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Research & Reports
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Dive computers and no extra penalty for repetitive dives
Alain Foret∗and Éric Frasquet†
Worldivers Research & Reports, Montpellier, France.
(Dated: 23 décembre 2023)
Some dive computers no longer apply an extra penalty for repetitive dives, without any justifi-
cation or warning in their instructions. This can result in stop times being reduced by a factor of
two or three compared to other dive computers. This raises the question of whether this practice is
dangerous.
INTRODUCTION
Scuba diving is practised around the world for "lei-
sure", commercial and military purposes.
The "leisure" activity, which originated in Europe
(France, Saint-Raphaël, Cdt Le Prieur, August 1933)[1],
is estimated to involve about 6.5 million[2] people world-
wide, including 2.5 million in the USA. It can be divided
into recreational, sports and technical activities.
Recreational diving involves buddies, fully autonomous
or following a dive leader, without mandatory stops and
to a maximum depth of 30 m of even 40m1. It is common
in North America.
Sport diving is practised in Europe and in certain
CMAS2countries. It goes beyond recreational diving,
training divers to dive breathing air, in fully autonomous
or instructor led teams, up to depths of 60 m with man-
datory decompression stops.
Technical diving allows you to go deeper than brea-
thing air, using a helium-based breathing mix.
All of these types of training may involve diving se-
veral times a day. The way in which repetitive dives are
managed is therefore crucial to avoiding the risk of de-
compression sickness (DCS).
PUTTING HISTORY IN PERSPECTIVE
John Scott Haldane, who was commissioned by the
Royal Navy in 1905[3], published the world’s first mo-
del of desaturation in 1907[4], before making it available
to the public in 1908[5][6].
1. This publication uses the International System of Units (SI
from French Système International) established and maintained by
the General Conference on Weights and Measures.
2. World Underwater Federation or Confédération Mondiale des
Activités Subaquatiques, created by Jacques-Yves Cousteau in Mo-
naco in 1959.
This model is still used today in almost 100% of dive
computers via the A. A. Bühlmann set of parameters,
mainly in the ZH-L 16 C dedicated to dive computers,
first published in 1986[8], even in the RGBM and VPM3.
However, Haldane’s model was designed for one dive
per day. Making several dives a day is therefore not hand-
led by the model. The set of parameters used makes no
difference[7].
The US-Navy, which had adopted Haldane’s tables
from the beginning, had already raised this problem in
1916 : "If a diver makes a second descent in deep water
with an interval of less than three hours between the two
dives, his body will be more highly saturated with nitro-
gen at the end of the second dive, and extra care will be
needed in bringing him to the surface. A safe rule is to
take the total combined time of the two dives and use
a table for that exposure, at the pressure at which the
diver was working"[9]. In any case, this method was too
punitive and was soon abandoned.
Subsequent research showed that the three hour in-
terval was far from sufficient and that repetitive dives
beyond three hours should be penalised[14].
We now know that taking into account the neutral gas
(nitrogen) from the previous dive is not enough. Two
other factors come into play, such as the creation of
bubbles and gas micronuclei[10] during the ascent phase
of the previous dive, which are still present during the
next dive.
3. Whether it’s called ZH-L 16 C ADT, ZH-L 16 C GF or some-
thing else (even ZH-L 6 or ZH-L 8), it’s the same set of parameters.
About RGBM, see B. Wienke, Reduced Gradient Bubble in depth,
Best Publising, p.34. About VPM see Fortran source code VPM-B
by Erik C. Baker : "This program uses the sixteen (16) half-time
compartments of the Buhlmann ZH-L16 model."
2
REPETITIVE DIVES
While the DCIEM model[12] handles repetitive dives
natively, the Haldane model does not.
Repetitive dives must therefore take into account not
only the residual neutral gas (nitrogen) from the previous
dive, but also the bubbles and gas micronuclei that have
been generated, which will promote the formation of new
bubbles during the next dive, an additional risk factor for
DCS.
The approach to the formation of gas micronuclei is ac-
tually not new ; it has been existing in physics for a long
time under the name of "nucleation theory" or "Classical
Nucleation Theory (CNT)". For example, it was mentio-
ned as early as 1967 in the book La Plongée by the French
navy.
