Historical Perspectives on Dive Tables and Decompression Models

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“The reliability of a decompression table or procedure is not determined by any mathematical process, but by what works in practice. What works…is what works!” –  John Crea III

“Any passive decompression device can only inform the diver of his or her decompression status. How that information is used is the responsibility of the diver.” —   Karl Huggins


The first research work in  decompression physiology was not directed at scuba divers. It was noticed that people working at elevated pressures in either caissons (a caisson is a water-tight box inside which men can do construction work underwater), or construction tunnels beneath rivers would succumb to symptoms of pain and paralysis.  These symptoms were first witnessed in 1841 and by the 1880′s were popularly called “the bends” because of the positions the workers took to alleviate the pain.  Soon this high pressure disease was referred to as caisson disease.  Later, in cases from hardhat divers, decompression sickness was termed “diver’s palsy”.

The DCS research conducted in the 1800′s eventually gave rise to a series of principles as well as a set of decompression tables that were published in 1908 by Boycott, Damant and Haldane.  The principles eventually came to be known as Haldane’s Principles of Decompression and, in combination with the decompression tables, formed the basis for current decompression theory including the development of the original U.S Navy Decompression Tables.

For all practical purposes, there are four principles involved:

1)The progress of saturation follows in general the line of a logarithmic curve . . . The curve of desaturation after decompression is the same as that of saturation, provided no bubbles have formed .”

2)The time in which an animal or man exposed to compressed air becomes saturated with nitrogen varies in different parts of the body from a few minutes to several hours.”

3) In decompressing men or animals from high pressure the first part should consist in rapidly halving the absolute pressure: subsequently, the rate of decompression must become slower and slower so that the nitrogen pressure in no part of the body ever becomes more than twice that of air.”

4) Decompression is not safe if the pressure of nitrogen inside the body becomes much more than twice that of the atmospheric pressure.”

The reader should note that although these four principles provided the earliest basis for decompression Table theory, the latter two principles have been proven flawed and have since been extensively modified.


Most divers of yesteryear tended to accept the U.S. NAVY diving tables as gospel and rarely questioned the validation of the model. Some interesting facts need to be considered, however, when we apply those Tables in sport diving applications. Such as: the NAVY tables were designed originally for single dives only. Further, the divers using them were to be closely supervised by a NAVY divemaster who dictated their dive profiles and controlled their decompression, if any, by in-water stages. Most diving operations were supported by on-site recompression chambers and access to a diving medical officer. Even then, an incidence rate of decompression sickness around 3 to 5% was considered acceptable (facilities being available for treatment).

Now consider that the NAVY made a grand total of approximately 120 (!!!) test dives with human subjects before accepting the repetitive dive tables for use. These tables still enjoy the widest use by sport divers who use Tables instead of diving computers, in spite of their apparent drawbacks when considered in the perspective of the average diver’s age and physical condition.

None the less, these tables have proved to be valid and with some sixty years of field use and millions of dives on them by sport divers, their worth must be accepted. Beginning in the early 1990s though, a plethora of new tables have undergone research and testing with an eye to producing tables more appropriate for actual sport diving needs.

All divers need to be aware of their dive exposure (time, depth, ascent rate) and track it  to determine decompression status via tables or computers.

All divers need to be aware of their dive exposure (time, depth, ascent rate) and track it to determine decompression status via tables or computers.

In 1908, Haldane conducted extensive studies of decompression on goats while formulating his original “decompression model”. Based on his work with goats in various hyperbaric chambers he derived what he concluded to be logical extrapolations to human physiological responses to pressure and subsequent decompression schedules. Some of his assumptions, of course, were later proved to be not entirely correct. But given the tools of research for his era and the primitive monitoring equipment at his disposal, his pioneering experiments and recommendations would provide the “seed” from which the “oak tree” of decompression science and diving tables would grow.

Originally, he felt that his animal studies had confirmed his hypothesis that if no symptoms of DCS where present post-decompression, then no bubbles were formed in the blood systems. Obviously, with the benefit of today’s technology and Doppler monitors, we know that bubbles do occur in a statistically large percentage of dives made that were previously thought to be “safe” from such development. In assessing the saturation exposure for goats, he applied a time factor of three hours to assume full inert gas loading and later postulated that humans would reach saturation in five hours.

