ceiling/GF

Please register or login

Welcome to ScubaBoard, the world's largest scuba diving community. Registration is not required to read the forums, but we encourage you to join. Joining has its benefits and enables you to participate in the discussions.

Benefits of registering include

  • Ability to post and comment on topics and discussions.
  • A Free photo gallery to share your dive photos with the world.
  • You can make this box go away

Joining is quick and easy. Log in or Register now!

Thanks, Rob!

You know, it's pretty amazing that this graph that has been reprinted and re-used in one form or the other for years by many different authors can have these issues. That's why I'm so happy that @Shearwater is willing to work with us to optimize it.

Again, I may be missing something, but I think that it would make a lot more sense to label the X axis "Partial pressure of inert gas in breathing mix", the Y axis as partial pressure of inert gas in controlling tissue compartment" and to rename the "ambient pressure line" as the "saturation line".

Now one problem with that (apart from the wordiness) is that the graph is supposed to help you visualize the process that happens during ascent, which is why the x-axis is usually labeled some variant of "depth or ambient pressure". Sure, gPPN2 is proportional to depth if you don't switch gasses, but that's not intuitively apparent to a new diver. With traditional labeling, it makes sense that as you move towards the surface, the ambient pressure drops, and decompression happens.

There are no units on the traditional graph, but you could make a graph with units and with the X and Y axes scaled differently. That way you could keep the slope of 1.0 for any given mix. The fact that it is generally depicted without units means that people assume that pressure is measured in the same units. But if that's the case, and if you are plotting tPPN2 vs gPPN2, you only would get a slope of 1.0 with 100% N2. You either have to change the slope of the "saturation line", or change the scale of one of the axes.
 
One can draw a graph with any x- and y-axis as you like. But remember there's a model behind it with arithmetic calculations where GF has a clearly defined meaning and these formulas are used in every Bühlmann decompression software. The graphs are only illustration. Please read "Clearing up the confusion about deep stops" by Erik Baker. If you follow the formulas, then you'll see that at GF=0: p(tis)=p(amb)>p(inspired).

In Bühlmann decompression planning software using Bühlmann's and Baker's formulas for the tolerated pressures and gradient factors, and the Schreiner equation for on-/off-gassing, tissues off-gas at GF=0. You can ascend and off-gas with GF=0. That's a mathematical consequence of the model and has nothing to do with any graphical illustration.

If you re-define that and declare that from now on GF=0 means saturation and no on-/off-gassing, then this new definition of GF in your graphs is different from the meaning of GF inside every decompression software.
 
Again, I may be missing something, but I think that it would make a lot more sense to label the X axis "Partial pressure of inert gas in breathing mix", the Y axis as partial pressure of inert gas in controlling tissue compartment" and to rename the "ambient pressure line" as the "saturation line".

Unfortunately, things are more complicated and ambient pressure is the better name: Consider (for simplicity) that you are breathing pure oxygen during decompression. That has the same amount of inert gas as vacuum. In particular, it's independent of depth. That means, if the criterium for deco were ambient inert gas pressure it would be dangerous to breath O2, because that increases the gradient even more.

But that is clearly not the case. This is why Bühlmann (and models derived from that like gradient factors) compare tissue inert gas pressure to total ambient pressure and not ambient inert gas pressure. It's more like the 45 degree line has less meaning than one might think and in fact GF=0 is not really special.
 
One can draw a graph with any x- and y-axis as you like. But remember there's a model behind it with arithmetic calculations where GF has a clearly defined meaning and these formulas are used in every Bühlmann decompression software. The graphs are only illustration. Please read "Clearing up the confusion about deep stops" by Erik Baker. If you follow the formulas, then you'll see that at GF=0: p(tis)=p(amb)>p(inspired).

In Bühlmann decompression planning software using Bühlmann's and Baker's formulas for the tolerated pressures and gradient factors, and the Schreiner equation for on-/off-gassing, tissues off-gas at GF=0. You can ascend and off-gas with GF=0. That's a mathematical consequence of the model and has nothing to do with any graphical illustration.

If you re-define that and declare that from now on GF=0 means saturation and no on-/off-gassing, then this new definition of GF in your graphs is different from the meaning of GF inside every decompression software.

I'm not personally redefining anything, I was citing how others (Pollack, Lewis, Antilla) seem to be describing GF0, in the context of improving the Shearwater graph. I have read Baker's articles, but I certainly don't pretend to be anything close to an expert on decompression. I do appreciate the time you are spending trying to explain this to me.

I think that the problem is that some authors (cited above) use GF0 to refer to a lack of overpressure gradient - it's not something that I just came up with . For example, the DiveRite article:

"..ascent and decompression occurs between the M-value line and Ambient Pressure line. Inert gas pressure in tissue compartments must exceed the ambient pressure to enable off-gassing. 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 from Steve Lewis, who has "gradient factor zero" coincident with the ambient pressure line in this graphic:

View attachment 483487


So maybe these are all oversimplifications at best or inaccuracies at worst. I do understand your point about drawing a line below the ambient pressure line to correspond with real breathable gasses that have some O2 in them, with a slope proportional to the inert gas in the mix. And of course I understand that decompression is driven by the gradient between the PPN2 in a tissue compartment and the PPN2 in the breathing gas mix, not ambient pressure.

So I think that the only issue perhaps is that the term GF0 has been widely used incorrectly? And that gets us back to the discussion of how to improve the decompression graph for teaching purposes. The implication in this chart (and in some teaching materials) is that the decompression zone is the space between the ambient pressure line and the M-value line. And that confusion seems to come from the fact that mix is not addressed in the chart, so you don't illustrate the space below the ambient pressure line where decompression is also occurring due to the gradient?

