FlightGlobal.com
Home
Premium
Archive
Video
Images
Forum
Atlas
Blogs
Jobs
Shop
RSS
Email Newsletters
You are in:
Home
Aviation History
1916
1916 - 0864.PDF
[fUChf] OCTOBER 5, 1916. «< THE AEROPLANE OF TO-MORROW." VARIABLE SURFACE AND STABILITY. By LOUIS DE BAZILLAC, Engineer (Ecole Superieure d'Aeronautique de Paris). Translated by B. BRUCE-WALKER, B.Sc. /A' our is;ue: 01 September 4//1 tt ay., 1914, toe published a scries of interesting article* by Mens, de Bazillac, in which the author shewed how an aeroplane that, an increase its lifting surface possesses considerable reserve oj lift, speed variation and safety from nose-diving. We are glad to be able to commence this week another article by Mom. de Bazillac, in which he deals with the effect of a variable surface on stability.—ED. In the majority of existing flying machines av and p are of the same order of magnitude. When the surface of the tail is increased the ratio an'p can only be diminished thereby. The order of magnitude fon;,'/tudinal Stability. IN what follow* it will be shown that a system of variable surface poseeseei a considerable reserve of automatic longitudinal stability if the shape of the variable surface can be automatic illy altered. Let us give the name of " central oouple" to the resultant moment of all the forces acting on the machine alrout the centre of gravity. We will suppose that tbc thrust of the propeller passes through the centre of gravity, and consider the machine as provided with a tail and having movements parallel to its plane of symmetry. Let: K,, R.. be the pressure* of the air <ra the whole machine and on the tail, ami I.,, L, the distances of R„ R. from the centre of gravity. The central couple is given (fig. 1) by : r = R, L, - R, U (1) W hen the michine deviate!, fro n its normal attitude, if the central Fig. 1. couple tends to bring it back, this couple plays the part of a restor ing couple, and it is thii that assures the stability of the machine. Denote by 1 V the instantaneous velocity of the machine ; S, the main surface; K1 a coefficient characteristic of this surface ; «> the angle qf normal flight ; the surface of the tail; K; a coefficient characteristic of thii surface : (a, ±r .) the an^le of tin tail with the direction of the speed. (The -f sign refers to the case in which the angle < is situated above Sj, and the - sign to the case in which it is situated below.) We can write as a tint approximation and for small variations of the angle of attack : R, = K, S, V« a, (2) R,=iKtS,V« («,+«) (3 When the normal condition is established the central couple is aero, and we have: R, L, - R. U - O (4) Consider the variations of this couple starting from its zero value for infinitely small deviations. Expression (1) gives: & r at (R, + 8 K,) (L, + 8 L,) - (R, + 8 Rs) (LtJL.) = L, 8 R, + R, 8 L, t R, L, i 8 R, 8 L, - (L. * R.. . R„ 8 L. + R. Lj + 8 R, 8 L,), whence, taking (4) into account and neglecting the second order of siliull quantities. : 8 r • L, 8 R, - L, 8 R. + (R, 8 Lt - R. 8 LJ (S) We may calculate the order of magnitude of these last two moments. For this consider the ratio R,»L, L,8 U " Pt-noting bv N| 1 coefficient which relates to the displacements in position ana direction of R,, we can write : L, • N, a,: and the above ratio becomes : R, 8 L, m K, S, V- K, «, la, _ N, K-SsVL-fc, L,' KsSt'K.S!' *L« I, „ N: -, Lj8R; I,." P' L,8R; whence, putting of the ratio ai/p is, therefore, no greater than unity. As far as the ratio N|/L« is concerned it is easy to see that it is hardly of the order of a hundredth, for Nj is generally at the most a few centi metres, whereas L> is always several metres. In short, we see that the ratio of the moments R, 8 L! and L> 8 R2 will be at the most of the order of a hundredth, and that consequently in a first approximation the moment R, 8 Lj is perfectly negligible compared to L. 8 Rj. With still greater reason is R? 8 L, negligible compared to the moment Lj J R„ for 8 Lj and 8 Li are of the same order of magni tude, and K; is generally smaller than R,. We see then that in a first approximation perfectly compatible with the whole of our considerations we can neglect the bracketed quantity (R,8L,-R» 8 L«). We can then write with sufficient accuracy: 8 r m Lt 8 R, - Lj 8 R,, and, taking (4) into account: 8r=LsR,,i51 - LjBR;. Ri Finally, substituting for R„ R3, 8 R,, 8 R.,, their values obtained from (2) and (3): 8 r = L, p K, S, V2 Q) 8a„ = 15R. - or 8 r = ± (L, K, S, - L, K, S.) V- 8a, ' (7) (The + sign refers to the case in which the rear surface is lifting and the - sign to the case in which it is non-lifting.) Suppose further that the surfaces S, or S= can be automatically increased or decreased under the influence of "the gust. The resistance of the air to the machine not remaining constant, the speed will vary during the disturbance. Can this variation in speed be neglected ? Let: y be the inclination of the velocity during a glide with the engine off (Fig. 2), 1 («i + 0 Sai (6) V a 0 R. -\-\H V 1 \ \ 1 \ 1 \ 1 * . - . . - i. .... 1 «t \* «/' doc/ e C - 3--^ s ft*£ *£ Fig. 2. C and C| the curves of the inclinations 7 relating to the surfaces S and S ! 8 S, and V0, and V«, + «<n the speeds corresponding to the angles o, and a, + So,. At the angle en the propulsive force per unit weight was o n. At the angle a, + Sot the propulsive force necessary for horizontal flight has become o m. Since the thrust of the propeller has remained constant the difference of force m n makes the machine climb and measures it» slope of ascent Si, or 8* = tan - ' mn. 860
Sign up to
Flight Digital Magazine
Flight Print Magazine
Airline Business Magazine
E-newsletters
RSS
Events
