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Aviation History
1914
1914 - 0925.PDF
SEPTEMBER 4, 1914. /ycHf "THE AEROPLANE OF TO-MORROW. f » VARIABLE SURFACE, CAMBER AND INCIDENCE, AND THEIR EFFECT ON SUSTENTATION. SPEED AND SAFETY. By L. DE BAZILLAC, Engineer, Ecole Superieure d'Aeronautique de Paris. A WIDE range of flying speeds is rightly regarded as one of the most desirable attributes in an aeroplane because of the benefit derived from the ability to rise from or alight within very restricted areas without necessitating any reduction in the higher limit of speed of which the machine may be capable ; and this is especially so in the case of aeroplanes intended for military purposes, since aerial reconnaissance and attack can be more effectively carried out when flying at low speeds. The problem of high speed flight has, however, in recent times, resolved itself, to a large extent, into one of landing safely, and this tends to become still more difficult as the maximum speed is increased. Hence it is well for us to see whether it is not possible to design an aeroplane having much wider limits of speeds than are at present customary ; and in so doing we shall consider the effect of both simultaneous and separate variations in the lifting surface, the camber, and the angle of attack. The slow speed of a machine may, however, also be diminished by the rational use of the second speed of flight. Variation of the Surface.—The equation for sustentation in hori zontal flight is W= KySV2, so that if the weight, H7, of the machine and the unit lift coefficient of the wing, Ky, are supposed to be constant, the speed for horizontal flight will be reduced to V+ A/2 = 0*707 Vior a surface, S, of twice the area. In doubling the surface, therefore, we reduce the speed by nearly 30 per cent. Simultaneous Variation of the Angle of Attack and the Surface.— Now consider a machine, the angle of attack of which is 2° at normal speed. From Eiffel's curve for wing No. 3 At 2°, Ky — 0*036 'Kx = 0*0035 At 6°, Ky — 0058 Kx — 00054. The equations which define horizontal flight are W= KySV'1. Power expended = P= (A'xS+\) V3, where A is the coefficient of total passive resistance, If we take into consideration the roughness of the surface, A includes a term proportional to S, i.e. A = Ao + AjA^, and A" is a coefficient approximately constant, but which is, how ever, as much greater as Ky is greater, for the same Kx. A0 and \x are the coefficients of passive resistance of the body and of the wings, respectively. K S" ' Write \ x = •!•„' where Sx is the equivalent detrimental surface and A", the coefficient of normal resistance. In trebling the angle of attack we have increased the lift in the proportion of I to I *6; and if, at the same time, we double the lifting surface the lift is then increased 3*2 times, and we can proceed • at 0*56 of the original speed. What will now be the power necessary ? If we substitute the value of V given in the expression for the lift, in the preceding expression for power expended, we find that X Ao+ AV?! P=W^._ Kx + •S=IV* Kx + ^'S.Kyi *S'S.Ky\ In doubling S and multiplying Ky by I '6 we have increased the denominator 2*86 times, and in trebling the angle of attack we have multiplied Kx by 1*54. In doubling the supporting surface we have halved A0 and diminished (A^T,) because the passive resistance increases at a slower rate than S. Hence we have reduced the power required for propulsion by between 40 and 50 per cent. We have considered, it is true, only small variations of Ky ; but the range of speed obtained to-day with a fixed surface varies to the extent of only about three times the minimum. Further, we have not taken account of the possible variations of the camber, which, in increasing the range of values of Ky and decreasing the speed, decreases also the power necessary. But a very much greater range of power, if required, could be obtained with two motors of unequal power working in conjunction. However, if we construct a machine capable of augmenting or diminishing its lifting surface, and, at the same time, its camber and angle of attack, it is possible for us to obtain, in ascending flight, and in gliding, a range of variations of the speeds much higher than at present. This we propose to show. At normal speed, the machine would fly with a reduced surface, and would start and land with increased surface. In this way we obtain the three most favourable conditions of flight :—(a) High climbing speed, (b) high speed in horizontal flight, (c) low speed at the end of a glide. Ascending Flight.—It is necessary, in ascending flight, in the case of a military aeroplane, to obtain the fastest climbing speed for a given angle of attack, weight, and power. Let G be the centre of gravity of the machine, IV the weight of the machine (supposed to be constant), V the velocity in the line of the flight path, 1 the angle of the flight-path with the horizontal. H the thrust of the propeller passing through G and directed parallel" to the flight-path of the machine. We will suppose this thrust to be constant, that is to say, independent of the variations of the angle of attack and of the speed of the motor, provided that one does not change either the ignition, the admission of the gas or the transmission after the start. This hypothesis is not absolutely exact because of the viscosity, and of the friction of the air on the propeller; in reality, for great decreases in speed, the thrust increases, but one can, without appreciable error, consider it as invariable for the speeds of the motor included within the limits of its power. If the forces which act on the machine are projected firstfon the flight-path and then on the normal to the flight-path, (see Fig. I), we can write— H - Wsin i = A, Jf cos i = A'y Kx, Ay being the total drag and lift coefficients. Dividing the right hand side of the first equation by that of the second, and the left hand side of the first by that of the second, H . Ax ave—777-rrr—tan«= „ , or, approximately, small, if.-y= o, IV cos i' . Kx -<=A/ Kx A = » = *,' as 1 is very 7. This is the case of a glide— i.e., during flight when the machine is not under engine power. If py = 8, when 1 = o, ,,* = 8 where 8 is the thrust per unit of weight in horizontal flight. It is seen by these relations, and referring to the experimental curve showing graphically the variation of the ratio .,* (Fig. 2) or Ay the curve of inclination, as a function of the angle of attack a measured from the fictitious plane (a plane placed parallel to the wind, when K y = 0) that if oa = 9, ob K R, Kx •*• A'y the magnitude of ob = ab, is the inclination the machine can attain above the horizontal, with the engine rotating at normal speed. The gradient will be as much steeper for the same angle of attack as the curve of inclination is more inclined in its power part, from the point with ordinate oa = 0 thrust per unit of weight for hori zontal flight. It is necessary, then, to diminish ob from this point, i.e. A\ Ry or \KX + A„ + K,St )•> Ky J and the steepest gradient, for the same 8, whatever be the angle of attack, will belong to the machine A 4- K 9 having the smallest T- , *.«•> one able to pass from the smallest to the greatest surface (because A0 remains approximately \ 1. Fig. constant, and KtSx increases much more slowly than S). The camber must increase with the angle of attack in such a way that it gives the greatest lifting force, the resistance to motion being equal. It is evident that the more the surface increases, and the more the if ratio i>* decreases by a rational increase of camber, the more the y angle of attack, a*, corresponding to the minimum of the curve ot inclination decreases. If S were able to become infinitely great or R If (Ao+AVSi) infinitely small, * would approach *. a, designat-A, Ky ing the angle which corresponds to the minimum value of this ratio, OQ and Oj would become the same point. 925 '
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