Center of Gravity plays a significant role in the ship's stability.Adding or moving masses from one point to another in any direction will affect the position of center of gravity .
How Center of gravity Changes due to adding weights (Loading)
If we add a mass to the ship's FWD starboard side, the center of gravity will get shifted to the direction of the mass added ie center of gravity will change to longitudinal, transverse and vertical directions.
Consider the mass of the ship as 'm' , center of gravity as ' G' and the distance of center of center of gravity from keel as ' h'. Add a mass of 'm1' to the ship . its Center of gravity G1 distance( shifts) from keel to center of gravity h1 respectively.
We know, moment Of the whole system(Added weight+ship weight) about the keel is equal to the moment of the individual masses about the keel.
ie, Mh2=mh+m1h1
Here M=m+m1(mass of ship+mass of added weight)
h2= New Distance of center of gravity from keel
h2=(mh+m1h1)/(m+m1) --------------------------I
Shift/change in center of gravity GG2=distance of new center of gravity from keel(H) -- Distance of old center of gravity of the ship from keel (h)
= h2-h
= (mh+m1h1)/(m+m1) - h
=(m1h1-m1h)/(m+m1)
=m1(h1-h)/m+m1
h1-h= distance between the CG if weight added or removed
we can say that,
Shift/change in center of gravity GG2 = mass added X distance between the CG weight added or removed/ Total mass
How Center of gravity Changes due to Shifting of weights.
Consider the same mass moving to a new position as shown in the fig below. The new distance to the center of gravity (G3) of moving mass from keel is h3 and the distance by which the weight is shifted 'd'.
Distance of Center of gravity from
keel due to change in weight =(m1h3+mh)/(m1+m)
Change in center of gravity ie G2G4 = h2-(m1h3+mh)/(m1+m)
= (mh+m1h1)/(m+m1)-(m1h3+mh)/(m1+m)---- from equ I
=(m1h1-m1h3)/(m1+m)
=m1(h1-h3)/m1+m
h1-h3 = d is the distance by which the weight is shifted.
Therefore Shift in center of gravity = m1d/m1+m
Suspended Weights
>When a weight is SUSPENDED, its CG is considered to be at the POINT OF SUSPENSION.
Important Points to remember
The CG of a ship moves TOWARDS the CG of weight ADDED .
The CG of a ship moves AWAY from the CG of any weight DISCHARGED.
The CG of a ship will move PARALLEL to the shift of the CG of any weight MOVED within the ship.
The shift of the CG of the ship in each case is given by the following formula:
GG1 = w x d/W
where w = weight added, removed or shifted.
W = total mass of the ship
d = distance between the CG if weight added or removed, or the distance by which the weight is shifted.