RGBM DATA BANK AND RISK ANALYSES
FOR SELECT DIVE TABLES, METERS, AND PROFILES
B.R. Wienke
C & C Dive Team Leader
Nuclear Weapons Technology/Simulation And Computing
Applied And Computational Physics Division
Los Alamos National Laboratory
Los Alamos, N.M. 87545
T.R. O’Leary
Director Technical Training
NAUI Technical Diving Operations
NAUI Worldwide
Tampa, Fl. 33689
PART 1: RISK BASICS
Introduction
Linking model (RGBM) with data (RGBM Data Bank), we have further correlatedmodel parameters
with diving profiles. The full analysis will be published in the Annals Of Biomedical Engineering,
but we would like to pass back salient aspects, particularly aspects impacting the RGBM Tables, in
this special ADM article (3 Parts). Much ground is covered, but the most interesting aspects likely
reside in various risk estimates deduced for tables, meters, and profiles. The RGBM Data Bank,
unlike previous profile compilations, incorporates deep stop data for correlation with a deep stop
diving paradigm. This is important, since earlier compilations impose shallow stop staging, a built
in bias for any model correlation.
At the outset, we should point out some often misquoted and misunderstood information (even
from people who should know better) about DCS risk and underlying DCS incidence in the data
structures from which risk is deduced. Risk and incidence are NOT the same thing. Incidence in a
data bank is just the number of DCS hits divided by the number of entries. Risk is the statistical
estimate of DCS probability for a given dive profile (mix, descent rate, bottom depth and time,
decompression stops, mix switches, ascent rate, and altitude). The estimated incidence rate across
all recreational diving, for instance, is something like 1/50,000 across all profiles. However, the risk
associated with diving air to popular NDLs is near 1.2%, considerably higher than the incidence rate.
This is seen later. The incidence rate across technical diving is estimated to be 10 times greater, yet
the risk associated with diving to helitrox NDLs is in the 1.6% range. With that in mind, let’s first
take a look at the RGBM Data Bank, a data bank providing profile information useful for statistical
analysis and related risk estimates, and a data structure with an incidence rate below 1%.
RGBM Profile Data Bank
Divers using bubble models are reporting their profiles to a Data Bank, located at LANL (also
NAUI Technical Diving Operations). The profile information requested is simple, but very important.
It is the only technical diving data bank presently existing.
Dive Data Structure
Information is both invited and tendered, but always filtered for reliability. Input information is
the usual dive profile:
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1. bottom mix/ppO2 , depth, and time (square wave equivalent);
2. ascent and descent rates;
3. stage and decompression mix/ppO2 , depths, and times;
4. surface intervals;
5. time to fly;
6. diver age, weight, and sex;
7. outcome (health problems), rated 1 - 5 in order of poor to well.
This information aids validation and extension of model application space. Some 2,823 profiles
now reside in the RGBM Data Bank. The are 19 cases of DCS in the data file. The underlying DCS
incidence rate is, p = 19/2823 = 0.0067, below 1%. Stored profiles range from 150 fsw down to 840
fsw, with the majority above 350 fsw. All data enters through the authors (BRW and TRO), that
is, divers, profiles, and outcomes are filtered. A summary breakdown of DCS hit data consists of the
following:
1. OC deep nitrox reverse profiles – 5 hits
2. OC deep nitrox – 3 hits
3. OC deep trimix reverse profiles – 2 hits
4. OC deep trimix – 2 hits
5. OC deep heliox – 2 hits
6. RB deep nitrox – 2 hits
7. RB deep trimix – 1 hit
8. RB deep heliox – 2 hits
Deep nitrox means a range beyond 150 fsw, deep trimix means a range beyond 200 fsw, and deep
heliox means a range beyond 250 fsw as a rough categorization. The abbreviation OC denotes open
circuit, while RB denotes rebreather. Reverse profiles are any sequence of dives in which the present
dive is deeper than the previous dive. Nitrox means an oxygen enriched nitrogen mixture (including
air), trimix denotes a breathing mixture of nitrogen, helium, oxygen, and heliox is a breathing mixture
of helium and oxygen. None of the trimix nor heliox cases involved oxygen enriched mixtures on
OC, and RB hits did not involve elevated oxygen partial pressures above 1.4 atm. Heavy-to-light gas
switches occured in 2 cases, violating contemporary ICD (isobaric counterdiffusion) protocols . None
of the set exhibited full body nor CNS (central nervous system) oxygen toxicity. The 19 cases come
after the fact, that is diver distress, most with, but some without, chamber treatment following
distress. The next section describes many of the profiles in the RGBM Data Bank, as well as broader
field testing reported to us. Profiles come from seasoned divers using wrist slate decompression
tables with computer backups. Some profiles come to us directly as computer downlaods, which we
transcribe to the requisite format.
Profiles come from the technical diving community at large, essentially mixed gas, extended range,
decompression, and extreme diving. Profiles from the recreational community are not included,
unless they are involve extreme exposures on air or nitrox (many repetitve dives, deeper than 150
fsw, altitude exposures, etc). This low rate makes statistical analysis difficult, and we use a global
approach to defining risk after we fit the model to the data using maximum likelihood. The maximum
likelihood fit links directly to the binomial probability structure of DCS incidence in divers and
aviators. It is a powerful, and time tested statistical technique.
