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Aviation History
1926
1926 - 0858.PDF
96 SUPPLEMENT TO FLIGHT NOVEMBER 25, 1926THE AIRCRAFT ENGINEER Statistics relating to aeroplanes already constructed should not be neglected as a suitable source of assistance in aero- technical investigation. Usually, in aircraft descriptions, the values of wing loading, power loading, and, more recently, of the ratio of engine power to wing area,* are stated. In addition to these values, which are not directly comparable, the following come into consideration :— (a) The " high-speed figure " (Schnellflugaahl), which is a comparative figure for the speed with reference to the " wing-power." (b) The "distance-figure" (Weitflugzahl), which is the speed converted according to the power loading (not an optimum value, but a quantity corresponding to the angle of incidence at the measured speed). (c) The "altitude-figure" (Hochflugzahl), which is the ceiling referred to unit "loading-figure" (Bauzahl), this, in turn, being the power loading multiplied by the square root of the wing loading. These three figures correspond to the propeller efficiency divided by : (a) The drag coefficient; (ft) The gliding angle or D/L, and (c) The " flight-figure " ( Flugzahl). Aircraft statistics do not yet occupy, within the scope of theoretical aeronautical investigation, the place which they deserve. The numerous data in the descriptive articles in the technical press still require to be sifted and utilised in accordance with certain viewpoints. In order to facilitate this for various purposes, it is intended that in the future the aircraft descriptions appearing in the " aviation review " of the Z.F.M., and the technical section of the (German) " Aviation Notices" (which correspond somewhat to our " Air Ministry Notices."—ED.) shall be supplemented in this direction. In these are given from the technical press, as well as from special rep arts from at home and abroad, data relating to dimensions, weights, performances and qualities which permit of either a direct comparison of individual machines, or of checking the data given for mis- prints or for intentional " colouring." This shortcoming is only partly remedied by always giving, provided the available data permit of doing so :— (1) The wing loading G/F. in kg./sq. m. (2) The power loading G/N, in kg./h.p. (3) The "wing-power" N/F, in h.p./sq. m. (3) is obtained by dividing (1) by (2) and is scarcely ever stated in technical literature on the subject, although it is of great importance for the purpose of speed estimates, as the following considerations will show. These three quantities in themselves mean very little, not least because they can be given for an aeroplane which has never flown. They should rather be compared with the results of reliable flying tests, and particularly with the measured speed and ceiling. "When that is done, it is possible to derive comparable values which afford a measure of the efficiency in one respect or another. In the case where no flying test results are available, but only estimated performance figures, these same quantities provide a means of ascertaining whether or not the predictions were too optimistic. Finally, the upper theoretical limits, or optimum values, of these comparative quantities can be quantitatively given, as well as the values already attained in practice, and thus the progress of development. To begin with, the following three quantities come into consideration :— (a) the " high-speed figure " — (b) the " distance-figure " — (c) the " altitude-figure " — in which the following notation is used :— TJ for the propeller efficiency, cw for the drag coefficient corresponding to * For this expression we suggest the English translation " Wing-power."—Ed. ca for the lift coefficient, e = — for the gliding angle, or D/L, K = = —— for the " flight-figure," all unknown. a Jca Concerning the notation we must go back to the well-known relations from the mechanics of flying :— Lift (kg.) A = ca 1V*F, in which— y = the weight of air, i.e., weight in kg./cu. m. — = the air density (kgs. 2/m.4) v = the velocity in metres per second, i.e., V = 36r in km/h. F = wing area in sq. m. For steady horizontal flight at any altitude, also at the ceiling, the following holds exactly, and for steady climbing flight approximately :— Weight = Lift, G = A. Furthermore, the propeller horse power 75iyN (kgm./sec.) is divided into two parts, of which one is required for sustentation in horizontal flight, while the other is a surplus required for acceleration and particularly for climbing :— 75?; N = Wv + GMJ ; in other words, the rate of climb w (m/s) equals the available surplus of power referred to unit weight:— N W _ _ N _ __ X G G G G Introduced here is the " unit speed " i\ (m/s) in abbreviated formf Vl = v \/cf, = G_, A G A F~V V, FV -7 F V 7 " Unit speed " is the speed corresponding to the angle of incidence at which ca — 1. For horizontal flight the " high-speed figure " is given by the thrust horse-power, together with the relation for the drag coefficient :— ,; I--' y F V:1 y F " High-speed figure »_ = _.-.- = i^.-._; At ground level the simple equation r, _ V:i F Yw = 56,000 ' X~ holds good. Thus the " high-speed figure " is obtained hy dividing the third power of the top speed by the " wing- power," and further multiplying by WT^KF. of the air density at which the speed was measured. In this way the speed is converted in a manner which is equal for all aeroplanes, and as a measure of the efficiency one obtains the relation between airscrew efficiency and the smallest, i.e., most favourable, drag coefficient. For very fast machines the optimum airscrew efficiency approaches very close to 1. The drag coefficient is composed of detrimental resistance, which may be reduced to round about 0017, the profile drag, for which one may assume an " ideal " value of 0 008, and the induced drag, which, for the low lifts that come into consideration here, may be neglected. Thus we arrive at an " ideal " value of the " high-speed figure " of 40. In machines hitherto constructed the practical value of this figure is considerably smaller, probably round about half. t The last form is due to the fact that at ground level — ~ | kg 6-,'mf 7646
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