Page 96 - Theory and Design of Air Cushion Craft

SO Air cushion theory

where

K 3 = vl(2 PM°- 5 = Q 0/h 0 (2.45)
Assume the cushion pressure is a linear function of heaving amplitude and velocity,
then

Using the equivalent terms of (2.46 and 2.44), we have
Go
z —
2p c0

where d/? c/3zis the velocity derivative of /? c with respect to z, i.e. the cushion damping
coefficient, dp c/dz the derivative of p with respect to z, i.e. heaving stability derivatives
and dQ/dp c the derivative of Q due to the characteristic curves of cushion air duct-fan
systems with respect to p c. Then

where dQ/dH^ is the slope of the fan characteristic, if //j = A + BQ + CQ, i.e.
2C0

dHj/dp c is the slope of the air duct characteristic and dpjdp c the derivative of bag pres-
sure with respect to cushion pressure, which can be calculated according to expression
(2.3).
It is then not difficult to calculate the natural heave frequency without damping and
heave damping rate:

M
(2.49)

3z 2Mco.
withou
where co. is the natural heave frequency y withoult damping (s ), £- the heaving
damping rate and M the mass of the craft (kg).