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Field Testing And Profile Data Entries
Models need validation and field testing. Often, strict chamber tests are not possible, economically
nor otherwise, and models employ a number of benchmarks and regimens to underscore viability.
The following are some supporting the RGBM phase model and (released) nitrox, heliox, and trimix
diving tables and meters. Profiles are recorded in the RGBM Data Bank, and are representative of
entries in terms of dive counts and technical diving applications.
1. Counterterror and Countermeasures Team (C & C) RB and OC exercises have used the RGBM
(iterative deep stop version) for a number of years, logging some 2245 dives on mixed gases
(trimix, heliox, nitrox) with 0.4% incidence of DCS – 85% were deco dives, and 55% were
repets with at least 2 hr SIs, with most in the forward direction (deepest dives first). Some 9
cases of DCS were logged by the Team, mainly in the deep reverse profile category on nitrox
and trimix, plus RB hits on heliox;
2. NAUI Technical Diving has been diving the deep stop version for the past 9 yrs, some estimated
22,000 dives, on mixed gases down to 300 fsw, with 2 reported cases of DCS, both on trimix.
Some 15 divers, late 1999, in France used the RGBM to make 2 mixed gas dives a day, without
mishap, in cold water and rough seas. Same thing in the warm waters of Roatan in 2000 and
2001;
3. NAUI Worldwide released a set of no-group, no-calc, no-fuss RGBM Tables for air, EAN32,
and EAN36 recreatational diving, from sea level to 10,000 ft, a few years ago. Minimum SIs
of 1 hour are supported for repetitive diving in all Tables, and safety stops for 2 min in the
15 fsw zone, plus 1 min deep stops at half bottom depth, are required always. Tables were
tested by NAUI Insructor Trainers, Instructors, and Divemasters over a 2 year period without
mishap, and continue so today as the the mainstay teaching Tables in NAUI basic air and
nitrox courses;
4. modified RGBM recreational algorithms (Haldane imbedded with bubble reduction factors
limiting reverse profile, repetitive, and multiday diving), as coded in Suunto, Mares, Dacor,
UTC, Zeagle, Steam Machines, GAP, ABYSS, HydroSpace, Plexus decometers, maintain an
already low DCS incidence rate of approximately 1/50,000 or less. More RGBM decompression
meters, including mixed gases, are in the works;
5. a cadre of divers and instructors in mountainous New Mexico, Utah, and Colorado have been
diving the modified RGBM at altitude, an estimated 1,200 dives, without peril. Again, not
surprising since the altitude RGBM is slightly more conservative than the usual Cross correction
used routinely up to about 8,000 ft elevation, and with estimated DCS incidence less than
1/10,000;
6. within decometer implementations of the RGBM, only a few scattered DCS hits have been
reported in nonstop and multidiving categories, beyond 1,300,000 dives or more, up to now,
according to statistics furnished the author (BRW) by meter vendors;
7. extreme chamber tests for mixed gas RGBM protocols are in the works, and less stressful
exposures will be addressed shortly – extreme here means 300 fsw and beyond;
8. as seen, probabilistic decompression analysis of selected RGBM profiles, calibrated against
similar calculations of the same profiles by Duke, help validate the RGBM on computational
bases, suggesting the RGBM has no more theoretical risk than other bubble or dissolved gas
models (Weathersby, Vann, Gerth methodology at USN and Duke);
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9. all divers and Instructors using RGBM decometers, tables, or Internet software have been
advised to report individual profiles to DAN Project Dive Exploration (Vann, Gerth, Denoble
and others at Duke), plus to the RGBM Data Bank (Wienke, O’Leary at LANL and NAUI);
10. GAP, HydroSpace RGBM Simulator, and ABYSS are NET software packages that offer the
modified RGBM (folded Buhlmann ZHL) and, especially, the full up, deep stop version for any
gas mixture, have a fairly large contingent of tech divers already using the RGBM and have
not received any reports of DCS to date. The EXPLORER RGBM Simulator is furnished to
meter owners of the HydroSpace EXPLORER;
11. outside of proprietary (commercial) and RGBM Tables, mixed gas tables are a smorgasboard
of no longer applicable Haldane dynamics and discretionary stop insertions, as witnessed by
the collective comments of a very vocal and extremely competent, experienced technical diving
community;
12. extreme WKPP profiles in the 300 fsw range on trimix were used to calibrate the RGBM.
