Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/102

§ 49 § 49. Unaccounted Factors (continued).—It is shown in the subsequent chapter that, under the conditions of natural gliding or uniform propulsion, the effect of resistance is to exercise a damping influence on the phugoid oscillations, tending to a continued increase in the value of C, and, unless adverse influences are at work, the flight path continually approximates more and more closely to the straight line or path of uniform gliding. This result is one that might well be anticipated from the action of the supposititions dynamic model of § 47. If we imagine a constant force applied to the aerodone parallel to the minor axis of its orbit in one direction, the supposed direction of flight, and a variable force in the opposite direction whose value is greater when opposed to the orbit motion, and less when in its favour; then it is evident that the mass in oscillation will do work in respect of the variable applied force, and therefore its amplitude will diminish.

The effect of taking into account the moment of inertia of the aerodone about a transverse axis is also dealt with in the chapter that follows, which constitutes an extension of the phugoid theory, carrying it to a point at which it becomes of the greatest practical utility. The influence of moment of inertia is the reverse to that of resistance, for it tends to an increase in the amplitude of the flight path oscillation. The result of this further investigation is quantitative and culminates in an equation which correlates every factor and constant essentially involved in the flight of a real material aerodone for phugoids of small amplitude.