SeaJay once bubbled...
D@mn... Nice picture. You shoulda drawn the ones for my article. 
I do have one issue with it... How did the diver manage to get his center of gravity way down beneath him like that?
This is a common nomenclature confusion/error: the Center of Gravity ("CG") is ofen expressed as a vertical line which extends from the body's Centriod (its proper X, Y, Z center of mass) all the way to the center of the Earth.
So if we assume the orange dot is the diver's centroid, then yes, its is misplaced along the vertical (Y) axis: it should be raised up to be within the diver's body
This does not mean, however, that the orange line that's with the dot is incorrectly located...its pretty close, and close enough for our needs here, since Y axis location isn't relevent to the Overturning Moment (Torque) of the axis of trim (head vs. heels) that's being discussed.
...And when placing the center of buoyancy, did you forget that the BC bladder goes up and behind the diver as well?
For some designs, true...but we could go nitpick the BP/W illustrations the same way.
In any event, its not really that important, because just like the above, such changes in the Y axis are of zero consequence for the axis of trim that's being discussed.
Note: what would make a difference is if making the bag higher results in a shift of the CP horizontally (left or right).
And did you forget that the diver's got lungs?
As a derivative work from
your illustrations, you might be asking the wrong person
In my assessment, the CG & CP locations on Matt's picture are generally correct, particularly since the "with gear" CG has not been moved an appreciable distance from the known "naked body" Centriod location.
Now, if he stops finning... Even if the forces aren't that great, his body will tend to float into a head-up position... So no, he's not properly trimmed.
The problem is that in order to attain perfect trim, the diver has to stop breathing too.
What this all really boils down to is (once again) a Significance Test: is the 'misallignment' really big enough to worry about?
Take a look at the following that I slapped together (BTW, I increased the volume of the BC's bladder for you SeaJay):
http://tinyurl.com/r5nh
The physics of any "trim problem" due to CP-CG mismatch is mathmatically expressed as an Overturning Moment (torque) which is calculated by: Force * Moment Arm
To maintain trim via dynamic control, the diver creates an equal counter-torque...a zero net effect. Hand-waving is one possible way to generate the counter-torque to do this. Finning (swimming) at an angle of attack is another.
Since we have to breathe (and consume our tank's air supply), it is impossible to have a perfect alligment between the CP and CG to prevent the creation of a moment arm.
What it really comes down to is that the only thing we can do are things that make the total Torque Force smaller. Since there's two contributing variables (Force * Distance), there's only two approaches:
- Reduce the Force
- Reduce the Moment Arm (length between CP & CG)
Because the humman body's density is very close to water, the first is mostly an equipment and weighting issue...if you carry less ballast, you need less air in the BC/Wing, which results in a smaller net force.
The second is what this discussion has focused on, but only in the broadest "Product Catagory A vs. Product Catagory B". While some specific designs are good/bad, the reality is that all BC's today have degrees of adjustability, and this makes the claims of profound differences between the general Product Catagories an incorrect generalization.
The proof is in the adjustability found on all systems, as these can and are used to better allign the CP to CG to minimize the Moment Arm's length. Examples of adjustability include shoulder strap length variation (this will raise/lower the entire BC/etc assembly versus the body and change the CP's location realative to the CG), and raising/lowering the primary scuba tank relative to the BC (shifts the CG relative to the CP), or relocation of lead weights on your body and other equipment (cannister lights, etc).
Finally, one last thing to remember here is that even a large number times zero becomes zero...and with two variables, either number can be the one to become zero (or both, even though that's unnecessary).
...And why is that important? Well... A diver who's trim-neutral can truly relax in the water... He doesn't have to waste energy and air working and finning and keeping himself properly situated. Furthermore, when that diver is diving in an environment that's sensitive to excess finning... Say, over a coral bed or over a particularly silty bottom... There's huge advantages to being properly trimmed.
Sure, but common sense also needs to prevail: there's generally no justification to go chasing after the last 1% for the average recreational diver. For example, what is the measurable difference in overall dive performance between swimming along with his fins thrust being perfectly horizontal (0 degrees) versus +/- 1 degree angle of attack?
While we can all agree that novices swimming along at 45 degree angles need a lot of help, basic trigonometry will tell us what the trade-off in thrust is per LBf-FT of trim-maintaining torque.
-hh
