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Thread: Understanding the shape of the curve… a technique for demystifying decompression

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    Understanding the shape of the curve… a technique for demystifying decompression

    In an earlier article, I presented reasons why dive computers simply aren’t the best option for general use in technical diving. It seems appropriate to follow it up with an article pointing out my idea of a better option.

    First of all, we should put things into some kind of perspective. This article is not a how-to guide to decompression diving without a computer. The topic of staged decompression diving is complex and can’t possible be covered adequately in a short article such as this. In any event, staged decompression diving is a very dangerous sport and my sincere advice is don’t take part in it at all.

    Secondly, the real intention of this article is to outline a technique I have taught to interested and qualified divers for several years. It’s not a foolproof way of producing a decompression schedule – there is no foolproof way of doing that – but it has been used without incident in various locations, most particularly in the Great Lakes region of North America, where the water is cold and conditions tough. Bear in mind, what is being presented here is just an outline. There are a couple of steps I have purposely glossed over to “disable” the information. I say again: Don’t try this you’ll die.

    Do you remember doing pre-calculus in high school? Functions, x-y coordinates, plotting, graph paper, sound familiar? No, most people are in the same boat, but no worries. There’s no math here, just some simple addition and subtraction that doesn’t even require a calculator.

    Anyhow, if you did remember your math classes, you’d recall that it’s possible to describe all sorts of complex calculations by drawing simple and elegant curves. The point being: There’s a pattern somewhere out there among all those f (x, y)’s and tangents, and if you can just find it, you can solve all sorts of complicated problems very fast and impress people.

    OK, so math wasn’t a core competency in school. How about music? Playing the guitar for instance? And if you didn’t play in the school band, perhaps you wore a Mohawk and played in a punk band! If you did, you’ll know that most songs about sex, drugs and rock an’ roll require you to know only three chords as long as you play them real fast. The trick to playing fast is using one chord shape (the pattern formed by your fingers pressing down on the strings) and sliding it up and down the neck of the guitar… an E played at the top of the guitar’s neck becomes an F one fret down, a G three down and an A if you move it down a couple more. Wow, that’s four chords for the price of one! The point being: There’s a pattern somewhere out there among all those B flats and C minors, and if you can just find it, you can play all sorts of neat sounding music very fast and impress people.

    So what does this have to do with plotting a decompression schedule? Well, everything. You see the calculations made within a decompression algorithm – any decompression algorithm – can be expressed quite nicely as a pattern, just like one of those functions from high school. In fact, in most cases, we can find an anchor point for the algorithm where that pattern becomes a very simple gentle curve expressed against time and depth.

    Broadly speaking, every gas mixture – every flavor of nitrox or trimix – has its own particular shape and anchor point, which can be learned and applied to any dive using that mix.

    If we apply the guitar analogy, each gas mixture has its shape and it can be moved up and down in the water column to cover longer, shorter, deeper and shallower dives with that gas just like we can move a chord shape up and down the guitar neck to play different notes.

    By adopting the practice of using standard mixes, we further simplify the learning process… effectively, be only have to learn a couple of chord shapes to cover just about every tune – or dive – we are going to do.

    Now all this is fine, but where do we start? What shape is an E chord?

    First, you have to pick an algorithm that makes you feel comfortable, safe and secure. There are plenty of them out there, so take your pick.

    Once you have your algorithm, you have to think about which gas mixes you intend to use as your gold standard.

    For my personal use, I’ve adopted the VPM-b algorithm as published by Ross Hemmingway from code developed by Erik C. Baker. What I like about this solution to the “deco challenge” is that both the mathematical premise and the physiological state it's designed to model, make sense to me. It’s also got enough of a track record for me to feel comfortable with it. Hemmingway’s version of it is inexpensive to buy, runs on most windows platforms, is simple to use, is relatively bug-free, and is supported and updated professionally and regularly by its creator. If you want to check it out, go to

    Standard gases for deep dives include a mix containing about 16% oxygen, 45% helium with nitrogen making up the remainder. This is a dangerous mix to breathe until you get about 10 feet underwater, so we need to use a travel mix with it… my choice is another helium, oxygen and nitrogen mix with 32% oxygen and 25% helium. To round things out, we need something to accelerate decompression. The standard mixes would be a 50% nitrox and pure oxygen.

