When the equipment in an aircraft is changed, such as the installation of a new radar system or ground proximity warning system, or the removal of a radio or seat, the weight and balance of an aircraft changes. An alteration performed on an aircraft, such as a cargo door being installed or a reinforcing plate being attached to the spar of a wing, also changes the weight and balance of an aircraft. Any time the equipment is changed or an alteration is performed, the new empty weight and EWCG must be determined. This can be accomplished by placing the aircraft on scales and weighing it, or by mathematically calculating the new weight and balance. The mathematical calculation is acceptable if the exact weight and arm of all the changes are known.
Example Calculation After an Equipment Change
A small, twinengine airplane has some new equipment installed and some of its existing equipment removed. The details of the equipment changes are shown in Figure 1. To calculate the new empty weight and EWCG, a fourcolumn chart is used. [Figure 2] In evaluating the weight and balance calculation shown in Figure 2, the following key points should be recognized.
 The weight of the equipment needs to be identified with a plus or minus to signify whether it is being installed or removed.
 The sign of the moment (plus or minus) is determined by the signs of the weight and arm.
 The strobe and the ADF are both being removed (negative weight), but only the strobe has a negative moment. This is because the arm for the ADF is also negative, and two negatives multiplied together produce a positive result.
 The total arm is the airplane’s CG and is found by dividing the total moment by the total weight.
 The result of the equipment change is that the airplane’s weight was reduced by 22.5 lb and the CG has moved forward 0.67".
Airplane
empty weight:

2,350 lb

Airplane
EWCG:

+24.7"

Airplane
datum:

Leading
edge of the wing

Radio
installed:

5.8 lb at
an arm of –28"

Global
positioning system installed:

7.3 lb at
an arm of –26"

Emergency
locater transmitter installed:

2.8 lb at
an arm of +105"

Strobe
light removed:

1.4 lb at
an arm of +75"

Automatic
direction finder (ADF) removed:

3 lb at an
arm of –28"

Seat
removed:

34 lb at an
arm of +60"

Figure 1. Twinengine airplane equipment changes
Item

Weight (lb)

Arm (inches)

Moment (inlb)

Empty
Weight

2,350.0

+24.70

58,045.0

Radio
Install

+5.8

28.00

162.4

GPS
Install

+7.3

26.00

189.8

ELT
Install

+2.8

+105.00

294.0

Strobe
Remove

1.4

+75.00

105.0

ADF
Remove

3.0

28.00

84.0

Seat
Remove

34.0

+60.00

2,040.0

Total

2,327.5

24.03

55,925.8

Figure 2. Center of gravity calculation after equipment change
Use of Ballast
Ballast is used in an aircraft to attain the desired CG balance, when the CG is not within limits or is not at the location desired by the operator. It is usually located as far aft or as far forward as possible to bring the CG within limits, while using a minimum amount of weight.
Temporary Ballast
Temporary ballast, in the form of lead bars, 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. To determine the amount of temporary ballast needed, use this formula:
Ballast weight needed = Total wt. × dist. needed to shift CG
Dist. between ballast and desired CG
Figures 3 and 4 show an aft adverseloaded CG check being performed on an airplane. In this previous example, the airplane’s CG was out of limits by 0.6". If there were a need or a desire to fly the airplane loaded this way, one way to make it possible would be the installation of temporary ballast in the front of the airplane. The logical choice for placement of this ballast is the forward baggage compartment. The CG for this airplane is 0.6" too far aft. If the forward baggage compartment is used as a temporary ballast location, the ballast calculation will be as shown in Figure 5.
Figure 3. Example airplane for extreme condition checks 
Item

Weight (lb)

Arm (inches)

Moment (inlb)

Empty
Weight

1,850

+92.45

171,032.5

Pilot

170

+88.00

14,960.0

2
Passengers

340

+105.00

35,700.0

2
Passengers

340

+125.00

42,500.0

Baggage

100

+140.00

14,000.0

Fuel

234

+102.00

23,868.0

Total

3,034

+99.60

302,060.5

Figure 4. Extreme condition check
Item

Weight (lb)

Arm (inches)

Moment (inlb)

Loaded
Weight

3,034

+99.60

302,060.5

Ballast

47

+60.00

2,820.0

Total

3,081

+98.96

304,880.5

Figure 5. Ballast calculation
Ballast weight needed = Total wt. × dist. needed to shift CG
Dist. between ballast and desired CG
= 3,034 lb × (0.6")
39"
= 46.68 lb
When ballast is calculated, the answer should always be rounded up to the next higher whole pound, or in this case, 47 lb of ballast would be used. To ensure the ballast calculation is correct, the weight of the ballast should be plugged back into the fourcolumn calculation and a new CG calculated.
The aft limit for the airplane was 99", and the new CG is at 98.96", which puts it within acceptable limits. The new CG did not fall exactly at 99" because the amount of needed ballast was rounded up to the next whole pound. If the ballast could have been placed farther forward, such as being bolted to the engine firewall, less ballast would have been needed. That is why ballast is always placed as far away from the affected limit as possible.
In evaluating the ballast calculation shown above, the following key points should be recognized.
The aft limit for the airplane was 99", and the new CG is at 98.96", which puts it within acceptable limits. The new CG did not fall exactly at 99" because the amount of needed ballast was rounded up to the next whole pound. If the ballast could have been placed farther forward, such as being bolted to the engine firewall, less ballast would have been needed. That is why ballast is always placed as far away from the affected limit as possible.
In evaluating the ballast calculation shown above, the following key points should be recognized.
 The loaded weight of the aircraft, as identified in the formula, is what the airplane weighed when the CG was out of limits.
 The distance the CG is out of limits is the difference between the CG location and the CG limit, in this case 99.6" minus 99".
 The affected limit identified in the formula is the CG limit which has been exceeded. If the CG is too far aft, it is the aft limit that has been exceeded.
 The aft limit for this example is 99", and the ballast is being placed in the baggage compartment at an arm of 60". The difference between the two is 39", the quantity divided by in the formula.
Viewed as a firstclass lever problem, Figure 6 shows what this ballast calculation would look like. A ballast weight of 46.68 lb on the left side of the lever multiplied by the arm of 39" (99 minus 60) would equal the aircraft weight of 3,034 lb multiplied by the distance the CG is out of limits, which is 0.6" (99.6 minus 99).
Figure 6. Ballast calculation as a first class lever 
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. The installation of permanent ballast results in an increase in the aircraft empty weight, and it reduces the useful load.
Two things must 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 lb has been altered so its EWCG is +32.2, and CG range for weights up to 2,250 lb 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 this formula:
Two things must 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 lb has been altered so its EWCG is +32.2, and CG range for weights up to 2,250 lb 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 this formula:
Dist. between ballast and desired CG
= 1,876 lb × 0.8"
228 – 33
= 1,500.8
195
= 7.7 lb
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.”
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