L’Isle sur la Sorgue, France

Two-dimensional unsteady motion of a smooth body over a water surface with multiple collisions and subsequent rebounds from this surface is considered. This problem is studied in connection with landing of aircraft on the water and flights of wing-in-ground-effect vehicles (WIG) in close proximity to the water surface. In the present analysis, the water is of small depth and its flow caused by the impacts is described by the shallow water model. Free body motions with subsequent water impacts and the corresponding hydrodynamic loads are of primary interest. In the past only a single impact between the water surface and a smooth body was studied [1-8]. These investigations revealed that the landing of a smooth body with high horizontal speed on water typically leads to the rebound of the body followed by skipping along the water surface. It was shown that the body rotation plays an important role in impacts and rebounds of a free body. This regime of the body motion with multiple impacts on the water surface may cause vibrations of the fuselage with significant bending stresses or even lead to the overturning of aircraft. It is interesting to note that regimes of the landing of a free body with a single impact on the water surface and the subsequent smooth planing along the water were not detected in the calculations. Motions of a free body are determined by its orientation and speeds befor