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Aviation History
1916
1916 - 0891.PDF
OCTOBER 12, 1916. \pML *t THE AEROPLANE OF TO-MORROW. ti VARIABLE SURFACE AND STABILITY. By LOUIS DE BAZILLAC, Engineer (Ecol* Supcriourt- iE Aeronaut tque d* Paria). Translated by B. BRUCE-WALKER, BJSc. (Conci*d*4 from prng* Ml.) V, at the incidence • + I* Th« iy«MBttefc»lbjr opposite atrip, T* will meet the air with a velodtv, V'„ at the tncttMOt a -fa. Let A be the chord of the wing (Fig. 5). The lifting force* of the strips considered were equal la <»«»« another, and equal to K£* t x V* before the disturbanca. After the disturbaaca torn Lateral Stability. The lateral oscillations of the aeroplane and its changes of azimuth take place, in horizontal flight, about two perpenoicu! ir axes situated in the plane of symmetry. These are the axis uf rolling and the axis of gyration. Suppose a small disturbance to make the plane of symmetry of the machine turn through an angle tj> absut its axis of rolling. If the speed keeps a constant direction the resistance R will not vary, and will remain with the speed in the plane of symmetry. But, from the time when the rotation Sip was effected, the pressure, which before the rotation annulled the weight W of the machine, now gives with this a resultant 0 which is not sero (Fig. 4). Under the action of this resultant the machine begins to take up an acceleration directed according to p, which will make the velocity depart from the plane of symmetry. R will also depart from this plane, and its moment about the axis of rolling wilt no longer be nil ; it will, therefore, make the machine turn about its axis. If this rotation decreases 8«> the machine will be stable; if it increases it, it will be unstable. The stability against gyration can be measured by the moment of the couple which tends to bring the plane of symmetry back to the direction of the relative wind immediately this has changed. It is easy to see that the couple of stability against rolling is just as much a couple of stability against gyration. The two problems of stability against rolling and stability against gyration are then intimately connected in the problem of lateral stability. This granted, let us consider an invariable aeroplane undergoing a deviation of rolling or of gyraion, and suppose that, whatever its form, it cannot return after,this displacement to its usual orienta tion. We should say that such a machine cannot realise lateral stability. Experience shows us that it is not so generally. In the case, however, in which the above hypothesis is borne out, does there not exist some means of rendering the machine auto matically stable ? We shall see that the automatically variable surface advocated above for longitudinal stability fulfils here again all the conditions Fig. 4. Fig. 5. farces, have become— K»~I +"4.A»jrVl»* j fc>. A < .« V,» and and h>. - *. A « * V ,« that U to ay l and and 1 - I Kr. *«* v,» The two first elements of each of the** force* are very seaadJy equal to one another and equal to the original lifting fatca*. The second elements arc also sensibly equal, and constitute a couple of leverage * the moment of which may t* written: 8 C« * « ty. x klx t* + V>. The variations of K*a for small angles of attack are practically pro. niirrtinfl to the variations of the incidence, or to %m say. But we have, when la is very small s t* • We can therefore put: I Kf. ss '' * Constant. We have then '8C« and, since r • x m 1 8C* C» V AH. <r" sc —£«, A 8 J (.(* =cC* <> "(V* X*4 I V>. *r* + V w»jr<) ' !> Integrating between 0 and / and twtween O and L (/ twlog the length of the wing not enlarged and I. that of the enlarged), and regarding » as a constant, we have : Ca = Ca = CA CA, j(V»*M •»**)*»•" • [w*< *«*•)«« I I V»jr» Vx* i J'x 5 •:i Ca = V- <L* 4 n+jiu i /*> I CA.I • V I '3 Neglecting ihetcrm a.8 (L° I /*) beside the term V« (L1 -I /») we have in the end : CA«V, Ca V -1 /'); necessary for practically assuring lateral stability, if the arrangement adopted for obtaining this variation is sensitive to rolling or to gyration. One can, in fact, determine a couple of lateral stability with variable surface just as we have determined the couple of longi tudinal stability, if by this is understood the stabilising couple obtained by means of enlarging one of the wings, the other, that which receives the gust of wind, remaining unaltered. The transverse stabilising couple due to the enlargement of the wing that does not receive the gust is counterbalanced by the damping couple due to the span. Let us calculate the damping couple. The part of the planes that goes down, that which does not receive the gust, i, for example (Fig. 5), may be split up into strips T situated at a distance .a from the axis of symmetry AB. If »is the angular velocity of the wing, and assuming that the distance from AB of the axis of rotation may be neglected, one of the strips Tt takes und *r the action of the original disturbance a velocity of rotation V m x v. But this strip has besides a velocity of translation V at the inci dence a. The velocities, V and *•, combine to give a resultant 887 and taking account of the total weight w of the wings, we have at the end oftne time 11 3 x 4 »(L 4 /) Thu>, when a disturbance is produced, thr damping couple to which it gives place is, taking into account the growth of an* of the wings, crop irtional to the sum of the cut** </f the two lengths of the wing*. This, couple then is made greater by the lengthenmc. al tl>< wing. Thii couple is counterbalanced by the transverse «*bili»ttig couple of the enlargement of the wing, which does not receive the gust of wind. This latter couple has for its value : r K;.*V',L1-/*1 "'(Lf/leos 360 w/ * (E - /) To measure the action of the transverse stabilising couple equate this couple to the damping couple and write : I*) »<*' * ^«» 360"' CA-V 3 K/.*V <L* i L* + n 4 «(L + /> V,, n ISO«' ~4<L4/)e"*(L vt "• r' • C(I;M !>)»• 2 3 25, Kj„ a o-oa, and C * 1/5. We n*4 • 1 m m >~~ These few considerations are without doubt simple enough since they depend on the principle of splitting up the resistance of the an whence: Let L = 2/, / 3, V
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