VPMechanics 3

Copyright 1999-2001 Eric Maiken

Actual Depth vs. Equivalent Air Depth

This notebook considers the role of hydrostatic pressure in setting the allowed VPM supersaturation gradients.

To illustrate the difference between the roles of hydrostatic pressure and tissue tensions in setting ascent profiles in the VPM, two computer-dives are made. The first on 36% nitrox to 100 fsw to the VPM NDL of 29 min. The second on air to the Equivalent Air Depth (EAD) of 75 ft for 29 min NDL, but with ascent on 36% nitrox .
The idea here is, that at the beginning of the ascent, the tissue tensions should be nearly identical. Nonetheless, because the allowed supersaturation gradients Pss are related to the maximum hydrostatic pressure obtained on the dive, there is a difference in the Pss for the 100 ft nitrox and "equivalent" 75 ft air dives. In the range of pressures and mix pp considered, this difference is, however, small.
Note that the conventional definition of EAD is slightly off for this purpose because it neglects the small effects of carbon dioxide and water vapor. Also, even though ascent gasses are identical, there is a small difference in the gas loadings for the travel between the surface and the 100 and 75 foot dives.

Equivalent Air Depth

The equivalent air depth (EAD) is the depth of an air dive that would result in the equivalent saturated pp as a nitrox dive.
This, with the actual depth of the nitrox dive deeper than the EAD of the air dive. Calculation of the EAD is made by neglecting water and carbon dioxide vapor, and setting the saturated pps of the air and nitrox dives equal to one another:
0.79*( +1) = fN2*(+1),  
where the depth units are converted to atmospheres by: [atm] = 10msw or 33fsw.
Solving for EAD in units of feet, we get the standard nitrox EAD relation, or trimix Equivalent Narcosis Depth:
EAD = ( + 33) -33
A plot of this equation is shown below for f = 36% as the green line, with the surface at Dactual = 0 ft. The blue line shows the result for air, where EAD = . The black line is the difference between the actual and equivalent depths. The plot extends from the 117 ft cut-off imposed by the toxicity limiting condition: pp <= 1.6 ata down to 0 pressure absolute ( -33 fsw )-- which is essentially an outer-space fiction.

Nitrox Dive

A 100 fsw dive on 36% nitrox to the 29 min VPM NDL is made.
The minimum supersaturation Pssmin, calculated on the first iteration is related to the dive depth as:
= 0.54 atm,
where Dactual = 100 fsw, and the EAD = 75 fsw.
After 3 iterations, the VPM program calculates the following allowed supersaturations PssNew for the ZHL-16 compartments.

The time dependence of the compartment tensions and supersaturation gradients for the nitrox dive are shown below.
Note that this same set of compartment gas loadings (tensions) applies to the air dive described below.

Equivalent Air Dive

A dive on air to 75 fsw up to the 29 min VPM NDL is made.
The minimum supersaturation Pssmin, calculated on the first VPM iteration is related to the dive depth as:
= 0.49 atm,
where EAD =  75 fsw. However, Because this depth is less than the depth of the nitrox dive, the allowed VPM saturations are lower for the "equivalent" air dive.
After 3 iterations, the VPM program calculates the following allowed supersaturations PssNew for the ZHL-16 compartments.

The time dependence of the compartment supersaturation gradients for the air dive are shown below. Although the compartment tensions are essentially identical for the two dives, the gradients differ until approximately the 60 minute point.