The disturbance imparted to water by a planing body give rise to a wave form of motion on the free surface, the length of the waves increasing indefinitely with increase in the Froude number and being directly proportional to the latter in the case of the plane or two-dimensional problem. At large Froude numbers the effect of the weight shows up to any appreciable extent only at some distance from the body, so that the flow near the body can be considered as part of a flow of an infinitely extending weightless fluid. This paper is a consideration of these characteristics as well as a formulation of the planing problem and its relation to the problem of a thin wing.

In the solution of a number of problems on the stability and controllability of airplanes, there arises the necessity for knowing the characteristics of the tail surfaces of the types in common use today. Of those characteristics, the most important are the effectiveness and hinge moments of the tail surfaces. As has been shown in the present paper, there exists the possibility of determining these characteristics by the formulas obtained with a degree of accuracy sufficient for the purposes of preliminary computation.