# W&B question

#### JrsyGuy

##### Well-Known Member
Im working on my ATP written and im actually trying to learn how to do these these questions rather then just memorizing everything. There are a bunch of weight and balance problems that talk about index arms. I understand MAC and LEMAC and %MAC but i cant figure out how index arms factor into all of it.

just an example question:
What is the new CG if the weight is shifted from the forward to the aft compartment under loading conditions W-5?

The table provides this info for W-5:
Loaded weight = 88,300
Loaded CG(%MAC) = 25.5%
Weight change(lbs) = 3,300
Forward compartment centroid - STA 352.1 and -227.1 index arm
Aft compartment centroid - STA 724.9 and +144.9 index arm
MAC 141.5 inches, LEMAC STA 549.13, and -30.87 index arm

the answer choices are
A. +19.15 index arm
B. +13.93 index arm
C. -97.92 index arm

Since im using gleim to study they tell you the formulas and such to get the answer but i just dont understand what index arms are. The answer is A by the way.

#### tgrayson

##### New Member
i cant figure out how index arms factor into all of it.
I've never worked the ATP W&B problems, but, according to the FAA Weight and Balance Handbook, the index arm is just the arm, like you used in GA aircraft. In the problem you provided, looks like it lies a bit behind the LEMAC. My guess is that it's intended to lie near the 1/4 chord point, which is where the aerodynamic center is located. The relationship of the CG to this point determines the longitudinal static stability of the aircraft.

I worked the problem successfully using the index arms as the arms, although I had to derive the index arm for the current CG location. (Actually, I got 19.11 as the final answer.) There's probably an easier way to do the problem.

#### JrsyGuy

##### Well-Known Member
I thought the STA number was the number used as the arm. There are other problems elsewhere in the exam that talk about using the station number as the regular arm.

#### tgrayson

##### New Member
I thought the STA number was the number used as the arm. There are other problems elsewhere in the exam that talk about using the station number as the regular arm.
You can choose as an arm anything whatsoever. I demonstrated to a student that you could use the moments based on the distance of the object in the airplane to downtown Boston and still get the right answer.

The station and the index arms are arms calculated from different locations. What's important is how your data in the AFM are presented. If you work the problem using the stations, I get an index arm of 19.145, which is slightly closer to the printed value. The difference is due to rounding.

#### JrsyGuy

##### Well-Known Member
ok i get it now. For anyone else reading this it might help if you take the difference between the fwd and aft station centroids and then take the difference between the aft and fwd compartment index arms and its the same number as tgrayson was alluding to. thanks for the help