Help me understand how deco stops are calculated.

[Gareth J]

I am by no means a physiologist, and have only a basic understanding.

1. There are multiple decompression theories and models.
2. They are a mathematical model that attempts to explain how the body is believed to work in terms of saturated tissues.

Note the phrase theoretical and model and believed.

It is known that the body can with stand a supersaturated state of an absorbed gas within its tissues, beyond a particular percentage a bend is likely to occur, below a certain percentage, a bend is unlikely to occur. This is what is often known as the M value. An M value exist for each compartment.
Models use multiple 'compartments' to simulate how different tissue types are likely to behave. i.e. tissues that are likely to on gas and off gas quickly, to tissues that are likely to on gas and off gas slowly.
Compartments are arbitrary numbers [1], at some point some one picked a number, when the model didn't work well, they picked some more numbers, either adjust existing compartment times, or adding new compartments to the model.
As such a relatively standardised set of compartment times have been developed.

The calculation (mathematical model) tracks each compartment.
For a no-stop dive, each compartment is tracked to ensure it won't exceed its M value for a given depth (& time). Thus allowing a direct ascent to the surface (within the limits of the model - ascent rate).
For dives where any one or groups of compartments exceed the safe M value are exceeded, a decompression stop will be required. The off gasing is calculated by the model, once the offending compartment(s) falls back within the safe limit (M-value), ascent can proceed, stoping again, as the pressure drops if the M value is calculated to be exceeded.

Stop depths are another arbitrary number [2], Fixed depths are a practical issue. For the original divers, hardhat divers, winching a diver to a particular depth, then leaving them there for a specified period of time was practical and simple.
It is possible to calculate stops on the fly allowing the divert progress ever shallower as they degas. The VR3 [3] allowed the 'diver on a rope' function rather than fixed stop depths, or as it was known in the UK, dick on a rope.

There are a number of good books on decompression theory available. Mark Powells book (deco for divers) is an excellent start. Even the PADI DM book has a good section on explaining the basics around decompression theory.

Nothing I have said here should be taken as fact. I am sure others will attempt to correct any error I have made.
Please always remember, what we know about decompression science is all theoretical, we still don't really understand it. No decompression model is 100% safe, all have an element of risk. There are personal actions you take that are highly likely to increase the risk of a decompression hit - irrespective of the model you wish to use.

Haladyn is probably regarded as the grandfather of decompression theory.
Bhulmann models are probably the most well known. A lot of this is the fact that Professor Buhlmann made is model free to all (un-licenced). So manufacturers have implemented into there equipment, all be it with manufacturer designed 'improvements'(?).


[1] A lot of these initial numbers where established by Haldane
[2] another series of numbers initially determined by Haldane
[3] Early technical computer

 

[swimlikethefish]

The graph in this post is wrong. Most of these diagrams are and the only confuse anyone that tries to properly read them.

The dotted red line purports to represent the interpolation of GF low to GF high. So where does GF lo apply on this graph? Where exactly is the GF 30? Apparently the lowest GF, at the first stop, is some number between 30 and 80, but not actually 30.

Compare this graph to the ones in “Technical Diving, an Introduction” about page 199. Those illustrate this with a line at 30% and a line at 80% so there is no need for this dotted line which doesn’t exist below the first stop, or ought to have a kink if you want to represent the limit.

I expect the typical SB’er will think I am being excessively pedantic but actually everything to do with this scheme needs to be looked at and understood properly, none of it can be left out or ignored.

Photo is brought to you by the wonderful gentleman at diverite. I just pulled the first one in Google search results. Although not drawn to perfect scale, I do feel it gives a good representation of the theory the OP was asking about.

 

[KenGordon]

Photo is brought to you by the wonderful gentleman at diverite. I just pulled the first one in Google search results. Although not drawn to perfect scale, I do feel it gives a good representation of the theory the OP was asking about.

Don’t trust the internet. It is full of lies. It is incorrect, correct ones are available. See figure 4 Delving Deeper into Deep Stops - Divernet

 

[dmaziuk]

For the small part that i understand from it, the low GF is the one that determines the depth of the first stop the high GF determines the duration of the last one.

The duration of the stops are determined by the time you need to be able to ascend to the next stop without passing the imaginary line between GFlo and GFhi.

This is my guess btw, I might be completely wrong.

Duration of the stop is how long until you can ascend to the next stop without crossing the M-value line. As far as stops etc. are concerned, everything is "below" M-value line or "above" M-value line, that's it.

