Question 3.3: A pontoon 15 m long, 7 m wide and 3 m high weighs 700 × 10³ ......
A pontoon 15 m long, 7 m wide and 3 m high weighs 700 × 10³ N unloaded and carries a load of 1600 × 10³ N. The load is placed symmetrically on the pontoon so that its centre of gravity is on the longitudinal centre line at a height of 0.5 m above the deck (3.5 m above the base). The centre of gravity of the pontoon can be assumed to be on the longitudinal centreline at a height of 1.5 m above the base. The pontoon floats in saline water of density 1025 kg/m³. Calculate the metacentric height of the pontoon.
Total weight of pontoon and load = (700 + 1600) × 10³ = 2300 × 10³ N
Volume of sea water displaced, V = total weight/weight density
= 2300 × 10³/(1025 × 9.81) = 228.74 m³
Depth of immersion, h = V/lb = 228.74/(15 × 7) = 2.18 m
Height of centre of buoyancy above base, OB = h/2 = 2.18/2 = 1.09 m
Now determine the height of the centre of gravity above the base, OG, by taking moments about O:
2300 × 10³ × OG = 1600 × 10³ × 3.5 + 700 × 10³ × 1.5
OG = (5600 × 10³ + 1050 × 10³)/2300 × 10³
OG = 2.89 m
BG = OG – OB = 2.89 – 1.09 = 1.80 m
Height of metacentre, M, above B is BM = {I_{WS}}/{V} where I_{WS} = lb³/12 so:
BM = (15 × 7³)/(12 × 228.74)
BM = 1.87 m
Metacentric height GM = BM – BG = 1.87 – 1.80 = 0.07 m
GM is +ve indicating stability but the value of 0.07 m is very small indicating that this is close to the condition of neutral stability, which would be unacceptable (see Self Test Question 3.1)