Hydrostatics and Stability
Core relationships
Hydrostatics fixes the displacement and the underwater geometry; stability uses those particulars to locate the centre of buoyancy B, the metacentre M and the centre of gravity G. At a given waterline, displacement Δ = ρ∇, TPC = A_w ρ/100 (t/cm with A_w in m² and ρ in t/m³), and MCT = Δ·GM_L/(100L). The transverse metacentric radius is BM = I_T/∇, so KM = KB + BM and GM = KM − KG. Slack liquid in a partly filled tank raises the effective KG by a free surface correction FSC = Σ(ρ_i i_i)/(ρ∇); it never alters the ship's real KG but always reduces effective GM.
What questions test
Candidates must keep KB, BM, KM, KG and GM distinct, and know that weight added below G raises GM while weight added above G lowers it. Check whether dimensions are moulded or extreme, and whether a tank is full (no free surface) or slack. At large angles initial GM is insufficient: use the GZ curve, the wall-sided expression GZ = sinθ(GM + ½BM tan²θ), the angle of vanishing stability and the area under the curve. Density changes matter as well - moving from salt to fresh water increases draft and alters TPC and GM.
Worked example
A box barge 60 m × 12 m × 4 m draft floats at KG = 2.0 m. ∇ = 60 × 12 × 4 = 2880 m³; I_T = 60 × 12³/12 = 8640 m⁴; BM = 8640/2880 = 3.0 m; KB = 2.0 m; KM = 5.0 m; GM = 5.0 − 2.0 = 3.0 m. Rule of thumb: for a box, BM ≈ B²/(12T).