The determination of aerodynamic coefficients for complex high-speed vehicles still requires experimental measurement. This paper details the development of the free-flight measurement technique within the University of Oxford High Density Tunnel. In particular, a novel image processing technique is developed for calculating the position of the model from high-speed video. This study focuses on the measurement of high Reynolds number experimental aerodynamic data for a subscale model of the Skylon space plane of Reaction Engines. Testing was undertaken at a Mach 7 test condition replicating flight at an altitude of 63.5 km. Results for lift, drag, and pitching moment coefficients were obtained over a range of angles of attack. Lift coefficient was nearly linear over the range of angles of attack tested, and drag coefficient was parabolic in shape, but sensitive to model yaw. The vehicle was also shown to be statically unstable, a common characteristic of canard configuration vehicles.