Why the U-shaped difference between air and Nitrox NDLs (PADI tables)?

[Esprise Me]

Short version: I noticed that, if you calculate the difference in NDL between air and 32% Nitrox using PADI tables as a percentage and plot those numbers on a graph, you get something of a U shape, with the least increase in bottom time at 90 feet. Why is that?

Long version for those avoiding work:
I was thinking again about the problem raised in this thread, of realizing during a dive that you've set your computer to Nitrox but you're actually diving air: In dive, manage having EAN programed into computer while diving air? I thought I had a solution at the time, but I realized after I posted it why it wouldn't work. (Basically, you can't go backwards and calculate a percentage of remaining NDL; you have to base it on your total NDL for the dive.)

I also began to question my back-of-the-envelope calculation that 32% offers roughly 50% more bottom time than air. I decided to go back and check for all depths listed on the PADI tables I have, starting with 50 feet. What I found was that the additional bottom time Nitrox gives decreased with depth, not only in number of minutes, but in percentage of additional time. At 50 feet, you get 75 extra minutes, or 94% more. That drops to 64% at 60 feet, and 50% at 70 and 80 feet. At 90 feet, you only get an extra 10 minutes, or 40% more.

But then I noticed something more surprising--past 90 feet, the trend reverses. At 100 feet, you also get 10 more minutes, which is 50% more. At 110, you get 9 minutes, which is 56% more. The Nitrox tables include 120 and 130 feet for contingency planning purposes only, since you'd be beyond the MOD for a max PPO2 of 1.4 (but still under 1.6) . At 120 you get only 7 minutes, or 54% more, but then at 130, you'd get an extra 8 minutes, which is 80% more!

Why is this? I'm guessing the little blip where it drops down a couple percent at 120 feet is due to rounding, but the overall U shape of the graph is pretty stark. Is this based on mathematical models of how bubbles behave, or is there some human factor being considered?

I did the same calculations using the dive planner on my Teric and did not get the same results. The percentage of additional bottom time decreased from 95% at 50 feet to 38% at 110 feet. (It would not let me calculate Nitrox bottom times beyond that--even though I switched off 21% as an available gas, it would only calculate 120 and 130 with that. In fact, it gave me slightly *less* time than when 21% was the gas I selected!)

I'd love to hear from anyone with a different set of tables or algorithm whether this trend can be observed elsewhere, or if it's unique to PADI tables.

 

[johndiver999]

My simplistic mental model is that nitrox just knocks off X feet of effective depth - relative to air. Obviously the X is a function of FO2.

The NDL limits for air are NOT linear versus depth over the entire range of rec. diving depths, so when you apply the "x-factor" on top of that function, you are not going to get a linear result... does that make sense?

 

[inquis]

Not a lot of insight to offer, but you probably want to view in terms of pressure, not depth.

As to the question, I suspect that's just how the math works out with different tissue compartment halftimes. A tissue loading graph has the opposite U shape (higher at medium tissue rates).

 

[tursiops]

Short version: I noticed that, if you calculate the difference in NDL between air and 32% Nitrox using PADI tables as a percentage and plot those numbers on a graph, you get something of a U shape, with the least increase in bottom time at 90 feet. Why is that?

Long version for those avoiding work:
I was thinking again about the problem raised in this thread, of realizing during a dive that you've set your computer to Nitrox but you're actually diving air: In dive, manage having EAN programed into computer while diving air? I thought I had a solution at the time, but I realized after I posted it why it wouldn't work. (Basically, you can't go backwards and calculate a percentage of remaining NDL; you have to base it on your total NDL for the dive.)

I also began to question my back-of-the-envelope calculation that 32% offers roughly 50% more bottom time than air. I decided to go back and check for all depths listed on the PADI tables I have, starting with 50 feet. What I found was that the additional bottom time Nitrox gives decreased with depth, not only in number of minutes, but in percentage of additional time. At 50 feet, you get 75 extra minutes, or 94% more. That drops to 64% at 60 feet, and 50% at 70 and 80 feet. At 90 feet, you only get an extra 10 minutes, or 40% more.

But then I noticed something more surprising--past 90 feet, the trend reverses. At 100 feet, you also get 10 more minutes, which is 50% more. At 110, you get 9 minutes, which is 56% more. The Nitrox tables include 120 and 130 feet for contingency planning purposes only, since you'd be beyond the MOD for a max PPO2 of 1.4 (but still under 1.6) . At 120 you get only 7 minutes, or 54% more, but then at 130, you'd get an extra 8 minutes, which is 80% more!

Why is this? I'm guessing the little blip where it drops down a couple percent at 120 feet is due to rounding, but the overall U shape of the graph is pretty stark. Is this based on mathematical models of how bubbles behave, or is there some human factor being considered?

