Page 102 - Theory and Design of Air Cushion Craft

Steady drag forces

33 Air cushion wave-making drag (RJ

Wave-making drag generated by a pressure distribution is a classical theme of hydro-
dynamics, since a ship's hull is generally represented by a surface consisting of a vary-
ing potential function which applies positive pressure in the forebody and suction
pressure around the stern [8,17].
The equivalent problem for a hovercraft was addressed by Newman and Poole [18],
who derived a calculation method for predicting the wave-making drag. They sim-
plified the air cushion to an equivalent rectangular surface with a uniform pressure
distribution and calculated the wave-making drag as
. 7
PC-'
[(P w.g)\ (3.1)
where
Cl = f (F r and
and R^ is the wave-making drag due to air cushion, (N), p c the cushion pressure
(N/m ), B c the cushion beam, (m), c the cushion length (m), p w the water mass density
l
4
2
2
(0.10177 - 0.1045) (N s /m ), g the gravitational acceleration (9.8066)(m/s ) and C w
the wave-making drag coefficient due to the air cushion travelling on a waterway with
infinite depth, as shown in Fig. 3.2.
Figure 3.2 shows that as cushion length is increased, so the primary hump at F r
approx. 0.56 reduces. Craft with IJB C in the range 2-A have a significantly higher drag
peak at F r approx. 0.33, so thrust margin at this speed should also be checked during
design. Figure 3.3 shows the variation of C w against IJB C for various F r, interpreted
from Fig. 3.2. It can be seen that below IJB C of about 6, the primary drag hump at F r
0.56 begins to build up. Figure 3.4 shows plots of C w vs F r for selected IJB C, taken from
Fig. 3.3.
It is important to note here that wave-making drag is proportional to p c and the
cushion width. Craft drag can therefore be significantly reduced by increasing craft
length. This was used successfully by BHC in stretching the SR.N6 craft in the UK,
and the US Navy SES-100 to SES-200.
In fact, the wave-making drag can be defined as
^w ^w .
= = sin a (3.2)
P CS C W
where a—a' is the average slope of the wave generated by a moving air cushion. This
is most suitable for a cushion moving at high F r, generating a wave, rather longer than
cushion length.
Meanwhile, equation (3.1) can also be written as

~ C^vu

3) --v