weight and balance calculation based on that table. In this  problem, the total weight of 2,799 pounds and moment of  2,278/100 are within the limits of the table.  Figure 10-10  is a sample of weight and balance computation  using an aircraft 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 10-11  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.  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 that the 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.  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  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:  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.  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.  Figure 10-11.  Sample weight and balance using an aircraft with a  published zero fuel weight.  Figure 10-10.  Sample weight and balance using a negative.  Weight Shifting  Shifting, Adding, and Removing Weight  Computations With Zero Fuel Weight  Computations With a Negative Arm  The shift has caused the CG to shift to station 78.5.  *Fuel for start, taxi, and takeoff is normally 24 pounds. Item  Weight  Arm  Moment  Basic empty weight  Front seat occupants  3$^{rd}$ & 4$^{th}$ seat occupants forward facing  5$^{th}$ & 6$^{th}$ seat occupants  Nose baggage  Aft baggage  Subtotal  Fuel  Subtotal ramp weight  * Less fuel for start,  taxi, and takeoff  Subtotal  takeoff weight  Less fuel to destination  Actual landing weight   3,230  335  350  200  100  25  4,240  822  5,062  −24  5,038  −450  4,588  292,315.0  29,815.0  44,100.0  31,400.0  1,000.0  4,575.0  403,205.0  92,886.0  496,091.0  −2,712.0  493,379.0  −50,850.0  442,529.0  CG 90.5  89.0  126.0  157.0  10.0  183.0  CG 95.1  113.0  CG 98.0  113.0  CG 97.9  113.0  CG 96.5  Zero fuel weight max 4,400 pounds  Ramp weight max 5,224 pounds  Max landing weight 4,940 pounds  Item Weight Arm Moment Licensed empty weight  Oil (6 quarts)  Fuel (18 gallons)  Fuel, auxiliary (18 gallons)  Pilot  Passenger  Baggage  1,011.9  11.0  108.0  108.0  170.0  170.0  70.0  68.6  −31.0  84.0  84.0  81.0  81.0  105.0  69,393.0  −341.0  9,072.0  9,072.0  13,770.0  13,770.0  7,350.0  Total 1,648.9  122,086.0  CG  74.0  10-10  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  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 