Page 159 - Theory and Design of Air Cushion Craft

142 Stability

Q^ = K^A^Jpl (4.6)
is the leakage area under sidewalls (m ) (they are a function of inner draft
where A j2
and heeling angle 6).
t {
4. Fan characteristic equation:
= A + BQ + CQ 2 (4.7)
H }
where A, B, C are fan characteristic coefficients which can be obtained according
to the type, speed, etc.
5. Weight equilibrium equation:
W = p cS c cos 0 + y (V, + V 2) (4.8)
where S c is the cushion area (m"), y the specific weight (N/m ), V l the volumetric
displacement of the immersed sidewalls (m), V 2 the volumetric displacement of
the emerged sidewalls (m) and W the craft weight (N).
Substitute equations (4.1)-(4.6) into equation (4.7), then we have
2
2
2 2
[1 + (2A j{ + A ]2fk flS 2 ~ 2C/p a(2A }l + A j2) k <f> ]p c
- B(A ]l + Ap)k<K2pM -A = 0 (4.9)
Equation (4.9) only includes p c and air leakage area A-^, A fl which are only
related to inner draft { and heeling angle 0. Therefore by combining the two equa-
t
tions (4.8) and (4.9), the p c and r i0 at different 0 can be solved by iteration with the
aid of a computer.
This method is similar to that used on conventional ships, i.e. determining the
equilibrium water line at the heeling condition, then the buoyancy of the sidewalls
and cushion pressure can be easily obtained; the difference is that the weight of the
craft must equal the sum of cushion lift and buoyancy provided by the sidewalls
and the cushion pressure has to satisfy the fan characteristic equation, flow equa-
tion and energy equation.
Based on the equilibrium water line, the righting moment can be obtained as
follows:

M, = (/ ml K, - / m2 V 2}y -(KG- t m) W sin 0 (4.10)
where M e is the righting moment of the craft at the heeling angle (Nm), / ml the trans-
verse distance between the centre of buoyancy of y V } and CG of the craft (m), / m2 the
transverse distance between the centre of buoyancy of y V 2 and CG of the craft (m) at
any given heeling angle and KG the height of the centre of gravity above the keel.
A block diagram for the calculation can be seen in Fig. 4.6.

Model and full-scale tests for static transverse stability of an SES
on cushion

Measurements of hovercraft static trim and heel can be made directly from a
scale model, or a full-scale craft. The trim or heel can be related to known shifts of
weight and therefore turning moment. Such data may be plotted against theoretical
calculations such as that described in 4.2 to verify the analysis, or allow empirical
adjustment to it. An example is described below, from MARIC experience.