Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/296

frictionless fluid, then its trailing and leading edges will be at the same level, for owing to considerations of symmetry it is then that the reaction is vertical. Under these conditions we see (Fig. 116) that the gliding angle will be $={\frac {\beta -\alpha }{2}}.$
Fig. 116.

This result may be deinonstrated more generally for, $x$ resistances being absent,—

$\gamma ={\frac {y}{W}}$ $={\frac {\beta ^{2}-\alpha ^{2}}{2\ (\beta +\alpha )}}={\frac {\beta -\alpha }{2}}.$ Compare §§ 174, 176.

Now the ratio of the angles $\alpha$ and $\beta$ does not depend upon the leading and trailing angles given to the aerofoil, but upon the aspect ratio, so that the design of the aerofoil requires to conform to the ratio so imposed. If we take an aerofoil of arc section there is a particular direction in which it must be propelled in order that it should fulfil the necessary condition, and this direction is in practice determined by a directive organ which usually takes the form of a tail plane.

Let us examine the effect of an incorrect adjustment of the directive organ; that is to say, we will examine the effect of incorrectly designing the aerofoil in respect to the value of $\epsilon \ (=\alpha /\beta ).$ Firstly, suppose it be adjusted so that the “dip” of the

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