GF99 = (p_gas - p_amb) / (M - p_amb) x 100
SurfGF = (p_gas - Surf_press) / (M - Surf_press) x 100
In my previous post I forgot to mention that in the GF99 and SurfGF formulas repeated here above, the M is equivalent to a GFHi of 100%. It is NOT equal to the GFHi you set on your dive computer unless you're setting the GFHi equal to 100!
The Shearwater Perdix manual mentions this. The GF99 on a dive computer gives you a real-time indication of how much inert gas your leading tissue compartment has absorbed. SurfGF uses the same m value (100%) but uses the surface as the basis as explained in the preceding post.
You might be asking well OK but where does the GFLo and GFHi come into use. GFLo is used only for deco dives that require an ascent schedule that includes deco stops, usually at equal increments of 10 ft or 3 m. GFLo determines the depth of the first stop. Here is the equation I use in my spreadsheet:
first_stop = ((p_gas - gf_lo * a_n2he) / (gf_lo / b_n2he - gf_lo + 1)) - sp
p_gas is the total inert gas pressure in the leading tissue compartment (LTC).
a_n2he and b_n2he are the combined a and b coefficients for nitrogen and helium.
sp is the surface pressure.
gf_lo is the GFLo value entered pre-dive by the diver.
GFHi is the percentage of Buhlmann's m-value for that LTC and becomes the limiting value upon surfacing. So, the first stop is set by GFLo and the surfacing segment is controlled by GFHi. As an example if the GF was 70/90 and the first stop was 50 ft. The GF progresses from 70 to 90 beginning at 50 ft. The first stop would use a GF of 70. The next stop at 40 ft would use a GF of 74. The next stop at 30 ft would use a GF of 78. 20 ft would use 82. 10 ft would use 86 and the surface would use a GF of 90. You can see this progression in GF on the chart reproduced below from page 14, with the m-value line (orange) running from GFLo at the top right to GFHi at the bottom left. The green line is Buhlmann's m-value line equal to a GF of 100%. The blue line is ambient pressure. Off gassing only occurs above the blue line. The green and orange lines shown below are only shown for one tissue compartment. The dive progresses from top to bottom and right to left along the black line. Where the black line hits the orange line marks the beginning of a stop. As time progresses at the stop the LTC off gasses which is shown by moving down the vertical black line. When the time at the stop is complete, the diver moves shallower to the next stop shown by the black line moving slightly down and to the left until it intersects with the orange line, which is the stop at the next shallower depth and the process repeats until the surface is reached.
Both types of dives (NDL and deco) calculate the ceiling. For deco dives a time is calculated for the current stop using the new GF until the ceiling equals the next shallower stop. NDL (non-deco) dives only use GFHi. There is no first stop so GFLo is not used. For NDL dives a time is calculated to remain at the current depth using GFHi until the ceiling drops from some negative depth (above the water) to zero depth (at the surface). Here's the formula I use from the spreadsheet:
Pamb = (p_gas - common(GF) * a_n2he) / (common(GF) / b_n2he - common(GF) + 1)
new_ceiling = Pamb - sp
For NDL dives common(GF) is equal to GFHi. For deco dives common(GF) is the GF that progresses from GFLo to GFHi as the stops progress from the first stop to the surface. The pressures calculated in the spreadsheet are absolute so subtracting the surface pressure converts absolute pressure to gauge pressure which is essentially the depth (negative if NDL, 0 at the surface, positive for deco dives).
If you're wondering about that last sentence, i.e., how a pressure can be a depth read the next section which was taken right out of the dive spreadsheet help page.
UNITS OF PRESSURE
All pressure values on the ss are displayed as absolute pressures in feet or meters of salt or fresh water rather than the typical units of psi (imperial) or Kpa (metric). This seems odd at first because a distance unit (feet or meters) is used to define a pressure unit. What seems even stranger is that the gauge pressure is equal to the depth in feet or meters. To understand why this is true consider this relationship:
33 fsw/33 ft (or 10 msw/10m). We can describe it this way: there is a pressure of 33 fsw which is equivalent to a pressure exerted by 33 ft (depth) of water. The spreadsheet converts depth to a pressure in order to calculate insP, the inspired inert gas pressure. For example, to convert 80 ft of depth to its equivalent gauge pressure (P) in fsw we could write: P = 80 ft x 33 fsw/33 ft. As a sanity check on the math the ft divide out leaving fsw which is what we want. The really interesting part is that the 33 divides out giving us an answer that is actually the depth but in pressure units of fsw. This is convenient because it eliminates the need to use cumbersome unit conversions in the formulas. Absolute pressures are obtained by adding the pressure of the atmosphere at the surface to the pressure exerted by the water (which is gauge pressure).
I know this is a lot to absorb but I thought I would give you a more complete picture of GF's and how they are used in dive programs (at least mine anyway).