How are NDL tables calculated?

[Spimon]

Just curious as to how dive tables are calculated...

I assume the max NDL time at a given depth is derived from a function of depth (and possibly other factors) and computers determine multi level dive limts by integrating this function. Is this correct?

Does anyone know what the actual formula for NDL tables is?


(Sorry, the inner geek in me had to make an appearance)

 

[fisherdvm]

I think an old guy by the name of Haldean or so killed a bunch of goats in pressure chambers to make up this table about 100 years ago. He theorized 5 "tissue" compartments, which stored nitrogen, and released them at different half life.

Eventually, the Navy expanded it to 6, then some guy expanded it 14 and marketed it as the Wheel and RDP table. Once you exceed the maximum partial pressure of nitrogen in these compartments, then little bubbles formed and you get sick. At first, Haldean used goats. The navy had better guinea pigs, they used dumb navy sailors. Then the last guys, he used man, woman, and people of all different ages and sizes, but he used doppler ultrasound instead.

Then, the computer folks got involved, and stuff the same original theories into some puters, and now we are diving based on data from goats, young navy guys, and later a bunch of other volunteers who were exposed to pressurized air, and using doppler....

Just google decompression theory, and you'll find all sort of neat stuff. It really is not a formula, but a very subjective table. I imagine that some guy used calculus and stuff to make a "formula" out of it for the computers... But in reality, it is based on relatively subjective data, gathered from real human, goats, and other creatures.

 

[Papa_Bear]

Well they are refined by each agency but were established based on Haldean's work by the Navy! They took hundreds of men and, based on Haldean, had them stay at depth and recorded how many bent over the years to develop the Navy Tables! They had the resources, the men, to see what worked through trial and error! They unlike computer companies didn't have to worry about being sued!

 

[ryanpublic]

Here's a link. I like fisherdvm's answer too.

Dive Tables and Dive Computers: Their History and Utility

 

[Gilldiver]

While the above has a good bit of truth in it, they didn’t just use people in the caviler fashion that it is presented in.

Goats were used as they had lung structures that are similar to humans. Haldane and others subjected the goats to simulated dives at different depths for differing times and watched as they were decompressed. The problem was that a goat couldn’t tell you when they were bent, you had to figure it out by observing what they did.

When they had enough data on the goats and they thought they had good models that kept the goats from getting bent, they did the human trials to proof out the models. This is the same thing as is done with any new drugs. Sooner or latter you have to try it on humans and see if it works.

The divers/humans can tell you when they were in pain and from this data they backed off till they got the tables that were used up through the late 50’s. In 1959 or so the “Navy Tables” came out which were used through the 1990’s. These are air tables and much of what we use today has its roots in them. Even NITROX tables.

There has been a lot of additions and the models have been refined many times by Bulhman, Boyd, Hamilton, and many others and computers have been a great aid. But, it all comes down to a theoretical model that is then checked against empirical data. In essence, you are helping to develop and refine the tables every time you dive as data is being collected on the estimated number of dives vs. the number of Bends cases with as much contributing data as can be got.

But it is all based on theory and that is why we have “undeserved bends” and such.

 

[SlowRain]

Here is a link that might help...and has some other links as a part of it.

Dive-Tech: Decompression theory - Paul Bert and John Scott Haldane

NDL formulas are varied depending on what model you use. There is Haldane's model, Buhlmann's model which holds with 16 tissue compartments over the original 5 and his models are actually geared more towards the use of helium as a full or partial replacement for nitrogen in the breathing gas (heliox) or a combination of O2, nitrogen, and Helium (trimix). Buhlmann's model holds to the theory of microbubbles and deeper 2 minute stops as a prevent to microbubble formation. There is also the VPM model which is becoming popular. I just bought a new Delta Vr3 which comes with the Buhlmann model, but you can also exercise a purchase option to install the VPM model and go back and forth between models between dives, however not during a dive.

The computer actually tracks your dives using both algorithms so that you can compare between the two to find out which one gives you the best dive profile for your next dive. I personally have not put that feature in mine as I have been using the Buhlmann model in the Vr2 for several years and now the Vr3, and have yet to have an issue....why mess with success?

The difference between decompression algorithms really comes into play when you get into tech diving or other diving that requires decompression stops. (Remember, the US Navy Dive Tables are geared towards men in their 20's and in the best shape of their life).

In general (and note I said in general!) the VPM model "smoothes" out the profile. VPM does not use deep micro-bubble stops and normal (as opposed to deeper 2 minute micro stops) decompression stops begin much deeper, in general the intermediate stops are longer and the shallow stops shorter than the Buhlmann model. It gets rather complicated insofar as what the best model is and is based on dive depth, time, and gas selections.

Note that not all computers use the same dive algorithms (although I think you will find most use Buhlmann's model, or a conservative version of it). You will find that there are a lot of theories and many swear by one as opposed to another. I am just using what works for me.

In the end, simply because of different models bouncing around, basic open water is taught using the Navy Dive Tables (a long accepted standard) and cautions to dive them being conservative. I think if you do a little research you will find that technology and study is continuing in the area of dive algorithms, and will continue to do so.

I would be remiss if I failed to say that unless trained for decompression diving, follow the US Navy Dive tables and dive them conservatively. If you elect to buy a computer, then become familiar with how it works.

 

[Spimon]

But in reality, it is based on relatively subjective data, gathered from real human, goats, and other creatures.

Mmm, reliable
I guess ignorance was bliss for those early volunteers

Thanks for the info everyone! Not nearly as scientific as I was expecting (was thinking more along the lines of the compresability of gasses and the ideal gas model or something more numeric).

 

[TSandM]

If you're interested in the actual math, you might find Bruce Wienke's books interesting.

 

[Thalassamania]

Already covered ... sorry.

 

[Gary D.]

The navy had better guinea pigs, they used dumb navy sailors.

I hope this isn't an example of how you feel about our men and women in uniform. The people working in the Navy EDU were trying to improve diving to a point YOU and everyone else could enjoy today. They were not just a bunch of dumb sailors.

Not much upsets me but this one was one of the exceptions.

Gary D.