WKPP profiles are the most impressive application of RGBM staging, with as much as 12 hours
less decompression time for WKPP helium based diving on RGBM schedules versus Haldane
schedules, with estimated 200 dives;
13. Ellyat, a TDI Instructor, dived the Baden in the North Sea to 540 fsw on RGBM Tables
on two different occasions, and 3 hours were shaved off conventional hang time by RGBM
application. Unfortunately, with diver error and mismatched gas switching strategies from
helium to nitrogen, dives to 840 fsw resulted in vestibular DCS;
14. NAUI Worldwide released sets of deep stop RGBM nitrox, heliox, and trimix technical and
recreational Tables that have been tested by NAUI Technical Diving Operations over the past
9 years, with success and no reported cases of DCS, for open circuit regulators and rebreathers,
15. Doppler and imaging tests in the laboratory, and analyses by Bennett, Marroni, Brubakk and
Wienke, and Neuman all suggest reduction in free phase counts with deep stop staging;
16. deep air RGBM Tables with surface oxygen decompression are employed by American oil patch
diving companies;
17. Scorese, a NAUI instructor, and his students made a total of 234 dives on the Andrea Doria
using rebreathers and RGBM (constant ppO2 ) RB Tables, and various nitrogen and trimix
diluents. Dive abortions off rebreathers employed ranged RGBM (open circuit) Tables as
bailouts, and witnessed no mishaps;
18. Freauf, a Navy SEAL in Hawaii, logged 20 trimix decompression dives beyond 250 fsw on
consecutive days using RGBM Tables (pure oxygen switch at 20 fsw);
19. Gerth, a US Navy researcher at NEDU, suggested that deep stops are necessary and cost
effective for air and nitrox Navy divers, that is, risk versus decompression time;
20. Melton, owner of HydroSpace Engineering and developer of the RGBM EXPLORER (OC plus
RB) dive computer reports 100s of dives in the 400 fsw range on the RGBM EXPLORER;
21. GAP, Gas Absorption Program, an RGBM software product out of the Netherlands, supports
brisk and sustained use of the RGBM within the tec and rec diving community;
22. NEDU in Panama City is performimg deep stop man trials in open water using a US Navy
bubble model;
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23. heliox RGBM Tables are being used by a commercial diving operation in Argentina;
24. Raine, a wreck diver in California, reports 100s of RGBM dives in the 250 fsw range with low
Doppler counts;
25. the RGBM site, RGBMdiving.com, receives 100s of hits weekly, and provides custom RGBM
Tables;
26. ANDI, a training agency, has adopted a custom version of GAP for diver training on mixed
gases, OC and RBs;
27. NAUI similarly employs a custom version of GAP for dive planning, with nominal GAP parameter
settings recovering released and published NAUI RGBM Tables;
28. O’Leary, Director NAUI Technical Operations, has made over 70 dives on OC and RB systems
using RGBM Table and the Hydrospace EXPLORER to depths beyond 250 fsw, with anywhere
from 6 - 9 other divers during NAUI Technical Instructor Training Courses;
29. O’Leary, Sharp, Scorese, Bell, Hunley, and 6 other NAUI Instructors used RGBM OC and RB
Tables to dive the USS Perry in Anguar in very strong currents, down to 260 fsw, logging 2
repetitive deco dives a day for a week or so.
With DCS binomially distributed in incidence probability, many trials are needed (or other close
profiles) to fully validate any model at the 1% level. Additionally, full validation requires DCS
incidences, the higher the number, the better, contrary to desired dive outcomes. While the foregoing
list of field tests and profiles are not controlled scientific experiments with attendant data collection,
the shear number of diving events and diversity of exposure spectrum might not be discounted nor
treated lightly. The collective information has been dubbed the living laboratory by segments of
the technical, scientific, and operational diving community.
Probabilistics
Decompression sickness is a hit, or no hit, situation. Statistics are binary, as in coin tossing.
Probabilities of occurrence are determined from the binomial distribution, which measures the numbers
of possibilities of occurrence and non-occurrence in any number of events, given the incidence
rate. Table 1 lists corresponding binomial decompression probabilities, P(n), for 1% and 10% underlying
incidence (99% and 90% nonincidence), yielding 0, 1, and 2 or more cases of decompression
sickness. The underlying incidence, p, is the (fractional) hit rate. The non-incidence, q, is just 1−p,
or the (fractional) non-hit rate.
As the number of trials increases, the probability of 0 or 1 occurrences drops, while the probability
of 2 or more occurrences increases. In the case of 5 dives, the probability might be as low as 5%,
while in the case of 50 dives, the probability could be 39%, both for p = 0.01. Clearly, odds even
percentages would require testing beyond 50 cases for an underlying incidence near 1%. Only by
increasing the number of trials for fixed incidences can the probabilities be increased. Turning that
around, a rejection procedure for 1 or more cases of decompression sickness at the 10% probability
level requires many more than 50 dives. If we are willing to lower the confidence of the acceptance,
or rejection, procedure, of course, the number of requisite trials drops. Table 1 also shows that the
test practice of accepting an exposure schedule following 10 trials without incidence of decompression
sickness is suspect, merely because the relative probability of nonincidence is high, near 35%.
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Table 1. Probabilities Of Decompression Sickness For Underlying Incidences.
