HEELING EXPERIMENT 509

*

But 0 M = G GI cot 6, and by substituting Equation ( I ) for G Gl we
get G M = cot 6, which is the general equation to find the initial

GM

The information may be written in 'the form of a question. Given
ship's displacement during the inclining experiment 2000 tons; weight of
10 tons moved transversely across the deck 20 feet; length of plumb
line 20 feet; deflection of plumb bob 12 inches. Required the G M —

_ . - , . d X w 240 ins, X 10 tons X 240 ins. rt

Equation: — G M = — — - cot 0= - - - — - =24 ins
* W 2000 tons X 12 ins.

The metacentric height is 2 feet.

This brief description indicates in general terms the principle of the
inclining experiment, but various adjustments have to be made before
the G M corresponding to the actual light condition of the ship can be
ascertained, because the experiment only determines the G M for the
particular condition of the ship at the time, and the effect of additional
weights on board and of those yet to come Jiave to be allowed for.

Example. — In a vessel of 4000 tons displacement it was found
desirable to lower the existing centre of gravity which was 18 feet above
the keel. A tank was filled with 300 tons of water, its centre of
gravity being 2 feet above the keel. Required the new vertical centre
of gravity.

Where G G: is the shift of 0
w the weight of water in the tank, 300 tons
d the vertical distance between the centres of gravity of ship and
tank
W the displacement after the tank is filled
., „ 300 tons x 16 feet , , .
G <£,= - -- - =1*1 feet
1 4300 tons
The new V.C.G. is 18—1-1=16-9 feet above keel.
GRAPHS.
Various graphs and curves are used by ship designers by which
irregular areas, positions of centres of gravity and of buoyancy and
other variable elements may be co-ordinated. It is the business of the
shipbuilder to ascertain from the plans of the ship the information