PPRuNe Forums - View Single Post - CG formula anyone ?
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Old 6th Jun 2008, 12:34
  #18 (permalink)  
john_tullamarine
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Thanks for the scan ... now we're cooking with gas ...

(a) bit late in the evening to do much tonight but will have a look in more detail tomorrow during the odd coffee break at work

(b) presuming that the A310F has a US TC the TCDS will give me most of the info I need .. any other stuff I will post for you to provide

(c) now clear that you are working not with a trimsheet but a (presumably) tabular system for doing the loading sums (which is all the normal trimsheet trimlines do) and then you transfer the total moments (IU) and weights to the envelope to check if the loading is OK

(d) the loading system envelope appears to be well designed. Notice that, with a bit of imagination, you can describe the envelope as being sort of squarish and boxy ... rather than being like the typical envelope one sees in a GAMA style light aircraft POH.

(e) your "reference point" is almost certainly the loading system datum (which is most usually referred to as a "trim datum" .. doesn't matter what you call it, of course)

(f) the loading system datum is 25% MAC which you can tell by a quick look at the envelope .. how ? .. that CG line is vertical ... at the datum the arm is zero so any weight x arm calculation must give a zero moment (and, in this case, IU)..

(g) the designer appears to have done a conventional error analysis for the load calculations


Now, I presume that what you are looking to end up with is the IU equation for this loading system ? (If not, do describe your goal in a bit more detail).

The IU equation, for just about any system, has the general form

IU = A + ((FS - trim datum) * weight)/B

(you might have some unit conversion constants stuck here and there as well but the form doesn't change ...)

where

IU = index units

A = a constant IU to get rid of the minus numbers on the IU scale. For your system, A=0. If you wanted to get rid of the negatives, you might put A=80 (depending on how long a scale you want to draw ... you only need to make it cover the likely range of entry IU values). If you used 80, then -80 on the scale would become 0, -70 would become 10 and so on.

FS = the (fuselage) station of interest (typically where a load is positioned). In your case, FS will be measured from the main datum (6.3825 m fwd of the nose).

trim datum = a convenient and useful FS value which gives you a suitably shaped CG envelope when drawn wt x IU. It appears that, in your case, this value is 26.67

Note that (FS-trim datum) gives you a revised arm measured from the trim datum rather than from the main FS datum .. no more, no less.

weight = is the weight located at the FS of interest

B = the non-dimensionalising constant moment used to convert the basic moment (=wt*arm) to an IU. You suggested that this value is 1000 .. we can check this out in due course as part of the reverse engineering exercise

Note that, if we put A=0 and don't use a trim datum (put trim datum = 0 .. ie the trim datum is at the FS datum) then the general equation becomes

IU = (FS * wt)/constant

which is the usual

IU = moment/constant

basic formula with which we are all familiar.
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