629. Mass Property Equations for a Minimum Weight Control Surface Ballast Design

Paper

Abstract

Aerodynamic characteristics and control system performance requirements establish the four desired control surface properties of mass, static moment, product of inertia (P0I) about the control surface hinge line and missile centerline, and moment of inertia (MOI) about the hinge line.
Normally all four criteria cannot be satisfied. The most important criteria are moment of inertia and product of inertia. These are considered in this paper. MOI and POI requirements are satisfied by incorporating a minimum weight ballast design.
Before a ballast design is considered, however, it is important that the mass properties of the remaining control surface are accurately known. General equations are presented which yield exact mass properties.
Ballast is moat efficient in the vicinity of the control surface apex. In this region a triangular wedge-shape ballast is used. General equations are presented which yield all the mass properties and geometry of such ballast with respect to the defined coordinate system. The apex of the ballast is at a fixed control surface location.
A minimum weight ballast design can be selected from moment of inertia and product of inertia data as a function of variable wedge shape of constant volume.
Such a selection yields a control surface with minimum ballast weight and a missile with increased performance due to reduced missile weight. Since the mass properties of a control surface can be accurately determined using the equations presented, a decision can readily be made concerning the need for equipment to measure moment of inertia and product of inertia.
The equations presented are applicable to a variety of problems encountered in weight control analysis and design.