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RB No. 3D26 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WAllTIM'E REPORT ORIGINALLY ISSUED April 1943 as Restricted Bulletin 3D26 A STUDY OF THE EFFECTS OF RADII OF GYRATIOR AND ALTITUDE O1 AILERON EFFECTIVENESS AT HIGH SPEED By Leo F. Fehlner Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 20 IMARSTCN SCIENCE UBRARY '. BOX 117011 ': L' 326117011 USA NC:i "t 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 249 Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smalhers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/studyofeffectsof001ang NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS RESTRICTED BULLETIN A STUDY OF THE EFFECTS OF RADII OF GYRATION AND. ALTITUDE Oi AILEROUI EFFECTIVENESS AT HIGH SPEED B:.' Leo F. Fehlner I"ITRODUCT :OI Because the time to bank combat aircraft has become increasingly imiortart and because information on the variation in the time to bank with altitude and with weight distribution along the wing is not available, the present theoretical investigation 'as made to determine the magnitude of these effects. The variation in the neceessar;. aileror. control and ijn the time required to bank to 450 and 900 with altitude and radii of gyration for a t.'Tpical fighter or a pursuit airplane have been computed and are rrewented herein. SY 0BOLS V true airspeed, miles per hour Vi indicated airspeed, miles per hour (correct reading of airspeed indicator calibrated to read true air soced at ?ero altitude) M Mach number ^" longitudinal flight:iqth anr'le, degrees KX ratio of radius of r:;ration about the X axis to span Kz ratio of radius of gyration about the Z axis to span t time, seconds CL rollingmoment coefficient, L L rolling moment foot pounds q dynamic pressure pounds per square foot qo impact pressure, pounds per square foot SW wing area, square feet b span, feet A.IEPLA:E CHARACTERISTICS AID METHOD The total weight of the airplane considered in the computations is 9300 pounds; wing loading, 30 pounds per square foot; aspect ratio, 6; and span, 40 feet. The ae,r dynamic characteristics were chosen to. be representa tive of pur:.it or fighter aircraft in hi,hspecd flight just below the critical speed. The altitude was varied from 0 to 50,00C0 feet under standard conditions. The ratio of the radius of gyration about the X axis to the wing span was varied from 0.06 to 0.16 and the ratio of the radius of g ration about the Z axia to the wing span was varied from 0.14 to ).22. This rEr.e of radiiofgyration ratios covers the complete r.nn^ge of all the values known for 42 existing con.vention al pursuit and fighter aircraft. The motions of the air plane were studied in vertical dive, highspeed glide, level flight, and climb attitudes at constant Iach num ber, constant true airspeed, and constant indicated air steed. The lateral motions were computed for the cases given in table I. The ir.,.act pressure for the various cordition2 mf fli<t are given in table II. The lateral motions of the airplane wnre determined by solving the differential einations of motion in a manner similar to, that used in reference 1. In the pre. ent report the ailerons were assumed to be deflected in such a way as to increase uniformly the rolling.oment coefficient applied to the airplane during Lhe first one tenth second and to hold it constant thereafter. RESULTS AND DISCUSSION The results are presented in figures 1 to 3. Figure 1 includes three types of variation with alti tude: one variation at constant true airspeed, another at constant L'ach number, an.'