Bühlmann, VPM, RGBM and the Rest: How Decompression Algorithms Work, and What the Evidence Says

Plan a 70 m trimix dive twice in the same program, once with Bühlmann at gradient factors 50/80 and once with VPM-B at +2, and the two plans surface two minutes apart. Look closer and they are different dives. The Bühlmann plan makes its first stop at 33 m. The VPM-B plan stops first at 45 m, spends more than twice as long below 21 m, and makes up for it with less time at 6 and 3 m.

From the mid-1990s technical divers argued for about fifteen years over which shape of ascent is better, until one navy experiment changed the argument. The story behind it runs through a century of goats, gelatin, pearl divers and navy statistics. This article follows that story: where each algorithm came from, how it works, what it has actually been tested on, and why Bühlmann with gradient factors has become the usual choice. It is written for a diver who has done a deco course and wondered what the computer is doing, and the equations sit in fold-out boxes for anyone who wants them. Every claim links to its source. None of it is dive training.

What a decompression algorithm has to decide

Breathing gas under pressure loads your body with inert gas, mostly nitrogen, and helium too if you breathe trimix. On the way up that gas has to leave. If it leaves through your lungs, nothing happens. If the pressure drops faster than the gas can get out, some of it comes out of solution as bubbles in your blood and tissues, and enough bubbles in the wrong place cause decompression sickness (DCS): joint pain, numbness, paralysis, or worse. The French physiologist Paul Bert showed in 1878 that these bubbles were the cause; the earlier article What Is Decompression? covers the physiology in more detail.

A decompression algorithm is a recipe for an ascent that avoids that outcome most of the time. It has to answer two questions. First, how much gas is in you right now? Nobody can measure that during a dive, so every algorithm estimates it from your depth, time and gas. Second, how much can you get away with? Physics cannot answer that one. It has to be learned from divers who got bent and divers who did not.

Every model answers those questions with a simplification. Ray Rogers, who designed the PADI Recreational Dive Planner, wrote in 1994 that the compartments and half-times in these models "have no demonstrated real basis in physiology", though he added that the concepts are "probably correct".^{[4 ]} A model is a tool fitted to data, and it can only be as good as the dives it was fitted to.

A short history

The story starts with goats. In 1908 the Scottish physiologist John Scott Haldane, working with Arthur Boycott and the naval officer Guybon Damant, ran 85 goats through a pressure chamber for the Royal Navy and found that a body tolerates some excess dissolved gas, a state called supersaturation, before bubbles cause trouble.^{[1 ]} From that came staged decompression: come up quickly at first, then slow down. Everything since has refined that idea or challenged it. The timeline below shows the main steps, coloured by family; the buttons show one family at a time.

Dissolved-gas models

Haldane pictured the body as a handful of imaginary "tissues", today called compartments, that take up and release gas at different speeds. Each has a half-time: the minutes it needs to fill halfway towards the pressure around it. Haldane used five, from 5 to 75 minutes. The 75 was an estimate: his goats' slowest tissue half-saturated in about 45 minutes, and he scaled that up for a person.^{[1 ]} The compartments are bookkeeping for one fact: blood loads in minutes, while fat takes hours.

Haldane's limit was a ratio: you could halve the absolute pressure in one step, from 2 bar to 1 bar, without symptoms. He was careful about how far it reached, noting that whether it held much beyond six atmospheres was "still doubtful, as no experimental data exist."^{[1 ]} In 1965 Robert Workman of the US Navy Experimental Diving Unit replaced the fixed ratios used until then with a limit for each compartment that changes with depth, and called it the M-value, for "maximum".^{[2 ]} Fast compartments tolerate more excess gas than slow ones, and every compartment tolerates more at depth than near the surface.

