Manual calculation for accelerated deco

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@Dr Simon Mitchell

I see.

My thought was that by scaling stops one would need to add many new ones (at altitude) as compared to the same dive at sea level. Then one could re-expand the stops to equate to a new and deeper (but now equivalent ?) sea level dive. This is where the added stop times would come from.
 
@Dr Simon Mitchell

I see.

My thought was that by scaling stops one would need to add many new ones (at altitude) as compared to the same dive at sea level. Then one could re-expand the stops to equate to a new and deeper (but now equivalent ?) sea level dive. This is where the added stop times would come from.

Hi again Lowviz,

I suspect we are not sharing a mental model on exactly what you mean by 'scaling stops'. At the end of the day you need more time for outgassing before you hit the surface at altitude and there are probably multiple ways you can acheive this from Dan's arbitary addition of shallow stop time, arbitrary assumptions about the depth of your dive (by assuming you went deeper than you did), and others (which is where your approach would probably fit in). If you are conservative many approaches would usually work! Some of the more formal model / software approaches will prescribe an exact decompression pathway to ensure you arrive at shalllow stops and the surface with the same supersaturation as you would at sea level.

Simon
 
Apologies, I don't want to drag this out overlong.

By scaling, I mean that one assigns a new depth to 'one atmosphere' where that reduced depth now correlates to the ambient pressure that is over the water column.

So at 1/2 of a standard sea level atmosphere (found at great elevation), one would use 5m as the depth that corresponds to one atmosphere. One would then use this new depth as a way to count how many atmospheres an equivalent dive would be if carried out at sea level. Depth/5 + 1 = equivalent_ATA
 
In the ZHL / VPM gas kinetic formula, this involves the "Buhlmann-Keller" weighted average formula for combining inert gas pressures and allowable values, into one value for creating ascent limits..

Ross, would you post or PM me the Buhlmann-Keller weighted average formula. Thanks.
 
Hello Lowviz,

No, I don't think so. As I alluded to above, the problem at altitude is that the diver will absorb inert gas at virtuallly the same rate (for a given depth and time) as they would at sea level because every metre of depth still adds the same increment gauge pressure, the regulator / rebreather will still supply gas at that ambient pressure, and the inspired inert gas pressure will be almost the same as at the same depth at sea level. Then on surfacing at altitude the ambient pressure is lower and the supersaturation is therefore higher. To avoid this, the diver needs to do more outgassing before they hit the surface (and quite possibly before they hit the shallowest stops). This will require more time. Simply scaling stop depths would not achieve that.

I think one of the things that people get hooked up on is the role that the small reduction in atmospheric pressure at altitude plays in all this. Put simply, it has little role in influencing inert gas absorption at depth, but it has a potentially significant role in determining tissue supersaturation back at the surface. For example, if we are at an altitude where the atmospheric pressure is 0.8 atm, then at a depth of 50m (165') the ambient pressure will be 5.8 atm absolute instead of 6 atm absolute for the same dive at sea level. This difference of 0.2 atm only represents a 3% reduction in ambient pressure, so inert gas uptake will be virtually unchanged. In contrast, if you decompressed from this dive using exactly the same protocol as you did at sea level, then you would arrive at the surface with potentially 20% greater tissue supersaturation because the ambient pressure is 0.8 atm instead of 1 atm.

Simon M
Thank you for this. You said it so much better than I did.
 
What matters at altitude is not just the difference in total pressure. What matters is what happens to the diver during the dive. At 2,000 meters, the atmospheric pressure is about .8 that of sea level. The water, however, weighs the same at any altitude. That means that a diver at 204 FFW at sea level is at 7 ATA. At 2,000 meters, that diver is at 6.8 ATA--not much difference (less than 3%) at all because nearly the entirety of the total ATA comes from the weight of the water. That means the diver will be ongassing at approximately the same rate as at sea level. As the diver ascends and breathes the same gases he or she would be diving at sea level, the diver offgases at about the same rate. What is different at altitude is that as the diver nears the surface, the lesser air pressure becomes more and more and more significant, with that last 34 feet (1 ATA fresh water) making the most difference. At 34 FFW, the ambient pressure at that altitude is 1.8, compared to 2.0 at sea level--nearly a 10% difference. The biggest difference at all comes when surfacing--about 20% difference. That means the gradient between tissue pressure and ambient pressure, the cause of DCS, is significantly greater at altitude.

John, this is the best explanation I've seen regarding diving and altitude.
 
To finish the thought (and accept my final judgement)

The new depth would present a whole new set of stops using standard tables/protocols for sea level. These times would not scale, they would be assigned to new shallower (but corresponding) depths in the altitude dive.

It appears to me that if this is not correct, then gas diffusion into tissue is highly dependent on absolute pressure and relative concentrations rather than relative concentrations alone.
 