In designating his half-times for his five “tissue” groups (now generally referred to as “compartments”), he selected his slowest group to be the 75 minute tissue. This was selected since it would be 95% saturated after five hours in keeping with his hypothesis on maximum time for humans to reach theoretical saturation loading. Certainly he was on the right track, but most table model experts now allow as much as 24 hours for such saturation to fully take place and current custom table models employ slow “compartments” rated up to 1200 minutes!

Haldane produced three table schedules for air diving:

Schedule One: for all dives requiring  less than 30 minutes of decompression time.

Schedule Two: for all dives requiring more than 30 minutes of decompression time.

Schedule Three: for deep air diving to 330 fsw using oxygen decompression.

These schedules were typified by a relatively rapid ascent from depth to the initial decompression stop depths, then followed by markedly slower ascents to the surface. The British Royal Navy adopted these in 1908 and continued to use them with revisions well into the late 1950′s. It should be noted that it was discovered that Schedule One proved to be too conservative for practical use and Schedule Two proved to be too “liberal”  with the percentage of DCS hits unacceptable. In 1915, the first tables for the U.S. Navy were produced called the C and R tables (Bureau of Construction and Repair); these were used with success in the salvage operation on the submarine F-4 at a depth of 306 fsw.

    Strong currents (exertion) and depth (faster inert gas loading) can increase susceptibilty to decompression sickness and should be  factored into any dive exposure model.

Strong currents (exertion) and depth (faster inert gas loading) can increase susceptibilty to decompression sickness and should be factored into any dive exposure model.

In 1912, Sir Leonard Hill offered his “Critical Pressure Hypothesis” wherein he questioned Haldane’s theory of staged decompression. Hill advocated the use of continuous uniform decompression and offered both experimental and theoretical evidence to support his position. Although the validity of his decompression schedules were not substantively disputed, the widespread use of staged decom stops remained in practice.

Other development included the works of Hawkins,Shilling and Hansen in the early 1930′s in which they determined that the allowable supersaturation ratio was a function of the tissue half-time and depth and duration of the dive. Yarborough expanded on their work by recomputing a set of tables for the U.S. Navy based only on the 20, 40 and 75 minute half-time groups. These were adopted by the Navy in 1937 and used until the modified U.S. Navy Standard Air Decompression Tables came into use in 1957. These tables remain in widespread use today although continued research is being conducted by the Naval Experimental Diving Unit (NEDU) including recent work with the Navy E-L Algorithm which assumes that nitrogen is absorbed  by tissues at an Exponential rate (as in other Haldanian models) but is discharged or “out-gassed” at a slower Linear rate. This predicts slower elimination during surface intervals and resultant higher residual nitrogen levels on repetitive dives.

The British Navy branched off slightly in 1958 to follow the theories of U.K. physiologist Hempleman. “He had observed that over a particular depth range, the first symptom  of DCS to appear was usually pain at or near a joint…and assumed that the tissue  involved (e.g. tendon) was, therefore, the tissue with the greatest over-pressure of nitrogen for that depth range, and that gas elimination from that tissue must control the decompression. He pictured the body as a single tissue and believed that the quantity of gas absorbed in the body could be calculated by a simple formula which related depth and time. Unlike Haldane, who believed that gas uptake and elimination took identical times, Hempleman assumed that gas elimination was one and a half times slower than uptake. Utilizing the theory that the tissues could tolerate an over-pressure of 30 fsw, (he) constructed a new set of decompression schedules…that are the current Royal Navy schedules.” (Deeper Into Diving, Lippman 1990)

Workman, in 1965, introduced the concept of “delta P” for gas partial pressures which was easier to handle than ratios and fitted the data better. He introduced the concept of “M values”: that each “tissue” or theoretical compartment would have a maximum nitrogen tension that can be safely tolerated at the surface without bubble formation. M is short for maximum and the M-value is the maximum allowable tissue tension at a specific depth.