Bühlmann

Albert Bühlmann, a physician at the University Hospital in Zürich, began decompression research in 1959 and spent three decades testing schedules on volunteers, in the chamber and in Swiss mountain lakes, where the low air pressure at altitude makes decompression harder.^{[2 ]} His model, ZH-L16 (Zürich, linear, sixteen pairs of coefficients), uses sixteen compartments with nitrogen half-times from 4 to 635 minutes and helium half-times from 1.5 to 240.^{[3 ]}

In his 1988 paper Bühlmann reported that "573 simulated air dives and 544 real dives in mountain lakes" agreed with the model's limits,^{[3 ]} and earlier series covered altitude diving and repeat dives. The paper reports no comparable trial series for helium: it says adapting the model to heliox and trimix "is simple".^{[3 ]} Its helium half-times follow from the nitrogen ones by calculation.^{[2 ]} US Navy authors later gave a larger count, 813 chamber air dives, and credited "many mixed-gas dives" as well, though the 1988 paper reports no helium series.^{[7 ]}

Bühlmann published three versions: ZH-L16A, derived mathematically, then B for printed tables and C for dive computers, each made more conservative in the middle compartments after A proved too liberal there.^{[2 ]}

The model spread because Bühlmann published all of it. His books printed the half-times and the coefficients, so any programmer could build the model and anyone could check it. Erik Baker, an engineer and cave diver who later wrote some of the most-read explanations of these models, said the book made the "Bühlmann algorithm" "the basis for most of the world's in-water decompression computers."^{[2 ]}

In 1998 Baker added the gradient factor, the piece that later made the model the usual choice in technical diving. A gradient factor is a percentage of the gap between the pressure around you and the M-value. GF 100 lets a compartment go right up to Bühlmann's limit; GF 50 lets it go halfway. The first number of a pair (GF Low) places the first stop, and the second (GF High) sets the margin at the surface.^{[2 ]} Divers had one setting, written the same way on every computer and planner, for how much of the model's allowance to use. Gradient factors were never part of Bühlmann's own trials. The companion article Unpacking Gradient Factors covers them in depth.

The rest of the family

Four other dissolved-gas models are still in use, and each has a published testing or service record.

• The PADI Recreational Dive Planner (DSAT). Released in 1988 and built on fourteen compartments, it was tested in 911 dives at a lab in Seattle, then a further 475 dives in a six-day repetitive series: 1,386 no-stop dives in all, every one checked for bubbles with Doppler ultrasound, with no cases of DCS.^{[4 ]} Pelagic's DSAT algorithm, in many Oceanic and Aqualung computers, comes from the same work.
• DCIEM (Canada). A different shape: four compartments in series, each passing gas to the next. The 1983 tables were tested in about 900 man-dives (one diver making one dive) over two years, watched by Doppler ultrasound. In 128 of the test dives that needed 48 to 88 minutes of decompression there were 12 cases of bends, some of them thought to have other contributing causes.^{[5 ]} Shearwater now sells DCIEM as an option for air and nitrox.
• MN90 (French Navy). Introduced in 1990. Over twelve years of navy use the service recorded 61 cases of DCS, about one per 30,000 dives overall and one per 3,000 for deep mine-clearance dives of 45 to 60 metres.^{[6 ]}
• The Thalmann algorithm (US Navy). Ed Thalmann's model lets gas leave a supersaturated compartment in a straight line rather than an exponential curve, which slows off-gassing and lengthens decompression for repetitive dives. It was built on 1,505 air and nitrox man-dives with 84 cases of DCS, and it runs the navy's tables and dive computers today.^{[7 ]}

Bubble models

Dissolved-gas models treat a bubble-free diver as the goal. Bubble models start from the opposite observation: divers bubble on ordinary dives without any symptoms. In the 1960s Brian Hills was a chemical-engineering doctoral student in Adelaide, and he switched his thesis from bubbles in molten nylon to divers. He studied the profiles of pearl divers recorded by the physician Hugh LeMessurier. In Hills's account the pearl divers decompressed in about two thirds of the time the US Navy tables required, and he put it down to "much deeper initial stops."^{[8 ]} He built his thermodynamic model on that idea.

The pearl-diver story is easy to read as proof that deep stops work, but Hills's own account shows what it cost. By his estimate the pearling industry's trial and error had cost 3,000 to 4,000 lives over the decades,^{[8 ]} and some of the recorded dives ended in bends. The pearl divers' method is what a population settled on after heavy losses, with no controlled comparison behind it.