One option (which I mentioned upthread) would be to have a version of the graph with the x-axis being PPN2 in the breathing gas as opposed to ambient, with the ambient line replaced by a similar (but sloped) saturation line, which would accurately represent the floor below which decompression cannot occur.
 
Hi All,

Gabe from Shearwater, who was responding to this thread and generating the graphs, is away on a diving trip. I will respond for Shearwater but I have not had time to fully read the thread.

I do see some discussion that the "Ambient Pressure Line" (i.e. the y=x line) is not a useful or proper reference point for defining the gradient factor during decompression, and instead the "Saturation Line" (perhaps better named the inspired inert gas pressure line) should be used. In fact, the ambient pressure line is the proper reference when looking at decompression risk.

The reason we compare against the ambient pressure line when deciding the ascent profile is that we are concerned with limiting bubble growth. We assume that micro-bubble seeds exist within the liquid tissues of the body. These bubbles are subject to the hydrostatic force of the surroundings (i.e. ambient pressure), so the total pressure inside the bubble is at least ambient pressure (but is in fact slightly higher due to surface tension of the bubble skin). Bubbles grow when the dissolved gas tensions in the tissues exceed the free-gas pressure in the bubble (i.e. exceed ambient pressure). This is a simplification (more details beyond scope here and can be found in most decompression texts), but explains why we compare tissue tensions against the ambient pressure line when evaluating decompression risk. The difference between tissue tensions and inspired inert-gas partial pressure is still used for calculating rates of on or off gassing, but isn't the gradient to evaluate when determining decompression sickness risk.

Best regards,
Tyler Coen
Shearwater Research
 
Thank you for staying with us on this thread!
If you have a chance before Gabe comes back, the other issue that you'll discover if you can wade through all the posts, is that we are wondering how Shearwater anchors GF Lo during ascent. There have been theoretical discussions of the implications of a very slow ascent just below the calculated ceiling that allows stops to clear before ascending to the target depth. Assuming a diver ascends in that fashion (clearly not the most efficient), and never reaches the GF Lo depth before the computer clears the need for that stop, how does Shearwater anchor the GF Lo so as to begin a transition to GF Hi?

Sorry if my question is confusing. It's better outlined earlier, but I was trying to spare you from reading all our discussions.
 
Thanks, Gabe!

So the references that say there is no supersaturation at GF0 are misleading or wrong? That's what I'm coming to understand, thanks to @leadduck.

For example, from Steve Lewis: "One can think of gradient factors (GF) as a way of adjusting the decompression algorithm to suit our needs, and 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)."

It's also confusing to say that decompression happens between the ambient line and the M-value line. For example, this is how it is described in the DiveRite article - "Inert gas pressure in tissue compartments must exceed the ambient pressure to enable off-gassing." - yet decompression happens below ambient pressure as long as there is a gradient between tissue saturation and gas saturation. I do understand your point about limiting bubble growth, but would it be correct to say that the offgassing that occurs between the saturation line and the ambient line is less of a concern than that that occurs above the ambient line?

In terms of editing the graphic, the ambient line has a slope of 1.0, and if you were to plot saturation lines, they would have slopes corresponding to the inert gas content of the mix. That might be confusing from a graphic design point of view, but maybe better to illustrate the concepts in this thread...?
 
A line y=0.79*x (let's call it the saturation line for an air dive) could be helpful as it would
(a) show the boundary between on-gassing and off-gassing regions and thereby help illustrate the conceptual difference between on-/off-gassing p(tis)-p(inspired) vs. DCS risk p(tis)-p(ambient), and
(b) mark the starting point for the ascent after a long bottom time (saturated tissue). In the last updated graph shown above, the ascent starts on the line y=x which it shouldn't.

@doctormike: considering your quotes from literature, I concede you're rightfully confused. I wasn't aware that these mistakes are so widespread in published texts.

The formulas are unambiguous. I think the confusion is caused by widespread ambiguous use of the terms "saturation" and "supersaturation". The physical definition is based on a liquid that has a surface to the gas phase, like a glass of water in a chamber filled with gas. "Saturation" means maximum solubility reached and no more on-/off-gassing whereas total ambient pressure doesn't matter; see Henry's law. In the Bühlmann model, p(tis)=p(inspired) is similar to that state.

Hence "supersaturation" means only "off-gassing" but doesn't say much about DCS risk. You can bring all tissues into strong supersaturation instantaneously by switching your breathing gas to oxygen without increasing DCS risk. Performing the exactly the same ascent replacing your oxygen stage with an air fill will give you less supersaturation yet higher DCS risk.

p(tis)>p(ambient) implies supersaturation because always p(ambient)>p(inspired). Things get wrong when one says that p(tis)>p(ambient) equals supersaturation and is required for off-gassing, which seems to be a widespread mistake.
 
This is really helpful, thanks so much, @leadduck..!

So, getting back to the original question of improving the graph, GF0 simply means p(tis) = p(ambient), but an offgassing gradient is already established by that point in the leading compartment at greater depths, to a degree inversely proportional to the inert gas percentage in the mix. And that also explains why switching to a richer mix changes that gradient (and offgassing efficiency), but doesn't change the current GF99 (using Shearwater terminology) and DCS risk. That scale is graded from ambient to M-value limit, not from p(inspired) to M-value limit, which seems to be poorly or inaccurately explained in several publications.

And now I understand your suggestion for changing the graph once again.
 

Back
Top Bottom