Incl. 58 illustrations

© 2014 by Wolfgang Wild. All rights reserved.

Publisher: epubli GmbH, Berlin (Germany)

www.epubli.de

ISBN: 978-3-7375-0616-8

No part of this book may be reproduced in any written, electronic, recording, or photocopying without written permission of the publisher or author. The exception would be in the case of brief quotations embodied in the critical articles or reviews and pages where permission is specifically granted by the publisher or author.

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Introduction

What exactly does “conservative” mean in diving?

Dive Tables – the STUP effect

An example for reliably developed, validated and documented dive tables – the Recreational Dive Planner (RDP)

Reflections on a proper ascent rate

Excursus – How do divers control their ascent rate?

Saturation, halftime and M-value

Halftime

M-value

Doppler ultrasound and other ways to detect bubbles in our tissues

Understanding decompression sickness

”Tissue Model” vs. “Bubble Model”

Tissue Model / 1-phase model

Bubble Model / 2-phases model – Part One

The Buhlmann models ZH-L12 and ZH-L16

Gradient factors

Bubble Model / 2-phases model – Part Two

The attack on bubbles at depth

The VPM model

The RGBM model

Deep Stops – what is that?

Which stop-depth is the correct one?

What to do? STUP is for divers no real alternative!

Dive computers in practice

From table towards computer – multilevel diving

Preliminary evaluations of dive data banks – Wienke & DAN

Dive Computers 1994 – results of own practice tests

Dive Computers 2009 – practice test magazine Diver

Dive Computers 2009 – practice test magazine Scuba Diving

Practice tests in the hyperbaric chamber – Catalina Island (USA) 2011

The crux with technology

Closing chapter and perspectives

Requirements for the validation of dive computers

Dreams of the future – alternatives to the traditional dive computer

Bibliography and Internet Links

1 – Introduction

Dive Computers – Computers?

Here a selection of dive computer recalls published on the homepage of the Consumer Product Safety Commission (CPSC) which is in charge of consumer protection in the United States of America:

•     AERIS Epic – decompression hazard

•     Atomic Aquatics Cobalt – impact injuries and drowning hazard

•     Dacor Darwin Air – serious injuries, including decompression sickness

•     Hollis DG03 – drowning hazard

•     Mares Nemo Air – drowning hazard

•     Oceanic ATOM 2.0 – decompression hazard

•     UWATEC Aladin Air X NitrOx – possible decompression sickness

Source: www.cpsc.gov

These few examples of dive computer recalls do not only concern various manufacturers, but also different mathematical calculation models (aka algorithms) and varied technical problems of our popular dive companions: A display which fails to display under water, a leaking O-ring leading to wrong remaining air times under water, a software defect which is known by the manufacturer who is forced seven years later to admit this before a United States District Court (see bibliography, San Francisco Chronicle) etc. etc. The reader will be well aware of such product recalls not being limited to diving equipment, and they are not only nerving, but actually inacceptable for us as consumers when our safety is concerned. Visiting above US government website cpsc.gov or using your favorite search engine and the proper term for “product recall” in your language reveals horrifying results. Aren’t we supposed to have fun when we go diving, and isn’t safety a prerequisite for that?

From the mechanic-pneumatic one-tissue (!) Decometer in 1959 (USA) via the legendary EDGE (USA, 1983) and Deco-Brain (Switzerland, 1983/1985) to present-day models, the dive computer has come a long way – more than half a century.

And the research which divers know as decompression theory is quite a bit older. If we take John Scott Haldane as “father” of all dive tables in 1908 this history extends well over one hundred years.

All diver training associations still regard it important that divers learn in any way why and how our body tissues are being enriched by gases which constitute the gas mixture divers breathe under water. And it is also still regarded essential for divers to get to know and manage the tools that are designed to avoid problems from this absorption of gases which always takes place in us when we use a “self-contained under water breathing apparatus” (aka “scuba”) to seek adventure and recreation in our fascinating under water realm.

Some diver training associations continue to proceed via the dive table, others have abandoned the tables completely, relying now fully on the dive computer and respective simulation programs for teaching divers the dive planning basics.

In this eBook the reader will not be pestered with lengthy mathematical equations of numerous dive computer algorithms – these can be studied in a wealth of internet articles and specialized literature that partially meets scientific requirements.

The intention of this eBook is rather to offer interested divers and diving professionals with pictures, illustrations, tables and charts deeper insights into the background and the potential of dive computers.

This will include the understanding of dive tables and some underlying specifics of the decompression models of modern dive computers.

The reader of this eBook can expect that the notorious STUP effect will be addressed – and that topics like ascent rate, ascent techniques and stop-depth are discussed is indispensable.

How does the future of dive computers look like? More gadgetry at the wrist of the diver with miniature display sizes overloaded by supposedly important information? A different path is taken by the SDC (smartphone dive computer), which leverages the enormous processing power of modern smartphones and their reasonable display sizes. This eBook also takes a look at such developments.