P(n) P(n)
N (dives) n (hits) p = 0.01 p = 0.10
q = 0.99 q = 0.90
5 0 0.95 0.59
1 0.04 0.33
2 or more 0.01 0.08
10 0 0.90 0.35
1 0.09 0.39
2 or more 0.01 0.26
20 0 0.82 0.12
1 0.16 0.27
2 or more 0.02 0.61
50 0 0.61 0.01
1 0.31 0.03
2 or more 0.08 0.96
RGBM Data Correlations And Risk Estimates
For the past 10-15 years, a probabilistic approach to assessing risk in diving has been in vogue.
Sometimes this can be confusing, or misleading, since definitions or terms, as presented, are often
mixed. Also confusing are risk estimates varying by factors of 10 to 1,000, and distributions serving
as basis for analysis, also varying in size by the same factors. In a word, the probabilistic approach
amounts to defining a risk function for diving, and then fitting the risk function to the data using
a statistical method called maximum likelihood. Risk functions might be supersaturations, Doppler
bubble counts, bubble formation and growth rates, separated bubble volumes, and combinations
thereof. For our RGBM analysis, the risk function is bubble growth rate over number of bubbles
initially excited into growth under compression-decompression.
Years ago, hundreds of air dives were analyzed using this procedure, yielding decompression
schedules with 95% and 99% non-incidence (5% and 1% incidence). Tables were published by US
Navy investigators, and Table 2 tabulates the corresponding nonstop time limits (p = 0.05, 0.01),
including standard US Navy (Workman) limits for comparison. Later re-evaluations of the standard
set of nonstop time limits estimate a probability rate of 1.25% for the limits. In practice, incidence
rates are below 0.001%, and most divers do not dive to the limits. The risk function used in Table 2 is
the dissolved gas oversaturation, that is, the difference between tissue tension and ambient pressure.
Table 2. Nonstop Time Limits For 1% And 5% DCS Probability.
depth nonstop limit nonstop limit nonstop limit
d (fsw) tn (min) tn (min) tn (min)
p = .05 p = .01 US Navy
30 240 170
40 170 100 200
50 120 70 100
60 80 40 60
70 80 25 50
80 60 15 40
90 50 10 30
100 50 8 25
110 40 5 20
120 40 5 15
130 30 5 10
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PART 2: SIMPLE DIVING RISKS
RGBM Single And Repetitive Air Dive Risks
To perform risk analysis with the RGBM Data Bank, a risk estimator need be selected. For diving,
dissolved gas and bubble estimators are useful. For recreational diving, all estimators are roughly
equivalent, because little dissolved gas has likely separated into free phases (bubbles). Analysis
shows this true for all cases examined. The only case where dissolved gas and phase estimators
differ (slightly here) is within repetitive diving profiles. The dissolved gas estimator cues on gas
buildup in the slow tissue compartments (staircasing for repets within an hour or two), while the
phase estimator cues on bubble gas diffusion in the fast compartments (dropping rapidly over hour
time spans). This holding true within all recreational diving distributions, we proceed to the risk
analysis.
Nonstop limits (NDLs), denoted tn, from the US Navy, PADI, NAUI, and ZHL (Buhlmann)
Tables provide a set for comparison of relative DCS risk. Listed in Table 3 are the NDLs and
corresponding risks for the profile, assuming ascent and descent rates of 60 fsw/min (no safety
stops). Dissolved gas, s, and phase, r, estimates vary little for cases, and only the phase estimates
are included.
Table 3. Risk Estimates For Standard Air NDLs.
USN NDL risk PADI NDL risk NAUI NDL risk ZHL NDL risk
d tn r tn r tn r tn r
(fsw) (min) (min) (min) (min)
35 310 4.3% 205 2.0% 181 1.3%
40 200 3.1% 140 1.5% 130 1.4% 137 1.5%
50 100 2.1% 80 1.1% 80 1.1% 80 1.1%
60 60 1.7% 55 1.4% 55 1.4% 57 1.5%
70 50 2.0% 40 1.2% 45 1.3% 40 1.2%
80 40 2.1% 30 1.3% 35 1.5% 30 1.3%
90 30 2.1% 25 1.5% 25 1.5% 24 1.4%
100 25 2.1% 20 1.3% 22 1.4% 19 1.2%
110 20 2.2% 13 1.1% 15 1.2% 16 1.3%
120 15 2.0% 13 1.3% 12 1.2% 13 1.3%
130 10 1.7% 10 1.7% 8 1.3% 10 1.7%
Risks are internally consistent across NDLs at each depth, and agree with the US Navy assessments in
Table 2. Greatest underlying risks occur in the USN shallow exposures. The PADI, NAUI, and ZHL
risks are all less than 2% for this set, and risks for single DCS incidence are less than 0.02. PADI and
NAUI have reported that incidence rates (p) across all exposures are less than 0.001%, so considering
their enviable track record of diving safety, our estimates are liberal. ZHL risk estimates track as the
PADI and NAUI risks, again, very safely. Estimates were also independently corroborated [Gerth,priv
comm, 2001] within USN and DAN data sets at Duke, both in Table 3 and Table 4.
