Example Problem II-7-7 (Concluded)

Individual stiffness for the head and stern lines is calculated from Equation II-7-29

177,900

' 65,900 N/m

2.7

Similarly, the stiffness for individual spring lines is

177,900

' 44,500 N/m

4.0

The vertical angles from the bow, stern, and spring lines are

7.0

' 13E

φHd ' arcsin

30.5

4.5

' 8E

φSt ' arcsin

30.5

4.5

' 6E

φSp ' arcsin

45.7

When the ship surges forward, the two stern lines and a spring line provide restoring forces.

Similarly, when the surge is in reverse, two head lines and a spring line provide the restoring forces.

The effective spring constant is calculated both ways and averaged from Equation II-7-28

' 122,600 % 44,100 ' 166,700 N/m

' 120,700 % 44,100 ' 164,800 N/m

166,700 % 164,800

' 165,750 N/m

2

Finally, the natural period in surge is calculated from Equation II-7-26

64,239,200

' 124 sec

165,750

If the rope had been new, the percent elongation would have been higher at 10.7 percent. This would

have resulted in a slightly higher surge natural period of approximately 136 sec.

Harbor Hydrodynamics

II-7-69

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