Finally a brief remark on the numerous sources referenced in this eBook: These are not only listed in the detailed bibliography but usually also directly in the text so that the reader is spared from frequently having to jump forward into the appendix and back into the text. And as many sources are publicly available in the internet the bibliography is providing corresponding links.

The valued reader will easily realize that the topics discussed in this eBook are addressed to all divers and diving professionals of all diver training associations.

Enjoy browsing through this eBook on your iphone, kindle, kobo, sony reader, tolino, tablet …

2 – What exactly does “conservative” mean in diving?

From the years in which divers had no alternative than using dive tables for their dive planning (because dive computers simply did not yet exist), older divers will remember the grandiose statement:

Our xyz dive table is more conservative than others.

Also dive computers and simulation programs for PC and/or tablet put forward that claim. What is suggested with such a claim or promised to divers?

Dive Tables – the STUP effect

A former both popular and trivial comparison of dive tables looked like this:

Take several dive tables, note their no-decompression limits in a graph – and without further ado the table with the shortest no-decompression times for certain depths was entitled to be the “safest” table, because this one obviously was the “most conservative”.

The following tables for air just serve as examples; the first three of them are dive tables which are or used to be popular in German speaking Europe.

Notes: “VDST” means “Verband Deutscher Sporttaucher”, which is the German CMAS federation branch; University Zurich [correctly spelled Zuerich with u-umlaut] refers to the hyperbaric chamber in the capital of Switzerland that Albert Buhlmann [correctly spelled Buehlmann with u-umlaut] used for developing his famous ZH-L algorithm which is discussed later in this eBook.

[Note for eBook readers with a device which cannot display colors: The upper broken line depicts the Deko '92 table, the lower dotted line shows the US Navy tables.]

The graph shows us the dive table with the most conservative values – correct?

Not really. There is another dive table with significantly shorter no-decompression times and no-decompression limits:

[Note for eBook readers with a device which cannot display colors: The upper unbroken line (green) shows the STUP effect.]

The reader will ask himself with good reason: From which dive table does this green line originate? Well, honestly spoken, from no dive table available on the market. But this table can be “produced” easily and quickly: Just take a pen, place above the former most “conservative” line some points and connect these. And – lo and behold – you have generated a safer because more conservative “dive table”. (Using EXCEL this is a matter of seconds ...)

Question: Is there perhaps even an enhancement of this awfully economic developing procedure?

Answer: Yes. The STUP principle – Stay Up. Because for divers it is of course safest not to go diving, staying at the surface or even better at home instead; this has the advantage of sparing all the grappling with dive equipment and avoiding the uncertainty of potentially being hit by decompression sickness (DCS).

Note: Actually even at home you can not be sure not to get hit by DCS. Raymond Rogers has pointed to that chance when criticizing a popular mathematical equation used by many decompression scientists that time; Rogers concluded that if this equation was valid an unlimited no-decompression limit could only be found to be “a fraction of a foot deep”:

“This would imply that if you lay in your half-filled bathtub long enough, you’d get decompression sickness when you stood up!”

Source: Rogers, Raymond, Renovating Haldane, The Undersea Journal, Third Quarter 1988, p. 17

The reader and enthusiastic diver will understand how this hint by Rogers is meant (animated, winking smileys unfortunately don’t show well in eBooks …). And smiling while reading this eBook is explicitly allowed.

So, this approach is of course not the way to seriously discuss the topic “conservative” no-decompression times.

If we really want to be able to test the “performance” of a dive table (or of a dive computer) and compare it with other dive tables (or dive computers) then we’d need to know from the developer (or more modern: from the designer) of the dive table resp. dive computer in which way the concept or design had been created. Which parameters (besides depth resp. pressure, and time) found their way into the design – and, above all: How has been validated whether a diver using it will come back home from his dives safely and healthily – i.e. without being hit by DCS (very likely not being hit, at least).

Unfortunately there is an inglorious “tradition” among the designers which perpetuated from dive tables to dive computers: Only with few exceptions the diver receives answers on such questioning – usually he doesn’t hear anything (or nothing specific).

What is the common language regime in advertising, promotion, and instruction manuals? ”Modified Haldanean model”, “US Navy values, adapted for recreational divers”, “Buhlmann ZH-L16 with gradient factors”, “based on RGBM”, etc.

It can be that a diver who respects the no-decompression limits of a certain dive table or dive computer will surface without any problems, and will continue diving after some surface interval, safely and healthy. But it can also be that this diver could have been even longer under water for some time.

Briefly speaking: Perhaps the diver has shed wonderful time under water with this dive table or dive computer, because he surfaced too early and therefore did not see the Whale Shark, Nautilus or any other creatures of our dreams. And in this case he’d also have shed valuable breathing gas because usually tank fills cost money.

