Some time ago I wrote: > > 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). > > > > 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. >
We seem to have got stuck on this one. I haven't pursued it because the Hurricane model wasn't ready. A beta version is now ready. It, along with the Spitfire and P51D need the attached modification to YASim. The diff provides a supercharger output which varies with engine rpm. It assumes that the normalized supercharger output is ~ 1 when the engine is at the nominated peak-power rpm (normalised). A 'power' equation of the form ((A*(B^x))*(x^C) has been derived empirically from some representative supercharger data. This provides near-linear output over the normal operating range, with fall-off in the over-speed situation. It proves an excellent match to published contemporary figures for the Merlin XX in the Hurricane II, and should also do so for other Merlin variants. It allows the engine to over-speed to 2.5 times the nominated peak-power rpm, and will not break beyond this (although the engine/supercharger probably would in real life!). Unlikely, but allows an unexpected YASim configuration. It also provides an additional control - Boost Control Cutout - which overrides the Boost Control (or wastgate in Yasim). The Spitfire, Hurricane and P51D all had this for use in combat. Finally, the diff corrects a minor bug in the output to the property tree and provides a Boost Gauge input. The beta version of the Hurricane IIB is available here: ftp://abbeytheatre.dyndns.org/fgfs/Hurricane/ There is a tarball (hurricane.tgz) or you can grab all the files individually. The diff is also available there. You WILL need to apply this to run the Hurricane, but so far as I can tell, no other YASim model is adversely affected. Some pictures are here: http://myweb.tiscali.co.uk/vmeazza/FlightGear/HurricaneIIb-3.jpg http://myweb.tiscali.co.uk/vmeazza/FlightGear/HurricaneIIb-4.jpg http://myweb.tiscali.co.uk/vmeazza/FlightGear/HurricaneIIb-5.jpg http://myweb.tiscali.co.uk/vmeazza/FlightGear/HurricaneIIb-6.jpg There remains some more eye-candy to do: nav lights, beam approach marker lamps, realistic rad and oil temperature readings etc. In the meantime I would be grateful for any comments, not least that it all downloads and installs correctly! If you do decide to give it a go you'll probably need this: http://home.clara.net/wolverine/BOB/misc/Spit_Hurri_Manuals.zip Regards Vivian
yasim.diff
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