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Abstract:
The ZH-86 air diving tables and A.A. Bühlmanns
underlying ZH-L16 algorithms are considered
„gold standard“ within the recreational diving community,
thus they are widely used in decompression planning software and dive
computers.
In order to achieve a transparent comparability between the various methods
of calculating a diving schedule and thus get insight into its theoretical risk or
inherent safety, we compiled a list of key-parameters by an in-depth
comparison of 8 paradigms at the borders of the printed ZH-86 tables.
Introduction: slides # 3, 4 & 5
Methods: slide # 6
Discussion: slides # 7 9
Data: slides # 10 19
References: slide # 20
Bonus Material: slides # 21 24
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Introduction (1):
The ZH-86 air diving table and its underlying deterministic
algorithm with 16 parallel perfused compartments,
A.A. Bühlmanns ZH-L16 [2], is considered a gold-standard in recreational air-
diving. It is implemented in many desktop decompression software-tools. As
well it is widely used in diver-carried dive computers: as per 01/2022 there are
ca. 270 various dive-computers from ca. 35 companies / brandnames
worldwide on the market, the majority using perfusion models as per
Workman-DSAT/RDP® or Bühlmann ZH-L16x, with or without Gradient
Factors (GF). The models are always modified with these GF, altered a-/b-
coefficients resp. the M0 / ΔM values and/or compartment half-times to adapt
a „NDL-model“ (the DSAT RDP® for eg.) to decompression and/or altitude
diving. These proprietary modifications, however, are usually not publicly
documented, as they are considered company secrets. Also the mentioned
software tools use modifications, normally undocumented and not transparent
to the user.
The 2002 edition of [2] features 147 air-diving profiles at sea level and ca. 90
profiles for each of the 2 altitude tables. Since the majority of these profiles
has never been tested the diving community needs to know if custom-cut run-
times from software or dive-computers are within the ZH-86 range.
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Introduction (3):
Our goal now was to achieve transparency and reproduceability of dive
computer and decompression-planning software generated
run-times by a 1:1 comparison with a mirrored ZH-86 schedule.
Thus we compiled a list of the key-parameters to recover the ZH-86 table
with a freely available desktop decompression software, the shareware
DIVE Version 3_11 [1]. The parameter-list could be used in any other
software tool, provided the tool allows for customizing of these parameters,
the Schreiner-equation is fully implemented ([3], p. 205) and the set of 16
compartment half-times matches exactly. As well this parameter list could be
used to compare with schedules, simulated with dive computers in the so-
called „planning mode“ (dive planner, simulator, etc..) normally available in
surface-mode operation of these devices.
When one or more of the key-parameters do not match the ZH-86
configuration, the generated run-times may loose their comparability with the
ZH-86 table and thus no meaningful assessment of risk or safety is possible
[4]. Even if the ZH-86 schedule in question was not tested, the analysis
should clearly unveil, if and how much there is deviation in the stop-times per
decompression-stage.
6
Methods:
We simulated 7 diving schedules on air for sea-level
in the range of:
12 m to 60 m bottom-depth and
21 min to 300 min bottom-time and one schedule
42 m, 24 min on air for altitude diving (701 – 2,500 m above sea level)
and mirrored them directly with the printed ZH-86 schedules.
The following key-parameters have been identified:
ambient air pressure pamb at start (and end) of the dives
instantaneous descent
ascent rates
transit times between decompression stages
water density
water temperature, and thus in turn: water density and thus, again
hydrostatic pressure
respiratory coefficient Rq
Bühlmann safety factor
rounding-off of integers
one ZH-L16 set of the a-& b-coefficients (these are found in [2], on p. 158)
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Discussion (1):
The ZH-86 parameters are found in [2], on p. 158 & 165:
despite their clear and concise description, there is lee-way in
the parameter values, resp. they are obviously not used as such in the table
calculations as described. We found the following values useful for our key-
parameters to get a maximal similarity for the 8 selected schedules:
non-standard air pressure: pamb < 1,013 mbar
non-standard water density of ca.: 1,020 kg/m3
(the used „water pressure: 10 m 1 Bar” (p. 86) yields a non-standard
water density of ca. 1,019.7162 kg/m3, the usual “Standard water density”
is, according to U.S. Navy sea water density standard 1.025 g/cc)
water temperature: ca. 25 ° C
respiratory coefficient: not clearly defined, but probably set to Rq = 1.0
Bühlmann safety factor: used depth = planned depth * 1.03 + 1.0 m
the ascent speed: described as 10 m/min, but is varying enormously
in the printed table from 7.5 13.5 m/min
transit-times of ca. 0.3 min incl. rounding-off integers varying
the set of ZH-L16B a-& b-coefficients (pls. cf. next slide):
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Discussion (2):
With the used set of ZH-L16B (“B” set for table calculations,
the “C” set is intended for use within a dive computer or for
the desktop decompression tools to mimic dive computers), there
yields for the a-& b-coefficients on table 25, p. 158 [2]:
the b-coefficient for compartment # 4 (0.7825) is not
according to the formula on p. 129 (0.7725);
for compartment # 5 the b-coefficient has been rounded up slightly from
0.8125 to 0.8126
The majority of the parameters from slides #6/7 is normally undocumented
and/or not accessible by the users, be it in the software-tool or the dive-
computer at hand, thus the run-times may differ from the mirrored ZH-86
values [4].
