.e., allowed to relax in a free static position, a few minutes before proceeding with the next run for any particular test. (3) The dial gauge was mounted between the moveable top plate and the axle to ob-tain both lateral and fore-aft deflections. Yoke and rim movement were observed to be negligible. (4) The zero point for vertical deflection was defined as that point when the tire just touched the top loading plate. (5) Inflated dimensions of the model tires were obtained by averaging readings taken at five places around the tire circumference. Both the width and diameter were measured directly. 34

VI. REFERENCES [1] Langhaar, H. L., "Dimensional Analysis and Theory of Models," John Wiley and Sons, New York, 1951. [2] Gordon, R. K., "Modeling of Tires," Soviet Rubber Technology, v. 24, n. 6, p. 30, 1965. [3] Nybakken, G. H. and S. K. Clark, "Vertical and Lateral Stiffness Characteristics of Aircraft Tires," The University of Michigan, Office of Research Administration, Report 05608-14-T, May 1969, Ann Arbor, Michigan. [4] Dodge, R. M., S. K. Clark, and K. L. Johnson, "An Analytical Model for Lateral Stiffness of Pneumatic Tires," The University of Michigan, Office of Research Administration, Report 02957-30-T, February 1967, Ann Arbor, Michigan. [5] Dodge, R. N., D. Orne, and S. K. Clark, "Fore-and-Aft Stiffness Characteristics of Pneumatic Tires, " NASA CR-900, National Aeronautics and Space Administration, Washington, D. C. October 1967. [6] Horne, W. B., and R. F. Smiley, "Low Speed Yawed Rolling Characteristics and Other Elastic Properties of a. Pair of 40 Inch Diameter 14 Ply Rating Type VII Aircraft Tires," N.A.C.A. Technical Note 4109, Washington, D.C. January 1958. [7] Tanner, John A. and Sidney A. Batterson, "An Experimental Study of the Elastic Properties of Several Aircraft Tires During the Application of Braking Loads," Langley Working Paper LWP-592, National Aeronautics and Space Administration, Langley Research Center, May 1968.

VII. ACKNOWLEDGMENTS The authors would like to acknowledge the very substantial assistance of the B. F. Goodrich Research Laboratories, Brecksville, Ohio, who furnished most of the materials used in this development. Thanks should also go to the General Tire and Rubber Company and to Uniroyal, Inc. for donating materials, and to Mr. Chester Budd of the B. F. Goodrich Company and Mr. Seymour Lippman of Uniroyal, Inc. for advice and assistance.

APPENDIX I METHODS FOR INTERPOLATING FORE-AFT TIRE STIFFNESS Due to the general scarcity of fore-aft stiffness data for tires, a method is needed for interpolation or estimation from available measurements, To do this, assume a linear relation between the important variables. Let the deflection 5 be dependent in the form x F ad = (Eh)d (27) x (Eh)'N-d where F = fore-aft force x d. = tire diameter E modulus of elasticity of the ply material h = thickness of one ply N = number of plies Equation (2';) is modeled on the expression for simple extension in shear or tension deformation of an idealized tire structure such as considered in Ref. By definition, the fore-aft spring stiffness is k = F /b, so that from Eq. (27) F kx = = (Eh)' N (28) x But due to the limited range of textile cord sizes used in aircraft tire manufacture, and due to the similarity of cord angle distributions, imposed by other

requirements, the product (Eh) is nearly constant for each ply in a tire. Hence, to a first approximation, k = C *N (29) x where C is a constant for each basic cord material, i.e., nylon, rayon, polyester, etc. Present manufacturing practice is to use nylon almost exclusively for aircraft tires. Equation (29) gives the surprising result that fore-aft stiffness is approximately proportional to the number of plies in the tire, and independent of all other factors except cord material. Tanner and Batterson [7] have recently performed fore-aft stiffness measurements on two modern aircraft tires. Their data, along with data from one tire measured at The University of Michigan, is given in Table II. TABLE II FORE-AND-AFT STIFFNESS DATA Tire Type | Tire Size Ply Rating I Source Measured k VIII 130 x 11.5 - 14. 26 Langley 12,900 lb/in. I I. VII 49 x 17 26 i Langley 12,320 lb/in. III j 7.50 x 14 1 8 University 3,250 lb/in. __________________| |of Michigan Using an average value of 12,600 lb/in. for a 26 PR tire, the value of k for the 14 PR 40 x 14 tire used here is 38

