RB No. 3D26 NATIONAL ADVISORy COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED April 19^3 as Restricted B\illetln 3D26 A STUDY OF THE EFFECTS OF RADII OF GYRATICW AND ALTITUDE OR AILERON EFFECTIVMESS AT HIGH SPEED By Leo F. Fehlner Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE UBRARY "''.0. BOX 11 7011 'A-N'-'VlLb FL 32611-7011 USA MAC A 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 ar.e now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite generail distribution. L - 21^9 \ Digitized by tlie Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/studyofeffectsofOOIang \1^iOio^^ jvo') 0-^ *> NATIONAL AEVISORY COMMITTEE FOR AERONAUTICS RESTRICTED BULLETIN A STUDY OE THE EEEECTS OF RADII OF GYRATION AND. ALTITUDE ON AILERON EFFECTIVENESS AT HIGH SPEED By Leo F. Fehlner INTRODUCTION Because the time to "bank com'bat aircraft has "become increasingly important and "because information on the variation in the time to "bank with altitude and with weight di st r i'biit i on along the v;ings is not availa'ble, the present theoretical investigation was made to determine the magnitude of t"npse effects. The variation in the necessary aileron control and in the time required to "bank to 45° and 90° with altitude and radii of gyration for a typical fighter or a pursuit airplane have "been comriuted and are rrepented 'nerein. SYMBOLS "V true airspeed, m:iles per hour "V^ indicated airspeed, miles per hour (correct reading of airspeed indicator cali"brated to read true air- speed at zero altitude) M Mach num"ber V longitudinal flight-path angle, degrees K-j^ ratio of radius of gyration a"bou- the X axis to span K2 ratio of radius of gyration a"bout the Z axis to span t time, seconds Cj rolling-moment cjefficient, '■ — a S,,"b w L rolling moment, foot pounds \ q dynamic pres^urp, pounds per so_uare foot a_ impact pressure, pounds per square foot S^, wing area, square feet span , feet AIRPLANE CHARACTERISTICS Al-TD METHOD The total weight of the airplane considered in the computations is 9300 pounds; wing leading, 35 pounds per square foot; aspect ratio, 6; and span, 40 feet. The aerodynamic characteristics were chosen to ho representa- tive of pursuit cr fighter aircraft in high-speed flight just telov; the critical speed. The altitude was varied fr standard conditions. The ratio about the X axis to the v^ing sp C.16 and the ratio of the radiu axia to the wing span was varic range of radii-of- gyration rati range of all the values known f al pur'-uit and fighter aircraft plane were studied in vertical level flight, and cliir.'b attitud "b e r , constant true airspeed, an speed. om to 50,0 CO feet under of the radius of gyration an was varied from 0.08 to s of gyration ah cut the Z d fror. 0.14 to 0.22. This OS covers the complete or 42 existing convention- The motions of the air- dive, high-speed glide, es at constant Mach num.- d constant indicated air- giv The lateral motions were commuted for the ;n in table I. cases The impact pres«iure for the various conditions nf flight are given in table II. The lateral motions of the airplane were determined by solving the differential equations of motion in a manner simiilar to, that used in reference 1. In the pres- ent report the ailerons were assumed to be deflected in such a way as to increase uniformly the r oil ing-r oment coefficient aprilied to the airrilane during the first one- tenth second and to hold it constant thereafter. P.ESULTS AITD DISCUSSION The result? are presented in figures 1 to -S. Figure 1 includes three types of variation with alti- tude: one variation at constant true airspeed, another at constant Kach numhei', and a third at constant indicated airspeed. Cases for constant true airspeed and constant Mach number are chosen to he identical at 20,000 feet and cases for constant indicated airspeed and constant Mach numher a. re chosen to "be identical at 50,000 feet, Figure 1(a) shov.'s the variation v;ith altitude of the rolling-moment c oe-<^f i cien t that must he applied hy aile- rons to perform two "tanking maneuvers; namely, the attain- m.ent of an angle of hank of 45° at the end of the first half second and 90° at the end of the fir'^t second. Figure l(h) shows the variation with altitude of the time to han]: to 45° and &C°. The rolling -moment coef- ficients applied at all altitiides are those that produce an angle of hank of 45"^ at the end of the first half s e c