On a NDL dive, which computers' NDLs are not affected by GFLo?

[NAM001]

I think you have a small misconception here. Let's say we're talking about a 5-minute compartment.

After 6 half-lives in any compartment, that compartment is >98% saturated. So, in a 5-minute compartment, after 30 minutes that compartment is essentially saturated (presuming you have stayed at a constant depth the whole time).

If, at that point, you were to descend, your compartment would no longer be saturated, but it would equalize to ambient fairly quickly and you'd be back to saturated.

So, imagine that you are now at some depth and have been there for >30 minutes. That 5-minute compartment is saturated. You begin to ascend. No matter what speed you ascend, you are now supersaturated. Which means you are off-gassing. If you ascent to the surface without stopping (no matter how quickly or slowly), you will be supersaturated the whole way. Meaning, you will be at 100% saturation the whole way.

What the Buhlmann (ZHL-16B/C w/GF) algorithm says is that there is a supersaturation ratio during your ascent.

Let's say you were breathing air and you were at 100' for 30 minutes. 100' is 4 ATA. For ease of math, let's pretend air is 80% Nitrogen (instead of ~79%). After 30 minutes at 100', your 5-minute compartment is saturated, so your tissue tension of Nitrogen is 80% (the fraction of N2 in your inspired gas) of 4 ATA, or 3.2 ATA (approximately - this is a little bit simplified).

If you ascended instantaneously to 33', where the ambient pressure would be 2 ATA, you would have tissue tension of 3.2 ATA of Nitrogen and the inspired partial pressure of Nitrogen (i.e. the ppN2 in the gas you're breathing) would be 80% of 2, or 1.6 ATA.

That ratio of 3.2 : 1.6 is the over-pressurization gradient (in your 5-minute compartment). So, at that moment that you arrive at 33', that compartment has an over-pressurization gradient of 2.0. The Buhlmann algorithm is accompanied by a set of M-values. Those M-values are the Maximum over-pressurization gradient for each compartment. I don't know what the M-value is for a 5-minute compartment, so let's just say it is 4.0. Then, that would mean that, after your instantaneous ascent from 100' to 33', your OPG is 2.0 and the M-value is 4.0. So, your current gradient factor for that tissue compartment would be 50% - i.e. GF50. In other words, at that moment, your 5-minute compartment is 50% of the way to its M-value.

If you ascended at 30' per minute, instead of instantaneously, yes you would off-gas some from that compartment, so when you arrived at 33', your tissue tension of N2 would no longer be 3.2. The math to calculate what it would actually be is what is called the Schreiner Equation, which is part of any implementation of the Buhlmann algorithm.

Regardless, where your post was off is that as you ascend, your saturation level does not drop, ever.* That saturation level only decreases when you are descending (and even then, it only decreases if you descend fast enough to overcome the rate of on-gassing that is trying to keep you saturated).

When you are breathing air during the dive, that means you started with a body that was saturated on the surface. So, it has 0.8 ATA of Nitrogen in your tissues. As you breathe air and descend, the ambient pressure increases and the pressure of Nitrogen in the air you're breathing increases correspondingly. If you drop to 33', your body has 0.8 ATA of N2 and the air you're breathing has 1.6 ATA of N2. So, you are not saturated and you are on-gassing. If you stay there for 30 minutes, that compartment will be saturated. I.e. your tissues will have 1.6 ATA of N2 - the same as the air you're breathing. As soon as you start to ascend after that, you will go from being saturated to being supersaturated. Your body will have 1.6 ATA of N2 and the air you're breathing will be less than 1.6 ATA of N2. It will drop from 1.6 to 0.8 when you get back to the surface. Your body will gradually follow suit until it changes from supersaturation back to saturated with 0.8 ATA of N2.


* Note: That statement applies to if you are breathing air during your dive. Your level of saturation is always relative to the inspired gas (i.e. the gas you're breathing). So, any time you change breathing gases, your saturation level instantly changes up or down, depending on what you were breathing, for how long, your dive profile up to that point, and what you changed to.

I think we agree and it is poor wording on my part. my point that some of the comments sounded like they did consider that off gassing was going on during the ascent. My thing about no longer being saturated was (my fault) in relation to the deep depth prior to ascending and not the current depth where you will be saturated like you say. OR a slow enough ascent and you will not have tissues at the deep level when you get to say 50 ft from 100 ft. both factors are changing the ambient and the tissue pressure that the difference is measured with. Decreasing the depth increases the ratio while off gassing is reducing the ratio. I really think we are on the same page if only I could word it better.

 

[huwporter]

It seems the reason they are of equal 3 msw sizes is the combination of "big enough", "not too big" and "we've always done it this way".