All of the variations in the key-parameters may seem at first marginal to
insignificant, but clearly, in sum and through error-propagation, the contrary is
the case and there results substantial divergence to the original air-tables, if
not compensated for as described in slide # 7.
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Discussion (3):
Finally, „executive editing“ (*) could not be found in [2],
at least not for the selected 8 schedules.
(*) „executive editing“ is the manual change of the values in the published
version of a table in comparison to the calculated ones, the result from an
algorithm. This is quite common since the first published
decompression table in 1907 from Haldane et al. and was, for e.g. a topic,
mentioned by Ed Thalmann for the USN tables (source: interview with Ed,
transcribed there.)
http://www.divetable.eu/BOOKS/113_Interviews.pdf
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Data:
Translation of some key words found in
Table 32 [2], p. 224:
Luftdekompressionstabelle: air decompression table
ü. NN: above sea level
Tiefe: bottom depth
Grundzeit: bottom time
Aufstieg zum 1. Halt: ascent time to the first stop
Haltezeiten: stop times per stage
Gesamtaufstiegszeit: TTS = sum of all stop times +
(bottom depth / ascent speed)
Repetitivgruppe: repetitive group
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Data:
Translation of some key words found in
Table 32 [2], p. 229:
Aufstieg zur Höhe 60 min oder länger:
ascent to altitude within 60 min or longer
TTS being the time-to-surface in [min] and generally defined as:
TTS = sum of all stop times + (bottom depth / ascent speed)
ascent speed = (bottom depth – depth of 1st. stop) / ascent time to 1st. stop
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42 m / 24 min @ altitude 701 – 2,500 m,
on p. 229 – 231 from [2] :
Adaptions required for DIVE V 3_11 to
reflect the altitude calculations from [2]:
„L“ : for reduced ambient pressure at altitude,
arithmetic average between pamb @ 701 m 2,500 m,
i.e. ca. 0.85
„D“: desaturation @ diving depth 0 m to
simulate the altitude adaption of 60 min or longer,
as per p. 229 ff.: „d“ „0.0“ „60.“
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References:
[1] Vered N., Rosenblat M., Salm A. (2021):
Synopsis & Fact Sheet DIVE Version 3_11,
DOI: https://dx.doi.org/10.13140/RG.2.2.17024.56326
[2] [65] Albert A. Bühlmann, Ernst B. Völlm (Mitarbeiter),
P. Nussberger (5. Auflage in 2002) Tauchmedizin, Springer, ISBN 3-540-
42979-4
[3] [101] Underwater Physiology: Proceedings of the Fourth Symposium,
edited by Christian J. Lambertsen, (Hardcover, 575 pages) Academic Press
Inc.,New York, U.S. (November 12, 1971) ISBN-10: 0-12-434750-9, ISBN-13:
978-0124347502
hard copy
[4] Rosenblat M., Vered N., Eisenstein Y., Salm A. (11.01.2022)
On the reliability of dive computer generated run-times, Part II
DOI: 10.13140/RG.2.2.11343.41126
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Additional Settings required for DIVE V 3_11 to
reflect the special ZH-86 calculations for the
printed air tables (slides # 10 – 19, the yellow display
is ours)
Source: https://www.divetable.info/beta/D3_11.exe
„B“ : Buehlmann Depth Safety Factor
„NC“: selection of the ZH-L16B set („7“)
„AR“: ascent rate, varies 7.5 13.5 m/min
„DI“: for water density 1020.
„L“: for ambient pressure at start of dive
„RQ“: respiratory quotient
„TE“: water temperature
Rq = 1.0 &
water temperature = 25.0 ° C
is default in DIVE 3_11
Bonus Material:
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BONUS material
for DIVE afficionados (1):
Adaptions for DIVE V 3_11 to reflect the required altitude adaption
during 60 min from [2], p. 229:
Instead of an instantaneous pressure reduction, you program
a desaturation ramp, say from 1.0 Bar to 0.8 Bar during these 60
min:
„L“ „0.8“
„AR“ „0.034“ (2 m / 60 min)
„D“ „2.0“ „1.“ (or anything you like …)
„A“ to get back to the altitude-“surface“
„AR“: do not forget to switch back to a standard ascent rate …
So after 60 min starting from 1.0 you reach .8 Bar on your
desaturation ramp: now you could start
simulating the altitude dive …
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BONUS material
for DIVE afficionados (2):
An instantaneous pressure reduction is just a deco stop („E“) or a
dive („D“) at diving depth 0.0 at the desired pamb at altitude during
the required length of your adaption, say 60 min.:,
„L“ „0.8“
„E“ „0.0“ „60.“
(or, equivalent: „D“ „0.0“ „60.“)
now you could start simulating the altitude dive …