🚀 go-pugleaf

In article <see-6C28F8.14281106102009@mail.eternal-september.org>,
 Barb Knox <see@sig.below> wrote:

> In article <EK-dnV5FoYzmRFTXnZ2dnUVZ_jKdnZ2d@westnet.com.au>,
>  Adam Nielsen <a.nielsen@remove.this.shikadi.net> wrote:
> 
> > > Note that for A >= 16, doubling A also doubles B'.
> > > The best fit is
> > >     B' = A/16 * 1.91, truncated to 1 decimal place.
> > > 
> > > 1.91/16 = 0.119375,
> > > and your rational approximation for that is 
> > >     1/10 + 1/52 = 31/260 = 0.1192307
> > > 
> > > Note that there are closer rational approximations, but any one that 
> > > provides the correct B' values to 1 decimal place is close enough.
> > 
> > Ah, glad to see I was close!  Thanks again.  I've got all the current 
> > values
> > sorted now, but I've discovered that the fan speeds seem to be reported on
> > some sort of logarithmic scale:
> > 
> >    A  |  B
> > ------+---------
> >   128 | 8943 RPM / 943 RPM *
> >   144 | 9727 RPM *
> >   256 | 5493 RPM
> >   512 | 2746 RPM
> >  1285 | 1094 RPM
> >  4096 | 343 RPM
> >  8192 | 171 RPM
> > 65535 | 21 RPM
> > 
> > I'm not 100% sure about the first two values (marked with *) because the
> > values were so large I'm not sure the manufacturer's program was drawing 
> > them
> > on the screen properly.
> > 
> > I *think* this is logarithmic - I can get an approximation of the curve 
> > using
> > variations of -log(x), but I'm afraid that's as far I as can remember :-)  
> > If
> > it's possible, an approximation using "simpler" operations (+, -, *, /) 
> > would
> > be even better from a runtime efficiency point of view!
> 
> A little hacking around in Excel shows that this is a log-log 
> relationship.  In particular:
>     log_2(B) = 20.44592638 - 1.002677224*log_2(A)
> with a maximum absolute error of 0.010795444
> 
> With these coefficients, the B value for A=128 would be 11015.

Oh bother.  I failed to appreciate the fact that -1.002677224 is 
probably close enough to -1 for this problem, so the log-log power 
relationship between B and A could be a simple reciprocal.  And indeed, 
here's an exact formula for the non-starred values that does not use 
logs:
    B = int(1406315/A)

With this formula, A=128 gives B=10986, and A=144 gives B=9766.


> > Thanks again,
> > Adam.
> 
> HTH

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