Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/103



§ 50. Introductory.—In the present chapter we shall discuss the influence of departures from the original hypothesis in respect of resistance and moment of inertia, both of which were initially assumed to be absent.

It has not been found possible to achieve any results by including these quantities in the original investigation of Chapter II.; the form of expression is far too unwieldy, and the integration and plotting become impossible.

It is consequently necessary to deal with the matter as a kind of correction, and to confine ourselves more especially to the investigation from a less general point of view, especially directing our attention to the practical aspect of the problem, as concerned in flight under normal conditions.

In the particular case of the uniform straight line phugoid, supposing a constant propelling force, or that which amounts to the same thing, an appropriately inclined path, it is evident that the conditions are those of equilibrium, for the resistance is at every instant balanced by a propulsive force, and since there is no rotary movement of the aerodone about a transverse axis, the existence or otherwise of moment of inertia can make no difference. Although the condition is one of equilibrium, it does not follow that the path of flight is stable, it is possible that it may be a condition of unstable equilibrium so that on the least