. ARE No. Ll;F02 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORONALLY ISSUED June 19kk as Advance Eestrlcted Eeport Ll|-F02 THE EFT^ECTS OF STATIC MARGIN AND ROTATIONAL DPi^ING IN PITCH ON TEE LONGITUDINAL STABILITy CHARACTERISTICS OF AN AIRPLANE AS DETERMINED BY TESTS OF A MODEL IN THE NACA FREE -FLIGHT TUNNEL By John P. CamplDell and John W. Pa-ulson Langley Memorial Aeronautical LahoratoJTr Langley Field, Ya. 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. 55 DOCUMENTS DEPARTMENT Digitized by tine Internet Arcliive 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/effectsofstaticmOOIang "7(2 (^01 OS HATIOML ADVISORY C0MMITT!]3 FOR AERONAUTICS ADVA TOE RESTRICTED REPORT THE EFFECTS OF STATIC IvLARGIN Ar© ROTATIONAL DAMPING IN PITCH ON TEE LOITGITUDIKAL STABILITY CHARACTERISTICS OF AN AIRPLAi^TE; as DETERMINED BY TESTS OF A MODEL IN THE NACA FREE-FLIGHT TUNNEL By John P. Cair.pbell and John W. Pa-alson SUJ,MARY The effects of static inar'g5.n and rotational damping in pitch, on the longitudinal stability characteristics of an airplane have been determined by flight tests of a model in the FAOA free -flight tunnel, in the investiga- tion, the rotational damping in pitch was varied over a wide range by using horizontal tails that varied in area from to 2b. percent of the v.dng area. A range of static margins from 2 to l6 percent of the mean aerodynamic chord was cox'^ered in the tests. .For each test condition the model was floTi/n and the longiti.idina]. steadiness char- It was found in the investigation that longitudinal steadiness v/as affected to a much greater extent by changes in static margin than by changes in rotational damping. The best longitudinal steadiness was noted at large values of static margin. For all values of rota- tional damping, the steadiness of the model decreased as the static margin was reduced. The model was especially unsteady at low valiies of static margin (0.03 ov less). Reduction in rotational damping had. little effect on longitudinal steadiness, except that with low values of static margin (O.OJ or less) the longitudinal divergences were som.etimes m.ore violent with the tailless (low rota- tional damping) condition. In the applications of the model test results to full-scale airplanes the sm.all scale of the mod.el and the method of control make the model tests conservative; that is, the steadiness of the airplane is expected to be some- what .greater than that of the model for .^-iven valxios of 2 MCA ARR Ho. lJi.P02 static margin and rotational damping in pitch. The m.odel test results indicate that the tailless airplane, in spite of Its low rotational damping in pitch, should have longitudinal steadiness characteristics similar to those of a conventional airplane with the same amount of static margin, provided the static margin is greater than O.O3. INTRODUCTION Full-scale flight Investigations have indicated that static longitudinal stabilit:/ and rotational dam.ping in pitch are two Important factors affecting the longitudinal handling characteristics of airplanes. Ho flight investi- gations have been made, however, in which both of these factors were system.atically varied. Such an Investigation v/as considered desirable especially because of the recent trend toward tailless airplanes, mich have inherently low damping in pitch. An investigation has therefore been carried out in the NACA free-flight tunnel to determine the effects of large changes in static m.argin and rota- tional damping in pitch on the longitudinal stability characteristics of airplanes. Static m.argin is a m.easure of static longitudinal stability and is defined as the distance between the center of gravity and the neutral point of an airplane expressed in term.s of the mean aero- dynamic chord. The investigation was m.ade with a free -flying, dynamic model. The longitudinal steadiness of the model was observed in flights made v;ith variations in horizontal tall area and center-of-gravity location that gave a wide range of values of rotational damping and static margin. In the investigation an attempt was made to determine the relation between the observed longitudinal stability char- acteristics in flight and the calculated characteristics of both the phugoid and the short -period longitudinal oscillations . SYBSOI,S Cl lift coefficient NACA AliR No. liiF02 -, .. 