# The Saul Dive Planner : Questions Answered

A comment by Craig on the Saul dive planner raised issues that may be of general interest, and merit a somewhat detailed answer, so here it is.

Thanks for posting the planner, interesting to try out. I could not get 130 feet for 32% to do any calculations.

With 32% O2, out of an abundance of caution (in order to avoid Oxygen toxicity), the depth is often limited to less than 120 feet, which is what I have done here.

Many algorithms have a slower ascent rate of 30 feet/min, or that rate when at 60 ft or less.

During free ascents, i.e. in the absence of an ascent/descent or anchor line, it is actually pretty difficult to maintain an ascent rate of 30 feet/min (or less). 60 feet/min is more common and easier to do, so the ascent rate calculations in the dive planner are for 60 feet/min.  Planning for an ascent rate of 30 feet/min when you’re unlikely to achieve that slow an ascent would be underestimating your actual level of risk.  A dive computer using Saul would, of course, be able to take actual ascent rates into account.

It is difficult for me to interpret the probability of DCS. I ran all the DSAT NDLs between 60-120 feet for 32%. All probabilities ran between 0.27 and 0.46%

The result you just found, that the DSAT NDLs are not “iso-risk” (i.e. they don’t all entail the same degree of risk), is something that many people have wondered about, but – in the absence of a probabilistic model – didn’t have a handle on. This is one of the many advantages that a probabilistic model provides.  But I presume that your immediate concern is with what those differences in probabilities mean in real life.

Firstly, the probabilities shown in the planner are stated as percentages, so that a 0.27 risk of decompression sickness means a .27 percent risk (or 2.7 chances in 1000, 27 chances in 10,000, or just a bit above 1 chance in 400).   Similarly, a .46 percent risk means 4.6 chances in 1000, 46 chances in 10,000, or  about 1 chance in 218.

With respect to interpreting the probabilities, it may be helpful to appreciate more fully what these numbers mean or imply, by seeing what they predict for large numbers of dives.  We’ve already looked at that a bit in a previous blog post (Probability in Relation to “The Bends”) where we showed that, for a probability of 1 in 400, over a series of 400 dives, the probability of getting no instance of decompression sickness in any of the dives was .367 while the probability of having one or multiple instances of sickness during the series was .633.  (So – very roughly – the probability of being hit at least once in 400 dives at that level of risk was almost double the probability of completing 400 dives unscathed.)   We looked at a series of 1000 dives at that same risk level, and found the probability of being hit at least once in the series works out to .918, while the probability of completing 1000 dives unscathed has decreased to a measly .082 (or less than 1 in 10).

How do the two P(DCS) extremities of 0.27 % and 0.46 %, obtained for the DSAT NDLs on 32 % O2 (above) compare?   If we do similar calculations on those probabilities, we find that – skipping right to a series of 1000 dives –

For a risk level of .27%,  the probabilities of no hits and at least one hit in a 1000 dive series are, respectively, .067 and .933.  (The chances of completing the series of 1000 dives unscathed is not looking too good – just under 7%.)

For a risk level of .46%, the probabilities of no hits and at least one hit in a 1000 dive series are, respectively, .010 and .990.  (The chances of completing the series of 1000 dives unscathed is highly unlikely – 1% .)

So the probability of getting at least one hit over the series of 1000 dives rises from about 93 % to about 99 %, depending on whether one dives the profile corresponding to the low or the high extremity for the range of  DSAT NDL’s for single-dive profiles.  Even the seemingly negligible difference between the 1 in 400 (.25%) level of risk in the initial example and the .27% risk level, when carried over 1000 dives, moves the probability of getting hit at least once from less than 92% to over 93%.

These and related calculations are described more fully at the end of Chapter 8 of the book I recently co-authored:

Saul Goldman, J.Manuel Solano-Altamirano, and Kenneth M. LeDez: “Gas Bubble Dynamics in the Human Body”. Elsevier/Academic Press (2017).

Hope this helps.