ceiling/GF

[KenGordon]

But @atdotde has a good point. As that moving target GFLo is determined by your accumulated depth/time, it is fixed at GF30 (or whatever). If you clear stops based on a gradual ascent (below GF30) the next calculated first stop is still at GF30. Unless the GFLo is anchored some other way, you could ascend at "GF31/31" all the way to the surface, never triggering the transition to GFHi.
I don't know how the programmers at Shearwater trigger the transition. On a planner, it's set in stone. Or am I misunderstanding how this works on dive computers completely?

My understanding is that the means of anchoring the GF lo is to use the deepest ceiling so far, regardless of the actual ascent. Otherwise what you describe would happen. You can force it in a planner by adding levels just below the stops so as to prevent hitting any stops until nearly at the surface.

The deepest ceiling thing is not nice but better than the alternatives while trying to match a planner.

The interpolation of GF is a nasty thing. Another scheme would have been to use a different slope and initial offset for the compartments. It is a bit hard to support without manned testing through. And he was probably not considering dive computers back then.

 

[rsingler]

Thanks, @KenGordon . Hopefully @Shearwater will weigh in and confirm.

 

[J-Vo]

Another scheme would have been to use a different slope and initial offset...

This is how I initially thought GF worked. As a modifier to the slope and intercept of the M value line, but looking in more detail that may be very hard to keep on the "Safe" side of the original algorithm.

 

[leadduck]

Not sure I understand that. I do understand that offgassing is driven by the gradient between the tissue PN2 and the inspired gas PN2, I don't think that I implied otherwise. If your leading compartment is saturated, that means that it is in equilibrium with the inspired gas, no matter what mix you are breathing. That is, at saturation, the tissue PN2 has to be equal to the inspired gas PN2 (Henry's law). Yes the gas PN2 is going to be less than ambient pressure (proportional to how rich the mix is), but that doesn't effect the basic process of offgassing.

If you are sitting at depth and your leading compartment is saturated, then you aren't going to offgas or ongas that compartment, no matter how long you sit there. Once you ascend, no matter how small an ascent, that results in supersaturation (GF>0) and therefore a pressure gradient between your tissues and the inspired gas. That happens because the PN2 in the gas changes instantly, and the PN2 in the tissues changes slowly, as nitrogen leaves the tissue. Once you have offgassed to the point that your new tissue PN2 matches your new gas PN2, the gradient is gone, you are once again saturated, and you are back on the AP line (GF 0).

So I don't see how you can ever ascend and stay at GF0.

GF=0 does not equal saturation. Saturation means, tissue partial pressure equals inspired partial pressure. GF=0 means, tissue partial pressure equals ambient pressure, which is larger. For an air dive, let's say you descended to 30m and stayed there until a fast tissue saturated to 0.79*4=3.16ata. Ascending to GF=0 means ambient pressure=3.16ata, that's 21.6m. At 21.6m your inspired nitrogen partial pressure is 0.79*3.16=2.5ata. There's a pressure gradient in the tissue of 0.66ata that makes the tissue supersaturated and off-gas at GF=0.

 

[doctormike]

GF=0 does not equal saturation. Saturation means, tissue partial pressure equals inspired partial pressure. GF=0 means, tissue partial pressure equals ambient pressure, which is larger. For an air dive, let's say you descended to 30m and stayed there until a fast tissue saturated to 0.79*4=3.16ata. Ascending to GF=0 means ambient pressure=3.16ata, that's 21.6m. At 21.6m your inspired nitrogen partial pressure is 0.79*3.16=2.5ata. There's a pressure gradient in the tissue of 0.66ata that makes the tissue supersaturated and off-gas at GF=0.

I don’t think that is correct. The GF number is an overpressure, measured on the scale between saturation (overpressure of zero) and the M-value line, which designates the amount of overpressure at various depths associated with a significant DCS risk (Haldane, Workman and Buhlmann). The GF scale goes from 0 (no overpressure) to 100 (intersection with the M-value line).

Taking your example, at depth your leading tissue (not always the fastest tissue) is saturated with a PPN2 of 3.16 when at a depth of 4 ATA (30 m). But you don’t “ascend to GF=0”, because GF=0 IS saturation. You can see this by looking at where the “ambient” pressure line intersects the GFLo and GFHi ranges. At both ends, it crosses at GF=0. If you are on the ambient line, you are at GF=0. So the fact that 21.6 m is when the total ambient pressure happens to equal the PPN2 of air at 30 M is irrelevant. If you ascend from 30m to 21.6 m, your GF will be well above 0, your leading tissue PPN2 would be above your breathing gas PPN2, which is why you would decompress.