    With this in mind, here’s a schedule kicked out by V-Planner for a dive to 245 feet for 30 minutes… a modest dive by some standards, but an excellent place to start to build a “deco baseline.” Look at it and see if you see any sort of pattern.

    Dec to 120ft (2) on Trimix 32.0/25.0, 50ft/min descent.
    Dec to 200ft (4) on Trimix 16.0/45.0, 50ft/min descent.
    Dec to 245ft (4) on Trimix 16.0/45.0, 60ft/min descent.
    Level 245ft 25:15 (30) on Trimix 16.0/45.0, 1.31 ppO2, 103ft EAD
    Asc to 200ft (30) on Trimix 16.0/45.0, -50ft/min ascent.
    Asc to 165ft (32) on Trimix 16.0/45.0, -30ft/min ascent.
    Stop at 165ft 0:56 (33) on Trimix 16.0/45.0, 0.94 ppO2, 64ft EAD
    Stop at 160ft 1:00 (34) on Trimix 16.0/45.0, 0.91 ppO2, 62ft EAD
    Stop at 155ft 1:00 (35) on Trimix 16.0/45.0, 0.89 ppO2, 59ft EAD
    Stop at 150ft 1:00 (36) on Trimix 16.0/45.0, 0.86 ppO2, 57ft EAD
    Stop at 145ft 1:00 (37) on Trimix 16.0/45.0, 0.84 ppO2, 54ft EAD
    Stop at 140ft 1:00 (38) on Trimix 16.0/45.0, 0.82 ppO2, 52ft EAD
    Stop at 135ft 2:00 (40) on Trimix 32.0/25.0, 1.59 ppO2, 58ft EAD
    Stop at 95ft 1:50 (43) on Trimix 32.0/25.0, 1.21 ppO2, 36ft EAD
    Stop at 90ft 1:00 (44) on Trimix 32.0/25.0, 1.16 ppO2, 33ft EAD
    Stop at 85ft 1:00 (45) on Trimix 32.0/25.0, 1.12 ppO2, 30ft EAD
    Stop at 80ft 1:00 (46) on Trimix 32.0/25.0, 1.07 ppO2, 28ft EAD
    Stop at 75ft 2:00 (48) on Nitrox 50.0, 1.60 ppO2, 35ft EAD
    Stop at 65ft 1:50 (50) on Nitrox 50.0, 1.45 ppO2, 28ft EAD
    Stop at 60ft 1:00 (51) on Nitrox 50.0, 1.38 ppO2, 25ft EAD
    Stop at 55ft 2:00 (53) on Nitrox 50.0, 1.30 ppO2, 22ft EAD
    Stop at 50ft 2:00 (55) on Nitrox 50.0, 1.23 ppO2, 19ft EAD
    Stop at 45ft 2:00 (57) on Nitrox 50.0, 1.15 ppO2, 16ft EAD
    Stop at 40ft 3:00 (60) on Nitrox 50.0, 1.08 ppO2, 12ft EAD
    Stop at 35ft 4:00 (64) on Nitrox 50.0, 1.01 ppO2, 9ft EAD
    Stop at 30ft 3:00 (67) on Nitrox 50.0, 0.93 ppO2, 6ft EAD
    Stop at 25ft 5:00 (72) on Nitrox 50.0, 0.86 ppO2, 3ft EAD
    Stop at 20ft 5:00 (77) on Oxygen, 1.57 ppO2, 0ft EAD
    Stop at 15ft 23:00 (100) on Oxygen, 1.42 ppO2, 0ft EAD
    Asc to sfc. 2:00 (102) on Oxygen, -10ft/min ascent.

    Off gassing starts at 197.5 ft

    (to be continued tomorrow)


    Before we continue with our search for the E chord in our algorithm, we need to consider – and generally agree with – a few basic principles on which we are going to build our understanding of the Deco Curve.

