ceiling/GF

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lermontov

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Awesome! Here's one more thought that just occurred to me, since we are having such fun with this graph.

Unlike the M-value line and the ambient pressure line, the ceiling line doesn't really represent any physical phenomenon that you could measure. It's just shorthand for saying "I'm making my first stop at 30%, I'm getting out of the water at 80%, and in between those two dive waypoints I'll just interpolate in a linear fashion to determine intermediary stops". But in this diagram, we have the line extending to the right of the first stop. Which raises some questions.

1) Does the line really exist before (deeper than) the first stop? I don't think that it does, because it is defined as having maximum depth at one end, and the surface at the other. If you make your dive deeper, then the algorithm is going to generate a different line, as opposed to tracing backwards along the same line.

2) What do you call the point where the ceiling line intersects the ambient line? Mathematically, if you extend them both to the right, they will cross somewhere, since they have different slopes. But given the fact that we represent the slope of the decompression line (blue) to be shallower than that of the ceiling line (green) during the ascent between stops, this intersect isn't at the point of ascent from maximum depth (at least, the way that it is drawn). I think that this intersection doesn't actually exist, because the ceiling line has no meaning beyond the depth range of the dive that generated it.

3) Complicating question #2 is the fact that the slopes of the M-value and ceiling lines are arbitrary, since there are no units on the graph, and the diagram is drawn to illustrate a concept rather than provide an accurate measurement. Even if you were to put PPN2 numbers on the X and Y axes, this diagram is just a simplification of 16 different compartments, each with different M-value lines (and even the 16 compartments are an arbitrary construct).

I'm not a mathematician, and I may be missing something here. What do you guys think?
I think you answered it with point 1- theoretically you could swim along the AP line wth GF of 0 the % only is relevant once you go above that so the GFlo is a moving target so to speak and not a vanishing point
 

doctormike

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I think you answered it with point 1- theoretically you could swim along the AP line wth GF of 0 the % only is relevant once you go above that so the GFlo is a moving target so to speak and not a vanishing point

Actually, it is impossible to decompress without the existence of a pressure gradient, otherwise gas will never leave the tissues. So there is no way to swim along the AP line. Any ascent that you do will transiently result in an overpressure (supersaturation) of any saturated compartment, which will then result in offgassing, which will bring you back to the AP line. You could model this in your mind by imagining running a GF of 1/1, in which case you would have an extremely slow (but very safe!) ascent with a very large number of tiny stops.

GFLo is just a decision that you make ahead of time as to how much supersaturation you will allow when you make your first stop. Not sure what you mean by a moving target.
 

leadduck

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Actually, it is impossible to decompress without the existence of a pressure gradient, otherwise gas will never leave the tissues. So there is no way to swim along the AP line.

The pressure gradient for off-gassing is between the tissue pressure and the inspired inert gas pressure, not between tissue pressure and ambient pressure. You can swim along the AP line (GF0) and decompress very well as long as your breathing gas has less than 100% nitrogen, which is a good idea anyway.
 

doctormike

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The pressure gradient for off-gassing is between the tissue pressure and the inspired inert gas pressure, not between tissue pressure and ambient pressure. You can swim along the AP line (GF0) and decompress very well as long as your breathing gas has less than 100% nitrogen, which is a good idea anyway.

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.
 

lermontov

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. Not sure what you mean by a moving target.
meaning the GFlo is not a fixed point somewhere off in the distance that we intersect when we ascend as the graph seem to indicate ( dotted line- which i think just confuses the issue)
The reference point (or starting point) for the GF% is the point when we pass the AP line, what happens before that is not relevant because were not off gassing
 

doctormike

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meaning the GFlo is not a fixed point somewhere off in the distance that we intersect when we ascend as the graph seem to indicate ( dotted line- which i think just confuses the issue)
The reference point (or starting point) for the GF% is the point when we pass the AP line, what happens before that is not relevant because were not off gassing

The GFLo is an arbitrary decision we make to generate an ascent profile and limit overpressure early in the dive, so we ascend until our overpressure reaches that limit. In practice, our first stop is probably a bit above GFLo based on the chart, since the line slopes from GFLo to GFHi, and we are already a bit of the way along that line by the first stop.

Not sure I understand what you mean by passing the AP line. Do you mean that on the AP line we are always at GF=0? That makes sense...
 

Sol518

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Awesome! Here's one more thought that just occurred to me, since we are having such fun with this graph.

Unlike the M-value line and the ambient pressure line, the ceiling line doesn't really represent any physical phenomenon that you could measure. It's just shorthand for saying "I'm making my first stop at 30%, I'm getting out of the water at 80%, and in between those two dive waypoints I'll just interpolate in a linear fashion to determine intermediary stops". But in this diagram, we have the line extending to the right of the first stop. Which raises some questions.

