ttrL'Wf ^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED June 19^2 ae Advance Restricted Report TIRE FRICTION COEFFICIENTS AND THEIR RELATION TO GROTJND-RTJN DISTANCE IN LANDING By F. B. Gustafson Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. BOX 11 7011 GAINESVILLE, FL 32611-7011 USA NACA WASHINGTON NACA WARTIME REPORTS are reprints of papers originally Issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. L - 2U5 Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/tirefrictioncoefOOIang i<30*2r9f^ ptttot NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS AT VANCE RESTRICTED REPORT TIRE FRICTION COEFFICIENTS AND THEIR RELATION TO GROUND -RUN DISTANCE IN LANDING Ey F. B. Gustafson SUMMARY A summary of published information on "braking fric- tion coefficients is presented. An analysis is included which indicates that the magnitude of the friction coef- ficient available will affect the technique required for' obtaining the shortest ground run only under extreme con- ditions. In this connection, technique refers to the choice between utilizing air drag and ground friction through choice of attitude. The analysis further shows that the landing attitude is almost never the attitude for the shortest ground run, A chart is presented for rapid estimation of ground-run distance for any set of values of friction coefficient, airclane attitude, initial drag-weight ratio, and initial velocity. Sample studies are presented for high- and low-wing loadings. INTRODUCTION At the suggestion of Dr. Edward Warner of the Civil Aeronautics Board, the NACA has recently reviewed avail- able information on tire friction coefficients, with par- ticular reference to the effect of field condition on co- efficients available for braking. A summary of the infor- mation found on braking friction coefficients is included in thi s report . An analysis was made to indicate the extent to which a variation in landing technique, from consideration of choice between utilizing air drag or ground friction through ciioice of attitude, becomes desirable as a result of changes in field conditions. For this purpose it was assumed that the choice was not influenced by nosing-over tendencies. It was further assumed that the load carried \ "by unbraked wheels was negligible. This analysis indicated that only tinder extreme conditions would the technique re- quired for obtaining the shortest ground run be affected by the value of the friction coefficient. The analysis did show, however, that the landing attitude is almost never the attitude for shortest ground run. a chart has been prepared for rapid estimation of ground-run distance for any set of values of friction coefficient, airplane attitude, initial drag -weight ratio, and initial velocity. Sample studies of ground-run distance are included for both high- and low-wing loadings. BKAKISTG FRICTION COEFFICIENTS Sufficient published information was found on the effect of surface type and condition and of tire tread on braking friction coefficients to establish the limits im- posed for most of the combination s normally anticipated. Kost of this information resulted from highway research, and these results are directly applicable to airplanes during ground runs. While all available datq of this nature were reviewed, reference? 1, 2, and 3 cover the subject well; other consulted sources largely served to check rather than to add to the information contained in these papers . Cn hnrd surfaces, such as concrete or asphalt, the coefficient available wnen the surface is clean and dry is likely to be 0.7 or higher, even for tires without tread. Although values 'above 1.0 are seldom reported for speeds above 10 or 15 miles per hour, coefficients in the neighborhood of 0.3 are common. The adverse conditions, however, normally govern the permissible length of run. Tne most common adverse condition is wetness of the sur- face. For smooth-tread tires skidding straight ahead at speeds in the neighborhood of 3 to 40 miles per hour, most highway surfaces, including Portland cement concrete in both smooth and rough condition, give coefficients be- tween 0.3 and 0.4 when wet. Reference 1 gives fairly complete data on coefficients for different surfaces. The following coefficients of sliding friction for smooth- tread tires skidding straight ahead on a wet surface at speeds of about 30 or 40 miles per hour are taken from this source: Surface Coefficient Penetration macadam, soft seal coat Pine aggregate asphalt plank Wooden plank Steel traffic plates Mud on concrete Ohio tar mac? dan High-type asphaltic pavements Iowa untreated gravel, loose Cinder s , loose J All values of coef f idient below 0.3 All values of coef f ici ent above 0.4 J Values for an incipient skid foregoing values for sliding tread is quite pronounced on the coefficient for a treaded one-quarter greater than the coefficient for a on the same surface. are usually higher than the friction. The effect of most hard surfaces when wet, tire being of the order of smooth tire Ice, including snow with an icy surface, provides the limiting condition for any field where such a condi- tion is anticipated. Values of braking coefficient of 0.05 and 0.06 for tires on ice have been reliably reported but are thought not to be the lowest values . obtainable . An approximate normal value is 0.10. Temperature has a very important effect on the coefficient for clean