Roll resonance probability for ballistic missiles with random configurational asymmetry
Abstract
To help assess the reliability of ballistic bodies in free flight, an integral equation was developed that expreses a vehicle's susceptibility to continuous roll resonance. It assumes that configurational irregularities evolve randomly, with a Gaussian or normal distribution. Although the equation has no obvious analytical solution, two governing parmeters emerge: a dimensionless form of the configuration's excess asymmetry torque over that needed to maintain resonance, and the ratio of the critical rolling moments due to inplane and outofplane asymmetries. Numerical solutions indicate that with a moment ratio of two, for example, an average of one out of approximately six flights will be expected to undergo persistent resonance if the maximum possible asymmetry torque exceeds the critical amount by 50 percent. As the configurational abnormalities grow larger, the resonance probability markedly increases, with the result that three out of four flights ultimately become involved in either resonance or the adverse effects of random supercritical asymmetries.
 Publication:

Journal of Guidance Control Dynamics
 Pub Date:
 June 1983
 DOI:
 10.2514/3.19822
 Bibcode:
 1983JGCD....6..222B
 Keywords:

 Ballistic Missiles;
 Free Flight;
 Missile Configurations;
 Rolling Moments;
 Aerodynamic Drag;
 Integral Equations;
 Parameterization;
 Torque;
 Trajectory Analysis;
 Astrodynamics