EM 1110-2-1100 (Part II)
30 Apr 02
EXAMPLE PROBLEM II-7-7
FIND:
The natural period of the vessel in surge for used mooring lines in good condition.
GIVEN:
A C9 containership is moored at a pier in Barbers Point Harbor, Oahu, Hawaii. Its fully-loaded
displacement is 54,978 long tons (55,860,231 kg). Karat Estalon fiber ropes with a 7-1/2-in.
circumference (6.3-cm-diam) are used for the two head, two stern, and two spring lines. Head and stern
lines are 30.5 m long and make an angle of 70 deg with the perpendicular breast lines. The spring lines
are 45.7 m long and form an angle of 85 deg with the breast lines. The tension in these lines is
maintained at 20 tons (177,900 N). The deck of the C9 is assumed to be 7 m above the dock at the bow
and 4.5 m at the stern.
SOLUTION:
Virtual mass is calculated from Equation II-7-27
mv ' 1.15(55,860,200) ' 64,239,200 kg
The next step is to calculate the effective spring constant. Karat lines are manufactured by Columbian
Rope Company, Guntown, MS, under license from Akzo, Holland. Estalon is a fiber that is a copolymer
of polyester and polypropylene. According to manufacturer's literature, the breaking strength for Karat
ropes is 526,000 N. The load as a percent of breaking strength is
177,900
' 33.8 %
Load ' 100
526,000
From the elongation chart for Karat lines (not shown), the percent elongation is 8.7 percent. The
elongation for the head and stern lines is the same and is calculated from Equation II-7-30
8.7 (30.5)
∆lHd ' ∆lSt '
' 2.7 m
100
Likewise, the elongation for the spring lines is given by
8.7 (45.7)
' 4.0 m
∆lSp '
100
Example Problem II-7-7 (Continued)
II-7-68
Harbor Hydrodynamics
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