In the early 1900s, navy divers were paralysed, and sometimes killed, during or after the ascent. It was known that ascending too fast caused the illness. There was no method for working out a safe rate.
In 1908 the physiologist John Scott Haldane, with Arthur Boycott and Lieutenant Guybon Damant of the Royal Navy, published a method. It was based on records of compressed-air workers and on experiments with goats in a pressure chamber. It introduced staged decompression, which every dive computer still uses.
- Gas in the goat's tissues
- Chamber pressure
- Half the tissue pressure
Bert’s finding: bubbles
In 1878 the French physiologist Paul Bert showed the cause of the illness. Gas dissolved in the body under pressure forms bubbles of nitrogen when the pressure falls too quickly.
He advised a slow, even ascent. This was safer than a fast one, but it gave no way to calculate how slow the ascent should be.
Pressure drops that caused no harm
Haldane studied the records of compressed-air workers. Workers at about 2 bar absolute, roughly 10 m of sea water, could return directly to the surface after any length of time without becoming ill.
Going from 2 bar to 1 bar halves the pressure. Their tissues held gas at twice the surrounding pressure, and no harmful bubbles formed.
The 2 to 1 ratio
Haldane proposed that the ratio of the pressures mattered, rather than the size of the drop in bar. If halving the pressure was safe from 2 bar, it might also be safe from 4 bar or 6 bar.
He tested this on goats in a pressure chamber, chosen because they are large enough to stand in for a person. The resulting rule: a diver may ascend until the surrounding pressure is half the gas pressure in their tissues, and no further. This is the 2 to 1 ratio.
Haldane’s 5 tissues
A diver is rarely saturated with gas. Haldane therefore modelled the body as 5 tissues, which take up and release gas with half-times of 5, 10, 20, 40 and 75 minutes (see tissues and half-times).
The 2 to 1 rule applies to each tissue. The tissue with the highest gas pressure sets the limit: after 25 minutes at 40 m, the diver may ascend until the surrounding pressure is half the pressure in that tissue.
The ratio gives the depth a diver can ascend to in one move. It also shows what was wrong with the slow, even ascent.
- Even ascent
- Haldane, 1908
- ZHL-16C, engine
The slow, even ascent
Before 1908, divers ascended at one slow, constant rate. Haldane’s rule shows that this is the wrong way round. At depth the pressure is high, so the depth at which it is halved is a long way up. The diver spends time crossing depth that could be crossed in a minute.
Near the surface each metre is a larger fraction of the total pressure. The even ascent crosses the shallow depths too quickly, where the tissues are closest to their limit.
Staged ascent
Haldane’s method reversed this. The diver ascends quickly at first, as far as the ratio allows. The diver then stops and waits while the tissues release gas, until the next stop 3 m shallower is allowed.
Each stop is longer than the one below it, because the last few metres reduce the pressure by the largest proportion. The profile is a series of steps that lengthen towards the surface.
The first stop
At 40 m the pressure is about 5 bar. Half of that is 2.5 bar, at about 15 m. After a dive like this the fastest tissue is close to saturated, so the rule allows the diver to ascend almost to 15 m straight away.
For the same total time in the water, the staged ascent spends less time deep and more time shallow. Less gas is taken up, more is released, and the ratio is never exceeded.
The same dive planned with ZHL-16C
This is the same dive planned by DiveLogic’s engine with Bühlmann ZHL-16C, which uses 16 tissues instead of 5. The ascent is still staged. The first stop is shallower, and the diver surfaces sooner.
The difference is the ratio. Later work, starting with Workman’s M-values, found that fast tissues tolerate much more than 2 to 1 and slow tissues somewhat less. A single ratio for every tissue was replaced. Staged decompression was kept.
Try it
Choose a depth and a bottom time on air. The white line is the dive staged by Haldane’s rule. The line labelled ZHL-16C is the same dive planned by the engine. On short, deep dives Haldane’s rule stops deeper, because 2 to 1 is strict for the fast tissues. On a long dive the result reverses. His slowest tissue has a 75-minute half-time, so his model does not track the slower tissues that control long dives, and his schedule surfaces sooner than the modern one. This is the main reason his tables were replaced.
- Haldane, 1908
- ZHL-16C, engine
- Haldane's first stop
- 15 msurface at 71 min
- Engine's first stop
- …planning…
What to remember
- Paul Bert showed that decompression sickness is caused by bubbles of gas forming in the body when pressure falls too fast.
- Haldane proposed that the body tolerates the pressure being halved, whatever the starting pressure. This is the 2 to 1 ratio.
- He modelled the body as 5 tissues, with half-times of 5 to 75 minutes, each held to the same ratio.
- The rule produces a staged ascent: ascend quickly, then make stops that get longer as you approach the surface.
- The single ratio was later replaced by a separate limit for each tissue, but every modern plan still uses staged decompression.
Staged stops in the planner
DiveLogic plans with Bühlmann ZHL-16C and Thalmann, both developed from Haldane’s rule. Plan a 40 m dive and read the schedule: a fast ascent to the first stop, then stops that get longer towards the surface.
Sources
- Bert P. (1878). La Pression barométrique: recherches de physiologie expérimentale. Masson, Paris.
- Boycott A. E., Damant G. C. C., Haldane J. S. (1908). The prevention of compressed-air illness. Journal of Hygiene 8(3): 342-443.
- Workman R. D. (1965). Calculation of decompression schedules for nitrogen-oxygen and helium-oxygen dives. US Navy Experimental Diving Unit, Research Report 6-65.
- Bühlmann A. A., Völlm E. B., Nussberger P. (2002). Tauchmedizin, 5th edition. Springer, Berlin. (ZHL-16C compartment table.)