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USEFUL LOAD -- Gross weight minus the empty aircraft weight.
STANDARD WEIGHTS -- Gasoline 6 lb. per gal; Oil 7.5 lb. per gal. (US Measure)
Methods of Determining Weight and Balance
The method of determining weight and balance may vary with aircraft manufacturer and type of aircraft.
These methods are:
1. Center of Gravity Calculations
2. Center of Gravity Graphs
3. Center of Gravity Tables
4. Loading Schedules (Placards)
Center of Gravity Calculations
To determine the location CG, add up all the weights and all the moments. Divide the sum of the
moments by the sum of the weights. This is illustrated in the diagram.
All moments aft of the datum are positive numbers. All moments forward of the datum are negative. In
the example, the oil is the only negative moment since it is forward of the DATUM.. Calculate the
weight of oil at 7.5 pounds per gallon. Calculate fuel at 6 pounds (US) per gallon.
The procedure to calculate the CG is as follows:
1. Add up all weights, including empty aircraft
2. Multiply each weight by it’s moment arm in inches to get the moment for that item.
3. Add up all the moments
4. Divide the sum of the moments by the total weight to get the CG
A TYPICAL W/B PROBLEM
ITEM WEIGHT lbs MOMENT ARM in. MOMENT LB IN
Weight and Balance
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A = AIRCRAFT 1000 6 6000
P = PILOT 150 11 1650
B = BAGGAGE 40 32 1280
O = OIL 7.5 -4 -30
F = FUEL 120 16 1920
TOTAL 1317.5 CG? 10820
In the example, CG? = 10820/1317.5 = 8.21 in. aft of the datum.
Loading Graph
Frequently the manufacturer provides a graphical method for determining weight and balance.
Determine the load moment for each load item using the appropriate line in the graph. For example, for
pilot and front seat passenger, total the combined load weight. Go up the Load Weight axis (Y axis) to
the pilot & passenger weight. Then go horizontal to the pilot & passenger line (Red line). Then go down
to the X axis to find the load moment/1000. Do the same for fuel (blue line), rear passengers (green Line)
and baggage (black line). Total up the weight and the Load Moments.
EXAMPLE: Determine the Load and moment from the loading graph above for each of the following
load items.
Weight and Balance
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Weight and Balance Using
Loading Graphs
Weight and Balance
Weight **Moment
Empty Weight 1,364 51.7
Front Seats 400 15.0
Baggage 120 11.5
Fuel (38 gal) 228 11.0
Oil (2 gal) 15 - 0.2
TOTAL 2,127 89.0
Derive the values as follows:
1. Empty Weight and moment are values provided by the manufacturer.
2. Pilot & Passenger - Add weight for Pilot and Passenger. In this example 400lb. Go up the left side (Y
axis) of the graph to 400 lb. weight, then horizontal to the “Pilot & Passenger” line. Read vertically down
from the intersection to the horizontal (X) axis, and read a Moment/1000 value of 15.0.
3. Baggage - The baggage weight is 120 lb. Go up left side of the upper graph to a load of 120 lb.
Continue horizontally to intersect the “baggage” line. Go downward from this intersection and read a
Moment/1000 value of 11.5.
4. Fuel -- 38 gallons at 6 pounds per gallon is 228 pounds. Go up the left side of graph to a weight value
of 228 lbs., then horizontally to intersect the“fuel line. Go downward to read a Moment/1000 value of
11.0.
5. Oil was not included in the empty weight of this aircraft, therefore it must be entered into the
calculation. Two gallons of oil is 15 lb. The moment is -0.2 lb-in.
Loading Envelope
Once the total weight and the total moment/1000 is found, use the load and CG envelope to ascertain that
the aircraft is properly loaded.
Go up the left side to a total load of 2127 lbs. Draw a horizontal line. Go along the bottom scale to find
the loaded aircraft moment / 100 value of 89.0. Draw a vertical line. The aircraft is properly loaded if the
intersection of the horizontal and vertical lines is within the envelope.
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According to this envelope, if the weight is greater than 2300 pounds, the aircraft is overloaded. If the
intersection is outside the envelope laterally, the loading is out of proper CG range.
Center of Gravity Tables
Some manufacturers provide tables instead of graphs or calculation. This method is fairly lengthy, and is
used infrequently for small aircraft. Therefore this method will not be covered herein.
Weight Shift and Change
The approach to solving both Weight Change and Weight Shift is the same. The simplest method is to
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