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TIICHNICAL Memorantitiks NATIONAL ADVISORY TIICHNICAL MEMORANtitikS NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS No. 941 SOME DATA ON ikii S9$ATId kb~dITUDINAL STABILITY ANi) CONTROL OF AIRPLANES (DESIGN OF CONTROL SURFACES) By A. Martinov and E. Kolosov Central Aero-Hydrodynamlcal Institute .. Washington May 1940 ,... ~ ~lllllllllllll 31176014407002 1 –— c NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL MEMORANDUbi NO. 941 ,. SOi@! DATA ON THE STATIC LONGITUDINAL STABILITY AND CONTROL OF AIRPLANES* (DESIGN OF CONTROL SURFACES) By A. Martinov and E. Kolosov 1. STATEMENT Ol? THE PROBLEM In connection with the increasing demands” made on the maneuverability and controllability of modern airplanes, the question of the so-called “allowable degree of stabili- ty” ha,s lost that clarity with which a number of authors have sought to define it (reference 1). There has arisen the necessity of building airplanes with a smaller reserve of stability, thereby approaching the “neutral” type. The problem of controllability and maneuverability can not otherwise be satisfactorily solved with the modern methods of airplane control. In line with this tendency toward airplanes with a small reserve of stability considerably stricter conditions are imposed on the airplane design and increased deinands are ,~ade on the pilot. At the same tir,e, greater responsi- bility is laid on the computer since small errors in compu- tation may lead to an unstable airplane. Fundamental in the computation of the static stability is the determination of the correct center of gravity posi- tion, s’hape of wing and method of attachment so as to assure small moments of the entire airplane without tail”. The choice of the tail itself is generally determined by the following met-hods: 1) kethod of selecting the tail surfaces from wind-tun- nel tests. 2) Method based on the comparison of curves obtained from tests on models of the airplane elements. 3) Analytical method. *Report NO. ~’78) of the Central Aero-Hydrodynamical Insti- tute, Moscow, 1936. I .—.—— — ‘1 2 . 3T.A. C.A. Technical Memorandum No. 941 .. In our opinl~n the first method Is Impracticable since it not only requires a large amount of wind-tunnel work but 1s at theeame time a Ilblindil method. The second method Is most, widely applied by aircraft designers. The third rmthod has come to attract more and more attention. Comparisons made of computations”, wind-tunnel tests and flight tests iE- dicate the very great possibilities of tho method, particu- larly for preliminary approxl]dations. The problem Is logl- cally expressed in the form of ‘seeking the limiting center- of-gravity positions for which the airplane Is still able to satisfy the stabllitx requirements put on it. There are naturally two such certer-of-gravity posi- tions to be considered, nai~ely, the forward and backward positions. For an airplane of the usual arrangement, the first corresponds to the lldtlng anglo of deflection of the control surface and the limiting force on tno control stick In landing, For an accurate d.etermlnation of these values, it Is necessary to establish standards of allowable limiting forces acting on.the control stick. It must be said that information in this connection is not available In the en- gineering literature and these standards must be newly es- tablished, based on full-scale tests on airplanes. The second llmlting center-of-gravity position corre- sponds to the state of the airplane at which it becomes en- tirely ni3utral.* A detailed analysis shows that the limiting forward center-of-gravity position must be determined in landtng with deflected flap and account must be taken of the ground , *After this paper had been written, there appeared the work of v.. S. Pishnov; IiAerodynamics of the Airplane, “ Part II, in which the author has introduced the conception of crltl- ~Cm~ cal center of gravity position only for —= o, i.e., ~a corresponding to the neutral state of tho airplane. Te con. siderod it useful, howevor, to Introduco tho conception of still another limiting center-of-gravity position determined by the maximum possible force on the pilotls stick. These two magnitudes will theri satisfactorily solve the problem of . center-of-gravity position. Aoreover, in designating a lim- iting backward center-of-gravity position, It Is necessary to take account of the dynauic stability of the airplane. N.A.C.A. Technical Memorandum No. 941 3 effect on the airplane characteristics. The limiting back- “ward center-of-gravity position in the computation is ob- tained in “hands-off “ flight. Thes”e two cases should be in- vestigated in determining the center-of-gravity position of the airplane. The analytical method of computation in combination with the accumulated mean characteristics of airplane ele- ments at the present time may serve as the most r“eliable metilod, since