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Aviation History
1927
1927 - 0563.PDF
JULY 28, 1927 47 THE AIRCRAFT ENGINEER SCFPLEMENT To FLIGHT kDl S, = 0-005 S, + 0-017S, + 0-16S, k-Ll, and kD2 S. = 0-005 S2 + 0-017 j-1 X S2 + O-16S2 khs must vary in a manner undeterminable without further assumptions, but if both khl and kj,2 are in the neighbourhood of 0-1, we get km S, = 0-0066 Sj + 0-017 Sx = 0-0236 St and kD2 s, = 0-0066S2 + 0-017 Si. Only 0-0066 out of 0-0236 or 28 per cent, of the original value of Ai, S has been reduced in proportion of the areas, the remaining 72 per cent, being unchanged. In the new formula proposed for this year's King's Cup Race, the familiar quantity — has disappeared and in its S place we find Horsepower(Equivalent Span)2 The symbols in which the formula was given in FLIGHT of June 2, 1927, are non-standard, so perhaps it may be given here with the new symbol Sp for " equivalent " span, while the standard * is used for semi-span. We then write V3 = K x up 106 X with K = 12 for water-cooled engines, while K for air-cooled engines varies according to a curve plotted HPagainst ——;. '" Equivalent " span for a monoplane is the normal span, for a biplane with equal span wings, Sp = 2s • 1-265 while for a sesquiplane Sp = 2s x -j- 2s2 .'•' 0-265, Sj being the greater span. Several queries immediately arise on inspection of these suggestions. Why use (span)- in place of wing area ? WTiat is the basis of the monoplane-biplane comparison ? Why penalise the water- cooled engine '/ Before investigating these points, we may take it for granted that any formula proposed by the committee appointed for this purpose does, in fact, '" fit " the machines on which then- investigations were based. The word " fit " is placed in inverted commas as it is clear that the formula is intended to under-estimate speeds, rather than to fit them accurately. Agreement with a selection of existing machines does not however, prove that a formula is fundamentally sound, as it may be possible by going outside the range of types considered to produce a machine whose speed would be hopelessly under- estimated, or alternatively that a good machine at the other end of the scale might be badly penalised. The first question to consider is the use of (span)2 instead of wing area. The reason for this choice appears to be that span is a characteristic of the machine which is very easily checked by the handicappers. Unless other advantages are obtained, this argument cannot carry much weight since the wing area of any machine must be known to the Airworthiness Department and could, if desired, be entered in the log book. This would apply not only to machines with airworthiness certificates, but also to special racing machines with certificates of exemption. For a monoplane with water-cooled engine the formula gives TTT> V3 = 12 X 10" X —4s2 4s-If A be the aspect ratio A = -—, and by substitution 12 Y 10" HP A X S By comparison with equation (1) 12 x 10« „ T = 73500 x 4-, 73500 _and hence k D = ^ x ^ „ .,- m The assumption implied in the formula is then that the overall drag coefficient varies directly as the aspect ratio. This is a very peculiar result, which would not on any theoretical basis be expected to give good agreement when applied to a fair range of different types. Investigation shows, however, that the assumptions made do actually fit a considerable number of present-day machines. It is evident that a machine of large aspect ratio specially designed to race under this formula could beat most ordinary types, but it is not probable that any such machine will take part in the next King's Cup Race. Even though the formula may give satisfactory results in this race, the curious assumptions which are hidden within it require careful consideration before it is adopted as a permanent standard, as there is grave danger of encouraging the building of freak machines to cheat the formula. Some direct evidence on the result of altering aspect ratio without any other change is available in R. and M. 859, " Lift and Drag of the Bristol Fighter with Wings of Three Aspect Ratios." The top speeds and weights of the machine in the three states are not recorded, but the speeds have been estimated from the drag curves given with assumptions as to the changes in wing weight. The alteration from the normal 7-72 aspect ratio to 9-73 gives a decrease of 5 m.p.h., against 8 m.p.h. from the formula, while the change from normal to 4-69 leaves the speed practically the same against an increase of 19 m.p.h. from the formula. The change from 4-69 to 9-73 is not likely to occur in normal design, but the figures show the extraordinary difference between actual and formula speeds for a really large change in aspect ratio. The next point for consideration is the relation between monoplane and biplane. The case of the equal span biplane only will be analysed as the sesquiplane is not amenable to simple mathematical treatment. We have already obtained the equation for the monoplane in terms of wing power and 12 X 100 HPaspect ratio, i.e., V '• = X — A a For the equal span biplane, still with water-cooled engine, we have ijp V'= 12 X 10° X — X (1-265)-'4s- 12 X 10" X 8s-From the definition of aspect ratio, we get A = —^-. S 12 X 10" HP 8s- 1 X • x ~r~ A 6'4s- & 12 X 106 HP (A X 0-8) X ~S~ In other words, where aspect ratio is used in the formula for a monoplane (aspect ratio X 0-8) should be used for an equal span biplane. This purely empirical relationship implies that a monoplane has a drag coefficient 25 per cent, higher than an equal span biplane of the same aspect ratio. If the two machines have the same extra-to-aerofoil drag, the fact that monoplanes generally have wings with a higher maximum lift coefficient, and, therefore, less area, would justify the greater value of kv. With regard to the last query raised, that of the different values of K for air-cooled engines, the evidence available to the writer is somewhat uncertain. Two examples may be quoted of machines which are substantially the same, except for a change from a water-cooled to an air-cooled engine. The formula underestimates the increase of speed between the Nimbus Martinsyde and the Jaguar Martinsyde, but over- estimates the simiiar increase between the D.H.50 with Puma, and the same machine with Jaguar. It will, however, be seen from the curves given in the figure that the difference between water-cooled and air-cooled does not become large in relation to the order of accuracy to be expected from the formula until high speeds are reached. The general argu- ments in favour of the two curves are that the decrease in weight, and therefore in wing area and wing drag, in using the air-cooled engine, are counter-balanced by the increase in engine and fuselage drag, and that this effect increases as the engine horse-power becomes greater. The real worth of the latest formula will be demonstrated in the King's Cup Race two days after these notes appear in print. The use of the curves given in the figure will enable those interested to estimate the speed of a machine with the 518c
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