The Varying Permeability Model

David Yount, a physicist at the University of Hawaii, spent the 1970s making bubbles in gelatin. The bubbles formed from tiny gas seeds that were already there. Yet a tiny pure gas bubble should dissolve in seconds, so something must stabilise these seeds. Yount proposed a skin of surface-active molecules around each seed, permeable to gas under most conditions but impermeable under large, fast pressure changes, hence "varying permeability". In 1986 he and D.C. Hoffman used the idea to compute complete air tables from four parameters, set so that the schedules came out similar to existing military tables.^{[9 ,20 ]}

Your tissues hold seeds of many sizes, and going down squeezes them smaller. On the way up, a seed only grows if the excess gas around it beats the squeeze of its own surface tension, and small seeds need a bigger excess to grow than large ones. So the model picks a critical radius and keeps the ascent gentle enough that only seeds bigger than it can grow. It then relaxes that rule a little, allowing some bubbles as long as the total free gas stays under a set volume. The result is a schedule with a deeper first stop, to keep the early excess low, and less time near the surface, because fewer bubbles are thought to have started. That is the shape of the VPM-B plan at the start of this article: first stop at 45 m, less time at 6 and 3 m.

In 2002 Erik Baker added Boyle's law compensation, which shrinks the allowance at each shallower stop because any bubble that did form gets bigger as the pressure drops. That version is VPM-B, and Baker released its code to be shared freely, which is why it appears in MultiDeco, V-Planner, Subsurface, Baltic and several dive computers.^{[10 ]} The conservatism setting works through the critical radius. Settings +1 to +5 enlarge it by 5%, 12%, 22%, 35% and 50% over the nominal size; a bigger seed is easier to grow, so the model allows less and the plan gets longer.^{[11 ]}

Later variants adjust the shallow end. VPM-B/E, for very long exposures, adds shallow time. VPM-B/GFS calculates a Bühlmann gradient-factor plan alongside the VPM-B plan and follows whichever is more restrictive at each stop, which in practice lengthens the shallow stops.^{[11 ]} HHS, the company behind MultiDeco and V-Planner, presents both as extra margin for very long or extreme dives. HHS is also plain about how far the testing of VPM-B goes:

Many thousands of technical dives have been made on VPM-based schedules, and most ended without DCS. That experience counts for something, but it is not a trial: some divers add their own extra time, no one dives to the limits on purpose, and mild cases may go unreported.^{[20 ]} A 2013 review by David Doolette of the US Navy Experimental Diving Unit and Simon Mitchell of the University of Auckland found no formal testing of VPM-based technical schedules.^{[20 ]} The one bubble study of VPM-planned trimix dives found heavy bubbling, with bubbles crossing from the veins into the arteries in five of seven divers, and no DCS.^{[29 ]} It had no comparison group, and deep trimix dives produce bubbles whatever the model.

The same caution applies to the other side. Doolette and Mitchell called gradient factors "a popular, but untested end-user modification".^{[20 ]} Neither Bühlmann at GF 50/80 nor VPM-B at +2 has been tested in a trial scored on DCS.

RGBM: two models with one name

Bruce Wienke, a physicist at Los Alamos National Laboratory who died in February 2020, published the Reduced Gradient Bubble Model in 1990, drawing on the same seed physics as VPM. The name causes confusion because it covers two different things.^{[12 ]} The full RGBM is a true bubble model that limits the volume of free gas and calls for deep stops. The recreational RGBM in most wrist computers is a dissolved-gas model with reduction factors added for repetitive dives, reverse profiles and multi-day diving. Suunto's 2003 description says its version "adjusts the M-values downwards."^{[13 ]} So "RGBM" on a computer tells you less about the shape of your ascent than it seems to.

Suunto put RGBM in its computers from 1999, starting with the Vyper, and later combined Wienke's full and technical models into Suunto Fused RGBM, now in its second version.^{[13 ]} Mares, Cressi and others licensed their own versions. The testing evidence comes almost entirely from Wienke and the companies using his model. In 2010 he described a Los Alamos data bank of 2,879 profiles with 20 cases of DCS and wrote that the model was "validated within" it; the data bank is not public.^{[12 ]} The dive counts in earlier documents vary from one to the next, and the implementations in commercial computers are closed.

