  The present study is concerned with the peak acceleration azmax occurring
during the water impact of a symmetric wedge. This aspect can be important for
design considerations of safe marine vehicles. The water-entry problem is
firstly studied numerically using the finite-volume discretization of the
incompressible Navier-Stokes equations and the volume-of-fluid method to
capture the air-water interface. The choice of the mesh size and time-step is
validated by comparison with experimental data of a free fall water-entry of a
wedge. The key original contribution of the article concerns the derivation of
a relationship for azmax (as well as the correlated parameters when azmax
occurs), the initial velocity, the deadrise angle and the mass of the wedge
based on the transformation of von Karman momentum theory which is extended
with the inclusion of the pile-up effect. The pile-up coefficient, which has
been proven dependent on the deadrise angle in the case of water-entry with a
constant velocity, is then investigated for the free fall motion and the
dependence law derived from Dobrovol'skaya is still valid for varying deadrise
angle. Reasonable good theoretical estimates of the kinematic parameters are
provided for a relatively wide range of initial velocity, deadrise angle and
mass using the extended von Karman momentum theory which is the combination of
the original von Karman method and Dobrovol'skaya's solution and this
theoretical approach can be extended to predict the kinematic parameters during
the whole impacting phase.
