Aircraft Design Weight and Balance Handbook Ch. 2a

Weight and Balance Theory

Two elements are vital in the weight and balance considerations of an aircraft:

• The total weight of the aircraft must be no greater than the maximum gross weight allowed by the FAA for the particular make and model of the aircraft.
• The center of gravity, or the point at which all of the weight of the aircraft is considered to be concentrated, must be maintained within the allowable range for the operational weight of the aircraft.

Aircraft Arms, Weights, and Moments

The term arm, usually measured in inches, refers to the distance between the center of gravity of an item or object and the reference datum. Arms ahead of, or to the left of the datum are negative (–), and those behind, or to the right of the datum are positive (+). When the datum is ahead of the aircraft, all of the arms are positive and computational errors are minimized.

Weight is normally measured in pounds. When weight is removed from an aircraft, it is negative (–), and when added, it is positive (+).

There are a number of weights that must be considered in aircraft weight and balance. The following are terms for various weights as used by the General Aviation Manufacturers Association (GAMA).

• The standard empty weight is the weight of the airframe, engines and all items of operating weight that have fixed locations and are permanently installed in the aircraft. This weight must be recorded in the aircraft weight and balance records. The basic empty weight includes the standard empty weight plus any optional equipment that has been installed.
• Maximum allowable gross weight is the maximum weight authorized for the aircraft and all of its contents as specified in the Type Certificate Data Sheets (TCDS) or Aircraft Specifications for the aircraft.
• Maximum landing weight is the greatest weight that an aircraft normally is allowed to have when it lands.
• Maximum takeoff weight is the maximum allowable weight at the start of the takeoff run.
• Maximum ramp weight is the total weight of a loaded aircraft, and includes all fuel. It is greater than the takeoff weight due to the fuel that will be burned during the taxi and run up operations. Ramp weight is also called taxi weight.

The manufacturer establishes the allowable gross weight and the range allowed for the CG, as measured in inches from a reference plane called the datum. In large aircraft, this range is measured in percentage of the mean aerodynamic chord (MAC), the leading edge of which is located a specified distance from the datum.
The datum may be located anywhere the manufacturer chooses; it is often the leading edge of the wing or some specific distance from an easily identified location. One popular location for the datum is a specified distance forward of the aircraft, measured in inches from some point such as the leading edge of the wing or the engine firewall.

The datum of some helicopters is the center of the rotor mast, but this location causes some arms to be positive and others negative. To simplify weight and balance computations, most modern helicopters, like airplanes, have the datum located at the nose of the aircraft or a specified distance ahead of it.
A moment is a force that tries to cause rotation, and is the product of the arm, in inches, and the weight, in pounds. Moments are generally expressed in pound-inches (lb-in) and may be either positive or negative. Figure 2-1 shows the way the algebraic sign of a moment is derived. Positive moments cause an airplane to nose up, while negative moments cause it to nose down.
figure 2-1

The Law of the Lever

All weight and balance problems are based on the physical law of the lever. This law states that a lever is balanced when the weight on one side of the fulcrum multiplied by its arm is equal to the weight on the opposite side multiplied by its arm. In other words, the lever is balanced when the algebraic sum of the moments about the fulcrum is zero. [Figure 2-2] This is the condition in which the positive moments (those that try to rotate the lever clockwise) are equal to the negative moments (those that try to rotate it counter- clockwise).

figure 2-2

Consider these facts about the lever in Figure 2-2: The 100-pound weight A is located 50 inches to the left of the fulcrum (the datum, in this instance), and it has a moment of 100°?–50 = –5,000 lb-in. The 200-pound weight B is located 25 inches to the right of the fulcrum, and its moment is 200° +25 = +5,000 lb-in. The sum of the moments is –5,000 +5,000 = 0, and the lever is balanced. [Figure 2-3] The forces that try to rotate it clockwise have the same magnitude as those that try to rotate it counterclockwise.
figure 2-3

Determining the CG
One of the easiest ways to understand weight and balance is to consider a board with weights placed at various locations. We can determine the CG of the board and observe the way the CG changes as the weights are moved. The CG of a board like the one in Figure 2-4 may be deter-mined by using these four steps:

1. Measure the arm of each weight in inches from a datum.
2. Multiply each arm by its weight in pounds to determine the moment in pound-inches of each weight.
3. Determine the total of all the weights and of all the moments. Disregard the weight of the board.
4. Divide the total moment by the total weight to determine the CG in inches from the datum.

figure 2-4

In Figure 2-4, the board has three weights, and the datum is located 50 inches to the left of the CG of weight A. Determine the CG by making a chart like the one in Figure 2-5.

figure 2-5

As noted in Figure 2-5, “A” weighs 100 pounds and is 50 inches from the datum; “B” weighs 100 pounds and is 90 inches from the datum; “C” weighs 200 pounds and is 150 inches from the datum. Thus the total of the three weights is 400 pounds, and the total moment is 44,000 lb-in. Determine the CG by dividing the total moment by the total weight.

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To prove this is the correct CG, move the datum to a location 110 inches to the right of the original datum and determine the arm of each weight from this new datum, as in Figure 2-6. Then make a new chart similar to the one in Figure 2- 7. If the CG is correct, the sum of the moments will be zero.

figure 2-6

The new arm of weight A is 110 – 50 = 60 inches, and since this weight is to the left of the datum, its arm is negative, or –60 inches. The new arm of weight B is 110 – 90 = 20 inches, and it is also to the left of the datum, so it is –20; the new arm of weight C is 150 – 110 = 40 inches. It is to the right of the datum and is therefore positive.

figure 2-7

The location of the datum used for determining the arms of the weights is not important; it can be anywhere. But all of the measurements must be made from the same datum location.

Determining the CG of an airplane is done in the same way as determining the CG of the board in the example on the previous page. [Figure 2-8] Prepare the airplane for weighing (as explained in Chapter 3) and place it on three scales. All tare weight, the weight of any chocks or devices used to hold the aircraft on the scales, is subtracted from the scale reading, and the net weight of the wheels is entered into a chart like the one in Figure 2-9. The arms of the weighing points are specified in the TCDS for the airplane in terms of stations, which are distances in inches from the datum.

figure 2-8 figure 2-9


The empty weight of this aircraft is 5,862 pounds. Its EWCG, determined by dividing the total moment by the total weight, is located at fuselage station 201.1. This is 201.1 inches behind the datum.
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