Attempting to improve the safety of his original tables, Hempleman revised them in 1968 to include using a variable ratio of tissue nitrogen tension to ambient pressure to predict safe decompression. However, the Navy was not happy with the newly restrictive results and refused to implement them. Following more trials and revisions with Hempleman more closely attentive to the Navy’s suggestions for practical work needs, the tables were modified, reproduced metrically, and adopted in 1972.

Long bottom times at intermediate depths (60-90 ft.) have proven to produce  the most bends hits in sport divers.

Long bottom times at intermediate depths (60-90 ft.) have proven to produce the most bends hits in sport divers.

Schreiner changed the accounting from “per gas” to “per compartment” in 1971, thus making it possible to handle different gases and gas mixtures. Table computation then is largely “bookkeeping”: keeping track of the gases in the compartments and comparing them with the “matrix” of M-values. Diving practitioners speak of “half-times” and “M-values” as if they were real entities, but it must not be forgotten that this is only a mathematical model. In fact, it is not really a “model” as that term is normally used, but rather a computational method.

In summation, we note that Haldane’s calculations are inadequate:

  1. Long, deep dives require more decompression than originally provided.
  2. Fixing these tables messes up the short, shallow ones which are working fine.
  3. Various tricks can be used to make the tables match the data using Haldanian calculations.
  4. Other ways to calculate tables have been proposed and any model will work if there are enough variables to adjust and a data base in making the adjustments.

Even today, divers are faced with a diversity of tables and decompression models incorporated into diving computers. Some are simple re-configurations of the basic U.S. Navy tables and others are distinctly different in their approach to decompression management.

New developments in bubble detection equipment prompted Dr. Merrill Spencer to suggest re-evaluation of recommended no-decompression limits with the goal of minimizing bubble development after a dive. His 1976 revisions where extensively tested by Dr. Andrew Pilmanis and Dr. Bruce Bassett and found to significantly decrease detectable bubble formation. In 1981, Karl Huggins, an assistant in Research at the University of Michigan generated a new set of decompression tables based on Spencer’s recommendations. These became known variously as the “Huggins tables”, “Huggins/Spencer tables”, “Michigan Sea Grant tables” etc. and were to be the basic algorithm used in the diving industry’s first practical electronic dive computer produced by ORCA Industries and known as THE EDGE.

Significantly, the Defence and Civil Institute of Environmental Medicine (DCIEM) in Canada has continued on-going revision to their tables based on ultra-sonic Doppler studies. These tables have gained wide popularity due their unique criteria for development geared to minimal bubble formation. John Crea, a professional consultant in custom table generation and a practicing anesthesiologist, specifically recommends the DCIEM tables for deep divers if a “stock” table reference is acceptable.

Capt. Bret Gilliam, a credentialed hyperbaric medical supervisor, operating recompression  chamber during trials for algorithm development for dive tables and computers. (1989)

Capt. Bret Gilliam, a credentialed hyperbaric medical supervisor, operating recompression chamber during trials for algorithm development for dive tables and computers. (1989)

Other models include the conservative Buhlmann Swiss tables based on the work of Dr. Albert Buhlmann of the Laboratory of Hyperbaric  Physiology of the University of Zurich. His algorithms were extensively integrated into popular diving computers of the era such as DACOR’s MicroBrain ProPlus and UWATEC Aladdin Pro as well as use in the form of custom tables.

A group of researchers at the University of Hawaii have come to be known as the “Tiny Bubble Group” after their theory of physical properties of bubble nucleation in aqueous media. Their Varying-Permeability Model indicates that cavitation nuclei, that are thought to “seed” bubble formation are “spherical gas phases that are small enough to remain in solution yet strong enough to resist collapse, their stability being provided by elastic skins or membranes consisting of surface-active molecules” (Hoffman 1985). In comparison of Table models, Huggins observes (1987), “the ascent criteria for this model is based on the volume of bubbles that are formed upon decompression. Growth in size and number of gas bubbles is computer based on the physical properties of the ‘skins’ and the surrounding environment. If the total volume of gas in the bubbles is less than a ‘critical volume’, then the diver is within the safe limits of the model”. Although tables have been produced based on this model, not enough actual human testing has been conducted to be considered statistically relevant. On square profile comparisons with the U.S. Navy tables, the “Tiny Bubble” model is more conservative down to the 140 fsw level.

