if, secondly, it be supposed of finite extent, then, since the cyclic motion is decaying, its equilibrium must vanish. In the case of the finite aerofoil we must consequently have the load in part supported by a reaction due to discontinuity, and in part only to the cyclic motion; the part of the reaction sustained by the discontinuity of motion may be regarded as that required to augment the cyclic motion at the same constant rate as its rate of decay. Hence: an aerofoil of finite lateral extent cannot be so designed that it shall be everywhere conformable to the lines of flow, and any such aerofoil must give rise to discontinuity in the motion of the fluid, involving surfaces of discontinuity, and presumably dead water regions.
We thus see that a perfectly conformable motion, such as we
Fig. 119.
have tacitly supposed possible, is not possible when dealing with a real fluid, and at some point or points along its length the aerofoil must give rise to a discontinuity. This does not affect the validity of the foregoing theory, which has been founded on a hypothesis that admittedly does not fully represent the actual conditions; but it may be found that the matter now under discussion renders this hypothesis less valid than would otherwise be the case, especially where we are concerned with the quantitative estimation of the work done, i.e., the computation of the gliding angle.
§ 190. Discontinuous Motion in the Periptery.— We may take as a simple example of the phenomenon under discussion the case of an aeroplane where, as we have seen, we have a system of flow of the Rayleigh-Kirchhoff type (Fig. 98). Let Fig. 119 represent such a plane in front elevation, then surfaces of
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