. a third at constant indicated airspeed. Cases for constant true airspeed and constant Mach number are chosen to be identical at 20,000 feet and cases for constant indi,ted airr'ped and constant Hach number arp chosen to be identical at 50,000 feet. Figure 1l.a) show the variation with altitude of the rollingmoment coe fi cient that must be aplied by aile ron? to perform t.wo banz:ir. ' maneuvers; namely, the at tain ment of an anle of ban;: of 450 at the and of the first half second ,ind 0 at the end of the fir t second. Fie:u'.re 1(b) how *.e varia+ io'., with altitude of the time to ban': to 1'' and 'C0. The roil 1 in moment coef fiient a lied at all alti'.udes are those thnt produce an angle of banrk of 45 at a ne end of the fi;r t half second :nd of c 0o at t'he end or th}e first second at zero alt i tude. The rollinr:_ir.mernt coefficient neces ar to bank to 45 in onenalf second i? greater than that neces.;ary to bank to '0o ir 1 second. Tnis difference in required rollingm.omen coefficient i= due to trhe f ct that the airplane acclerate= in roll during all or a large part of the time interval considered. The n ent of inertia in roll tr.erefore ha an im,;,ortant influence on very short rolling; maneuver=. The rolling. moment coefficient re quired to bank to any other anrile in the sa.Te time is directly. proportional to the angle; that is to bank to 450 in I second requires half the rollinFmcment coef ficient necessar" to bank to 900 in 1 second. The decrease in. re'uired rollirn mor ent coefficient shown for increa i n altitude w'it:. indicated airsoeed con stant is cqai ed by the large increase in true airspeed that i reuired to maintain a gi',en indicated girpreed. (See table I. The rolli nmoment coefficient necessary to bank the airplane i n a given ti e is r, ct a function of v P 1ocit alone, how ever, a is Ih own by the variation of rollingmomnnt coeffi irnt with iltitule wnen true air speed is constant (fig. ). At a Mach number of 0.75 and also at a true airspeed of 530 miles per hour, a greater rollingmomerjt coeffi cient is required to bank thp airplane to 900 in 1 second at hirh altitudes than at low altitudes. At a Vach number of 0.75 the increase in rollingmoment coefficient re quired in chaning from 20,000 to 40,COO feet is about 40 percent for tho airplane considered. If the hinge moment is assumed to be proportional to the rolling moment, a relative hinge moment may be com putd by multirlyine the rollingmoment coefficients of figure 1 by the corresponding impact Iressures presented in table II. These relative hinge moments are presented in figure 2 in a manner similar to that used for the roll ingLLoment coefficients oF fig'ire 1. The factor of proportionality between the rolling moment and the hirac:e moment depend on the aerodynamic characteristics of the particular airplane. The variation ef stick force with hinge moment varied with linkage and booster system,. The coIrutaticr of the variation of stick force with altituie from the hir.Feinoment variation requires a knowledge of The variation in stick force with hin.e moment for a particular case. The hinge moments applied in fi.ure 2(b) qre those that produce an angle of bank of 450 Pt the end cf the first half second and 0O at the end of the first second at zero altitude. The hinge moment r.ecessar" to bark to 450 and 900 in the stated time intervals io girentl:,' decreased 1h in creases in altitude. For the 90") maneuver at a Mach num ber of 0.75 the hinge moment is 44 percent less at 40,000 feet than at 2',0000 feet. The time to bank to 90 arid 450 gr'eaPtly decreases as altitude increases if the hine r.omiEnt i.g held constant at all altitudes. The decrea3s in tht time to bank to i0 .is 3% percent for a cainrgCe in altitude from 20,000 to 40,000 feet. AlthDt'h figure 2(b) does show the variation of the time to bank to eiven ?anl PF with altitude for various constant hingCe moLents, the corres:.onding rollingmoment coefficients required at high altitude exceed those ob tainable with present designs. The decrease in the time to bank to a given an4le as shown in figure 2(b) is there fore limited by the maximlum rollingmoment coefficient available. 