Albert Bühlmann ran the hyperbaric laboratory at the University Hospital in Zürich for 3 decades, testing schedules in chambers, in the sea and in mountain lakes. In 1983 he published his model in full, including the coefficients, at the time when microprocessors made wrist-mounted dive computers possible.
Most dive computers today run a version of those numbers, usually ZHL-16C. It uses Workman’s straight-line limit, rewritten so that it works at any altitude, across 16 tissues.
- Ambient pressure
- M-value line
- Tissue
Bühlmann’s form of the M-value
Workman expressed his limits in depth, measured from sea level. Bühlmann wrote the same kind of straight line against absolute ambient pressure: M = a + P/b, where P is ambient pressure and a and b are 2 coefficients for each tissue.
Because it uses absolute pressure rather than depth, the same line applies on a lake at altitude, where the surface pressure is below 1 atmosphere. The shaded area is the supersaturation this tissue is allowed.
The 16 compartments
ZHL-16C has 16 compartments, with half-times from 5 to 635 minutes, and each has its own a and b. The fastest has a = 1.1696 bar and b = 0.5578; the slowest has a = 0.2327 bar and b = 0.9653.
On the graph they follow Workman’s pattern. Fast lines are high and steep; slow lines lie close to the diagonal. Each compartment also has a second pair of coefficients for helium. On trimix, its limit is a blend of the two pairs, weighted by how much of each gas the tissue holds.
One tissue during the ascent
This is the 12.5-minute tissue over the last 16 m of a 45 m air dive. Each ascent moves the point left, towards its line, because the ambient pressure falls faster than the tissue can release gas.
At a stop the ambient pressure is constant and the tissue releases gas, so the point moves down, away from its line. The planner keeps you at the stop until ascending the next 3 m would not take any tissue above its line. The same limit, solved for depth, gives the ceiling: the shallowest depth at which a tissue is still below its line.
The leading compartment
This shows all 16 compartments at the same ambient pressure as the ascent progresses. Each point has its own line above it. The compartment with the smallest fraction of its margin remaining is the leading compartment, highlighted.
On this dive the lead passes from the 12.5-minute tissue to the 18.5, then the 27, then the 38.3 as the stops get shallower. No single tissue controls the whole decompression.
Over the whole dive, the engine reports the depth, the ceiling above it and the compartment that sets the ceiling.
- Depth
- Ceiling
- Leading tissue
The dive profile
The same dive: a descent to 45 m on air, 25 minutes on the bottom, then the ascent. This is the unmodified model, ZHL-16C with no gradient factors, the setting planners call 100/100.
The engine’s schedule: 1 minute each at 12 m and 9 m, 7 minutes at 6 m, 18 minutes at 3 m. The last stop is the longest.
How the ceiling develops
For the first minutes on the bottom there is no ceiling, and a direct ascent to the surface is allowed. About 6 minutes into the bottom time a ceiling appears, and it becomes deeper as the bottom time continues. At the end of the bottom time it is about 9 m.
The planner takes the next stop depth below the ceiling, 12 m, as the first stop. Each stop lasts until the ceiling is shallower than the next stop depth, so the diver always stays deeper than the ceiling (red).
Which compartment leads
The strip below the profile shows the leading compartment. On the bottom the 5-minute tissue leads, then the 8-minute one. During the ascent the lead passes to the 12.5, 18.5, 27 and 38.3-minute tissues in turn.
Fast tissues control the deep stops; slower tissues control the shallow ones. Slow tissues release gas slowly and have a small margin between their line and the ambient pressure, so the 3 m stop is the longest.
Load as a percentage of the M-value
The ascent again, with each tissue’s load shown as a percentage of its M-value. The dashed line is 100 percent, the M-value itself.
As the ascent begins, the fast tissues’ bars rise quickly and lead. At each stop they fall as the tissues release gas, and a slower tissue, whose bar is still rising, becomes the leading compartment.
Try it
Choose a depth, a bottom time and a gas. The engine plans the dive with unmodified ZHL-16C and draws the schedule: one bar per stop, one segment per minute, each segment coloured by the compartment that led in that minute. On longer dives slower tissues lead the shallow stops. A deco gas shortens the stops, but the lead still passes from faster to slower tissues. How the planner chooses the depth of the first stop is covered on the Handbook’s first stop page.
What to remember
- Bühlmann kept Workman’s straight-line limit and wrote it against absolute pressure, M = a + P/b, so it also applies at altitude.
- ZHL-16C has 16 compartments, 5 to 635 minutes, each with its own a and b for nitrogen and a second pair for helium.
- The ceiling is the M-value solved for depth: the shallowest depth at which every tissue is still below its line.
- The leading compartment changes during the ascent. Fast tissues control the deep stops; slow tissues control the shallow ones.
- The model tracks dissolved gas only. Its lines were set where tested dives were mostly tolerated; they are not a threshold of injury.
The leading compartment in the planner
DiveLogic plans with ZHL-16C by default. Plan this 45 m dive, open its tissue view and move through the ascent. The leading compartment is marked at every step, and the schedule’s Advanced view shows the ceiling at each stop.
Sources
- Bühlmann A. A. (1984). Decompression-Decompression Sickness. Springer, Berlin.
- Bühlmann A. A., Völlm E. B., Nussberger P. (2002). Tauchmedizin, 5th edition. Springer, Berlin. (ZHL-16C coefficients.)
- Workman R. D. (1965). Calculation of decompression schedules for nitrogen-oxygen and helium-oxygen dives. Research Report 6-65, US Navy Experimental Diving Unit.
- Baker E. C. (1998). Understanding M-values. Immersed 3(3).