A simpler solution may be obtained by using a computer  or calculator and a proportional formula. This can be done  because the CG will shift a distance that is proportional to  the distance the weight is shifted.  In many instances, the weight and balance of the aircraft will  be changed by the addition or removal of weight. When this  happens, a new CG must be calculated and checked against  the limitations to see if the location is acceptable. This type  of weight and balance problem is commonly encountered  when the aircraft burns fuel in flight, thereby reducing the  weight located at the fuel tanks. Most small aircraft are  designed with the fuel tanks positioned close to the CG;  therefore, the consumption of fuel does not affect the CG to  any great extent.  The addition or removal of cargo presents a CG change  problem that must be calculated before flight. The problem  may always be solved by calculations involving total  moments. A typical problem may involve the calculation  of a new CG for an aircraft which, when loaded and ready  for flight, receives some additional cargo or passengers just  before departure time.  Operating an aircraft within the weight and balance limits  is critical to flight safety. Pilots must ensure that the CG is  and remains within approved limits throughout all phases of  a flight. For additional information on weight, balance, CG,  and aircraft stability refer to the FAA handbook appropriate  to the specific aircraft category.  In the previous examples, the  r CG is either added or  subtracted from the old CG. Deciding which to accomplish is  best handled by mentally calculating which way the CG will  shift for the particular weight change. If the CG is shifting  aft, the  r CG is added to the old CG; if the CG is shifting  forward, the  r CG is subtracted from the old CG.  Chapter Summary  Weight Addition or Removal  10-11  Example  The change of CG is added to (or subtracted from when appropriate)  the original CG to determine the new CG:  77 + 1.5 = 78.5 inches aft of datum  The shifting weight proportion formula can also be used to determine  how much weight must be shifted to achieve a particular shift of the CG.  The following problem illustrates a solution of this type.  Weight shifted  Total weight  ∆CG (changGLYPH<df00> of CG)  Distance weight is shifted  =  100  8,000  ∆CG  120  =  ∆CG  1.5 in =  Example  Determine how much cargo must be shifted from the aft cargo compart-  ment at station 150 to the forward cargo compartment at station 30 to  move the CG to exactly the aft limit.  Solution:  Weight to be shifted  Total weight  CG  Distance weight is shifted  =  Weight to be shifted  7,800 lb  Weight to be shifted  1.0 in  120 in  =  65 lb =  Example  Solution:  Subtract ∆CG from old CG  NGLYPH<df00>w CG = 80 in − 1.2 in = 78.8 in  Weight removed  New total weight  ∆CG  DistancGLYPH<df00> bGLYPH<df00>twGLYPH<df00>GLYPH<df00>n wGLYPH<df00>ight and old CG  ∆CG  150 in − 80 in  =  100 lb  6,100 lb − 100 lb  =  100 lb  6,000 lb  =  ∆CG  70 in  CG  1.2 in forward =  DGLYPH<df00>tGLYPH<df00>rminGLYPH<df00> thGLYPH<df00> location of thGLYPH<df00> CG if 100 pounds is rGLYPH<df00>movGLYPH<df00>d from station 150.  Add ∆CG to old CG  NGLYPH<df00>w CG = 80 in + 1.4 in = 81.4 in  DGLYPH<df00>tGLYPH<df00>rminGLYPH<df00> thGLYPH<df00> location of thGLYPH<df00> CG if 140 pounds of baggagGLYPH<df00> is addGLYPH<df00>d to station 150.  Solution:  Added weight  New total weight  ∆CG  DistancGLYPH<df00> bGLYPH<df00>twGLYPH<df00>GLYPH<df00>n wGLYPH<df00>ight and old CG  ∆CG 150 in − 80 in  =  140 lb  6,860 lb + 140 lb  =  140 lb  7,000 lb  =  ∆CG  70 in  CG  1.4 in aft =  Example  Aircraft total wGLYPH<df00>ight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6,860 lb  CG station. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.0 in  GivGLYPH<df00>n:  Aircraft total weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6,100 lb  CG station. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  80.0 in  GivGLYPH<df00>n:  Aircraft total weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7,800 lb  CG station. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 in  Aft CG limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.5 in  Given: 