PPRuNe Forums - View Single Post - Mathematically find forward CG limit on the sloping envelope?
Old 16th Feb 2005, 10:26
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john_tullamarine
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Genghis is being a little tough on you Tinny...

In general, if you are looking at a graph of weight against CG, the upper forward limit usually is a sloping straight line (which appears to be your object of interest).

Recall a long ways back to secondary school and the equation for a straight line of known slope m, and vertical intercept b, is

y = m.x + b

A bit of algebraic juggling (and it was rather difficult on this occasion as I have had a number of very nice glasses of wine this evening so do check that I have come up with the correct oranges and lemons ..) gives, for such a straight line passing through known points (x1,y1) and (x2,y2),

m = (y2-y1)/(x2-x1)

b = y1 - m.x1

So, for instance, the straight line through (-6,-33) and (6,3) is

y = 3.x - 15

In the case of the sloping upper forward limit one usually sees in lighties, one can magically call

x = weight and

y = CG

and do the same thing with two known points on the line, albeit this time of the form (w, CG) rather than (x,y).

Keep in mind that, if you are looking at the typical ICAO/GAMA POH chart presentation, the axes are weight and moment (IU, if you prefer) rather than weight and arm. In this case the straight line becomes a parabola and the equation a bit more complicated.

So, good Tinnie .. go forth and put your POH data into a spreadsheet and calculate CG loading things to your heart's desire.

If you check my things above and they don't work out, do let me know and I shall revisit the exercise in the morning ....
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