k 12,600 x = 6800 lb/in. x 26 This value will be used for subsequent calculations, since the Type VII and Type. VIII tires are geometrically similar in cross-section to the present 40 x 12 tire. Notice, however, that even the much smaller Type III 7.50 x 14 tire gives a similar result, since if one uses it as a standard of comparison, then the 40 x 12 tire is predicted to have a fore-aft stiffness of k 3250 x1 = 5700 lb/in. x 8 Care should be taken in using this method, since in many cases the ply rating available for a tire is not equal to the number of plies in its carcass. 39

APPENDIX 2 MODEL TIRE CONSTRUCTION AND DEVELOPMENT GENERAL COMMENTS The initial model tire experiments were carried out with a commercial Veco* model airplane tire of 4.5 in. diameter. These experiments demonstrated the general feasibility of small scale tire modeling, but also exposed serious shortcomings in the Veco tire. These tires tended to creep, or grow with time, so that their dimensions and mechanical stiffness properties changed slowly. They had no cord structure, and so did not truly represent the elastic properties of an aircraft tire. Since scale modeling was our objective, it appeared necessary to find ways of obtaining or making a model tire similar in structure to a real tire. Experiments showed that it was possible to form a small cord-structure tire of model size using an inflatable bladder, similar to commercial tire practice. Equipment was manufactured or purchased for making such tires. The most important elements of this equipment were: (a) A loom for hand winding tire carcass fabric, with provision for variable cord end count. This is shown in Figure 12. (b) A mold frame, or holder, in which the actual tire molds are inserted, and which serves to hold the two mold halves tightly together. This is shown in Figure 13. *Trade name. 40

Figure 12. Loom for stringing tire cord. IN~~~~~~~~~~~~~~~~~~~ L~~Fiur 15.Mod nsrt ad oler ~~~~4

(c) A tire mold, which forms the outer surface of the tire as also shown in Figure 13. (d) A bladder for forming the tire against the moldo (e) A laboratory oven for curing the tire. The materials used for these tires were conventional tire cord, dipped into an adhesion promoter, and unvulcanized rubber sheet stock. The bead of a tire is an area where considerable hand work is done in fabric cating a commercial, full size tire. It did not appear possible to be able to duplicate bead constructions readily in. small scale tires, nor did it seem particularly important to do so since the bead does not enter into any of the mechanical properties of the tire~ These considerations led to a choice of a beadless tire design, which greatly simplifies tire construction and molding but at the expense of a somewhat more complicated wheel and rim. This is because the rim must now center, locate and grip the tire, functions which normally are at least in part performed by the bead. Figure 14 shows the rim with a dismounted tire. This rim has two side caps which screw inward and clamp the tire against a flange, one side cap being shown separately on the right hand side of Figure 14, along with its spanner. Using this rim design, inflation is carried out through one hollow' axle, which is stationary, while the wheel is mounted on the axle with bearings and seals. Leakage is minimal. This design allows various force transducers to be built into the nonrotating axle without the use of slip ringso SCALE MODELING OF 40 x 12 TIRE The 40 x 12 14 PR Type VII tire was chosen as a specific prototype since 42

Figure 14. Unmounted model tire rim and spanner for dis-assembly. o. 0 1 V 1..' 4 7 7 7 7.I I i i DISTANCE.7 FROM 7 - MOLD.6 EDGE 454

Jit had been the subject of extensive mechanical property measurements by Homrne and Smiley [6]. The mold was designed to be geometrically similar to the deflated outside cross-section of this tire, but with additional. sect,ion height as dictated by the beadless design. Figure 15 shows the mold contour usedO The mounted section height would, of course, be geomet:rically similar due to the presence of the rim flanges~ Table I in SecDtion TV shows the inf:L]atJed dimensions of the model. tires tc) be approximately correc+t, although model t:.z:e widths t-end to be slightl..y hi.gh Molds were contour machined from alumi.n.um, and wi.:re in.serts used..ci, form the tread groovesJ The first step in building a, model tire is -writing a, speci.fCication. sheet' This is done so that a permanent construction record is av'ailableo A typi ca specification sheet is given in Table III for a, two ply bias tire~ Next, cord must be selected and the tire carcass fabri c. made up. Three different cords were tested during this development, these being(a,) An. 840/2 nylon, which is the most common cord now used in full size aircraft tire construction (b) One strand of the two-.stranded 840/2 cord (c) A single strand from a three strand special_ elastic -cord~ The single strand had a strong helical wivr.nding set., and exhibited a very low modulus Of these three, it was found that the full 840/2 nylon cord appeared to be most adequate, and is further desirable since it is readily available commercially. 44

