First thing to remember is that this stuff is not rocket science by any stretch of the imagination .. just needs a bit of housekeeping to keep the numbers under control ....
the CG%MAC numbers which we can read off the Chart seem off by a tiny bit compared to what we can calculate
The CG (or %MAC) grid is reasonably accurate on this chart .. providing you use the formula as I gave it.
For any of these reverse engineering exercises, there will always be a bit of residual error due to
(a) drafting errors in the chart
(b) reading errors when you are trying to work out what the numbers are against whatever scale you are trying to read
hopeful.... but not too far fetched ??
Stay with it ... there's nothing hard here .. just might take a little while for you to get the hang of what you are doing .. then it all becomes quite easy
x being indices and y the weights
Correct
how to scale it i.e pixels vs Drafted Chart
You will need to be able to program at pixel level .. shouldn't be too hard to find out how to do that on your system.. then it's just a matter of generating a suitable scaling factor .. I haven't needed to do that sort of thing for years ...
Be careful if you are not going to plot point by point .. generally with weight by moment (or IU) loads give straight lines (although the fuel line won't).
Limits for the CG%MAC's
If I follow your concern correctly here .. the AFM will give you a CG envelope .. either FS (or %MAC) against weight. You can convert FS to %MAC (or vice versa) using the standard equations. If you are looking at working out the forward and aft limit at a given weight, the easiest way is to set up equations for the limits from the AFM envelope. Once you have calculated the weight/CG co-ordinate, you can use the weight to calculate the forward and aft limits .. and then test to see if the calculated CG is acceptable or not.
Suggest you work through the problems and pose questions as you need ... my guess is that there will be a few other readers who will maintain an interest in the way one needs to go about this work ....