Question regarding Baker's Decolessons

[rsingler]

I finally found an answer to this question which came as a "light bulb going on moment" in another thread.

So, for those of us less mathematically facile, please carry your paragraph on to its logical conclusion. The Baker 91% value is now functionally equivalent to its 75% GFHi, because...

Thanks!

 

[dmaziuk]

The Baker 91% value is now functionally equivalent to its 75% GFHi, because...

... apples and, well, not quite oranges... mom's apple pie. M-value is pressure, and "gradient factor" used in this context refers to difference between two pressures. GFHi and GFLow refer to Baker's modification to Buhlmann's a and b coefficients that are dimensionless quantities for use in Buhlmann's formula. They are derived from M-value formula but they are not M-value (edit: and by they I mean Buhlmann's coefficients, not Baker's GFs).

PS here's how "GF 99", "GFHi", "SurfGF", and "GFLo" are related to each other:

'The name of the song is called "Haddocks' Eyes".'

'Oh, that's the name of the song, is it?' Alice said, trying to feel interested.

'No, you don't understand,' the Knight said, looking a little vexed. 'That's what the name is called. The name really is "The Aged Aged Man".'

'Then I ought to have said "That's what the song is called"?' Alice corrected herself.

'No, you oughtn't: that's quite another thing! The song is called "Ways and Means": but that's only what it's called, you know!'

'Well, what is the song, then?' said Alice, who was by this time completely bewildered.

'I was coming to that,' the Knight said. 'The song really is "A-sitting On a Gate": and the tune's my own invention.'

 

[rsingler]

Arrrrrrgh!

 

[Jay]

So, for those of us less mathematically facile, please carry your paragraph on to its logical conclusion. The Baker 91% value is now functionally equivalent to its 75% GFHi, because...

Thanks!

c/d = 91% ,whereas slope_c/slope_d=75%.

 

[rsingler]

c/d = 91% ,whereas slope_c/slope_d=75%.

@dmaziuk , whaddya think?

 

[EFX]

So, for those of us less mathematically facile, please carry your paragraph on to its logical conclusion. The Baker 91% value is now functionally equivalent to its 75% GFHi, because...Thanks!

because.....it's another way to represent the current m-value using a different base in the calculation.

The 91% m-value pressure is relative to 0 pressure with 100% being the maximum m-value. Using a theoretical example let's assume at our depth that ambient pressure is 62% of the maximum m-value. A GFHi of 75% is with respect to ambient pressure which is 0.75 x (100 - 62) ~ 29 or (62 + 29) = 91% with respect to 0 pressure. In this example a GFHi of 75% is equivalent to Baker's max m-value of 91%. The base of GFHi is ambient pressure. The base for the max m-value is 0.

I know this is more math but try to understand it in terms of the graph in figure 3 of Baker's paper "Understanding M-values".

 

[Storker]

c/d = 91% ,whereas slope_c/slope_d=75%.

Which means that c/d varies with whatever ordinate it's plotted against. Or, IOW, that c and d varies differently with whatever ordinate they're plotted against.

 

[FreeFlyFreak]

All this math is hurting my head.

Im still trying to comprehend the different approaches to the M gradient calculations. I have read it, not just here but elsewhere, but I don't fully understand it. It seems to stem from a difference in the way Buhlmann and was it Workman or someone else based their calculations. That is what I vaguely recall.

Would it be fair to say that one method is applicable to calculating for sea level pressure diving only. Whereas the other one can be used for calculations for sea level diving and will also produce results for diving at altitude?
Or am I miss interpreting it.

I guess in the end I don't need to understand, that's why I bought a computer, but I would like to understand.

 

[dmaziuk]

@dmaziuk , whaddya think?

It makes my inner math geek cringe... but as a hand-waving illustration of how the two representation of the same concept may give different numbers, OK.

(To my inner math geek "slope" means derivative and slope_x/slope_y sounds like a second-order derivative and it soo hurtz my brane... make it stop!)

 

[Storker]

All this math is hurting my head.

Well, math(s) is (are) necessary to properly understand these things.

If that makes your head hurt, don't despair. Work through it. And take a couple of Tylenols (as I understand they're called on your side of the pond).