Page 95 - Theory and Design of Air Cushion Craft

Calculation of cushion stability derivatives 79

where Q 0 is the outflow rate from the cushion (m /s), Q { the inflow rate into the cush-
3
3
2
ion (m /s), Fthe cushion volume (m ), m the mass of air in the cushion (Ns /m) and
4
2
the air density (Ns /m ).
p. d
Considering the cushion as incompressible, thus dpjdt = 0. Then
= \i/A,(2pJp &f 5
Q 0
is the area of air leakage (m). Now Q { can be written as
where A t
a = fiio
is the cushion pressure at equilibrium feed mode is the
where Ap c = p c — p c0, p c() and p c
instantaneous cushion pressure.
If we assume that z, the displacement of the ground, is upward positive and there
is no rotation of ground motion, then
dV/dt = -S cz
and

S c = A m + (cUj/dz) z = 4 0 - h
where S c is the cushion area (m ), A i0 the area of air leakage at equilibrium flow mode
2
(m ) and 1 the peripheral length for air leakage (m). Then substitute the foregoing
equation into (2.41), which gives
-S cz = [Q io + (30/3/0 4>J - y/G4 io - *i) ' (2/> c/A/ 5
or
-S cz = Q l0 + (dQ/dp c) Ap^ - i//A io (2pjp a + y/l 2(2p c/p a s
Taylor
Extend the (2p clp a)°' )°' s s term into a Taylo series and neglect the nonlinear terms, and
term
into
a
(2p clp a
then these expressions can be written as
0.5
\ /
3/? c yO a
then
(2.42)

= - A P c - A P c + -. (2.43)
2
We PcO «0
where /z 0 is the skirt clearance at equilibrium flow mode (m), Q t0 the inflow rate at
3
equilibrium flow mode (m /s) and p c0 the cushion pressure at equilibrium mode
2
(N/m ).
Equation (2.43) can be written as
K, Ap c= -K 2z - K 3z
or

4 > c = z - z (2.44)