Boost Phase Trajectory Analysis Techniques

Analysis of the boost-phase performance of a rocketboosted missile generally requires the solution of a set of differential equations with variable coefficients. Analytical methods are difficult and time consuming if not impossi­ ble. This paper discusses four numerical approaches to the solution of the equations for a cruciform, uncontrolled missile booster. The first of these, called the "exact" method, will yield results which are as accurate as one cares to make them. The second, referred to as the ""semiexact," assumes that deviations from the flight path are small and oscillatory. With this assumption the solution may be completed in two parts: (a) Computation of the speed-time history and (b) substitution of the speed into the remaining equations. The accuracy for short time oblique launch or for long time vertical launch is as good as the "exact." The third, applicable under the same conditions as the "semi-exact" and referred to as "linear speed-time history," assumes a constant acceleration from launch to the end of boost. The accuracy of this method is very good (on the order of 2 per cent for the terminal speed) provided the thrust-time diagram is nearly trape­ zoidal. The fourth, called "iterative solution for separa­ tion speed," yields an approximate value for the terminal speed with accuracy on the order of 2-4 per cent. The various uses of the different methods are also discussed as well as techniques for including cross winds, estimating separation speeds and tolerances allowed in estimation of step-wise acceleration. Sample calculations for the three approximate methods are given.