ERDC/CHL CHETN-IX-14
March 2004
The second empirical equation is based on work by Barrass (1979, 1981) for maximum squat Smax
CbS2 / 3Vk2.08
2
=
Smax
(3)
30
where S2 is the blockage ratio = As/Aw, Aw = Ach - As, and Vk is ship speed relative to water in knots.
The final empirical equation is by Romisch (1989) for maximum bow or stern squat S
S = CV CF K∆T T
(4)
where coefficients CV, CF, and K∆T are defined in the paragraphs that follow. The coefficient CV is
defined as
⎡⎛ V
⎤
2
4
⎛V ⎞
⎞
CV = 8 ⎜ ⎟ ⎢⎜
- 0.5 ⎟ + 0.0625⎥
(5)
Vcr ⎠ ⎢⎝ Vcr
⎥
⎝
⎠
⎣
⎦
For unrestricted shallow water, the critical ship speed Vcr is defined as
0.125
⎛ hL ⎞
Vcr = 0.58 ⎜
gh
(6)
⎟
⎝ TB ⎠
For bow squat, CF is defined as
2
⎛ 10Cb B ⎞
CF = ⎜
(7)
⎜ Lpp ⎟
⎟
⎝
⎠
and CF = 1 for stern squat. The coefficient K∆T is defined as
h
K∆T = 0.155
(8)
T
The following assumptions (PIANC 1997) were used in these equations.
a. For ships with different bow and stern draft, the average draft was used in the equations and
in the calculation of ship cross-sectional area.
b. In the Barrass equation, unrestricted shallow water exists when bottom width (W) is greater
than about 8 beam widths (B) of the ship. Although not stated in PIANC (1997), channel
cross-sectional area for unrestricted shallow water was assumed to be equivalent to 8*B*h.
c. The length between perpendiculars and the block coefficient were not known for all ships. If
unknown, both parameters were taken from the table of typical values given in PIANC
(1997).
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