Note:

Let us finally check how the dive tables which we have used above differ when strained for a repetitive dive:

To properly do that (divers who were trained to handle dive tables know this) we need the so-called pressure group (PG) which represents the residual nitrogen from the previous dive, and we need of course the duration of the pause at the surface, the so-called surface interval (SI). For our example let’s assume that we want to return after a surface interval of one hour again to the same depth of the first dive, which was 18 meters/60 feet (in the hope to revisit the curious-playful Octopus there). How long could we stay there for another no-stop dive? For dive number one let’s assume a dive time of 50 minutes:

•     Dive #1 – depth: 18 m/60 ft, time: 50 minutes

•     SI – 60 minutes

•     Dive #2 – depth: 18 m/60 ft, time: maximum no-stop time

Above dive tables would allow the following no-stop limits for the second dive to 18 m/60 ft:

•     6 minutes – Deko 2000 and US Navy (2007)

•     10 minutes – Deko '92

•     24 minutes – NAUI (1995)

•     34 minutes – Hyperbaric Chamber University Zurich (1986) and RDP/DSAT (1988)

What does that mean? Do these results mean that the tables allowing only 6 minutes are several 100% “safer” than the others, and the extensively validated DSAT table with its 34 minutes should be regarded as “unsafe”, then? Think of the following: Grammatically a comparison of the adjective “safe” is possible (safe – safer – safest), but content-wise this does not make any sense. Either safe – or not. And as we have learned before: only STUP is safe, somewhat at least. So the answer to above question is as before: Can be, but not necessarily. And, being honest: Who of us would really assemble all our equipment for just another 6 minutes under water? Alternatively, the flexible diver could have switched to a different table from the very beginning …

Bottom line: A pure comparison of dive table no-stop times is of no substantial value for the diver – and this is equally true for dive computers. Divers need to know much more about no-stop times, in particularly where they originate from and how they were tested (i.e. validated).

An example for reliably developed, validated and documented dive tables – the Recreational Dive Planner (RDP)

From a diver’s perspective there is little to complain about the development and validation of the Recreational Dive Planners (RDP) by DSAT (Diving Science and Technology): The mathematical equation which is used to calculate absorption and desaturation has been worked out in a time consuming procedure (for details please see the documentation referenced below); then extensive “dry dive” testing followed in the hyperbaric chamber under medical supervision and guidance; and if such dry dives produced bubbles that could be heard and documented by the use of Doppler ultrasound technology, exceeding a beforehand defined grade, the coefficients of the mathematical equation were adapted.

Only then came the next, ultimate step in the validation process of the model: 228 real “wet dives” in the Puget Sound close to the Canadian border in the west of the USA, next to Seattle (yes, it’s a bit fresh there under water, around 12°C/54°F in summer, i.e. the test dives are to be regarded rather strenuous than just relaxing).

The test subjects were young and old divers, male/female, with much/little dive experience, with quite a bit bioprene / athletic / slim – a representative average, so to say. The dives were conducted over several days, incl. multilevel dives and repetitive multilevel dives.

After each dive the test subjects were checked by the means of Doppler ultrasound if any bubbles could be heard, and only after no problems could be stated any more the mathematical model (i.e. the algorithm) was released by DSAT.

Result of the lengthy validation process:

“No cases of decompression sickness were encountered in any test, either in the hyperbaric chamber or in open water. … Doppler detectable bubbles were found in 4% of the profiles. In subjects who did deep knee bends during compression, bubbles were found in 12% of the profiles. The Doppler Grade in the subjects while resting was almost exclusively Grade 1. The after-exercise grades were mostly 1 and 2, with one subject having a Grade 3. Some of these grades could have been caused by objects in the bloodstream other than bubbles, but as mentioned previously, when in question, it was resolved in favor of gas bubbles and a higher grade.”

Source: Richardson, Drew, The Recreational Dive Planner: History and Development, The Undersea Journal, First Quarter 1988, p. 8

Here the “Doppler Bubble Grade” scale from 0 to 4 according to Dr. Merrill Spencer, 1974 (Source: ibid.)

The total number of test dives (both hyperbaric chamber and open water) which were conducted and evaluated was 911. The validation was done externally, that means: not by DSAT itself, but rather under the direction of Dr. Michael Powell at the Institute of Applied Physiology and Medicine (IAPM) in Seattle, USA.

Today the complete final documentation is available for free download (link see bibliography):

Diving Science and Technology (DSAT), Development of no-stop decompression procedures for recreational diving: The DSAT Recreational Dive Planner (1994)

A preliminary version which had been mailed for information and review to over 800 experts in hyperbaric medicine, PADI instructor development professionals and various institutions appeared already end of 1997 under the title:

Diving Science and Technology (DSAT), Recreational Dive Planning … The Next Generation – New Frontiers in Hyperbaric Research; Santa Ana, California (USA) 1987

The following snapshot from the 1994 DSAT documentation (p. 27) shows a diver in the hyperbaric chamber trying by means of a rowing machine to drive as many potential bubbles out of any tissue niche where the might have been hiding. Only after these efforts and additional knee bends Doppler was used.

