Estimating Transonic Drag


  • Brendan James Florio CSIRO Mineral Resources, University of Western Australia
  • Robert McKibbin Massey University
  • Calum Braham University of Western Australia
  • John Ockendon University of Oxford
  • Colin Please University of Oxford



Ballistics, fluid mechanics, optimisation


To predict the trajectory of projectiles such as bullets and mortar shells, we require knowledge of the acting forces, including drag. For the most part, the drag coefficient (which is dependent on the local Mach number) is well-understood for subsonic and supersonic velocities. However, there is often a rapid and unintuitive change in the drag behaviour near the speed of sound. The transonic behaviour of the projectiles is addressed in two major ways. First we explain the underlying physics of drag in the three major regimes. The appearance of shock waves alters the drag forces dramatically. In some situations, the physical models are simplified to directly obtain the drag coefficient profile. Then we tackle an inverse problem, where firing table data gives the drag coefficient profile. The drag profile obtained by both point-by-point optimisation and by parametrising a suitable family of functions. Finally, transonic data is difficult to obtain in wind-tunnel experiments, so based on our understanding of the physics, alternative experiments are suggested. This research was undertaken as part of the 2017 Mathematics in Industry Study Group (Adelaide) with industry partner, the Defence Science and Technology group.

Author Biography

Brendan James Florio, CSIRO Mineral Resources, University of Western Australia

Postdoctoral Fellow at CSIRO Mineral Resources, and the School of Mathematics and Statistics, University of Western Australia





Proceedings of the Mathematics in Industry Study Group