Next, the analysis is extended to profiles with varying ascent and descent rates, safety stops, and
repetitive sequence. Table 4 lists nominal profiles (recreational) for various depths, exposure and
travel times, and safety stops at 5 msw. Mean DCS estimates are tabulated for both dissolved gas
supersaturation ratio (ZHL), s, and excited bubble volume (RGBM), r, risk functions, with nominal
variance, r± = r ± 0, 004, across all profiles.
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Table 4. Dissolved And Separated Phase Risk Estimates For Nominal Profiles.
profile descent rate ascent rate safety stop risk risk
(depth/time) (msw/min) (msw/min) (depth/time) r s
14 msw/38 min 18 9 5 msw/3 min 0.0034 0.0062
19 msw/38 min 18 9 5 msw/3 min 0.0095 0.0110
28 msw/32 min 18 9 0.0200 0.0213
37 msw/17 min 18 9 5 msw/3 min 0.0165 0.0151
18 msw/31 min 18 9 5 msw/3 min 0.0063 0.0072
18 9 0.0088 0.0084
18 18 0.0101 0.0135
18 18 5 msw/3 min 0.0069 0.0084
17 msw/32 min 18 9 5 msw/3 min
SI 176 min
13 msw/37 min 18 9 5 msw/3 min
SI 174 min
23 msw/17 min 18 18 5 msw/3 min 0.0127 0.0232
The ZHL (Buhlmann) NDLs and staging regimens are widespread across decompression meters
presently, and are good representations for dissolved gas risk analysis. The RGBM is newer, more
modern, and is coming online in decometers and associated software. For recreational exposures, the
RGBM collapses to a dissolved gas algorithm. This is reflected in the risk estimates above, where
estimates for both models differ little .
Simple comments hold for the analyzed profile risks. The maximum relative risk is 0.0232 for the
3 dive repetitive sequence according to the dissolved risk estimator. This translates to 2% profile
risk, which is comparable to the maximum NDL risk for the PADI, NAUI, and ZHL NDLs. This
type of dive profile is common, practiced daily on liveaboards, and benign. According to Gilliam, the
absolute incidence rate for this type of diving is less than 0.02%. Again, our analyses overestimate
risk. Effects of slower ascent rates and safety stops are seen only at the 0.25% to 0.5% level in
relative surfacing risk. Safety stops at 5 msw for 3 min lower relative risk an average of 0.3%, while
reducing the ascent rate from 18 msw/min to 9 msw/min reduces relative risk an average of 0.35%.
Staging, NDLs, and contraints imposed by decometer algorithms are consistent with acceptable and
safe recreational diving protocols. Estimated absolute risk associated across all ZHL NDLs and
staging regimens analyzed herein is less than 2.32%, probably much less in actual practice. That is,
we use p = 0.0067, and much evidence suggests incidence p < 0.0001, some ten times safer.
Implicit in such formulations of risk tables are assumptions that given decompression stress is
more likely to produce symptoms if it is sustained in time, and that large numbers of separate events
may culminate in the same probability after time integration. Though individual schedule segments
may not be replicated enough to offer total statistical validation, categories of predicted safety might
be grouped within subsets of corroborating data. For instance, risks on air dives might be estimated
from just nitrox data, risks on trimix from just trimix data, risks on heliox just from heliox data,
etc. Since the method is general, any model parameter or meaningful index, properly defined, can be
applied to decompression data, and the full power of statistical methods employed to quantify overall
risk. While powerful, such statistical methods are neither deterministic nor mechanistic, and cannot
predict on first principles. But as a means to table fabrication with quoted risk, such approaches
offer attractive pathways for analysis.
Questions of what risk is acceptable to the diver vary. Sport and research divers would probably
opt for small risk (1% or less), while military and commercial divers might live with higher risk
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(5%), considering the nearness of medical attention in general. Many factors influence these two
populations, but fitness and acclimatization would probably play strategically.
UW Seafood Diver Air Tables
As another application of the RGBM Data Bank to table construction and analysis, we detail a
set of tables of interest to the University of Wisconsin (UW), along with estimated risk for various
nonstop limits gleaned from the data. These Tables have no groups, and simple rules. Released
mixed gas RGBM Tables resulted from similar analyses across both the technical and recreational
segments. Such Tables are certainly useful for a broad spectrum of diving, and are easy to use.
Table 5 lists the maximum NDLs for any series of dives (up to 3) with 60 min SIs between dives.
Divers need make a deep stop at 1/2 the maximum bottom pressure for 1 min, plus a shallow safety
stop in the 15 fsw zone for 2 min. Descent rate is 60 fsw/min, and ascent rate is 30 fsw/min.
The NDLs are listed for maximum risk after 3 repetitive dives to the (same) depth indicated, or to
a lesser depth.
Table 5. RGBM Repetitive Risks For Air Dives
r r r
5.14% 3.29% 1.37%
depth maximum time maximum time maximum time
(fsw) (min) (min) (min)
100 24 20 14 deep stop 60/1
shallow stop 15/2
80 38 32 24 deep stop 50/1
shallow stop 15/2
60 50 42 32 deep stop 40/1
shallow stop 15/2
40 130 120 100 deep stop 30/1
shallow stop 15/2
Tables like these are of interest to Puerto Rican diving fishermen, and fishing sport divers. NAUI
uses a variant, detailed next, for training. Technical Training Agencies also employ mixed gas tables
for decompression diving, as well as dive planning software, all based on the RGBM algorithm. Some
risk estimates of profiles in these RGBM Technical Tables also follow.
