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Aviation History
1926
1926 - 0203.PDF
MARCH 25, 1926 29 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT paper to the Institute of Naval Architects, quoted on p. 351 of Bairstow's Applied Aerodynamics) the resulting flow is as in Fig. 4 (shown by the full lines AA). Experimentally, also see Fiji. 178 in Bairstow's " Applied Aerodynamics!!" demonstrated by Hele Shaw's flow pattern machine. For a demonstration of this method and references to Stokes' Fig. A. correlation of '" super-viscous " and non-viscous flow, see Chapter VII. ibid. The type of flow A A would lead to impossibly high velocities at the leading and trailing edges, and can only be made conformable by moving the stagnation points, as indicated Figs. 5 and G, which have been taken from A. R. Low's paper on " The Circulation Theory of Lift." read at the Inter- national Air Congress, London, 1923. If the stream is taken to be flowing from left to right the cyclic flow in Fig. 6 is clockwise. Accordingly, the velocity in the stream-lines will be increased on the top of the cylinder, decreased on the bottom. From Bernouilli's equation the pressure normal to the streamlines will be diminished on the top and increased on the bottom, causing a force in the direction of the arrow (lift). It should be, perhaps, made clear that the terms p and ^ pV2 in Bernouilli's equation are the static and dynamic pressures respectively. The static pressure is normal to the streamlines, and the dynamic is the " face " pressure in the streamline. Where the flow past a point is zero, as at the front stagnation-point, the dynamic pressure •' pV2 acts normal to the surface at this point. One may compare the action of the dynamic and static heads of an air-speed indicator. Everyone will have recognised that we have here the Flettner rotor. The cyclic flow can only be communicated to the fluid by virtue of viscosity, and there will, of course, be a boundary layer with rollers. It can be shown that the compounding of cyclic flow round an infinitely small filament and translational motion gives rise to a force (lift) at right angles to the direction of motion proportional to the strength of the cyclic flow and the velocity. As this force is at right angles to the direction of motion, there is no energy commu- nicated to the stream and there is no resisUtvce. The resistance Fig. 5. Fig. 6. by the dotted lines. This can be achieved by adding cyclic flow in the direction shown by the arrow. By cyclic flow is meant motion round a filament, the velocity being inversely proportional to the distance from the core (the analogy with comes from the imperfectly conformable flow and the eddy making, including the boundary layer rollers. The stream- line flow round a cylinder can be determined from a sink- and-source system, and, assuming that the boundary layer c *L =-S v - -A—v/\ i i i i i i i i ii i i i i i i i i i IWVIWI i i i i i i i i i i 1 i • _—-—— • --= >_—• _. —r— ——'-—-' i ~ r— . — —•' - -• i • — — \ \ \ \ \ \ s. it —— —— ——.——.—^- —- — — 1 1 •=; 1 ^=;—~_ —— I •-—J •—-. "—• i i | I I I I j [ I I i I I I | 1 I ! I . j 1 I f 1 I I 1 1 1 1 I \ 1 1 1 1 1 I I 1 f •i -2 -3 -4 -5 6 -7 -8 -9 CHORD MAX. CAMBER GI\/EN BY /= ~zrf i ii 1 p i i I- Z 0 Fig. 7. a sink or source by the interchange of flux and potential may be noted). The influence of cyclic flow on the flow pattern round a cylinder in a uniformly moving stream can be seen from is negligibly thin, the whole flow and pressure system can be calculated for any cyclic flow (or circulation, as we may now call it) and any velocity, provided that the flow is approximately conformable.
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