On the reliability of dive computer generated run-times (01.01.2023) Part X: a conciliatory proposal of a benchmark

Abstract

Here, in Part X, we offer our conciliatory proposal of a performance benchmark
for diver-carried computers, as these devices are usually sold as “black boxes”,
i.e.: the end-user, that is: the diver, is kept completely in the
dark concerning the safety/security performance of his/her equipment.
This yields also for desktop decompression software.

As well dive computers and decompression software offer deviations from proven
algorithms/dive tables which go unnoticed by the divers resp. are undocumented
from the side of the diving-equipment manufacturers.

Full text

1
On the reliability of
dive computer generated run-times
01.01.2023, Part X:
a conciliatory proposal of a benchmark
Miri Rosenblat, TAU
Nurit Vered, Technion Haifa
Albi Salm, SubMarineConsulting
DOI:

2
On the reliability of dive computer
generated run-times, Part X:
a conciliatory proposal of a benchmark
Abstract:
Here, in Part X, we offer our conciliatory proposal of a performance
benchmark for diver-carried computers, as these devices are usually sold as
“black boxes”, i.e.: the end-user, that is: the diver, is kept completely in the
dark concerning the safety/security performance of his/her equipment. This
yields also for desktop decompression software.
As well dive computers and decompression software offer deviations from
proven algorithms/dive tables which go unnoticed by the divers resp. are
undocumented from the side of the diving-equipment manufacturers.
Introduction: slides # 3  8
Methods: slides # 9  14
Data: slide # 15
Proposed Benchmark: slide # 16  19
References: slides # 20  23

3
Introduction (1):
Diver carried computers
are electronic devices
which measure ambient
pressure (diving depth),
(water-) temperature
and (dive-) time.
Is the oxygen- or
inertgascontent of the
breathing gas known,
the dive computers
could calculate the
inertgas saturation in
models for human bodies via simple exponential take-on / -off equations.
With the help of a published decompression algorithm a ball-park for a „safe“
decompression, i.e. the divers route to the water-surface with only a limited
risk of contracting a DCS (decompression sickness), is calculated on-line.
Fig. 1.: Underwater Fieldtest of dive computers

4
Introduction (2):
Basically, during the last
10 years [12] and in all
of the 9 presentations
([1] to [9]), we found
deviations from
documented algorithms or
decompression models in
varying degrees.
As these deviations are neither
documented nor justified on the
part of the manufacturers,
the end user of these devices,
i.e. the diver, is kept completely
in the dark about the
safety- & security performance
of his/her dive computer.
This yields as well for desktop decompression software.
Fig. 2.: Underwater Fieldtest of dive computers

5
Introduction (3):
Figs. 3 & 4: Various test
scenarios for dive
computers:
Pool test for oxygen-
toxicity doses (CNS-OT)

Altitude test in a
commercial air-craft
↓
Figs. 3 & 4:

6
Introduction (4):
As these deviations have not been, up to now, evaluated in a
systematic manner, we tried to fill this gap ([1]  [12] and all the
references therein).
A basic handicap is the relatively in-complete publicly available
documentation for a dive computer, and, making matters worse, are the
incomplete, sometimes cryptic and often missing, answers from dive
computer manufacturers to our questions.
In order to circumvent the dilemma between the need for company-secrets
and advertisements to promote dive computer features, we propose a simple
benchmark the dive computer user could follow and thus get insight
into the safety-& security performance of the equipment.
The benchmark consists of a list of simple box-/square dive profiles from
accepted/proven dive tables. Now the dive computer users could utilize
the planning-/simulation tools of his/her computer to compare these outcomes
with our compiled list. These profiles could be compared as well with the
simulations from desktop decompression software.

7
Introduction (5):
There are (per 12/2021) ca. 280 dive computers from ca.
35 manufacturers / brands available. We restricted our tests to
the  technically most advanced
 most popular
 most reliable devices.
In a limited, private and non-representative telephony-survey in dive shops /
dive centers in the SFO / US, ETH / IL, TLV / IL and STR / DE regions in the
vicinity of our offices, we found out that these have been units from:
 Shearwater ® ( https://www.shearwater.com/ )
Scubapro ®/ UWATEC ®( https://www.scubapro.com/ )
which feature a relatively low failure rate in practical diving. Both enjoy
regularly a perfusion-dominated decompression model with 16 compartments,
utilizing a set of coefficients following the so-called „ZH-L 16“ system from
A. A. Bühlmann [13], where „ZH“ denotes Zuerich / CH, „L“ is for linear, as the
equation for the tolerated inertgas pressure is a simple, linear equation and
16 denotes here the number of linear independant compartments (i.e.:
mathematical models of human body-tissues).

