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.

script...

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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Aircraft Design Weight and Balance Handbook Ch. 1b

Weight Changes

The maximum allowable gross weight for an aircraft is determined by design considerations. However, the maximum operational weight may be less than the maximum allowable due to such considerations as high density altitude or high-drag field conditions caused by wet grass or water on the runway. The maximum gross weight may also be limited by the departure or arrival airport’s runway length.
One important preflight consideration is the distribution of the load in the aircraft. Loading an aircraft so the gross weight is less than the maximum allowable is not enough. This weight must be distributed to keep the CG within the limits specified in the POH or AFM.
If the CG is too far forward, a heavy passenger can be moved to one of the rear seats or baggage can be shifted from a forward baggage compartment to a rear compartment. If the CG is too far aft, passenger weight or baggage can be shifted forward. The fuel load should be balanced laterally: the pilot should pay special attention to the POH or AFM regarding the operation of the fuel system, in order to keep the aircraft balanced in flight.


Weight and balance of a helicopter is far more critical than for an airplane. A helicopter may be properly loaded for takeoff, but near the end of a long flight when the fuel tanks are almost empty, the CG may have shifted enough for the helicopter to be out of balance laterally or longitudinally. Before making any long flight, the CG with the fuel available for landing must be checked to ensure it will be within the allowable range.
Airplanes with tandem seating normally have a limitation requiring solo flight to be made from the front seat in some airplanes or the rear seat in others. Some of the smaller helicopters also require solo flight be made from a specific seat, either the right or the left. These seating limitations will be noted by a placard, usually on the instrument panel, and they should be strictly adhered to.

As an aircraft ages, its weight usually increases due to trash and dirt collecting in hard-to-reach locations, and moisture absorbed in the cabin insulation. This growth in weight is normally small, but it can only be determined by accurately weighing the aircraft.

Changes of fixed equipment may have a major effect upon the weight of the aircraft. Many aircraft are overloaded by the installation of extra radios or instruments. Fortunately, the replacement of older, heavy electronic equipment with newer, lighter types results in a weight reduction. This weight change, however helpful, will probably cause the CG to shift and this must be computed and annotated in the weight and balance data.

Repairs and alterations are the major sources of weight changes, and it is the responsibility of the AMT making any repair or alteration to know the weight and location of these changes, and to compute the new CG and record the new empty weight and EWCG in the aircraft weight and balance data.
The AMT conducting an annual or 100-hour inspection must ensure the weight and balance data in the aircraft records is current and accurate. It is the responsibility of the pilot in command to use the most current weight and balance data when operating the aircraft.

Has the Aircraft Gained Weight?
As an aircraft ages, its weight usually increases. Repairs and alterations are the major sources of weight change.
AMTs conducting an annual or 100-hour inspection must ensure the weight and balance data in the aircraft records is current and accurate. The pilot in command’s responsibility is to use the most current weight and balance data when planning a flight.

Stability and Balance Control

Balance control refers to the location of the CG of an aircraft. This is of primary importance to aircraft stability, which determines safety in flight. The CG is the point at which the total weight of the aircraft is assumed to be concentrated, and the CG must be located within specific limits for safe flight. Both lateral and longitudinal balance are important, but the prime concern is longitudinal balance; that is, the location of the CG along the longitudinal or lengthwise axis.

An airplane is designed to have stability that allows it to be trimmed so it will maintain straight and level flight with hands off of the controls. Longitudinal stability is maintained by ensuring the CG is slightly ahead of the center of lift. This produces a fixed nose-down force independent of the airspeed. This is balanced by a variable nose-up force, which is produced by a downward aerodynamic force on the horizontal tail surfaces that varies directly with airspeed.

[Figure 1-1]

If a rising air current should cause the nose to pitch up, the airplane will slow down and the downward force on the tail will decrease. The weight concentrated at the CG will pull the nose back down. If the nose should drop in flight, the airspeed will increase and the increased downward tail load will bring the nose back up to level flight.
 
