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Last night I was thinking about Bill Mayne's note on using the Navy model for
comparing O2 vs. air deco, and thumbing through my handy copy of Wienke's book. 
At lunch today I set up a spreadsheet to compare decompression times for each 
Navy tissue compartment on air vs. O2 at the 10 fsw stop.  Here 
are the results.  They are still a little back-of-the-envelope, but some
might find them interesting:

In the Navy model, the tissue N2 partial pressure after some  time t is given by
the equation 

P  = Pa  + (Pi - Pa)*exp(-L*t) 

where Pa is arterial gas tension, Pi is the initial tension at t=0, and L
is a perfusion constant which depends on tissue compartment half time.  At 
the 10 fsw stop, Pa=0 for O2, and Pa=.79*(33+10)=34 fsw for air.

Tissue tensions at depth d must never exceed M = M0 + (delta M)*d, where
M0 and delta M are determined empirically for each compartment (M0=51 for the
120 minute compartment, as Bill mentioned).  

If we invert the tissue partial pressure equation, we get the following 
equation (for each tissue compartment) for time remaining at the 10 fsw stop 
before surfacing, based on current tension P:

Trem = (1/L) * ln [(P-Pa)/(M0 - Pa)]

where ln is the natural log and M0 is defined as above.  This is because 
one must wait until the tissue tension has decayed to M0 before one can 
surface.  Just to make things easy, I assumed in my spreadsheet that each 
tissue compartment was as full of N2 as it could be at the 10 fsw stop.  That
is, for each tissue, I assumed P=M0+10*deltaM.  I then used the standard values
for M0 and delta M for each compartment, plugged in the numbers, and got the 
following relative advantages for using O2 vs. air for each compartment:

5     10     20     40    80    120
1.42  1.54   1.74   2.12  2.43  2.51

What this means is that if a diver has done a dive where the slowest tissue is
the dominant factor for decompression at the 10 fsw stop, then decompressing on
O2 is 2.51 times as fast as air, whereas if the fastest tissue is dominant 
then O2 is 1.42 times as fast.  Intermediate tissues have intermediate 
advantages for O2.

John Heimann
jheimann@sc*.gt*.co*

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