On 3 March 2016 at 05:15, Linus Torvalds <[email protected]> wrote: > On Wed, Mar 2, 2016 at 6:45 PM, Linus Torvalds > <[email protected]> wrote: >> >> But having looked at the profiles, the "nosedive" happens closer to >> 450 bar (and only for oxygen at that). And it may not be great at 400 >> bar, but it's not a disaster. > > Google is actually better at graphing this than wolfram alpha. Wolfram > has some low limit on the size of the cut-and-paste. > > I pasted this nasty-ass expression into google: > > y = > 1.0002556612420115-0.0003115084635183305*x+0.00000227808965401253*x^2+1.91596422989e-9*x^3-8.78421542e-12*x^4+6.77746e-15*x^5 > > -0.21*(1.0002231211532653-0.0007471497056767194*x+0.00000200444854807816*x^2+2.91501995188e-9*x^3-4.48294663e-12*x^4-6.11529e-15*x^5) > > -0.79*(1.0001898816185364-0.00030793319362077315*x+0.00000327557417347714*x^2-1.93872574476e-9*x^3-2.7732353e-12*x^4-2.8921e-16*x^5) > from 0 to 500 > > which is the difference between our air polynomial (good to 500 bar) > and the linear combination of the oxygen and nitrogen polynomials > (each should be good to ~275 bar). > > The thing actually looks *really* good. The difference is basically > less than 0.005 up to 200 bar. > > Even up to 275 bar, the error is less than one percentage point. Now, > notice the difference between "one percent" and "one percentage > _point_". > > At 275 bar, the real Z factor should be 1.087 according to Wikipedia. > The linear mixing gives us 1.078. > > However, even that almost one percentage point difference turns out to > be not because the linear mixing doesn't work. Just taking the _air_ > plots from baue.org shows that baue says 1.079 for air at 275. > > So the linear mixing actually matches the baue air compressibility > factor almost exactly. It's just that baue.org and the Wikipedia > tables don't agree at 275 bar. >
like you said in the other thread, the AIR @ baue.org could be an actual gas mix calculation. being able to skip one measurement is a pretty big time saver for the one who is doing the quantization. > And then it starts growing, but at t 300 bar the difference is still > just 0.012. So it's one percentage point off: the proper Z factor > value for air is 1.108, and the "linear mixing" version is at 1.097. > That strikes me as "not perfect, but it's damn close to good". > > At 400 bar, we're about 4 percentage points off, which is not great > (the real Z factor is 1.20, the linear mixing is at just 1.166). I > suspect the linear mixing is still reasonably fine, and we're seeing > an effect of the curve fitting starting to fail more. > > At 500 bar, the error is big. I still don't blame the linear mixing, > that's just the Oxygen curve that is way off at that point because the > last table point was 275 bar. > things are looking good, up to the reasonable ranges. i'm sorry i didn't do the mix comparison, but it was 4-5AM already. > My takeaway from this: > > - the linear mixing seems to work very well at least for air. > > - it starts getting less precise at some point past 200 bar, but even > at 300 bar the error is arguably more due to the difference from > Wikipedia to Baue rather than anything else. > > - google is pretty good at graphing, and it's pretty easy to just > cut-and-paste your functions like the above. > > Anyway, it all looks quite reasonable. I have very little reason to > believe that the code doesn't give us way more accuracy than anybody > will ever need. > just in case, i've just emailed the chief science officer @ baue.org to see if the have some more secret data - i.e. just a single measurement at 500 bars for all gases would make all the functions marginally better. but, i have the suspicion that they took the data from a website which isn't online anymore. lubomir -- _______________________________________________ subsurface mailing list [email protected] http://lists.subsurface-divelog.org/cgi-bin/mailman/listinfo/subsurface
