PPRuNe Forums - View Single Post - help with some relevant maths for perf calcs
Old 4th Dec 2004, 11:44
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enicalyth
 
Join Date: Jul 2004
Location: Sydney NSW
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designing an FF emulator

Evening All,

An insight into what has worked for me in the past.

I've always had to hand lift/drag polars or a means of deriving them very closely. If stallie lives in Podea the lissys website unwittingly gives some useful information for free. Mebbe one of the examples is his aircraft! saves $45k!! Please do not use Boeings or Eurocontrol's BADA drag polars as these are estimates for deconfliction situations and even by their own estimates can be 25% wrong!


Starting with a stab at cd0 it follows from CL pretty much what CDi is and initially a straight guess at CDcc (try Stanford University site for all these or Richard Shevell's textbook) allows you to deduce from FF what sfc is.

If the engine maker gives a cruise sfc, say 35,000ft ISA, increase it slightly 2-3% eg B747 0.59, B777 0.57, A320 0.67 for intake/bleed/pack losses proceeding to refine your drag equation using a number of points on the envelope.

By and by with a few passes you have increasing confidence in your drag equation because your deduced sfc values conform ever more closely with engine makers figures, offset slightly to account for intake losses and bleed as I've hinted. Everything is tied of course still to published FF at spot "locations".

It really doesn't take long. You use look-up tables of speed, weight and altitude to direct you to a manual FF figure. The first three help you derive CL and CDi and you can quickly reconcile your preferred value for CD0 with your CDcc algorithm if deduced sfc becomes wildly erratic. Then..

This allows you after one or two drafts to create another look-up table of deduced and believable sfc values, pinned to maker's values and broadly speaking within a tight std dev at all quoted cruise values. They may be slightly erroneous but provided that you don't change the CD0 and CDcc estimation from which they derived the spreadsheet will return you to fuel flow accurately.

I then smooth these deduced sfc values with any good line regression technique. Then...

Now that I have the tables, including a compressibility drag algorithm, to draw up FF anew based on Breguet's equation I can test the hypothesis that my figures, as samples, fit the POH population. that's page 1.

Page 2 is just a spreadsheet of more intimate jet mechanics to model engine performance and begin to feed in non-ISA temperatures. Search for Rogers & Mayhew, Saravannamuttoo; Hill & Petersen; and of course, the inestimable Richard S Shevell late of Douglas Aircraft and this world.

I've had a fair degree of success with this. For visual presentation I use the same graphical software as the www.glass-ware.com people do for their hi-fi tubes. Then as you drag you mouse about, for any set of givens eg speed, weight, height, temperature you have a readout of L, D, sfc, NAM/1000lb, lb/hr, etc etc. And it all interpolates FF smoothly and accurately.

Last edited by enicalyth; 4th Dec 2004 at 11:56.
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