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

Rh systems of phugoids based on different values of Hn are geometrically similar, and consequently a phugoid chart (such as Fig. 42), may be read to any scale appropriate to the value of Hn 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 Hn the following relations:—

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

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

But we know from equation (14),

$\frac{\mbox{C}}{\sqrt{H}} = \cos \Theta - \frac{H}{3 H_n}$,|undefined

hence $$\frac{\mbox{C}}{\sqrt{H}}$$ is constant for the point chosen, whatever the value of Hn 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 = Hn) we have K = ⅔ and C = ⅔Hn, this is the condition of the maximum value of K.

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