8
Introduction (6):
In order to get a meaningful comparison between the
dive computers output and a published/printed dive table, we identified
some pivotal parameters ([10], [11]) which have to match.
As well we restricted these comparisons to dives with only one breathing-mix
containing a single inertgas, i.e. Air, Nitrox (EAN) or Heliox. Trimix (O2, N2 &
He) is not used here in these benchmarks, as well no other hyperoxic mixes
for (accelerated) decompression or hypoxic mixes for travel purposes.
As well no gradient factors (GF) or other proprietary security- or
conservativism knobs are used.
The underlying ideas are, that the here used dive tables have a certain,
defined and documented statistical risk of DCS (P(DCS)). The idea is further,
that these risks are generally accepted by the (professional-) diving
community and are as well applicable to recreational divers, even if the
biometrics, diving skills and technologies of these 2 populations are
somewhat divergent.

9
Methods (1):
We took sample box-/square profiles from the following
dive tables / diving manuals:
-ZH-86 air diving table from A.A. Bühlmann [13]
- DCIEM 1983 [14]
- United States Navy Rev. 7 2018 [15]
The profiles follow a constant depth (bottom depth) during the complete dive-
time (bottom time), thus they are called „box-“ or „square“ profiles.
Some of the benchmarks are extreme in terms of depth or time:
it is not insinuated, by no means! that a recreational diver should follow
these dive plans. Instead, these benchmarks allow a quick identification
of the above cited deviations from proven standard-procedures and standard
tables. As well typical recreational dive profiles are multi-level and not of the
„box“-type, usual in professional environment.
As usually all tables in question do, the descent from surface to the bottom
depth is done instantly, i.e. is simulated with a Heaviside Step-Function which
jumps immediately to the ambient pressure at bottom depth.

10
Methods (2):
The dive computers simulations tools, aka „deco planner“,
„dive planner“ or the like, follow the same rule. As the user inputs bottom depth
and bottom time, so are the tabulated entries for the dive tables.
The parameters of comparison (pls. cf. slide # 15, DATA) are:
depth & stop times per each decompression stop
 the TTS (time-to-surface), with:
TTS = sum of all stop times + (bottom depth / ascent speed)
The dive tables depth entries are usually in 3 m / 10 feet increments, the
time entries in 5 to 10 min increments. Thus, if the desired benchmark
parameters are not tabulated in the dive tables, we
developed the target decompression plan with our own planning software,
the DIVE Version 3 framework [10]. As we showed recently, this framework
could reproduce the decompression plans from the dive tables / manuals in
question within an acceptable error limit (pls. cf. for the ZH-86 table: [11],
for the DCIEM air tables: [16], for the USN Rev. 7 air tables: [17]).

11
Methods (3):
The next 4 slides show the suggested procedure along only
one of our benchmark profiles:
Bottom Depth 42 m
Bottom Time 27 min
Air as breathing gas
This profile could be found exactly in [13] on p. 227, but not in the other tables /
manuals, thus we used DIVE parametrized accordingly [16] & [17].
N.B. / remarks for the DATA slide #15: the densities for fresh - & seawater are
not unequivocallly defined, but the DIN 13 319 water density is.
The gradient factor (GF) method as such is as well not generally binding, and
so is the linear interpolation from GF Low to GF High ([18], p.14), i.e.: a
GF High = GF Low = GF 99 / 99 from the Shearwater PERDIX, is, for all
practical purposes, considered identical to a GF 100 / 100 (Scubapro G2 TEK).
The ZH-L 16 B set is for comparison with ZH-86 table, whereas the ZH-L 16 C
set compares directly to dive computers ([13], p. 157, 158).