Real, wet test dives were only conducted after successful dry dives in the hyperbaric chamber.

Without going too deep into that (thanks to the free download possibility everything can be studied in detail today) only a few more aspects in bullet point form which might be of most interest for the reader of this eBook:

•     As the development of the mathematical equation had been financially sponsored by PADI (Professional Association of Diving Instructors), they had secured the exclusive rights for PADI to develop and distribute a new dive planner for recreational divers based on the DSAT findings; so, in 1988 the Recreational Dive Planner (RDP) was launched. With the RDP divers had for the first time a dive table which does not penalize the recreational diver with too short no-decompression times and limits. Just to remember: the until then traditionally used US Navy tables had never been thought for recreational diving (and for female divers not at all). Some other dive tables reacted on the RDP by shortening their (somehow created) no-decompression limits to increase their safety margin.

•     Later, DAN and PADI subjected the RDP to further testing: 4 (four) dives daily during 6 (six) consecutive days; these dives were conducted in the controlled environment of a hyperbaric chamber, i.e. dry dives; after each dive the 20 divers were evaluated for bubbles by the use of Doppler ultrasound. Result after 475 dives: „No decompression sickness and minimal detectable bubbles.“ (Richardson, Drew, How Much Diving Is Too Much?, The Undersea Journal, Second Quarter 1990, p. 14)

•     Because DSAT had released the algorithm for free use (except for the production of dive tables), several smart diving equipment manufacturers seized the chance, ordered together the production of a chip resp. microprocessor and had it installed in their newly developed dive computers; this was truly smart because they saved a lot of development costs. As far as the author of this eBook is informed, in the USA these manufacturers were Dacor, Oceanic, Sherwood, and US Divers (even though not all dive computer models of these companies were equipped with the DSAT algorithm). In this way they had a dive computer which was calculating both saturation and desaturation with an extensively validated mathematical equation.

•     In the RDP 14 theoretical tissues or “compartments” are used: 5 – 10 – 20 – 30 – 40 – 60 – 80 – 100 – 120 – 160 – 200 – 240 – 360 and 480 minutes (the term “compartment” will be discussed later). As “controlling tissue” for the RDP finally the 60-minutes compartment was selected. A few points to the concept of a controlling tissue which are probably known by diving professionals and may therefore be skipped by them. All dive tables and dive computers which are based on a so-called “tissue-model” (see further below) use a specific controlling tissue which is defined as follows: this is the theoretical tissue, which came closest to its maximum but still safe gas-loading during a dive. The criterion for this closest margin meant for the development of the Recreational Dive Planner (RDP), as already shortly mentioned <no Doppler Grade as defined by Dr. Merrill Spencer above Grade 3> or, in other words, no Doppler audible bubbles which could have lead to DCS symptoms. Result for utilizing this concept in the development and validation of the RDP: “No cases of decompression sickness occurred in any test.” (DSAT, Recreational Dive Planning … The Next Generation – New Frontiers in Hyperbaric Research, 1987, Executive Summary, p. 4)

•     As said, the controlling tissue of the RDP is the 60-minute compartment, while for the original US Navy tables it’s the 120-minute compartment. For military divers with their given dive objectives and profiles a 120-minute compartment may be quite adequate, for recreational diving it is unnecessary conservative. The calculated (still safe) saturation level of this controlling tissue is further used for planning the maximum safe dive time for a repetitive dive which divers know to have shorter no-decompression times than the previous dive. Just so much at this point on that topic, later in this eBook a bit more. One additional hint regarding the number of compartments which are used in the algorithm of the RDP. For planning dives on sea level and to a maximum altitude of 300 meters/1.000 feet the RDP is based on above presented 14 compartments; for altitudes above 300 meters/1.000 feet as many as 20 compartments were used to calculate the RDP altitude conversion. (See Richardson, Drew, Deep, Repetitive Diving – A New Rule Applies, The Undersea Journal, Third Quarter 1989, p. 26)

•     Following the RDP “Wheel” and RDP table launch in 1988, further dive tables were introduced for using the RDP not only with air but also with Enriched Air / Nitrox: the EANx32 and EANx36 RDPs, released in 1996; and years later also “electronic” dive tables followed: the eRDP (2005) und the eRDPML (2008). The eRDPML uses the validated data of the RDP in its original “Wheel“ version, so that even multilevel dives for up to three levels can be calculated as no-stop dives. [Note: This dive planner is no dive computer and can not be taken under water.]

