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Aviation History
1927
1927 - 0391.PDF
JUNE 2, 1927 NEW FORMULA FOR SPEED CALCULATIONS A BRIEF reference was made in THE AIRCRAFT ENGINEER last week to the new formula which is to be used for calculating the speed of machines for purposes of handicapping in the King's Cup Race, which is to be flown at Bournemouth on July 30 next. Unfortunately, a printer's error crept into the notes concerning the formula last week, a plus sign having dropped out without the fact being noticed in time for the necessary correction to be made. This occurred in the state- ment concerning biplanes of unequal span, S, and S.., the reference to which should have read " For a biplane in which the upper and lower wing spans are unequal, S is taken as = Sj + 0-265S2, where Sj is the greater and S, the lesser span." The complete Handicap Speed Formula is as follows :— 'Vs = K x 10" X P/S2, in which V is the handicap speed in miles per hour, K a coefficient the value of which is taken as 12 for all machines with water-cooled engines, P the brake horse-power of the speed from falling off in proportion to the handicap speed given according to the formula, it will be necessary to reduce chord correspondingly, and structural considerations will very quickly put a limit to the extent to which chord reduction can be carried. In a general way, therefore, the formula may be expected to give reasonably close speed estimates. In order to obtain an idea of what sorts of handicap speeds will obtain, it may be of interest to examine a few typcal cases. First of all, let us assume that an equal span biplane of 40 ft. span is fitted with an engine developing 400 h.p. at " maximum permissible revs." The '' equivalent span " will be 1-265 X 40 = 50-6, and PS2 will be 0-156. If the machine is fitted with a water-cooled engine, the value of K will be 12, and the handicap speed will be V3 = 12 x 10" x 0-156, from which V = 123-3 m.p.h. A similar machine, but fitted with an air-cooled engine, will have a value of K (from curve) of 11 -58. and V3 = 11-58 X 12-0 11-5 11-0 K 10-5 ?6-o 9-0 ( ! 1 t t 1 1 k ) 01 0-2 0-3 0-4 0-5 £ 0-6 . 07 08 09 1-0 type " engine at. " maximum permissible " revolutions, and S the " equivalent span " in feet. For a monoplane, the " equivalent span " is simply S. In the case of a biplane with upper and lower wings of equal span, the " equivalent span " is 1 -265 >: wing span. For machines fitted with air-cooled engines, the value of K is taken from the accompanying curve. It will be seen that at small values of P/S2, or in other words, for machines having a low power in proportion to the wing span, the value of K is not very much lower than the value of 12 taken for all machines fitted with water-cooled engines. When, how- ever, the ratio of power to wing span is high, as in the case of machines with very small wing span and engines of high power, the value of K falls off considerably, the lowest value covered by the curve corresponding to the fastest machines taken into consideration, being about 9-87 at P/Ss = 0-9. In the formula used last year for handicap purposes, account was taken of wing loading and power loading, or in other words, of "wing-power," as defined by Professor Everling in his article in THE AIRCRAFT ENGINEER of November 25, 1926. This year's formula does not take either wing loading or iower loading into consideration, but merely wing span in relation to power, or what we may for want of a better term call " span power." Since the object of designers will be to get the lowest speed >ossible (under the handicap rule, of course, and not in reality !), t will pay them to fit wings with large span ; but to keep down he wing area, or in other words, to prevent the actual top 106 x 0-156, giving V= 121 S m.p.h. Thus, at this value of P/S2, the air-cooled is not given the benefit of much lower speed. If, however, we take two machines at the " high-speed end," i.e., with very small wing span and high power, the formula comes into operation to a much greater extent. Let us assume that, as before, the power is 400 b.h.p. at " maximum per- missible revolutions," but that the span is only 20 ft. In that case the " equivalent span " of an equal-span biplane is 1-265 x 20 = 25-3 ft., and P S2 = 0-625, which gives for a water-cooled engine, V3 = 12 x 106 x 0-625 = 8,500,000, and V = 204 m.p.h. A similar machine, with air-cooled engine, will have a K (from curve) of 10-44, giving V3 = 10-44 X 106 X 0-625, or V = 186-8 m.p.h. In this case the formula has operated in favour of the machine with the air-cooled engine, which will be handicapped at a speed of about 17 m.p.h. lower than a similar machine with water-cooled engine of same power. The light 'plane class may be assumed represented by a power of 70 h.p. and a wing span of 30 ft. An equal-span biplane would have an " equivalent span " of 35 ft., and a P/S2 of 0-057, while its handicap V would be 88-2 m.p.h. for a water-cooled engine, and S7-75 m.p.h. for an air cooled. This small difference in speed is of academic interest only, since there is not likely to be in the King's Cup Race a light 'plane with a water-cooled engine of this low power. Monoplanes with the same power, and with, a wing span of 36 ft., would be handicapped at about 86 m.p.h. 353
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