Understanding Stability of an Object: CG vs CB & Metacentre

[Urmi Roy]

Hi,

As shown in the attachment, the different situations that occur in an object with 1. the CG above the Centre of buoyancy (CB) and 2. CG below the CB are shown.

A. It is said that the more stable state is when CG is below CB...however, I don't understand this point, since as seen in the figure, in both cases, there is a net moment that seems to tip the boat over.



B. Also, what is the significance of the metacentre?

 

[stewartcs]

Hi,

As shown in the attachment, the different situations that occur in an object with 1. the CG above the Centre of buoyancy (CB) and 2. CG below the CB are shown.

A. It is said that the more stable state is when CG is below CB...however, I don't understand this point, since as seen in the figure, in both cases, there is a net moment that seems to tip the boat over.



B. Also, what is the significance of the metacentre?

Center of Buoyancy (B) below the Center of Gravity (G) doesn't necessarily mean a floating body is stable. As your intuition tells you, it depends on the righting arm (i.e. restoring moment). In the examples you show, the floating body is not stable.

If your floating body has the G directly above the B on a line of action then when the body is perturbed the B moves to a new position such that the righting arm creates a restoring moment. In your examples the new position of B has moved beyond the stability condition (i.e. B is in a position such that it creates an overturning moment).

The Metacenter (M) is significant since a positive GM generally means the floating body is stable.

CS