Research bubble models

One research model matters more to the science than to any dive computer. BVM(3), by Wayne Gerth and Richard Vann at Duke, computes the volume of bubbles in three compartments and turns it into a probability of DCS, so it belongs to both families. It was fitted to 2,383 navy dives with known outcomes.^{[30 ]} Its makers were candid that many of the fitted values fell "outside of the physiologic range": the model matched outcomes without describing real bubbles.^{[30 ]} It matters because in 2011 the US Navy tested a deep-stop schedule that BVM(3) had designed (below).

Probabilistic models: how navies count risk

Dissolved-gas and bubble models both draw a line: on one side the dive is "inside the limits", on the other it is not. DCS does not behave like a line. The same dive bends one diver and not the next, and the same diver on one day and not another. In 1984 Paul Weathersby, Louis Homer and Edward Flynn at the US Naval Medical Research Institute (NMRI) proposed treating it as a matter of probability, and fitting models to dives with known outcomes by the statistical method of maximum likelihood.^{[14 ]} Instead of a pass or a fail, such a model gives a number: the chance that a dive like this, done by divers like those in the data, ends in DCS.

The navy had good reason to look for a better method. Its 1956 air tables, the ancestor of many recreational tables, were accepted after testing about 40 of some 300 schedules with fewer than six dives each, under a rule that zero bends in four dives counted as a pass. As the NMRI team later pointed out, a schedule that passes that test could have a true DCS rate anywhere from 0 to 60%.^{[16 ]} Their analysis found risks in the 1956 tables ranging from about 1 to 7% on short or shallow dives to 40 to 45% on some extreme exposures.^{[16 ]}

Yet the navy did not switch to probabilistic tables. It kept a deterministic model, Thalmann's, for the tables and computers divers use, and used probabilistic models to measure them. When the Revision 6 air tables were prepared in 2007, the authors wrote that they had not been extensively man-tested, and that probabilistic models were used to estimate their risk instead.^{[17 ]} Navy researchers also proposed a "risk slide" of acceptable risk, used as a yardstick: about 2.3% for dives with little decompression, rising to 5% for normal exposures and 10% for exceptional ones.^{[17 ]} Not every test went as predicted. When the navy tested some of the longer no-stop limits proposed for the new tables, there was less DCS than predicted, but every case was severe, involving the central nervous system, and the Revision 6 tables, published in 2008, kept the older, shorter no-stop limits.^{[7 ]}

Those percentages look alarming next to what recreational divers experience. For one 40-foot, 200-minute no-stop air dive, a navy model predicted 3.9%, a laboratory trial measured 2 cases in 91 dives (2.2%), and the fleet's own records showed 0.11%.^{[18 ]} Laboratory divers dive exactly to the limit, often cold and working, and are examined for any symptom; most real dives stay well inside the limits, and mild cases go unreported. So a model's predicted risk is the risk of a dive made right at the table's limit, by divers like those in the trials.

Why DCS is hard to test

One problem applies to every model in this article: DCS is rare. Recreational divers in DAN's Project Dive Exploration had 38 cases in 122,129 recorded dives, about 3 per 10,000.^{[28 ]} To show that a schedule's risk is low, you have to watch a great many dives without a single case. Homer and Weathersby showed in 1985 that "even after 40 dives it may be impossible to distinguish" a table with a 0.6% risk from one with a 17% risk.^{[15 ]} When the navy tested a short, deep air schedule from its 2016 tables in 96 dives, there was no DCS at all, which still only places its risk below about 3%.^{[33 ]} Figure 3 shows how this works for real test series: pick one, and it shows the highest DCS rate that a clean result can still hide.

