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 (change of CG)
Distance weight is shifted =
100
8,000
∆CG
120 =
∆CG 1.5 in =
Example
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 =
Given:
Aircraft total weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7,800 lb
CG station. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 in
Aft CG limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.5 in
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:
Example
Added weight
New total weight
∆CG
Distance between weight 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 =
Given:
Aircraft total weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6,860 lb
CG station. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.0 in
Determine the location of the CG if 140 pounds of baggage is added to
station 150.
Solution:
Add ∆CG to old CG
New CG = 80 in + 1.4 in = 81.4 in
Example
Weight removed
New total weight
∆CG
Distance between weight 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 =
Given:
Aircraft total weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6,100 lb
CG station. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.0 in
Determine the location of the CG if 100 pounds is removed from
station 150.
Solution:
Subtract ∆CG from old CG
New CG = 80 in − 1.2 in = 78.8 in
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.
Weight Addition or Removal
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.
In the previous examples, the rCG 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 rCG is added to the old CG; if the CG is shifting
forward, the rCG is subtracted from the old CG.
Chapter Summary
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.