The center of gravity and the center of buoyancy are both theoretical points in an object. Both these points are often used to represent individual bodies or different parts of the same body in different states of matter, in our case of floating bodies, and are used to study how the forces act on the bodies and how they relate to each other.
The two terms are most commonly found in relation to the stability aspects of floating bodies. The balance between the two determines if a body is in stable or unstable conditions.
The center of gravity (COG) of any object can be defined as the theoretical point at which the object’s total weight is assumed to be concentrated due to the presence of gravitational forces. The direction of this force acts downwards and its location totally depends on how the weights are arranged. If you could balance the boat on a certain point, this would be the point where it balances, similar to the center of a seesaw we see in playgrounds.
The center of buoyancy (COB) can be defined as the theoretical center of the immersed part of an object where the upward buoyant forces act on. It is the center of the underwater volume of an object.
Effects of the center of gravity and center of buoyancy on floating objects
Before we get into how the center of gravity and buoyancy effects a vessel, let’s learn about an additional term that plays a huge role in correlating both the forces called metacenter.
What is the metacenter?
The metacenter is a theoretical point at some height above the center of gravity measured from the keel of the vessel. To make it easier, relating the vessel to a pendulum, is the point about which the pendulum swings can be considered as the metacenter.
Technically it can be defined as the point obtained by drawing an imaginary line vertically through the center of buoyancy and the center of gravity, then heeling the vessel to a few degrees and again drawing an imaginary vertical line through the new center of buoyancy along the center of gravity, the point at which these two imaginary lines meet is called as the metacenter and the height from the center of gravity to the metacenter is called as the metacentric height (GM).
As the vessel heels, the underwater area changes which correspondingly changes the underwater volume and the center of buoyancy moves from its initial location to a new one. The center of buoyancy is no longer under the center of gravity, and the vessel is in an unstable or heeled condition. The vessel can be brought back to its stable upright condition by shifting weights on board.
The Righting lever and its relation to COG and COB
If you measure the distance the COB moves from its initial location, and subtract the distance the COG moves from its initial position, the difference is called the righting lever. The bigger the value of righting lever the better chances the vessel comes back to its initial condition.
Metacentric Height and its relation to COG and COB
If the metacentric height GM is much higher than the COG and COB, then you have a stiff and stable vessel that easily stays upright but a vessel with a higher GM will be tougher to maneuver. As the value of GM gets smaller the vessel becomes less stable and it tends to roll more easily.
If GM is negative, that is, below the center of gravity then the boat is unstable and leans to either the port or starboard side. The side it leans on depends on the weight distribution of the vessel. Most vessels have a design threshold up to 30 degrees to which they can roll after which it comes back to their initial position.
When a vessel heels the underwater volume changes, and say for example if the vessel has a flare, which is, the upper side plating angled outward at an angle to deflect water, typically found on fishing vessels, it again becomes more stable, because the center of buoyancy moves outward towards the way the boat is leaning. But the center of gravity remains unchanged. GM changes and becomes positive and the boat becomes stable, but with an angle of heel.
The flare adds additional volume to the compartments above the waterline. This is what is called reserve buoyancy, the ability of a vessel to regain its initial stability as it leans over and has more resistance to leaning farther with the help of enclosed spaces above the water line such as water-tight compartments.
Methods to alter the COG
The traditional method of adding weights causes the vessel to sink down a little deeper and can move the center of buoyancy slightly upward and the center of gravity slightly downward which makes GM a little higher.
If weight is added at the same location as the COG or if more weight is added without any calculations the COG can go below the value of COB and bring out negative effects making the GM smaller.
If cargo or persons are added on board the value of COG goes up significantly higher and which slightly raises the center of buoyancy, reducing the GM and maybe even making it more negative causing the boat to heel even more until it heels to a point where the center of buoyancy shifts farther outwards than the COG and the boat starts to gain righting moment; the tendency to come back to its initial position right itself.
This assumes the person or cargo is placed on the center line and doesn’t shift its position. If they move toward either port or starboard side, the COG moves that way too and the boat heels more and the COB shifts outwards as well. However, if the COG shifts more outwards than the COB, then the boat rolls over.
During the design stage, it is easy to find solutions to meet the required stability criteria. Some design considerations like providing a shallower deadrise angle, having a wider hull, and so on can be allotted for smaller vessels which can improve the stability characteristics
But how do you fix an existing boat? The best solution is not to add weight and redistribute the weights on board so that the weight is distributed in a way to lowers the center of gravity. And for existing larger vessels install passive stabilization devices such as bilge keels and so on.
How COG varies during a voyage
During a voyage, a vessel normally starts off with fully loaded fuel. During the voyage, the level of fuel comes down which has a direct effect on the values of the center of gravity. As the amount of fuel in a tank starts decreasing, the overall weight also comes down which moves the center of gravity upwards and the value of GM becomes smaller. The boat tends to be lighter and less stable.
A good way to remember this is if you add weight the COG moves in the direction of the added weight and the COB moves up. So, if you put the weights in the lower decks, to lower the COG then the metacentric height is lower and the boat is less stable.
If you reduce the weight, the COG moves away from where the weights were taken, so if the weights were taken from the deck the COG moves down and the COB moves down. (Less weight, less immersed hull, less buoyancy, lower COB.). This may increase the value of GM.
In smaller vessels, such as powerboats we should also think about the waterline with respect to the chines. If the water line is above the chine, the width of the boat at the waterline is not significantly reduced even if weight is offloaded from the boat.
But if the waterline is below the chines, subsequent weight reductions from the vessel can lead to shallower drafts which can significantly reduce the width of the boat. That reduction in beam correspondingly reduces the righting moment, making the vessel more prone to rolling and less stable.