The term overpressure itself refers to supersaturation, that is, how much more gas is held in solution by a tissue than would be when the tissue is in Henry’s Law equilibrium. So at GF=0, there is no supersaturation (of the leading compartment), and therefore no offgasing is possible. You can’t offgas if there isn’t a difference in inert gas pressure between tissue and breathing gas.

I think that the point of confusion is that this diagram is simplified and is without units, to illustrate the concept of gradient factors. The line labeled “ambient” is misleadingly labeled. It’s better to think of it as the partial pressure of inert gas, which varies directly with total ambient pressure. The thing is that there are actually an infinite number of lines, corresponding to various mixes. 100% O2 is an exception that doesn’t work in this model, because PPN2 is always zero. That’s why the efficiency of decompression on pure O2 is independent of depth.

So yes, it is true that ambient pressure only equals PPN2 for 100% nitrogen (as mentioned upthread, a poor choice of a breathing gas!). But in the diagram, being on the ambient line implies saturation - that is, the PPN2 of the leading tissue compartment is the same as the PPN2 of the breathing gas.

As far as ascending and staying on the ambient pressure line, that simply isn’t physically possible. If you stay at one point on the line, you will never ascend and never decompress. If you ascend, you will always generate a gradient between your breathing gas (instantaneous change in PPN2 due to ambient pressure change), and your leading tissue compartment (ALWAYS delayed since it takes a non-zero amount of time to return to saturation equilibrium).

 

[J-Vo]

My understanding is that ambient pressure is total pressure for you inspired gas. If you have not ascended yet, your GF will be somewhere < 0%. GF0 is where tissue inert GAS = ambient. Assuming you didn't switch gas, if your GF = 0 then your tissue inert gas pressure must be > inspired inert gas pressure. Either that or you don't have any O2 in you mix.

 

[doctormike]

My understanding is that ambient pressure is total pressure for you inspired gas. If you have not ascended yet, your GF will be somewhere < 0%. GF0 is where tissue inert GAS = ambient. Assuming you didn't switch gas, if your GF = 0 then your tissue inert gas pressure must be > inspired inert gas pressure. Either that or you don't have any O2 in you mix.

I’m pretty sure that you don’t have a gradient or offgas at GF=0, by definition. Let me go over what I think is happening here…

While I think that I understand decompression fairly well, the commonly cited graph that we are discussing here really needs some clarification for me, even after reading Baker’s paper on Understanding M-Values. I’m coming to the conclusion that there may be a graphic design issue here.

I think that the problem is confusing labeling. In order to have the “ambient pressure line” have a slope of 1.0, you need to make the Y-axis the tissue PPN2, (tPPN2, which is how it is usually labeled) and the X-axis to be the PPN2 in the inspired gas (gPPN2). But the X-axis is commonly labeled “ambient pressure”. If it was really the total ambient pressure in your breathing gas (which is what the label implies), then the slope would vary dependent on the mix, and would only have a slope of 1.0 if you were breathing 100% N2. Yes, I know that it’s really the total partial pressure of inert gas, including helium or anything else, I am just using PPN2 for clarity.

So the choice would be to have a separate chart or line for every breathing gas, or to just normalize it by labeling the x-axis as the actual relevant variable - gPPN2. When tPPN2 = gPPN2 for the controlling compartment, that compartment is fully saturated according to Henry’s law. When you ascend, gPPN2 drops instantly, temporarily becoming lower than tPPN2, resulting in supersaturation of the controlling tissue compartment (GF>0), an inert gas gradient, and off gassing.

If you are on the ambient pressure line, that means that your controlling compartment tissue PPN2 is equal to the PPN2 in your breathing gas (i.e. saturation), assuming that the x-axis is correctly labeled. If you haven't ascended, and if your leading compartment is fully saturated, then your GF=0 (GF is defined as a percentage of the distance between saturation and the M-value for that depth). If your GF>0 you will be offfgassing (supersaturation). If your GF<0 (have never heard that term, don't know if anyone uses the concept of negative gradient factors but I see what you mean), then you would still be ongassing.

