Implementation of a Gumbel Distribution Function in Interior Ballistic Calculations for Deterred Propellants

Abstract

Based on the available bibliography three types of deterrent concentration profiles were identified. The cumulative distribution function of Gumbel distribution has the ability to reproduce all identified deterrent concentration variation profiles. The relationships between the ballistics characteristics and deterrent concentration can be expressed using the Gumbel function combined with a polynomial function. In order to deal with variability of mean values of burned propellant characteristics the interior ballistic specific equations should by modified accordingly. Based on available experimental data and the calculated variable ballistic characteristics the developed 0D model and the proposed functions are validated.