Figure 7-4. Weight, arm, and moment changes caused by typical alteration or repair.
Item Weight (lb) Arm (in) Moment (lb-in) New CG
67,723.6
−192.8
−874.0
−432.0
+122.6
+229.5
+2,037.0
68,613.9 +36.4
Airplane
Radio removed
Power supply removed
ELT removed
Radio installed
ELT installed
Passenger seat installed
Total
1,876.0
−12.2
−9.2
−3.2
+8.4
+1.7
+21.0
1,882.5
36.1
15.8
95.0
135.0
14.6
135.0
97.0
x =
Figure 7-5. Weight and moment index changes caused by a typical alteration or repair.
Item Weight (lb) Moment indexes (lb-in/100) New CG (inches from datum)
+677.2
−1.93
−8.74
−4.32
+1.23
+2.29
+20.37
+686.1 +36.4
Airplane
Radio removed
Power supply removed
ELT removed
Radio installed
ELT installed
Passenger seat installed
Total
1,876.0
−12.2
−9.2
−3.2
+8.4
+1.7
+21.0
1,882.5
The weight and balance revision sheet should clearly show
the revised empty weight, empty weight arm and/or moment
index, and the new useful load. An example of these entries
can be found at the bottom of Figure 7-3.
Weight Changes Caused by a Repair or
Alteration
A typical alteration might consist of removing two pieces
of radio equipment from the instrument panel and a power
supply that was located in the baggage compartment behind
the rear seat. In this example, these two pieces are replaced
with a single lightweight, self-contained radio. At the
same time, an old emergency locator transmitter (ELT) is
removed from its mount near the tail, and a lighter weight
unit is installed. A passenger seat is installed in the baggage
compartment.
Computations Using Weight, Arm, and Moment
The first step in the weight and balance computation is to
make a chart like the one in Figure 7-4, listing all of the
items that are involved. The new center of gravity (CG) of
36.4 inches aft of the datum is determined by dividing the
new moment by the new weight.
Computations Using Weight and Moment Indexes
If the weight and balance data uses moment indexes rather
than arms and moments, this same alteration can be computed
using a chart such as the one in Figure 7-5. Subtract the
weight and moment indexes of all the removed equipment
from the empty weight and moment index of the airplane.
Add the weight and moment indexes of all equipment
installed to determine the total weight and the total moment
index. To determine the position of the new CG in inches
aft of the datum, multiply the total moment index by 100 to
get the moment, and divide this by the total weight to get
the new CG.
Figure 7-8. Formula for determining the CG in percent MAC.
CG in % MAC CG in inches from LEMAC x 100
MAC=
10.42 x 100
58.0=
17.9% MAC=
Figure 7-7. Loading conditions.
CG
range
Datum Front seats Rear seats +74 Baggage B +116
Fuel +48.2 Baggage A +97
Forward
limit
Aft limit 46.0
Figure 7-6. Weight and balance information.
3,200
3,000
2,800
2,600
2,400
2,200
2,000
1,800 32 34 36 38 40 42 44 46 48
Fuselage station (in)
Loaded aircraft weight (lb)
Airplane EW and EWCG 1,876.0 lb at +36.14
Engine METO horsepower 230
CG range (+40.9) to (+46.0) at 3,100 lb
(+33.0) to (+46.0) at 2,250 lb or less
Straight line variation between points given
Empty weight CG range None
Maximum weight 3,100 lb takeoff/flight
2,950 lb landing
Datum to LEMAC 25.98
MAC 58.00
No. of seats 4 (2 front at +34.0)
(2 rear at +74.0)
Fuel capacity 92 gal (88 gal usable)
two 46-gal integral tanks in wings at +48.2
See NOTE 1 for data on unusable fuel.
Minimum fuel (METO HP ÷ 2) 115 lb at +48
Maximum baggage 160 lb
Area A (100 lb at +97.0)
Area B (60 lb at +116.0
Oil capacity 12 qt (−15) (6 qt usable)
See NOTE 1 for data on undrainable oil.
NOTE 1: The certificated empty weight and corresponding center of
gravity location must include unusable fuel of 30 lb (+46) and
undrainable oil of 0 lb.
Determining the CG in Percentage of Mean
Aerodynamic Chord (Percent MAC)
This procedure is the same as found in Chapter 5, Single-
Engine Aircraft Weight and Balance Computations.
Refer to the load conditions and CG information found in
Figures 7-5, 7-6, and 7-7 to compute the CG in percent MAC:
The loaded CG is +36.4 inches aft of the datum.
The MAC is 58.0 inches long.
The leading edge mean aerodynamic chord (LEMAC)
is located at station 25.98.
The CG is +36.4 – 25.98 = 10.42 inches aft of LEMAC.
Use the formula in Figure 7-8 to determine CG in MAC
percentages.
The loaded CG after alteration or repair is located at 17.9
percent MAC.
Empty Weight CG (EWCG) Range
The fuel tanks, seats, and baggage compartments of some
aircraft are so located that changes in the fuel or occupant
load have a very limited effect on the balance of the aircraft.
Aircraft of such a configuration show an empty weight CG
(EWCG) range in the Type Certificate Data Sheet (TCDS).
If the EWCG is located within this range, it is impossible to
legally load the aircraft so that its loaded CG falls outside
its allowable range.
If the TCDS lists an EWCG range, and after the alteration is
completed the EWCG falls within this range, then there is no
need to compute a fore and aft check for adverse loading. But
if the TCDS lists the EWCG range as “None” (and most of
them do), a check must be made to determine whether or not
it is possible by any combination of legal loading to cause the
aircraft CG to move outside of either its forward or aft limits.