Figure 1. Nucleation theory in La Plongée, Marine nationale,
Arthaud, 1967, p. 125.
Many authors have written about repetitive dives[11],
in particular :
— "Most available techniques, including dive compu-
ters, use the gas loading of the previous dive, adjus-
ted to account for the surface interval, and take a
little or no account of the possible generation or des-
truction of bubble generation of gas micronuclei."
Peter Bennett [13]
— "It may take more than 24 or even 48 hours for us
to desaturate completely. This cause problems with
a second dive which occurs following a relatively
short surface interval after the first dive. It can also
cause problems during diving holidays where you
are doing multiple dives per day for several days at
a time. On the second and subsequent diving days
the slower tissues may still have residual nitrogen
present at the start of the next day which can build
up over the course of the holiday. Research from
the Divers Alert Network (DAN) has shown that
divers who make multiple dive per days have a hi-
gher than average risk of decompression illness."
Mark Powell[14]
As the model not could take into account the bubbles
and gas micronuclei from the previous dive, the only so-
lution found was to over penalise the following dive by
artificially increasing the residual nitrogen.
This has led to the development of a specific calcula-
tion in the dive tables, called Repetitive Group (RG), in
addition to the Haldane model.
DIVING TABLES : REPETITIVE GROUP (RG)
With Haldane model, after a dive, it is not sufficient
to consider only the residual neutral gas in the various
tissue compartments to ensure the safety of repetitive
dives. This is because, in most cases, the leading tissue
compartment has a comparatively short half-time (e.g.
12.5 or 18.5 min for ZH-L 16 C). As total desaturation
takes place in 6 times the half-time tissue compartments,
very quickly there is little or no penalty (e.g. after 75 min
or 111 min, respectively).
It was therefore decided to consider a tissue compart-
ment with a relatively long half-time in order to calculate
an artificial increase of the dive time that would be appli-
cable to all other tissue compartments. This approach has
been adopted by all dive tables in the world. In this logic
Bühlmann repeatedly used the 80 and 90 min tissue com-
partments, followed by the 635 min (Bühlmann-Hahn).
The US Navy and the French Navy used the 120 min tis-
sue compartment. The RDP-PADI tables (derived from
the US Navy tables) used the 60 min tissue compartment
(limited to recreational diving).
DIVE COMPUTERS
Repetitive dives
The advent of dive computers led to the abandonment
of the RG method, as it was impossible to implement it
in a real-time calculation. Other solutions have been im-
plemented, generally protected by intellectual property
rights : Uwatec Aladin Pro, Aladin AIR X, Scubapro,
Suunto Companion, Suunto Solution, Suunto RGBM,
Mares, Aqualung, etc.
For example, the ZH-L8 ADT4algorithm (derived from
ZH-L 16 C but with fewer compartments) was developed
for Uwatec by Ernst Völlm of Dynatron AG in collabo-
ration with Professor Albert Bühlmann.
Max Hahn, for his part, developed a specific algorithm
called Delayed Surface Desaturation (DSD) in the early
1990s after "conducting controlled, repetitive, manned
dives. It is a little bit more conservative than Bühlmann’s
original"5.
Erik C. Baker states in the VPM-B source code : "This
program extends the 1986 VPM algorithm (Yount and
Hoffman) to include (...) repetitive (...)" dives.
4. For the first Aladin computers, the ZH-L16 model had to be
simplified by reducing the number of tissue compartments (ZH-L 6
in 1989, ZH-L 8 in 1994) for technical reasons linked to the compu-
ting capacity available at the time. In practice, this simplification
does not affect the calculation of stops.
5. See www.apdiving.com
3
All this work has found its way into the various dive
computers on the market, with the aim of overpenalising
repetitive dives.
In addition to the Haldane model, based on the work
of D.J. Kidd and R.A. Stubbs in 1962, Ronald Y. Nishi
developed a new approach in 1971, known as DCIEM6
model[12], which has been implemented in recent Shear-
water computers. This approach, which models compart-
ments in series rather than in parallel as in Haldane, pro-
vides native management of repetitive dives. With this
model there is no need to add an additional algorithm to
account for these dives.
