Building on the previous work of John Scott Haldane and Robert Workman, and working off funding from Shell Oil Company, Bühlmann designed studies to establish the longest half-times of nitrogen and helium in human tissues. These studies were confirmed by the Capshell experiments in the Mediterranean Sea in 1966.
Compartment
Half-time N2
N2 'a' value
N2 'b' value
Half-time He
He 'a' value
He 'b' value
1
4
1.2599
0.5050
1.5
1.7435
0.1911
2
8
1.0000
0.6514
3.0
1.3838
0.4295
3
12.5
0.8618
0.7222
4.7
1.1925
0.5446
4
18.5
0.7562
0.7725
7.0
1.0465
0.6265
5
27
0.6667
0.8125
10.2
0.9226
0.6917
6
38.3
0.5933
0.8434
14.5
0.8211
0.7420
7
54.3
0.5282
0.8693
20.5
0.7309
0.7841
8
77
0.4701
0.8910
29.1
0.6506
0.8195
9
109
0.4187
0.9092
41.1
0.5794
0.8491
10
146
0.3798
0.9222
55.1
0.5256
0.8703
11
187
0.3497
0.9319
70.6
0.4840
0.8860
12
239
0.3223
0.9403
90.2
0.4460
0.8997
13
305
0.2971
0.9477
115.1
0.4112
0.9118
14
390
0.2737
0.9544
147.2
0.3788
0.9226
15
498
0.2523
0.9602
187.9
0.3492
0.9321
16
635
0.2327
0.9653
239.6
0.3220
0.9404
Versions
Several versions of the Bühlmann algorithm have been developed, both by Bühlmann and by later workers. The naming convention used to identify the algorithms is a code starting ZH-L, from Zürich, limits followed by the number of tissue compartments, and other unique identifiers. For example:
ZHL-16 or ZH-L16A: The original 16 compartment algorithm.
ZHL-16B: The 16 compartment algorithm modified for dive table production, using slightly more conservative “a” values, mainly in the middle compartments. Recently used in dive computers with high performance processor units, is it more flexible compared to the ZHL16C
ZHL-16C:The 16 compartment algorithm with further modification to the middle and faster “a” values, intended for use in dive computers as a "package". It can be used with almost all low-level processor units but it is less flexible compared to the ZHL16B.
ZHL-8: A version using a reduced number of tissue compartments to reduce the computational load for personal dive computers.
ZHL-8 ADT: 8-compartment adaptive model used by Uwatec. This model may reduce the no-stop limit or require the diver to complete a compensatory decompression stop after an ascent rate violation, high work level during the dive, or low water temperature. This algorithm is used in computers which can accurately monitor air consumption and instantaneous rate of air consumption to model work load via changes in the rate of gas consumption, which allows plausible modelling of additional decompression obligation based on exertion at depth. It also monitors ambient temperature and selects the choice of risk tissue accordingly. This results in earlier and longer decompression requirements in colder water.
ZHL-8 ADT MB: A version of the ZHL-8 ADT claimed to suppress microbubble formation.
ZHL-16 ADT DD: 16-compartment adaptive model used by Uwatec for their trimix-enabled computers. Modified in the middle compartments from the original ZHL-C, is adaptive to diver workload and includes Profile-Determined Intermediate Stops. Profile modification is by means of "MB Levels", personal option conservatism settings, which are not defined in the manual.
ZHL-12
Tables
Max Hahn first used Bühlmann's algorithm to develop dive tables for the Swiss Underwater Sport Association. In 1987, the SAA Bühlmann System was developed by Bob Cole. This system used the dive tables and a set of rules so that people could dive safely and stay below their no-decompression limit. The tables are still used today and are very popular; many dive computers still use the ZHL-8 algorithm and many tables are based on the ZHL-16 algorithm or derivatives. These calculations also include considerations for repetitive and altitude diving.