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 highspeed airplanes, the aileron effectiv"eness increase with altitude. At a given limiting IYach number, the increase in effectiveness results largely from tht larger deflections produce by,' a given force applied to the stick and the increase in ef fectiveness will cortinup cnly to the altitude at which the maximum design deflection of the aileron is reached. Above this altitude the aileron effectiveness will de crease. The aileron system, therefore, should be de signed for roll i ngnoment re.ui rementis at high altitude and the hingemoment limitpt ionr. at low altitude. Figure 3 includes variationr.s of the radius of gyra tion about the X axi of the airrlne inr a glide and in level flight at 530 miles per hour and at an altitude of 20,000 feet. The rndii of ;.rat ion of airi lanes of widely different cla; ifications fall within the ran.e of radii of g.ratior, consid. red. .hese czlazsifizations include all conv ren tional sir. , c and t .,iner.gine pursuit and fighter airlene .c ith 1'ide variations an wei.rt distribution along tne r'inge. Figure 3(?) show. the vari,ti r '.ith the radius of gyration about the X axi s of the rollir.gaToient coeffi cient necessary, to a tai.i an angle of bar. of 4,.O at the end of the first half spco.d and of '2 st the end of the first secnd. Figure 3(b) shows t'ie vari tion of the time to bank to 450 and c0O with the radiis of .:'"ratio n about the X axis. The rolii n mov.ent coefficient.s appliei for all values of the r.dius of gyrstion are those that produce an anile of banr: of qt thr end of the first half second and of '3'C at the end of the first second with the ratio of radiu cf ,yvratior, about t h1 X aris to the span er'u.al to c ..>?. The effect of changes i the radius of gyration in roll on the rollir...omer.t coefficient nezeesary to bank to 90 in 1 record is larce becaue of the large percent age of the maneuver spent in acc.eleratine: the airplane in roll. The roll gmoer.ent re. ii rrn ent s are increased about 2. percent b:, increisina'r the radius of gyration about the X axis from O.OS t 0.16. The effect on the banking maneuvers considered of variations in the radius of gy.ration about the Z axis are negli .ible. The longitudinal flight path was varied from a ver tical dive to a 13.90 climb at F'30 miles per hour and at 20,000 feet. The effects on the banking :aneuver of var iations in longitudinal flight iath angle are negligible in the range investigated. For all the assumed co.nditiocr of 'light, the angle of sideslip resulting from a rollingmomert coefficient of 0.05 deviates in an oscillator' mrnner during the first 2 seconds and does not exceed ar. anrLle of the order of 20. Largley Memorial Aeroanutical Laboratory, National Advisory Corm:ittee fir Aeronautics, Langley Field, Va. RYiERE~TCE 1. Fehlner, Leo F;. A Stud;: of tne Effects of Vertical Tail Area and Dihedral on the Lateral Maneuvera bility of an Airplane. 1ACA A.R.R., Oct. 1941. TALE I CASES FOR WHICH{ LATERAL MO0TIOUS WERE COMPUTED Case M Altitude KA, 1 C e <(.mph) .mplh) (ft ) (,leg) I 1 0O.V50 7?0 T5" 0 ."0." 2 "125 j15 0 .06 2 .750 530 400 20,0,0> 1 .9 .1 5F .175 .088 3 .750 496 25 40,000 1 .125 .175 .224 4 .750 46 2'04 0,0 3 4.4 .1 5 .175 .365 5 .C96 550 520 0 27.0 .125, .175 .043 S .300 53C 2' 40,00 125 .175 .l'1 S ._300[ 30 220 750,03 4. .1]5 .175 .n3 0 8 .269 2204 204 I 0 4. 125 175 .325 9> '4 4 0 4" 20,00' 4.7 .125 .175 .329 10 .50? C 204 4 4.5 125 .175 550 11 C l 530 400 20, 000 13. 2 .0 .140 .C0 8 12 ?. 5:0 400 i 20 ,00 1 .U'' 220 .0 8 13 .750 530' 4,0.' 2,0, :0 ': 13.C 1.:. .22'0 .0689 14 .750 5?0 400 20,000 ', Cl 1 '5 .175 .01l 15 .750 530 400 20,00: 0 .0 :0 .140 .0 1 16 .75C 530 400 C 0,00 0 .0.30 20 .091 17 .7?50 530 400 20,0:'0 '' .110 .220 .0:1 1s .750 50 400 20,000 1 .9 .125 .15 .088 19 .F0 530 400 20,000 .90.0 .125 .175 0 TABLE II VARIATIO'T OF IMPACT PRESSURE W',ITH ALTITUDE Altitude '___ S i' = 0..750 V = 53 r.mph Vi = 204 mr.h I 1 0 40, 000 50 00 .*50.0 436.5 17 0 1 0 J. 1 .;05 . 433.5 203. 9 126.5 109.1 10'. 1 10 1 109.1 NACA Fig. I N N N  SaI S\ I C 0 /. > l I o ^_ 7^  co SI I ,\ Q / \ I ..C 0 0 L g al N 0  t__ ___ _ 1. CO N \o o o) V cv o 0 0 0 0 60< '0 r !J.U11 .; H 20 J.LUai O WLI Ll'i/O^J NACAo = 0 ) Fig. 2 c ci ,c/ i / r^4 4z / '  H ^  / 4 / ~ / I~ s 1 / A 0 0 E   ,,... "K ra KE nac V.40 ~  t \ UI' o w * /  1 a:u/   LZy/L \L \ NACA .49 q ____ c:Z~i ~ ~ I i 4 f  I F 0 1 S o o a' 0 0 o 0 0' 0 E .4 0 a : if .4 0 I MO@ F S. 0 OS O S C 0 U^ 41 c B CJ t::. BE o! a. 0 >  a ot F. I j o * 0 0JQ . ... F OC 04 5..14 Fig. 3 o pa0,2.;'ao0 pJau.ioj 6&'U.lol IL I f I : t !* I i I : r i i;, UNIVERSITY OF FLORIDA 31262 8 4601 i UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE LIBRARY F'. BOX 117011 SThESVILLE, FL 326117011 USA 