A novel approach for determining the trajectory and speed of a supersonic object

An experimental set-up is presented for tracking the trajectory of a supersonic object using minimal resources. The proposed set-up, based on the use of low-cost pressure transducers, a general-purpose conditioning system and off-the-shelf instrumentation, is capable of determining the bullet trajectory, speed and hit point in open air use. The methodology is based on the post-processing of shock wave information gathered by means of three spaced sensor clusters, each one comprising three pressure transducers. The pressure sensors are used to detect the times of arrival of the shock wave generated by the bullet; on the basis of geometrical considerations, from the six time delays measured by means of the nine pressure sensors, the bullet direction and its speed are calculated. The novel contribution of the methodology described here, with respect to similar methods described in the literature, is the post-processing method used. The metrological performance of the realized experimental set-up was calculated by means of a priori analysis to theoretically determine the uncertainty maps as a function of bullet direction, after the geometry of the clusters, their relative positions and the time resolution were chosen. The theoretical analysis was then verified with field tests in a marksmanship training range with series of straight shots hitting the target plane from different positions at a distance of about 100 m, with both perpendicular and inclined shots. The results obtained with the shots perpendicular to target plate are: the error in hit points is always less than 65 mm while the error associated in angle values lies in the range from −0.017 to 0.010 rad (from −1.0◦ to 0.6◦). The worst results obtained with inclined shots, i.e. those not perpendicular to the target plane, are: hit point error always less than 196 mm and range of variation of error angle of −0.017 and 0.038 rad (−1.0◦ and 6.8◦). Overall examination of the theoretical and experimental results indicates the critical strengths of the method, namely accounting for environmental parameter fluctuations and accuracy in the evaluation of relative positions among the clusters.