Comparing two schedules is harder still. Telling a 1% schedule from a 2% one, with the usual statistical standards, takes about 2,300 dives on each. Telling 1 in 10,000 from 2 in 10,000 would take about 235,000 dives on each, nearly twice the whole of Project Dive Exploration. No study could recruit that many dives. Wayne Gerth of the US Navy Experimental Diving Unit put another side of the problem plainly at a 2011 workshop: a clean record says nothing about how much margin is left. After 10,000 dives without DCS, "you have not learned anything about how far away you are from DCS."^{[7 ]}

That is why researchers often count bubbles instead. Doppler ultrasound can grade the gas bubbles passing through the heart after a dive, and a group of divers bubbles far more often than it gets bent, so differences show up with dozens of dives rather than thousands. Bubbles are a stand-in, though. Doolette found that a clear difference in bubble grades probably reflects a difference in DCS risk, while failing to find a difference does not show there is none.^{[46 ]}

One dive, several models

The two plans at the start of this article came from MultiDeco, which offers both Bühlmann and VPM-B. I planned two dives with the same gases, rates and depths for every plan, changing only the model and its conservatism setting: 50 m for 25 minutes on trimix 18/45, and 70 m for 20 minutes on trimix 15/55 with three decompression gases. Figure 4 shows five plans for each.

On the 70 m dive, VPM-B at +2 and Bühlmann at GF 50/80 spend almost the same total time at stops, about 47 minutes each. They spend it in different places. VPM-B starts 12 m deeper and spends 9.6 minutes below 21 m against 3.9, then 20 minutes at 6 and 3 m against 24. That is the bubble-model shape described above. VPM-B/GFS (switch it on in the figure) puts four of those shallow minutes back. Bühlmann at GF 30/70 is the longest plan of all, at 83 minutes, and it also starts deep, at 42 m. Its low GF Low imitates a bubble model's first stop, and its low GF High adds shallow time on top.

On the 50 m dive the gaps are smaller: the first stops fall between 24 and 30 m and the run times between 58 and 64 minutes. On both dives, changing Bühlmann's settings moved the run time as much as changing the model did, or more, while changing the model moved the first stop further.

Whether moving the same minutes deeper helps is the question the US Navy tested in 2011.

The deep-stops question

Where the first stop falls is the biggest practical difference between the families, and for about fifteen years it split technical diving. In 1996 the fish biologist Richard Pyle described adding short stops far below his first required stop and feeling much better after dives. He was careful to call himself "a fish-nerd" rather than a decompression expert.^{[50 ]} VPM and full RGBM gave the idea a theory, and divers on Bühlmann computers imitated it by setting GF Low to 10 or 20. In a 2008 survey of PADI technical divers, 97.9% had made deep stops, and 37.7% of those did so by using a bubble algorithm.^{[24 ]} At a workshop of the leading researchers that same year, the only statement on whether deep stops work that everyone could agree on was that the evidence was conflicting.^{[24 ]}

Bubble-model users objected that NEDU tested neither their model nor their gases, and they were right on both counts. Doolette and Mitchell replied that VPM schedules stop even deeper than the tested one. They also pointed to an analysis of more than half a million other ways of arranging the same stop time, which showed the same pattern: deeper stops ease the fast compartments at the cost of the slow ones.^{[20 ]}

Most of the other studies split along one line: whether the deep stops added time or moved it. When a deep stop was added on top of the normal stops, as in DAN Europe's recreational studies from 2004, Doppler bubbles went down. When the same total time was moved deeper, as in a Dutch study of 20 m dives in 2008 and at NEDU, bubbles or DCS went up.^{[31 ]} Adding stops did not always help: French Navy trials that added deep stops to deep air dives found no benefit, and in one protocol more bubbling.^{[31 ]} An Italian study in 2017 compared ratio deco, a rule-of-thumb method with extra deep stops, against Bühlmann at GF 30/85 on a 50 m trimix dive. It found no difference in bubbles, but higher markers of inflammation after the ratio-deco schedule.^{[22 ]} A study by a Norwegian-led group in 2008 suggested the answer depends on bottom time. After 70 minutes at 24 m, a deeper procedure gave fewer bubbles; after 16 minutes at 45 m, a VPM schedule gave more. Neither difference was statistically significant.^{[24 ]}

The evidence is not all one way. In 2026 a DAN Europe team reported a pool study of 18 divers. Each made two trimix dives to 40 m with an EAN50 switch and the same total time, one with stops from 21 m up and one with stops only at 9, 6 and 3 m. The deep-stop dives produced fewer bubbles. Three divers had skin symptoms (cutis marmorata, a mild form of DCS), all after the shallow-stop dives, a difference too small to be statistically significant.^{[23 ]} Both schedules were Bühlmann-style: the authors liken the deep one to GF 30/80 and the shallow one to GF 100/75, a setting with no margin at the first stop and some at the surface. The study's main measure was bubbles, and it was far too small to compare DCS. It does not support stops as deep as VPM's, but it does question very high GF Low settings on trimix with an EAN50 switch.

