Journal of Engineering Mathematics 48: 279–303, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. Initial water impact of a wedge at vertical and oblique angles C. JUDGE ∗ , A. TROESCH and M. PERLIN Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA Received 2 January 2003; accepted in revised form 28 July 2003 Abstract. This paper examines initial asymmetric wedge-impact flows with horizontal as well as vertical impact velocity. The method of two-dimensional vortex distributions is employed to model the initial-boundary-value problem. The numerical analysis involves discretization of the body surface and an iterative solution technique. Ex- perimental drop tests of a prismatic wedge were performed to gain understanding and provide data for comparison of initial water impact when asymmetry and horizontal impact velocity are present. The experimental investigation of initial flow separation off the wedge vertex (i.e., keel) during impact is described. Initial separation-ventilation of the flow from the vertex due to asymmetric impact or horizontal-vertical impact velocity is examined in relation to the present theory. Agreement between the data and the numerical predictions was demonstrated for small degrees of asymmetry and small ratios of horizontal to vertical impact velocity. The initial flow detachment from the vertex also revealed interesting hydrodynamic characteristics. Key words: asymmetric wedge impact, oblique entry, vortex distributions 1. Introduction High-speed planing boats are widely popular, but little is understood about their stability at high speeds where a significant number of these craft are known to experience unexpected behavior. Research at the University of Michigan intending to understand dynamic instability has included a water-impact model to determine the flow over a cross-section of the hull. This first step towards developing a more complete dynamic model approximates the steady planing of symmetric and asymmetric hulls with constant forward and transverse velocities. The work presented here would be appropriate for determining the restoring forces and moments, i.e., stiffness terms in the equations of motion, in a more general dynamic model. By using a low-order strip theory based upon slenderness assumptions (sometimes referred to as a 2-1/2 D solution) and viewing the planing hull as a series of cross-sections at different points of impact (near the bow the hull is just starting to enter the water while near the transom the hull has mostly entered the water), the model approximates the transverse flow characteristics over the entire hull. The resulting boundary-value problem with appropriate simplifications can be solved numerically using two-dimensional vortex distributions. This paper examines one aspect of the model: asymmetric wedge-impact flows with com- bined vertical and horizontal impact velocities. Included in the flow types is initially ventilated flow due to asymmetry and/or horizontal impact velocity. The general model provides initial conditions to start arbitrary, time-dependent, impact simulations [1]. The numerical process involves discretization of the surfaces and an iterative solution technique. The method of two-dimensional vortex distributions is employed to model the boundary-value problem. Ex- perimental investigation into initial flow separation-ventilation off the wedge vertex (i.e., keel) ∗ Presently at the Department of Naval Architecture and Ocean Engineering, United States Naval Academy.