Appeared in DIVER February 2007

Buoyancy by numbers
The
The test rig in the pool, with

How much difference does a lungful of air make to your buoyancy What about an emptied cylinder, or fresh as opposed to sea water John Liddiard devised a series of experiments to help him answer 10 pressing questions about what exactly you need to put on your weightbelt in different circumstances

AS I TRAVEL AND DIVE, I am constantly faced with different combinations of diving suit and cylinders. These range from the drysuit and rebreather I usually use at home to various thicknesses of wetsuit, steel cylinders from 10 to 15 litres and twin-sets, and aluminium cylinders, both European specification 10.4 litre and the US spec 80, with its floaty reputation.
With all these variables to play with, I need to be systematic about deciding how much lead to strap to my belt. I keep notes in the back of my logbook for each configuration.
When faced with a new combination, I can do some sums on previous records and make a pretty good guess, usually getting it right to within a couple of kilograms.
As long as Im close enough, I can make up for the rest by BC and lungs, then make a minor adjustment to my belt for the next dive. Its a strategy that seems to work - but why does it work What are the numbers behind this approach
To carry out buoyancy-measuring experiments, I needed equipment and helpers. DIR (Doing It Right) diver Steve Murray volunteered as stunt diver. I have always found that DIR divers make great experimental animals.
To help with the measurements I enlisted Stephen Woodward and Emma Yates.
They are divers with PhDs in aerospace engineering and chemistry respectively, so I was confident that I could rely on their handling of the experiment.
The key item of equipment was the digital hanging scale from www.scalesworld.co.uk that we used to weigh airline baggage in the January issue (Packing For Travel). This was hung from a diving board, with a line that fell to just short of the bottom of the pool.
At the bottom of the line, Stephen added weights to keep any buoyant tests under water, and in the middle of the line clipped in our experimental animal (EA) or whatever else we were measuring buoyancy for.
Emma took the measurements, handed kit in and out of the water and checked that the scale was properly zeroed between each measurement.
Having measured everything and validated the initial measurements, the data for cylinders was normalised to a standard 50 bar with a regulator attached, so that we could compare like with like.

Q: HOW MUCH DOES BUOYANCY VARY WHEN BREATHING IN AND OUT

A: An average male at rest will breathe 1 litre in and out, so his buoyancy will vary by 1 kg.
Breathing in and out all the way is known as vital capacity. For an average male this is about 5 litres, which equates to buoyancy adjustment of plus or minus 2.5kg.
Such a big range would not be easy to maintain, and could even carry a risk of burst lung if breathing in all the way during ascent.
The size of lungs obviously varies with size of diver. Even while resting, the buoyancy of our experimental animal varied by 2kg over each breath.
Breathing with almost full or empty lungs, he could adjust his buoyancy by plus or minus 3kg, though he would not be comfortable with this over more than a few breaths.

Q: HOW MUCH WEIGHT SHOULD I ALLOW FOR AN EMPTY CYLINDER

A: A litre of air at sea level at 10C weighs 1.247gm (the cylinders in our experiments came in from the shed on a cold day). Multiply this by the volume and working pressure of a 10-litre cylinder and we have:
10 litres x (232 - 50) bar x 1.247/1000 = 2.27kg
This will be the same for steel or aluminium cylinders, because it is the mass of air inside that causes the variation. The amount of steel or aluminium in the cylinder walls remains constant.
Rather than sticking with theory, we measured the buoyancy changes for a 10-litre Faber steel cylinder and a 10.4 litre Luxfer aluminium cylinder as 2.26kg and 2.21kg respectively.
This was a close enough result to validate the theoretical values.
To generalise, the buoyancy change from full to 50 bar is 0.227kg per litre of cylinder capacity.
For example, a 15-litre cylinder would gain 15 x 0.227 kg = 3.4kg. Twin 12-litre cylinders would gain 2 x 12 x 0.227kg = 5.45kg.
The bigger the cylinder, the more over-weighted you need to be at the start of a dive to end up correctly weighted at the end.

Q: HOW MUCH WEIGHT SHOULD I ALLOW FOR DIFFERENT CYLINDER SIZES

A: Cylinders displace water according to their capacity plus the thickness of the cylinder walls. From this, we can subtract the weight of the walls, and the weight of 50 bar of additional gas carried as we want to adjust our weight for the end of a dive (see Table 1).
For single cylinders, we can assume that the tap, boot and regulator remain constant. What we are interested in is the buoyancy difference:
Buoyancy difference = capacity difference + buoyancy of additional metal - weight difference - weight of 50 bar of additional air.
(Buoyancy of additional metal = weight difference divided by metal relative density)
This also ties in with our experimental data and the numbers in the back of my logbook. Moving from 10 to 15 litres, I leave my weightbelt alone. For a 12-litre cylinder I might add 1kg. Larger adjustments are needed only for older-specification cylinders with thick walls.

Q: JUST HOW FLOATY ARE ALUMINIUM CYLINDERS

A: For this experiment we measured the difference in buoyancy between a 10-litre steel and a European specification 10.4-litre Luxfer aluminium cylinder as 1.79kg. Again, this ties in with the rule of thumb in my logbook to add 2kg.
For the well-travelled US-specification aluminium cylinder, a similar calculation to those above, combining theoretical and experimental data, gives a difference from a steel 10 of 3.5kg, provided that all other equipment is the same. The back of my logbook tells me to add 3-4kg.

