ERDC/CHL CHETN-IX-14
March 2004
NGVD29. Both of these routines are contained in the USACE program Corpscon. The Geoid96 was
used to transform the benchmark elevations around Fort Johnson to ellipsoid heights. All of the ship
track data were processed as ellipsoid heights. The Corpscon was then used to convert the data to
NGVD29. The conversion process was checked against a NOAA tidal benchmark.
EMPIRICAL SQUAT EQUATIONS: The PIANC (1997) classifies channels as unrestricted
shallow water, restricted channel, or canal. Although the Charleston reach has all three types, this
analysis focuses on the areas where squat is largest in unrestricted shallow water. Relatively wide
channels can be classified as unrestricted shallow-water channels.
The PIANC (1997) lists three empirical equations for predicting ship squat that are applicable for
this type of channel cross section. They include equations by (a) Huuska (1976), (b) Barrass (1979,
1981), and (c) Romisch (1989). The equation by Eryuzlu et al. (1994) is also applicable for
unrestricted shallow water, but requires block coefficients Cb > 0.8 (i.e., a measure of ship fineness
equal to the ratio of the ship's volume divided by an equivalent rectangular volume with the same
length, beam, and draft). None of the ships in this study satisfy this last requirement for Cb, however.
Ship squat is a function of the depth Froude Number Fr, defined as
V
Fr =
(1)
gh
where V is ship speed relative to the water, g is gravitational acceleration, and h is water depth.
The first empirical equation for predicting ship squat is by Huuska (1976). It is based on previous
work by Guliev (1971) for ship squat at the bow Sb, and is similar to the equation in ICORELS
(1980)
Fr2
∇
Sb = 2.4 2
(2)
Ks
Lpp 1 - Fr2
where ∇ is ship displacement volume = Cb*L*B*T, L is overall length of the ship (i.e., LOA) at the
waterline, B is the beam, T is draft, and Lpp is ship length between perpendiculars. The coefficient Ks
is defined as
K s = 7.45 s1 + 0.76
for s1 > 0.03
for s1 ≤ 0.03
Ks = 1
and
s1 = (As/Ach)K1
where As is the midship cross-sectional area = 0.98*B*T, Ach cross-sectional area of the channel, and
K1 varies with As/Ach and T/h and is equal to 1 for an unrestricted channel width. Additional
information on the calculation of K1 is contained in PIANC (1997).
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