Reflections on a proper ascent rate

The Recreational Dive Planner (RDP) has been tested and validated for a maximum ascent rate of 18 meters/60 feet per minute; for diving at higher altitudes, which means for the RDP beyond 300 meters/1.000 feet above sea level, the ascent rate is limited to 9 meters/30 feet per minute. Other dive tables and present-day dive computers usually stipulate 10 meters/33 feet per minute or even slower; other dive computers also use varying ascent rates for different depth ranges.

Note: The US Navy dive tables also prescribed a maximum ascent rate of 60 ft/min until 1993; since then 30 ft/min is the official US Navy limit – „with no change made in any of the table entries“.

Source: NEDU - US Navy Experimental Diving Unit, Graphical Analysis: Decompression Tables and Dive-Outcome Data; Panama City, Florida (USA) 2004, p. 2; download link see bibliography

What is known about the background of the ascent rate?

During a workshop of the well-reputed American Academy of Underwater Sciences (AAUS) in 1989 this question was investigated. The surprising discovery was that the traditional 60 ft/minute limit obviously does not originate from diving, but rather from a regulation for exiting submarines under water, and this regulation was not one issued by the US Navy, but rather from the British Royal Navy. In a presentation during this AAUS workshop Dr. Edward Lanphier, a member of the US Navy Experimental Diving Unit (NEDU) since 1951, commented this surprising finding as follows: “The concern seemed to be less with the rate of ascent itself than with the chance that the diver would miss his first decompression stop if he were coming up too fast.” So, of primary concern was not the ascent rate but to ensure that the diver leaving a submarine under water would be able to stop his ascent at the prescribed depth.

If divers reading this should be asking: So, the traditional maximum ascent rate has no documented physiological foundation? – here another quotation from the same workshop: “Bill Hamilton noted that from the way Ed Lanphier described it, the 60 fpm ascent rate was for operational reasons, rather than for optimal decompression. Ed Lanphier: Yes, surely.”

Source: Lanphier, Edward, A Historical Look at Ascent; in: Lang, MA & Egstrom, GH, Biomechanics of Safe Ascents Workshop, AAUS 1989, pp. 6 and 9; download link see bibliography

Let us reflect a moment on this interesting hint.

For practical reasons a stop before the final ascent to the surface serves two main purposes:

•     To check for neutral buoyancy and adjust as necessary.

•     To give the body time to get rid of excessive gas absorbed in the tissues during the dive – i.e. off-gassing or gas-washout, as it is called.

Diving instructors among the readers who have ever asked their students in the classroom to walk the distance of 60 feet/18 meters in one minute know how slow that is; so strolling instead of walking might be the more appropriate expression. Also well known is that under water air in the BCD (and the dry suit) expands during ascent. This means that on the way up to the surface, especially during the last 33 feet/10 meters where the water pressure decreases by 100% and the air volume in the BCD would increase proportionally (if the diver would not deflate appropriately) – during these final feet it becomes more and more difficult for the diver to control his ascent rate. This is especially difficult for the unexperienced diver because he not only has to release air from his BCD and/or dry suit, but he also should watch up to the surface to make sure nothing blocks his way home and to ensure free airways, and at the same time he should keep an eye on his depth gauge and watch or his dive computer to control his ascent rate. This is far from easy for novice divers. And we were just talking about 60 feet/18 meters per minute, and not about 30 ft/9 m per minute, or even slower …

In so far nothing has to be changed in the statement, which we could read in May 1989 in the US magazine Skin Diver as the headline of an editorial by publisher Bill Gleason:

60 FEET A MINUTE IS A LONG, LONG TIME

Following a suggestion in this Skin Diver editorial the author of this eBook conducted a small experiment with staff and candidates during an instructor training course: Along the ascent line which led from an anchored platform in 16 meters/52 feet to the surface, clearly visible depth markers were attached; clearly visible, however, only for the staff – the participating divers were asked to look into the beautiful clear waters of this Austrian lake and watch endemic fish swim by. Their only assignment was to ascend continuously and as slow as possible.

We can make it short: most of the divers were pretty much convinced that their ascent rate never exceeded the recommended maximum of 18 meters/60 feet per minute – which had meant a total of 52 seconds from a depth of 16m/52 ft [here the quick and easy calculation in feet: 1 minute = 60 seconds for 60 ft; this equals one second for one foot, or 52 seconds from the depth of 52 feet].

Well, for good reasons several staff was positioned at various depths next to the depth markers on the ascent line, and their assignment was to note the time which the divers needed from 52 to 40 ft, from 40 to 30 ft, from 30 to 16 ft, and from 16 ft to the surface.

The reader will already smell the outcome: A maximum of 60 feet per minute? Not really. For the last 16 feet to the surface several voluntary participants only needed 6 seconds, which equals to possibly record breaking, hardly to believe 160 feet per minute. Not only the time taking staff was frowning, imagine the faces of the participating divers. After all, we hadn’t invited dive beginners to this self-experiment, but ambitioned, future instructors.

