"Buoyancy and trim" stability: physics principles behind it

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Roberto Inzerillo

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Location
Palermo - Italy
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Does anybody know of any (more or less) detailed source about this topic? I'm searching for any kind of related articles, but it has to be something that discusses the issue with a physics/mathematical approach.

Just to be clear, I'm not looking for vague statements like "to correct your trim you move your weights around and see what happens".

I'm particularly interested in the stability of equilibrium, how to achieve/maintain/correct it while diving, by means of proper weight placement, BPW/Jacket/Side configs, breathing, body positioning and what not.

And I'd really like to see/study proper free body diagrams with close to reality forces and moments ;-)
 
Would I be wrong to say that in a dynamic environment there will be no equilibrium?

...and that moving weights to their optimal placement usually does the trick, giving a 'best fit' solution that the diver then manages through the changing buoyancy and trim of a dive, but without moving those weights.

Also practice, since it gets easier with experience. I recall watching my instructors and they made diving look effortless. I certainly didn't.
 
I think the key here is to understand that there are two separate forces forces in play, which are pointing in opposite directions: gravity is pulling you down toward the bottom, and buoyancy is pushing you up toward the surface. Every little bit of your body + your exposure gear + your rig, and anything else you're carrying has its own pair of forces, and you could diagram each of these with a little up vector for buoyancy and a little down vector for gravity.

Newton's second law tells us that we can sum up each of those little vectors into one single up vector for buoyancy, and one single down vector for gravity. If the height of the vectors are equal, then they will cancel out, and Newton's first law tells us that the diver won't move up or down. We say that the diver is "neutrally buoyant." In other words, if we are just as buoyant as we are heavy, then we won't move up or down. To achieve that, we can use our lung volume, and if that's not enough, we can inflate / deflate our BCD. Because we're always breathing in and out every few seconds, the buoyancy vector will always be slightly oscillating over time, so when we say that a diver "isn't moving" in the water column, what we really mean is that they aren't moving very much.

The buoyancy vector will be located at the diver's center of buoyancy, which is the center of the volume of water which they are displacing. The gravity vector will be located at the diver's center of mass.

Consider an object of uniform density -- anything made of a single material, like a block of lead or an empty water bottle. Since the mass is uniformly distributed, the center of buoyancy and the center of gravity will be in the same place. But consider an object of heterogeneous density, say a 1kg/2lb block of lead attached to a typical 1 liter empty plastic water bottle (empty meaning, full of air with the lid closed). The center of buoyancy will be somewhere inside the water bottle, since it is displacing most of the water, but the center of gravity will be very close to the middle of the lead block, since the water bottle weighs so little.

If the buoyancy vector and the gravity vector are in a vertical line, then the diver will have a tendency not to rotate around. In physical terms, this is known as stability; in diving terms, we can say that the have achieved good trim. If you drop lead-block-attached-to-bottle in the water, no matter what the orientation you drop it with, it will rotate until the lead block is on the bottom. That's because it is the orientation where the two vectors line up vertically, so is the only stable orientation.

Human divers are much like the lead-block-water-bottle system, only with a lot more complexity, since we are made out of so many materials (flesh, plastic, metal, breathing gas, exposure gear, lead ballast, etc etc). But the principle is the same: If the buoyancy vector and the gravity vector are in a vertical line, then the diver's trim will be stable, so they will not have a tendency to rotate out of trim. Taking as a given some particular exposure gear, there's not much a diver can do to easily manage the location of their buoyancy vector*. That's exactly why we like having small, movable pieces of ballast, so that we can leave the buoyancy vector alone, and just make small changes to the gravity vector's location, which is what we do when we move lead around (swapping to heavier or lighter fins has a similar effect).

* If you have a drysuit with enough gas in it, you can intentionally move the air bubble around to change your buoyancy vector. Personally, I find this to be more of a hindrance than a help, so I like to dive with less gas in my suit than that, but some other divers have told me that they do find this useful. Also, you can make small changes to your center of buoyancy by repositioning your arms. If you raise them up like you're trying to catch a baseball, you'll move the buoyancy vector headward, and vice versa if you put your arms down near your hips. You'll also find that if you have perfect trim with your legs in some position (say, thighs in line with torso, and knees bent 90 degrees), then changing the leg position (say, straightening your knee), will throw things off. That's because you are moving both vectors, but not by the same amount. For me, straightening my knees will make me tend rotate to a feet-up position, for others it may do the opposite.