As long as the CG is maintained within the allowable limits for its weight, the airplane will have adequate longitudinal stability and control. If the CG is too far aft, it will be too near the center of lift and the airplane will be unstable, and difficult to recover from a stall. [Figure 1-2] If the unstable airplane should ever enter a spin, the spin could become flat and recovery would be difficult or impossible.

[figure 1-2]

If the CG is too far forward, the downward tail load will have to be increased to maintain level flight. This increased tail load has the same effect as carrying additional weight — the aircraft will have to fly at a higher angle of attack, and drag will increase.

A more serious problem caused by the CG being too far forward is the lack of sufficient elevator authority. At slow takeoff speeds, the elevator might not produce enough nose- up force to rotate and on landing there may not be enough elevator force to flare the airplane. [Figure 1-3] Both takeoff and landing runs will be lengthened if the CG is too far forward.

figure 1-3


The efficiency of some modern high-performance military fighter airplanes is increased by giving them neutral longitudinal stability. This is normally a very dangerous situation; but these aircraft are flown by autopilots which react far faster than a human pilot, and they are safe for their special operations.

The basic aircraft design assumes that lateral symmetry exists. For each item of weight added to the left of the centerline of the aircraft (also known as buttock line zero, or BL-0), there is generally an equal weight at a corresponding location on the right.

The lateral balance can be upset by uneven fuel loading or burnoff. The position of the lateral CG is not normally computed for an airplane, but the pilot must be aware of the adverse effects that will result from a laterally unbalanced condition. [Figure 1-4] This is corrected by using the aileron trim tab until enough fuel has been used from the tank on the heavy side to balance the airplane. The deflected trim tab deflects the aileron to produce additional lift on the heavy side, but it also produces additional drag, and the airplane flies inefficiently.

figure 1-4


Helicopters are affected by lateral imbalance more than airplanes. If a helicopter is loaded with heavy occupants and fuel on the same side, it could be enough out of balance to make it unsafe to fly. It is also possible that if external loads are carried in such a position to require large lateral displacement of the cyclic control to maintain level flight, the fore-and-aft cyclic control effectiveness will be limited.

Sweptwing airplanes are more critical due to fuel imbalance because as the fuel is used from the outboard tanks the CG shifts forward, and as it is used from the inboard tanks the CG shifts aft. [Figure 1-5] For this reason, fuel-use scheduling in high-speed jet aircraft operation is critical.

figure 1-5


Aircraft can perform safely and achieve their designed efficiency only when they are operated and maintained in the way their designers intended. This safety and efficiency is determined to a large degree by holding the aircraft’s weight and balance parameters within the limits specified for its design. The remainder of this book describes the way in which this is done.

Aircraft Design Weight and Balance Handbook Ch. 1a

Why is Weight and Balance Important?

Weight and balance is one of the most important factors affecting safety of flight. An overweight aircraft, or one whose center of gravity is outside the allowable limits, is inefficient and dangerous to fly. The responsibility for proper weight and balance control begins with the engineers and designers and extends to the pilot who operates and the Aviation Maintenance Technician (AMT) who maintains the aircraft.
Modern aircraft are engineered utilizing state-of-the-art technology and materials to lift the maximum amount of weight and carry it the greatest distance at the highest speed. As much care and expertise must be exercised in operating and maintaining these efficient aircraft as was taken in their design and manufacturing.
Various types of aircraft have different load requirements. Transport aircraft must carry huge loads of passengers and cargo for long distances at high altitude and high speed. Military aircraft must be highly maneuverable and extremely sturdy. Corporate aircraft must carry a reasonable load at a high speed for long distances. Agricultural aircraft must carry large loads short distances and be extremely maneuverable. Trainers and private aircraft must be lightweight, low cost, simple, and safe to operate. All aircraft regardless of their function have two characteristics in common: all are sensitive to weight, and the center of gravity of the aircraft must be maintained within a specified range.