RGBM Air And Nitrox Recreational Tables (sea level - 10,000 ft)
For comparison, consider similar RGBM Tables employed by NAUI for air and nitrox diver
training, sea level up to 10,000 ft. They are basically the same as the Puerto Rican seafood diver
tables above, except that successive dives must always be shallower than the previous. Descent and
ascent rates are 75 fsw/min and 30 fsw/min, and SIs are 60 min. At sea level to 2,000 ft elevation,
three dives may be made in a day on air or nitrox. At elevations above 2,000 ft, only two dives
are sanctioned. There are 9 RGBM Tables in all, 3 for air, 3 for EAN32, and 3 for EAN36, ranging
in altitude, 0 - 2,000 ft, 2,000 - 6,000 ft, and 9,000 - 10,000 ft. In Tables 9a through 9i, risks
are tabulated at the end of the 3 or 2 dive sequence. Moving from left to right (first dive through
last permitted dive) successive decrements in permissible depths are seen. Safety stops at half the
bottom depth are required for 1 min, and an additional safety stop in the 15 fsw zone for 2 min is
part of the protocol. Maximum risk is seen in the air tables at 10,000 ft elevation, and minimum
risk in the EAN36 tables at sea level.
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Table 6a. RGBM Air Tables (0 - 2,000 ft)
Maximum Risk After Dive 3, r = 1.69%
Dive 1 Dive 2 Dive 3
depth time depth time depth time
(fsw) (min) (fsw) (min) (fsw) (min)
130 10 80 30 30 150
120 13 75 30 30 150
110 16 70 40 30 150
100 20 65 40 30 150
90 25 60 55 30 150
80 30 55 55 30 150
70 40 50 80 30 100
60 55 45 80 30 150
50 80 40 110 30 150
40 110 35 110 30 150
30 150 30 150 30 150
Table 6b. RGBM Air Tables (2,000 - 6,000 ft)
Maximum Risk After Dive 2, r = 1.92%
Dive 1 Dive 2
depth time depth time
(fsw) (min) (fsw) (min)
110 9 70 28
100 13 65 28
90 17 60 38
80 22 55 38
70 28 50 54
60 38 45 54
50 54 40 85
40 85 35 85
30 125 30 125
Table 6c. RGBM Air Tables (6,000 - 10,000 ft)
Maximum Risk After Dive 2, r = 2.36%
Dive 1 Dive 2
depth time depth time
(fsw) (min) (fsw) (min)
90 11 60 28
80 15 55 28
70 21 50 40
60 28 45 40
50 40 40 64
40 64 35 64
30 103 30 103
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Table 6d. RGBM EAN32 Tables (0 - 2,000 ft)
Maximum Risk After Dive 3, r = 1.44%
Dive 1 Dive 2 Dive 3
depth time depth time depth time
(fsw) (min) (fsw) (min) (fsw) (min)
120 20 80 47 40 150
110 25 75 47 40 150
100 30 70 60 40 150
90 38 65 60 40 150
80 47 60 85 40 150
70 60 55 85 40 150
60 85 50 115 40 150
50 115 45 115 40 150
40 150 40 150 40 150
Table 6e. RGBM EAN32 Tables (2,000 - 6,000 ft)
Maximum Risk After Dive 2, r = 1.65%
Dive 1 Dive 2
depth time depth time
(fsw) (min) (fsw) (min)
100 20 65 43
90 26 60 57
80 33 55 57
70 43 50 84
60 57 45 84
50 84 40 120
40 120 35 120
30 150 30 150
Table 6f. RGBM EAN32 Tables (6,000 - 10,000 ft)
Maximum Risk After Dive 2, r = 1.84%
Dive 1 Dive 2
depth time depth time
(fsw) (min) (fsw) (min)
90 17 60 43
80 24 55 43
70 32 50 60
60 43 45 60
50 60 40 96
40 96 35 96
30 140 30 140
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Table 6g. RGBM EAN36 Tables (0 - 2,000 ft)
Maximum Risk After Dive 3, r = 1.12%
Dive 1 Dive 2 Dive 3
depth time depth time depth time
(fsw) (min) (fsw) (min) (fsw) (min)
110 31 80 60 50 150
100 35 75 60 50 150
90 46 70 85 50 150
80 60 65 85 50 150
70 85 60 115 50 150
60 115 55 115 50 150
50 150 50 150 50 150
Table 6h. RGBM EAN36 Tables (2,000 - 6,000 ft)
Maximum Risk After Dive 2, r = 1.24%
Dive 1 Dive 2
depth time depth time
(fsw) (min) (fsw) (min)
90 21 60 79
80 39 55 79
70 54 50 114
60 79 45 114
50 114 40 150
40 150 35 150
30 150 30 150
Table 6i. RGBM EAN36 Tables (6,000 - 10,000 ft)
Maximum Risk After Dive 2, r = 1.66%
Dive 1 Dive 2
depth time depth time
(fsw) (min) (fsw) (min)
80 29 55 54
70 37 50 84
60 54 45 84
50 84 40 128
40 128 35 128
30 150 30 150
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PART 3: COMPLEX DIVING RISKS
Helitrox Nonstop Limits (NDLs)
Helitrox is enriched trimix, that is, the oxygen fraction is above 21 % in the breathing mixture.
