Shifting CG

[jwzumwalt]

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

[martymayes]

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

JZ, the FAA put those problems in the test then hid behind a one-way mirror so they could watch the smoke come out of the poor students ears.


Shifting weight is not too bad because the total weight does not change. So it would be:

weight shifted / total weight = change in cg. / distance weight was shifted

(sorry for the formatting) You know the amount weight being shifted, total a/c weight and distance the wt. is shifted; just solve equation for change in c,g,


Probably a better way to explain it to a student is showing what happens mathematically. Calculate moment of the item in current location (weight x arm); then calculate moment of item in new location. The difference in the two moments is the moment change which is then added to the total moment (depending on which way the bag was moved, it's added or subtracted). New c.g. location is new total moment divided by total weight.

That fits in better with the wt x arm = moment which is how they learn basic wt. & bal. and better than rote learning a formula.

[dougbush]

From where it was to 16" forward of that.

[Gunslinger37]

Easy to get the answer on a circular slide rule (E6B).

[martymayes]

Easy to get the answer on a circular slide rule (E6B).

yes it is...just set up calculator side so that -- weight shifted / total weight = change in cg. / distance weight was shifted

[jwzumwalt]

Ok I worked a scenario and it does work.

shift weight cg change dist
-------------- = ----------------
total weight shift dist

Ratios can be re-written using the cross product

shift dist = (total weight * cg change) / shift weight

also

shift weight = (total weight * cg change) / shift dist

1980 C152
1500lbs * 33.9in = 50,850 moment
100lbs * 84in = 8400 moment
cg = 37in = (50,850+8400) / 1600lbs

We want to move 100lbs so the cg is moved 1in.

shift dist = (total weight * cg change) / weight shifted
16in = (1600lb * 1in) / 100lb

Reworking the problem with 100lbs moved from 84in to 68in does move the cg 1in.

[jwzumwalt]

Oh... E6B... isn't that the new solar powered Apple Ipod?