There's a physical reason the stop must be at some X bar above ambient pressure: to get the off-gassing going effectively. Obviously, it can't be so large it takes you over the M-value. E.g. Buhlmann says (on p.41 of Decompression 1884 English edition) :

Apologies, I thought it was clear that I was referring to the steps between the gradient factors that are allowed at each stop, not the stops themselves, I've edited my post to try and make it clearer. (I agree with what you say about the 3m/10ft interval between the actual stops themselves, by the way, and in addition it also works nicely in both Metric and Imperial systems.)

To clarify further for the example I gave, for a 20/80 dive with seven stops and the first at 18m, each step in "allowed" gradient factor is an equal size of 10%, giving a sequence 20% (at first stop) -30%-40%-50%-60%-70%-80% (at surface). If it was a 30/85 dive with first stop at 45m, then there would be equal steps of 3.4375% over the 16 stops required, giving a sequence 30% (at first stop) - 33.4375% - 36.875% - 40.3125% -etc etc up to 81.5624% at the 3m stop, and 85% at the surface,

There is no mathematical reason why these GF steps must be equal sizes (other than it is easy to programme, and works kinda consistently for any number of stops and any total GF gap), mathematically no reason why you couldn't do, say, an exponential decay between first and last stop, e.g. 20%-50%-65%-72.5%-76.25%-78.125%-close enough call-it-80%, or something else. I've experimented with a few alternative approaches myself.

Before Ross Hemmingway finally went completely off the rails and got himself banned, one of the few things he said in his epic VPM-fundamentalist gish-gallop ranting that I actually agreed with was that gradient factors are a 'kludge' - and honestly, they kind of are. However, they are also a kludge that is mostly useful and valuable (even if they occasionally show odd things at edge cases, like at the edge case between no-deco and deco).

 

[NAM001]

In the case of NDL diving, I think GFHi is an end of dive limit rather than acting one end of the adjusted m-value line. During the dive you're just compared to where you would be if you surfaced now (regular ascent). More or less like DSAT; as I've come to learn there is no DSAT m-line.

So now we have SW, Deep6, Dive Rite all agreeing that for all intents and purposes it's GFHi that affects NDL on a NDL dive, and I suspect once we get info on the other computers we'll be able to say that with some certainty

if you are going to interpulate values at any depth you have to have two end points those end points would be gf hi and lo. with out them you could not determine the 50 or 30 ft values. I view the GF line as interstate 80 and saying you can not cross north of I80 with out getting a motel, You can not define I-80 by saying identifying its start in the west only. with out the end in the east you dont know where I80 lies in nebraska or ohio.

 

[huwporter]

Not only this is correct, I don't believe "NDL", "no stop", or "no decompression" is mentioned even once in the entire Erik Baker's "Clearing up the confusion about 'Deep Stops'", where he proposed and defined the GF system.

No-stop diving was not a part of the problem statement in the first place.

No stop diving is mentioned in Erik Baker's "understanding M-values" paper though, to quote:

M-value sets can be classified into two categories, no-decompression sets and decompression sets. No-decompression M-values are surfacing values only. The DSAT RDP M-values are an example. No-stop dive profiles are designed so that the calculated gas loadings in the compartments do not exceed the surfacing M-values. This allows for direct ascent to the surface at any time during the dive.

Perhaps not directly relevant to discussion about gradient factors, but interesting that he classifies no-deco and deco separately.

 

[stuartv]

if you are going to interpulate values at any depth you have to have two end points those end points would be gf hi and lo. with out them you could not determine the 50 or 30 ft values. I view the GF line as interstate 80 and saying you can not cross north of I80 with out getting a motel, You can not define I-80 by saying identifying its start in the west only. with out the end in the east you dont know where I80 lies in nebraska or ohio.

But you don't HAVE to interpolate, if you don't want to. You could just use the same GF value for all depths. You'll still get a sloped line from your starting depth to the surface.

It's just like if they had designed I-80 by saying "it will be at latitude 38 degrees North, from east coast to west coast."

 

[NAM001]

But you don't HAVE to interpolate, if you don't want to. You could just use the same GF value for all depths. You'll still get a sloped line from your starting depth to the surface.

It's just like if they had designed I-80 by saying "it will be at latitude 38 degrees North, from east coast to west coast."

absolutely but even the 38 north defines both ends of hte line. And in one of my comments i suggested that perhaps what you said may actually happen using the gf hi and parrellelling the gf line toteh m line and that line used for NDL dives and then it would change to redefine using teh desired gf lo when you exceed the ndl established by gf hi. It was really programming lligic comments more than any thing else. by doing that making a gf line parrellel tothe gf hi it would be something line 85/85 instead of 30/85 untill you exceed NDL and then it would swotch form 85 85 to the actual 30 85 in order to use teh same logic but applied on a diferent set point to establish teh first stop. 85 85 would pretty well guarantee a non stop trip to the surface so long as it was with in assumed ascent rates. but if you would magically go from 120 to 30 ft in a split second you would generate a stop. it would not happen because the ascent time allows degass asnf the same tissue pressure of deep ins not the same at 120 as it is at 30 because of hte off gassing for the 2 minutes to ascend from 120 to 30. So even programming wold allow a deco stop in an ndl dive. The legistics of the dive would never create the situation to call a atop. Example go back to teh 60's when we used a hhoerse collar and a co2 charge. pull the cord at 120 ft and ,30 sec you are on the surface. you would probably , with todays computers, generate a stop. the loop hole would be there but would never be activated because we do controlled ascents at programmed rates.

