View Full Version : Re: Center of buoyancy problem

Leonard G. Caillouet
02-01-1995, 08:45 AM
On Wed, 25 Jan 1995, Hinrichs, Rick wrote:

> I have a dilemma that I hope someone out there can help me with.
> W
> |
> CB \|/------x-------|
> Head ___________._____.___________________ Feet
> ^ CM ^
> | |
> |--d--| |
> B R
> In the above FBD, we know W, R, and x. We would like to know d (the
> distance between the CM and CB). Using equations of static
> equilibrium for translation (B=W-R) and rotation (Bd=Rx), we can
> arrive at B and then d (no big deal).
> However, if we move the point of application of the supporting force
> (R) higher up the leg, keeping the body position the same, we
> decrease the distance x. Everything else about the body SHOULD have
> stayed the same, i.e., the same body position in the water, same body
> weight, same buoyant force, and same locations of the CM and CB. To
> satisfy the rotational equilibrium condition, Bd=Rx regardless of the
> value of x. So if x gets smaller then R must increase to produce the
> same torque. However, [AND THIS IS WHERE I AM HAVING PROBLEMS], if R
> gets larger, then the only way to satisfy the translational
> equilibrium condition (B=W-R) is for B to decrease. This doesn't

I think that here (below) is where your evaluation is faulty. You are
correct about the amount of bouyant force not changing. However, when the body
floats differently with the force R applied the center of bouyancy has
moved, so d is what changes. You have assumed that the position of CB is
the same under two diferent rotational conditions.
> make sense, however, because the buoyant force (B) is (by definition)
> the weight of the displaced water which has not changed. If W, B,
> and the locations of CB and CM have not changed, then we have an
> impossible situation. We cannot satisfy both the rotational and
> translational equilibrium equations. CAN ANYONE OUT THERE SEE THE
> NOTE: We have tried this with the body totally submerged and on the
> surface and for different amounts of air in the lungs. We have also
> put supports at two locations (with a strap around the chest as well
> as the ankles) and have come up with the same dilemma; the FBD is
> only slightly more complicated).
The location of CB has to change if the forces creating the rotation of
the body are changed.

Hope this has been a help.

Now can someone tell me why, when composing a reply using PINE, I cannot
post a reply that contains more text from the original message than new
text that I have included?

Leonard G Caillouet
L.S.U. Kinesiology