Decompression theory for goats
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 dissolved 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 intravenous 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 century ago, many other people have proposed
changes to his compartment model and also other models but one of the most
reputable is probably a Swiss gentleman, Professor Albert A Bühlmann, Dr.
med. who worked for thirty years at Zürich 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.)
minimum safe pressure = (ppInert Gas - ai) * bi
where there are seperate a and b values for each compartment.
Here are the numbers for Nitrogen:
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 approximation 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 adequately covered by the values derived for the 12.5 and the 18.5
Let us calculate some safe depths (based on the pressures) for different
Now what is this graph? Along the top we have the inert gas tension in the
compartment from 1 to 6 bar and the vertical scale is the safe depth for that
tissue in meters. Remember we take each inert gas individually but diving Air
to 40 meters gives you 5*0.79 = 3.95 bar of Nitrogen to cope with.
The black line represents the original Haldane 'double' law so at one end you
could surface with 2 bar of inert gas (say diving air 19m forever ie: 69%
Nitrogen at 2.9bar = 2bar) and at 6bar you are to stop at 20meters (3bar).
The other lines represent the Bühlmann limits for the compartments
starting with 5 minute compartment in blue at the top right through to the 635
minute compartment in grey at the bottom.
Now at first sight the slowest compartment keeps you deepest so why worry about
the others? Well remember the graphs for the compartments in part 1. For a
reasonable duration dive although the shorter time compartments rushed up to
their saturation values the slower ones never made it. We have to model all the
compartments for inert gas in and out and then when it comes to stops we choose
the compartment that keeps us deepest to set our first stop and wait there
until all the compartments permit us to move to the stop depth
OK let's get a goat and go diving.
Let's do 40 meters for 30 minutes again because we already know what the
compartments look like.
Remember we aren't changing the rules for gassing on and gassing off, just
changing how we calculate the 'safe' limits.
Right. Similar graph but, naturally, more compartments.
Again the five minute compartment rushes up to nearly get to the 3.95 bar
target while the new 635 minute compartment barely moves. The spread sheet that
is drawing my graph here is also using the Bühlmann a and b
constants to calculate a minimum safe depth for each compartment and then
selects the maximum (deepest) value. This is plotted in bar as the broken black
line. You can see the bumps in it as the different compartments take over as
who is deepest. Don't forget this is bar absolute while the others are just
Nitrogen loading in the tissues. At 30 minutes this stands at 8.12 meters from
the 12.5 minute compartment so, rounding to sensible units, we need a 9 meter
After four minutes at 1.9 bar absolute pressure the minimum safe depth has
dropped to 5.53 meters so we can go for a 6 meter stop at 35 minutes run time.
This time the controlling compartment is the 18.5 minute one but only by 15
Now in the sea I would stop at 6 meters as otherwise I am in the swell and I
tend towards seasickness but a goat in a chamber doesn't have these problems so
we can go to a 3 meter stop at 41 minutes run time when 18.5 minute compartment
Finally, at 57 minutes run time, the 38.3 minute compartment is the last to
pass 1 bar so zero depth and we are allowed to surface our goat.
OK so what can we say is different from the early Haldane model we started
Well actually a lot of what Bühlmann is doing here is based on Haldane's
later work so Dr. H deserves more credit than I'm handing out. The first thing
you see is a longer profile overall and less obviously a much longer profile
for longer, deeper dives as the use of compartments of over 10 hours become the
dominant factors. The derivation of different 'safe' limit constants for
different compartments is non-intuitive but the compression chambers in use by
Zürich university produced good numbers and millions of dives on
Bühlmann tables and Bühlmann based dive computers seem to bear it
Probably many people would disagree but I tend to see most later models as
tweaks on Bühlmann and the parallel work by Robert D. Workman for the US
Navy. If you come up with a wonderful theory that gets people out of the water
faster they get bent. The advances are in leaving them longer.
OK? You want to leave them longer?
Well the decompression theory is OK, it's just the wretched divers don't come in
a standard model so we can work things out. They come in all sorts of shapes and
sizes and have a nasty habit of having slightly different chemical makeups and
certainly don't all stay at the same temperature.
All this adds up to messing our nice clean mathematical model about. We can get
it right for most of them most of the time but they don't seem to like that.
What do we do to keep them happy?
This is called adding conservatism. It is a way of going beyond the model to
make things safer in case we don't fit the model that particular day.
A popular system was to plan the dive for a bit deeper than it really was or
plan for a gas mixture with a bit more nitrogen in it than it really had but
I believe there are better ways.
Dr. Richard Pyle is an Ichthyologist and I'd rather let him explain his
deep stops thinking himself but in brief he studies fish and has probably
done more deep diving than most UK clubs have in total for all their members.
He picked up the fact that even diving reputable tables it was the dives where
his care for his specimens caused him to make extra, deeper stops that left him feeling
a lot better aprés dive so he derived a protocol to do them normally.
These are really deep stops, stops near the bottom of the ascent and not an
obvious intuitive step when the object of decompression seems to be to get out
from the pressure so you are off-gassing as soon as possible.
What is happening here? Well look at my graphs. On the ascent the lines on the
graph are steep so the 'safe depth' value is changing fast. This is the point
where you want to be wary and stay well away from the bent/not bent line so a
slow ascent and deep stops helps the gas get out without actually costing you
much in your total dive time. OK the longer compartments will still be
on gassing but let's get up to the shallow stops without generating any
bubbles. The older tables zoomed up and then compensated with longer stops at
shallow and are often termed 'bend and mend'.
When we finally arrive at the shallow stops the graphs are no longer steep but
nice and flat. As our goat started his ascent the 'safe depth' was coming down
towards him at nearly 30cms a minute but when he is clearing his 3 meter stop
the rate of change is a mere 3cms a minute. If you want to do extra time to be
safe you need to do it at the deep end of the scale where it will bite you and
it is less imperative shallow.
We now put the 'feeling a bit rough' sensation that comes from diving close to
the bent/not bent limits down as 'sub-clinical' bent and with deep stops and
padding the shallow ones and breathing richer nitroxs we seem to avoid it.
by Nigel Hewitt
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