To finish the thought (and accept my final judgement)

The new depth would present a whole new set of stops using standard tables/protocols for sea level. These times would not scale, they would be assigned to new shallower (but corresponding) depths in the altitude dive.

It appears to me that if this is not correct, then gas diffusion into tissue is highly dependent on absolute pressure and relative concentrations rather than relative concentrations alone.

Honestly, you could check if Buhlmann and VPM compensate for altitude in a similar way. You could create a dive profile at sea level, compensate it for altitude (like 30m@SL and 24m@2000m altitude) and validate it that way yourself. It wouldn't be perfect, but a very similar result would give credence to the concept.
 
To finish the thought (and accept my final judgement)

The new depth would present a whole new set of stops using standard tables/protocols for sea level. These times would not scale, they would be assigned to new shallower (but corresponding) depths in the altitude dive.

It appears to me that if this is not correct, then gas diffusion into tissue is highly dependent on absolute pressure and relative concentrations rather than relative concentrations alone.

Honestly, you could check if Buhlmann and VPM compensate for altitude in a similar way. You could create a dive profile at sea level, compensate it for altitude (like 30m@SL and 24m@2000m altitude) and validate it that way yourself. It wouldn't be perfect, but a very similar result would give credence to the concept.
Remember that decompression models are based on pressure ratios, rather than on absolute pressures. In determining how your body rids itself of excess inert gas, decompression models rely upon the ratios of the pressures you experience at depth, and the surfacing atmospheric pressure you experience after the dive. The key to not forming inert gas bubbles in your body -and thereby avoiding DCI- is to keep those pressure ratios within tolerable limits.

So if you're at altitude using a classic dissolved gas Buhlmann Model and ascending to the leading tissue compartment's M-value with the highest allowable gradient between dissolved inert gas tensions and ambient pressure at a particular deco stop depth -and maximizing your offgas rate ideally without bubbling- then you would have to compensate a sea level deco table for a deeper theoretical ocean depth with corresponding time in order to convert an actual given depth at altitude (as well as depth in ffw versus fsw if indicated), because of the greater decompression stress brought on by driving a steep pressure gradient, and subsequent tissue surfacing supersaturation tensions post-dive at a lesser ambient atmospheric pressure at altitude.

A simple NDL compensated sea level dive table example:

For a given altitude A, the atmospheric pressure Pa (in atm) at that altitude is

Pa = (1 atm) * exp(5.255876 * ln(1 – (C * A))).

where C = 0. 0000068756 per 1 foot; or C = 0. 000022558 per 1 meter, depending on whether the altitude is given in feet above sea level or in meters above sea level.

With a calculated Pa (Pressure at Altitude determined from the above equation) and given Da (actual depth at Altitude in ffw), we have the general equation below yielding a Theoretical Ocean Depth (TOD), and with these compensated depths we can use dive tables that are based upon sea level diving in the ocean:

TOD = Da * (1 atm / Pa) * (33 fsw / 34 ffw);

or TOD = Da * (1 atm / Pa) * (10 msw / 10.3 mfw).


So given a dive to 60ffw at 4600ft altitude:

Pa
= (1 atm) * exp(5.255876 * ln(1 – (C * A))).
Where C= 6.8756E-6, and Given A=4600 ft.
Evaluating for Pa:
Pa = 0.844 atm;

So a dive to Da = 60 ffw with Pa = 0.844 atm:
TOD = Da * (1 atm/Pa)* (33fsw/34ffw) = 68.9 fsw (approx 70fsw).

Therefore a 60 ffw at 4600ft altitude, is equivalent to a 70 fsw sea level referenced dive table with a conservative NDL time of 40 min (see table http://scuba-training.net/scuba/images/hugi.pdf).

Some Equivalent TOD's for actual depths given in ffw at 4600ft altitude are:

50 ffw => 57.5 fsw
60 ffw => 68.9 fsw
70 ffw => 80.4 fsw
80 ffw => 91.9 fsw
90 ffw => 103.4 fsw
100 ffw => 114.9 fsw
110 ffw => 126.4 fsw

17 ffw => Safety Stop 20 fsw
9 ffw => Safety Stop 10 fsw.
 
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...//... With a calculated Pa (Pressure at Altitude determined from the above equation) and given Da (actual depth at Altitude in ffw), we have the general equation below yielding a Theoretical Ocean Depth (TOD), and with these compensated depths we can use dive tables that are based upon sea level diving in the ocean: ...
Thank you for your insights, @Kevrumbo

This is exactly where I was going with this. My 'MO' is to put my first principles out to test and see if they hold up to expert review. After that, I will compare numerical profiles for similarity.

I don't start by claiming that an approximation is valid. We all know that two things that give the same answer are not necessarily equivalent.

Thx.
 
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