Further projects in table models include the Maximum Likelihood Statistical Method developed by the Naval Medical Research Institute (NMRI). In consideration of a diver’s exposure to depth/time “doses”, they have produced a statistical model that reflects probabilities of DCS occurrence and are expressed as 1% and 5% tables. The diving supervisor would have the option of selecting his risk factor based upon the priority of work to be accomplished.

What tables, then should divers use? It’s really too broad a question to pin down to a single answer as to “this table is the best”. Many experienced diving professionals prefer to work with custom or proprietary tables specifically designed for their application. Crea (1991) makes this observation: ”Computations can compare different tables or practices, but cannot determine what is best. As stated before, what works…is what works. Good tables are at the current state of knowledge empirical. The algorithms are good, however, to use yesterday’s experience to predict tomorrow’s dive.”

In the process of table development and validation, several basic and separate steps are employed with feedback on field use:

  1. Concept or “algorithm” for a table, usually based on some experience.
    Laboratory trials, with feedback and revision as needed.
    Move to provisional operational use at some point.
    Provisional use “at sea”.
    Acceptance as “operational”.
    Results fed back, revisions as necessary.
  2. Judgement needed as to when to take the next step; this should be a responsible body of the developing organization;
    This body decides how many trial dives under what conditions etc.
  3. This process, laid out in a workshop by the Undersea and Hyperbaric Society, is more or less what is currently practiced, but there is no set protocol for making the formal judgements.

For a more detailed history of tables and model evolutions I recommend reading “Development of Dive Tables” by Karl Huggins as contained in “Microprocessor Applications to Multi-level Air Decompression Problems” (Michigan Sea Grant publication 1987) and “Deeper Into Diving” by John Lippman (Aqua Quest Publications 1990)

Much debate still centers on what is the “best” table to use, and there clearly is no pat answer to that question. My opinion is that the best possible scenario for safe  diving would include the use of a custom table matched to the individual and the dive application but obviously many divers will not utilize this level of technical support. But the reader is urged to make an informed choice in table selection. Don’t just grab the first thing that’s handy and expect it to suit a myriad of dive situations. And in all cases, do not push a model to the edge of its limits.

In all cases, caution and prudence are recommended but the overly conservative “prohibitions” still offered by some academicians may not necessarily be proven in the field.

As has been noted several times in this chapter, “what works is what works”. Tables and determination of “safe” dive profiles are very much an experimental science. Of course, tables, per se, have become something of a lesson in old technology as most divers have transitioned to using the modern diving computer. I was involved directly in the development of the UWATEC models and several other manufacturers. It’s hard for me to believe that any diver is not better off using a computer… if only due to their automatic functions for keeping track of depth, bottom times, ascent rates, and surface intervals. Far too many bends incidents used to occur simply due to poor record keeping. Computers eliminate that human error. But it’s important to appreciate the evolution of decompression models and the era when tables dominated how we conducted dives. I’m a firm advocate of studying history in order to be best informed about future technology and innovations.

The work done by the pioneers of tables and decompression models laid the groundwork for all that followed. We owe a huge debit to those researchers and, especially, to those who served as test subjects during actual human trials. Ask yourself if you’d be willing to subject yourself to such risks… And if you ever bump into Glenn Butler at a dive show (an early brave volunteer for table research with the late Dr. Bill Hamilton), be sure to buy him a drink and maybe a dog biscuit. He’ll be the stooped-over drooling dweeb at the end of the bar blissfully filling his diaper without a care and without notice. As they in the south, “Bless his heart…”

Just kidding, Glenn. Glenn, over here… this way, Glen! Hey, it’s me Bret. No please don’t sit down here… whoops, don’t worry… they’ll clean that up. So… how’ve you been? Any interesting projects you’ve been involved with lately? New dive computer trials? Sounds like fun…