1 . a- ^^^.. . . /pitchlno; moment G pi oching -moment coeilicicnt / ^ — ^ ^^■m di ■dCL rate of change of pitcrilng-moment coefficient t per degree staloilizei' incidence i. angle of incidence of horizontal tall, positive v/hen trailing edge is dcvui, degrees Cjjj rate of change of pltching-nioi'.ient coefficient ^ /dC^\ with pitching angul3.r velocity / — '— \ I cc p mass density of air, slugs per cubic foot q pitching angular velocity, radians per second V airspeed, feet per second "c mean aeroc'nnriairilc chord, feet static 'nargln, chords (x/c, for propeller off) X distance from center of gravity to neutral point, feet S v/lng area, square feet k,^ radius of gyration ahout Y-axls, feet b v;lng span, feet -t/2 time to damp to cne-half amplitude, seconds P period of longitudinal oscillation, seconds 9 angle of pitch, degrees APPARATUS The investigation was carried out in the MCA free- flight tunnel, which is fully described in reference 1. k NACA ARR No. LI4PO2 A photograph of the test section of the tunnel showing a model in flight is presented as figiore 1. Force tests made to determine the static stability characteristics of the model were run on the free-f light -t\innel six- component balance. (See reference 2.) A free-oscillation apparatii.s similar to that described in reference 5 ^^'a-s used to obtain values of C^,-, . A three-viev; drawing of the model used in the inves- tigation is given in figure 2. The model was constructed principally of balsa and was fitted with control surfaces similar to those described in references 1 and 2. In addition, a movable elevator was installed on the inboard portion of the ?jing (fig. 2) to provide longitudinal trim and control during flights with the horizontal tail re- moved. Three geom.etrically similar horizontal tails were used on the model. (See fig. 2 and table I. ) For the tailless condition, the horizontal tail was rem.oved while the vertical tail and the fuselage were retained on the m.odel. The center-of-gravity location of the model was varied by shifting lead v;eights located in the nose and the tail. IvffiTHODS Calculations The period and the time to damp to one -half am.pli- tude for both the short-period longitu.dinal oscillation and the phugoid, or long-period longitudinal oscillation, were com.puted for each tail condition for a range of values of static miargln from 0.02 to O.16 mean aero- dynamic chord. Values of the static longitudinal stability derivatives used In making the calculations were obtained from force tests of the model, and values of the rotational damping derivative Cm v/ere obtained o mq by a free-oscillation-test m.ethod sirailar to that de- scribed in reference 3' -^-H the calculations were made for a lift coefficient of 0.5. Flight-Testing Procedixre The model was flown with various amounts of static margin for each value of rotational damping and a rating NACA AP.R No. li^q^02 of lonritiidinal steadiness v:as a.ssigned by the pilot to each Goriditjon tested. Tlie model motion v/as observed Y/ith controls fixed and also during controlled flight. One uieas-ure of steadiness was the frequency with which elevator deflections had to be applied to keep the raodel flying smoothly in the center of the tunjiel. For very steady conditions, elevator control y»as seldom necessary; for unsteady' conditions, hov/ever, alternate up and down elevator deflections v;ere required almost continuously. Another measure of steadiness was the magnitude of ver- tical motions of the rocdel in the tunnel while the model was being controlled. Large vertical displacements and rapid rr^otions were the usual indications of unsteadiness and slew, easily controlled motions of small magnitude v;ere obtained in steadj^-f light conditions. !Iotion-pictirre records were taken with a camera mounted at the side of the test section of the tunnel for sore conditions to supplement the pilot's observa- tions of steadiness. Most of these records v/ere made of controlled model motions because elevator control v;as us^^ally required to keep the model flying in the center of the tunnel. Three differences between the method of controlling the longitudinal motions in model flight and in airplane flight sho-ald be noted: (1) The micdel is controlled by abrupt elevator de- flections of 2<^ to 5° o^ more, which are applied for very short periods of time; v.hereas, the airplane control can be applied slowly and smoothly. This difference probably makes the model flights more jampy than those of an air- plane \¥ith the saiiie values of static margin and rota- tional d amp 1 ng . (2) For the m.odel, abrupt elevator control is given frora a fixed neutral position and upon release the ele- vator returns to the neutral position. \?