Fwd: Re: Profile display affected by planning parameters

[Rick Walsh]

On 19 Mar 2016 00:33, "Willem Ferguson" <willemferguson at zoology.up.ac.za>
wrote:
>
> ---------- Forwarded message ----------
> From: "Willem Ferguson" <willemferguson at zoology.up.ac.za>
> Date: 18 Mar 2016 15:32
> Subject: Re: Profile display affected by planning parameters
> To: "Robert Helling" <helling at atdotde.de>
> 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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