> The real data is series 1, but only up to rpm-normalised = 1. For values
> above 1, it's just a continuation by eye of the data.
> (See http://www.turbotechnics.com/supercharger/expo.htm Note that max power
> is at 6500 rpm, and that the supercharger output is nearly flat at 7000
> I selected
> y = -0.25x^3 + 0.15x^2 + 1.11x
> because that had the best fit between 0 and ~ 1.2, which was the region in
> which I was most interested. This was based on the working assumption that
> an engine develops rated power at more or less the full supercharger output.
> At the moment, the equation gives a reasonable match to the known
> performance. All the other curves are possibilities; that's why they are
> there :-).
> I discarded the linear option because of the lack of tail-off, and the other
> polynomial as a poor fit in the operating region. On further consideration,
> perhaps the 'ln' solution doesn't tail off quickly enough, although it's a
> very good fit indeed up to ~1.1.
> So far as I can see supercharger design and matching it to an engine is as
> much art as science, and there are many different options. I'm reasonably
> convinced that the supercharger output should tail off quite sharply after
> max power, otherwise an engine would just go on developing more and more
> power at higher and higher rpm until it broke or the supercharger did!. In
> practice this doesn't happen because the cross section of the inlet is
> carefully chosen.
> I'm sure that you can come up with some more alternatives. Let's try them
> and see if we like them.
IMHO, it's best to use interpolation tables rather than equations if
you're trying to curve fit empirical data. Equations are great for
modeling physical principles (e.g. F=ma), but for something like
this, if you use a table, you can adjust the values to your heart's
content without having to worry about how one adjustment affects other
entries, or how it behaves outside the domain of interest.
Does FlightGear have a format and utilities for table lookups?
Perhaps it's worth developing some if they don't already exist (I'd be
willing to contribute).
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