12
Methods (4):
 ZH-86 [13] , p. 227:
4 min @ 9 m; 7 min @ 6 m, 19 min @ 3m, with a TTS = 33 min
 DIVE Version 3_11, pls. cf. [10]:
5 min @ 9 m; 7 min @ 6 m, 17 min @ 3m, with a TTS = 33 min
Fig. 5 : ZH-86 [13], p 227
Fig. 6 : DIVE 3_11 [10]

13
Methods (5):
The output of 3 dive computers planning tools
top row, L.H.S.: Scubapro G2 TEK; R.H.S.: Scubapro Galileo 2
bottom row; Shearwater PERDIX:
Figs. 7, 8 & 9: dive computer planning tools

14
Methods (6)
The ΔTTS is the difference between your dive computers
output (or your deco software) of the simulated dive scenario with the
benchmarks partner dive tables TTS:
ΔTTS = TTSBenchmark - TTS your dive computer :
If:
 ΔTTS: +/- ca. 3 – 5 min (*):
 ΔTTS > +/- ca. 6 min:
 ΔT / decompression step > +/- ca. 3 min:
(*) ΔTTS in the „green“ region is, for all practical purposes, acceptable due
to the restricted precision of dive computers and oxygen analyzers. It
becomes even irrelevant due to the limited skills of divers to follow a run-
time within +/- 2 min or +/- 2 m and the daily variation of the ambient
airpressure.

15
Data:
Synopsis for: 42 m, 27 min, Air
stop times @ 12; 9; 6; 3 m in [min], TTS [time-to-surface) in [min],
[*]: Benchmarked result
Method
12
9 6 3 TTS
[*]
ZH
-86 4 7 19
33
DIVE 3_11 DIN 13319, ZH
-L16B 5 7 17
33
DIVE / USN
1
2 5 21
33
DIVE 3_11
fresh water, ZH-L16C 4 8 20
36
DIVE / DCIEM
1
4 9 22
40
Perdix
fresh water, GF 99/99 1 7 15
27
Perdix
DIN 13319, GF 99/99 2 7 16
29
Perdix
seawater, GF 99/99 2 7 17
30
G2
TEK fresh water, GF 100/100 3 36
G2 V 2.0
fresh water, MB
Level = 0
4 49 4

16
Benchmark (1):
Benchmark #1, Quick Test:
1) 42 m, 27 min, Air (as per slide # 15)
2) same profile as per 1): 42 m, 27 min; but with other breathing gas:
Heliox21 (21 % O2, 79 % Helium) (**)
3) 40 m, 45 min, EAN32 (enriched air nitrox with 32 % O2)
4) 6 m, 45 min, EAN99 / 100 % O2
Rem.:
1) & 2) are checking if the coefficients of the decompression model in
question are properly implemented.
2) here the average TTS from various tables / procedures is ca. 80 +/- 10
min.
N.B.: as the inert gas content of 1) & 2) are identical, the check 2) is by the
same token a check:
if the mechanism of ICD (Isobaric inertgas Counter-Diffusion) is properly
implemented;
if a proper numerical solution to calculate the mix-gas stop-times is
implemented [19].

17
Benchmark (2):
3) & 4) are checking, if the rule-of-three for NOAA
CNS-OT (central nervous oxygen toxicity) is properly implemented:
a 100% CNS dose according to NOAA is reached @
pO2 = 1,6 atm after 45 min. A pO2 = 1,6 Bar is with EAN32 at ca. 40 m
depth, with EAN99 already at ca. 6 m.
But since the dive computers are normally expecting metric / Bar input
with only limited precision, a 100% dose could not be reached exactly as:
1,6 atm corresponds to ca. 1,63 Bar;
so the according depth in m should be increased by approx. 30 cm in fresh
water: the dive computers planning tools do normally not allow for a decimal
place.
Thus an acceptable average after 45 min would be ca. 85  115 %.
For the fun of it, you could check as well also the Oxygen Tolerance Units
(OTU values), they should be around ca. 80 – 90 Units.
An average of the TTS is for 3): ca. 40 +/- 5 min.

18
Benchmark (3):
Benchmark #2, extended tests:
Air as breathing gas, only the metric / SI units
entries are directly comparable! N.B.: the depth of the last stop @ USN is
20 feet / ca. 6m.
12 m (39,37 feet) / 300 min:
 ZH-86, p. 225, TTS = 43 @ 3 m
 DCIEM, p. 1B-6, TTS = 44 min @ 3 m
 [USN (40 fsw), p. 492, TTS = 128 min @ 20 feet]
21 m (68,9 feet) / 180 min:
 ZH-86, p. 225, TTS = 130 min (4/37/88)
 DCIEM, p. 1B-8, TTS = 130 min (29/101)
 [USN (70 fsw), p. 497, TTS = 295 min (4/289)]
30 m (98,4 feet) / 90 min:
 ZH-86, p. 226, TTS = 102 min (16/28/56)
 DCIEM, p. 1B-11, TTS = 109 min (2/8/24/75)
 [USN (100 fsw), p. 499, TTS = 174 min (13/158)]