TABLE III SPECIFICATION SHEET FOR TIRE A-14 Ply Stock: Cord - 840/2 nylon dipped cord Rubber -.012" USR on each side Loom - 10 cords/inch Green cord angle - 600 Ply width - 6-5/8 Green Tire: No. of pieces Location Width x Thickness Rubber (1) Liner 1 on i 2-3/4" x.0241 BFG soft 2 5/8"' from, 5/8" x.024" BFG soft (2) Ply 1 (3) Separator 1 on g, 6-5/8" x. 024" BFG soft 1 on, 2" x.024" BFG soft (4) Ply 2 (5) Tread 2 3/4"4 from i 3/8" x.024?? BFG soft 1 on ~ 2-1/2" x.024" USR 2 1-7/8" from i 1/2" x.024" USR Final Width - 6-1/2" Bladder - made from bicycle tube Curing: 2:40 PM'80~F in oven 3:40 PM 270 F } 1/6 3:55 PM 300F}1 4:10 PM 320 F 4:25 PM 320~F } 1/4 4:33 PM 3520 F out

The first step of the actual construction is the fabrication of the pl.y stock. The loom is strung as previously shownr in Figure 12o A cord count- of 10 ends per inch was chosen for the model tires used in this report, si.nce two plies of this material are approximately equal in elastic sti.ffness to on.e ply of tfhe actual tire fabric used in the prototype tire, A thin sheet of unvuly, canized rubber is laid on either side of the paral lel. cords, as shown in Figures 1.6 and 17, and is rolled down -tight lyo The completed ply fabric is then cut to the proper bias angle as shown.in Figure 180 The tread, liner and separator rubber pieces are cut t',o si.ze, as gi-.ven in the specifications, from unmvulcanized rubber sheet of the proper th.bicknesso As shown in Figure 19, a two inch tube mounted in a, met.alworking lathe serves a,s the buildixg drum~ The tube is coverted with Saran Wrap t4o all.ow' the green tire to be removed easily after building. Typical is the layup of tfire A-6. First, a, rubber liner is rolled on. and stic.hed down. show-n in Figure 20. Then pl.y 1 is rolled on, Figure 21, followed by ply 2 and the first layer of tread, Figure 22. Finally., after the tread is completed, a, tread cover is rolled on with the lathe knurling tool, Figure 2?3 The green t;ire cylinder. is then cut to desired length and labeled with a silver ink pen, wh:ich -Thcn, cuved, leaves a permanent identification marking. Figure 24 shows the finished green tire flanked by the mold inserts. The tire is now ready for molding and curing. First the tire is covered with talcum powder which serves as a, mold release agent. The bladder is then made ready by stretching it over its tapered end plugs, and is then inserted into the uncured tiree This is shown in Figure 29. The most successful bladders 46

Figure 16. First step in rubberizing the tire c 47

Figure 17. Completing the rubberized fabric. Figure 18. Finished fabric cut to a bias angle.

Figure 19. Mandrel for laying up the tire. Figure 20. Rubber liner on building drum. 49

Figure 21. First ply of fabric on building drum. Figure 22. Ply 2 and tread on building drum. 50

Figure 23. Rolling on the tread cover. IM..............Q............ ~ ~~ C~~~~~~~~~~~~~~~~~~~~~~~~~~~r7~77

