Page 208 - Theory and Design of Air Cushion Craft

Water surface deformation in ACV air cushion 191

n = -pjy
where rj is the depth of depression, upward positive.
In the case of a craft moving over a water surface, the dynamic deformation of the
water surface caused by the ACV has to be determined. According to linear water
wave theory, when an air cushion with the length of L, beam of b and pressure distri-
bution of p(x,y) running on the free surface of calm water with the depth of H at con-
stant speed of c, the disturbance velocity potential can be written by [53]

—i r r r r
\SQc9\ABdk\ Cdmdn (5.1)
4ncp v
J-TT J 0 J -J -oo
where
ik(xcos 0 + v sin 6)
A= e
k - [g/c~] tanh kH (sec 0) + i file sec 9

cosh k (H + z)
B =
cosh kH
C = p(m,ri) e iA-(m cos 0 + n sin 0)
and c is the moving velocity of the cushion (m/s), // the water depth (m), m,n any
2
given variate, g the acceleration of gravity (9.81 m/s ), /? w the water density (kg/m ),
(sea water 1021 at 20°C, fresh water 998.2 at 20°C), r the aspect ratio of the air cush-
2
ion, r = bjl c and// the dynamic viscosity coefficient (Ns/m ) (1.3 at 10°C, 1.009 at
20°C, 0.8 at 30°C).
Assuming the pressure of the rectangular air cushion to be uniformly distributed,
then the exciting disturbance potential can be written as

r r~
sec0d0 \DBEF kdk (5.2)
J— rr JO
where

£> 2 2
- [g/c ] (sec 9) tanh kH + i ju/c sec
sin (kl cos
—
Ac cos 9 sin

_ sin (krl cos
J* — —
cos 9 sin 0
Thus, the water surface deformation should meet the relation
_ PL. (5-3)
= o y

where x, y, z form the perpendicular coordinates, x denotes the direction of air cush-
ion movement and forward positive z denotes the vertical coordinate, upward positive.