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Name: Toqueer
Status: Other
Grade: Other
Location: N/A
Country: United States
Date: June 2006


Question:
If the center of buoyancy is below to center of gravity the body will tilt. What will happen if the center of buoyancy is above to center of gravity?



Replies:
Hi Toqueer,

If the center of buoyancy is above the center of gravity in a floating object (such as a boat), the boat will be unconditionally stable. When tipped at any angle (short of that which allows water to flow into the boat) the boat will right itself.

But your first statement is not necessarily correct. Nearly all boats have their center of buoyancy BELOW their center of gravity, and are said to be "metastable". What happens is this: As a typical boat tips, more of the hull on one side tips deeper into the water, and the hull on the other side moves out of the water. The result is that the center of buoyancy shifts to the side where more water is displaced. The center of gravity, of course, remains in the same place in the boat since the boat itself has not changed. The upward force concentrated at the center of buoyancy, has shifted laterally away from the center of gravity, and therefore there is a now a torque, equivalent to the buoyancy force multiplied by the distance that the center of buoyancy has shifted laterally away from the center of gravity. This torque is the "righting moment"; that is, the torque that opposes the tipping of the boat. This only works for relatively small tipping angles. If you tip such a boat too far, it becomes unstable and capsizes.

It is very difficult or even impossible to design practical boats or ships to ensure their center of buoyancy is above their center of mass, to ensure unconditional stability. Essentially all boats and ships are therefore designed to be metastable, with their center of buoyancy below their center of gravity. This is why ships stay upright in normal conditions, but can capsize if excessively stormy conditions cause them to tip too far.

Regards,

Bob Wilson.


Hi, Touqeer.

If the center of buoyancy is above the center of gravity then the body is stable. If you tip it, it will tend to right itself. This is because of the torque (also called a moment) created by the weight acting down and the buoyant force acting up. (Such a moment created by two forces is also called a couple.)

In the case you mention, the couple acts to right the body. In the other case, where the center of gravity is above the center of buoyancy, the couple acts to tip the body over.

David Brandt


Dear Touqeer,

Your are right and, I suspect, understand the situation well.

Just to make it perfectly clear, you can compare it to a pendulum. For the usual pendulum, the bob (which contains most of the mass), is below the pivot. In that case, if the bob is pushed slightly to one side, it oscillates back and forth about the equilibrium position. If, on the other hand, the bob is balanced directly above the pivot, a slight push will cause it to rotate all the way to the bottom (and back up again if it is frictionless.)

The center of gravity is close to the bob and the pivot is analogous to the center of buoyancy. In fact, a stable boat (one with the center of buoyancy above the center of gravity) which is tilted slightly will oscillate very much like a pendulum.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University



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