4 /. 4A'P~-~e:q 4k~::. 4&4~-.4 Figue 25 Bldderinsetedin geen ire "';"" I, "S~~~~~~~~~~~~~~~~ii "'/4' "4" "' 5'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:'&i~j-'~~QiS::~:_::~~ 414~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~::~:::- -ii'~3: ~~~Figure 26. Bl adder adgentr insrerte int oene hal te mld 52~

found for this work were short lengths of bicycle inner tube, although other materials were occasionally used. In commercial tire production a bladder is especially molded for this purpose, and that would undoubtedly be the best solution for the model tire. The uncured tire and bladder are carfully positioned in the mold halves as shown in Figures 26 and 27, where in the latter photograph the two halves are partially closed together. The partially closed mold halves are placed in a laboratory oven and attached to an air line. The bladder is slowly inflated as the mold halves are brought'together. When they are completely closed, the air pressure is raised to 60 to 100 psi and the oven temperature to 3600F. The mold temperature is monitored with a, contact pyrometer, and the time-temperature curve of the mold is integrated in an approximate, step-wise fashion to obtain the proper total cure. The cured tire is removed from the mold and finished by cutting off the vents and end caps formed by the tapered plugs. Figure 28 shows tire A-6 after curing, The tire is then mounted on the rim, Figure 29, and exercised on the road wheel for three to four hours. The tire is now ready for mechanical property tests.

''~~~~~~~ #~~~~~~~' ~ ~ ~ ~ ~ Fiue2. odasmbywt gentr As iibe ro t itn * <~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<****~~~~~~~~~~~~~~~~~~~~~~~~~~~-:: —i~9;:~i- - Figure 28 Completed tire A-.6 after removal from mold and trimming.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~l

Figure 29. Tire A-6 mounted on rim. TIRE DEVELOPMENT A number of tires were built and tested in order to develop the techniques described in this report. A complete description of this work would be prohibitively long. However, several important conclusions can be gleaned from the mass of accumulated experience. These are given below: A. The most important single property which the model tire builder must control is modulus of elasticity of the tire carcass, since this controls inflation pressures, loads and model test speeds. B. Tire carcass elasticity can be controlled by: 1. End count of the fabric 2. Number of plies used

3. Cord denier or modulus 4. Rubber modulus 5. Ply decoupling by means of a separator 6. Cord angle All of these factors have been interplayed in the present work to produce a low modulus model tire, yet one whose modulus distribution is similar to that of the full size prototype. C. Design changes can be readily seen in the model tires. For example, Table IV describes a set of eight model. tires, one purchased coma mercially and the other seven built especially for this project. Wide variations in structure are present, from conventional bias-ply to radial to pure rubber tires. Their dimensions are not too different from one another, yet their mechanical properties differ widely, as shown in Figure 30. In general, it appears that the influence of tire structure should be as readily apparent in these model tires as in their full sized counterparts.

TABLE IV CONSTRUJCTION An. DIMENSIONS OF TYPICAL hWA? SERIES MODEL TIRES A2 A ] A6 A7 A12 A17 VECO Ali Type Bias Bias Bias Bias Radial Bias Rubber Bias Cord-nylon 840/2 840/2 840/1 840/1 840/1 840/1 840/2 helical Cut Green Angle 620 620 62" 62" 90 370 6o" Approximately Cured Crown Angle 4o0 35 4o0 40 900 3 500 Approximate Rated Pressure, psi 73 24 5 25 10 18 7 (using fore-aft method) 2 Tread No No Yes Yes Yes Yes Yes Yes Dimensions (12.5 psi) Diameter 4.52 4.54 4.59 4.63 4.83 4.60 4.73 4.~ 6 Width 1.56 1.62 1.61 1.68 1.49 1.72 1.82

3 A3Ai AA AS 1 I0 Z l -- 0.040.080, 12,160.ao o.e(o 280 o3'aO,3G0 AOO,aq AS. C,,) 9 AS A'7-A4 - A 3 a L VERTCAL.LOAD 2- 0 16 2016 7 (lb) e.020.040.060 o80.100 10,10.(GO160 (80.200.a.0 Figure 30. Comparison of model tires static load-deflection at 12.5 psi inflation.

XXVERT ICL LOAN o l 2 3 4 S 6 7 8 9 to I/ (S (Jtes) ~ A2 == &',A AI4 A3 - o.010.o o.030.o0.OSO.06.0.070 D08O,090.Oo.1/10 Ax Car,) Figure 30.. ConcludedE 59~~~~~2 i

DISTRIBUTION LIST No. of Agency Copies Scientific and Technical Information Division Code US National Aeronautical and Space Administration Washington, D.C. 20546 25 NASA Headquarters Langley Research Center Dynamic Loads Division Hampton, Virginia 23365 Attn: Walter Horne 5 6o

UNIV"Hb IIY OF MICHIGAN II IIIIIIi11111111 11111 I02827 I4 3 9015 02827 443