Homework 4
OCEN 402
1. A bathing raft shown in the figure is made of two lines of oil drums, 8 ft long and 2 ft in diameter, onto which is lashed a wooden platform. A man weighing 120 lbs. standing in the middle of the platform and the waterline (W.L.) passes through the center of drums. The center of gravity (bathing raft + man) is one foot above W.L. Calculate the angle to which the raft heels when the man is standing at the middle of
a.) the long side.
b.) the short side.
(Hint: the inclination angle is small and ft.
2. Find the moment to alter trim one inch for a ship for which the following information is known.
Length, L = 450 ft
Displacement, Δ = 11280 tons
(KG), Zg = 24 ft
683.2 ft (distance from buoyancy center to longitudinal metacenter),
10.8 ft
3. A ship 400 ft long floats at forward draft TF = 16’ and afterward draft TA = 14’. A weight of 100 tons is added at a point 60 ft forward of midship section and a weight of 120 tons is added 70 ft aft of midship section. If the tons per inch immersion is 28.3 and MTI = 520 ft-ton. It is assumed that the center of flotation remains 8 ft aft of midship section. Please find new drafts (mean, forward and afterward).
4. A twin-hulled pontoon has the constant cross-section shown in the figure. With the hulls empty, it floats at a draught of 6 in. in fresh water.
If each hull is filled with water to a depth of 6 in. calculate the
a.) neglecting free surface,
b.) allowing for free surface,
at an angle of heel of 45˚.
5. A ship has a designed displacement Δ = 10,000 ton. With an assumed vertical position of CG, Zg = 20 ft, its transverse metacenter height = 2.5 ft, and the righting arm value read from a set of cross curves (at Δ = 10,000 tons) are as below:
10˚ / 20˚ / 30˚ / 40˚ / 50˚ / 60˚ / 70˚(ft) / 0.4 / 1.0 / 1.55 / 1.75 / 1.45 / 0.75 / -0.2
Please plot the static stability curve for Δ = 10,000 ton.
If later, the vertical position of C.G. is found to be = 20.5 ft instead of Zg = 20 ft, please compute and again, and plot the modified static stability curve.