Optimisation of a sensor cluster for supersonic object trajectory and velocity determination

An evaluation of errors for a method for determination of trajectories and velocities of supersonic objects is conducted. The analytical study of a cluster, composed of three pressure transducers and generally used as an apparatus for cinematic determination of parameters of supersonic objects, is developed. Furthermore, detailed investigation into the accuracy of this cluster on determination of the slope of an incoming shock wave is carried out for optimization of the device. In particular, a specific non-dimensional parameter is proposed in order to evaluate accuracies for various values of parameters and reference graphs are provided in order to properly design the sensor cluster. Finally, on the basis of the error analysis conducted, a discussion on the best estimation of the relative distance for the sensor as a function of temporal resolution of the measuring system is presented.