midwest_matt
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Anyone know what formula is used to calculate the no decompression limit for recreational diving?
Formula used to calculate NDL?
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cornfed
Mindless lemming
donacheson
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midwest_matt:
There's lots of old threads on Scubaboard dealing with this and closely related questions. One is "math behind divetables?".
There are many answers to your question because there are many models used to describe the effects of compressed "inert" gases and time upon the human body.
OP
midwest_matt
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cornfed:
Excellent document, lots of good information in there. If you are into the more technical aspects of your scuba setup and breathing underwater
Dr Deco
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Hi Midwest matt:
I do not recall the formula for NDLs, but it should be remembered that any formula is simply a description of no-decompression limits determined by experiment. The larger the group, the better will be the description. Several points are of importance to scuba divers.
Individual Variations
There is actually a separate set of NDLs for every diver. There are distinct differences between individuals that vary their resistance, or susceptibility, to DCS. This is not to say that differences are radical, but there will be differences. One would find, in practice, that many of these NDLs group together, and the differences are basically imperceptible, in practice. Nevertheless, some individuals are more susceptible and some are more resistant. Other than a decompression, there currently does not exist any way to determine where exactly you lie on the spectrum.
Activity Level
This has been discussed on this FORUM on numerous occasions. NDLs are determined for individuals who have returned to the surface and are essentially inactive at the surface. I know of no lab experiment where the subjects were given tasks such as hauling gear and climbing stars or ladders after they reached "topside." On the contrary, most simply sit around and (today anyways) wait their turn for Doppler bubble monitoring. Were aggressive surface activity to be included, the NDLs would be shorter for every depth.
Additionally, I do not know of any test subjects who are told to exercise vigorously prior to descent to determine the NDLs. This activity level would be very noticeable in altitude (flyers) DCS, although the quantitative aspects of this have not yet be checked with diving.
Tables
Table designers will adjust the NDLs for their tables. This is virtually always in the direction to make table safer, that is, more conservative bottom times. Depending on the table designers desires, the reductions will appear as different bottom times. Divers note that different meters and tables will give various results for each dive. This is simply a reflection of table design philosophy. But - all are safe.
It is important to recognize that NDLs are always in the very safe range. There does not exist an all-or nothing response for DCS for a GROUP of divers. There does not exist a sharp cutoff where you are at the edge of the table. What happens in practice that, as the bottom times were lengthened, a few percent of divers would have small problems (sometimes called niggles.) Then, with further extensions of bottom time, a few more would have niggles and others would begin to get more intense joint pain.
Safety :07:
Safe diving indicates that safety stops be added and excessive exercise be minimized on the surface.
Dr Deco (on vacation this week).
I do not recall the formula for NDLs, but it should be remembered that any formula is simply a description of no-decompression limits determined by experiment. The larger the group, the better will be the description. Several points are of importance to scuba divers.
Individual Variations
There is actually a separate set of NDLs for every diver. There are distinct differences between individuals that vary their resistance, or susceptibility, to DCS. This is not to say that differences are radical, but there will be differences. One would find, in practice, that many of these NDLs group together, and the differences are basically imperceptible, in practice. Nevertheless, some individuals are more susceptible and some are more resistant. Other than a decompression, there currently does not exist any way to determine where exactly you lie on the spectrum.
Activity Level
This has been discussed on this FORUM on numerous occasions. NDLs are determined for individuals who have returned to the surface and are essentially inactive at the surface. I know of no lab experiment where the subjects were given tasks such as hauling gear and climbing stars or ladders after they reached "topside." On the contrary, most simply sit around and (today anyways) wait their turn for Doppler bubble monitoring. Were aggressive surface activity to be included, the NDLs would be shorter for every depth.
Additionally, I do not know of any test subjects who are told to exercise vigorously prior to descent to determine the NDLs. This activity level would be very noticeable in altitude (flyers) DCS, although the quantitative aspects of this have not yet be checked with diving.
Tables
Table designers will adjust the NDLs for their tables. This is virtually always in the direction to make table safer, that is, more conservative bottom times. Depending on the table designers desires, the reductions will appear as different bottom times. Divers note that different meters and tables will give various results for each dive. This is simply a reflection of table design philosophy. But - all are safe.