Practice has moved anyway. Simon Mitchell's 2024 review describes technical divers walking back from bubble-model depths. They typically choose a GF Low "around 50 or 60 instead of 10 or 20", and the review notes that "the path of optimal decompression is still not established."^{[26 ]} In 2023 a Belgian Navy study advised its divers against the Shearwater Perdix's 30/70 default for air dives to 60 m.^{[34 ]} In November 2025 Shearwater set the default GF Low to 50 in every mode on its current computers, moving the Tec default from 30/70 to 50/70, without stating a reason.^{[27 ]}

What each model has actually been tested on

Step back from deep stops and the whole testing record looks like this. In controlled man-dives with DCS as the outcome, the US Navy and its allies have far more data than anyone else. Bühlmann's trials and the Canadian and PADI programmes are solid for what they covered. The bubble models divers use have very little behind them that their own authors did not produce.

Which algorithm is the most field-tested depends on what counts. In carefully observed lab dives with known outcomes, the navy pool, with British and Canadian data folded in, holds thousands of dives and is published. In sheer numbers of dives logged, Bühlmann-family and RGBM-family computers are far ahead, but almost none of those dives is linked to an outcome, and most are nowhere near the limits. A 2011 workshop on dive computer validation noted that manufacturers had not published the inner workings of their models or any substantial human testing. The same workshop noted that computers had been used to good effect in recreational diving for more than 25 years.^{[7 ]}

New and little-known models

Several other approaches exist beyond the three big names, from computers you can buy today to ideas still in the lab.

• Adaptive Bühlmann (Scubapro). Scubapro's ZH-L16 ADT MB algorithm estimates workload from heart rate or breathing, takes skin or water temperature into account, and adds "microbubble levels" L0 to L5 for extra conservatism.^{[36 ]} It has shipped for years. No peer-reviewed test of the adjustments has been published.
• Measured bubbles (O'Dive). A French company, Azoth Systems, sells a small Doppler sensor that a diver places below the collarbone after a dive. The app scores the bubbles alongside the computer's profile and suggests changes for next time. A first field study on a liveaboard found bubbles after 39% of 157 dives; one diver bubbled after nearly all of hers.^{[37 ]} It personalises advice, and nobody has yet tested it as an algorithm.
• Copernicus. A Norwegian model from Christian Gutvik and Alf Brubakk that predicts the bubbles themselves, so it can be checked against ultrasound rather than DCS, and can take heart rate as an input. It was calibrated on 457 dives and remains a research model.^{[38 ]}
• Tissue Bubble Dynamics Model. Michael Gernhardt, an astronaut and former commercial diver, models bubble growth from surface tension and tissue elasticity; NASA uses the model for spacewalk preparation.^{[39 ]}
• One central compartment. Saul Goldman of the University of Guelph proposed in 2007 that the compartments are connected around a single risk-bearing compartment rather than side by side.^{[41 ]} A dive computer maker was reported to be working on it; no product shipped.
• Hydrophobic spots. Ran Arieli in Israel argues that bubbles start at "active hydrophobic spots" on the inside of blood vessels rather than from free-floating seeds, and has proposed a vascular bubble model built on the idea, so far backed by animal work.^{[40 ]}
• Variable gradient factors. Kevin Gurr's VR Technology computers, and later his MCM100, used a Variable Gradient Model that changes the gradient factors with the exposure instead of fixing one pair for every dive.^{[49 ]}
• Bayesian and machine-learning risk models. At Duke, Laurens Howle and colleagues have refitted the navy data with Bayesian methods and with models that predict mild and serious DCS separately.^{[42 ]} A 2026 study trained a probabilistic model by gradient descent on 924 profiles from navy helium tables.^{[43 ]} And an open archive of 10,099 annotated Doppler recordings, published in 2026, has already trained an algorithm that grades bubbles without a human listener.^{[44 ]}
• Surfacing supersaturation as a risk score. DAN Europe's analysis of 127,957 dives found that the supersaturation left at the surface, a quantity close to the surfacing gradient factor (the GF a diver would be at on surfacing right now) that some computers display, was the strongest single predictor of DCS in its data.^{[45 ]} The data are observational, so this is an association that has not been tested as a rule.
• Iso-risk navy tables. The US Navy's newer helium work and the Swedish Armed Forces' 2023 air tables use probabilistic fitting to aim every schedule at one chosen risk; the Swedish target was 1% or less.^{[32 ,43 ]} These tables are for military use.

