On 19 Mar 2016 00:33, "Willem Ferguson" <[email protected]> wrote: > > ---------- Forwarded message ---------- > From: "Willem Ferguson" <[email protected]> > Date: 18 Mar 2016 15:32 > Subject: Re: Profile display affected by planning parameters > To: "Robert Helling" <[email protected]> > Cc: > > Thanks a lot, Robert. > Along which principles is the VPM-B ceiling calculated?
Black magic... In all seriousness, the ceiling (both in the planner and for real dives) is calculated using the principles of the published VPM-B model. In many ways the it is similar to the Buhlmann model in that on- and off-gassing is tracked in nearly the same way according to partial pressures of nitrogen and helium, and an allowable gradient (= difference between partial pressures of gasses in tissues and ambient pressure) is calculated. The ceiling is a representation of the shallowest depth (lowest ambient pressure) allowable without exceeding the gradient of any "tissue". It's important to note that both Buhlmann and VPM-B attempt to fit essentially the same empirical data to determine an allowable gradient. The formulae look quite different, but the end result is usually reasonably similar. The main difference between Buhlmann and VPM-B is how the allowable gradient for each tissue is determined. With Buhlmann it's a relatively simple calculation, using factors a and b for each tissue, which have been determined empirically, then factored with gradient factors. VPM-B is more complicated - the model attempts to represent theoretical bubbles within tissues shrinking and growing with increase and decrease in ambient pressure, then compare the size of the bubble to the largest theoretical bubble (with a critical radius) that could exist without causing decompression illness. The calculated bubble radii aren't real - it's a theoretical model based on some physics, but with parameters chosen to fit empirical data (who did/didn't get bent doing what dives). But that didn't quite fit the data: it was found that a quantity of oversize bubbles could be tolerated without causing problems, so the critical volume algorithm (CVA) was introduced, which is an iterative procedure to factor the calculated gradients according to what total volume of theoretical oversize bubbles will exist at the end of the dive. Again this fudge is semi-rational with numbers chosen to fit data. Then there is another adjustment to account for Boyle's law (for a given gas mass and temperature, volume is inversely proportional to pressure), which meant that new values for all the parameters needed to be chosen in order to fit the data. The published VPM-B model is about dive planning, not calculating the ceiling for an actual dive. For both the Boyle's law adjustment and the CVA, a distinction needs to be made between the bottom phase of a dive, and the ascent phase. That's known in a planned dive, but we need to make assumptions when using real dive data. From the commit message for the patch that enables creation of the ceiling: However, we can infer these values to be: - first_stop_pressure (i.e. the reference pressure for Boyle's law compensation) is the deepest ceiling in the dive - deco_time (i.e. the duration of the ascent phase, used in the CVA) is dive time from the deepest ceiling until the ceiling clears (or would have cleared if the diver finished their deco obligations) With these assumptions, the CVA converges rapidly. Cheers, Rick
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