Vessel Quotas and Operating Requirements Vessel Quotas and ...

Predictions of maximum wave height at a given distance from the track line are based on empirical
findings. Weggel and Sorensen (1986) predict maximum wave height, H m , at track offset distance, x, on
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the basis of F, water depth, d, and the cube root of ship displacement, V . See pages 4, 5 and 6 of
Attachment “Wave generation model calculations” for details of the formulation. Figure 4 illustrates an
example application for a cruise ship. Note that the predicted maximum wave height decreases as the
wake travels farther from the vessel that produced the wake. This equation is conservative in comparison
to other similar formulations and measurements (Blaauw et al 1984, PIANC 1987, Sorensen 1989, Hüsig
et al 2000, and Veri-Tech 2002).
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Example, Weggel & Sorensen (1986)
Maximum wave height (ft)
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3
2
1
0
0 500 1000 1500 2000
Offset distance from ship track (ft)
FIGURE 4EXAMPLE APPLICATION OF WEGGEL AND SORENSEN (1986). GIVEN A SHIP OF 1000 TONS DISPLACEMENT WITH A
SPEED OF 15 KNOTS THROUGH THE WATER IN 100 FATHOMS DEPTH. THE WAKE IS PREDICTED TO PROPAGATE AT C = 12.2 KNOTS
WITH AN ANGLE θ = 35.3 DEGREES TO THE SHIP TRACK AND TO HAVE A PERIOD T = 4.0 SECONDS AND WAVELENGTH L = 83.4 FT.
WAVE HEIGHTS BEFORE AND AFTER THE MAXIMUM WILL BE DIMINISHED AS SHOWN IN FIGURE 3.
Table 1 provides the maximum wave height generated by a series of vessels at a speed of 10 knots, as
presented in Sorensen (1973). Sorensen’s measurements demonstrate that vessels of varying sizes all had
wakes with maximum wave heights of less than 1-foot at a distance of 500 feet from the sailing line.
Similar findings were reported in a study which measured vessel wakes on the Kenai River and Johnson
Lake (Maynord 2001). In this study Maynord looked at the vessel wakes of 16 to 20-foot long boats of
various hull shapes and beams. He found that these vessels generated maximum waves at speeds of
approximately 8-knots. The waves were less than one foot measured between 30 and 50 feet from the
track line. Although the wave height dropped off rapidly with distance from the track line, the wave’s
periods remained constant.
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