Bühlmann’s model sets a limit for every tissue: the most gas it may hold at each depth. A plan made exactly to that limit is the model unmodified, with no margin. For years, divers who wanted a margin had to adjust the plan by hand: plan the dive as deeper or longer than it was, or add minutes to the stops.
In the late 1990s Erik Baker, an engineer who wrote decompression software, proposed a different method. Instead of changing the dive, he limited how close to the limit the ascent may go. Two numbers set this, one for the start of the ascent and one for the surface. These are the gradient factors, and most technical dive computers now ask for them.
- Water pressure
- M-value
- Tissue at 30/70
The pressure graph
Baker explained his method on a pressure graph. The horizontal axis is the pressure of the surrounding water; the vertical axis is the gas pressure in one tissue.
The dashed diagonal marks where the two are equal. At the bottom the tissue is below it and takes on gas. During the ascent the water pressure falls faster than the tissue can unload, so the tissue rises above the line: it holds more gas than the surrounding water pressure. This is supersaturation. It occurs on every ascent. Gas leaves a tissue whenever its pressure is above the inert gas pressure you breathe; supersaturation is what the model has to limit.
The M-value line
A limited amount of supersaturation is tolerated; too much and bubbles grow. Bühlmann gave each tissue a straight line, its M-value, marking the most gas it may hold at each pressure. The engine draws that line here from its own values.
The band between the water line and the M-value line is the gradient: the range of supersaturation the model permits. The dashed track is the same dive planned at 100/100, which lets the tissue rise almost to the red line.
GF low and the first stop
A gradient factor is a fraction of that band. GF low sets how much of it the tissues may use at the start of decompression.
At 30 %, the tissue may rise only 30 % of the way from the water line to the M-value line. The ascent reaches that limit sooner, so the planner stops you deeper: GF low sets the depth of the first stop.
GF high and the surface
GF high is the fraction allowed when you surface. At 70 %, you surface with 30 % of the band unused.
Between the two, the allowance changes linearly with depth, from GF low at the first stop to GF high at the surface. The planner decompresses you against this lit line, stop by stop.
Effect on the schedule
The pressure graph shows one tissue. The schedule shows the stops the diver makes. The example dive is 40 m for 25 minutes on air, with EAN50 from 21 m, planned by the engine at 3 settings.
- GF 100/100
100/100: the unmodified model
With both factors at 100, the ascent may use the whole gradient. This is Bühlmann as published: the shallowest first stop and the shortest dive the model allows.
This setting has no margin of its own. Every conservative setting is measured against it.
Lower GF low
Reduce GF low to 30 and leave GF high unchanged. The first stop moves much deeper, because the tissues may use far less of the gradient before decompression begins.
The total time increases only slightly. GF low moves the first stop but adds little time. The early stops are short because the fast tissues that control them unload quickly.
Lower GF high
Now reduce GF high to 70. The deep part of the ascent hardly changes, but the stops at 9, 6 and 3 m become longer.
Most of the added time comes from GF high. Near the surface the slow tissues control the stops. They release gas slowly, so each point of GF high removed adds significant time.
Stop by stop
This view shows the 30/70 schedule in detail. The lit steps are the allowance at each stop depth. The blue trace is the tissue closest to its limit, measured as a percentage of its own gradient.
At each stop the trace falls as gas leaves. When the move to the next stop would keep it under the line, the planner allows the ascent, and the trace drops below the next step. GF low and GF high together define that stepped line.
Try it
Drag GF low and GF high, or choose a common pair. The engine plans the same dive again after each change. Note the first stop depth as you move GF low, and the runtime as you move GF high.
- GF 30/70
- 100/100
What to remember
- A gradient factor is a fraction of the difference between the water pressure and a tissue’s M-value. 100 % is the model’s own limit.
- GF low applies at the first stop and sets its depth; GF high applies at the surface and sets how long the shallow stops last.
- Between them the allowance changes linearly with depth. The planner holds each stop until the next step up stays under it.
- Lowering GF high costs far more time than lowering GF low.
- A gradient factor is not a probability: 70 does not mean a 70 % chance of anything. Gradient factors apply only to Bühlmann.
Gradient factors in the planner
The DiveLogic planner takes GF low and GF high in its Decompression settings and redraws the schedule when you change them. To find the pair that comes closest to a Thalmann schedule for the same dive, see GF calibration in the Handbook. The limit that the factors are a fraction of is explained in the Bühlmann guide.
Sources
- Baker E. C. (1998). Understanding M-values. Immersed 3(3).
- Baker E. C. (1998). Clearing up the confusion about “deep stops”. Immersed 3(4).
- Bühlmann A. A. (1984). Decompression-Decompression Sickness. Springer, Berlin.
- Doolette D. J., Gerth W. A., Gault K. A. (2011). Redistribution of decompression stop time from shallow to deeper stops increases incidence of decompression sickness in air decompression dives. NEDU Technical Report 11-06. Navy Experimental Diving Unit, Panama City, FL.