1815. Predicting Radial Center of Gravity Statistical Distributions for Ballistic Reentry Vehicles

Paper

Abstract

The requirements for increased performance from each new generation of spin-stabilized projectiles has forced the need for more accurate mass properties predictions than ever before. Today the mass properties engineer must not only predict the nominal properties, he must also predict the variations about the nominals caused by manufacturing tolerances and measurement uncertainties. To accomplish this requires both a statistical data base from previous programs and the mathematics to combine and/or modify the data to account for the differences in material, mechanical designs and geometric tolerancing. The mathematics to combine component and subsystem uncertainties into total system uncertainties exists and has been well documented in SAWE technical papers as well as in the general literature. However, mass properties and their uncertainties are usually calculated in Cartesian coordinates while ballistic projectile uncertainties are often needed in polar coordinates. To convert to polar, the pitch and yaw axes center of gravity statistical distributions must be combined to create a radial center of gravity statistical distribution. This paper presents a brief discussion of the flight events of a ballistic projectile entering the earth’s atmosphere and of the significance of the various mass properties during these events. The importance of the statistical distribution for radial center of gravity is discussed in detail, and a mathematical method for deriving this distribution from the pitch and yaw axes distributions is presented. A Monte Carlo method is used to demonstrate the validity of this approach. The mathematical derivation for a special case of this radial center of gravity distribution is shown and the application of this special case to influence vehicle design is also discussed.