Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/87

systems of phugoids based on different values of H_n are geometrically similar, and consequently a phugoid chart (such as Fig. 42), may be read to any scale appropriate to the value of H_n chosen. Then, for any particular curve and point on that curve as defining the position of the aerodone, we have for different values assigned to H_n the following relations:—

${\frac {H}{3H_{n}}}$ = constant; also $\cos \Theta$ = constant.

∴ $\cos \Theta -{\frac {H}{3H_{n}}}$ = constant.

But we know from equation (14),

${\frac {\mbox{C}}{\sqrt {H}}}=\cos \Theta -{\frac {H}{3H_{n}}}$,

hence ${\frac {\mbox{C}}{\sqrt {H}}}$ is constant for the point chosen, whatever the value of H_n that is to say, whatever the scale assigned to the curve, and ${\frac {\mbox{C}}{\sqrt {H_{n}}}}$ may be taken as an invariable constant relating to the particular curve and is independent of the scale to which the curve is read. We will represent this constant by the symbol K.

This constant K will be termed the amplitude constant, and all curves for a given value of K are geometrically similar.

Also for the straight path (H = H_n) we have K = ⅔ and C = ⅔H_n, this is the condition of the maximum value of K.

The variations of K with H and cos Θ for any given value of H_n follow the same law, and curve, as variations in C. K is in fact the constant C deprived of its dimensionality.

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