Free surface effect
When a tank is partially filled, the liquid’s centre of gravity position will change as the ship is inclined. Liquid in partially filled tank always decreases the initial metacentric height GM, righting lever GZ, and angle of vanishing stability.
A partially filled tank is know as a “slack tank”. The reduction of stability caused by the liquids in slack tanks is known as free-surface effect. This adverse effect on the stability is referred to as a “loss in GM” or as a “virtual rise in vertical centre of gravity KG” and is calculated as follows:
Loss in GM due to free surface effects (in metres) = Free surface moment (tones metres) x Specific gravity of liquid in tank/Displacement of vessel in tonnes
The free-surface effect can endanger the ship or even lead to a negative metacentric height. Therefore the number of partially filled tanks should be kept to a minimum. When ballasting the vessel, only one transverse pair or a single centerline ballast tank should be filled up. At sea, as far as possible, ballast tanks shall be 100% full or empty. When ballasted, wide double bottom tanks must be always 100% full.