The Thalmann exponential-linear (E-L) model is the US Navy’s decompression algorithm. It is a dissolved-gas model like Bühlmann, with one structural difference: once a tissue compartment is supersaturated, it off-gasses at a fixed linear rate instead of an exponential one.
History
The model was developed at the Navy Experimental Diving Unit in the late 1970s, when the Navy fielded a rebreather that holds oxygen at a constant partial pressure. The breathing mix on such a rig changes with depth, so no printed table covers it, and the schedule has to be computed in real time.
The first attempt used the same symmetric exponential kinetics as the existing tables. In manned chamber testing it produced too much decompression sickness. Edward Thalmann, the medical officer running the program, traced the problem to the ascent: the model assumed supersaturated tissues wash out fast, and the outcomes said they do not. In the early 1980s he changed off-gassing to a fixed linear rate during supersaturation, which lengthens the shallow stops. The retested schedules performed better, and the parameters were then refined for two decades against the Navy’s database of recorded dives and outcomes.
The algorithm’s air parameter set became the basis of the US Navy’s air decompression tables in 2008 and runs in the Navy’s own dive computer. It was never adopted by civilian dive computers, which standardised on Bühlmann with gradient factors. The most recent parameter sets, from 2018, were fitted so this algorithm reproduces the schedules of the Navy’s newer probabilistic models, which compute a probability of decompression sickness rather than a single schedule but are too computationally heavy to run on a dive computer.
How it differs from Bühlmann
Gas uptake is identical: each compartment closes half its gap to the breathed pressure per half-time. The models diverge when a compartment holds more gas than the current depth supports. Bühlmann keeps the exponential curve, so a big gradient means fast washout; Thalmann holds washout to a constant rate until the compartment drops back below saturation.
The practical differences on a schedule:
- Longer shallow stops. The extra time lands at 9 m, 6 m and 3 m, where tissues are most supersaturated. Deep stops are similar to Bühlmann’s.
- No gradient factors. Selecting Thalmann removes the GF fields; the ceiling is the model’s own limit, and conservatism comes from which parameter set you select instead.
- A different risk target. Navy schedules are planned against an explicit probability of decompression sickness that is far higher than recreational practice runs, because a working diver decompresses next to a chamber. A Thalmann runtime and a Bühlmann runtime are answers to different questions about acceptable risk, not two estimates of the same thing.
The parameter sets
The selector offers seven sets.
VVal-79 is the air and nitrogen-oxygen set, in the lineage of the US Navy’s air tables. It has no helium behaviour: on a trimix it treats the helium as if it were not there.
The XVal-He sets are the 2018 generation, fitted for constant-ppO₂
helium-oxygen rebreather diving. The suffix is the target probability of
decompression sickness the schedules were optimised for: _023 for 2.3 %,
the Navy’s standard planning target, _040 for 4 % and _050 for 5 %. A
lower target produces a longer schedule. The 9-series is the primary fit and
the 8-series a leaner variant with fewer compartments. An open-circuit
trimix plan is outside the diving any of them was calibrated against.
The model’s main use here is comparison: running the same dive under Bühlmann and under Thalmann shows how much of a schedule is model assumption rather than measurement.
Like Bühlmann, E-L has no bubbles, no anatomy and no diver. The linear rate is an assumption that fitted trial outcomes, not an observation of what tissues do.
Next
- Bühlmann ZHL-16C: the default model.
- GF calibration: a Thalmann schedule expressed as a gradient-factor pair.