    1. Decompression algorithms are just pure mathematics trying to model biology
    2. Biology is weird and is difficult to model with pure math
    3. Decompression theories contain varying amounts of guesswork – some more than others since goats and jello couldn’t explain how they felt
    4. Decompression theory is constantly being refined (The only constant is change)
    5. There is no such thing as a foolproof decompression schedule
    6. Decompression is affected by several variables: some, like hydration, we can control. Others we can’t.
    8. Given all the above, you realize and accept that by conducting staged decompression dives, you have become part of the experiment. TAKE LAB NOTES!
    9. Whenever you exit the water after a staged decompression dive – and regardless of what your decompression schedule or (gods forbid) your computer is telling you, LISTEN to what your BODY is TELLING YOU.
    10. Given a few basic rules and some simple “memory work” almost anyone can produce a decompression schedule on the fly that’ll work

    So let’s look again at our v-planner example. Frankly, we could have used any algorithm – US Navy, Buhlmann, DCIEM, Ben & Jerry’s, it really makes no difference. You be the judge. I use VPM and v-planner as previously stated because it works nicely.

    If you want to run the profile yourself, please note a couple of things… I set the conservatism to zero or actually “Nominal.” This may not be the way you or I would choose to dive but it does show us the “pure” algorithm… more or less… so it’s where we start.

    Also, I have set the staged stops at 5-foot intervals. This is actually the way I deco when doing “my thing” on deep exposures in Great Lakes conditions and after deep cave dives whenever practical. The best way I can describe the reason for doing it this way is to quote the guy who taught me a lot about trimix diving… a guy called Larry Green. He said it’s like paying your house mortgage every two weeks instead of every month. Don’t think Larry nor I can really explain compound interest but it made sense to me then and still does.

    Additionally, I think it better models the actual behaviour I’ve found to work well in cold water after deepish dives… a gentle rise through the water column with few hesitations, rather than the 10 foot hops and stops that one commonly sees – and in fact that most of us were taught.

    It also helps illustrate the shape of the “curve.”

    On the down side, this produces a hell of a lot of information… not something that’s gonna fit on your dive slate!

    There are three “whoopses” in the example I posted yesterday, I set the final stop at 15 feet, I left extended stops turned on, and the altitude should have been set to sea level but was at something else. These were mistakes. But we’ll deal with that later.

    Basically, you can see that apart from the two minute stops at gas switches – one whoops – the algorithm is asking us to stop for one minute every five feet all the way from 165 feet to 70 feet! (Well, hold on there’s a nasty gap there on account of the extended gas switches… the other two whoops allow me to switch something over and repost a purer example)

    Here… same gases, same depth, same bottom time…. This should be clearer! What you’ll notice without too much analysis is that we can separate the dive into several distinct phases… that I notate.

    DESCENT AND BOTTOM TIME (NOTE AS WELL THAT THE DEPTH 245 feet IS THE SAFE MOD FOR THIS MIX… APPROX. PO2 1.3 100 feet EAD (this is crucial when setting the baseline for finding the curve)

    Dec to 120ft (2) on Trimix 32.0/25.0, 50ft/min descent.
    Dec to 200ft (4) on Trimix 16.0/45.0, 50ft/min descent.
    Dec to 245ft (4) on Trimix 16.0/45.0, 60ft/min descent.
    Level 245ft 25:15 (30) on Trimix 16.0/45.0, 1.32 ppO2, 104ft EAD

    Asc to 200ft (30) on Trimix 16.0/45.0, -50ft/min ascent.

    Asc to 165ft (32) on Trimix 16.0/45.0, -30ft/min ascent.
    Stop at 165ft 0:56 (33) on Trimix 16.0/45.0, 0.94 ppO2, 64ft EAD
    Stop at 160ft 1:00 (34) on Trimix 16.0/45.0, 0.91 ppO2, 62ft EAD
    Stop at 155ft 1:00 (35) on Trimix 16.0/45.0, 0.89 ppO2, 59ft EAD
    Stop at 150ft 1:00 (36) on Trimix 16.0/45.0, 0.87 ppO2, 57ft EAD
    Stop at 145ft 1:00 (37) on Trimix 16.0/45.0, 0.84 ppO2, 54ft EAD
    Stop at 140ft 1:00 (38) on Trimix 16.0/45.0, 0.82 ppO2, 52ft EAD
    Stop at 135ft 1:00 (39) on Trimix 16.0/45.0, 0.80 ppO2, 49ft EAD
    Stop at 130ft 1:00 (40) on Trimix 16.0/45.0, 0.77 ppO2, 47ft EAD