Adverse-Load CG Checks
Many modern aircraft have multiple rows of seats and often
more than one baggage compartment. After any repair or
alteration that changes the weight and balance, the Airframe
and Powerplant (A&P) FAA-certificated mechanic or
repairman must ensure that no legal condition of loading can
Figure 7-9. Load conditions for forward adverse-load CG check.
Item Weight (lb) Arm (in) Moment (lb-in) Most forward CG +33.0
67,798.6
5,780.0
5,520.0
79,098.6 +36.6
Airplane (empty)
Pilot
Fuel (minimum)
Total
1,876.0
170.0
115.0
2,161.0
36.14
34.0
48.0
x =
When rear row of seats is occupied, 120 pounds of
baggage or ballast must be carried in forward baggage
compartment. For additional loading instruction,
see Weight and Balance Data.
Figure 7-11. Typical baggage compartment placard.
Figure 7-10. Load conditions for aft adverse-load CG check.
Item Weight (lb) Arm (in) Moment (lb-in) Most Aft CG +46.0
67,798.6
5,780.0
25,449.6
25,160.0
9,700.0
6,960.0
140,848.2 +45.8
Airplane (empty)
Pilot
Fuel (full tanks – 88 gal)
Rear seat occupants (2)
Baggage A
Baggage B
Total
1,876.0
170.0
528.0
340.0
100.0
60.0
3,074.0
36.14
34.0
48.2
74.0
97.0
116.0
x =
move the CG outside of its allowable limits. To determine
this, adverse-loaded CG checks must be performed and
the results noted in the weight and balance revision sheet.
[Figure 7-3]
Forward Adverse-Load CG Check
To conduct a forward CG check, make a chart that includes
the airplane and any occupants and items of the load located
in front of the forward CG limit. Include only those items
behind the forward limit that are essential to flight: the pilot,
and the minimum fuel.
In this example, the pilot, whose nominal weight is 170
pounds, is behind the forward CG limit. The fuel is also
behind the forward limit, so the minimum fuel is used. For
weight and balance purposes, the minimum fuel is no more
than the quantity needed for one-half hour of operation at
rated maximum continuous power. This is considered to
be 1⁄12 gallon for each maximum except takeoff (METO)
horsepower. Because aviation gasoline weighs 6 pounds per
gallon, determine the number of pounds of the minimum fuel
by dividing the METO horsepower by two. In this example,
minimum fuel is 115 pounds. The front and rear seats and the
baggage are all behind the forward CG limit, so no passengers
or baggage are considered.
Make a chart like the one in Figure 7-9 to determine the CG
with the aircraft loaded for its most forward CG. With the
load consisting of only a pilot and the minimum fuel, the CG
is +36.6, which is behind the most forward allowable limit
for this weight of +33.0.
Aft Adverse-Load CG Check
To conduct an aft or rearward CG check, make a chart that
includes the empty weight and EWCG of the aircraft after
the alteration and all occupants and items of the load behind
the aft CG limit of 46.0. The pilot is in front of this limit but
is essential for flight and must be included. In this example,
only the pilot occupies the front seats. Since the CG of the
fuel is behind the aft limit, full fuel is used, as well as the
nominal weight (170 lb) for both rear seat passengers and
the maximum allowable baggage.
Under these loading conditions, the CG is located at +45.8,
which is ahead of the aft limit of +46.0. [Figure 7-10] With
only the pilot in front of the aft CG limit and maximum of all
items behind the aft limit, the CG is at +45.8 inches, which
is ahead of the aft limit of +46.0 inches.
Ballast
It is possible to load most modern airplanes so the CG
shifts outside of the allowable limit. Placards and loading
instructions in the weight and balance data inform the pilot
of the restrictions that prevent such a shift from occurring.
A typical placard in the baggage compartment of an airplane
is shown in Figure 7-11. When the CG of an aircraft falls
outside of the limits, it can usually be brought back in by
using ballast.
Figure 7-13. Formula for determining ballast.
Ballast weight Aircraft empty weight × Dist. out of limits
Distance between ballast and desired CG=
Temporary Ballast
Temporary ballast, in the form of lead bars or heavy canvas
bags of sand or lead shot, is often carried in the baggage
compartments to adjust the balance for certain flight
conditions. The bags are marked “Ballast XX Pounds—
Removal Requires Weight and Balance Check.” Temporary
ballast must be secured so it cannot shift its location in flight
and the structural limits of the baggage compartment must not
be exceeded. All temporary ballast must be removed before
the aircraft is weighed.
Temporary Ballast Formula
The CG of a loaded airplane can be moved into its allowable
range by shifting passengers or cargo or by adding temporary
ballast.
Permanent Ballast
If a repair or alteration causes the aircraft CG to fall outside
of its limit, permanent ballast can be installed. Usually
permanent ballast is made of blocks of lead painted red and
marked “Permanent Ballast—Do Not Remove.” It should be
attached to the structure so that it does not interfere with any
control action and attached rigidly enough that it cannot be
dislodged by any flight maneuvers or rough landing
Two things must first be known to determine the amount of
ballast needed to bring the CG within limits: the amount the
CG is out of limits, and the distance between the location of
the ballast and the limit that is affected.
If an airplane with an empty weight of 1,876 pounds has been
altered so its EWCG is +32.2, and CG range for weights up
to 2,250 pounds is +33.0 to +46.0, permanent ballast must be
installed to move the EWCG from +32.2 to +33.0. There is
a bulkhead at fuselage station 228 strong enough to support
the ballast.
To determine the amount of ballast needed, use the formula
in Figure 7-13.
Ballast needed = 1.876 × 0.8
228 – 33
= 1500.8
195
= 7.7 pounds
A block of lead weighing 7.7 pounds, attached to the bulkhead
at fuselage station 228, moves the EWCG back to its proper
forward limit of +33. This block should be painted red and
marked “Permanent Ballast—Do Not Remove.”