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Aviation History
1911
1911 - 0039.PDF
JANUARY 14, 1911 (/0 GHT ASPECT.RATIOS. By L. BLIN DESBLEDS, IT is with the object of trying to elucidate certain points in connection with the question of " aspect-ratio," which I have found to be commonly the source of confusion with students, that this note is written. If a plane rectangular surface, A, moves in the direction of the arrow, the ratio of the length, Z, to the length, / (Fig. 1), is "'> "3- called the called the aspect-ratio = — ' aspect-ratio" of the surface. The length, Z, is : span," and the length, /, the " chord," so that _ span chord. It is found that the aspect-ratio of a surface has a great influence on the resistance that the surface experiences when it moves through air. It is in order to take advantage of this influence that " sus taining surfaces " of aeroplanes are arranged to move broadside on. Fy.3. It was in order to determine in what way, and to what extent, this influence affected the resistance of a plane surface moving through the air that Soreau made his extensive experiments. From these he was able to obtain an expression showing how the air- resistance of a surface depends on its aspect-ratio. In each case the air-resistance of a surface varies with a certain quantity, which he has called the " coefficient of influence of aspect- ratio." The " coefficient of influence of aspect-ratio " is denoted by the Greek letter A. Its value may, in each, case, be calculated by means of the expression 1 - m tan a where m — surface. (1 + mf aspect-ratio - I aspect-ratio + 1 tan a 4 2 tan- a and « = inclination of the plane :\ A,«\ \ Ar«a V* k \.' F 1 \ ... is Fiq.A-. Lecturer in Aerodynamics, The Polytechnic. The expression for the air-resistance of a plane surface is then R = «A Av'1 sin a, where R — resistance, K — coefficient of air- resistance, A = coefficient of aspect-ratio, v = speed, and a = inclina tion of surface. It must not be imagined that the coefficient of influence of aspect- ratio varies directly with the aspect-ratio. Thus if we have a surface, A, of aspect-ratio 1 "5, and a surface, B, of aspect-ratio 3, the value of A for B is NOT twice the value of A for A. But if we work out the values of A for aspect-ratios of I 5 and 3 respectively, if the inclinaticn of the plane is say 2C, we shall have for A, A = 2'4, and for B, A = 3*09. Hence, if the surface A B C D (Fig. 2) moves in the direction of the arrow, at an angle o, the air-resistance is measured by R = K \ Av- sin a, = 3^09 K AV'2 sin a. Now, if we bisect the surfaces A B C D by the straight line £ F, we shall have two surfaces A B E F and F £ C D each of aspect-ratio I-5 and of area AJ2. So long as the two surfaces A B £ F and FECI") are placed side by side, as in Fig. 2, such that when the surfaces are in motion no air can escape along E F, then we may consider the two surfaces to be equivalent to the whole surface. If, however, the two surfaces, A B E F, and F E C D, are rigidly connected at a sufficient distance apart (Fig. 3), then the air- resistance to the motion of A B C D is equal to the resistance to the motion of A B E F phis the resistance to the motion of F £ C D. But the resistance to the motion of A B £ F is equal to the resistance to the motion of F E C IK Therefore, the resistance to the motion of A B C I) is equal to twice the resistance to the motion of A B E F. That is resistance to motion of A B C D = 2(KA - v- sin a). 2 A = 2(2'4 K - 7J- Sin o). 2 = 2*4 K A z>'2 sin o. Now, if instead of placing the surfaces, ABE F, and F E C D, in the same plane as in Fig. 3, we place them one above the other, as in Fig. 4, at a sufficient distance apart and rigidly connected, then the air-resistance to the biplane thus formed is also twice the resistance to the motion of the plane ABE F, A , • i.e., = 2 x 2-4 x K v- sin a., = 2*4 K Av-sm a. We thus see that a monoplane of aspect-ratio 3, of area A, and moving at a speed v at an inclination a = 2°, encounters an air-resistance = 3 '09 K AV2 sin a ; whereas a biplane of half the span of the monoplane, and of the same chord, moving under the same conditions of speed and inclination, has an air-resistance = 2'4 K Air sin a, res. of monoplane of area A and aspect-ratio 3 res. of biplane of area A and aspect-ratio I '5 3 09 K Av1 sin o 3'09 1 28 ~ 2'4 K Av1 sin a — 2'4 — I Hence, the monoplane which is equivalent to a biplane is NOT the monoplane obtained by placing the two surfaces of the biplane side by side. Also the air-resistance to the motion of a monoplane of area A and aspect-ratio l-5 is K A Av2 sin a = 2"4 K Av2 sin a = air- resistance to the motion of two planes, each of area A/2, and of aspect-ratio 1 "5. Therefore the aspect-ratio of a biplane, just as the span aspect-ratio of a monoplane, is = -r—%. We thus see that a biplane will have the same lijl and drift as a monoplane of the same area and of the same aspect-ratio. .e., Bosch Magneto Successes. As a proof of the popularity ot the Bosch system of magneto it is interesting to note that 634,330 of them have now been sold. Bosch magnetos were fitted to the Howard Wright biplane on which Mr. Sopwith won the Baron de Forest Prize, and also on the Cody biplane on which Mr. Cody won the Michelin Cup. Other machines so fitted were M. Legagneux's Bleriot, on which he beat the altitude record, and Mr. Henry Farman's biplane on which he improved the duration record. Speed Alarm Competition. SEVERAL readers still continue to submit designs for the above competition, which closed last October. We take this opportunity of drawing their attention to the fact, as the contributions in question cannot be acknowledged. 3''
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