Experimental and analytical techniques for extracting the aerodynamic damping-in-pitch parameter for orbital re-entry vehicles: An investigation of stability for space capsules

Aerodynamic damping is investigated in the subsonic, transonic and supersonic flight regimes for the Apollo and Expert orbital re-entry vehicles. Static moment and forced oscillation experiments are carried out on replica models in the von Karman Institute (VKI) S-1 Transonic-Supersonic wind tunnel. This is the first investigation to be done using the forced oscillation experimental technique in the VKI-S1. Oscillations are induced to match the reduced frequencies of flight vehicles based on their natural frequencies. A variety of mathematical models are developed to extract the aerodynamic damping-in-pitch parameter from the forced oscillation data. The results are compared to one another as well as to published data (where applicable). Free-to-tumble experimental data obtained for an Apollo model prior to this investigation is also evaluated using various mathematical models. Results show that classical analysis methods for extracting the aerodynamic damping-in-pitch parameter, which have been used many times prior to this investigation, continue to yield the most accurate measure for aerodynamic damping extraction. These include an outer-extremity envelope distribution method, which assumes a constant damping from one peak of pitch attitude to the next for free-to-tumble analysis and an energy conservation method based on hysteresis loops of pitching moment against pitch attitude for forced oscillation analysis.