This thread is starting to confuse me mightily. It may be that folk are being a little lax in the use of terminology .. and, I note, I am regularly guilty of the same .. However, the subject material is pretty important to flight safety so it is worth gnawing at the bone until we get it sorted out ..
The bold figures are the balance units (%MAC) concatenated with the weight
I suggest not.
%MAC is just another way of writing CG.
One cannot add CGs of loads to end up with a final figure with any sense. The addition has to be one of either moment or IU.
The bold figures, presuming they are IU, can be derived easily if one has, as the IU equation, a trim datum of 905 and a IU constant of 225000. This equation may not be precise as we only have three examples to play with, With a few more example combinations. it could be refined quite easily.
When these adjusted weights are summated, they provide both an aircraft weight, indicated by the digits to the left of the decimal point, and the Centre of Gravity (C.G.) value, indicated by the right hand digits
So far, searches of the net and this thread have given nothing concrete as to the derivation of the method (other than for the index equation which is quite conventional). Probably, I am going to have spend some time trying to make sense of the two other "equations" cited in the earlier post ...
Unless someone can present a rational derivation, it is my present contention that you cannot add CG values to get any sensible result ....
The essence of the Adjusted Weight Index Loading System (AWIS) is that balance units (expressed to one decimal place), are added to each element of weight on the Load Manifest, to give adjusted weights.
When these adjusted weights are summated, they provide both an aircraft weight, indicated by the digits to the left of the decimal point, and the Centre of Gravity (C.G.) value, indicated by the right hand digits.
Balance Units are increments of moment about a reference datum
(My bolding)
You can't have it both ways .. what are balance units ? CG or moment values ?
Balance Units are increments of moment about a reference datum, and at take-off they correspond closely to Mean Aerodynamic Chord (M.A.C.).
At the risk of offending, I suggest that the second part of your statement is nonsensical. The MAC is a fixed length so, if your statement were to be corrent, balance units would be invariant and pretty meaningless ? If you mean %MAC, then how does one relate a moment to a CG .. other than to the extent that, as the moment increases in number line magnitude (ie to the right), the CG moves aft ?
The datum must be selected and is normally a typical take-off weight with a lever arm located at the aircraft Centre of Gravity datum
Again, this appears to be nonsense. Datum is a position on the fuse station line .. ie a distance from somewhere else but, now, you are suggesting it is a weight ?
An example Datum for a B767-200 would be :-
320000.0 lb. 24.0 % M.A.C.
Balance units will correspond exactly to % M.A.C. at the above datum weight
The datum might well be 24%MAC but has naught to do with 320000lb. Can you provide the balance units value for your example and that might lift the veil of confusion somewhat ?
yours in confusion .... JT