Page 215 - Theory and Design of Air Cushion Craft

198 Trim and water surface deformation under the cushion

Fig. 5.9 Co-ordinate system and principal dimensions of SES for calculating the inboard/outboard wave pro-
file of SES running on calm water.

P R
where the (/> denotes the distribution of pressure sources on the cushion surface, </> ,
(f> the source distribution on the centre longitudinal sidewalls, and doublet <£ the
action of interference caused by various factors, each of them meeting the given equa-
tions and their boundary conditions. Meanwhile, the amplitude of water surface
deformation can also be broken down as follows:
P . R . L . M
= 77 + rj + 77 +77 (5.8)
The terms on the right-hand side in equation (5.8) denote the deformation of the
water surface induced by each equivalent source. Figures 5.10 and 5.11 show a com-
parison of wave profile between calculations and experimental results on the inside (y
= b) and outside (y = 1.2/3), of the sidewalls. Experiments were carried out in a tow-
ing tank and the results were obtained by analysing photographs. From comparison
of the results, MARIC have concluded as follows:
1. The calculated results show that the wave amplitude induced by cushion air pres-
sure is the main component of the total wave height. The wave amplitude induced
by interference of both sidewalls and cushion pressure is small relative to the
former.
It may be noted that the volume displacement of sidewalls of this craft only
occupy 10% of craft displacement. For an air cushion catamaran with wider side-
walls and larger sidewall displacement, the interference effect will increase some-
what. The cushion pressure induced wave components are nevertheless dominant.
The theoretical results generally agree with the tests, which means that the influ-
ence of thin sidewalls on the deformation of the water surface induced by cushion
air is small.
2. The fluctuations of calculated wave profile (77) shown in Fig. 5.11 may be a reflec-
tion of the linear equation used as a mathematical model. In practice the fluctua-
tion can be smoothed by nonlinearity of real water waves and viscosity effects.