The results obtained with the overpenalisation system
developed by Uwatec, Scubapro, Suunto or by means of
the DCIEM are comparable (see Table I).
The Bühlmann ZH-L 16 C sets of parameters (1986)
have many advantages from a dive computer manufactu-
rer’s point of view. They are publicly available, free of
charge and cover both nitrogen (air, nitrox) and helium
(heliox, trimix). Following in the footsteps of the histo-
ric manufacturers, new entrants to the market have used
them, first in technical diving and then in recreational
and sport diving. The special feature of these computers
is that the user can enter his own gradient factors (GF).
For marketing purposes the set of parameters was called
ZH-L 16 C "GF". This is in fact the original Bühlmann
set of parameters with manual GF setting. In this ca-
tegory we find Shearwater, Garmin, OSTC, some new
models from Scubapro or Mares, etc.
First alert on the operation of certain dive
computers
Sport dives, with mandatory decompression stops,
both for teaching and exploration in the Med Sea, bet-
ween March and October 2023, led us to question the
management of repetitive dives by the computers offe-
ring ZH-L 16 C with manual adjustment of the GFs.
This warning was shared by some diving instructors,
both in France and in Spain. Some instructors were even
using two dive computers, conscious of the low penalty for
repetitive dives. One with manual adjustment of the GFs
to find out what indications their clients had when using
this type of machine. The other, with real management
of repetitive dives, in order to know precisely the time
remaining without stops or the duration of stops.
So at the end of the summer of 2023, we decided to
carry out systematic tests to analyse the differences in
repetitive dive management between different dive com-
puter models.
6. Defense and Civil Institute of Environmental Medicine, Ca-
nada
Test equipment and methodology
The equipment used is a Uwatec chamber, supplied
with compressed air from a cylinder, enabling tests to be
carried out at up to 10 bar.
One of the difficulties encountered with this type of
test is the need for identical reproducibility between each
test, to ensure that the results are comparable. We have
therefore added software control to the equipment to gua-
rantee this.
As far as measuring depth is concerned, we are well
aware that this is not reliable information because, de-
pending on the conversion factors (atmospheric pressure,
fresh water, salt water), it can vary significantly from one
computer to another. We therefore chose to set the soft-
ware to a given pressure, which ensures that all the tests
were carried out at the same pressure.
As far as the dive computer settings are concerned,
for all the machines we used either the default mode (L0,
MBL0, P0, R0, SF0, etc.), or GF 90/90 when the settings
were manual. The fact that this default mode uses in
most dive computers corresponds to GF 90/90 has been
reported in 20217. We checked this before continuing with
the tests (see Dive 1, Table I). This enable a reliable
comparison.
With regard to the duration and depth pair to be tes-
ted, the aim was to find values that would enable us to
highlight any differences in the management of repetitive
dives. We used the depth of 30 m, which had already
been tested for some time by A. A. Bühlmann. For the
duration, we used the historical US-Navy tables at 30
m : 30 min. As for the surface interval, 90 min seemed
sufficient to allow a certain desaturation of the tissue-
compartments, while requiring over-penalisation for re-
petitive dives.
To date, we have tested the computers listed in Table I.
Although not exhaustive, this test is sufficiently signi-
ficant to allow analysis and conclusions to be drawn.
In this way, all our tests can easily be verified by the
same procedure.
Results
Analysis of the results shows that several groups of
computers can be distinguished :
— Those within + or - 3 min of the DCIEM results.
— Those who are well above the DCIEM and who are
probably too conservative.
— Those well below the DCIEM.
7. Rosenblat, Miri & Vered, Nurit & Salm, Albi. (2021). On
the reliability of dive computer generated run-times, Part I.
10.13140/RG.2.2.16260.65929.
4
— Those who are even further below the DCIEM and
do not overpenalise (less than 20 minutes of decom-
pression on the 2nd dive).
— There is also a big difference in the duration of stops
between computer models within the same brand.