The following illustration sketches the set-up of this attempt.

(In case the reader should be puzzled by the very special fish which curiously sneaked into the picture – this is a species found only in a lake by the name of “Erlaufsee” in the mountains of Austria: Harryensis endemicus, and it is by no way instructor training staff in camouflage equipment; readers who wish to go diving in this beautiful Austrian lake find the web and email address of dive center owner Harry in the bibliography.)

As an effort to reconcile everybody, including himself, the following day a new attempt with a different approach was offered. The participating divers should make a short stop during their ascent at 9 meters/30 feet, if necessary adjust their buoyancy, then continue their ascent to 5 meters/16 feet, stop again and adjust their buoyancy again as necessary, and then finally ascend to the surface. (The stop time was irrelevant as the dive time was far from any no-decompression times.) And now, not really surprising, satisfied faces everywhere during the debriefing after the dive. The cozy ambience in the traditional Austrian restaurant “Seewirt”, located right at the lake, with a special cup of coffee with whipped cream contributed to the reviving good mood.

Occasional contact with participants of this practical field test indicate that a lasting impression has remained which contributed to a sustained change in diving habits.

One question is still open: What about trying to abide by an ascent rate of, let’s say, 10 meters/33 feet per minute?

The answer is a practical one: try it, dear reader of this eBook, try it – and have yourself be critically observed by your buddy. „If anyone wants to go slower, they should be encouraged. ... The problem lies not in the theory but in the practice.“ (Richardson, Drew, Slower Ascent Rates, The Undersea Journal, Third Quarter 1988, pp. 5-6)

Impatient, eager readers will perhaps have the following argument in their mind: But my dive computer does show me if I am ascending too fast, and in addition it warns me with an audible signal. Good objection. Annoyingly at least in the past some dive computers issued such “warnings” – but without any consequences if ignored by the diver.

“Virtually all of the dive computer user's manuals call for a rate of ascent that is less than 60 fpm, and during our tests, which were all conducted using a rate of ascent of 60 fpm, they beeped and blinked and did everything short of electrically shocking us. Some advise the user to use a variable rate and some of the rates are as low as 20 fpm. Anyone who has tried to achieve such a rate, let alone tried to teach it to a new diver, would be happy to hear that the dive computers performance is not linked to these impractical values. Unfortunately, while we believe that this is true, there is no practical way of testing it.”

Source: Lewis, John & Shreeves, Karl, The Recreational Diver’s Guide to Decompression Theory, Dive Tables and Dive Computers; Santa Ana, California (USA), 2nd Edition 1993, p. 76

And the advice for the baffled reader was in 1994 the same as is in 2014:

“We can do nothing more than advise the reader to contact the manufacturer directly and ask for himself what, if any, requirements are a necessary element of the dive computer's design. Until advised otherwise by the computer manufacturer, you are best advised to follow the ascent procedure prescribed by the dive computer manual.” (ibid.)

In our later parts Deep Stops – what is that? and Which stop-depth is the correct one? we will come back to this topic once again.

Excursus – How do divers control their ascent rate?

As stated above, the challenges during the ascent are quite complex: looking up to the surface to make sure no Manta Ray, boat or the like is blocking your way; ensuring at the same time that your airways are free so releasing excessive air from your lungs is not hindered; controlling your depth & timing device to avoid coming up too fast, and deflating your BCD and/or dry suit – all at the same time.

Good idea trying this in practice, which we also did (again with instructor candidates). And the voluntary participants in action were of course captured on fotos. Before showing them this undisputable sort of proof some of the participants refused to believe or just denied how they had performed their ascents. A few examples only: Not looking up but rather down to the instrument console with depth-gauge or dive computer; or: in fact looking up and reaching up, with the left hand holding up the BCD hose, ready for deflation – but what about looking at the instrument console or the dive computer at the left wrist?

The following pictures have been reconstructed with staff members to protect the privacy of the participating instructor candidates; the pictures speak for themselves:

As can be seen on the pictures there are always practical solutions for both console and wrist models. The diver just has to remember to look up, having everything in his view, including his dive computer, and his airways open. A simple piece of string with a loop attached to the console, and it can easily be hung over your thumb.

After this short excursion to diving techniques let us now move on to the inner workings of the dive computer.

3 – Saturation, halftime and M-value

For this eBook it is assumed that the reader has some basic knowledge about the saturation which always takes place in the human body whenever a diver uses a compressed breathing gas; a proportion of that gas is always being absorbed by our tissues while diving. So the reader of this eBook is expected to know that the human body consists of different “materials” – i.e. tissues – which absorb at different rates the suspected villain for DCS, nitrogen, and other gases in our breathing gas mixture. Usual listings of tissues include blood, which saturates especially fast, brain, spinal cord, skin, muscles, the inner ear, joints, and finally bones, which saturate slowest of the mentioned tissues; the same applies vice versa during the desaturation process. That a hard bone absorbs a gas slower and needs more time to release it again, is obvious and easy to imagine. Also, the reader will know that the mathematical equations (algorithms) of dive tables and dive computers don’t work with real tissues of the human body but rather with theoretical tissues, and for clearer distinction these are usually called compartments.

