Question regarding Baker's Decolessons

[EFX]

I have a question regarding the output of a decompression program written by Erik Baker, PE in the paper "Decolessons". His paper is attached below. There are two columns: Max %M-value and Gradient Factor (GF). The dive uses a GF of 30/75 and the output clearly shows the gradual increase of GF from .30 to .75 upon surfacing. Under the Max %M-value column the value upon surfacing is 91.2%. My question is: why isn't the surfacing %M-value equal or less than the GFHi of .75 or 75%?

 

[dmaziuk]

I really didn't like fortran even back when I knew it... Are you sure the exact value is at 91.2% of Buhlmann's original M-value and not the adjusted one?

 

[EFX]

Yes. Here is what he says in regards to the m-value calculation:

"Note that these calculations are referenced to the straight (unmodified) M-values (i.e. NO conservatism factors are applicable) because we are comparing the gas loadings against these standard values."

 

[dmaziuk]

Well, it compiles with gfortran after replacing systemqqs with plain system (and cleaning up indents after pdf to text conversion), and runs and produces the same output...

He has, in the description of SAFASC sub, the lines for calculating the ceiling with and without the gradient factor. In the code he uses the "with" version. Replacing it with the "without" version makes for very different deco stops that end with
42 0.3 80.3 | 4 | 0. -10.0 99.2% | 0.75
FWIW

 

[EFX]

Thanks Dmaziuk for running the program. I assume the 99.2% is the max m-value upon surfacing. So, the question remains; Why isn't the max m-value equal to or less than GFHi? It makes no sense to me. I would like to ask Erik Baker but I couldn't find his email address or any link to contact him.

 

[dmaziuk]

Keep in mind that GF modifies Buhlmann's coefficients and not the Workman's M-value directly. In order to calculate for tissue loading you have to convert from Buhlmann to Workman and that requires the actual gas loading in the tissue compartment. (Or dig out that linear algebra text book and try to solve them linear equations with GFs thrown in.)

I played with it a bit: M0 for the "B" version 4-minute compartment is 3.24 bar. Using that as the loading, GF .75 modifies the "safe ascent ceiling" to about 75%. I.e. at GF 1 your ceiling is at 1 bar, obviously, whereas at GF .75 the ceiling is at 1.3-ish. However to get from there to surfacing tissue loading, you'd need to complete your minimal deco stop at 1.3 bar, surface, and see what tissue loading is at that point. It's not hard but I've useful work(tm) to do.

I don't think it'll be at 75% of the 3.24 bar though. I think it's gonna be above that. I.e. GFs are not equal M-value %s.

 

[dmaziuk]

PS on second thought, after 2 minutes at 1.3 bar depth the loading goes from 3.24 bar down to 2.7: about 83%. The ceiling at this point is at 1.01 bar so if you round down, you should be OK to surface -- with 83%, not 75%. That's less than Erik's 91% but I'm using the exact M0 gas loading for 1 gas in 1 tissue compartment, so...

 

[EFX]

In Baker's paper "Decolessons" his surfacing %m-value is 91.2% and not the GFHi of 75%. In his paper "Clearing up the confusion about deep stops" there is a graph that depicts the GF line from first stop to the surface. The surfacing value is GFHi on the graph. You don't need to convert from/to the Buhlmann/Workman equations to calculate m-value. Baker, in "Decolessons", says the two forms of the equations produce the same result provided you keep the proper units between the equations. Buhlmann uses absolute pressures and Workman uses gauge pressures.

Baker uses the Buhlmann equation in his program. From "Understanding M-values": M = (Pamb / b) + a. To get the leading tissue compartment % of m-value he takes the total inert gas pressure for the TC and divides it by M and multiplies by 100 to get %. The same value can be found by using the Workman equation: M = slope(depth) + Mo. The Workman equation is easier to work with when considering m-values when surfacing. Using Workman, the surface segment depth equals 0 so M = Mo. Mo is the surfacing m-value from the table in "Understanding M-values". The M or Mo value in this case is the value when GFHi = 100% not 75%. Baker does have access to the actual tissue compartment gas loadings.

 

[dmaziuk]

Baker does have access to the actual tissue compartment gas loadings.

Huh? That's only what the program does: calculate the actual tissue loading at every step of the dive.

 

[dmaziuk]

Actually, here is a simpler answer:

Workman: M = D * dM + M0
Workman + GF: M = D * (dM * GF - GF + 1) + (Psb + GF * (M0 - Psb))

For surfacing M-value, M = M0 for GF 1 and for GF 0.75: Psb + 0.75 * (M0 - Psb)

Now if you can figure from Deep Stops" what the "Psb" stands for, you can work out how it affects the surfacing M-value. For it to be 0.75 * M0, Psb has to be 0, obviously.