ii cora-oines the advantages of correspondence to actual conditions with clearness of a picture of’ the phe- nomenon, thus permitting a conscious improvement of the bal- ancing and stability. It would be quite incorrect to say that the analytical method of computation is rendered entirely feasible by the amount of data available. In regard to some subjects, as for exain~le, the effects of interference between elements of the airplane on the stability, the data are as Jet too meager to allow any generzl conclusions to be drawn. It is clear that in such cases more factual material obtained from wind-tunnel and flight tests is required. The most rational method of co.mnutation t’hus appears to be a combination of the analytical supplei~ented by curves obtained from tests on models, and, as more data are accumulated, the part played by the supplementary tests will become smaller and smaller. Notation Adopted pitching- moment coefficient ‘c mw I ,moment coefficient of wing cmf , moment coefficient of fuselage moment coefficient arising from wing-fuselage interference c moment coefficient of landing gear mlg’ c moment coefficient due to propeller thrust ‘T ‘ cmt 9 moment coefficient of tail CY ‘ cX9 Cn, Ct, coefficients of aerodynamic forces Ch , hinge moment of control surface 4 .N.A, C.A, Technical Mem”orandtun No. 941 s, area b, chord .- , 1, span t, mean chord of servo-control tab = %3c/tac L, digtance from center of gravity of airplane to hinge of control surface .. x/b, position along longitudinal axis of center of gravity (sign + iw taken In direction toward tail) y/b, position along vertical axis af center of gravity (sign + for down direction) ‘cent surf n= / ‘tail Ji, epeed a, angle of attack . 6, angle of deflection of control surface (sign + for down deflection) e, angle of deflection of servo control (sign + for down deflection) v, angle of deflection of stabilizer (+ upward) e K,= kinematic coefficient of linkage between servo- X control and main-control surface 6 = const (see section 5) a = const (see section 1.1) I?.A. C,A. Technical Memorandum No. 941 5 R, Reynolds number -J- 6, measure of the turbulence, c = — Vmean Subscripts a, airplane T, thrust w, Wing SC. servo control t’, tail St , stabilizer f, fuselage int, interference lg, landing gear Cs, control surface The basic equation of the equilibrium of the moments acting on tho airplane about its center of gravity in its plane of symmetry may be written in the following nondimen- sional form (1) Of these coefficients Crew, Ctfllp,CmT, and Cmt may be computed. The effect of tho fu~el.age, however, and tho in- terference effect cf the airplane elements must be deter- mined trom test data. Differentiating equation (1) with respect to CJ we obtai.1 the condition for the limiting aft location of the center of gravity. dcm,x acuf acclt —-l- —-l-. -t — = o (2) a~ am au The center of gravity position is found from the component acmw in which it enters. x’ .. -. .— r. — .- . 6 ., .. :. .“ . ac~ ~cal x acn y act .. ‘: + (3) ‘~=r--— b au ‘—b, am . .. The effect of the center-of-gravity location on the other mouents acting on the airplane” Is negligible by comparison with the uonont of the wing; The basic nouent, which the pilot is capable of chang- ing in flight, is the tail uo:.lent C.Jt StLt ~Vt a c= =. Cyi— — (4) t 6tbw ‘V ) since with modern airplane =rangouents Cn =Y be re- placed by Cy and the “aonent due” to Ct &y be neglected even for neutral airplanes for which the accuracy requiro- aents are rained, and C may be e~reseed in the eiEl- Yt plost case of control surface without balance and cut-out a (3Y — [at + n~cs] (5) cYt = ~at Let us. now considor what change is introduced into the phenomenon by the condition of free control stick. We shall sinplify the pl(zture by hot touching upon tho dynanic ele- aents of the phonoaenon. The control surface, which is statically balanced, is adjusted with respect to the flow In such a manner that it foras with the stabilizer a certnln angle Sa (fig. 1). The alrplano trimmed by tho pilot to a certain attitude with the aid of tke control surface inclined at tno anglo 6L i~aediately passes into the otiler attituae corresponding to the deflection ~s the value of which may bo found fron the condition of zero .value of the hinge mo- aent . .- ach .. a Cll Ch = —at+~~ = Klat + Ka8a = O (6) aut Cs I E. A. C.A. Technical Monorandum No. 941 7 A linear ilependenoe of this kind uny, as shown ty tests, bo appl!ed to the fundamental types of tail sur. faces wlthln the rang~ below flow separation. Theroforti (7) Thus . Ey formulas (7) anil (8) It IS possible to estimate the ac and the derivatives: 49; %; 3; cnan~es both of C7 t Ga aa ac for choice of center-of-gravity location and solution o; the problem of stability rlth controls free, The weight of the control eurface may be taken into ac- count without any difficulty.
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