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In this analysis, we consider the effects of non-quiescent initial conditionsdriven by pre-impact air-water interactions on the classical Wagner model ofimpact theory. We consider the problem of a rigid, solid impactor movingvertically towards a liquid pool. Prior to impact, viscous forces in the airact to deform the liquid free surface, inducing a flow in the pool. Theseinteractions are then incorporated as initial conditions in the post-impactanalysis. We derive expressions for the size of the effective contact set, theleading-order pressure and force on the impactor, and the speed and thicknessof the jet at its base. In all cases, we show that the effect of the pre-impactbehaviour is to cushion the impactor, reducing the size of the effectivecontact set and, hence, the force on the impactor. Small- and large-timeasymptotic solutions are derived for general power-law impactors, and we showthat the effects of the air die away as the impact progresses, so that weapproach the classical Wagner solution.

Introducing pre-impact air-cushioning effects into the Wagner model of impact theory