An unstable ship has a negative GM (the centre of gravity is above the metacentre), so it heels to a large angle. It can be made stable by:

• Lowering the centre of gravity: add weight low (ballast in the double bottom), remove top weight (deck cargo, high tanks), or transfer weight from high to low positions.
• Increasing the metacentric height: increase the waterplane area and beam (BM increases with the cube of beam), e.g. by increasing beam (rare) or by improving the waterplane; more practically, increase GM by lowering KG.
• Removing free-surface effects: press up or empty tanks to eliminate the free-surface loss of GM.
• Adding buoyancy high or increasing freeboard/reserve buoyancy to increase the range of stability and the righting levers.
• Reducing the height of the centre of gravity by discharging high weights or by flooding low tanks (carefully, as this also increases displacement).
• In an emergency, jettisoning top weight or transferring ballast to the double bottom to lower KG and restore positive GM.

The most effective and common method is to lower KG (add low ballast, remove top weight) and to eliminate free surfaces.

A mass of 25 t is shifted 15 m transversely across the deck of a ship of 8,000 t displacement, causing a deflection of 20 cm in a plumb line 4 m long. KM = 7.5 m.

The plumb line deflection gives the angle of heel: tan(theta) = 0.20/4 = 0.05, so theta = 2.86 deg.

The transverse shift of the centre of gravity: GG' = w x d / Delta = 25 x 15/8000 = 0.046875 m.

At equilibrium the centre of gravity is over the centre of buoyancy, so tan(theta) = GG'/GM.

GM = GG'/tan(theta) = 0.046875/0.05 = 0.9375 m.

KG = KM - GM = 7.5 - 0.9375 = 6.5625 m.

Answer: KG = 6.56 m.