Stability Of Ships..Quick Notes!

Stability Of Ships..Quick Notes!

Ships' s are not stationary at all, the only time they are, its when in dry dock.
It is considered that all the weight of the vessel acts along the Centre of Gravity, i.e, CG.
The CG acts downwards and CB (centre of buoyancy) acts upwards.

When the ship is inclined by any external force then it makes an angle theeta.
CG remains at same position, CB moves to CB1.
This gives birth to GZ.
delta x GZ = rightening moment (tends to upright the ship)
Thus we conclude,
GZ=GM x sin(theeta)

From above figure, we find that, KM=KB+BM

In the figure above,
KG = height of the centre of gravity above the keel
KB = height of centre of buoyancy above keel
KM = height of metacentre above the keel
GM = Metacentric Height
GZ = Rightening Lever (this lever is responsible to get the ship back to initial position)

It is interesting to know that when,
GM is small -> Rightening Lever is small -> Tender Ship -> Easy Rolling -> Comfortable
GM is large -> Large rightening lever resists roll -> Stiff Ship -> Difficult Rolling -> Uncomfortable

Also remember,
If G lies below M, then vessel is said to be stable.
Ig G lies above M, this state is reffered to as Negative metacentric height and the vessel tends to capsize.

Condition Of Neutral Equilibrium,

This condition arises when,
Points G and M( KM=KG), coincide.
Here, ship is neither stable nor unstable.
Increase in G, will make ship unstable and lead to capsize.
Decrease in G, will make the vessel stable.

How to find KM

Finding metacentric height, using the formula

KM= KB+BM

For BM,

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