Any way if different makers use different methods in their programming they may give the same results so long as ascent rates are controlled. when they don't the different makers would start outputting differnt results. I read form other posts that some conservative settngs are done by adding depth to the dive or changing your puter calculations for altitude diving and others use sets of GF's. And they probably all perform nearly the same so long as baseline assumptiion are also maintained.

 

[dmaziuk]

Apologies, I thought it was clear that I was referring to the steps between the gradient factors that are allowed at each stop, not the stops themselves, I've edited my post to try and make it clearer. (I agree with what you say about the 3m/10ft interval between the actual stops themselves, by the way, and in addition it also works nicely in both Metric and Imperial systems.)

But since the GF formula itself provides the straight-line slope, the steps between the factors mirror the steps between the stops. There is no math reason to use the "straight line kludge", you could probably come up with a formula to e.g. mimic Thalmann's linear off-gassing above some threshold value.

No stop diving is mentioned in Erik Baker's "understanding M-values" paper though

Not the same paper though. Yes, that is rather clear on the use of GF Hi for calculating NDL, I just don't think he ever considered the corner case of transition from no-stop to deco with a ridiculous GF pair.

 

[huwporter]

But since the GF formula itself provides the straight-line slope, the steps between the factors mirror the steps between the stops. There is no math reason to use the "straight line kludge", you could probably come up with a formula to e.g. mimic Thalmann's linear off-gassing above some threshold value.

Yeah exactly. I think one of the specific downsides of the current implementation is that it can occasionally throw up disconcertingly long deep stops that don't really make physiological sense . Example:

=========================================================================
 FIRST DIVE: Standard GF Plan:
 65m for 40 mins OC on 15/55 with 50%+O2, GF 20/85

 Phase                Depth   Time       RunTime   Mix O2/He Ceiling GF
 -----                -----   ----       -------   --------- ------- --
 Descent To:          65m     3.6 min    3:37      15/55     0m      0
 Bottom Phase:        65m     36.4 min   40:0      15/55     27m     0
 Ascent To:           42m     2.6 min    42:34     15/55     26m     20
 Stop:                42m     2.0 min    44:34     15/55     25m     20
 Stop:                39m     2.0 min    46:34     15/55     24m     24
 Stop:                36m     3.0 min    49:34     15/55     23m     29
 Stop:                33m     3.0 min    52:34     15/55     22m     32
 Stop:                30m     5.0 min    57:34     15/55     20m     39
 Stop:                27m     6.0 min    63:34     15/55     18m     42
 Stop:                24m     8.0 min    71:34     15/55     16m     47
 Stop:                21m     4.0 min    75:34     50/0      14m     52
 Stop:                18m     5.0 min    80:34     50/0      12m     55
 Stop:                15m     8.0 min    88:34     50/0      10m     62
 Stop:                12m     10.0 min   98:34     50/0      8m      63
 Stop:                9m      17.0 min   115:34    50/0      5m      71
 Stop:                6m      59.0 min   174:34    100/0     0m      75
 Surface:                                174:34                      85

 Deco Time (21-6) = 103
 Estimated Total Runtime (including switches and gas breaks): 202 mins.
=========================================================================

I mean, waiting eight whole minutes at 24m on 15/55 just to get down to 47% of the M-value, when you have a deco gas waiting for you just one stop shallower? And total 30 whole minutes creeping up between 42 and 24m before you can get on a deco gas? Outside the internal logic of the model, It just doesn't make sense, and means you have to do a whole lot more deco shallower to compensate for it. This model behaviour is at least part of what people are complaining about when the 'deep stops are good/bad' discussions come up.

Some alternatives I've played with are:
Setting a maximum tolerable GF for each compartment separately, which then remain fixed through the dive rather than varying. example, you could set for, "never allow compartment 1 to exceed 20% of allowable M-value, compartment 2 to never exceed 40% of allowable M-value, etc etc.

