When I took my private in the 70's there was a question about an airplane that was something like 13 lbs and 6in too rearward in cg. The answer required moving a certain amount of baggage to a new location. To pass my test, I randomly chose an answer (worked the calculations) until I found the one that worked.
When I got my A&P license we also discussed this problem. So far as anyone knew at the university, there is no formula or rule of thumb that answers this question, just trial and error.
I am helping a new pilot with this question. Does anyone now of an actual formula that can be used to solve this question? I would hope that there might be a formula that says you can take a 20lb bag and move it from x location and move it y number of inches and end up with a total moment arm of z.
Thx JZ