Beam deflection correction model of wedge-shaped shock waves over hypersonic vehicles

Celestial attitude determination is one of the important technical means for high precision autonomous navigation of aircraft. Shock waves are generated along the surfaces of hypersonic vehicles, which cause beam deflection, affect the observation of star trackers and celestial navigation performances of these vehicles. Most modern hypersonic vehicles adopt the wave-rider design, and the payload bay can be simplified into a wedge plane structure. The shock waves over hypersonic vehicles with wedge-shaped upper surfaces were analyzed. Based on aero-optical theories an analytical calculation method of the structure parameters of the wedge shock wave and a quantitative calculation model of the impact of the shock wave on the deflection of light were given. A correction model was proposed to control the deflection of beam by using the analytical calculation results. The propagation of shock angle measurement error in this model was discussed, and it was proved that the shock angle measurement error was negatively linear correlated with the correction effect deviation caused by it. The simulation results show that under the condition of altitude 20 km and Mach number 5-8, a stable shock wave structure is formed above the wedge surface, and the deflection of incident beam can be up to 6.8 arcseconds. The error between the shock angle parameters obtained by the analytical calculation method and the test results is within 0.1 arcseconds. This means that the error of beam deflection correction by using this model can be controlled at the order of the shock angle measurement error, and the observation accuracy can be significantly improved.