Question 3.5: A vessel has a weight of 40 × 10^6 N and a moment of inertia......
A vessel has a weight of 40 × 10^{6} N and a moment of inertia of 55 × 10^{6} kg m². It is possible to construct the vessel in different ways so that its metacentric height is 2.0 m, 1.0 m, 0.5 m or 0.25 m. Assuming that the weight and moment of inertia remain unchanged, what is the roll period for each of the metacentric heights?
Using equation (3.5):
t = 2 \pi \sqrt{\frac{I_{M}}{W \times GM} } (3.5)
If GM = 2.0 m then t = 2 \pi ( 55 \times {10^{6}}/{40} \times 10^{6} \times 2.0)^{{1}/{2}} = 5.2 s
If GM = 1.0 m then t = 2 \pi ( 55 \times {10^{6}}/{40} \times 10^{6} \times 1.0)^{{1}/{2}} = 7.4 s
If GM = 0.5 m then t = 2 \pi ( 55 \times {10^{6}}/{40} \times 10^{6} \times 0.5)^{{1}/{2}} = 10.4 s
If GM = 0.25 m then t = 2 \pi ( 55 \times {10^{6}}/{40} \times 10^{6} \times 0.25)^{{1}/{2}} = 14.7 s