From: mayne@dup.cs.fsu.edu (William Mayne)
Subject: Re: Mixed gas algorithms
Reply-To: mayne@cs.fsu.edu
Organization: Florida State University Computer Science Department
Date: Thu, 7 Jan 93 19:22:08 GMT

In article <1993Jan5.164101.14469@freenet.carleton.ca> aa372@Freenet.carleton.ca (Mike Dusseault) writes:
>
>I thank you for the information.  I will have to pick up the Buhlman book.

You may also want to get "Mixed Gas Diving - The Ultimate Challenge
for Technical Divers" by Tom Mount and Bret Gilliam, just published
by Watersport Press. The chapter on decompression theory (by Tom
Mount, I think) doesn't include the math or address the issue of how
the Haldane or Buhlmann models handle the combination of multiple
inert gases, but it is a decent introduction. It is a marked improvement
over the treatment of the same subject in "Deep Diving" (Bret Gilliam
and others), which had a misleading description of conditions for
bubble formation, IMO. Both books suffer from sloppy editting, with typos,
grammatical errors, and malapropisms showing up now and then. But they
are the best texts I know of on their subjects.

Even though "Mixed Gas Diving" won't directly help you with a
decompression program it will help you understand how mixed gas diving
is done, including gas selection, the use of nitrox and oxygen for
decompression, etc. A realistic program for trimix needs to include
appropriate decompression gases. (No body doing serious decompression
from trimix or heliox would plan to use their bottom gas during
decompression except for the deepest stops, if at all. It would be
interesting to study the consequences of using the bottom gas for deco,
possibly as a last ditch emergency technique. The tables I've seen
don't give any guidance for this contingency.)

Unfortunately the book does not include a set of trimix tables which
would be useful for checking your calculations. They say this was
deliberate to discourage people reading the book from trying mixed gas
diving on their own without going through proper training. I suspect
copyright considerations and propriety interests also played a part.

>The reason I'm asking is I have written my own deco program.  Works with
>any NITROX, uses values like the USN, but a tad more conservative...

There are several other sets of M_0 and delta M values published which
you might want to consider. Also be advised that even the USN tables
aren't really computed using just the list of 5, 10, 20, 40, 80 and
120 minute compartments you usually see in introductions to the
theory. In fact they kept adding compartments. I've see published
papers saying that up to 14 or so compartments are used.

How are you making your program more conservative? An obvious
approach is to decrease the M_0 and deltaM values. You can also
add a constant depth increment when computing partial pressures
to go into the diffusion equations for bottom time. This is like
the method of adding 10 feet to the actual max depth for padding
when reading the tables. An appoach I like better, and one used by
Jim King's program, is to add 5% or some other factor you select
to the partial pressures, giving more adjustment for greater depths.

>...Although I have no
>practical uses for mixed gas diving at this time, I don't see why I can't
>put them into the program.

In that case I can suggest a simple approach which will be fine for
playing around and educational purposes, though I wouldn't use it
to compute tables for actual use. In the Buhlmann ZHL-12 model
the parameters for helium and nitrogen are the same for the first
nine (of 16) compartments. This includes all compartments with
helium halftimes of 43 minutes or less, and consequently nitrogen
halftimes of 114 minutes or less. Hence if you are using the
published USN model where the slowest compartment has a nitrogen
halftime of only 120 minutes it is quite reasonable to just use
the same M_0 and deltaM values you already have. The helium
parameters are different only for the slow compartments you
aren't considering.

For each compartment the helium halftime is just the nitrogen halftime
divided by 2.65. For each step of the dive profile compute the
helium and nitrogen loadings separately for each compartment,
but use the sum of the two just like you would have used the
nitrogen load alone when determining ceilings. The catch is you
can't solve for "t" in the diffusion equation to get the time
required for a compartment to off gas enough to move up to the
next stop. At least I haven't been able to do that. Maybe some
math whiz out there can. If you are already computing stop lengths
by an iterative loop with time as the index this is no problem.

I've found with ZHL-12 that the slow compartments don't wind up
controling the decompression for most realistic single-dive profiles
I care about anyway. For example, on a dive to 300 feet for 30
minutes breathing 14% oxygen and 50% helium the first decompression
stop (by calculation) is at 170 feet. Only one of the slowest 7
compartments has a ceiling below the surface, and that ceiling is
just 4.7 feet (for the 55 minute compartment, the fastest for which
the helium and nitrogen parameters are different). The 43 minute
compartment has a ceiling of 51 feet at the start of decompression.
The decompression, using nitrox after reaching 110 feet and oxygen
at 20 and 10 feet, is 111 minutes, not counting air breaks.
(CAVEAT: As of now the program has not be thoroughly checked and is
much less conservative than the tables I am using for testing. I am
working on that.) Clearly the 55 minute compartment is not going to
control even the 10 foot stop.

My conclusion is that it takes an extreme exposure, approaching a
saturation dive, to load the slow compartments enough to have them
control. A decompression controlled by the slowest compartments would
be outside the range of what all but a few recreational mixed gas
divers would be able and willing to endure. Saturation divers
decompressing in a chamber and Sheck Exley are different.

Bill Mayne
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