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Unmanned ground vehicle obstacle crossing generally relies on two strategies: (i) applying a wheel torque for climbing and (ii) modifying the vehicle shape by using a wheel-leg or wheel-paddle to lift the wheel on top of the obstacle. However, most of those strategies sacrifice speed in order to have a longer contact duration between the wheels and the obstacle. This paper investigates the behaviour of a 4WD high-speed vehicle while crossing a step obstacle using a design of experiment (DoE). A 3D multibody vehicle model is equipped with a novel 2-DoF suspension system, which horizontal damping coefficient is modify to dampen wheel motion in longitudinal and vertical directions in relation to the chassis, for a given speed and obstacle height. The DoE results allow to propose a novel high-speed obstacle crossing strategy based on three metrics: (i) the kinetic energy variation of the vehicle, (ii) the contact duration between the wheel and the obstacle, and (iii) the pitch rate at the start of the ballistic phase. Experimental function are proposed to be able modify these metric in real time.