Finally back onto this one ...
First, it appears that your suggested trim datum (reference position) of 26.67 m (equivalent to 25.275% MAC) is not quite on the mark. Possibly, you quoted from a company document which, at some time in the past, has had a typo sneak into the story. One of the problems with any imperial/metric conversion is round off and/or conversion factor errors .. just one of the problems with which we have to contend.
Working just with the MAC grid, the most reasonable story for this system is ..
IU = (FS - 26.654) * weight / 1000
where the system is metric .. ie FS in metres, weight in kilogrammes, and moments in kg.m. Note that IU has no dimension and is just a number.
Derivation follows a simple logic of fitting the observations to the standard equation.
The standard equation is
IU = A + (FS - TD) * weight / NDC
where
IU = trimsheet entry IU.
A = a constant IU used to "shift" the entry scale to get rid of negative IU values. Note that A is only relevant to the entry line and envelope and doesn't figure in delta IU calculations for the loading position trim lines. For the present loading system, where the zero IU coincides with the trim datum, A = 0.
FS = loading arm referred to the OEM "standard" datum ie a fuselage station
TD = trim datum. The purpose of using a trim datum is to change the datum for internal loading system calculations. This is only of use for graphical systems and provides the opportunity to give the best graphical execution accuracy. The TD can be seen most easily if the trim sheet has an overlay CG grid. The CG line which is vertical on the sheet is the trim datum position. For the present system, the trim datum is 25% MAC, which corresponds to a fuselage station of 26.654 m.
weight = the weight located at the loading arm, FS
NDC = a non-dimensionalising constant IU, used mainly to make the numbers a bit more manageable . .especially if the system is worked in millimetres ... For this system, NDC = 1000 kg.m
To work out the value of the numbers, read off some MAC co-ordinates as accurately as you can do reasonably.
For my calculations, I imported the chart into a drafting package, squared the scan, and then scaled off the co-ordinates directly. (Note that the chart, while being quite neat in its drawing, is not well drafted as the scale is a bit variable across the sheet).
My read-off IU values were
%MAC______18_______29_______40
FS value__26.246___ 26.887____27.528
weight
150,000___-60.93____35.20____131.29
70,000____-28.70____16.35_____61.46
(apologies for the underscores .. I've forgotten how to script tabs)
Rearranging the standard MAC equation
%MAC = (FS - LEMAC)*100/MAC
gives
FS = (%MAC * MAC/100) + LEMAC
to convert from the known %MAC to the equivalent FS
The FS and weight values can be fed into the system equation
IU = (FS - 26.654) * weight /1000
to come up with calculated IU values.
For the present system, the equation fell out near immediately. Sometimes you will need to play with the calculations a bit until things start to make sense. This is best done in a convenient spreadsheet package. You may need to play a bit with conversions kg/lb and in/ft/m/mm as well as the NDC value until the numbers start to make sense. If there is no CG grid, an indication of the TD will come from consideration of the envelope lines and may require some iteration to get sensible numbers. In any case, the numbers usually fall out within a couple of minutes work ..
Comparing the calculated values to the values read off from the sheet gives "errors" (delta between read and calculated values) in the range -0.1 to +0.3 IU .. ie functionally zero.
If we had used the suggested trim datum of 26,67, the "errors" move to values in the range +1.0 to +2.7 which is a bit strange as there is no central zero tendency in the distribution.
As the TCDS doesn't give any envelope data, I can only look at the MAC grid but I am pretty confident that the equation suggested will fit when you check the envelope against the AFM envelope data.