A finite element model was developed to identify the motion mitigation provided by a suspended hull design, an elastomer coated hull and a reduced stiffness

aluminium hull, to a freefalling drop (0.75 m) into water. The model, based on the human–seat two degree of freedom mass–spring–damper model developed by Coe et al. (2009) and a finite element model of a high speed craft hull cross section, i.e., a wedge, is shown in Fig. 5. The model was implemented in ANSYS, a commercial finite element package. The human–seat components were modelled as mass, spring and damper elements represented by MASS21 and COMBIN14 elements and the wedge was modelled using ANSYS geometric primitives and meshed with quadrilateral SHELL63 elements, assuming linear isotropic material RG7422 properties. The modelled material and physical properties are summarised in Table 7. A theoretical model was used to predict the acceleration SB431542 chemical structure of the wedge entering the water, based on Zarnick (1978) methods and the experimentally measured pressures for a freefalling wedge presented by Lewis et al. (2010). The initial conditions at the point of wedge entry were calculated from classical mechanics, ignoring air resistance, to provide the velocity of the wedge at the moment of water entry. From which the force on the wedge was calculated by equation(3) Fw=Vw×DmaDt+z¨×ma+(cosβ×ρVw2ywetted)+(gmytotall)where V  w represents the wedge velocity, Dma/DtDma/Dt the rate of change of added mass

with time, z¨ the acceleration in the vertical direction, ββ the wedge deadrise angle, ρρ the water velocity, y  wetted the wetted half beam, g   acceleration due to gravity, m   the wedge mass, y  total the wedge total half beam and l   the wedge length. The added mass was assumed to be equation(4)

ma=Camρ12πywetted2where CamCam represents the coefficient of added mass. The wetted half beam, taking into account the deformation of water up the side of the wedge, was calculated by equation(5) ywetted=π2−π2−πβ1801−2πyy represents the geometrically wetted half beam, calculated from the depth of immersion and the deadrise angle. The coefficient of added mass was calculated Adenosine triphosphate as equation(6) Cam=π41−π2−πβ180π2 This provided a time history of the wedge motion during impact. Verification of the human–seat two degree of freedom mass–spring–damper model can be found in Coe et al. (2009). To verify the finite element model of the wedge section a cantilever beam deflection comparison and a modal analysis were performed. Cantilever beam deflection comparison: Assuming the wedge section to be an Euler–Bernoulli cantilever beam with an applied load in the vertical direction, the deflection z of the cantilever beam can be expressed as equation(7) z=FL33EIwhere F is the applied load at the free end, L is the length of the wedge, E is Young’s modulus of the structure and I is the cross sectional second moment of area. For the modelled wedge, the second moment of area was calculated as 0.