Deep vs shallow SPORTS diving... which is safer?

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Sorry, I don't believe in "no deco" dives, and that a "required stop" is not a deco stop. You can call it "safety absence of upward motion" or you can call it "pink floyd with fucsia tinge", that's entirely up to you, to me: it's a stop and it is non-optional.
Since you say you refuse to use words the way they are used by others and prefer to use your own definitions, you may be interested in someone else who has the same belief--Humpty Dumpty in Alice through the Looking Glass. Here is the relevant section so you can see your kinship.

When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean—neither more nor less.’

‘The question is,’ said Alice, ‘whether you can make words mean so many different things.’

‘The question is,’ said Humpty Dumpty, ‘which is to be master—that’s all.’

Alice was too much puzzled to say anything, so after a minute Humpty Dumpty began again. ‘They’ve a temper, some of them—particularly verbs, they’re the proudest—adjectives you can do anything with, but not verbs—however, I can manage the whole lot of them! Impenetrability! That’s what I say!’

‘Would you tell me, please,’ said Alice ‘what that means?’

‘Now you talk like a reasonable child,’ said Humpty Dumpty, looking very much pleased. ‘I meant by “impenetrability” that we’ve had enough of that subject, and it would be just as well if you’d mention what you mean to do next, as I suppose you don’t mean to stop here all the rest of your life.’

‘That’s a great deal to make one word mean,’ Alice said in a thoughtful tone.

‘When I make a word do a lot of work like that,’ said Humpty Dumpty, ‘I always pay it extra.’

‘Oh!’ said Alice. She was too much puzzled to make any other remark.

‘Ah, you should see ‘em come round me of a Saturday night,’ Humpty Dumpty went on, wagging his head gravely from side to side: ‘for to get their wages, you know.’
 
Alice is the required reading in my profession, but I use the word the way Powell et al used it in the DSAT '94 report.
 
Alice is the required reading in my profession, but I use the word the way Powell et al used it in the DSAT '94 report.
Try using the words the way PADI uses them. It is their table. Powell et al made input to it, a quarter-century ago. Things have evolved.
 
I've got my mind into a muddle thinking through all this decompression theory and hoping someone can kindly switch my light bulb back on...

Where I dive it has become common practice to do the last dive deepest simply because people controlling the dives think that a short deep dive (31m for 40 minutes) is safer than a long shallow one (say 18m max for 60 minutes)... so we would have done two 18-24m-ish dives on Friday, same again on Saturday, and then a 'quick' deep dive on the Sunday before getting away to drive back home after the long weekend away.

On the one hand I understand that tissue saturation is a time vs depth equation... it's driven by half-life's of the various tissues... so on a short dive you'd in-gas the fast tissues but not as much of the slower tissues as you would on a longer dive. But Henry’s Law of diving physics states that the amount of gas absorbed by a tissue is directly proportional to the partial pressure of the gas in contact with the tissue...

I know that decompression theory is not a 'simplistic' thing but is it rather at a simple level just a time driven thing, based on tissue half life's...?

In recreational no-deco-stop diving, IS a deep short dive safer than a longer shallower dive, assuming all else is equal in terms of ascent rate control, safety stops, hydration, etc...?

Research debated at the "Reverse Dive Profiles Workshop", conducted at the Smithsonian Institution in Washington D.C., in October 1999, resulted in the conclusion that in fact reverse profile diving (on the same dive or over a sequence of multi-day dives) was perfectly acceptable as long as the generally accepted 40m depth limit was not exceeded and that any repetitive dive was not more than 12m deeper than the preceding dive. This has subsequently however been disputed more recently (2013) in some dive medical books I've read and all seems to be endlessly in debate (as much around decompression theory seems to be).

If on both dives a diver has breathed their cylinder 'empty' (from say 230bar down to 50bar), haven't they both in fact breathed and thus in-gassed the same volume of inert gas? As an aside I've always questioned in my mind whether gas loading is influenced or not then by our breathing rate too rather than just something time-based...? So, to my original question, if you breathe the same volume of gas on both the deep and shallow dives isn't the in-gassing near enough the same and thus one isn't necessarily safer than the other at all...?

I appreciate and value any guidance and clarity...

This addresses your question indirectly, but Hobbs et al have done probabilistic modeling of dive profiles. Below is one we did a few years ago for trimix dives. In general, with all of the decompression models we looked at, the probability of DCS increased with both depth and bottom time.

Hobbs GW, Murphy FG, Gault KA, Hexdall E, Howle LE, Walker JR. Decompression risk evaluation for trimix divers derived from commercially available desktop decompression algorithms. Abstract/poster, Undersea and Hyperbaric Medical Society annual scientific meeting, June 2014

Best regards,
DDM
 
This addresses your question indirectly, but Hobbs et al have done probabilistic modeling of dive profiles. Below is one we did a few years ago for trimix dives. In general, with all of the decompression models we looked at, the probability of DCS increased with both depth and bottom time.

Cool. You can plot time vs. depth where the "most conservative" estimate crosses the 2% risk line, but with only 5 points it's hard to tell if the dependency is linear or a curve... but either way longer shallower dives actually look "better" to me on that one.
 
The exact percentages aren't so significant as the slopes of the lines. The model that was used was based on HeO2 and Nitrox dives, so it isn't perfectly suited for trimix. Can you clarify "only 5 points"?
 
The exact percentages aren't so significant as the slopes of the lines. The model that was used was based on HeO2 and Nitrox dives, so it isn't perfectly suited for trimix. Can you clarify "only 5 points"?

There's 5 graphs for 5 depths. You can take time vs depth point where estimated risk becomes e.g. 2% on each graph. You get 5 points for 5 depths. I.e. you're taking a derivative to look at the dependency of risk on depth and time.

Then you plot it, look at the slope, and tell the OP that risk increases with depth faster than it does with time. Or not.

With the actual numbers you could do it per-model and/or per risk level and see how they stack up. Not sure it's of much practical use for dive medicine, it's just studying software behaviours, but that's what I frequently do at work, so...
 
That would be awesome except like you said, part of it is software behavior. I don't think you can draw hard conclusions about specific depths and times from any of this, aside from the idea that none of them are, as Gene Hobbs put it, iso-risk.
 
That would be awesome except like you said, part of it is software behavior. I don't think you can draw hard conclusions about specific depths and times from any of this, aside from the idea that none of them are, as Gene Hobbs put it, iso-risk.

Right. Part of the OP's question was about the belief that "deep and short" is "safer" than "long and shallow", I'd say it's about trends rather than specific depth and times. Those plots could show the trends as per the current models and we could see if they match the belief. We do trust the models on real dives to real depth, so why not trust them on trends as well?
 

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