NACA-TN-3283

Abstract

The problem of determining the total forces, moments, and stability derivatives for a slender body performing slow maneuvers in a compressible fluid is treated within the assumptions of slender-body theory. General expressions for the total forces (except drag) and moments are developed in terms of the geometry and motions of the airplane, and formulas for the stability derivatives are derived in terms of the mapping functions of the cross sections. <br>All components of the motion are treated simultaneously and second derivatives as well as first are obtained, with respect to both the motion components and their time rates of change. Coupling of the longitudinal and lateral motions is thus automatically included. A number of general relationships among the various stability derivatives are found which are independent of the configuration, so that at most, only 35 of a total of 325 first and second derivatives need be calculated directly. Calculations of stability derivatives are carried out for two triangular wings with camber and thickness, one with a blunt trailing edge, and for two wing-body combinations, one having a plane wing and vertical fin. <br>The influence on the stability derivatives of the squared terms in the pressure relation is demonstrated, and the apparent mass concept as applied to slender-body theory is discussed at some length in the light of the present analysis. It is shown that the stability derivatives can be calculated by apparent mass although the general expressions for the total forces and moments involve additional terms.