Q: HOW DOES MOVING TO A TWIN-SET AFFECT BUOYANCY

A: We measured the buoyancy of a single 10-litre steel cylinder as -1.83kg with regulator attached. The simplest form of twin-set, just adding a second cylinder and regulator, with no manifold, would therefore give a 1.83kg buoyancy difference or, as my logbook suggests, remove 2kg from the weightbelt.
With crossover tap and steel bands, by moving from a single 10-litre steel to ever-popular manifolded twin 12s a diver will need to remove about 6kg from his belt, or a few kilos more if moving from a plastic cam-back to a stainless-steel backplate.
Most large aluminium cylinders, with regulator attached, are only just negatively buoyant, so twinning them up makes next to no difference to buoyancy. You could have as many aluminium cylinders as you like at 50bar and still not need to adjust your weightbelt.
This is one of the reasons for many technical divers liking to use aluminium cylinders for side-mounts.

Q: HOW DO PONY AND STAGE CYLINDERS AFFECT BUOYANCY

A: Pony and stage cylinders are carried in addition to existing kit, rather than instead of it. So what we are interested in is how adding such a cylinder, with regulator, will change the overall buoyancy of a diver.
There are no theoretical values this time, just the experimental values measured in the pool, for cylinders with a regulator attached (see Chart 1).
If a pony is going to be permanently attached - back-mounted, for example - weight can be taken off the divers belt.
If, on the other hand, a stage cylinder is going to be side-mounted, perhaps it will be left somewhere and collected later. In this case, removing weight from the belt may not be such a practical course of action, because removing the cylinder could leave the diver positively buoyant.
Referring to my logbook again, my notes tell me to remove 2kg for a steel pony and 1kg for an aluminium pony.

Q: WHAT IS THE BUOYANCY DIFFERENCE BETWEEN SALT AND FRESH WATER

A: Sea water is about 3.5% denser than fresh water. I admit that there are minor mathematical inaccuracies in using
a conversion factor of 3.5% in both directions, but anyone who knows enough to catch me on this will also know enough to realise that the error involved is so small as to be irrelevant.
Buoyancy difference = displacement x relative density
Displacement is the entire displacement of the diver with all equipment that counts, not just the amount of weight on his belt. A very rough estimate is the sum of the weight of the diver, the displacement of the cylinder, the buoyancy of the cylinder and the weight-belt needed for neutral buoyancy (see Table 2).
This ties in with what most experienced divers already know.
When moving from salt to fresh water, we remove one or two weights from our belts.

Q: DO I NEED EXTRA WEIGHT IN THE RED SEA

A: Salt water varies between being 3.2% and 3.8% denser than fresh water. The higher density is generally found in enclosed areas of sea with a hot climate and low rainfall. The surface water evaporates, leaving its salt content behind, resulting in increased salinity
for the remaining water.
The highest-salinity sea water is in the eastern Mediterranean and the Red Sea. Barring a few areas of river estuaries, the lowest salinity is found in the Arctic and Antarctic.
In the worst case, a diver going from the weakest- (Arctic) to the highest-salinity sea water (Red Sea) will experience a buoyancy change of 0.6%, all other factors being equal.
For our two divers in the previous example, this would give a buoyancy difference of between 0.48kg and 0.64kg.
Divers complaining of high buoyancy in the Red Sea compared to what they are used to in the English Channel are more likely to be experiencing floating aluminium cylinders than any noticeable difference in water density.

Q: HOW MUCH DOES BUOYANCY VARY WITH WETSUIT THICKNESS

A: Every diver is different, so while we cant tell you exactly how much weight to wear, we could measure the buoyancy of different types of wetsuit. All the suits we tested came from my kit cupboard, so smaller divers can expect to have less neoprene in their suits and so less buoyancy. Larger divers will need more neoprene.
We can use these numbers as a guide to how much weight to add or remove for different wetsuits. For example, when moving between 3 and 5mm suits, add 2kg. From 5mm to a 7mm suit with vest and hood, add 6kg (see Chart 2).

Q: HOW MUCH BUOYANCY DO I LOSE IF A DRYSUIT FLOODS

A: We unzipped the drysuit of our experimental animal, shook him about until his suit was fully flooded, and measured the buoyancy loss as 6.4kg.
The type of suit worn will make no difference. More relevant is the undersuit, as that is what governs buoyancy within the suit and hence buoyancy lost in a total flood. In our experiment this was a 200gm thinsulate.
Being DIR, our experimental animal was wearing a minimal Halcyon wing designed for single tank use. Fully inflated, it gave him +13kg of buoyancy - gratifyingly enough to compensate for a flooded suit, but only if the diver was correctly weighted in the first place.
Another means of regaining the surface was to simply turn upside-down and fill the legs of his suit. Doing this, our EA managed to achieve +20kg lift.
This +20kg is also a guide to the amount of buoyancy that could be driving an uncontrolled buoyant suit inversion (Dont Go Upside-Down Ballistic, November 2005).
Before flooding the suit, we measured the buoyancy available from suit inflation, until air started escaping from the dump valve and seals. Here our EA achieved +9.5kg. So an inverted diver can become a lot more buoyant than one the right way up.

Divernet
Steve
Steve Murray empties his deliberately flooded drysuit after one of the tests.
Emma
Emma Yates prepares a cylinder for testing.
Demonstrating
Demonstrating that an inverted diver can become a lot more buoyant than one the right way up.
Stephen
Stephen Woodward sets up the suit buoyancy test.
Buoyancy
Buoyancy of Side Mount Cylinders
Buoyancy
Buoyancy of wetsuits