OK. In part one we looked at the general idea and the
history of decompression planning but now we need to move on a bit.
When I first thought about deco theory I wondered how much gas is actually
involved and search as I might I could not find anybody quoting it. <sigh>
However a dig in the usual sources (The old Rubber book) turned up the molar
fraction solubility for nitrogen in water that leads me believe that at 0.79bar
ppN2 (on the surface) we have about 0.72 grams of disolved nitrogen in a 70Kg
person. So a good exposure to breathing air at 25 meters will give us 2.5gms of
nitrogen which is 3.2 surface litres.
Admittedly quite a bit of our bodies are not going to get the full exposure but the blood and the immediate soft tissues it bathes are going to get their share. I have watched a tiny bubble in an intravenious drip run up the hose into my arm with serious trepidation thinking about the size of the average blood vessel so this deco stuff needs taking seriously.
After Haldane's work, nearly a centuary ago, many other people have proposed changes to his compartment model and also other models but the most reputable is probably a Swiss gentleman, Proffesor A A Bühlmann of Geneva University.
Over a period of many years the team at Geneva studied the biology and
physics of diving and improved the Haldane model. They, and others, made
several significant adjustments:
Firstly The simple rule for bubble formation at 'double' the
anticipated ppInertGas for that depth is too simplistic. Haldane used more
complex formulations on his later models but Bühlmann produced a simple
formula published in his book Tauchmedizin. (Yes it is in German.
I did say he was Swiss.)
| time (mins) | 5.0 | 8.0 | 12.5 | 18.5 | 27.0 | 38.3 | 54.3 | 77.0 | 109.0 | 146.0 | 187.0 | 239.0 | 305.0 | 390.0 | 498.0 | 635.0 |
| a value | 1.1696 | 1.0000 | 0.8618 | 0.7562 | 0.6667 | 0.5600 | 0.4947 | 0.4500 | 0.4187 | 0.3798 | 0.3497 | 0.3223 | 0.2850 | 0.2737 | 0.2523 | 0.2327 |
| b value | 0.5578 | 0.6514 | 0.7222 | 0.7825 | 0.8126 | 0.8434 | 0.8693 | 0.8910 | 0.9092 | 0.9222 | 0.9319 | 0.9403 | 0.9477 | 0.9544 | 0.9602 | 0.9653 |
Now what does this do to us? Well firstly remember that the compartments are mythical creatures. You can't look on an X-ray and see the 27 minute compartment nestled behind your spleen. You can't actually say that a certain organ of your body is in an X minute compartment as the actual interactions are more complex than that. Blood tends to the fast end and bone to the slow but the whole point about compartment is that when you model them the total effect is a good aproxomation of what is going on. Bühlmann introduces more compartments so he can both run to higher periods and also get more overlap so a tissue that if you tested it in isolation and got a 15 minute half-time would be covered by the values derived for the 12.5 and the 18.5 compartments.
Let us calculate some safe depths (based on the pressures) for different tissue loadings:
Now what is this graph? Along the bottom we have the inert gas pressure in the
compartment from 1 to 6 bar hence pressures equivalent to surface to 70 meters
and the vertical scale is the safe depth for that tissue in meters.