It is important to recognize that NDLs are always in the very safe range. There does not exist an all-or nothing response for DCS for a GROUP of divers. There does not exist a sharp cutoff where you are at the edge of the table. What happens in practice that, as the bottom times were lengthened, a few percent of divers would have small problems (sometimes called niggles.) Then, with further extensions of bottom time, a few more would have niggles and others would begin to get more intense joint pain.
Safety :07:
Safe diving indicates that safety stops be added and excessive exercise be minimized on the surface.
Dr Deco (on vacation this week).
OP
midwest_matt
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More good information... I know there are many variables the contribute to the no deco time. What I was looking for was a formula that was based on one of the major rec diver institute dive tables. NAUI, SSI, PADI..... I'm looking at writing a small app for myself to do some calculations and I didn't want to enter in all the data from the tables by hand, if I could use a formula to calculate it.
MM,
For air/nitrox it's straightforward, The NDL, tNDL, is
computed for a particular tissue compartment, tau,
from the nitrogen M-value, where ln is the natural
logarithm,
tNDL = (tau/.693) ln [ (po-pa)/(M-pa)]
where po is the initial nitrogen partial presure (usually
0.79 x 33 fsw at the surface), pa is the ambient
partial of nitrogen at depth,pa = fn x (d + 33), with
fn the nitrogen mix fraction and d the depth, M is the
M-value, and tau is the tissue halftime. At any
depth, d, the above expression is evaluated at all tissue
tensions, and the smallest value of tNDL across all
compartments is the "table" NDL.
Various air/nitrox tables use different halftimes, tau,
but more importantly for biggest variation, different
M-values, M.
With helium, and trimix, the above formula is still used,
but gets a little more complicated physics wise. For
evaluation of pure helium NDL, the effect of surface air
must be subtracted off M to account for nitrogen loading
alongwith helium loading. For mixes of helium and nitrogen,
the same holds in evaluating tNDL across both helium
and nitrogen, and the smallest is the "table" NDL. In mixed
helium evaluations, pa = fh x (d +33) for helium, with fh the
helium fraction at depth. Nitrogen loading is subtracted
off the helium M-value. For mixed nitrogen, pa = fn x (d +33),
and helium loading is subtracted off the nitrogen M-value.
Halftimes for helium are roughly 1/2.65 faster than those
for nitrogen. And the process proceeds across all nitrogen and
helium tissues.
See FTP posting this site (as somebody mentioned), or
books offered by Best -- TDID, RGBM In Depths, Deco
Theory And Apps.
Hope this helps a little,
BW
For air/nitrox it's straightforward, The NDL, tNDL, is
computed for a particular tissue compartment, tau,
from the nitrogen M-value, where ln is the natural
logarithm,
tNDL = (tau/.693) ln [ (po-pa)/(M-pa)]
where po is the initial nitrogen partial presure (usually
0.79 x 33 fsw at the surface), pa is the ambient
partial of nitrogen at depth,pa = fn x (d + 33), with
fn the nitrogen mix fraction and d the depth, M is the
M-value, and tau is the tissue halftime. At any
depth, d, the above expression is evaluated at all tissue
tensions, and the smallest value of tNDL across all
compartments is the "table" NDL.
Various air/nitrox tables use different halftimes, tau,
but more importantly for biggest variation, different
M-values, M.
With helium, and trimix, the above formula is still used,
but gets a little more complicated physics wise. For
evaluation of pure helium NDL, the effect of surface air
must be subtracted off M to account for nitrogen loading
alongwith helium loading. For mixes of helium and nitrogen,
the same holds in evaluating tNDL across both helium
and nitrogen, and the smallest is the "table" NDL. In mixed
helium evaluations, pa = fh x (d +33) for helium, with fh the
helium fraction at depth. Nitrogen loading is subtracted
off the helium M-value. For mixed nitrogen, pa = fn x (d +33),
and helium loading is subtracted off the nitrogen M-value.
Halftimes for helium are roughly 1/2.65 faster than those
for nitrogen. And the process proceeds across all nitrogen and
helium tissues.
See FTP posting this site (as somebody mentioned), or
books offered by Best -- TDID, RGBM In Depths, Deco
Theory And Apps.
Hope this helps a little,
BW
midwest_matt:
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midwest_matt
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Thank you much, that helps more than a little.
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