The ambient pressure line is clearly GF=0, since it is labeled as such at both ends (it intersects the GFLo and GFHi bars at 0%). On that diagram, decompression and offgassing only occurs above the ambient pressure line. Excerpted from the DiveRite article:

"...ascent and decompression occurs between the M-value line and Ambient Pressure line....The Gradient Factor defines the amount of inert gas supersaturation in leading tissue compartment. Thus, GF 0% means that there is no supersaturation occurring and inert gas partial pressure equals ambient pressure in leading compartment"

And thinking about it, that last sentence could be a little clearer. Maybe ".. inert gas partial pressure in the leading compartment equals inert gas partial pressure in the inspired gas"..?

Or maybe I'm missing something...

 

[leadduck]

GF=0 is NOT saturation. At GF=0, tissue partial pressure equals ambient pressure and hence exceeds inspired inert gas partial pressure, and is already far in supersaturation region. Your quote above from the Diverite document could use some clarification ... "there is no supersaturation occurring and inert gas partial pressure equals ambient pressure in leading compartment" is a contradiction in itself.

One could draw another line y=0.79*x for air that shows the inspired inert gas partial pressure as a function of ambient pressure for air. This is the line of saturation where tissue partial pressure equals inspired gas partial pressure. On this line p(tissue)=0.79*p(ambient), no on-gassing or off-gassing happens. The gap between y=x and y=0.79*x is the region where GF is negative, yet the tissue is supersaturated and off-gasses.

This additional line depends on the inspired gas. Saturation, on-gassing and off-gassing of course depends on the inspired gas. When you switch from bottom gas to EAN50 deco gas, some tissue that has been previously on-gassing on bottom gas may start off-gassing on deco gas instantaneously.

 

[doctormike]

GF=0 is NOT saturation. At GF=0, tissue partial pressure equals ambient pressure and hence exceeds inspired inert gas partial pressure, and is already far in supersaturation region.

I don't think so, because then there would be offgassing at GF=0, because there would be supersaturation, right? Again, I think that this is a terminology issue, using the word "ambient" in a confusing fashion. Inert gas partial pressure does vary directly with ambient pressure but with the multiplier derived from the mix percentage. So in doing that chart, to get a slope of 1 (which is how the ambient pressure line is usually drawn, although it's a bit off in the Shearwater version) you have to assume a multiplier of 1 (100% N2).

From Steve Lewis:

"GF can range between 0 and 100 percent. One hundred percent is the point where M-Value is on the verge of critical bubbling (1), and zero percent is the same as ambient pressure (M-Value of 0 where there is no force driving gas out of solution at all). Therefore, effective decompression can be found somewhere between those two points."


Fron Neal Pollock:

"Dive computers that incorporate gradient factors typically provide either a limited number of choices or allow fully user-adjustable ranges. The figure below shows two example settings. The 0 percent line on the percent of M-value scale (Y-axis) is the point of no supersaturation; this can be thought of as the bottom depth from which a diver will depart to surface."


From Matti Anttila:

"The Gradient Factor defines the amount of inert gas supersaturation in leading tissue compartment. Thus, GF 0% means that there is no supersaturation occurring"


I mean, maybe I'm missing something. I'm not a hyperbaric doc, I'm not a decompression scientist, I'm not an instructor. But from everything I have read, it seems that that the x-axis on that graph would make more sense if it was labeled as the partial pressure of inert gas and not as "ambient pressure" because then how would the GF0 line have a slope of 1 unless you are breathing 100% nitrogen? Again, I think that choice is for visual simplicity, to avoid having charts specific for every mix.

 

[rsingler]

I think @doctormike put his finger on it, and @leadduck , I agree with you conceptually, but I don't think that is what the GF graphs are portraying.
If you look at this picture from post #59, page 6, you'll see that the lines and axes are labelled differently than in the others graphs on the same subject that we have been discussing. This portrayal is conceptually clearer.

What we have been calling the ambient pressure line is here called the "Saturation Line". And here the x-axis is labeled Ambient Pressure, rather than depth. What this does, is remove the absolute tie between Ambient Pressure and Saturation.
So @leadduck , while total ambient pressure is indeed greater than PPN2 at any depth, I think this graph better shows that the saturation line is GF 0, which may not be equal to total ambient pressure, but rather saturated N2 pressure for the leading compartment. That pressure is related to, but not the same as, ambient.

So I think you both are right, but @doctormike has described the graph more in line with what I think is the intent.
A good discussion!