Andy Ross:
> > If you do mean this equation then I can certainly live with that. If
> > not, I'll need to put my thinking cap on ... I've updated the
> > graphical representation here:
>
> Remind me again which one of these is the "real" engine data, and what
> the source is? The only line on this graph that has the dropoff seems
> to be the polynomial you posted. The others (including the linear
> one) all have better agreement, qualitatively. We can play with other
> forms too, like c((x+1)^e - 1) (for some e < 1, and with a c that makes
> the
> slope through the origin ~ 1).
>

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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
rpm.)
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.
Regards,
Vivian
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