19
Benchmark (4):
Air as breathing gas, only the imperial entries are
directly comparable! N.B.: the depth of the
last stop @ USN is 20 feet / ca. 6m.
60 m (196,85 feet) / 15 min:
 ZH-86, p. 228, TTS = 31 min (2/4/6/15)
 DCIEM, p. 1B-17, TTS = 35 min (5/6/8/16)
USN (200 fsw), p. 510, TTS = 35 min (2/3/5/19)
60 m (196,85 feet) / 21 & 20 min:
 ZH-86 (21‘), p. 228, TTS = 56 min (3/4/6/11/28)
 DCIEM (20‘), p. 1B-17, TTS = 59 min (5/5/6/10/33)
USN (20‘, 200 fsw), p. 510, TTS = 68 min (2/4/6/7/43)
50 feet / 240 min:
 DCIEM, p. 1A-6, TTS = 74 min @ 10 feet
USN (50 fsw), p. 494, TTS = 198 min @ 20 feet
220 feet / 40 min:
 DCIEM, p. 1A-18, TTS = 247 min
 USN (220 fsw), p. 511, TTS = 417 min

20
On the reliability of dive computer
generated run-times: Part X
References:
[1] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (26.07.2021)
On the reliability of dive computer generated run-times, Part I;
DOI: 10.13140/RG.2.2.16260.65929
[2] 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
[3] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (02.02.2022)
On the reliability of dive computer generated run-times, Part III;
DOI: 10.13140/RG.2.2.21973.50405
[4] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (22.02.2022)
On the reliability of dive computer generated run-times, Part IV;
DOI: 10.13140/RG.2.2.11469.72169
[5] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (07.02.2022)
On the reliability of dive computer generated run-times, Part V;
DOI: 10.13140/RG.2.2.18129.81763

21
On the reliability of dive computer
generated run-times: Part X
[6] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (23.02.2022)
On the reliability of dive computer generated run-times, Part VI;
DOI: https://dx.doi.org/10.13140/RG.2.2.36242.32969
[7] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (01.07.2022)
On the reliability of dive computer generated run-times, Part VII;
DOI: 10.13140/RG.2.2.14589.64487
[8] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (27.07.2022)
On the reliability of dive computer generated run-times, Part VIII;
DOI: 10.13140/RG.2.2.22374.50247
[9] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (01.11.2022)
On the reliability of dive computer generated run-times, Part IX;
DOI: 10.13140/RG.2.2.16961.84326

22
On the reliability of dive computer
generated run-times: Part X
[10] 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
[11] Rosenblat, M., Vered, N., Eisenstein, Y., Salm, A. (2022)
Recovery of selected ZH-86 air-diving schedules via a decompression shareware
DOI: 10.13140/RG.2.2.34235.13609
[12] Salm, A. (2012) Variations in the TTS: where do they come from?
International Journal of the Society for Underwater Technology, Vol 31, No 1, pp 43–47
[13] Bühlmann, Albert Alois, Völlm, Ernst B. (Mitarbeiter), Nussberger, P.
(2002): Tauchmedizin, 5. Auflage, Springer, ISBN: 3-540-42979-4
[14] DCIEM Diving Manual, DCIEM No. 86-R-35 (1992): Part 1 Air Diving
Tables and Procedures, DCIEM No. 92-50 (1992)
[15] United States Navy Diving Manual Rev. 7 2018 ChangeA-6.6.18

23
On the reliability of dive computer
generated run-times: Part X
[16] Salm, A. (28.03.2022 ) The mapping of the DCIEM Air-diving table to
a standard Haldane-/Workman-/Schreiner-algorithm.
[17] Salm, A. (19.05.2022 ) Recovery of selected U.S.N. Rev. 7 air-diving
schedules via a decompression shareware.
[18] Salm, A. (18.12.2022) Gradientenfaktoren auf dem Vormarsch?
Jahrestagung der ÖGTH Wien: update Tauchmedizin;
DOI: https://dx.doi.org/10.13140/RG.2.2.24866.30403
[19] Salm, A. (03/2021) update on the CAISSON 2010 paper