Question

How do you calculate the weight shift required to bring the CG within limits?

A) w/W = D/d (W to move/W of acft = Dist to move CG / Dist to move arms)
B) W/w = d/D (W of acft/W to move = Dist to move arms / Dist to move CG)
C) D/d = W/w (Dist to move CG / Dist to move arms = W of acft / W to move)
D) d/D = W/W (Dist to move arms / Dist to move CG = W to move / W of acft)

Answer 1

To calculate the weight shift required to bring the CG within limits, use formula A) w/W = D/d, where w is the weight to move, W is the total weight of the aircraft, D is the distance to move the CG, and d is the distance of the arms.

Step-by-step explanation:

To calculate the weight shift required to bring the CG within limits, the correct formula is expressed as the ratio of the weight to move (w) to the total weight of the aircraft (W) being equal to the ratio of the distance to move the center of gravity (D) to the arms distance (d). Therefore, the correct formula from the given options is A) w/W = D/d. This can also be written as w = (W * D) / d. This formula is derived from the understanding that weight is mass times the acceleration due to gravity. When considering moments about a pivot point to balance, the moment caused by the weight to be moved must counteract the offset of the center of gravity (CG) from the desired location.

As an example, assume the total weight of the aircraft (W) is known, and the distances D (to move the CG) and d (the arm where weight is added or removed) are given. By rearranging the formula for w, the calculation for the precise weight shift needed to adjust the center of gravity can be made.