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Aviation History
1927
1927 - 0562.PDF
SUPPLEMENT TO FLIGHT 46 THE AIRCRAFT ENGINEER JULY 28, 1927 one on April 15, 1926, which was intended for use in the King's Cup race of that year, and the other on June 2, 1927, for the next King's Cup race to be flown on July 30. The first formula gave very satisfactory results, but has apparently not been used since the 1926 King's Cup race, while the second will be on trial for the first time on July 30. The object of these notes is to consider the assumptions which have to be made in deducing handicapping formula1 and to compare the two types of formula1 mentioned above. The starting point for this investigation must be the standard equation for level flight. JTP V3 = 73500 x j- X — (1) kd fc> Where V = speed in m.p.h. at ground level. TJ = propeller efficiency kd = overall drag coefficient. S = wing area in sq. ft. This shows that for a given value of the " wing power," tTT> „ ——, the speed depends upon the quantity — (this quantity w ill be recognised as twice the Everling " high speed figure "' -f =0-0314 -0-228 h2. If we make the arbitrary assumption that rj = 0-7 we get the further simplification : kd = 0-022 + 0-16 k K If profile drag = -005, kR, coefficient for extra-to-aerofoil drag = -017. From Mr. North's article on " Aircraft Performance," in the AIRCRAFT ENGINEER of April 29, 1926, we find that induced drag for a monoplane has the value 2 kin = — X A"i,2 where A =- aspect ratio. If the whole of the kj? term represents profile drag, 2— = 0-lti or A = 4. irA The aspect ratio for an equivalent biplane would be greater, but the correction due to gap/span is assumed to leave the induced drag the same. It is clear that the formula will under- estimate the speed of a monoplane with aspect ratio greater than 4. and of a biplane with aspect ratio and gap/span giving so. WATER- COOLED CNQINCS rt . 1" 265 x SPAN FOR E<WN-SPMN + -265XSMALL FOR SeSQUPLATCS . K ~ I £ FOR WATER- COOLED BNONM8, AND t-2 TOITIWCOaC! CM O'E as 1O-3 j described by Prof. Everling in the AIRCRAFT ENGINEER of November 25, 1926, and reproduced in English units by the present writer in the AIRCRAFT ENGINEER of February 24, 1927). The most obvious basis for handicapping appears therefore, to rest on the wing power and — and this basis was used in the first of the two formulae mentioned. In FilGHT of April 15, 1926, will be found the formula, —, with a curve of F plotted against V A / !L.X V <» o> IT HPSince — = -TT7 = — , this can be re-written X W S HP HP V3 = F*. -. (2). By comparison with the fundamental equation (1) we get n / p F3 = 73500 —. F is assumed to vary with V A/ -, which i 14 its turn is equal to in Analysis of the curve given for F leads to the following basic equation : a better induced drag than this monoplane. It is possible to gauge the importance of this term if we assume the highest value of ifcj, at which a light!v-loaded machine is likely to fly in a race. For example, the Bristol Brownie with a top speed of 70 m.p.h. and wine loading of 4-26 lbs. per sq. ft. flies at A,-L = 0-17. If we assume the extreme value of ki. = 0-20, km f°r aspect ratio 4 = -16 X (0-2)2 = 0-0064. and overall kd on this formula == 0-0284. If aspect ratio be increased to 8, k,,i = 0-0032, an improvement in overall kd of about 13 per cent, and an increase in speed of 4 per cent. This increase, would, undoubtedly, be somewhat reduced by increase of drag of bracing, and possibly by increase in profile drag due to a thicker section being required to accommodate suitable spars in a narrower chord. In most normal cases the value of fcL for top speed would be smaller and the possible improve- ment due to increase of aspect ratio very much less. It is evident from inspection of the formula that increases in speed can also be obtained either by reduction of kn through careful streamlining, or by reduction of wing area for the siune horse-power. The latter can be achieved either by usiiu: a high lift wing section or by increasing the landing speed. I*1S important to note, however, that for the same body, a simple- decrease in area does not lead to a directly proportions increase in V3. If Sj be the original area and S2 the new h i i b d »j g 2 extra-to-aerofoil drag is not altered by change in wing bracing? 5186
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