As already noted, the Recreational Dive Planner (RDP) from DSAT and the dive computers which use the original DSAT algorithm is based on 14 compartments, with halftimes of 5 – 10 – 20 – 30 – 40 – 60 – 80 – 100 – 120 – 160 – 200 – 240 – 360 and 480 minutes.

The Buhlmann algorithms ZH-L12 and ZH-L16 are both based on 16 compartments, but Buhlmann has assigned with few exceptions different halftimes to these compartments:

The halftimes of the Buhlmann ZH-L12 model are 2.65 – 7.94 – 12.2 – 18.5 – 26.5 – 37 – 53 – 79 – 114 – 146 – 185 – 238 – 304 – 397 – 503 and 635 minutes.

The halftimes of the Buhlmann ZH-L16 model are 4 – 5 – 12.5 – 18.5 – 27 – 38.3 – 54.3 – 77 – 109 – 146 – 187 – 239 – 305 – 390 – 498 and 635 minutes.

In a later section we will look at that more in detail.

It is not possible in this eBook to explore in-depth the question how the designers of various models arrived at these halftimes (this can be studied in numerous internet articles and other publications), but we need to examine carefully the terms “halftime” and “M-value” as these are central terms for understanding dive computers.

Halftime

Related to diving the complete term of halftime is “saturation halftime“. The term halftime alone is usually used to describe the period of time for the decay of radioactive elements and their radiation to its half. In diving the concept of saturation halftimes describes the time in minutes which is needed by a compartment to saturate or desaturate to its half. When nuclear power is the issue, usually the halftimes of Plutonium and Uranium are addressed; examples: the Plutonium Isotope 244 enjoys a halftime of roughly 80 million years, the radioactive Uranium Isotope 238 in comparison can “only” come up with a bit over 4 million years.

Given those hardly conceivable periods of time it is not really surprising that the temporary disposal and the safe permanent disposal of burned out fuel rods of nuclear power plants are unsolved problems of human mankind. In Germany, for instance, in 2014 there has again been initiated the search for such a disposal site – which should be safe for at least one million years …

In diving, saturation and desaturation of tissues and compartments do of course not last that long. Mathematically not absolutely correct but sufficient for practical diving purposes it is assumed, that a full saturation and desaturation is reached after 6 halftimes. In other words saturation halftime is understood as the time in minutes, which is needed by a specific “tissue” so that the initial pressure inside this tissue reaches half of the gas pressure outside the tissue in the new depth; and after 6 of these half-times the tissue is regarded as having reached its surrounding pressure (resp. is back to its initial pressure). Mathematically speaking it is the time in which an exponentially increasing or decreasing value is halved.

During the desaturation or off-gassing process the amount which has remained after one halftime is halved again during the second halftime, so only 1/4 remains, after three halftimes it will be 1/8, then 1/16, 1/32, 1/64 and so forth, or in percent:

50% [100% minus 1/2 of 100]

25% [50 minus 1/2 of 50]

12.5% [25 minus 1/2 of 25]

6.25% [12.5 minus 1/2 von 12.5]

3.13% (rounded) [6.25 minus 1/2 of 6.25 = 3.125]

1.56% (rounded) [3.125 minus 1/2 of 3.125 = 1.5625] – etc.

During the saturation process (gas absorption) accordingly:

50% [“0” plus 50%]

75% [50 plus 1/2 of 50]

87.5% [75 plus 1/2 of 25]

93.8% (rounded) [87.5 plus 1/2 of 12.5 = 93.75]

96.9% (rounded) [93.75 plus 1/2 of 6.25 = 96.875]

98.4% (rounded) [96.875 plus 1/2 of 3.125 = 98.4375] – etc.

Nobody needs to be a mathematical crack to understand that 100% saturation will never be reached this way, because the last value always only changes by half of the difference to the value before – half of the half of the half etc. This has lead to the simplified but for practical diving purposes sufficient assumption that after 6 halftimes a “tissue” can be regarded as completely saturated resp. desaturated. Diving professionals among the readers will know this relationship as an exponential curve, mathematically speaking:

Less well known than this saturation curve will be that the first dive computer, that really deserved this designation according to widespread opinion, also had a curve on its LCD display. This was the EDGE from the US company Orca (1983), and the curve represented the M-values of the EGDE (more on M-values in the next section). This actual seeing how each of the compartments “filled with nitrogen” had a direct effect on the diver. When you saw on the display that one of the 12 compartments with halftimes of 5 – 11 – 17 – 24 – 37 – 61 – 87 – 125 – 197 – 271 – 392 and 480 minutes “got filled” and approached the M-values curve, you just ascended a bit and could see on the display how that compartment “emptied” again gradually, and how another compartment started its way to the curve.

