The figure shows the skirt of an air cushion vehicle. A supply at pressure P s and temperature T s fills the skirt volume, so that the vehicle “floats” on a cushion of air, while air escapes under the...

The figure shows the skirt of an air cushion vehicle. A supply at pressure P_s
and temperature T_s
fills the skirt volume, so that the vehicle “floats” on a cushion of air, while air escapes under the skirt to atmosphere. The height of the skirt above ground is called h and is time varying as the vehicle negotiates an uneven terrain. The ground input is the velocity v_i(t)

Construct a model of this system that, if solved, would predict the vertical motion time history of the vehicle. Since h(t) is very small, it is all right to consider the relative motion between base and skirt as creating a volume change in the skirt.