On air cushioning in axisymmetric impacts - Moore, Matthew; Oliver, James (IMA Journal of Applied Mathematics, 2014)
This paper extends the work of Moore et al. (2013, Air-cushioning in impact problems. IMA J. Appl. Math., 78, 818–838) by using a displacement potential formulation to analyse the post-impact effect of an air-cushioning layer on the normal impact of an axisymmetric rigid body on a liquid half-space. The liquid and the air are both incompressible, inviscid and their flows are irrotational. The leading-order problem is reduced to a pair of Titchmarsh integral equations and a far-field analysis shows that the method applies for impactors whose elevation grows at least as fast as a paraboloid, but breaks down in particular for a cone.We focus on cases when the density ratio between the air and the liquid is small. For an impacting paraboloid, we find the correction to the turnover curve location in classical Wagner theory due to the presence of the air layer.
Keywords: Applied Mathematics