An analytical approach to the problem of longitudinal stability of flying boats in the planing conditions

The subject of the longitudinal stability, or "porpoising", of flying boats has been the subject of investigation both in this country and abroad. In many cases, recourse to dynamically similar models has been had to determine the stability characteristics of the design in question. In general, however, the bare hull is tested in towing tanks, and the data are presented in the form of curves of resistance, moment, draft, speed, and angle of trim. Conclusions regarding "porpoising" of the full scale airplane cannot be drawn from these tests alone, but it is considered possible to evaluate certain of the hydrodynamic derivatives which in conjunction with aerodynamic derivatives obtained from wind tunnel tests, can be used in the stability equation to determine the behavior of the flying boat in the planing region. In the analysis of the problem presented here, most of the derivations of the formulae have been omitted. For a more detailed derivation, reference is made to the thesis of Lieutenant George A. Hatton, U. S. N., entitled "The Longitudinal Stability of a Flying Boat in the Planing Condition as Computed from Tank Test Data of a Hull Model." Throughout the analysis, the effect of a drag has been neglected. A discussion of this omission will be made in the conclusion of the paper. The first part of the paper will be concerned with a presentation of the formulae and an example of their use with results of calculations made. The second part will cover the dynamic model tests and a discussion of the equipment used. The conclusion will cover the entire paper. It must be noted that the analysis here is restricted to only the planing condition or that part of the take-off run past the hump, and the formulae are derived for that condition