Center of Buoyancy and Center of Gravity

name         Touqeer
status       other
grade        other
location     N/A

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?
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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.
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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
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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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