The first real work on the subject was Dr. John Scott Haldane who got a British
Navy budget to try and make divers last longer. They were expensive to train
and expensive to retire when the MO said they were unfit for further service.
He knew the basics, that nitrogen dissolved in the diver's blood and when they
came up it undissolved and it hurt and sometimes they fell over and had to be
carried off to sick bay.
So in 1905 Haldane started a series of experiments in a compression chamber
that today would have the animal rights people up in arms. However in those
days Haldane escaped vilification as a serial goat bender and worked back from
what he saw to the underlying conditions below and laid the foundations for
modern decompression medicine.
Boycott AE, Damant GCC, Haldane JS. The prevention of compressed-air illness.
Journal of Hygiene. Cambridge 1908
Haldane's model of nitrogen and people says that for any bit of your body there is a rate that nitrogen, or any other inert gas, builds up. He had Henry's law that says that the amount of gas that will dissolve is proportional to the partial pressure of that gas applied and Haldane needed to put time to that. In essence he discovered that the gas dissolves at a rate that is proportional to the difference from the final value of the current value. So if we know the level we are moving towards is 10 units and we are at 8 units the rate is based on the difference 2 units so it is twice as fast as if we were at 9 units (difference 1) but only half that if we were at 6 (difference 4). Usefully the rate of undissolving works the same way more difference equates to a faster change.
This is an exponential and is mathematically easy to model but Haldane soon realised that what may work for a liquid in a jar, which has a simple constant called a half time, does not work for a goat. The simple liquid has a number that represents the period of time it takes for the dissolved gas to move half way to the final value so if the half-time is 10 minutes and the initial difference is 12 units then after 10 minutes the difference has dropped to 6 units, after 20 minutes it is down to 3 units and after half an hour it is only 1.5 units. You will notice that it keeps getting closer but never gets there.
Haldane's best trick was to realise that he did not need to model every bit of a goat and know its half times just to have representative numbers that were near enough so that their effects overlapped. These are called Compartments.
Haldane's other discovery was that once the partial pressure of dissolved nitrogen was double the absolute pressure it started to spontaneously undissolve and you got bubbles. Now double is considered a bit simplistic these days but it was a lot better than nothing. Haldane's table stopped the British Navy routinely bending divers and reduced the Admiralty's bills.
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The problem with compartments is that blood is fast, that is it has a short
half time and takes on enough Nitrogen to be a problem long before bone has
accumulated enough to care about but conversely after a long dive the nitrogen
in the bone takes a long time to dribble out so the blood may be decompressed
but you still need to stay down. Haldane used five half times in his model
and his first dive tables were based on the idea of adding up the nitrogen
dissolved and subsequently undissolved in half times of 5, 10, 20, 40 and 75
mins. Look at the graph. The start is 0.79 bar, that is the nitrogen in normal
pressure air, and the target is 3.95 bar which is the nitrogen in air at 40
meters. You can see the 5 minute compartment (blue line) shoot up and get very
close. The 10 minute compartment (purple) goes slower and never gets above 3.6
in the half hour under pressure. The 75 minute compartment (cyan) only gets to
1.6. After half an hour the outside pressure reverts to 1 bar and the poor old
goat decompresses like a freshly opened can of coke. Notice that the 5 minute
compartment is virtually clear by 70 minutes but by 100 minutes the compartment
with the most nitrogen is the 75. Now if the bend limit was 1.58 (double) this was one badly bent goat when he stepped out of the chamber. |
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Not much good that one. Goat for supper again. Right get me another goat and
we'll give this one a couple of deco stops. The compartment with the most nitrogen after 30 minutes is the 5 minute one (blue) with 3.9 bar so if that was to be no more than double then the outside absolute pressure would be half that at 1.95 bar. Call it 10 meters where the pressure would be 2 bar and we'll keep him there for five minutes, i.e. thirty five minutes into his dive. Look at the graph. The 5 minute compartment rushes down towards 1.58 bar being the ppN2 in air at 2 bar but the 75 minute compartment is unchanged as 1.56 is just where it is so it has virtually no reason to change. I'm sorry but the kinks at 35 minutes are a bit hard to see but our worst nitrogen level at the end of the stop is now 2.97 so we can afford to go to a level that is half that i.e. 1.5 bar so let's do a 5 meter stop where the absolute pressure is 1.5 bar and we'll stay here till we can surface. To surface the max ppN2 must be less than 2 bar which happens at 52 minutes when the 20 minute compartment finally falls below 2 Time to knock off for the afternoon and take our remaining goat down the pub for a beer but he is still decompressing. Watch my graphs. After 100 minutes from the start of his dive he still has 1.125 bar of nitrogen in his 75 minute compartment. Remind this goat not to fly above a limit of 0.56 bar pressure. Say 15,000 feet. |
part two
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