Shape effects in the water impact of panels

Abstract

The water impact of free-falling two-dimensional curved rigid panels with low deadrise angles was considered. Through theory and experiment, the influence of panel shape on purely vertical trajectories was examined using the Wagner model corrected by Oliver. This theory assumes an ideal fluid and imposes severe approximations on the geometric aspects of the problem. Despite these limitations, the original Wagner model has been surprisingly successful in describing qualitative and approximating quantitative aspects of the pressure during forced water entry of wedges. In the present work, analytical solutions for the free-fall trajectories of a class of surfaces are presented and compared with tabletop-scale experiments from several drop heights. One of the more interesting testable predictions is that surfaces whose profile curves upwards more strongly than a parabola will continue to accelerate, while profiles of weaker power will decelerate. This was not observed in the experimental data. However, a remarkably good agreement for both position and velocity was attained for shapes with square root profiles, that is, shapes curving downwards more strongly than a wedge.