Ricochet Off Water of Spherical Projectiles

Abstract

The oblique water-entry problem of a spherical projectile is analytically analyzed with special reference to the ricocheting phenomena of the object off a free surface. Under the assumption of large impact velocity, the Kelvin-Kirchoff-Lagrange equations of motion are formulated in terms of the various time-dependent added-mass coefficients and their time derivatives. The actual trajectory of the sphere below the free surface is obtained by integration of these equations, and a critical value for the projectile incident angle (ricochet) is obtained in terms of the initial Froude number and the specific density of the solid. It is demonstrated that for infintely large Froude numbers this solution reduces to the well-known empirical expression for the critical angle of a sphere in oblique water-entry.