All GFs do is change the slope of the M-value line and, if used as intended, shift it closer to the ambient pressure line. GF Hi is the M value you surface with (the surface is the "last stop"), GF Lo is the M-value at the first stop -- expressed as percent of the Buhlmann model's original M values for those depths.

 

[dmaziuk]

Don’t trust the internet. It is full of lies. It is incorrect, correct ones are available. See figure 4 Delving Deeper into Deep Stops - Divernet

The bad part about this picture from DiveRite site is: on Erik Baker's original it does not say "safety margin" anywhere. I don't think that entire paper he ever says anything other than "more conservative", with no claims about them being "more safe" or "less risky". Everyone looking at that shiny infographic walks away thinking "lower GFs = safer GFs" whereas the original intent was for the diver to figure out what profile they consider safe, then adjust gradient factors so their computer would match it.

Or at least that's my reading of his paper.

 

[hammet]

Read this: DIY DECOMPRESSION -- he may be skimming over a few details but it's a good and concise explanation. What you're asking is from step 3b on.

Edit: the calculations are typically done in a loop, as you'll see in the above. Yes, you could do it with pen and paper but it would really suck because you'd have to repeat the same thing over and over again. It's much easier to e.g. learn a bit of python and do it in a jupyter notebook.

This is excellent. Gonna take a while to absorb it but it's along the lines of what i'm looking for!

 

[scubadada]

@Gareth J

Haldane, John Scott

 

[Gareth J]

@scubadada

Yep, I do something similar with Buhlmann, Bhulmann

I'll correct the original post

How I get Haldane wrong I don't know, Haldane with the goats in the loft ...

 

[hammet]

Found this article very helpful too.
Decompression Theory ~ Gear & Training ~ New Jersey Scuba Diving

The notation stinks but has an easy example to follow.

 

[NAM001]

hammet. Let me make a crude example of how it works. You have a balloon at 100 ft that can hold 1 cuft before it bust's (M line) because the balloon is older and does not have the flexibility it used to hav,,,, you only let it fill to 90% full to be safe. (gf hi line) now you ascend and the balloon gets larger untill it gets to .50% and you stop and vent it down to .25 cuft., then you go up till it gets to 65% and again you stop and vent . you do this till yo get to the surface. your depths would be 100 50 25 12 6 and surface. when you were deep you started with the ballon at 30% and a stop and vent at 50%,,, that defined when you had to stop the first time to vent off. as you went up you gradually increased your max inflation from the 50 to about 90%,,, your last stop you vented such that if you went to the surface so the ballon would not be fuller than 90%. In this case your GF would be 50/90. Hadf you set it go rt40 90 you would have stopped the first time a little deeper but the rest would have been the same. The computer keeps track of a hypothetical body and tracks how much gas pressure in the balloon and compares it with the surrounding water pressure to determine how much the gas expanded and inflated the balloon which it knows will bust at a somewhat known point. NOw imagine that with 16 different balloons of different strengths. The 100% inflated lime or the M line is the place when you start to bubble such that you will highly prone to getting the bends or the balloon is highly prone to bursting. the gf ilne is a changing line limit that graduates you to larger allowed pressure changes so that most the gas is off loaded or vented in the water rather than on the boat. the schedule of stop and vent is such that when you are on the boat you have close to the M line value or GF hi where you can sit calmly for an hour while you do your highest rate of off gassing starting from a level that is less than the M line or gf hi max limit. M line is a physiological limit. gf is a lower limit assigned to provide a safety buffer between what you will do and the max allowed by M line. If this was a highway the m line is the posted 75mph speed limit. when it rains or snows you lower your personal max to 65 mph (gf hi). A somewhat identical process happens when you ascend and have to vent the bcd from time to time t control the ascent rate. the the case of deco the ascent rate/stops are used to control the off gas rate and max rate. So with that in mind the computer tracks teh tissue pressures adn water pressure. compares them through out a projected hypothetical ascent that must follow rules such as 30 ft /min. given that the computer says at that rate at a depth of 53.8 ft you will reach the max limit set by gf low and you are to stop to x minutes. when completed ascent at 30/min till you get to 25 ft when you reach the interpolated gf between gf hi and low as it applies to that depth. If gf lo was 30 at 65 ft and gf hi is 85 on surface than 25 ft would be computed to be around 65.

The process is not difficult to do because like dropping a stone from a tall building you can calculate time to hit the street because of constants like accelleration and time. If everything was perfect you could do deco with no stops but use a for instance 8 ft / minute ascent rate. everything is inter linked to each other. Ibn case yo screw one of them up you lower teh limit of the M line to a lower gf hi limit to make up for your unknown deviations from the ascent assumptions the deco is based on.