Ship Construction and Stability
Ship construction and stability questions test your grasp of transverse stability, free surface effect, load distribution and hull stresses, and your ability to calculate a simple GM from a load condition.
Transverse stability
The metacentric height is GM = KM − KG. A positive GM means the ship is initially stable; a negative GM produces an angle of loll. The GZ curve gives righting lever at each angle; the area under the curve represents dynamic stability. Angle of vanishing stability is where GZ becomes zero. Damage stability depends on subdivision, permeability and cross-flooding arrangements.
Free surface effect
A slack tank moves the centre of gravity and reduces GM. The free surface correction is FSC = i × ρ_liquid / (ρ_water × displacement), where i is the second moment of area of the free surface about its centreline: i = length × breadth³ / 12. Because breadth is cubed, longitudinal subdivision is the most effective way to reduce FSC.
Load distribution and stress
Shearing force and bending moment vary along the hull. Hogging is excessive buoyancy amidships or excessive weight at the ends; sagging is excessive weight amidships or excessive buoyancy at the ends. Heavy cargo at the ends increases hogging stress; heavy cargo amidships increases sagging stress. Torsion matters in container ships with wide hatches.
Worked example: GM with free surface
A vessel displaces 8,000 t, KM 7.2 m and KG 6.4 m. A rectangular tank 12 m fore-and-aft by 8 m athwartships by 3 m deep is slack with seawater of the same density as the sea. Calculate GM.
Solid GM = 7.2 − 6.4 = 0.8 m. The free surface inertia is i = 12 × 8³ / 12 = 512 m⁴. FSC = 512 / 8,000 = 0.064 m. Fluid GM = 0.8 − 0.064 = 0.736 m. The ship remains stable, but the reduction is significant for a small tank because the athwartship breadth is cubed.
Traps
- Forgetting that free surface always reduces GM.
- Using the tank length instead of the athwartship breadth in i = l b³ / 12.
- Confusing KG with KM.
- Treating angle of loll as list and filling the high side.
- Ignoring subdivision when assessing free surface.
- Confusing hogging and sagging load patterns.