Science behind GF

[dmaziuk]

Being physicists or pendants isn't a hobby??

Dangling physicists... gotta wonder if you blame the autocorrupt spillchuker or finger macros?

 

[dmaziuk]

That is what I assumed. Thanks for the reply! So in theory by using GF to add conservatism we are also going a little outside of what little bit of scientific research has been conducted on decompression theory. Again, I like and use GF, I just like to know what I'm doing to the best of my ability.

Not really since you're essentially staying "inside" all the research behind Buhlmann's model. You're just aiming for lower M-values.

If you use GF low to generate longer deeper stops, then you might be in the deep stops study land, but still: it has been researched, there are a couple of studies.

 

[BenjaminF]

Dangling physicists... gotta wonder if you blame the autocorrupt spillchuker or finger macros?

I blame the beer that I was helping to transport from the tap to the world outside the bar

 

[ajduplessis]

The science behind GF is how you apply the gradients to match your physiological makeup and the dive profiles you want to execute. There is no magic number...

 

[Michael Guerrero]

are we not just playing with fire and being test dummies???

Surely you knew this to be true prior to posting this message and irrespective of the replies to this thread .

 

[EFX]

My question to you fine folks is this... Is the rate of off-gassing at a constant pressure (depth and therefore gas pressure) completely linear??? Meaning it would increase due to a greater pressure differential between the absorbed gas in the tissue and the ambient pressure. In theory the greater the differential the faster the off-gassing. In other words, the more supersaturated you are the faster you would offgas said compartment. Is that rate of off-gassing linear from the supersaturation line to the supersaturation max limit for the algorithm?

The reason I ask is say for ease of discussion you have a GF of 50/50 using ZHL16C, If the rate of off-gassing is not a linear increase from the supersaturation line to the max line are we not just playing with fire and being test dummies??? If the rate of off-gassing at 50/50 isn't exactly 50% slower than 100% then how can we be certain we are doing the right thing mathematically?

Here is the constant depth version of the Schreiner equation used to calculate the amount of gas in a theoretical tissue compartment:

P = Po + (Pi - Po)(1 - e^-kt)

where Po equals the initial TC pressure, Pi is the inspired gas pressure, k is the half-time constant, t is the time interval, and P is the final TC pressure. For any interval of time t the resultant final pressure will be proportional to the difference in pressure between the inspired inert gas pressure and the TC inert gas pressure. However, the exponential term makes the rate non-linear. The published numbers for m-value are the pressures (P) upon surfacing equal to a GF of 100 or 100% of the m-value. The GF (Hi) is not a percentage of the rate of on or offgassing but a percentage of the surfacing m-values. Using the Buhlmann ZH-L16C table the surfacing m-value is 47.2 fsw for compartment 10. Assuming a sea level dive and a Pi equal to the pressure at our current depth, a GFHi of 50 means that P cannot be greater than 50% of 47.2 if we wanted to ascend instantly to the surface. The above calculation will need to be repeated for each TC and the TC with the highest pressure will be the controlling compartment for that time interval of the dive.

The equation used in dive computer algorithms is more complicated because there is an additional rate term to correctly calculate P for descents and ascents as well as constant depths. The exponential term e^-kt is used in equations that mimic other natural systems. Are we doing the right thing mathematically? Judging by the amount of dives being done using the Buhlmann tables and applying GF's I'd say yes. Are the results from the model optimal? No, because there are too many other factors that influence the rate of on and off gassing, i.e. hydration, age, physical fitness, injury, etc., that are not included in the calculations.

 

[dave22387]

Here is the constant depth version of the Schreiner equation used to calculate the amount of gas in a theoretical tissue compartment:

P = Po + (Pi - Po)(1 - e^-kt)

where Po equals the initial TC pressure, Pi is the inspired gas pressure, k is the half-time constant, t is the time interval, and P is the final TC pressure. For any interval of time t the resultant final pressure will be proportional to the difference in pressure between the inspired inert gas pressure and the TC inert gas pressure. However, the exponential term makes the rate non-linear. The published numbers for m-value are the pressures (P) upon surfacing equal to a GF of 100. The GF (Hi) is not a percentage of the rate of on or offgassing but a percentage of the surfacing m-values. Using the Buhlmann ZH-L16C table the surfacing m-value is 47.2 fsw for compartment 10. Assuming a sea level dive and a Pi equal to the pressure at our current depth, a GFHi of 50 means that P cannot be greater than 50% of 47.2 if we wanted to ascend instantly to the surface. The above calculation will need to be repeated for each TC and the TC with the highest pressure will be the controlling compartment for that time interval of the dive.

The equation used in dive computer algorithms is more complicated because there is an additional rate term to correctly calculate P for descents and ascents as well as constant depths. The exponential term e^-kt is used in equations that mimic other natural systems. Are we doing the right thing mathematically? Judging by the amount of dives being done using the Buhlmann tables and applying GF's I'd say yes. Are the results from the model optimal? No, because there are too many other factors that influence the rate of on and off gassing, i.e. hydration, age, physical fitness, injury, etc., that are not included in the calculations.

Thank you very much for taking the time to give a well thought out informative response. I'll need to read this one a couple times but so far makes sense.

 

[atdotde]

What you have written is the equation of the tissue pressure as a function of time P(t). But that is not the rate. The rate is the derivative of that with respect to time. To compute that, let's first simplify your expression by expanding out the product to obtain after a cancelation

P(t) = Pi + (Po-Pi) e^-kt

And with a little bit of calculus you find for the rate

dP/dt = (Po-Pi) (-k) e^-kt = -k (P(t) - Pi)

this is a linear (in P) in (P(t)-Pi) actually. The rate of change is being proportional to the difference between the tissue pressure and the inspired pressure. This is what was meant by the original poster. Your Schreiner equation is the solution to this differential equation with P(t=0) = P0.

 

[dmaziuk]

It is linear to half-time. After that it's linear again, to the next half-time, only with a different slope. Rinse, lather, repeat up to six times.

 

[rjack321]

It is linear to half-time. After that it's linear again, to the next half-time, only with a different slope. Rinse, lather, repeat up to sixteen times.

There