Questions via email
(a) calculating %MAC
This is done as a standard pilot-type CG calculation with a final conversion to %MAC
empty a/c_________EW_______ECG_______EM______EIU
load 1
load 2
......
ramp load_________W___________________M_______IU
CG=M/W
If you prefer to work in IU, then this becomes
CG=(IU*IU constant)/W
To convert CG to %MAC
%MAC=(CG-LEMAC)*100/MAC
(b) checking whether CG is inside/outside the envelope
This requires that you know
(i) the forward and aft limits at the weight of interest
(ii) the loaded CG at the weight of interest
The loaded CG is done as in (a) and the limits are worked out from the envelope. Generally easiest to work in CG rather than moment as the lines usually are either constant limit or straight line variations of limit with weight. If the limit is constant, that is the answer for that weight range, if a straight line variation you use the normal equation to work out the limits ..
For a straight line through points (a,b) and (c,d) the standard straight line equation is
y = mx + n
where
m = (d-b)/(c-a)
n = d - mc (or b - ma, as you prefer)
(You replace x and y with whatever variables are on the axes)
For example, the straight line through (1,1) and (4,10) has
m = 3 and n = -2
where
m = (10-1)/(4-1) = 9/3 = 3
n = 10 - 3*4 = 10 - 12 = -2
or
n = 1 - 3*1 = 1 - 3 = -2
If you were to come across an envelope with curved lines, there are plenty of curve fitting routines available on the net to help you out.
(iii) once you have the limits and the CG, it is a simple matter of checking that the CG lies between the two limits at the weight.
90% of the effort goes into the programming (especially error trapping), not working out the basics ...