Ah .. progress.
The index equation (#3) makes it clear what is going on as it concatenates the weight with the standard IU calculation.
In a conventional manual tabulation style of calculation one would total weight and IU values taken from tabulated data sheets. The resulting totals would then be plotted on an envelope to test for correct loading.
What the adjusted weight technique does is concatenate the two columns by rounding off the weight entries to make room for the IU values. Innovative but, in my view, not a great deal of value in the field ?
My concerns are -
(a) the technique introduces an increased level of error via round off considerations for both weights and IU.
(b) the technique is so un-intuitive and not amenable to commonsense (sanity) checks by the person running the sums that I would expect an increased level of arithmetic errors and, in all likelihood, some occasional significant error events.
(c) design considerations would need to be constraining to avoid ill-conditioned results and a nonsensical IU total.
(d) error considerations dictate that it not be used for small aircraft
(e) doing the same calculation set via a load and trimsheet for a larger aircraft would provide both better accuracy and quicker results. Indeed, using a load sheet tabulation for weights and a prayer wheel trimsheet for the IU calculations would win hands down every time for speed and accuracy over the adjusted weight technique.
It needs to be kept in mind that a well designed trimsheet is as accurate as a longhand calculation to all practical intents and purposes .. assuming a modest endeavour to execute the working with a little care.
That is to say, the adjusted weight technique is workable ... but why would anyone want to use it ? I just don't see any rational advantage to be gained.
However, I stand by for those who have used such systems routinely to offer contrary comment .. it may well be that my concerns are unduly conservative due to unfamiliarity with using the technique in the field.
I will have to play with #1 and #2 to see what is going on there as the relationships don't offer any immediate understanding.
Perhaps you might define what is meant by
(a) reference weight
(b) BA/trim unit
(c) datum trim unit
(d) BA/%MAC
(e) datum%MAC
as none readily fits with an attempt to start with #3 and derive the other relationships.