1) Does the line really exist before (deeper than) the first stop? I don't think that it does, because it is defined as having maximum depth at one end, and the surface at the other. If you make your dive deeper, then the algorithm is going to generate a different line, as opposed to tracing backwards along the same line.

2) What do you call the point where the ceiling line intersects the ambient line? Mathematically, if you extend them both to the right, they will cross somewhere, since they have different slopes. But given the fact that we represent the slope of the decompression line (blue) to be shallower than that of the ceiling line (green) during the ascent between stops, this intersect isn't at the point of ascent from maximum depth (at least, the way that it is drawn). I think that this intersection doesn't actually exist, because the ceiling line has no meaning beyond the depth range of the dive that generated it.

3) Complicating question #2 is the fact that the slopes of the M-value and ceiling lines are arbitrary, since there are no units on the graph, and the diagram is drawn to illustrate a concept rather than provide an accurate measurement. Even if you were to put PPN2 numbers on the X and Y axes, this diagram is just a simplification of 16 different compartments, each with different M-value lines (and even the 16 compartments are an arbitrary construct).

I'm not a mathematician, and I may be missing something here. What do you guys think?


It seems to me that the ceiling line should be parallel to the ambient pressure line to the right of the first stop. That’s what triggers the first stop. When that first stop it triggered the angle changes and it connects the point that triggered the first stop and the point that represents the GFhigh on the surface.

At least that’s the way it makes sense in my head. Thoughts?
 

doctormike

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It seems to me that the ceiling line should be parallel to the ambient pressure line to the right of the first stop. That’s what triggers the first stop. When that first stop it triggered the angle changes and it connects the point that triggered the first stop and the point that represents the GFhigh on the surface.

At least that’s the way it makes sense in my head. Thoughts?

But why does the ceiling line exist before the first stop? What does it mean? At every point on the ascent, the ceiling line represents the overpressure limit, somewhere between GFLo and GFHi, and it represents what you as a diver have decided ahead of time will be the maximum supersaturation you will allow for your limiting component at that depth.

So when you say "this is what my ascent ceiling will be at points below my maximum depth", that seems like a non-sequitur. If you say "I'm going to change my dive plan and dive deeper than I had originally planned", that's fine, but then you aren't using some new part of a previously generated graph, you have a new graph with your GFLo at your new maximum depth.
 

rsingler

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It seems to me that the ceiling line should be parallel to the ambient pressure line
That is not quite correct.
If we define (for this example only) a ceiling of 30% for the first stop, we can draw a line thirty percent of the distance between the ambient pressure line and the M-value line. It will not parallel the ambient line, but rather extend out at the same relative distance from the two reference lines. In fact, most of the early GF depictions did exactly that: there was an AP line, an M-value line, and between them, GFLo and GFHi lines, all spreading out visually like rays of sunlight.
Screenshot_20181002-194346_Google.jpg

Shearwater, in order to declutter their graphic, eliminated the GF lines, since for any given max depth, there is only one point starting at a given max depth and rate of ascent where GFLo is reached, and one point (the surface) where GFHi is reached.
We are struggling here because we forget that any new GFLo point will come about because (as @doctormike pointed out) it must have required a new max depth. As he stated, the ceiling occurs when we reach 30% of M-value for the leading compartment. Having a dotted line that extends past that point to the right is no longer at 30%, because that line is sloped at 30/80 for that max depth only.
Apples and oranges, I'm afraid. You could have a GF line that parallels the ambient pressure line (GF 50/60 comes pretty close), but that's a coincidence only. Furthermore, the ceiling reached when you ascend to that "parallel" line will only be 50% for one depth. Anywhere else, you will have reached a ceiling of more or less than 50% of M-value, depending upon what your new max depth was when you started your ascent.
 

Sol518

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That is not quite correct.
If we define (for this example only) a ceiling of 30% for the first stop, we can draw a line thirty percent of the distance between the ambient pressure line and the M-value line. It will not parallel the ambient line, but rather extend out at the same relative distance from the two reference lines. In fact, most of the early GF depictions did exactly that: there was an AP line, an M-value line, and between them, GFLo and GFHi lines, all spreading out visually like rays of sunlight.
View attachment 482572
Shearwater, in order to declutter their graphic, eliminated the GF lines, since for any given max depth, there is only one point starting at a given max depth and rate of ascent where GFLo is reached, and one point (the surface) where GFHi is reached.
We are struggling here because we forget that any new GFLo point will come about because (as @doctormike pointed out) it must have required a new max depth. As he stated, the ceiling occurs when we reach 30% of M-value for the leading compartment. Having a dotted line that extends past that point to the right is no longer at 30%, because that line is sloped at 30/80 for that max depth only.
Apples and oranges, I'm afraid.

Got it, that makes sense to me.

Rephrasing to make sure, the GFLow point becomes defined what you get to a point that a compartment is at X% of the M-value. That point can be predicted when you begin you ascent, but can change based of your ascent rate. Once that point is defined it creates the ceiling.
 
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