One proposes a combined analytical-numerical method for the supersonic combustion around a conical obstacle, considering variable specific heats with temperature. One important aspect is to avoid the dissociation what is not possible if normal detonation waves (of Chapman-Jouguet type) occur. The Clarke model where the detonation wave is separated in a shock wave and a deflagation wave is able to reduce the temperature. Here conical waves are used. In order to characterize the combustion speed and intensity, new parameters are proposed. A comparison with the Chapman-Jouguet combustion is also presented.