simbrooks:
Actually there is one thing we are missing from this mechanical analysis.
There's actually a lot missing. I simplified this down to Sophomore Year "Statics".
...resistance of the water to the rotating motion, although water cant hold a shear force, there is friction/resistance of sorts - we feel it every time we move due to the viscosity of the water.
True, but that mostly just determines how long it takes for the 'face down' rotation to occur, not "if" it will occur. The buoyancy and gravity forces are acting constantly, so they require an equally constant force to counteract them for the simpler "Steady State" situation.
There is also the effect of creating a lever arm if you were turning over from things that were in line with the COG (fulcrum about which you are creating a moment couple), thus the weight belt worn on the waist becomes a factor and helps to form a righting action/moment as well.
Don't use a more complex model when a simpler one will do
Cranking up the model's refinement, we can ignore the location of the weightbelt if we assume that the diver and the rest of his negatively buoyant widgets is a rigid system: he can be reduced to a point mass. However, you are on track to the very important recognition that our "weight" and "buoyancy" values are acting along the local gravity vector, which means that our moment arms lengths are the value of the perpendicular (horizontal) distances between them and that this will change as the system is rotated. This has three implications:
First, at "some rotation", the CB (Center of Buoyancy) will be directly above the CG, so the Moment Arm magnitude is zero, so there will be no rotating torque: this is as stable as a hot air balloon above the whicker basket. Coincidentally, this also happens to be the general configuration of a Back Inflate BC, which means that arguements that it is an easier configuration to dive are generally true...at least for that portion of your dive where you're horizontal. While this may be more comfortable during a dive, it does not necessarily mean that its more comfortable --or safer-- when vertical on the surface after the dive.
Second, since the "diver horizontal" and the "diver vertical" orientations are perpendicular to each other, the theoretically ideal system is the one with the greatest insensitivity to orientation change, which means that the distance between the CB and CG has been minimized for _all_ possible rotations. This infers that the Jacket is the more desirable design solution, although we do also have the option of moving around ballast, so we can also shift around the CG too, some. This helps to define our trade-off's.
Third, astute engineers will point out that there's a "second rotation", 180 degrees from the first, where there is also no rotating torque because of CB-CG vertical allignment. While technically true, this is also a point of dynamic stability because the mass is located directly above the buoyancy! Try diving with a horsecollar to get a feel for the effect, preferably a deep coldwater dive in a wetsuit so as to get enough compression to need to pump up the HC.
Obviously in RR's example his total weight is about the same in all 3 conditions, not sure if the location/lever arms differ greatly, ie if the weight is placed at the back or front of the belt. In the case of the options presented i would think the steel tank or 9# BP would give the best option above and UW, i am guessing your trim is more out with a 10# weight belt.
Yes, but if this is a diver on vacation somehwhere, the Hotel Resort is going to have AL80's, not Steels, so that option's not available. Similarly, a weighted BP may "have to be" be left at home in order to be able to carry UW photo equipment within the airline's allowed weight budget, although replacing it with 10# in the small of the back will result in a relatively small net change. Both are YMMV's in the trade-space.
-hh