CTn d and of alt i tude . • at the end of t }i e first second, at zero The rolling-moment coefficient necessar;-' to hank to 45° in one -half second is greater than that necessary to hank to 90° in 1 second. This difference in renuired rolling-moment coefficii^nt is due to the fact that the airplane accelerates in roll during all or a large part of the time intervals considered. The raom.ent of inertia in roll therefore has an imrportant influence on very s'nort rolling m.aneuver<=. The rolling-moment coefficient re- q_uired to hank to any other angle in the same time is directly proportional to the angle; that is, to hank to 45° in 1 second I'ei aires half the rolling-moment coef- ficient necessar:^ to hank to 90° in 1 second. The dec !■ ease in required rolling-momient coefficient shown for increasing altitude with indicated airsoeed con- stant is caused hy the large increase in true airspeed that is required to maintain a given indicated airsi:eed. (See tahle I.) The rolling-moment coefficient necessary to hank the airplane in a given time is not a function of velocity alone, however, as Is shown hy the variation of r oil ing-m.ompnt coefficirnt with altitude when true air- speed is constant (fig. l). \ At a Mach number of 0.75 and also at a true airspeed of 530 mile? per hour, a fcreater r ol 1 ing-noment coeffi- cient is required to tank: the airplane to 90° in 1 second at hi^h altitudes than at low altitudes. At a Hach nuir-ber of 0.75 the increase in r oil Ing-moinent coefficient re- quired in changing from 20,000 to 40,000 feet is about 40 percent for the air • ) lane considered. If the hinge moment is assumed to he proportional to the rolling moment, a relative hinge moment may he com- puted by multiplying the rolling-moment coefficients of figure 1 by the corresponding im.pac: pressures presented in table II. These relative hinge mom,ents are presented in figure 3 in a manner similar to that used for the roll- ing- uoment coefficients o^' figure 1. The factor of proportionality betv/een the rolling moment and the hinge moment depends on the aerodynamic cnaract era st ic o of the particular airplane. The variation cf stick force with hinge moment varies with linkage and booster system-,. The coiu '-'Ut at i on of the variation of stick force with altitude from the hinge-moment variation requires a knov/ledge of the variation in stick force with hinge m.ojient for a particular case. The hinge micment? ap ol i ed in figure 2(b) are those that produce an angle of bank of 45^ st the end cf the first half second and at zero altitude. •0° at the end of the first second The hinge moment necessar^^ to bank to 45^ and 90 in the stated time intervals is greatly decreased by in- creases in altitude. For the 90° m.aneuver at a Mach num- ber of 0.?b the hinge mom. en t is 44 percent less at 40,0 00 feet than at 20,000 feet. The time to bank to 90° and 45° greatly decreases as altitude increares if the hinge moment is held constant at all altitudes. The decrease in the. time to bank to ^0° is 50 percent for a change in altitude from 20,000 to 40,000 feet. Although figure i;(b) does shov; the variation of the time to bank to given angles with altitude for various constant hinge moments, the corresponding r olli ng-moffient coefficients required at high altitude exceed those ob- tainable with present designs. The decrease in the time to bank to a given angle as shown in figure 2(b) is there- fore lim.itcd by the maximum rolling-moment coefficient aval labl e . From figures 1 and 2, it is concluded that if the strength of the pilot limits the aileron deflection, as is usually the case for present high-speed airplanes, the aileron ef f ect i vpne s s increase^ with altitude. ■ At a given limiting Kach numher, the increase in effectiveness results largely from the larger deflections produce! ty a given force applied to the stick and the increase in ef- fectiveness will continue only to the altitude at which the Gaximum design deflection of thp aileron is reached. Above this altitude the aileron effectiveness vrill de- crease. The aileron system, therefore, should he de- signed for rolling-moment requirements at high altitude and the hinge-moment limitations at low altitude. Figure 3 includes variations of the radius of gyra- tion ahout the X axis of the airplane in a glide and in level flight at 530 miles per hour and at an altitude of 20,000 feet. The radii of