Page 212 - Theory and Design of Air Cushion Craft

Water surface deformation in ACV air cushion 195

where
i
r
„ smd. /e ia.v
2
2
H(a + ft )- Fn aH - icjualg
= c/(g//) 05
Fn H
tan 0 = ft/a
y = bll
This equation can be developed into an algebraic equation for practical use:
1. When Fn H > 0, let
05
2
a = (x- l)/[l(Fn H - I) ]
05
b = (x + l)/[l (Fnff - I) ]
c = [sgn(—a + r - y/l) + sgn(a + r — y/l) + sgn(—a + r + y/l)
+ sgn(a + r + y/l)]
d = [sgn(-b + r - y/l) + sgn(b + r - y/l) + sgn(-b + r + y/l)

+ sgn(b + r + y/l)]

- 0.25[sgn((>V/) + r) - sgn((y//) - r)] [sgn((x//) + 1)

- sgn((x//) - 1)] (5.5)
2. WhenFn H< 1, let
2 2
2 05
e = arctan [r/|x - 1| (1 - Fn H) ]/[ (x - I) 2 + (y 2 - r / )
(1 - Fnfj)]
2 2
2 5
f = arctan [r/|x + 1| (1 - Fn Hf ]/[ (x + I) 2 + (y 2 - r ! }
(1 - Fnjj)}
2 2
= [Fn H/(2n(\ - Fn )] e sgn((x/l) - 1) - f sgn((x//) + 1)
(pvjgrj)/p c
- 0.25 [sgn((y//) + r) - sgn((y/7) - r)] [sgn((x/7) + 1)
- sgn((jc//) - 1] (5.5a)
where
( 0 1 when x > 0
x
= 0

and H(x) is the unit step function.
The wave-making of an ACV running over shallow water can be calculated according
to equations (5.5) and (5.5a) in the case where Fn H = (v/(gH) ) >1. The maximum
height of the wave can be simplified [55] as