Computers Parameters Dive 1 Dive 2
Suunto Vyper RGBM 13 42
Aqualung i300C ZH-L 24 41
Suunto D4i RGBM 18 41
Suunto Favor Spencer (US-Navy) 15 40
Scubapro A1 ZH-L16C ADT (L0) 17 39
Suunto Companion Spencer (US-Navy) 14 39
Aqualung i100 ZH-L 20 38
Scubapro G2 ZH-L16C ADT (L0) 16 38
Scubapro Pro I ZH-L6 14 38
Scubapro Luna 2 ZH-L16C ADT (L0) 16 37
Mares M1 RGBM RGBM 13 36
Mares M1 Rogers Powel (USN) 11 36
Shearwater Peregrine DCIEM 13 35
Scubapro Sol ZH-L8 ADT (L0) 16 34
Scubapro Pro II ZH-L8 ADT 16 34
Suunto Octopus 2 Spencer (USN) 12 34
Mares Guardian RGBM 9 34
Scubapro HUD ZH-L16C ADT (L0) 14 33
Suunto Alpha Spencer (US-Navy) 13 33
Scubapro Pro Ultra ZH-L16C ADT (L0) 15 32
Scubapro Square ZH-L16C ADT (L0) 14 32
Scubapro Luna 2 ZH-L16C GF 90/90 13 26
OSTC OSTC 2 ZH-L16C GF 90/90 11 20
Shearwater Teric ZH-L16C GF 90/90 13 17
Shearwater Peregrine ZH-L16C GF 90/90 13 17
Scubapro HUD ZH-L16C GF 90/90 11 16
Shearwater Petrel 3 ZH-L16C GF 90/90 11 16
Garmin MK2 ZH-L16C GF 90/90 11 15
Table I. Dive computers : Total duration stops (min). First
dive of 30 min at 30 m with a surface interval of 90 min,
followed by a second dive of 30 min at 30 m.
Conclusion
With the exception of the implementation in Scuba-
pro’s LUNA 2, none of the computers using the ZH-L
16 C GF apply over-penalisation to repetitive dives. All
the brands involved in our tests have been contacted.
We asked them for the reasons for this absence of over-
penalisation. To date, we have received no response.
Whatever the cause, this can lead to decompression
times being divided by 2 or 3 compared with dive com-
puters that do overpenalize.
We believe that :
— The manufacturers concerned should give reasons
for this practice and mention it in the instructions
for use.
— Further studies should be carried out in the field to
analyse diving accidents as a function of the dive
computers used and the associated settings, both
for recreational diving and for sport and technical
diving.
∗Corresponding author : alain.foret@worldivers.com
†Corresponding author : eric@aventurebleue.com
[1] Foret A. & Pierre Martin-Razi, Une histoire de la plongée
et des sports subaquatiques, Subaqua, 2007, p. 64.
[2] DEMA, Diving Fast Facts, 2023.
[3] Admiralty, S.W., C.N. 11713/19049, 8th August 1905 .
[4] Royal Navy, Report of a Committee Appointed by Lords
Commissioners of The Admiralty, Deep Water Diving,
1907.
[5] Haldane J.-S. et coll., The prevention of decompression
air Illness, J. Hyg., 1908.
[6] Haldane J.-S. et coll., Translation in French by Foret A.,
Prévention de la maladie de décompression, Téthys, 2008,
By permission of Cambridge University Press.
[7] Hamilton R. W., The effectiveness of dive computers in
repetitive diving, Undersea and Hyperbaric Medical So-
ciety, Inc, 1995.
[8] Bühmann A. A., Völlm E.B., Nussberger P., Tauchmedi-
zin, Springer-Verlag, 2002.
[9] US NavyDiving Manual, 1916, Chapter X, p.84.
[10] Arieli R., Marmur A., Decompression sickness bubbles :
are gas micronuclei formed on a flat hydrophobic sur-
face ? Respir Physiol Neurobiol. 2011 Jun 30 ;177(1) :19-
23.
[11] Lang M. A. et Vann R. D., Proceedings of Repetitive
Diving Workshop, American University of Undewater
Sciences, Duke University, 1991.
[12] Ronald Y. Nishi et al, Digital Computation of Decom-
pression Profiles, DCIEM-NTIS, 1973.
[13] Bennet and Elliott’s, Physiology and Medicine of Diving,
Saunders, 2003, pp. 471-473.
[14] Powell M., Deco for divers, Aquapress, 2021, p. 62..