Helitrox is gaining in popularity over nitrox when helium is available for gas mixing. Diving agencies
often use helitrox in the beginning sequence of technical diver training. Listed below in Table 7 are
nonstop time limits and corresponding risks, r, for exposures at that depth-time. The mixture is
helitrox (enriched 26/17 trimix), sometimes called triox.
Table 7. Helitrox NDLs And Risk
depth time risk
d (fsw) tn (min) r
70 35 1.4%
80 25 1.4%
90 20 1.4%
100 15 1.4%
110 10 1.5%
120 8 1.5%
130 6 1.4%
140 5 1.5%
150 4 1.6%
These NDL triox risks track closely with NDL risks for air and nitrox.
Comparative Helium And Nitrogen Staging And Risk
Consider a deep trimix dive with multiple switches on the way up. This is a risky technical dive,
performed only by seasoned professionals. Table 8 contrasts stop times for two gas choices at the
100 fsw switch. The dive is a short 10 min at 400 fsw on 10/65/25 trimix, with switches at 235
fsw, 100 fsw, and 30 fsw. Descent and ascent rates are 75 fsw/min and 25 fsw/min. Obviously,
there are many other choices for switch depths, mixtures, and strategies. In this comparison, the
oxygen fractions were the same in all mixes, at all switches. Differences between a nitrogen or a
helium based decompression strategy, even for this short exposure, are nominal. Such usually is the
case when oxygen fraction is held constant in helium or nitrogen mixes at the switch.
Comparative profile reports suggest that riding helium to the 70 fsw level with a switch to EAN50
is good strategy, one that couples the benefits of well being on helium with minimal decompression
time and stress following isobaric switch to nitrogen. Shallower switches to enriched air also work,
with only a nominal increase in overall decompression time, but with deeper switches off helium to
nitrox a source of isobaric counterdiffusion (ICD) issues that might best be avoided. Note the risk,
r, for the helium strategy, 40/20/40 trimix at 100 fsw, is slightly safer than the nitrogen strategy,
EAN40 at 100 fsw, but in either case, the risk is high.
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Table 8. Comparative Helium And Nitrogen Gas Switches
r r
6.42% 6.97%
depth (fsw) stoptime(min) stoptime(min)
10/65/25 trimix 10/65/25 trimix
400 10.0 10.0
260 1.5 1.5
250 1.0 1.0
240 1.0 1.0
18/50/32 trimix 18/50/32 trimix
230 0.5 0.5
220 0.5 0.5
210 0.5 0.5
200 0.5 0.5
190 1.0 1.0
180 1.5 1.5
170 1.5 1.0
160 1.5 1.5
150 1.5 2.0
140 2.0 1.5
130 2.0 2.5
120 4.0 4.0
110 4.5 4.0
40/20/40 trimix EAN40
100 2.5 2.0
90 2.5 2.0
80 2.5 2.0
70 5.0 4.0
60 6.5 5.5
50 8.0 6.5
40 9.5 7.5
EAN80 EAN80
30 10.5 10.5
20 14.0 14.0
10 21.0 20.5
——- ——-
123.0 116.0
WKPP Extreme Exploration Dives
The Woodville Karst Plain Project (WKPP) has reported a number of 300 fsw dives with OC
and RB systems on trimix for many hours bottom time, and some 8 hrs of deompression. Pure
oxygen is employed in the 30 fsw zone with the help of an underwater habitat. Successful regimens
systematically roll back the helium fraction and increase the oxygen fraction in roughly the same
proportions, thus maintaing nitrogen fractions low and fairly constant. Diving starts in the cave
systems of Wakulla Springs in Florida. Table 9 summarizes the ascent and decompression profile.
The risk is, of course, high, but WKPP professionals continue to attempt and complete such extreme
exposures, pushing the exploration envelope. These dives served as calibration points for the RGBM
algorithm on whole.
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Table 9. WKPP Extreme Trimix Dives
Surfacing Risk, r = 16.67%
depth stop time mixture
(fsw) (min)
270 360 10.5/50 trimix
260 1
250 1
240 1 18/40 trimix
230 2
220 2
210 2
200 3
190 3
180 3 21/35 trimix
170 4
160 4
150 5
140 5
130 6
120 7 35/25 trimix
110 8
100 9
90 10
80 12
70 16 50/16 trimix
60 21
50 27
60 34
50 41
40 49
30 150 pure O2
World Record OC Trimix Dive
Consider risk after an OC dive to 1040 fsw on trimix, with matched ICD switches maintaining the
relative fraction of nitrogen constant as helium is reduced in the same measure as oxygen is increased.
