A Practical Mathematical Approach to Grain Design

Equations were developed relating solid propellant grain geometry to the important ballistic parameters of crosssectional loading density, sliver or tail-off fraction, progressivity ratio, initial surface and web. The equations were then solved by means of high speed computers and the results graphed in a readily usable form. If the loading fraction, sliver, progressivity ratio and web are given, grain designs which meet or most nearly meet given requirements can be found from the graphs. The graphs are useful in determining the effect of slight variations in design parameters. Illustrations of the use of the graphs are given for the internal-burning star and the internal-burning wagon wheel configurations. Calculations have also been made on a modified form of the wagon wheel which permits one, two or three levels of thrust during burning.