Heat map timing and colours

Rick Walsh rickmwalsh at gmail.com
Tue Oct 4 18:40:26 PDT 2016

Hi Willem,

Your deduction of the colours is close.  Most significant point is that the
"offgassing" colours are relative to the M value (i.e. that used when GF =
100/100), rather than the specified gradient factors (or VPM-B
conservatism).  Making it relative to the M value makes it easier to
compare different profiles using the same scale.  E.g. comparison of deco
profile with deep stops (e.g. GF 30/85 or VPM-B) vs no deep stops (e.g. GF
= 80/80), which is what was done in the Simon Mitchell presentation.

On 4 October 2016 at 22:45, Willem Ferguson <willemferguson at zoology.up.ac.za
> wrote:

> I did some measurements on the heat map after the latest release
> (5.2-1640-gb3a0ab dated Oct 3rd) which I assume is the 4.6 beta release and
> which incorporates Robert's latest patch.
> Attached two dives using the Buehlmann algorithm. The time difference
> between events in the the heat map and those in the dive profile looks to
> be more or less constant during a dive. In dive 1 (attached) the difference
> is approx 100 seconds, while in dive 2 (attached) the difference is about
> 65 seconds. However, in both dives the difference is close to 35 horizontal
> pixels.
> With respect to the colours used in the heat map, I deduce the following:
> Light blue:  Inert gas tissue pressure far below ambient inert gas
> pressure and close to pressure when dive started.
technically the colour is cyan, but light blue is a good enough description

> Dark blue:  Some ongassing has occurred but tissue pressures still far
> below ambient pressure.
not actually dark, but an intense blue

> Purple:       Tissue gas pressure approaches that of the ambient inert gas
> pressure.

> Black:         Tissue gas pressure roughly equal to ambient gas pressure.
actually at ambient pressure * fraction N2 in air, so equal to where you
tissues end up breathing air on the surface

Grey-green: Tissue gas pressure greater than, but close to ambient pressure.
actually about ambient pressure

> Bright green: Tissue gas pressure significantly above ambient pressure but
> below Gradient factor limit. Efficient offgassing is taking place in the
> tissue groups in

tissue slightly above ambient pressure: GF = 10%

> green.
> Green-yellow: Tissue gas pressure approximately at limit imposed by
> gradient factor.
> Yellow:           Tissue gas pressure exceeds limit imposed by gradient
> factor.
tissue at GF = 55%

> Orange ?      Approaching GF100 gas pressure   ???
> Red ?            Exceeding GF100 gas pressure   ???
tissue at GF = 100%

Below ambient pressure, the value is the scaled from the ratio (inert
tissue saturation) / (ambient pressure).
Above ambient pressure, the value is relative to the M value

The exact points on the colour scale are interpolated between points on the
HSV (hue, saturation, value) colours scale

Tissue pressure below ambient pressure points are:
tissue pressure negligible relative to ambient pressure (rapid descent to
depth): "bright" cyan (HSV = 180 deg, 1, 1)
tissue pressure ~ 53% of (ambient pressure * fraction inert gas in air):
"bright" blue (HSV = 240 deg, 1, 1)
tissue pressure = 80% of (ambient pressure * fraction inert gas in air):
"bright" purple (HSV = 270 deg, 1, 1)
tissue pressure = (ambient pressure * fraction inert gas in air): black
(HSV = 270 deg, 1, 0)    <---- this is special because it is where your
tissues end up if you breath air on the surface
tissue pressure = ambient pressure: "medium" green (HSV = 270 deg, 1, 0.68)

Tissue pressure above ambient pressure points relative to M value (tissue
"gradient factor") are:
10% of M value = "bright" green (HSV = 120 deg, 1, 1)
55% of M value = "bright" yellow (HSV = 60 deg, 1, 1)
100% of M value = "bright" red (HSV = 0 deg, 1, 1)
140% of M value = white (HSV = 0 deg, 0, 1)

I hope you never see the colours beyond red in an actual dive - but you can
in a test plan if you set GF > 100%, or VPM-B with zero conservatism and a
deco dive with a reasonably long bottom time, which can result in an
equivalent GFhigh >100%.

> In the user manual, I would like to but an example of the gas pressure
> graph in the Information box next to the representation of the same instant
> as a vertical slice through the heat map. In order to do that, one needs to
> understand the colours.

That's a good idea.  The colour graph and pressure graph in info box are
calculated from the same variable.  The equivalent points and colours in
that graph are
GF 100 (top line) = red in tissue plot (HSV = 0 deg, 1, 1)
GF = 0 (inert gas equilibrium pressure) = "medium" green (HSV = 270 deg, 1,
base of graph = tissue pressure relative to ambient pressure negligible =
cyan (HSV = 180 deg, 1, 1)

Note that the variable being plotted in both cases is actually
entry->percentages[j], which is on its own special scale, where 50 equates
to zero gradient, and 100 equates to M value (c code copied below).  In the
descriptions above, I have back-calculated it to gradient factors and
tissue pressure to ambient pressure ratio.

1021                         for (j = 0; j < 16; j++) {
1022                                 double m_value =
buehlmann_inertgas_a[j] + entry->ambpressure / buehlmann_inertgas_b[j];
1023                                 entry->ceilings[j] =
deco_allowed_depth(tolerated_by_tissue[j], surface_pressure, dive, 1);
1024                                 entry->percentages[j] =
tissue_inertgas_saturation[j] < entry->ambpressure ?
tissue_inertgas_saturation[j] / entry->ambpressure * AMB_PERCENTAGE :
AMB_PERCENTAGE + (tissue_inertgas_saturation[j] - entry->ambpressure) /
(m_value - entry->ambpressure) * (100.0 - AMB_PERCENTAGE);

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