    Stop at 125ft 1:00 (41) on Trimix 32.0/25.0, 1.50 ppO2, 53ft EAD
    Stop at 120ft 1:00 (42) on Trimix 32.0/25.0, 1.45 ppO2, 50ft EAD
    Stop at 115ft 1:00 (43) on Trimix 32.0/25.0, 1.40 ppO2, 47ft EAD
    Stop at 110ft 1:00 (44) on Trimix 32.0/25.0, 1.36 ppO2, 44ft EAD
    Stop at 105ft 1:00 (45) on Trimix 32.0/25.0, 1.31 ppO2, 42ft EAD
    Stop at 100ft 1:00 (46) on Trimix 32.0/25.0, 1.26 ppO2, 39ft EAD
    Stop at 95ft 1:00 (47) on Trimix 32.0/25.0, 1.22 ppO2, 36ft EAD
    Stop at 90ft 1:00 (48) on Trimix 32.0/25.0, 1.17 ppO2, 34ft EAD
    Stop at 85ft 1:00 (49) on Trimix 32.0/25.0, 1.12 ppO2, 31ft EAD
    Stop at 80ft 1:00 (50) on Trimix 32.0/25.0, 1.07 ppO2, 28ft EAD
    Stop at 75ft 1:00 (51) on Trimix 32.0/25.0, 1.03 ppO2, 25ft EAD

    Stop at 70ft 1:00 (52) on Nitrox 50.0, 1.53 ppO2, 32ft EAD
    Stop at 65ft 1:00 (53) on Nitrox 50.0, 1.46 ppO2, 29ft EAD
    Stop at 60ft 1:00 (54) on Nitrox 50.0, 1.38 ppO2, 26ft EAD

    Stop at 55ft 2:00 (56) on Nitrox 50.0, 1.31 ppO2, 22ft EAD
    Stop at 50ft 2:00 (58) on Nitrox 50.0, 1.24 ppO2, 19ft EAD
    Stop at 45ft 2:00 (60) on Nitrox 50.0, 1.16 ppO2, 16ft EAD
    Stop at 40ft 3:00 (63) on Nitrox 50.0, 1.09 ppO2, 13ft EAD
    Stop at 35ft 4:00 (67) on Nitrox 50.0, 1.02 ppO2, 10ft EAD
    Stop at 30ft 4:00 (71) on Nitrox 50.0, 0.94 ppO2, 7ft EAD
    Stop at 25ft 4:00 (75) on Nitrox 50.0, 0.87 ppO2, 3ft EAD

    Stop at 20ft 5:00 (80) on Oxygen, 1.59 ppO2, 0ft EAD
    Stop at 15ft 6:00 (86) on Oxygen, 1.44 ppO2, 0ft EAD
    Stop at 10ft 8:00 (94) on Oxygen, 1.29 ppO2, 0ft EAD
    Stop at 5ft 10:00 (104) on Oxygen, 1.15 ppO2, 0ft EAD

    Asc to sfc. 0:30 (104) on Oxygen, -10ft/min ascent.

    By the way, the CNS loading for this dive is rated at about 55% thanks to our behaviour in the danger zone and the 1.3 ata po2 delivered by our back mix at depth.

    So, what do we have? Basically, the VPM-b algorithm is telling us that the decompression portion of our 16/45 trimix dive is divided into five distinct phases each of which has certain behaviours associated with it:

    Phase One: once we leave the bottom, we travel at a pretty good clip up to the off-gassing ceiling… the point at which the math tells us our body starts to kick out more gas than it takes in… then we slow down ‘til we reach the start of Phase Two

    The Phase Two is essentially a slow ascent taking about one minute to transit 5 feet. This is the coolest part of the dive – here in the Great Lakes this is both a virtual and literal statement – but drifty up slowly through the water column is my favourite part of the dive… especially in open water and a current. This phase lasts until the gas switch to EAN50 but more often 5 or 10 feet shallower… always! Well, always is a heavy statement, but in the Great Lakes, it’s difficult to get enough bottom time WITH THIS GAS MIX to bring the third phase – classic deco – any deeper in the water column. So always!

