I agree, I'm almost quite over-simplifying, just to make it easy to discuss.
I agree, all that has to do with the equilibrium part only, though, not the stability of it.
I disagree. Let me explain what I mean and please tell me what you think about it.
I'm going to stress the term stable here, I'm trying to deal with the stability of the equilibrium regarding the trim, i.e. only what deals with the rotation.
Granted that I'm talking about a neutrally buoyant config in the first place at all times.
View attachment 618185
Fp=buoyancy force
Fn=weight force
Fp=Fn
Diver starts in an horizontal and steady position.
Case A. Fp is applied on a point on top of the diver. Fn is applied on the bottom. Fp and Fn are aligned (no torque).
Case B. Fp and Fn are still aligned but placed the other way around.
In both cases (A and B) the equilibrium (force and momentum) is granted.
Now, what happens if the diver experiences a change in his trim?
e.g. something, anything, makes him rotate clockwise a bit.
Well, those two forces are not aligned anymore => a moment (do you call it a moment, a torque or what?) is being generated.
In case A, Fp and Fn will generate a counter-clockwise torque which will push the diver back into an horizontal position, hence the starting config A is a trim-stable configuration. The torque resulting from the altered configuration will take the diver back to it's original equilibrium state (and the torque will eventually be zero again) .
In case B, they generate a clockwise torque which will keep pushing the diver away from its initial horizontal position, hence the starting config B is a trim-unstable configuration. The resulting torque will keep pushing the diver away from it's starting equilibrium. Id est to get back to an horizontal state (and counteract this torque) the diver has to actively do something (use fins, exhale, anything ...).
I see what you mean. Taken as a given that the two vectors are vertically aligned, there are two points of equilibrium -- one is stable, and the other is 180 degrees off of it, and is unstable. The point I learned from your diagrams is that you want your center of mass to be as low as possible (low as in, close to your belly), and your center of buoyancy as high as possible (as in, close to your back). So that the stable alignment is face-down, rather than face-up. That makes a great deal of sense to me mathematically, I would be curious to see what @The Chairman and other experienced instructors have to say about it.
Edit to add this paragraph: On second thought, it seems to me that regardless of which vector is above the other, you want the distance between them to be as small as possible. That's because whenever they are out of vertical alignment, the moment / net torque will be proportional to the horizontal distance between the two vectors. The closer they are together, the smaller that torque will be, with the ideal distance being zero. Theoretically, zero distance between these 2 would yield stable trim in all orientations. Since we cannot achieve that, aiming for them to be as close as possible is a good thing, with mass being below buoyancy better than vice versa, so that face-down is stable instead of face-up.
Having your wing on your back as opposed to wrapped around your waist would help to bring your center of buoyancy higher. However I think the thing with the tanks is misleading: it's true that tanks are very heavy, but they are not very negatively buoyant, and some are positively buoyant. @tmassey has a great thread documenting the relative buoyancy of various tanks here. The takeaway there for me is that a typical single tank will be "close" to neutral, full steels are around -8lbs, while empty aluminums are more like +3lbs. So the tank might not be the dominating factor here, compared to your body, your backplate, and your lead for example.
With negative tanks, I can totally see why sidemount would be more stable than backmount. With buoyant tanks, I would guess that the opposite may be true.