Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/104

§ 50 disturbance taking place, the resulting phugoid tends to a continual increase of amplitude.

The conclusions of the present chapter have been to some extent anticipated by the statements made in §§ 48 and 49; in short, it will be shown, firstly, that the effect of resistance is to damp out oscillations, whereas that of moment of inertia is the converse; and, secondly, it will be shown that for small amplitude these two influences may be pitted one against the other so as to leave the amplitude of the phugoid path unaffected. This condition marks the limit of stability of the gliding flight path.

§ 51. Influence of Resistance on Amplitude.—It is, as before, assumed that the total resistance varies as the square of the velocity of flight, and that the propelling force is constant.

Let R be total resistance.

V, Vn, H and Hn stand as before.

Q = uniform applied thrust.

Then—

or

or

Referring to Fig. 45, we have the path of mean gliding p p, and the phugoid path p1 p1, separated by a varying distance h to which we have shown q proportional. Now, when q is positive as when the aerodone is "cresting" (in the vicinity of the crest of its wave-like path), it is receiving energy, and its H value is consequently increasing; this is equivalent to the aerodone being