Bret Gilliam
54 Stonetree Rd.
Arrowsic, ME 04530

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13 comments for “Historical Perspectives on Dive Tables and Decompression Models

  1. Nigel
    June 5, 2012 at 7:24 am

    As always a well researched and readable piece from someone who was on the sidelines if he wasn’t being a guinea-pig. I love dive-computers and the freedom to to extended dives that traditional square profile tables didn’t. Sure some computers are more/less conservative than others, so one size obviously doesn’t fit all (think of young, disciplined, superfit Navy divers, with fast access to a chamber versus middleaged, unfit recreational guys who may be relaxed about protIocols). I used a 1991 Uwatec till last year, now have a Suunto Viper. In over 800 dives in cold water, mostly in 30-60m range, I got bent once (a shoulder. It hurt, but rest of me was fine, I could walk, had no tingling/numbness anywhere else. I knew why too, we were decompressing in a 3m swell and very strong side currents. The combination made depth control at shallow depths challenging. But a couple of aspirin, 24 hour break, and I was good to go again. Today – 37 years later – I’ve downrated the safety factor on the Viper from 100% to 50% but I do 3 mins at 10-9m, 3 mins 6-5m and 3 mins at 3m. All ascents are hand over hand slow. And so far, so good. My empirical belief that slow lingering ascents in the 0-10m range are very protective – but I’ve no formal data to back this up…Thanks once again for a great article. All the best, Nigel

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  2. Peter Norris
    June 14, 2012 at 2:51 am

    Thank you very much for a nice brief history. I started on tables in the eighties, various computers and programs through the 90s and now mindlessly run my ccr wwith my computer. :-) A couple of chamber rides have convinced me to be very carefull. My hat is off to those who paved the way.


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  3. August 31, 2012 at 5:18 am

    “The work done by the pioneers of tables and decompression models laid the groundwork for all that followed. We owe a huge debit to those researchers and, especially, to those who served as test subjects during actual human trials.” – Indeed. Thank you for sharing this with us Bret, it’s really informative and a real eye-opener.

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  4. September 12, 2012 at 9:08 am

    1) “The progress of saturation in general follows the line of a logarithmic curve.”

    Desaturation and saturation in these models is the exponential function, the other opposed to the logarithmic function.

    It do not make school mistakes or consult work.

    “Significantly, the Defence and Civil Institute of Environmental Medicine (DCIEM) in Canada has continued the on-going revision is based on tables Their ultra-sonic Doppler studies.”

    You may want to tell that occupied a parallel series models, in which some tissues are saturated by contact with others, which alters the function of saturation and off-gassing.

    rc greet (pozdrawiam rc

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  5. bret gilliam
    September 12, 2012 at 10:29 am

    To “Demolant”,

    I assume that English is not your first language… my information in the article is accurate. I’m not exactly certain what you are trying to say but you are not even excerpting the quotes accurately. Perhaps you could have someone more fluent in English give you a hand. What you seem to be commenting on is a combination of original theory and later refined practical usage in decompression models. You may need someone with a strong background in diving physiology to read the article to you and explain each section context. Good luck!

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  6. September 13, 2012 at 7:04 am

    Bret Gilliam

    “The progress of saturation in general follows the line of a logarithmic curve.”
    ” my information in the article is accurate. ”

    Desaturation and saturation is not a logarithmic function, is an exponential function, in this class modelers.

    Pti(t) = Po + (Pa + Po)(1-exp(-0.693(t/T))
    exp is the exponential function.

    Check it out in decent publications and correct his mistake.

    Model Hempelmana a formula Prt.

    Pressure times the square root of time is constant.
    It should say specifically.

    You may want to say about the contribution to the theory of decompression such authors as Zuntz (1897), Schrötter (1096), Widmark (1919), Haggard (1924), Kety (1949), Copperman (1950), Jones (1951), Riggs (1963).

    rc greet

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  7. Bret Gilliam
    September 13, 2012 at 1:08 pm

    To “demolant”:

    Your reference from that quote is to the turn-of-the-20th century theory of Haldane’s four basic tenets of decompression modeling. The article notes this and, with specificity to item one, also contains the disclaimer “in general”. The paragraph ends by noting that these were the broad guidelines of Haldane’s Theory and have since been extensively modified. We are talking about a historical reference to a physiological theoretician’s work from over a hundred years ago.

