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Aviation History
1917
1917 - 0188.PDF
t/QCHT FEBRUARY 22, 1917. THE AEROPLANE OF TO-MORROW. By LOUIS DE BAZILLAC, Engineer (Ecole Superienre d'Aeronautique de Paris). Translated by B. BRUCE-WALKER, B.Sc. (Continued from page 889, Vol. VIII.)APPENDIX I. Practical incompatibility of the expression tan y = the formula tan 7 Rx Ry necessity and ofYO. + t + '.—Practical awriting : s = a + ra -—Advantages of the new formula—Application to ascending flight in the case of variable surface- Consequences .When an aeroplane descends with the engine off, and in still air, it tends, as we know, to take a certain speed and arectilinear trajectory that depend on the angle of attack that is given to it by the relative position of the differentsurfaces composing it. Let:—W be the weight of the machine ; RAT and Ky the coefficients of drift and of total pressuredetermined experimentally with a small model of the aero- plane, i/nth scale, for different angles of attack o, measuredto the imaginary plane (a plane lying in line with the wind when pressure is zero) ;F the sustaining force normal to the trajectory of slope 7, and R the total resistance to forward motion.We know that if the normal uniform speed V is reached, the forces present are in equilibrium, and we have :—-.; tic; .;;.:• ,'. F = W cos 7 = Ry »2 V2 "'." •.."] ci ..'.•. R = W sin 7 = R* «2 V2from which we obtain :— „*• *•. in the particular limiting case of S infinite, it is not in accordwith the hyperbola found from experience. We will study this limiting case. This will lead us to modifythe construction of equation (Bj), and substitute a new formula for it. System (Bx) is practically incompatible with System (A). Consider for a moment equation (A). This equation can be written :— (A) Now, ,'w- = /(o) is represented by Eiffel's experimental curves (Fig. i), consequently these curves give the value of the angle of descent as a function of the angle of attack. Fig.l. As these curves all have the same form—a hyperbola—ithas been attempted to represent them analytically in a first approximation by the following expression :— : ' ±. , _.- , s m > tan 7 = ra + t + - * IS^) tta being the angle of attack measured to the imaginary plane ; r a coefficient smaller than i for a cambered surface ;a coefficient generally negative, zero for a flat surface and for an infinite surface, and s a coefficient relating to thebody and the wings. Also it is admitted that the components of the resistanceof the air can be represented in a first approximation and for small angles by the following formulae :—R# = KSV- (y«a + ta + s). Ry = KSW (C)S being the total wing surface and K a coefficient sensibly constant. -Although these formulas certainly do not apply very well to curved surfaces, they are applied to the aeroplane as awhole, and it is from them that have arisen the theories of the various principles of the aeroplane. It is true that thestudy of the principles of the aeroplane, from the dynamical point ©f view at any rate, rests above all on an all-round agree-ment with facts ; and it can be proved that the hyperbolic form which represents the formula (Bi) is general and inde-pendent of the approximation admitted for the laws of the resistance of the air.But this formula should not be incorrect in any case; yet, Tan 7 — "' Ky KyKx and Ky being the coefficients of drift and lift for unit area of the whole of the wing surface ; S the total area of the wings ;\ the coefficient of total extra head resistance ; \a the coefficient of extra head resistance of the body,K,S, that of the wings ; K, the coefficient of resistance of a normal plane, and S,the equivalent detrimental surface. Suppose that the coefficient A can become infinitely small, or the area S infinitely great; the term K tends to become zero, for K1S1 increases less rapidly than S, and ^ tends to become =-••. Now ^r- is shown experimentallyKy Ky Ky to be a function of o according to a curve (Fig. 2), which is that of the total wing surface taken separately. The curve fe cc Fig. 2. of inclinations (1) relating to the aeroplane tends as a conse-quence towards the curve (2) relating to the wings ; and as the minimum of the first corresponds to the best angle of theaeroplane o 0, and the minimum of the second to the bestangle of the wings a u the best angle of the aeroplane tendsto become the best angle of the wings, a,, and c^ tending to coincide. Now Kx can, in practice, with a cambered wing section never become zero ; so -— cannot vanish, and as Ky=O when a = o- is infinitely great when a is nothing. This is 'Kywhat is borne out by experience. Curve (2) has, in fact, the form of a hyperbola, of which one of the asymptotes isthe axis of y. a t does not vanish. For a = oj, tan 7 has there-fore a finite positive value. What, now, does equation (B^ give us ? Putting s = L equation (B,) may be written tan 7 = ra + and «n2 ; x KSa When \ tends to become zero or S infinite, do tends to bezero, and tan 7 is represented by a point, of which the ordinate at the origin is t.a, is always theoretically nothing. For a = a, = o, tan 7 can thus take all values from / to infinity. Such a systematic expression of the value of ox is incom-patible with the usual data furnished by experience. The result is that the equations (A) and (Bj) are prac- 188
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