Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/59



§ 18. Introductory.—The Phugoid theory deals with the longitudinal stability, and the form and equations of the flight path of an aerodone.

It has been proved by the experiments of the author and others that a simple aerodone can be constructed possessing, within certain practical limits, complete longitudinal stability, and the general considerations on which this stability depends have been stated.

We have seen firstly that there exists a stable state of equilibrium between the attitude of the aerodone and the direction of flight path in the vertical plane; and, further, that there is a complex system of equilibrium of a stable kind maintained between the said direction of the flight path and the velocity of flight, due to an interchange of kinetic and potential energy that automatically takes place if the conditions of uniform gliding are disturbed.

In the investigations that follow the character and form of the flight path of an aerodone in free flight are deduced from purely dynamical considerations, the argument being in the main mathematical, aided by graphic methods, and reasoning of other kinds. Constituting the foundation is a mathematical analysis based on hypothetical conditions, the problem being presented first in its simplest form; the superstructure comprises an extension of the initial theory to deal with the problem in its more complete form, and the interpretation and application of the results achieved.