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

[EFX]

Well spotted, although measuring depth in units of pressure needs to be (and probably was, now that I come to think of it) stated up-front.

It's actually measuring pressure in units of depth. I wrote a spreadsheet that displays tissue compartment pressures as well as other data for a particular dive(s). Here is an excerpt from the help tab (ss = spreadsheet):

UNITS OF PRESSURE
All pressure values on the ss are displayed as absolute pressures in feet or meters of salt or fresh water rather than the typical units of psi (imperial) or Kpa (metric). This seems odd at first because a distance unit (feet or meters) is used to define a pressure unit. What seems even stranger is that the gauge pressure is equal to the depth in feet or meters. To understand why this is true consider this relationship: 33 fsw/33 ft (or 10 msw/10m). We can describe it this way: there is a pressure of 33 fsw which is equivalent to a pressure exerted by 33 ft (depth) of water. The spreadsheet converts depth to a pressure in order to calculate insP, the inspired inert gas pressure. For example, to convert 80 ft of depth to its equivalent gauge pressure (P) in fsw we could write: P = 80 ft x 33 fsw/33 ft. As a sanity check on the math the ft divide out leaving fsw which is what we want. The really interesting part is that the 33 divides out giving us an answer that is actually the depth but in pressure units of fsw. This is convenient because it eliminates the need to use cumbersome unit conversions in the formulas. Absolute pressures are obtained by adding the pressure of the atmosphere at the surface to the pressure exerted by the water (which is gauge pressure).

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Since pressures are absolute subtracting the atmospheric pressure gives gauge pressure which is already equivalent to a depth of water which is what the ceiling requires. Here's the equation to calculate ceiling from my previous post.

D = ((P - GF * a) / (GF / b - GF + 1)) - Psb

 

[EFX]

You are absolutely correct that on and off-gassing during ascent must be taken into account to calculate both the NDL and stop durations, and also that a closed-form solution only exists for the special case of a single inert gas.

I'm not sure what you mean by "closed-form" solution. In my spreadsheet I calculate the tissue pressures for nitrogen and helium separately, then add them together to be used to determine a ceiling with its stop times.

 

[inquis]

In my spreadsheet I calculate the tissue pressures for nitrogen and helium separately, then add them together to be used to determine a ceiling with its stop times.

So your ceiling calculation ignores future off-gassing. After you perform the calculations related to ascent and off-gassing, you may find that you didn't need to stop in some cases. That is an implementation choice (and I'd make the same choice in a spreadsheet-based planner). Shearwater choose to do the ascent/off-gassing and ceiling calculation simultaneously.

 

[EFX]

Off-gassing is handled by the R term in the general form of the Schreiner equation. The ceiling and stop times then are calculated based on the tissue pressures at the current depth at the current moment. So, yes, I don't include any future off-gassing in the calculation. I'm curious. How do you know Shearwater includes future off-gassing in their calculation?

If the DC assumes a future off-gassing on the ascent for the ceiling calculation what value do you use? 30 ft/min? 40 ft/min? Since it's safer to ascent at a faster rate when deeper does the DC assume one rate below a certain depth then switch to a slower rate in shallower water? What happens when the diver ascends at a different rate than assumed? I would think the DC would then need to do a recalculation. But, most DC's are doing all the calculations: inspired pressure, tissue pressures, NDL, ceilings and stop times, etc. every second. Using assumed values and recalculating is superfluous and a waste of memory and programming time. Any deviations from standard and/or safe ascents are being adjusted for before the diver reaches the next stop. So, what is gained by assuming a future ascent rate in deco calculations (or for that matter in NDL calculations)?

Shearwater probably does use an assumed ascent rate in predicting TTS (time to surface) but that value is a future prediction. Ceilings don't need to make future predictions and therefore don't rely on assumed values.

 

[David Carron]

If the DC assumes a future off-gassing on the ascent for the ceiling calculation what value do you use? 30 ft/min? 40 ft/min? Since it's safer to ascent at a faster rate when deeper does the DC assume one rate below a certain depth then switch to a slower rate in shallower water? What happens when the diver ascends at a different rate than assumed? I would think the DC would then need to do a recalculation. But, most DC's are doing all the calculations: inspired pressure, tissue pressures, NDL, ceilings and stop times, etc. every second. Using assumed values and recalculating is superfluous and a waste of memory and programming time. Any deviations from standard and/or safe ascents are being adjusted for before the diver reaches the next stop. So, what is gained by assuming a future ascent rate in deco calculations (or for that matter in NDL calculations)?

You are correct; a dive computer will essentially throw away all predictions and start again from scratch making new predictions based on the diver's actual behaviour.

In fact, a good dive computer will be doing all of this twice in parallel so that it can make multiple simultaneous predictions such as "lost deco gas ascent" or (for ccr divers) bail out ascent.

Optimisation is a significant part of programming a dive computer.

 

[EFX]

If the DC is "throwing" away old predictions because the "idiot" diver is not following them then what's the point in making new predictions? The fact that a "good" DC has the power and memory to do parallel multiple predictions is beside the point. Again, what is gained by assuming an ascent rate or by doing a prediction for NDL or for deco stops?

 

[dmaziuk]

That is the point of NDL: it's a purely predictive value that is subject to change the next second. With transient ceilings and theoretical conservatism tweaks on top. That's why nobody wants to study no-stop dives: planned decompression where you know a priori that tissues are over their M0 values, there are stops, etc., and your target user base is trained to follow the plan, is much cleaner.

 

[David Carron]

If the DC is "throwing" away old predictions because the "idiot" diver is not following them then what's the point in making new predictions? The fact that a "good" DC has the power and memory to do parallel multiple predictions is beside the point. Again, what is gained by assuming an ascent rate or by doing a prediction for NDL or for deco stops?

Almost everything about the NDL and ascent profile is based on assumptions. The computer assumes that the diver will maintain the same depth when it calculates NDL, it assumes that the diver will ascend immediately when it calculates the first stop depth, it assumes that the diver will be at exactly the stop depth and breathing the correct gas when it calculates a stop duration, it assumes that deeper stops were executed precisely as indicated when calculating shallower ones.

For iterative solutions, previous predictions are typically used as a seed value for the next iteration, but for direct solutions they really do throw everything away and start from scratch, maintaining only the tissue loading and latched deepest stop.

If you don't assume and take into account p an ascent speed then what tends to happen is that you calculate 0 NDL because the instantaneous ceiling is deeper than the surface but, because of offgassing during the ascent the diver actually has a couple more minutes on NDL.

Now, you might be thinking "a couple of minutes, who cares?" But a dive computer can't have its numbers jumping around all over the place: ndl must drop.continuously and when it reaches zero, stops must start appearing. The stop duration you see displayed at the start of your ascent must correspond pretty well to what you actually end up doing.

That's just the way that dive computers work.