ice, the value dropping ran idly as the surface temperature rises toward the melting point. The spreading of abrasives on ice is quite effective. Some information on this point is given in reference 1, and a fairly thorough treatment may be found in references 2 and 3. It appears that the value with abrasives is quite independent of temperature and that a coefficient of the order of 0.30 can be quickly reached by thorougnly practi- cable methods of spreading. Reference 1 states that a value of 0.4? was readied several days after the applica- tion of cinders, as a result of their having become em- bedded . The importance of the good performance credited to abrasives is enhanced by the fact that tire tread does not offer even a potential solution to the problem of stopping on ice and packed snow. Although tread provides a marked advantage over smooth tires on nearly all bare, wet roadway surfaces, as has been already noted, the ef- fect on ice or snow is quite different. References 2 and \ 3 show that on ice at a temperature near freezing, tires with tread have higher braking coefficients than smooth tires but, at lower temperatures, smooth-t real tires give higher values. On loose snow a lug tread shows advan- tages, but on packed snow stopping distances are usually shorter with smooth tires than with treaded tires. Values for an impending skid are likely to be somewhat better for the treaded tire than for the smooth tire on either ice or packed snow, but with brakes locked the grooves fill and the coefficients drop. In brief, the differences pro- duced by tread on packed snow and smooth ice are small, and whenever ice and snow are anticipated, the limiting condition will not be appreciably altered by the use of tread on tires. In spite of the predominant use of hard-surfaced run- ways, landings on turf must still be given consideration; for example, for temporary or emergency airports. Exper- imental value? for braking friction coefficients on grass are rather scarce. From horizontal and vertical accel- erations recorded at contact during a series of landing tests conducted by the NACA on the turf surface at Langley Field, Va., it is concludpd that such a surface when in typical condition has a friction coefficient of about 0,5. The highest continuous deceleration recorded during fully braked runs was 0.43, and it is felt that this value represents very nearly the friction coefficient available during that run. For a turf field when wet, very little data are available. The values found do not appear to be conclu- sive and more information on this point is desired. Inf orr.a t i or. is also lacking on the effects of high speed and of tire size on braking coefficients. The values given, with the exception of the data obtained from NACA landing tests, are for automobile tires tested at speeds not exceeding 45 miles per hour. The evidence at hand, however, does not point to the likelihood of any radical changes in the general conclusions when these factors become known. Likewise, although reference 1 shows an increase in friction coefficient on wet concrete with a decrease in temperature, ir.tro auction of this fac- tor would appear to constitute a refinement rather than a fundamental revision. 3y way of a general conclusion, it is believed from this study that, on a well-maintained airport, a minimum value of the coefficient of braking friction of 0.20 should "be expected. Lower values, such as would exist on newly formed ice prior to treatment, should be considered as present under emergency conditions. Where ice is not expected, the minimum value should he 0.30, provided the surface has been properly chosen and is kept free of mud; minimum value may, of course, be still higher, depend- the ing on the particular surface used, APPLICATION OF FEICTION COEFFICIENTS TO CALCULATION OF LANDING DISTANCE Two forces add together t drag 'and wheel friction. The change during the ground run i I.n the preparation of figure 1 to make the run at an angle of and it was further assumed tha between wneels and ground of By a qui?.k reluct ion of the an i n t a o t , great idi ti on is pi 2 with figur 'ter contact ; round fr'icti will -nroduc plane following co: friction; this con: parison of figure angle of attack afi than it gains in g: assumed, and hence o ma 3 t a J J- s r ot e sa on stop the airplane: air nner in which these- forces illustrated in figure 1. he airplane was assumed ttack close to the stall, a coefficient of friction was utilized throughout. e of attack of the air- use may be made of wheel ted in figure ?, A com- 1 shows tha-t reducing the ori'ices less in air drag force, for the conditions the shorter run. If advantag that i s , Figure 3 which th the samp change t at t itude and Cj, flaps ex it also an incre change t coef f ici attack w wise, if than the the friction coef e will obviously in making the gr was prepared to is result might b 1 e polar s hown i n o lift change for between the limi = C T max tended; for values ficient is sufficiently low, the lie in the reverse procedure; eatest possible use of air drag, indicate the conditions under e expected. It illustrates, for figure 4, the ratio of drag any instantaneous change in = ts represented by C^ Figure 3 was drawn for the polar of Ct/C- i lower than 0.5, and for max applies to the polar for flaps retracted. When a^e in angle of attack gives a ratio of drag o lift change