CETN I-63
March 1999
height. Net depth allowance for waves is 1.2H for deep-draft and 0.5H for shallow-draft
channels where H is the wave height."
The above estimates provide ample safety margins, but may be overly conservative based on
fundamentals of naval architecture and rigid-body ship motions. Recent advances in data-
acquisition technology and ship-motion modeling can provide accurate estimation of vessel
motion from waves. Vessel RAOs are strongly dependent on the height, period, and direction of
waves as well as the encounter frequency, the relative frequency of waves with respect to the
forward speed of a moving vessel. Vessel responses vary substantially from restricted, shallow-
water to unrestricted, deep-water conditions. Ship-response prediction models are now available
that provide accurate estimates of the vessel motions in open seas resulting from the combined
action of winds, waves, and currents. Extending these predictive tools to shallow water is an
area of ongoing research.
Because vessel motions enter the design and operations of navigation channels, ports, and
harbors, a RAO curve representing a bulk carrier (Harkins and Dorrell, in preparation), is shown
in Figure 3 as an example of ship motions. This RAO curve represents only one of many
possible combinations of vessel displacement for a wave heading of 45 deg and 3-ft underkeel
clearance. The RAOs of the vertical DOFs, heave, roll, and pitch, are shown together with their
respective phases. The RAO for each DOF represents the maximum excursion of the ship
bottom for unit wave amplitude, indicating the degree to which each principal DOF contributes
to the total excursion. The total RAO (combining the individual RAO and phase relationships)
shown in Figure 3 suggests a maximum amplification of 1.5 for wave periods of 16 to 24 sec
versus the present guidance of 2.4 for all wave periods or, conversely, a limiting wave height of
4 ft versus 2.5 ft. The present USACE estimate would require 50 percent more allowance for
wave motion contribution to the channel depth.
When a deep-draft cargo vessel is underway, water passes around its hull, creating a depression
into which the vessel sits (USACE 1995; SNAME 1985). This phenomenon is called squat,
defined as the combined effects of sinkage (heave), trim (pitch), and heel (roll) caused by the
forward speed of the vessel. Vessel squat depends on many factors including ship geometry
(length, beam, draft, shape, etc.), channel geometry (depth, width, area, etc.), ship position
(proximity to channel bank), and forward speed. Several empirical formulas have been proposed
for estimating vessel squat. The estimation of vessel squat in shallow water and restricted
channels is more complicated than its prediction in deep water. Some progress in shallow-water
squat prediction has been made since 1990 (SNAME 1996).
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