    And now, Phase Three: the start of decompression. Up until this point we’ve only needed to know two things to execute a safe decompression: Where’s the off-gassing start and where do we switch gases? Since we use standard mixes, we already have one answer. However, here in Phase Three, we need a little more information. Basically it looks like this is where we start search for a pattern.

    The Fourth Phase always starts at 20 feet and again, looks as though it may be exhibiting a pattern… in fact, it may be drive the pattern in Phase Three or perhaps it’s the other way around… I wonder?

    The Fifth Phase is the slow rise to the surface and the beginning of the surface interval. Always a constant. But don’t ignore procedures during this final stage. I have seen people who would otherwise have been OK hurt themselves by lifting, struggling out of gear and banging knees and elbows on dive ladders and boat decks.

    Before we move on to discuss Phases Three and Four, let’s recap three points that are really germane to the way this technique works… indeed, they make it work.

    The first is gas choice. The gases I’ve used in this example are the gases I generally use for a dive of this type to this depth… I have used these flavours of gas for years and know how to mix them and understand the shape of the decompression curve for them. However, please don’t think because you use something different or you disagree with my use of, say 32/25, that this system is invalid. Fact is, this system will work with any gas you care to name – well, I guess that depends on what you name, but sensible gases work -- only the shape of the curve WILL change and its anchor points (foci) WILL be altered.

    Secondly, is how much of slop are we allowed in our schedule. What I mean is how much latitude do we have with timing and depths. The simple answer to this is that there is no simple answer. I’ve made errors where I have calculated on the fly and buggered up the total transit time for Phase Two on similar dives to this example making it three, four or five minutes less than it should have been, and had absolutely no side effects. But perhaps that was because I was well hydrated, rested, in a good mood and warm and fuzzy throughout the whole dive. If I did the same thing tomorrow, I might be calling DAN. My advice is this: If you cut some corners and it doesn’t work, don’t do it again. If any of this makes you uncomfortable, don’t do it at all. OK?

    Thirdly, and most importantly, what we have talked about is the shape of the algorithm and the curve it produces. I have avoided the subject of ACTUAL APPLICATION. That may very well add a different slant to the whole picture, and it’s that that I am leaving out of this article – after all, I have to have something left to teach my trimix students!

    OK, back to finding the elusive E chord for this gas mix. I think some of you already have it though don’t you?

    It has to do with a simple ratio and it’s sitting there in Phase Four. For this gas at this depth oxygen time and bottom time are just about the same. Thirty minutes of bottom time and 29 minutes thirty seconds of oxygen time. If you have v-planner at home, cut the bottom time to 20 minutes. Increase it to 40 minutes… what do we have. Damn, that was easy. I like this gas!

    We still have to decipher Phase Three, and we need to work out some sort of rule to tell us exactly where Phase Two starts, but essentially we have discovered some things that are quite informative… Simply stated, at its safe MOD, the ratio of 16/45’s bottom time to oxygen time is approximately 1:1 for any dives we’re likely to do with it. Phase Two (slow ascent) starts someplace above the off gassing ceiling and finishes someplace around 70 feet… in our example, these anchor points are 165 feet and 60 feet. (Hey, that’s about 100 feet. Wonder if that means anything?)

    Think about Phase Three tonight (I think you can work out how it’s related to the oxygen phase) and I’ll post the final chapter tomorrow.

    To be continued…

    Final piece

    So let’s try to wrap this up now.

    Starting from the bottom and ascending:

    Phase One starts at 245 feet and runs to the off gassing ceiling (at about 197 feet) and up to the first stop, which is at 165. Is there a pattern here? Yes. As a rough guide we can say off gassing (gas reversal) for this helium mix starts at maximum depth –1.5ata and that the first stop is off gassing –1.0ata. Another way to fix these points is to say gas reversal or off gassing starts at about 80% of the max depth and the first stop should be taken at 65% of max depth.

    Phase Two starts at the first stop, which is [gas reversal depth –1.0ata] or 65% of max depth and runs up to some point around the gas switch to EAN50. There are no real stops here, just a gentle rise through the water column. The output from v-planner indicates a minute for every five feet, which is easy to remember. (We’re going to revisit this later.) So the pattern is pretty simple. Where’s that upper limit again?

