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Weight and balance is directly related to the stability of the aircraft. Exceeding weight and balance limitations voids any assurance of the aircraft's ability to perform in flight. Instructions and examples can be found in the aircraft manual under section 6 for your specific aircraft.
Introduction. Compliance with the weight and balance limits of any aircraft is critical to flight safety. Operating above the maximum weight limitation compromises the structural integrity of an aircraft and adversely affects its performance. Operation with the center of gravity (CG) outside the approved limits results in control difficulty.
Airplane performance is the capability of the airplane, if operated within its limitations, to accomplish maneuvers which serve a specific purpose. For example, most present-day airplanes are designed clean and sleek, which results in greater range, speed, payload, and increased efficiency.
As variable load items are shifted or expended, there is a resultant shift in CG location. The distance between the forward and back limits for the position of the center for gravity or CG range is certified for an aircraft by the manufacturer.
Both fore and aft Center-of-gravity issues have caused airline crashes in the past although usually not from passengers but rather shifting cargo not properly secured. I am not aware of any sideways loading issues that could not be corrected with aileron (assuming both wings are attached).
In an airplane, the propeller moves and pushes back the air; consequently, the air pushes the propeller (and thus the aircraft) in the opposite direction (forward). This principle applies whenever two things act upon each other.
Each year there are a number of aircraft accidents related to weight and balance issues. Such accidents have occurred due to for instance incorrect loading of the aircraft and the use of wrong takeoff weight for performance calculations amongst others. The present paper gives a review of