Page 209 - Theory and Design of Air Cushion Craft

192 Trim and water surface deformation under the cushion

The water surface deformation caused as the air cushion with uniformly distributed
pressure moves forward may be defined by equations (5.2) and (5.3).
To determine the actual water surface profile, one has to take into account both the
depression of the water surface induced by the air cushion hovering statically over the
water and the water surface deformation caused by the air cushion moving on the
water, i.e. the ratio between the x direction component of disturbing velocity on the
free surface and its forward velocity.
Calculated results are shown in Fig. 5.3, where it can be seen that the water surface
deformations will be rather different between in and beyond the cushion, and are a
function of Froude number. Figs 5.4-5.6 show calculation results selected from ref.
54. They can be compared as follows:
1. From Fig. 5.4, it is found that the bow wave amplitude in the cushion is equal to
that beyond the cushion. At high values of Fr } the bow water surface deformation
both in the cushion and also beyond the cushion decreases so as to keep the same
value. This agrees with test results.

(a)

Fig. 5.3 Water surface deformation due to a moving air cushion pressure distribution £//= r= 0.4: (a) ver-
tical displacement of free water surface at Fr - 0.9, (b) vertical displacement of free water surface at Fr= 3.0.