Have I understood the basics of decompression theory, GF99 and SurfGF?

[lowwall]

Assuming an identical surfacing maximum tissue compartment overpressure (aka SurfGF), is there any actual evidence that setting GFlow below GFhigh decreases deco risk?

I'm asking this because the invention of gradient factors was based on what we now believe to be the flawed premise that the Varying Permeability Model was a more accurate model for determining deco risk. Baker invented Gradient Factors to allow Haldanean models like Buhlmann to mimic VPMs requirements for deeper stops, But somehow, Gradient Factors - specifically GFlow being set lower than GFhigh - have persisted even though VPM has largely been rejected.

Thinking about what this means in terms of actual deco dive profiles (GFlow does not come into play on NDL profiles), using a smaller GFlow will result in a somewhat greater loadings in the slower tissues on surfacing in exchange for limiting the maximum tissue loadings in the fastest tissues during the dive. Is that really an advantageous tradeoff?

In addition, the smaller the GFlow realtive to GFhigh, the longer the deco schedule. If you were to add that time to the shallowest stop in a profile where GFhigh = GFlow, you would end up with a lower SurfGF. Why wouldn't this be a decisive advantage for setting them equal?

 

[EFX]

Can you give Baker's actual program code? I can't but I can offer you what Baker wrote in his paper "Intro to deco lessons". In that paper he presents two subroutines that calculate a new pressure needed to calculate a new ceiling: one based on constant depth and one based on a change of depth. Here is the general case of the Schreiner equation that can be used for all depth scenarios from his paper:

//-------------------------
The efficient and direct calculation for gas loading during ascent and descent profiles is with the
general solution given by Schreiner:

P = Pio + R(t - 1/k) - [Pio - Po - (R/k)]e^-kt

Where:
Pio = initial inspired (alveolar) inert gas pressure
(Pio = initial ambient pressure minus water vapor pressure)
Po = initial compartment inert gas pressure
R = rate of change in inspired gas pressure with change in ambient pressure
(this is simply rate of ascent/descent times the fraction of inert gas)
t = time
k = half-time constant = ln2/half-time (same as familiar equation)
//-----------------

The rate (R) above is calculated from a change of depth and will correctly calculate the new pressure whether the diver is ascending, descending, or at constant depth. Once we have the new pressure a new ceiling can be be calculated that takes into account the GFLo and GFHi. The equation needed is:

calculate the stop at the current GF using the formula:
D = ((P - GF * a) / (GF / b - GF + 1)) - Psb

'where: D = depth, P = total gas pressure, GF = gradient factor,
'a = coefficient a, b = coefficient b, Psb = ambient surface pressure
'the first part within parentheses calculates a pressure. Subtracting
'the surface pressure converts the result to a gauge depth.

 

[dmaziuk]

Can you give Baker's actual program code?

I am assuming he wasn't interested in coding that, just like everybody else. No one cares for us vacation divers, DSAT folks were the only ones ever.

 

[EFX]

Of course he was interested in ascents/descents in decompression calculations. For accuracy and safety decompression calculations have to take account of on-gassing and off-gassing from descents and ascents. The paper is a guide on how to program a decompression program.

 

[EFX]

Baker invented Gradient Factors to allow Haldanean models like Buhlmann to mimic VPMs requirements for deeper stops, But somehow, Gradient Factors - specifically GFlow being set lower than GFhigh - have persisted even though VPM has largely been rejected.

I disagree. As you know we all have different risk factors determined by age, physical shape, hydration, previous decompression stress to name a few. Baker's gradient factors allowed divers to adjust their risk factors by raising or lowering the maximum allowed pressure in the tissue compartments throughout the dive. The fact that it mimics VPM in creating lower first stops is coincidental.

 

[lowwall]

Can you give Baker's actual program code?

First link on VPM Links

 

[inquis]

The equation needed is:

calculate the stop at the current GF using the formula:
D = ((P - GF * a) / (GF / b - GF + 1)) - Psb

First, there is no time dependence on this ceiling calculation as described. If P is a function of time (via Schreiner), then so is the stop depth from this equation. You would need to find where this D(t) equals the ascent D(t). While you could do this in closed form for nitrox, the equation would necessarily include the starting depth, which is not present in the above.

Second, a and b are not constants when Trimix is involved. You could assume they are for the ascent, but it's much easier to ignore the ascent for the ceiling/stop calculation, as that's a conservative choice.

It's not a huge deal showing a stop that's deeper than necessary (because it used the tension at the start of the ascent). The off-gassing during ascent is certainly included during the actual ascent, and the ceiling & stop is recomputed accordingly during the ascent. In other words, the stop will clear on the way up.

My primary point is that some computers today have the horsepower to find the intersection of those two time-dependent depth curves (the ceiling depth and the diver depth). They skip showing a stop that will clear when ascending at the assumed rate. This avoids the discontinuity mentioned when NDL hits 0.

 

[inquis]

Where did you read that Baker's implementation ignored off-gassing on ascent?

Perhaps to clarify, I was saying it ignores future off-gassing in the ceiling calculation. It does update tissues and the ceiling on the way up, accounting for any off-gassing up to that point.

 

[inquis]

The fact that it mimics VPM in creating lower first stops is coincidental.

Overall conservatism was achieved with one GF. He needed the second one to yield profiles similar to the ones in vogue at the time -- i.e., change the slope in order to protect the fast tissues.

 

[inquis]

using a smaller GFlow will result in a somewhat greater loadings in the slower tissues on surfacing in exchange for limiting the maximum tissue loadings in the fastest tissues during the dive. Is that really an advantageous tradeoff?

It's not been explicitly studied. However, in the Navy's current probabilistic algorithms, the slope of the M-value line is approximately 1. This is why Doolette sets his GFLow at 0.83*GFHigh, as that results in a slope of around 1 for ZHL-16C. Basically, Buhlmann felt the fast tissues could tolerate greater tension. VPM wanted them to have less tension. The Navy is in the middle.