Page 113 - Theory and Design of Air Cushion Craft

Differential air momentum drag from leakage 97

= Qp av (3.7)
R m
where R m is the aerodynamic momentum drag (N), Q the air inflow rate (m /s), p a the
4
air mass density (NsVm ) and v the craft speed (m/s). Q is generally calculated by
including the cushion air inflow rate together with the air inflow rate for gas turbine
intake systems and engine cooling systems.

3.6 Differential air momentum drag from leakage under
bow/stern seals

According to momentum theory this drag can be written as
(<f>h\B cP - <f>H 2B cP)P - Wa" (3.8)
R a. = p a
where R a is the air momentum drag from differential leakage under bow/stern skirts,
$ the discharge coefficient of air leakage (in general we take 0 = 0.5-0.6), h { the bow
air leakage clearance, i.e. the vertical distance between the lower tip of bow skirt/seal
and the corresponding inner water-line, (m), h 2 the stern air leakage clearance (m), a"
the declined angle between the inner water line and the line linking the lower tips
of the bow/stern seals, while the craft is travelling on the cushion (°), p c the cushion
pressure, (N/rrT) and P = V(2/? c//? a). From Fig. 5.12, R a can be written as

[(r b - r w) - (2 S - fj] (3.9)
R (f = Wll c
where z b, z s are the vertical distances of the lower tip of bow/stern skirts over the craft
base-line (m) and / bi, the vertical distance between the inner water line and the craft
? si
base-line (m). Because the r b, z s are given for the given craft and f bi , can be obtained
? si
by the equation listing in Chapter 5, R u can be obtained using equation (3.9).
relates to cushion length-beam ratio, Fr, and cushion pressure-length ratio (these
R a
parameters influence the profile of the inner wave surface), and the location of the
centre of gravity (CG), (which influences the trim angle and inner/outer water line of
the craft), as well as to z b and z s.
In order to reduce R a>, or to increase the jet thrust from a stern seal to increase
craft speed, drivers can sometimes increase the stern seal clearance to make R a less
than zero. In fact it is very difficult to predict this drag. According to the general cus-
tom of ACV designers and also for reasons of conservatism, we often take a" =
0.25-0.5° for ACVs, and neglect this drag term for SES. This may be validated by pro-
totype tests, in which a lot of spray will be seen behind the stern seal.
With the aid of Fig. 3.13, we can demonstrate this concept. In this figure, we have
AB as the line linking the lower tip of the bow/stern seal (skirts), and i//' the angle
between sea level SL and AB. i//' does not denote the trim angle of the craft, except if
the line AB is parallel to the base-line of the craft, a' is the slope angle of the inner
wave surface, and R w the wave-making drag. From Fig. 3.13, we derive the following:
• When y/' > 0, i.e. the craft operates with bow up, then
R a.= Wtznv' - R w (3.10)

If line AB is parallel to the base-line of the craft, then the drag due to the