greater than the val\ie of friction ent available, the use of the higher angle of ill result in greater total deceleration. Like- a decrease in angle of attack gives a ratio less value of friction coefficient available, the use N of the lower angle of attack will result in greater total deceleration. For example, assume that the choice is "be- tween an angle of attack represented "by Ct/Ct =0.9 max and an angle of attack represented by Ct/Ct = 0.4. max Changing from one angle of attack to the other gives a ratio of drag change to lift change of 0.13. If the fric- tion coefficient is less than 0.13, the use of the higher angle of attack will therefore result in a greater total deceleration. Inasmuch as the lowest value of friction coefficient expected on a well-maintained airport is 0.20, the higher angle of attack will insure the quicker stop only under emergency conditions. As another example, assume that the friction coefficient available is 0.20 and that a value of C L /C L of 1.0 can be used. Figure 3 max shows that, if any value of C./C T less than 0.5 can h -"max be reached, the use of this lower angle of attack will pro- duce the greater deceleration. Examination of figure 3 shows that the greatest decel- eration will always be present at one of the two extremes; that is, either at the highest or the lowest angle of at- tack that can be reached. This result will be true for any polar that is concave upward throughout because oper- ation at intermediate angles of attack is then equivalent to operation near maximum L/D , an obviously undesirable condition. With this fact in mind, the second example given yields two interesting conclusions. First, since an angle of attack below C^/C^ =0.5 can be reached " max with most airplanes and since the friction coefficient is nearly always above 0.20, it is concluded from figure 3 that only under extreme conditions will the magnitude of the friction coefficient available affect the technique required for obtaining the shortest ground run. In other words, the best technique nearly always consists in making the greatest possible use of ground friction rather than of air drag. Second, since an airplane seldom lands at the lowest angle of attack that can be maintained during the ground run, especially if the pilot keeps the approach speed down for the sake of a short run, it is likewise concluded that the landing attitude is rarely the attitude for the shortest ground run. It should be pointed out that, in the case of con- ventional gear, another factor enters into the choice of attitude; namely, the tendency of the airplane to nose over. After the air forces have dropped off, it is desir- able to have the tail low enough to permit fullest possible use of the available wheel-friction force. This considera- tion o b v i ou s 1 j' does not arise in the case of the tricycle landing gear. Conclusions d ures 1 , 2 , and 3 a enable calculation for any given valu eauation has been prepared. The e^u include the effect procedure was ad op of attitude sugges because consider ab is feasible, and s landing gear. r awn f r e pur s t o b e of f derive ation of an ted no ted by le cha ome ch rorn the study represented by fig- ely qualitative. In order to e made of the ground-run distance riction coefficient, a general d and a convenient form of chart and the chart have been made to gle of attack directly. This t only because of the importance the qualitative study but also nge in attitude following contact ang6 inevitable, with the tricycle the The decelerating force at a given instant sum of the air force and the wViooi -Fr jiven lusi/ctiiu will be wheel friction foi sr ce ■ L + p. ( V - L ) a = M */, where W weight D drag L lift p. friction coefficient between airplane and ground and k ratio of lift at start of run to weight (L 1 /\!) V velocity, feet per second Assume C, and C^ to be constant during the run. Use the subscript i to represent conditions at the start of the run. Tne expression kW i n" j can be substituted for \ /I N nd Vy [ — ) , for D. This procedure gives a = g (1\ W By substitution in the equation 6 = r 1*1 ^ a V=0 where s is the distance covered, tne expression becomes md by integration, 2g v log. - &\i J Dj ku. M- For a given value of Ii}/W or k the average de- celeration, and hence the distance for an airspeed equal to 1 for any given ratio of Dj/W to u- , is proportional either to ^i/W or M-. The result is shown in figure 5, in which the value of I^/W the distance s' for + n has been plotted against Vi = 1 and |X = lj curves are shown for values of angle of attack, as represented by k, from k = to k = 1 . . A value of ground-run distance can be calculated from this chart as follows: First, calculate the ratio Dj/W + u. This step is most easily taken, as a rule, by the use of the drag coefficient and the lift coefficient that would be required for support at the initial speed, or D a /W V- r I I (1.1 L \V, max\ v 1 where V is stalling speed. Then, calculate the value of k, which is simply the lift coefficient divided by the lift coefficient that would he reouired for support at the initial speed, or k = max /V \3 I s Using these two values, read the value of s' from the chart. Multiply s ! hy the square of the initial speed and divide by the value of ground-run distance. U. The answer is the This chart should be useful for design e-stimates for both airplanes and airports, inasmuch