=========================================================================
 FIRST DIVE: Modified GF Plan:
 65m for 40 mins OC on 15/55 with 50%+O2, GF 85

 Phase                Depth   Time       RunTime   Mix O2/He Ceiling GF
 -----                -----   ----       -------   --------- ------- --
 Descent To:          65m     3.6 min    3:37      15/55     0m      0
 Bottom Phase:        65m     36.4 min   40:0      15/55     27m     0
 Ascent To:           39m     2.9 min    42:54     15/55     26m     31
 Stop:                39m     1.0 min    43:54     15/55     25m     31
 Stop:                36m     1.0 min    44:54     15/55     25m     39
 Stop:                33m     2.0 min    46:54     15/55     23m     47
 Stop:                30m     2.0 min    48:54     15/55     22m     54
 Stop:                27m     3.0 min    51:54     15/55     21m     63
 Stop:                24m     5.0 min    56:54     15/55     19m     71
 Stop:                21m     3.0 min    59:54     50/0      16m     75
 Stop:                18m     5.0 min    64:54     50/0      13m     79
 Stop:                15m     6.0 min    70:54     50/0      11m     77
 Stop:                12m     9.0 min    79:54     50/0      8m      81
 Stop:                9m      14.0 min   93:54     50/0      5m      82
 Stop:                6m      53.0 min   146:54    100/0     0m      84
 Surface:                                146:54                      85

 Deco Time (21-6) = 90
 Estimated Total Runtime (including switches and gas breaks): 174 mins.
=========================================================================

Now reduced to 14 minutes on stops below the first gas switch, a lot better. This approach can give "nicer looking" results for some dives, particularly dives with multiple deco gases (like the one above) but not so well for others - it doesn't work well at all for planning backgas deco (you can get into situations where the model can't ever let you surface), and the limits per compartment aren't based on any kind of science, just totally made up from gut feel.

One rather neat solution is to have rules along the lines of; have an initial GF threshold at which you slow your ascent from say 9m/min to 3m/min, then ascend at this rate til you arrive at a second GF threshold, then do a conventional linear interpolation from there to the surface. Example for this, say, do 9m/min up to GF20, then 3m/min up to GF 65, then a linear interpolation from there to GF85 at surface:

=========================================================================
 FIRST DIVE: Multi-Stage GF Plan:
 65m for 40 mins OC on 15/55 with 50%+O2, GF 20/65/85

 Phase                Depth   Time       RunTime   Mix O2/He Ceiling GF
 -----                -----   ----       -------   --------- ------- --
 Descent To:          65m     3.6 min    3:37      15/55     0m      0
 Bottom Phase:        65m     36.4 min   40:0      15/55     27m     0
 Ascent To:           42m     2.6 min    42:34     15/55     26m     20
 Deep Stop:           42m     1.0 min    43:34     15/55     26m     20
 Deep Stop:           39m     1.0 min    44:34     15/55     25m     28
 Deep Stop:           36m     1.0 min    45:34     15/55     24m     36
 Deep Stop:           33m     1.0 min    46:34     15/55     24m     45
 Stop:                30m     2.0 min    48:34     15/55     22m     57
 Stop:                27m     4.0 min    52:34     15/55     21m     65
 Stop:                24m     6.0 min    58:34     15/55     18m     69
 Stop:                21m     4.0 min    62:34     50/0      15m     70
 Stop:                18m     4.0 min    66:34     50/0      13m     69
 Stop:                15m     7.0 min    73:34     50/0      11m     75
 Stop:                12m     9.0 min    82:34     50/0      8m      75
 Stop:                9m      14.0 min   96:34     50/0      5m      77
 Stop:                6m      53.0 min   149:34    100/0     0m      81
 Surface:                                149:34                      85

 Deco Time (21-6) = 91
 Estimated Total Runtime (including switches and gas breaks): 177 mins.
=========================================================================

This reduces many of the oddities of the normal GF implementation and works well in most situations. I would argue that deep stops are not bad in and of themselves as a principle, but that excessive deep stops are pointless and counterproductive.

I'll have a think about how to implement linear off-gassing.

Bit of thread drift going on here.

 

[Jay]

Bit of thread drift going on here.

Yeah I noticed ... change of tact ... no worries ...

If/when there's more dive computer info form other brands I'll post an updated list.

 

[stuartv]

@huwporter : If you are willing to get out of the water with your inert gas loading at 85% of the way to its M-value (in your leading compartment, of course), why are you not willing to let your body get up to 85% of the M-value on the way up to your first stop?

The ratio of your tissue tension of inert gas to inspired inert gas is the same, either way. So, why do you think it's important to keep that ratio lower at, say, 42m than at the surface? (presuming you do, just because your post uses GF20/85).

As noted, by insisting on having a lower GF99 at your first stop, you are increasing the amount of on-gassing you do in your slower compartments. Doing that, with a GFHi of 85, means that your leading compartment is bumping against 85% when you surface, either way. But, with a GFLo of 20, you are getting out of the water with a greater amount of inert gas still in your slower compartments compared to if you ascended with a GFLo of 85.