Scubapro's temperature input, first in the list above, points at a finding that applies to every model. Navy trials found that being cold on the bottom lowers DCS risk, while being cold during decompression raises it. The authors advised keeping any heating minimal on the bottom and turning it up for the stops.^{[47 ]} Bühlmann's model has no temperature term at all.

Who uses what, and why

The move away from deep stops shows in the surveys. In the 2008 survey above, more than a third of the divers who made deep stops (37.7%) used a bubble algorithm.^{[24 ]} In a 2025 international survey of 558 trimix divers, 85.3% planned with Bühlmann and 13.4% with a bubble model.^{[25 ]} The two surveys reached different groups by different methods, so the comparison shows only a direction: away from bubble models.

The computer makers have moved the same way, including the two brands most closely tied to RGBM. Mares's Genius "employs the unmodified Bühlmann ZH-L16C algorithm with gradient factors", and its newer Puck 4 does too. Suunto's Ocean runs only "Suunto's Bühlmann 16 GF", while its EON computers offer Bühlmann alongside Fused RGBM 2. Shearwater, Garmin, Divesoft and the Apple Watch's Oceanic+ app all use Bühlmann with gradient factors.^{[35 ]} VPM-B lives on mainly in planners (MultiDeco, V-Planner, Baltic, Subsurface) and as an option on some technical computers. No public, method-backed market-share figures exist for dive computers, so nobody can say exactly how many divers use each model.

Bühlmann's lead did not come from a trial. It is published, so it can be checked and reproduced. Gradient factors give one shared language for conservatism, so a buddy team can match settings across brands. And after 2011, a model that put first stops shallower stopped looking like a compromise. Divers who prefer VPM-B usually point to shorter total run times on big dives; the main argument against it is the evidence above about deep first stops. A diver who never opens the settings dives whatever the computer ships with, so the factory settings can matter more than the model's name.

Two divers on "the same algorithm" can therefore be diving quite different plans, and two computers on the same settings can still differ slightly in how they implement the details. The companion article Same Dive, Different Stops goes through those differences with real numbers.

What this means when you plan a dive

The evidence cannot name a best algorithm, but it does say a few things that help when you plan.

First, a model's limit is not a line between a good dive and a bent one. DAN Europe found that 312 of 320 DCS cases in its database, the same one behind the surfacing finding above, fell within Bühlmann's limits when the dives were recalculated.^{[48 ]} Every dive carries some risk, and the model describes how that risk changes with the profile.

Second, settings matter as much as the model's name. On the 70 m dive in Figure 4, moving Bühlmann from GF 50/80 to 30/70 added 11 minutes, while switching to VPM-B at +2 changed the run time by 2, though it moved the first stop 12 m deeper. Know what your computer is set to, and why.

Third, very deep first stops have the weakest support. Most trials that moved stop time deeper found more bubbles or more DCS. The exception so far is the small 2026 DAN Europe pool study, and it compared two Bühlmann-style schedules.

Finally, plan with the model you dive, or know how the two differ. When two plans disagree, compare where the extra time sits as well as the total: the evidence above is about where stop time goes, not only how much there is.

Back to the two plans at the start. Neither model has been tested in a trial on a dive like that one. Of the two, the 45 m first stop has the weaker evidence behind it today. The rest, how much margin to add, is set by the numbers you choose, a GF pair or a +N, and it is better made with those numbers in view.

Questions divers ask