\;'ith this method of control it is im.possible for longitudinal motions of the model to be induced by oscillations of the elevator itself as is somie times the case for airplanes. (3) The m.odel is usually controlled to maintain a constant vertical position in the tvinael rather than a constant attitude as in the case of an airplane. This method of control introduces lag difficulties at times and caiises motions that are probably well damped with 6 MCA ARR No. l1+F02 controls fixed to appear lightly damped when the elevator control is being used. RANGE OP VARIABLES During the investigation, the rotational damping in pitch and the static margin v/ere varied while the weight of the m.odel and the m.oment of inertia about the Y-axis were held constant. The rotational damping factor Cjv^ was varied from -5.1 to -llj-.J by use of horizontal tail areas that ranged from to 2[|_ percent of the wing area. (See table I.) The static margin was varied for each tail condition by shifting the center of gravity known distances ahead of the neutral point. The neutral points for the different tail conditions were determined from a consideration of the values of — — obtained in force dCL tests of the model. The maximmn variation of static margin for the different tall conditions was from 0.02 to b.l6. The weight of "the model was held constant at a value of approximately 6.1 pounds, which corresponds to a wing loading of 2.7 pounds per square foot for the model or to a wing loading of 27 pounds per square foot for an airplane 10 times the size of the model. The moment of inertia of the m.odel for all test conditions was such that the ratio of the pitching radius of g^nr'atlon to the wing span ky/b was O.I7. This value of ky/b is within the range of values for conventional airplanes and is onl^r slightly belov/ the average ratio obtained from values for over a hundred airplanes. The flight tests were m.ade over a range of lift coefficien-cs from 0.1\. to O.7. The lovi/est lift coeffi- cient obtainable (0.[|.) was established by the maximum airspeed of the tunnel. The highest lift coefficient (0,7) was limited by the maximum lift coefficient of the model. Most of the flight tests were made at a lift coefficient of approximately 0.5. MCA APuR xTo. ll^F02 7 RESULTS The results of the calcule.tions made to determine the time to damp to one -half a:nplitnde and the period of the longitudinal oscillations are ppj'e sented in figures 5 and h> Results are given for the short-period oscilla- tion in figure 3 and for the long-period or ph\i£-oid oscillation in figure '4.. The steadiness ratings assigned by the pilot to different flight conditions are shown In table II. Data from motion-picture records showing tiine histories of the vertical motion and pitching m.otion of the model with different amounts of rotational damping and static miargln are presented in figures 5 "^o 7« DISCUSSION Effect of Variation of Static •.largin The ratings of table II show that the steadiness of the i'iicdel decreased as the static miargin was reduced for all values of rotational damping. The model was particu- larly unsteady at lov.r values of static margin ("below O.Ok). The m.odel flev/ very steadily with large values of static m.argin, and only occasional elevator deflections were required to keep the model flying sm.oothly in the tunnel. The time histories at the bottom of figures 5 and 6 show that the vertical motions of the m-odel driving controlled flight with large static m.argins were slow, smooth, and of sm.all m.agnituae „ With low valij.es of stable m.argin, however, the motions became faster, sharper, and larger, as shown by the upper time histories in figures S S-J""-"^ "• Table II shows that, \vith 0.02 static margin, the model was very unsteady v/ith any am_ount cf rotational dam.Dlnfi-, Flights at this condition were /ery jimipy, and strong tendencies toward longitudinal divergence were noted, ■'■lost flights with tnis am.ount of static margin, ended in crashes because of the e.xtreme di.fflculty experienced by the pilot In applying elevator control at the exact instant that it was needed to prevent longitudinal divergence. At timiss, because of unavoidable lag in the Toilet's reactions, the control was applied in such a V'/ay as to reinforce rather than to oppose the divergent motions. 8 NACA ARR No. lJ+F02 In this connection, it should be pointed out that the pitching velocities of the small-scale models tested in the I'JACA free -flight tunnel are more than three times as great as the pitching velocities of the corresponding airplanes. It is expected, therefore, that the airplane should he easier to fly than the model with the same amount of static margin, and it is not believed that an airplane corresponding to the model tested would neces- sarily^ exhibit poor flight characteristics similar to those that were noted in the tests of the model with 0.02 static margin. The results of the calculations of dynamic longitu- dinal stability (figs. 5 S-^id I4.) show that reducing the static margin increases the period of both the phugoid and the short-period oscillation and reduces the damping of the TDhugoid but does not affect the dam.ping of the short-period oscillation. The only agreement noted between the calculations and the flight -test results was that the period of the short -period oscillation was approximately the same as the period of the controlled motion of the m-odel. Theo- retically, the damping of the short-period oscillation is heavy and does not vary with static