    I know I said we wouldn’t discuss actual execution but I have to touch on something to convince you of the upper set point for this dive phase. The switch to a mix containing 50% oxygen is a good spot to wait for a few minutes… a place to spike the oxygen. I use this as the upper limit of Phase Two. Depending on the dive and what happened, I might put a two or three minute buffer ahead of it, but my 70-foot halt is an actual pause and wait for some minutes… always. And is always the start of the next phase.

    Phase Three begins the longer stops… but not really that long. In our example it is three 2s, one 3 and three 4s. And that’s the gold standard. The “adjustments” are that if you needed to add time to a stop or two on the other side of the 70-foot gas switch, mirror the changes in the 4-minute stops. For example, if I were to add a minute to the 75-foot stop, I would add a minute to last 4-minute stop.

    The corollary to this adjustment is that if the bottom time is shorter or the target depth is shallower, time comes off.

    Phase Four is the oxygen treatment. Simple really. Try to remember that the total time on oxygen is slightly less than your bottom time… maybe a minute, sometimes two. Also try to remember that the five-foot stop is about one-third of the bottom time. In our example, a third of 30 minutes is 10 minutes. Looks about right.

    Now what about the rest? Well the 20-foot and the 15-foot equal the 5-foot… so the two of them added together is about 10 minutes. You have to split that two ways… 5 minutes each. (Not quite what our example says, but we know that stop times get longer as we get shallower so the 15-foot stop should always be a bit longer. A minute sounds OK to me. So we could have guessed the 15-foot should be 6 minutes!)

    How about the 10-foot stop? It’s the remainder. In this case, 30minutes minus 10, minus 11 (5 and 6 minutes) leaves 9 minutes. Take a minute away, because the oxygen time is always a minute or two less. Wow. Close.

    What happens if we use the Oxygen pattern for a 45-minute bottom time and then check it against v-planner?

    A third of 45 is 15. So that’s the 5-foot stop time. The 20-foot and the 15-foot have to equal that so divide 15 into two portions giving some extra to the 15-foot stop… that’s 7 minutes for 20 feet and 8 for 15 feet. Correct? The remainder is 15 minus one or two because the oxygen time is always a little less than bottom time. So let’s say 13 minutes.

    What does v-planner say? 7, 8, 12, 15! We were close.

    Let’s do a final recap. What did we set out to do and where did we end up?

    Our goal at the outset was to find a technique we can use to find a curve, shape or pattern that describes the basic decompression schedule of an algorithm… The reason we want to go to the trouble of doing this is so that we can produce – on the fly – a table that stands a good chance of working.

    We’ve touched on a way that mimics what VPM does very well. We first set a baseline – basically the MOD of the gas and a time that reflected our probable maximum bottom time… in this case we used 30 minutes. We dissected the ascent curve and found it had five parts. And we looked at rules that apply to each part of the dive.

    As I said in the beginning, this is a brief and therefore inadequate discussion of the topic, but it’s gonna have to do. You may have other ways to do the same thing. And they may be better. No problems there. The point is, this is not rocket science. Get familiar with an algorithm, cut lots of tables with it and you’ll find yourself seeing that there are patterns to all of them.

    I took me about a year of diving with a series of baselines in the front of my Wetnotes to get comfortable with producing tables this way.

    OK a little sense check.

    I am not suggesting you use this technique instead of running real tables on a real computer program and doing the required planning work. This technique is for contingencies and for diving with Murphy.

    Also, in the example given here, the configuration file was set to default the minimum stops to one minute. This was done intentionally to help simplify the curve and to drive certain results in the final schedule. In fact, if I were to execute this dive, this part of the configuration would change. So would some other things.

    I intentionally glossed over one calculation for Phase Three. Sorry.

    Finally, please don’t try any of this stuff without some knowledge of when and where it’s applicable and a good understanding of how YOUR BODY responds to the rigors of decompression diving. What I hope not to see is someone trying to apply this stuff to a 120-foot dive on EAN30!

    Many thanks to Ross Hemmingway for his suggestions and help with this article… and for writing a bloody decent piece of software.


    Last edited by raxafarian; 10-22-2003 at 22:44.
    Steve Lewis

    Doppler is just a regular guy teaching advanced trimix, DCCCR, CCR, sidemount and overhead programs...

    Contact me or search Amazon for copies of my books, The Six Skills, and the latest: Staying Alive.

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