    Of course, the principles have evolved… that’s the point of the entire article. Up until the the last 15 years or so, the capability of computer calculative devices also limited algorithmic expansion but most professionals widely considered the work of Albert Buhlmann to be the most enlightened. I knew Buhlmann personally and worked with him on proprietary deco models for UWATEC diving computers. But when he got off on an “in-depth” discussion, almost everyone (including the M.D.s and Ph.D.s) got lost. The man was brilliant… but always tried to keep the narrative on a base line that all could follow without total intellectual confusion due to the mix of expertise from doctors, chamber operators, professional divers, software modelers, technicians building circuit boards, and guys like me that had a little bit of grasp from each segment and had to run a $50 million company effectively. Communication was, and will always be, the key to a successful outcome.

    Things change… science evolves… beta-testing expands… field evaluation widely becomes more rigorous…

    That’s the entire point of the article. Also, I have tried to put a complicated subject into language that a layperson can reasonably understand. You are needlessly muddling the issue. The best conclusion for all involved is still: buy a modern diving computer!

    I guess you are well-intended… but I doubt if you have moved the bar any higher for readers about the subject.

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  8. September 13, 2012 at 9:13 pm

    To Bret Gilliam
    1) “The progress of saturation in general follows the line of a logarithmic curve.”
    We are talking about off-gassing and saturation function that is not was logarithmic, in that and Buhlmann model.

    Describes the exponential function off-gassing and saturation in this class modelers.

    Correct the error and did not embarrass himself

    rc greet

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  9. Bret Gilliam
    September 13, 2012 at 9:30 pm

    To: “demolant”

    Look and listen carefully: This is my last chance to try to explain the obvious to you: the quote about Haldane’s Theory was Haldane’s… in 1908… not mine… not Buhlmann… not Elmer Fudd… not Mickey Mouse… not John Wayne… not Bevis and Butthead. It is over one hundred years old. That’s older than Keith Richards looks.

    It was Haldane’s theory at the time and precisely as he expressed it. That is what we intellectually refer to as a “historical narrative excerpt”. Try to grasp that… The world of decompression modeling has moved on. I suggest you do the same.

    I will not be replying to you again.

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  10. September 14, 2012 at 7:15 am

    To “Bret Gilliam”

    You do not know what it is logarithmic function, which is the exponential function.
    Derivation of this equation takes a few minutes a student one year, maybe 15 minutes from the high school student efficient.

    The exponential function in the description of the process of change inert gas pressure in the tissues is consistent with the law of Henry.
    The log is contrary to the law.

    You prescribe the content of a shallow understanding.

    rc greet

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  11. mike
    October 24, 2012 at 12:33 am

    i am a 65 year old male

    the original navy dive tables were designed for young health males.
    i only fit one of those criteria now.

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  12. ozarkdiver
    October 24, 2012 at 4:02 pm

    Oh man, I was really enjoying the tit-for-tat between Bret and Demolant, until Bret’s “older than Keith Richards looks” comment. Now I’m wiping the tears from my eyes.

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  13. gary
    January 1, 2016 at 6:27 pm

    Question for Brett:
    As I have examined the various tables at my disposal (PADI, NAUI, NOAA/Navy1999, and NOAA/Navy2008), the biggest difference from a recreational diver point of view is the very much shorter surface interval in the PADI table. This is a concern for repetitive dives because that is the table that is used in the dive travel industry. If you go on vacation with a dive charter, the dive masters will likely be planning the dives with those short surface intervals. It works for them from an economics point of view, but my question is more about the safety. I have heard of travel divers getting bent on vacation.

    Do you have any comment on why PADI has 3x shorter surface intervals than the others? Are the others just that much more conservative? I have used the NAUI table for decades with success, so I am a little concerned about such short surface intervals if forced to go by the PADI table.


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