Expert: Roberto Gomes - 9/14/2006

Question
Dear Roberto

What are the terms used to calculate the balance of an airplane?

Answer
Dear Renee,

I will try to explain briefly, since this issue is very long.

1. The Datum

The datum is an imaginary vertical plane from which all horizontal measurements are taken for balance purposes, with the aircraft in level flight attitude. It is a plane at right angles to the longitudinal axis of the aircraft. For each aircraft make and model, all locations of equipment, tanks, baggage compartments, seats, engines, propellers, etc., are listed in the Aircraft Specification or Type Certificate Data Sheets as being so many inches from the datum.

2. The Arm

The arm is the horizontal distance that an item of equipment is located from the datum. The arm's distance is always given or measured in inches, and, except for a location which might be exactly on the datum (0), it is preceded by the algebraic sign for plus (+) or minus (-). The plus (+) sign indicates a distance aft of the datum and the minus (-) sign indicates a distance forward of the datum.

3. The Moment

A moment is the product of a weight multiplied by its arm. The moment of an item about the datum is obtained by multiplying the weight of the item by its horizontal distance from the datum. Likewise, the moment of an item about the center of gravity (CG) can be computed by multiplying its weight by the horizontal distance from the CG.

4. Center of Gravity

The CG of an aircraft is a point about which the nose heavy and tail heavy moments are exactly equal in magnitude. An aircraft suspended from this point would have no tendency to rotate in either a nose up or nose down attitude. It is the point about which the weight of an airplane or any object is concentrated.

5. Operating Center of Gravity Range

The operating CG range is the distance between the forward and rearward CG limits indicated in the pertinent Aircraft Specification or Type Certificate Data Sheets. These limits, determined at the time of design and manufacture, are the extreme loaded CG positions allowable within the applicable regulations controlling the design of the aircraft. These limits are shown in either percent of MAC (mean aerodynamic chord) or inches from the datum of the aircraft.

6. Mean Aerodynamic Chord

The MAC is the mean average chord of the wing. An airfoil section is a cross section of a wing from leading edge to trailing edge. A chord is usually defined as an imaginary straight line drawn parallel to the airfoil through the leading and trailing edges of the section. The MAC of a constant chord wing would be the same as the actual chord of the wing.

In order to calculate the stabilizer trim and speeds used for take-off, airline dispatchers need to know the determine the CG and the percentage of MAC.

To do this they add the aircraft basic weight (imagine placing and aircraft in a scale to determine its weight with all the oil, fluids, water, crew members and food) to the payload (total weight of passengers and the pallets/contaneirs used to transport baggage, cargo and mail.)

This sum is named Zero Fuel Weight (ZFW).

The ZFW plus the weight of the fuel for the trip equals to the Take-off Weight (TOW).

Depending on the airport used, its runways, temperature and the atmospheric pressure the ZFW and and TOW are limited.

To do all this calculations airlines use special softwares, but dispatchers are required to make at least one monthly manual calculation in case of a computer failure.

Hope this helps. If you need any additional info, please let me know.

Best Regards,
R. Gomes