## Pilot's Handbook of Aeronautical Knowledge Weight and Balance Determining Loaded Weight and CG

 Pilot's Handbook of Aeronautical Knowledge Preface Acknowledgements Appendix Glossary Index Computations With a Negative Arm Figure 9-10 is a sample of weight and balance computation using an airplane with a negative arm. It is important to remember that a positive times a negative equals a negative, and a negative would be subtracted from the total moments. Figure 9-10. Sample weight and balance using a negative. Computations With Zero Fuel Weight Figure 9-11 is a sample of weight and balance computation using an aircraft with a zero fuel weight. In this example, the total weight of the aircraft less fuel is 4,240 pounds, which is under the zero fuel weight of 4,400 pounds. If the total weight of the aircraft without fuel had exceeded 4,400 pounds, passengers or cargo would have needed to be reduced to bring the weight at or below the max zero fuel weight. . Figure 9-11. Sample weight and balance using an aircraft with a published zero fuel weight. Shifting, Adding, and Removing Weight A pilot must be able to solve any problems accurately that involve the shift, addition, or removal of weight. For example, the pilot may load the aircraft within the allowable takeoff weight limit, then find a CG limit has been exceeded. The most satisfactory solution to this problem is to shift baggage, passengers, or both. The pilot should be able to determine the minimum load shift needed to make the aircraft safe for flight Pilots should be able to determine if shifting a load to a new location will correct an out-of-limit condition. There are some standardized calculations that can help make these determinations. Weight Shifting When weight is shifted from one location to another, the total weight of the aircraft is unchanged. The total moments, however, do change in relation and proportion to the direction and distance the weight is moved. When weight is moved forward, the total moments decrease; when weight is moved aft, total moments increase. The moment change is proportional to the amount of weight moved. Since many aircraft have forward and aft baggage compartments, weight may be shifted from one to the other to change the CG. If starting with a known aircraft weight, CG, and total moments, calculate the new CG (after the weight shift) by dividing the new total moments by the total aircraft weight. To determine the new total moments, find out how many moments are gained or lost when the weight is shifted. Assume that 100 pounds has been shifted from station 30 to station 150. This movement increases the total moments of the aircraft by 12,000 in-lb. Moment when at station 150 = 100 lb x 150 in = 15,000 in-lb Moment when at station 30 = 100 lb x 30 in = 3,000 in-lb Moment change = [15,000 - 3,000] = 12,000 in-lb By adding the moment change to the original moment (or subtracting if the weight has been moved forward instead of aft), the new total moments are obtained. Then determine the new CG by dividing the new moments by the total weight: Total moments = 616,000 in-lb + 12,000 in-lb = 628,000 in-lb CG = 628,000 in-lb = 78.5 in 8,000 lb The shift has caused the CG to shift to station 78.5.

9-10