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

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.

Let„ V, V_n, H and H_n stand as before.

Let„ Q = uniform applied thrust.

Let„ h = H_n — H = height of aerodone above path of mean gliding.

Let„ q = Q - R = difference of thrust and resistance representing net force of propulsion acting on aerodone.

Then—

$R/V^{2}=Q/V_{n}^{2}$

or

$R/H=Q/H_{n}$

 

$\therefore Q-R\propto H_{n}-H$

or

$q\propto h.$

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

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