How is the aircraft center of gravity computed and why must it stay within the approved envelope?

• A. CG = sum(weight_i × arm_i) / total weight; must stay within envelope to maintain stability and controllability
• B. CG equals sum(weight_i) × arm_i / total weight
• C. CG equals total weight divided by sum of arms
• D. CG equals sum(weight_i × arm_i) / total weight plus an offset

Answer: (A)

The key idea is that the center of gravity is the balance point of the airplane, found by taking a weighted average of all weights with their distances from a reference point (the arm). You determine where the total weight acts by summing each weight times how far it sits from the datum, and then dividing by the total weight. That gives CG = sum(weight_i × arm_i) / total weight. This location tells you how the airplane will behave in pitch and how much up- or down-pitch force you’ll need to trim and control it.

Why this method is the best: it uses the actual distribution of weight around the aircraft to locate the resultant gravity’s line of action. That line directly affects longitudinal stability (how naturally the aircraft tends to level after a disturbance) and controllability (how much elevator input is required to pitch up or down). If the CG is too far forward, the airplane becomes more stable but harder to rotate and may have higher stall speeds and reduced performance. If the CG is too far aft, stability suffers, and you can lose safe pitch control, even though elevator authority might feel more responsive. The approved CG envelope is the range where the aircraft’s structure, aerodynamics, and control system have been shown to perform safely under expected loading and flight conditions, including takeoff, cruise, turns, and landing. Staying inside that envelope keeps stability, controllability, and structural limits within tested, safe margins.

The other ways of calculating CG are not correct because they don’t produce the proper weighted average. Multiplying the total weight by the sum of arms or adding an offset to the ratio changes the units and the fundamental meaning of the result. The correct formula uses a true weight-armed average and divides by total weight to locate the actual balance point.