muddiver:
PADI tables and Navy tables are based on Haldane theory and are empirically derived (i.e. probability calculated from real world data). Only the HUGI tables are non-Navy based. They were done using Doppler ultrasound technology to research silent bubbles in the blood stream after exposure to a hyperbarric environment.
What is the source of your info Muddiver?
On the HUGI table itself the first sentence is "These tables have been developed mathematically and have not been subjected to testing to validate them". Taking a short look at them, it appears that they are based upon the doppler adjusted USN/Workmann table, just like many other tables such as NAUI, SSI, and YMCA. The difference is that they have arranged the repetitive letter groups differently, so that that going up to the NDL will always put you in letter group N. Offgassing is assumed to occur at a 120 minute halftime rate, just like all of the other USN-derived tables. Expressed in a different way, the Hugi tables are based upon the USN Doppler limits, with the faster ongassing compartments assumed to have a 120 minute halftime for offgassing. This is similar to the "surface credit control" feature of some dive computers, such as the Pelagic/Oceanic series where compartments faster than 60 minutes are restricted to offgassing at a 60 minute halftime once you have surfaced.
The PADI/DSAT tables were based upon real life testing, including doppler monitoring. As Oly5050user mentioned, the PADI table repetitive dive calculations are based upon a 1 hour compartment, while the USN-derived (and Hugi) tables are based upon the 2 hour compartment. The 2 hour compartment is important only in very long, shallow dives such as spending hours working on the bottom of a 35' draft ship using surface supplied air. Normal single tank recreational dives are normally limited by much faster compartment. As a rule of thumb, the limiting compartment for a square profile dive has a halftime about 2/3 of the NDL for that depth. More specifically, it is only for NDL dives at 40' and shallower that even the 1 hour compartment becomes the limiting one, and only for even shallower dives dives does the 2 hour compartment become a limit.
The net effect is that the USN-derived (and Hugi) tables are poor choices for tracking recreational dives, in the sense that the actual risk from diving to a table limit varies dramatically. To put it another way, the USN tables (and USN-derived tables) are very conservative on 2nd dives compared to dive computers that fully implement the underlying model. The same is true for the PADI table when compared to dive computers running the same model, but the variance between table and computer is not as dramatic.
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The PADI tables, the USN tables, the Hugi table, the tables at
www.dir-diver.com are all based on a neo-Haldane model of mutiple dissolved gas compartments of varying halftimes. While not perfect, this model has been a very useful tool for 100+ years. The Canadian DCIEM tables are also based upon a dissolved gas model, but one which assumes a serial transfer from faster to slower compartments rather than the all parallel model of the neo-Haldanian models. NAUI has issued in the last year or so a set of RGBM tables based upon a dual phase, aka "bubble", model. There are several decompression programs that implement the VPM model, a well documented dual phase/bubble model. The Buhlmann model is yet another popular neo-Haldanian model. There are both tables, dive computers, and decompression programs that use this model.
For NDL diving, particularly table-based diving, the choice of model isn't all that important.
On a practical basis, most diving is done using old fashioned dissolved gas / neo-Haldane models while shaping the ascent and stops based experience that show that deep stops and safety stops improve safety and reduce post-dive fatigue. The thermodynamic and bubble models came along later and provided some theoretical confirmation of what divers had already discovered empirically.
Tables and computers only set limits. The diver determines what is actually done in terms of ascent and stops.