The designers of an aircraft have determined the maximum weight, based on the amount of lift the wings or rotors can provide under the operating conditions for which the aircraft is designed. The structural strength of the aircraft also limits the maximum weight the aircraft can safely carry. The ideal location of the center of gravity (CG) was very carefully determined by the designers, and the maximum deviation allowed from this specific location has been calculated. The manufacturer provides the aircraft operator with the empty weight of the aircraft and the location of its empty- weight center of gravity (EWCG) at the time the aircraft left the factory. The AMT who maintains the aircraft and performs the maintenance inspections keeps the weight and balance records current, recording any changes that have been made because of repairs or alterations.
The pilot in command of the aircraft has the responsibility on every flight to know the maximum allowable gross weight of the aircraft and its CG limits. This allows the pilot to determine on the preflight inspection that the aircraft is loaded in such a way that the CG is within the allowable limits.

Weight and balance technology, like all other aspects of aviation, has become more complex as the efficiency and capability of aircraft and engines have increased. Therefore, this requires all pilots and AMTs to understand weight and balance control, and to operate and maintain their aircraft so its weight and CG location are within the limitations established when the aircraft was designed, manufactured, and certified by the FAA.

Weight Control

Weight is a major factor in airplane construction and operation, and it demands respect from all pilots and particular diligence by all AMTs. Excessive weight reduces the efficiency of an aircraft and the safety margin available if an emergency condition should arise.

When an aircraft is designed, it is made as light as the required structural strength will allow, and the wings or rotors are designed to support the maximum allowable gross weight. When the weight of an aircraft is increased, the wings or rotors must produce additional lift and the structure must support not only the additional static loads , but also the dynamic loads imposed by flight maneuvers. For example, the wings of a 3,000-pound airplane must support 3,000 pounds in level flight, but when the airplane is turned smoothly and sharply using a bank angle of 60°, the dynamic load requires the wings to support twice this, or 6,000 pounds.

Severe uncoordinated maneuvers or flight into turbulence can impose dynamic loads on the structure great enough to cause failure. The structure of a normal category airplane must be strong enough to sustain a load factor of 3.8 times its weight; that is, every pound of weight added to an aircraft requires that the structure be strong enough to support an additional 3.8 pounds. An aircraft operating in the utility category must sustain a load factor of 4.4, and acrobatic category aircraft must be strong enough to withstand 6.0 times their weight.

The lift produced by a wing is determined by its airfoil shape, angle of attack, speed through the air, and the air density. When an aircraft takes off from an airport with a high density altitude, it must accelerate to a speed faster than would be required at sea level to produce enough lift to allow takeoff; therefore, a longer takeoff run is necessary. The distance needed may be longer than the available runway. When operating from a high density altitude airport, the Pilot’s Operating Handbook (POH) or Airplane Flight Manual (AFM) must be consulted to determine the maximum weight allowed for the aircraft under the conditions of altitude, temperature, wind, and runway conditions.

Effects of Weight

Most modern aircraft are so designed that if all seats are occupied, all baggage allowed by the baggage compartment structure is carried, and all of the fuel tanks are full, the aircraft will be grossly overloaded. This type of design gives the pilot a great deal of latitude in loading the aircraft for a particular flight. If maximum range is required, occupants or baggage must be left behind, or if the maximum load must be carried, the range, dictated by the amount of fuel on board, must be reduced.

Some of the problems caused by overloading an aircraft are:
• The aircraft will need a higher takeoff speed, which results in a longer takeoff run.
• Both the rate and angle of climb will be reduced.
• The service ceiling will be lowered.
• The cruising speed will be reduced.
• The cruising range will be shortened.
• Maneuverability will be decreased.
• A longer landing roll will be required because the landing speed will be higher.
• Excessive loads will be imposed on the structure, especially the landing gear.

The POH or AFM includes tables or charts that give the pilot an indication of the performance expected for any gross weight. An important part of careful preflight planning includes a check of these charts to determine the aircraft is loaded so the proposed flight can be safely made.

High Density Altitude Airport Operations
Consult the POH or AFM to determine the maximum weight allowed for the aircraft under the conditions of altitude, temperature, wind, and runway conditions.
Your preflight planning must include a careful check of gross weight performance charts to determine the aircraft is loaded properly and the proposed flight can be safely made.