Dives without this rather well known strategy ended in some serious chamber time for treatment
of vestibular DCS. Reports hint this dive was attempted, maybe accomplished, but contradictions
abound. We merely treat it as academic exercise for risk prediction.
Table 10 roughly summarizes the RGBM profile and ascent protocol. Stops range from 740 fsw
to 10 fsw for times ranging 0.5 min to 31.0 min. Descent rate is assumed to be 60 fsw/min, and
ascent rate between stages is assumed to be 30 fsw/min. Mixes and switch depths are indicated, as
in Table 9.
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Table 10. Trimix Dive To 1040 fsw And Risk
Surfacing Risk, r = 29.24%
depth range stop range mixture
(fsw) (min)
1040 1 5/67 trimix
740 - 530 0.5 - 1.5
520 - 300 2.0 - 3.5
290 - 180 4.0 - 6.5 14/56 trimix
170 - 140 7.0 - 9.5
130 - 70 10.0 - 15.0 27/56 trimix
60 - 40 16.0 - 20.50
30 - 20 24.5 80/20 nitrox
10 31.0 pure O2
The computed risk for this dive is very high, near 30%. Total decompression time is near 415 min.
Logistics for stage cylinders are beyond formidable, and the risk for deep support divers is also high.
Extreme RB Profile
The following, Table 11, is a deep RB dive downloaded off the HydroSpace EXPLORER computer.
From a number of corners, reports of 400 fsw dives on rebreather systems are becoming
commonplace. Consider this one to 444 fsw for 15 min. Diluent is 10/85 trimix, and ppO2 setpoint
is 1.1 atm. From a decompression standpoint, rebreather systems are the quickest and most efficient
systems for underwater activities. The higher the ppO2 , the shorter the overall decompression time.
That advantage, however, needs to be played off against increasing risks of oxygen toxicity as oxygen
partial pressures increase, especially above 1.4 atm. The higher percentage of oxygen and lower
percentage of inert gases in higher ppO2 setpoints of CCRs results in reduced risks, simply because
gas loadings and bubble couplings are less in magnitude and importance. This shows up in any set
of comparative ppO2 RB calculations, as well as in OC versus RB risk estimates.
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Table 11. Extreme RB Dive And Risk
Surfacing Risk r = 5.79%
depth time
(fsw) (min)
444 15.
290 0.5
280 0.5
270 0.5
260 0.5
250 0.5
240 0.5
230 1.0
220 1.0
210 1.0
200 1.0
190 1.5
180 1.5
170 1.5
160 1.5
150 2.0
140 2.0
130 2.0
120 2.5
110 3.0
100 3.5
90 4.0
80 4.5
70 5.0
60 7.0
50 7.5
40 8.0
30 12.5
20 14.0
10 18.5
The risk associated with this 400 fsw is less than a similar dive on trimix to roughly the same depth
for a shorter period of time, that is, Table 8.
USS Perry Deep RB Wreck Dives
A team of divers uncovered the wreck of the USS Perry in approximately 250 fsw off Anguar,
and explored it for a week on RBs. Diving in extremely hazardous and changing currents, their
repetitive decompression profile appears in Table 12. Profiles and risk for the two dives, separated
by 4 hrs SI, are nominal, with no accounting of exertion effort in current implied. Diluent is 10/50
trimix, with a ppO2 setpoint of 1.3 atm.
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Table 12. USS Perry RB Repetitive Decompression Dives And Risk
Surfacing Risk After Dive 1, r = 7.48%
Surfacing Risk After Dive 2, r = 7.79%
depth time
(fsw) (min)
260 40
170 1
160 1
150 1
140 1
130 1
120 1
100 2
90 2
80 2
70 3
60 3
50 4
40 5
30 6
20 9
10 12
0 270
210 20
90 1
80 1
70 1
60 1
50 2
40 2
20 4
10 5
Summary
The reduced gradient bubble model (RGBM) has been correlated with profiles housed in the
RGBM Data Bank. The Bank stores technical, mixed gas diving profiles with outcome. Some
2800+ deep stop profiles reside in the Bank, with 19 cases of DCS. Parameters in the RGBM are
calibrated against data using maximum likelihood. Risk estimates for select NDLs, tables, meter
algorithms, and diver profiles in the RGBM Data Bank were tabulated, using a bubble phase volume
estimator integrated over the whole profile.
A few points important points need be reiterated here:
1. deep stop date is intrinsically different from date collected in the past for diving validation,
in that previous data is based on shallow stop diver staging, a bias in dissolved gas model
correlations;
18
2. deep stop data and shallow stop data yield the same risk estimates for nominal, shallow, and
nonstop diving because bubble models and dissolved gas models converge in the limit of very
small phase separation;
3. if shallow stop data is employed in all the cases detailed, dissolved gas (only) risk estimates
will be categorically higher than those computed herein;
4. data entry in the RGBM Data Bank is a ongoing process of profile addition, extended exposuredepth
range, and mixed gas diving application.
19
Diving Concerns
Condition Related
