A Simplified Analysis of Static Longitudinal Stability

The first section of this paper describes the development of a single family of curves which illustrates the variation of the pitching moment coefficient with the lift coefficient for all wings and for all e.g. locations. The second consists of an analysis of the characteristics of these curves and their derivatives in conjunction with the known properties of tailplanes; the elements of a simplified theory of static stability are stated in four general theorems. In the third section, a direct method for the determination of tailplane area is given. An example of the use of the simplified analysis is appended. O ALL the problems which confront the airplane designer, that of providing an airplane with specified characteristics of static longitudinal stability is one of those least amenable to direct solution. This situation has its root in the difficulty of clearly describing the apparently complex relation between the wing pitching moment coefficient and the several variables which control its value. To be sure, there are analytical and nomographic methods, notably those developed by Stalker and Higgins, which enable fairly accurate calculation of the slope of the wing moment curve when the location of the center of gravity is known. However, visualization of more than the outstanding qualitative characteristics of the underlying relationship is precluded by the fact that for each e.g. position there is an unique relation between the slope of the wing moment curve and the lift coefficient. Such complexity precludes an entirely clear conception of the specific problems of design and makes the use of "cut and try" methods almost universal. The present paper describes a method of correlating the pitching moment characteristics of all practically useful wings, outlines the elements of the simplified theory of static longitudinal stability which naturally follows and illustrates the applicability of these principles to practical design problems. WING PITCHING MOMENTS The theorem of statics which states that any force may be replaced by a force and a couple justifies the replacement of the conventional wing vector sheaf, Fig. la, by its equivalent, Fig. lb, in which each force vector is accompanied by the couple Cm QmCm (Diagrams c 6 1 Edward A. Stalker, Principles of Flight, Chapter 14, The Ronald Press Company, New York, 1931. 2 George J. Higgins, A Study of the Pitching Moments and the Stability Characteristics of Monoplanes, N.A.C.A. Technical Note No. 511,1934. c 6 a