I did the same calculations using the dive planner on my Teric and did not get the same results. The percentage of additional bottom time decreased from 95% at 50 feet to 38% at 110 feet. (It would not let me calculate Nitrox bottom times beyond that--even though I switched off 21% as an available gas, it would only calculate 120 and 130 with that. In fact, it gave me slightly *less* time than when 21% was the gas I selected!)

I'd love to hear from anyone with a different set of tables or algorithm whether this trend can be observed elsewhere, or if it's unique to PADI tables.

I think you need to include the fundamental concept that NDL depends on which "compartments" are being filled up, which is a function of their time constant and their m-values. The longer the dive (i.e., mid-depths) then the more that the longer time-constant compartments come into play. At greater depths, only the short-time-constant compartments come into play. So your "U-effect is as likely to be an artifact of which compartments are controlling and their associated time-constants and m-values, than anything else. And, yes, PADI tables do NOT have the same compartments as your Teric.

ADDED: basically the same comment just made by inquisit.

 

[mc42]

Remember that Nitrox calculations are done as an equivalent air depth. So the EAD for 100' on 32% would be 81' on air, 90' -> 73', etc. The pressure groups on my air table at 80' match up pretty nicely with the 100' @ 32% pressure groups, to within 1 minute or so (which I presume is rounding and/or the more precise calculation done for 80 feet). The NDL is identical as well, 30 minutes.

Checking a few more, EAD for 80' on 32% is 64' on air. The numbers also match, if you interpolate between 60 and 70'. The NDL for 60' and 70' on air are 55 and 40 minutes, respectively, and for 80' on 32% it is 45 minutes. The rest of the pressure groups also interpolate in between.

Just like there's no rule that says that half the depth = 2x the NDL, I don't think there would be a hard "Nitrox gives you X%" more NDL mainly because this is just a mapping back to the air table, and would be dependent on what the air table says, which in turn is based upon the different controlling compartments at various times in the dive, but I'd have to give it more thought.

The PADI RDP air table of course is based upon the underlying DSAT 14 compartment model, which is different from the Teric's 16 compartment model, so the different algorithms, fine-tuning of RDP for no-stop rec diving, plus gradient factors on the Teric will give different, though grossly similar values. The NDL calculations only seem to get close between the two when you use high gradient factors, like 95%.

As for the U-shape non-linearity, it's likely rounding-related as a one minute difference either way will make the discrepancy vanish. At least the trends on the individual air and nitrox tables are in the right direction (deeper = less NDL).

Edit: comment on the U-shape.

 

[BRT]

The theory we were taught was that you could stay at 32' forever on air and still go directly to the surface. I know that is questioned now, but nitrox just moves that limit deeper, and 50' is just barely over that limit. So the starting point for NDL calcs is not the surface, it is at about 1 additional atmosphere of water pressure.

 

[Raphus]

I think the u shape is there because after 90ft the NDL drops very fast.
For nitrox(like other already said) a 100 ft dive is the same then a lower dive on air.

Because of the fast decrease of NDl, after 90 ft, the nitrox NDL doesnt catch up that fast, because the nitrox diver is shallower(on the tables).

Thats why the percentage of extra NDL is higher after 90ft. So its not about the function of nitrox NDL, its about the fast decrease of air NDL,because its not linear. Does this make sense?

 

[yle]

Part of the issue is that the times are rounded to the nearest 5 minutes. So when you're dealing with times that are 10 to 20 minutes, rounding to the nearest 5 minutes creates a pretty big uncertainty as a percentage.

If you misinterpret the numbers as exact, then it looks "U shaped". If you recognize that at the deeper end the uncertainty becomes almost as large as the numbers themselves, the "U" becomes very fuzzy.

 

[lowwall]

Remember that Nitrox calculations are done as an equivalent air depth.

This is the answer. The depth/time curves are identical in shape, just offset the appropriate amount to equalize the nitrogen percentage.

I grabbed the first free Android deco planner I saw and can confirm NDLs that are either identical or within 1 minute at the EADs for the 32% vs 21% pairs of 120' & 99', 110' & 90', 100' & 81', 90' & 73', and 80' & 64'.

Of course, this will only be true up to the point where Oxygen toxicity becomes the limiting factor instead of nitrogen loading. So don't use equivalent air depth as a replacement for the full set of calculations on a day where you will be spending multiple hours in the water.

 

[dmaziuk]

I'd love to hear from anyone with a different set of tables or algorithm whether this trend can be observed elsewhere, or if it's unique to PADI tables.

My money is on the latter: the base gal loading formula simply ignores the O2 so the difference from the mix is not depth-dependent. Rate of on-gassing is: it's proportional to delta-pressure, so you'd expect dP to trump the mix at greater depths.

I can't think of a reason for the trend to change at 90' (or any depth): I'd think a switch in controlling tissue compartment could cause a "bump" but not a full "U". So I'm guessing you're looking at round-offs etc.