margin. -It is possible, hov/ever,. that the short-period motion could be reinforced by elevator control m.ovements or gu^t dis- turbances in such a way as to prevent it from dam.ping quickly. If such conditions were present, an unsteady, ].lghtly damped longitudinal motion having approxim.ately the same period as the short-period oscillation might occur . Effect of Variation of Rotational Damping The ratings of table II show^ that variation of rota- tional damp.ing had very little effect on the longitudinal steadinesr of the model. Decreasing the rotational damping had virtually no effect on the steadiness at large values of static m.argin but decreased the steadi- ness slightly at low values of static margin. The time histories of figures S to 7 show that the vertical motions of the model during controlled flight with dif- ferent values of 0,^^ were roughly sim.ilar for a given value of static margin. With low values of static margin NAG A ARE No. li^POa (0.02 and 0. C3 ) , the lon'<;ltudl.nal divergences were some- times i:iore violent with the tailless (low Cjj-,.. ) condi- ticn. The snifll effect? of chanrj;es in rotational damping on tlie longitudinal steadiness of the inodel indicate that a tailless airplane, in s^oite of its Inherently lov^f rota- tional damping in pitch, should have longitudinal steadi- ness characteristics Sj°.milar to thor.e of a conventional airplane with the same static raargin. Tn the investigation no quantitative data were ob- tained concerning the effect of changes in rotational darr/ping on the elevator effectiveness required to maintain a given degree of controllahility. It was noted in the flight tests, however, that as the horizontal tail area. (and thus the elevator effectiveness) vras reduced, the magnitude of the elevatcr coritro]. deflections required to kset.. the model flying satisfactorily in the tu.nnel did not increase in direct proportion to the reduction in elevator effectiveness. It thiis appeared, that, as the rotational dar;;ping in pitch was red.uced, less powerful elevator control was required to obtain satis- factory- flights v;ith the model. The calctilations (figs. 5 and h.) show that reducing the rotational damx)lng factor On, increases the neriod of the short-period oscillation and decreases the period of the phugold. Reducing the valine of C:;,i reduces the damping of the short-period oscillation for all values of static margin and reduces the damping cf the phugoid 05'cillation for the lower values of static margin. COhCLUDING REMARKS The results, of the investigation to determine the effects en longitudinal steadiness of varying sts-tic margin and rotational damiping are siimmarized in the fol- lov/ing paragraphs. In the ai.^plications of these results to the fixll-scale airplane the small scale of the model and the method of control probably make the model tests conservative; that is, the steadiness of the airplane is expected to be somewhat greater than that of the miodel for given values of static m^argin and rotational damping. 10 MCA ARR ITo. L[!l''02 1. The "best lonrltudirial steadiness was noted at large valixes of static margin wlille the lear:t steady conditions v;ere obtained ^/Ith very small values of static raargin (0,05 or less), 2. Ci).anges in rotational darping had little effect on longitudinal steadiness except that for .lovv values of static margin (0,03 or less) the longitudinal divergences v/ere soiretiiaes more violent for conditions of lov/ rota- tional d amp i ng . 'S , The irodel teat results indicated that a tailless airplane, in spite of its inherently low rotational dajr.ping in pitch, should have longitudinal steadiness characteristics similar to those of a conventional air- plane ¥/ith the same static rriargin, provided the static margin is greater than O.O3. Langley Memorial Aeronautlca.1 Laboratory National Advisory Ccnmittee for Aeronautics Langley Field, Va-. REFLiREI'CES 1. Shortalj Joseph A., and Osterhout, Clayton J,t Preliminary Stability and Control Tests in the FACA Free-Plight Wind TunnsZ and Correlation with Full-scale Flight Tests. i^.CA T!T ]^o . 81O, 1914-1." 2. Shcrtal, Joseph A., and Draper, John -J . ; Free-Flight - Tunnel Investigation of the Piffect of the Fuselage I,ength and the Aspect Ratio and Size of the Vertical Tail on lateral Stability and Control, MCA APR No. 3D17, 19k3. 3. Campbell, John P., and ffathev/s, '''^ard 0.; Experimental Determination of the Ya'.i7ing r^^.'oment Due to Yawing Contributed by the •.■/Ing ," p-ase lago , and Vertical Tail of a Midwing Airplane Fodel, MCA ARR ITo. 3F28, I9U3. NACA ARR No. lli.P02 11 >^^QU ■ CO M H U C rrvrt"^ rH rH >H P u3 H 4-3 O^ ■» * • e ^d 4-3 P: & _:j-0 l>- K^ N\ CC ccl B cd iH rH 1 I 1 0^ S U^ 03 ^i I 1 c/1 ■d M p_-; 1 ■H U a CD a 4J H • LPiOCO CVI -d- S^q 1:3 Jh < N~iC\l rH rH H
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