VPMechanics 1

The VPM Algorithm

Copyright 1999-2001 Eric Maiken

This notebook discusses the mechanics of the VPM decompression algorithm developed by Yount and Hoffman (Y&H). With just a little mirth, I refer to this as the Increased Gradient Bubble Model.

A non-staged-decompression dive to 100 ft for 16 min on air serves to illustrate how the algorithm handles the ascent calculation by sequentially updating the allowable supersaturation gradients.

Program Settings

The dive extends to the 16-min NDL predicted by the VPM, with a linear descent rate of 100 ft/min to 100 feet, followed by a linear ascent at 33 ft/min to the first decompression stop.
Plots of the supersaturation gradients Pss are displayed along with decompression tables for the first and final iteration of the VPM program. The gradients are tracked for 1hr after surfacing.
The constants used in the calculations differ from the Yount and Hoffman values (1986 paper).
I used:
Symmetric ZHL-16 half-time set: {4.,8.,12.5,18.5,27.,38.3,64.3,77.,109.,146.,187.,239.,305.,390.,498.,635.} [min]

pp + pp = [atm]
= 0.79
= 0.21
pp = ()

pDeepest = 1 + [ata]
pSurface = 1 [ata]

First iteration

On the first iteration, the following supersaturation was used to calculate a conservative ascent schedule

Pss = 0.54 [atm] for all compartments and all stages.

FIRST ITERATION ASCENT SCHEDULE
    (25 min Total Decompression)

          Depth(ft)   Run-time(min)    

0.`	0.`
0.`

The supersaturation gradients for all 16 compartments are shown below, with red corresponding to 4-min half time, and purple corresponding to  the 635 min half time. After surfacing at a run-time of 41 min, the gradients decay to the inherent-unsaturated value of ~ (0.68 -1) Ata, determined by the choice of alvealor water and carbon dioxide partial pressures.

Final Iteration

After iterations, the set of Pss show dispersion by compartment half-time as determined by the Y&H equations  4a-c.  For each compartment, these are:

The resulting PssNew are tabulated below against ZHL16 compartments:

The ascent schedule converges after four iterations, which subsequently reduce the required decompression (tDeco in eqs. 4) as 24,10,3, and finaly 0 min.
CONVERGED ASCENT SCHEDULE
      (0 minutes decompression)

          Depth(ft)   Run-time(min)  

0.`	0.`
0.`

Plot of the Pss gradients corresponding to the converged ascent schedule