Calculations have been performed for the inviscid hypervelocity flow of nitrogen past a 15° semi-angle sharp cone at an incidence of 30°, at an enthalpy sufficiently high to produce dissociation/recombination chemistry downstream of the bow shock wave. A spatially second-order-accurate scheme for the numerical solution of the inviscid Euler equations was used combined with the Lighthill–Freeman model of the non-equilibrium ideal dissociating gas. The computational method has been used as a ‘numerical wind tunnel’ in order to gain understanding of the interaction between the gas dynamics and the finite-rate gas chemistry. Inviscid flow has been considered to ensure that the only physical lengthscales in the flow are those associated with the chemical reactions. It was found that a chemical lengthscale Ls based on the local dissociation length behind the shock on the windward plane of symmetry is an important governing parameter of the flow. However, as the flow lengthscale becomes large and the flow approaches the limiting case of equilibrium chemistry, Ls is not the dominant chemical lengthscale. This is particularly true of the leeward flow, which contains a shock–vortex structure. A simple modelling technique has been used to determine a more appropriate lengthscale, Lr, t, for the leeward flow as the equilibrium limit is approached. This lengthscale is based on the expected equilibrium conditions behind the cross-flow shock.