EM 1110-2-1100 (Part II)
30 Apr 02
Example Problem II-7-7 (Concluded)
Individual stiffness for the head and stern lines is calculated from Equation II-7-29
' 65,900 N/m
kHd ' kSt '
Similarly, the stiffness for individual spring lines is
' 44,500 N/m
The vertical angles from the bow, stern, and spring lines are
φHd ' arcsin
φSt ' arcsin
φSp ' arcsin
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
ktot ' 2 (65,900) sin 70E cos 8E % 44,500 sin 85E cos 6E
' 122,600 % 44,100 ' 166,700 N/m
ktot ' 2 (65,900) sin 70E cos 13E % 44,500 sin 85E cos 6E
' 120,700 % 44,100 ' 164,800 N/m
166,700 % 164,800
' 165,750 N/m
Finally, the natural period in surge is calculated from Equation II-7-26
Ts ' 2 (3.14)
' 124 sec
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.