Analytic Solutions for Volume, Mass, Center of Gravity, and Inertia of Wing Segments and Rotors of Constant Density

Abstract

In the preliminary design of aircraft lifting surfaces, accurate mass and inertia properties can be difficult to obtain. Typically, such methods as computer-aided design or statistical processes are used to determine these properties. These methods require significant time and effort to implement. The present paper presents an exact analytic method for calculating the volume, mass, center of gravity, and inertia properties of wing segments and rotors of constant density. The influence of taper, spanwise thickness distribution, airfoil geometry, and sweep are included. The utility of the method is presented, and the accuracy is evaluated with various test cases via percent difference with a corresponding computer-aided design model. These case studies demonstrate the present method to be accurate to within about 1% for typical wing geometries and within about 1.3% for typical propeller geometries.