Hope this helps, best of luck.
 
I think the key here is to understand that there are two separate forces forces in play, which are pointing in opposite directions: gravity is pulling you down toward the bottom, and buoyancy is pushing you up toward the surface. Every little bit of your body + your exposure gear + your rig, and anything else you're carrying has its own pair of forces, and you could diagram each of these with a little up vector for buoyancy and a little down vector for gravity.

Newton's second law tells us that we can sum up each of those little vectors into one single up vector for buoyancy, and one single down vector for gravity. If the height of the vectors are equal, then they will cancel out, and Newton's first law tells us that the diver won't move up or down. We say that the diver is "neutrally buoyant." In other words, if we are just as buoyant as we are heavy, then we won't move up or down. To achieve that, we can use our lung volume, and if that's not enough, we can inflate deflate our BCD. Because we're always breathing in and out every few seconds, the buoyancy vector will always be slightly oscillating over time, so when we say that a diver "isn't moving" in the water column, what we really mean is that they aren't moving very much.

The buoyancy vector will be located at the diver's center of buoyancy, which is the center of the volume of water which they are displacing. The gravity vector will be located at the diver's center of mass.

Consider an object of uniform density -- anything made of a single material, like a block of lead or an empty water bottle. Since the mass is uniformly distributed, the center of buoyancy and the center of gravity will be in the same place. But consider an object of heterogeneous density, say a 1kg/2lb block of lead attached to a typical 1 liter empty plastic water bottle (empty meaning, full of air with the lid closed). The center of buoyancy will be somewhere inside the water bottle, since it is displacing most of the water, but the center of gravity will be very close to the middle of the lead block, since the water bottle weighs so little.

If the buoyancy vector and the gravity vector are in a vertical line, then the diver will have a tendency not to rotate around. In physical terms, this is known as stability; in diving terms, we can say that the have achieved good trim. If you drop lead-block-attached-to-bottle in the water, no matter what the orientation you drop it with, it will rotate until the lead block is on the bottom. That's because it is the orientation where the two vectors line up vertically, so is the only stable orientation.

Human divers are much like the lead-block-water-bottle system, only with a lot more complexity, since we are made out of so many materials (flesh, plastic, metal, breathing gas, exposure gear, lead ballast, etc etc). But the principle is the same: If the buoyancy vector and the gravity vector are in a vertical line, then the diver's trim will be stable, so they will not have a tendency to rotate out of trim. Taking as a given some particular exposure gear, there's not much a diver can do to easily manage the location of their buoyancy vector*. That's exactly why we like having small, movable pieces of ballast, so that we can leave the buoyancy vector alone, and just make small changes to the gravity vector's location, which is what we do when we move lead around (swapping to heavier or lighter fins has a similar effect).

* If you have a drysuit with enough gas in it, you can intentionally move the air bubble around to change your buoyancy vector. Personally, I find this to be more of a hindrance than a help, so I like to dive with less gas in my suit than that, but some other divers have told me that they do find this useful. Also, you can make small changes to your center of buoyancy by repositioning your arms. If you raise them up like you're trying to catch a baseball, you'll move the buoyancy vector headward, and vice versa if you put your arms down near your hips. You'll also find that if you have perfect trim with your legs in some position (say, thighs in line with torso, and knees bent 90 degrees), then changing the leg position (say, straightening your knee), will throw things off. That's because you are moving both vectors, but not by the same amount. For me, straightening my knees will make me tend rotate to a feet-up position, for others it may do the opposite.

Hope this helps, best of luck.
That's what I was looking for!!! Very nice indeed! And so well explained. It's been a pleasure reading your post. Respect!!

Much of it I've already understood by myself but you added a few precious details here and there that made my day. I appreciate it soooo much. That's food for thoughts.
 
Anyway ... still looking for more. I'm still even more interested in the stability of it all. And yes, there is something called Dynamic Stability ;-)
 
https://www.shearwater.com/products/teric/

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