as it is possible to examine the effect of changes in ground-friction coef- ficient, air drag, and angle of attack, as well as initial velocity, either singly or in combination. SAMPLE STUDIES The significance of the ground-friction coefficient and of tne related problem of angle of attack during the ground run cannot be precisely stated except for specific cases. Foi" this reason, the following sample study is presented. It is .assumed that a coefficient of friction of 0,4 is utilized between tires and ground. It is also assumed that brakes are used on all wheels. The effect of the time reauired to change the angle of attack following con- tact has been indicated by making- calculations for zero transition time and for a 2-second transition period. The conditions, the encircled numbers used to represent them, and the corresponding values of lift and drag assumed are as f ol 1 ows : s 10 ©Airplane at stall; C T = 2.0, C- = 0.30 L max D (2) Thrust axis horizontal, flaps not retracted; C L = 0.93, C D = 0.12 (Zj Thrust axis horizontal, flaps retracted; = 0,33, C D = 0.025 When a transition from one angle of attack to another is involved, "both encircled numbers are used. (See fig. 6.) Thus,. (T) - (i) means that (lj and a transition made contact was made at condition to condition C'^J. The runs with zero transition time were calculated "by means of figure 5 in the manner already explained, using the lower angle of attack as the initial condition. For the runs with 2-second transition period, the dis- tance covered and the velocity lost during this period were calculated on the basis of two 1-second intervals, assuming that half the decrease in angle of attack had "been attained during the first second. Successive ap- proximations were used to determine the deceleration during each second. The rest of the run was calculated by means of figure 5, using the speed and the angle of attack at the end of the 2-second period as the initial condit i on. The calculations were carried out over two ranges of wing loading to indicate the effect of this factor. The values obtained are plotted against effective wing load- ing in figures 6 and 7. The effective wing loading tf/aS, where W/s is the wing loading in pounds per square foot and c is the density ratio, was used so that a single plot could be readily used for any density altitude. The effect of change of angle of attack, and of transition time required for this change, on ground-run distance is summarized in figure 8, in which average deceleration is plotted against reduction in lift coefficient following contact for the lowest and highest wing loadings covered by figures 6 and 7, respectively. The effect of a fixed transition time is shown to be appreciably less at the higher value of contact speed. Further, in every case examined in this study, the effect of reduction in angle of attack at or following contact is shown to be a reduc- tion in ground-run distance. 11 CONCLUDING- REMARKS The values found for the "braking friction coeffi- cients of smooth-tread tires on various surfaces indicate that such coefficients under adverse conditions, includ- ing rain and snow, are commonly above 0.2 and that the outstanding exception, fresh ice, can he raised to this value by appropriate treatment. Values for smooth-tread tires on wet surfaces commonly fall "between 0,3 and 0.4. Exceptions are common enough and the divergences in values are wide enough to necessitate attention to specific val- ues in designing or rating airports when the landing run may he critical. The analysis of the effect of low values of "braking friction coefficient on the relative merit of tail-high and tail-low attitudes during the ground run indicates that, if the friction coefficient available is greater than 0.2, the technique should he directed toward utiliz- ing "braking friction rather than air drag. For values "below 0.2 consideration of the individual case is neces- sary. The chart presented for estimation of -ground-run distance should facilitate quantitative study of the ef- fect of changes in ground friction for specific cases. Except where full knowledge of applicable assumptions exist, however, it should he used chiefly to determine relative rather than absolute values. Langley Kemorial Aeronautical Laboratory, National Advisory Committee for Aeronautics, Langley Field, 7a, \ 12 REFERENCES 1. Moyer, R. A.: Skidding Characteristics of Automobile Tires on Roadway Surfaces and Their Relation to Highway Safety. Eng. Exp. Sta. Bull. No. 120, Iowa State Col., vol. XXXIII, no. 10, Aug. 8, 1934. 2. anon.: Committee on Winter Driving Hazards. 1940 Report to Street and Highway Traffic Section, National Safety Council. Safe Winter Driving. Nat. Safety Council, Inc., (20 N. Wacker Drive), Chicago, 111 . , 1940. 3. Anon.: Committee on Winter Driving Hazards. Lake Cadillac Skidding and Traction Tests. (Tech. Supp. to reference 2.) Hat. Safety Council, Inc. NACA Figs. 1,2 Cn 8 I 8 3 Wheel-friction contribution if no lift- .Z - Airplane mokes contact SO percentage of total time of ground run Figure /.— I/aria t/or> of air one/ lArhee/ fr/ct/on forces dc/ri/ig grour- rc/r, cf of Q_ reo'vct'/or) at or //7?/7? ai/erc/ rc/r?. C ima = J?.Oj V Hc , horizontal velocity at contact. \ UNIVERSITY OF FLORIDA 3 1262 08106 564 *s UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE LIBRARY PO. BOX 117011 GAINESVILLE, FL 32611-7011 USA