This paper describes the design optimisation study used to aerodynamically optimise the fairings that cover the rear wheels of the Land Speed Record vehicle, BLOODHOUND SuperSonic Car (SSC). Initially, using a Design of Experiments approach, a series of Computational Fluid Dynamics simulations were performed on a set of parametric geometries, with the goal of identifying a fairing geometry that was aerodynamically optimised for the target speed of 1,000 mph. Several aerodynamic properties were considered when deciding what design objectives the fairings would be optimised to achieve; chief amongst these was the minimisation of aerodynamic drag. A parallel, finite-volume Navier–Stokes solver was used on unstructured meshes in order to simulate the complex aerodynamic behaviour of the flow around the vehicle’s rear wheel structure, which involved a rotating wheel, and shockwaves generated close to a supersonic rolling ground plane. It was found that the simple response surface fitting approach did not sufficiently capture the complexities of the optimisation objective function across the high-dimensional design space. As a result, a Nelder–Mead optimisation approach was implemented, coupled with Radial Basis Function design space interpolation to find the final optimised fairing design. This paper presents the results of the optimisation study as well as indicating the likely impact this optimisation will have on the ultimate top speed of this unique vehicle.