For illustration purposes here some snapshots from the EDGE manual, which speak for themselves. EDGE, by the way, was the modest abbreviation for “Electronic Dive Guide Experience”, but it was at those times a first-class dive computer which had been validated by the use of Doppler ultrasound. At the left side of the pictures the depth is shown in feet, but a metric version was also available.

In the right picture you can see two things:

1) On the left you see the fastest compartment touching the M-values curve.

2) This causes an arrow to appear at the bottom of the display pointing upwards.

After the diver has ascended sufficiently the display will look again similar to the left picture – all compartments in good distance to their M-values.

For comparison with present-day dive computers the dimensions of the EDGE were as follows:

Width = 73mm/2.9”  Length = 182mm/7.2”  Height = 33mm/1.3”

Display Width = 47.65mm/1.875”

Display Length = 57.15mm/2.250”

Weight 680 g/1.5 lbs (aluminum)

Too large and too heavy?

Well, here the dimensions of a smartphone-integrated dive computer housing from 2014:

M-value

The „M“ denotes “maximum”; the M-value is a term from hyperbaric research for the maximum (internal) pressure which a “tissue” can tolerate so that the diver is not required to make staged decompression stops at the end of his dive, when he is ascending to the surface.

In other words: if the M-values of a specific algorithm for various compartments are not exceeded the diver makes a no-decompression dive, also called a no-stop dive.

The above shown right snapshot of the EDGE display makes us understand easily what is meant: At the left of the display the first compartment represents the 5-minutes compartment of the EDGE model. As we can see, it is just touching the curve which means, it has just reached its M-value, causing the up-arrow to appear at the bottom of on the display. This arrow signals the diver in addition to the curve-touching tissue that he needs to ascend in order to avoid a decompression-stop, according to the algorithm of the EDGE.

Let us take one more snapshot from the EDGE manual. Here we can see, that the fast 5-minutes compartment (left) has desaturated already a bit, but other compartments instead are now quite close to the curve, i.e. close to reaching their M-values:

The M-value concept we owe to Robert Workman (USA, 1965); the letter “M” was used by Workman for “Maximum Allowable Tissue Tensions” which then was shortened to “M-values”. An informative explanation of M-values offers an article by Erik Baker: Understanding M-values, Immersed, Vol. 3 (1998), No. 3, pp. 23-27. This Baker article also includes several listings of M-values, the original Workman M-values see Workman, 1965, in the bibliography (incl. a link for downloading).

The following overview shows the compartments with their saturation halftimes and M-values from Workman, EDGE and RDP in comparison. As can be seen, there is only one single consistency among the three models, and this is regarding the compartments (all of them begin with the 5-minutes-compartment); between the M-values there is no consistency at all, but rather differences of roughly 10 minutes maximum.

When we discuss the Buhlmann models ZH-L12 und ZH-L16 further below, such a comparison will be presented again (see Section 4.3).

During the development of the DSAT RDP by Raymond Rogers, starting approx. in the mid 1980s, one of the tasks for repetitive dives was to determine the slowest compartment, which would just be touching its M-value on no-stop dives. As already noted the choice finally fell on the 60-minutes compartment as the “controlling tissue” for the surface interval following a dive. Applying the theory of halftimes it takes 6 hours (6 halftimes x 60 minutes = 6 x 1 hour) until this compartment will have reached its M-value, and accordingly also 6 hours until it will be fully desaturated again (more correctly said: until its saturation is back to its initial level). Dives which follow within 6 hours of a previous dive are then regarded as repetitive dives, allowing shorter no-decompression times than the first dive when all compartments were “clean”.

What are the M-values of dive tables? These are the pressure groups (PG), with “pressure” pointing to the reached level of the pressure inside the compartment. The RDP uses the full alphabet from A thru Z:

•     Pressure Group “A” = low nitrogen level resp. low pressure inside the compartment

•     Pressure Group “Z” = high nitrogen level resp. high pressure inside the compartment

The most important cornerstones of the relation between compartment, halftime and M-value are in short:

•     The faster the compartment, the shorter its halftime.

•     The slower the compartment, the lower its M-value.

Above we already compared the M-values of Workman, EDGE and RDP in a table – here this comparison again, now in form of a diagram.

Note: The M-values are Excel interpolated so that curves can be presented; this does not match the empirical data completely. The purpose of the diagram is only to provide a visual impression of how and where the M-values differ.

The illustration has been turned vertically for full-page display in this eBook:

Note for eBook readers with a device which cannot display colors:

upper line = EDGE, middle line = RDP, lower line = Workman