PPRuNe Forums - View Single Post - Mathematically find forward CG limit on the sloping envelope?
Old 16th Feb 2005, 14:45
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Genghis the Engineer
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I'm having trouble working out what the '+ b' part should be in the formula X=Y m + b, where X is the arm to be found, Y the calculated weight, m the slope & b a constant: Is it the distance up the Y axis where the line would intercept at x=0?
If X=Ym+b, then b=X-Ym.

If you know X and Y for any point, and m (the slope) then it's easy. If you don't know m, then you need two points - we'll call them 1 and 2, so..

(#1) X1=Y1m + b
(#2) X2=Y2m + b

Subtract #2 from #1, and you get...

(#3) X1-X2 = Y1m - Y2m = (Y1-Y2)m

Divide through by (Y1-Y2) and you get...

(#4) m = (X1-X2) / (Y1-Y2)

Plug this back into your original equation and you get...

b = X1 - (Y1*(X1-X2)/(Y1-Y2))

G
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