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Aviation History
1940
1940 - 0923.PDF
MARCH 28, T940 2S7 and parasitics will not he materially greater (or Hit combination than for the individual components in sum, and so the ioial drag of the hypothetical combination will be less. Here it is only necessary to point out, (a) that the aspect ratio of the combination is greater than for the individual component machinesf, and (b) that (as will subsequently be made clear) the speed of flight, for least resistance, will be lower for the combination, and so for a given value of V the conditions are not fully comparable. The Best Compromise The writer regards the " V " formation as the nearest approach and the best we can do towards a realisation of the tip-to-tip formation represented in Fig. 2a, the latter being obviously and candidly hypothetical. Thus in Fig. 2b the five machines shown flying in echelon, a " V " formation, tread the same band of air as would be trod by the same number of machines tip-to-tip as in Fig. 2a. It is clear that a part, not the whole, of the reduction in drag may be realised by this means. Tn an appendix to a paper in November, 1936,* the writer presented his theory of sustentation in an un- familiar form. This is illustrated in Fig. 3, in which a board B represents the track of the aerofoil of a machine represented in silhouette at A, the board B being sup- posed to extend indefinitely in both directions. If we consider the board as rigid, and as being subject to an impulsive force at right angles to its surface, it will give rise to a system of flow whose streamlines are given in Fig. 4, which represents a section at right angles to the direction of flight. Tfie writer has shown that this system of flow is dynamically equivalent to a mass of air to which a uniform downward velocity is given, the mass in question being denned as that contained in an imaginary cylinder of circular section, whose axis coin- t Impracticably so ; otherwise the advantage might be a reality. * See the Journal of the Roval Aeronautical Society, Feb. 1037, p. 11 ^ cides with the line of flight and whose diameter is equal to the span, i.e. in Fig. 3 the width of the board. This is as suggested 'by the dotted lines in the figure. The work done in seating up this system of flow is that which gives rise to the induced drag, and the equivalent as given provides the data by which it may be calculated. In the hypothetical mechanism by which the impulse is applied it is supposed that the implement (the board) is immediately dissolved ; this is a convention familiar to all who have studied classic hydrodynamic theory from any of the standard works, such as Basset or Lamb. In accordance with the writer's theory, the aeroplane in its passage is deemed to " spread " the impulse, the resultant system of flow being identical with that pro- duced by the hypothetical instantaneous action of the force applied to the board.* The quantitative interpretation of this may be ex- pressed in the following manner. Consider a " length " of the imaginary board = L corresponding to a certain time of flight, say one second. Then the impulse on this length will correspond to the weight W acting for one second. But an " impulse " in strict theory has no sensible duration in time; its jneasure is momentum. In practice we may consider it as a finite force applied ior a brief period, provided that the momentum is correct. As before, let V= velocity ot flight, and W be the load sustained, acting on a mass m for a time / to * Compare Proc. Inst. A.E. 1915, p. 200. " Flight " phvtograph. An early Whitley photographed from an Avro Commodore. There was a distinct lifting of the wing tip when it approached close to that of the Whitley.
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