gyration of airplanes of widely different classifications fall within the range of radii of gyration considered. These classifications include all conventional single- and twin-engine pursuit and fighter airplanes with w i along the wings. .e variations in weight distribution Figure 3(a) shows the varir^tior '-.'ith the radius of gyration about the X axis of the rolling-moment coeffi- cient necessary to attain an angle of bank of 45° at the end of the first half second and of SC^ at the end of the first second. Figure 3(b) shows the variation of the time to bank to 45° and S0° with the radius of gyration about the X axis. The rolling-moment coefficients applied for all values of the rndius of gyration are those that produce an angle of bank of 45° at the end of the first half second and of '30° at the end of the first second with the ratio of radius of gyration about the X aris to the span eaual to 0. 03 . The effect of changes i'^ the radius of gyration in roll on the rolling-moment coef'ficient necessary to bank to 90° in 1 second is large becau=e of the large percent- age of the maneuver spent in accelerating the airplane in roll. The rolling-moment r e oui remient s are increased about 28 percent by increasing the radius of gyration about the X axis from 0.08 to 0.16. N The effect en the banking maneuvers considered of variations in the radius of gyration about the Z axis are negligible. The 1 on^ri tud inal flifvht path was varied from a ver- tical dive to R 15.9'-' clinh at 530 miles per hour and at 20,000 feet. The effects on the banking maneuver of var- iations in longitudinal flight path angle are negligible in the range investigated. For all the as^iiried conditions of flight, the angle of sideslip resulting from a rolling-moment coefficient of 0.05 deviates in an oscillatory manner during the first leconds and does not exceed an angle of the order of 2' Langley Mem-Ori-il Aer oanu': i cal Laboratory, National Advisory Com.mittee for Aeronautics, Langley Field, Va, RZFEEEjJCS i'ehlner, Leo F.: A Study of tiie Effects of Vertical Tail Area and Dihedrsl on the Lateral Maneuvera- bility of an Airplane. KACA .-^ . R . H . , Oct. 1S41. TAPLE I CASES FOR WHICH LATERAL MOTIOITS WERE COMPUTED Gas e M V (mph ) (mph) Altitude (ft) (deg) ■'x Yn Li ^L 1 0.750 57 570 -30. 7 0.125 0.175 0.036 2 .750 5?0 400 20, 000 -13.9 .125 .175 .088 3 .750 496 258 40,000 -6.1 .125 .175 .224 4 .750 496 204 50,000 -4.4 .125 .175 .365 5 . 696 530 530 -27.0 .125 .175 . 042 9 .800 530 27 8 40,0 00 -6.7 . 125 .175 . 198 1 .300 530 220 5 , 00 -4. & .125 .175 . 320 8 .269 204 204 -4.7 .125 .175 .325 9 .3iJ4 27 8 204 20,000 -4.7 .125 .17 5 .323 10 .50 2 400 204 40 ,0 00 -4.5 .125 .175 .350 11 .750 530 400 20,000 -13.9 .08 .140 .088 12 .75 5 30 400 20 , 000 -13.9 .080 .220 .088 13 .750 530 400 20,000 -13.9 . 1 6.0 , 2 30 .088 14 .750 530 400 20,000 .125 .175 . 091 15 .750 530 400 20,000 .08 .140 .091 15 .750 530 400 20,000 .080 .220 .031 17 .750 5 30 400 20,000 .160 .220 .091 18 .750 530 400 20,000 13.9 .125 .175 .088 19 .750 530 400 20,000 -90. .125 .175 TABLE II VARIATION OF IMPACT PRESSURE WITH ALTITUDE Alt i tude «^c (ft.) i'- =■ 0.760 V = 5 50 mph ^i = 2 04 mph 950.0 605.3 109.1 20,000 436.5 43 5.5 109.1 40,000 176. 203.9 10 9.1 50,000 10 9.1 126.5 109.1 \ NACA ^ QO o, fM '*■ ■o tVI ^ ^fl •O Q <:i \ s \ K \ ■ \ -1 — ' 1 1 II \ \ \ s. \ i\ 1 \ \ N \ 1 - \ \ \ / \ \ \ / / \\ i->. \ \\ / / / \ \ ~i~ -c -c _ \ \ \ / \\ t \\ / / \\ 1 1 c _ A / / / \\ \\ 1 1 ^ II •5: n / / 1 <^J 039 ' ^ tV ^:i: -M^ II Fig. I to o X c> "O i <7\ « «^ C 3 ^r a •-t o *» trv <-t -^ C0 o j:: <^ -1- 4J •H ^ ■31 c O o ■T3 o C> ■4-> -2 XI o r 1 f ^ ^ ^ ^ ^ / k^ / / N / / / \\ ^ / / \ ^ ^ N. \ \ \ / \N. \\ / ^ • / \ / / 1 i \ L rr / / /o A \' ^ i I / /^ V. \ ■/ \\ I 1 / 1 I / / j \} ' y / ' \ \ i 1 00 ^4- 'O ' j.ua/ofij.900 y.wsLuo UJ bui II o ^ c> CCt) a o c -o o o o u one 4J n V. ais: u V n 6 "9 oi« C BOO C C£l o //°^ \ NACA 0b/ock-/0/3Z") Fig. 2 >- "5 ^1 '^i 1 \ 1 /; / r 1 // 1 / / / // / y / / / / / / / / / S- / / // / / 1 7 1 \ 1 / / / // \ r"' / / /' / / / 1/ V — ^ CM ■J / / 1 1 1 /, / / 1 1 1 y ^ / 7 1 ! 1 1 y // ,A // 1 1 1 1 y y V ' \ 1 1 1 1 :* 5J 00 ^ c ^0 ' 1'^'^'^°'^ aSuiu SAitojdyj o ON o c d O o ■a a ■0' >3 c d 1 d c Cv , E Q «1 a) S, c ®t3 one *i > t- >>rH © 4J t* 01 ED a £ (U n tj r-< ID (, »H U « -<4-i C s- c •P »* c j:w •H g-^ 4J ^ 04-. 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