Sounding Rocket Boost-Phase Gust Angle of Attack

Abstract

This paper derives approximate angle-of-attack statistics suitable for boost-phase structural loading estimates on unguided, fin-stabilized sounding rockets. Sounding rockets are assumed to lift off with a large constant vertical acceleration.Theirrigid-bodyrotationsaremodeledasundampedshort-period motionswithoutanyvelocityvector rotation;the onlysource ofpitch/yawtorquesisviaaerodynamic staticstability. Theverticalacceleration causesthe dynamic pressure to increase rapidly, leading to time-varying coefficients in the short-period equations and, therefore, gust responses that require nonstationary analyses. Transforming the independent variable from time to altitude enables calculation of a simple lateral velocity sinusoidal gust impulse response function. Next, the total response for a single instantiation is found by superposition of all its gust impulses. Then, convolution to find the variance in transverse velocity is found based on the Dryden gust autocorrelations. A closed-form result for the standard deviation in boost-phase gust angle of attack is obtained and compared with both its high-altitude asymptote and the classical sharp-edged (step function) gust response. At altitudes above about two pitch wavelengths, the asymptote provides an accurate result, whereas the classical sharp-edged gust model significantly underestimates the gust response, except for regions very near the ground.