
American Flyers is happy to provide Chapter 8 from the Pilot's Handbook of Aeronautical Knowledge , an FAA Publication Would you like to purchase a hard copy of the Pilot's Handbook of Aeronautical Knowledge? Click here for the American Flyers Pilot Shop. Chapter 1 • Chapter 2 • Chapter 3 • Chapter 4 • Chapter 5 • Chapter 6 • Chapter 7 • Chapter 8 • Chapter 9 • Chapter 10 
Compliance with the weight and balance limits of any airplane is critical to flight safety. Operating an airplane above the maximum weight limitation compromises the structural integrity of the airplane and adversely affects its performance. Operation with the center of gravity (CG) outside the approved limits may result in control difficulty.
Weight is the force with which gravity attracts a body toward the center of the earth. It is a product of the mass of a body and the acceleration acting on the body. Weight is a major factor in airplane construction and operation, and demands respect from all pilots.
The force of gravity continually attempts to pull the airplane down toward earth. The force of lift is the only force that counteracts weight and sustains the airplane in flight. However, the amount of lift produced by an airfoil is limited by the airfoil design, angle of attack, airspeed, and air density. Therefore, to assure that the lift generated is sufficient to counteract weight, loading the airplane beyond the manufacturer’s recommended weight must be avoided. If the weight is greater than the lift generated, the airplane may be incapable of flight.
Any item aboard the airplane that increases the total weight is undesirable as far as performance is concerned. Manufacturers attempt to make the airplane as light as possible without sacrificing strength or safety.
The pilot of an airplane should always be aware of the consequences of overloading. An overloaded airplane may not be able to leave the ground, or if it does become airborne, it may exhibit unexpected and unusually poor flight characteristics. If an airplane is not properly loaded, the initial indication of poor performance usually takes place during takeoff.
Excessive weight reduces the flight performance of an airplane in almost every respect. The most important performance deficiencies of the overloaded airplane are:
The pilot must be knowledgeable in the effect of weight on the performance of the particular airplane being flown. Preflight planning should include a check of performance charts to determine if the airplane’s weight may contribute to hazardous flight operations. Excessive weight in itself reduces the safety margins available to the pilot, and becomes even more hazardous when other performancereducing factors are combined with overweight. The pilot must also consider the consequences of an overweight airplane if an emergency condition arises. If an engine fails on takeoff or airframe ice forms at low altitude, it is usually too late to reduce the airplane’s weight to keep it in the air.
The weight of the airplane can be changed by altering the fuel load. Gasoline has considerable weight—6 pounds per gallon—30 gallons may weigh more than one passenger. But it must be remembered that if weight is lowered by reducing fuel, the range of the airplane is decreased. During flight, fuel burn is normally the only weight change that takes place. As fuel is used, the airplane becomes lighter and performance is improved.
Changes of fixed equipment have a major effect upon the weight of the airplane. An airplane can be overloaded by the installation of extra radios or instruments. Repairs or modifications may also affect the weight of the airplane.
Balance refers to the location of the center of gravity (CG) of an airplane, and is important to airplane stability and safety in flight. The center of gravity is a point at which an airplane would balance if it were suspended at that point.
The prime concern of airplane balancing is the fore and aft location of the CG along the longitudinal axis. The center of gravity is not necessarily a fixed point; its location depends on the distribution of weight in the airplane. As variable load items are shifted or expended, there is a resultant shift in CG location. The pilot should realize that if the CG of an airplane is displaced too far forward on the longitudinal axis, a noseheavy condition will result. Conversely, if the CG is displaced too far aft on the longitudinal axis, a tailheavy condition will result. It is possible that an unfavorable location of the CG could produce such an unstable condition that the pilot could not control the airplane. [Figure 81]
Location of the CG with reference to the lateral axis is also important. For each item of weight existing to the left of the fuselage centerline, there is an equal weight existing at a corresponding location on the right. This may be upset, however, by unbalanced lateral loading. The position of the lateral CG is not computed, but the pilot must be aware that adverse effects will certainly arise as a result of a laterally unbalanced condition. Lateral unbalance will occur if the fuel load is mismanaged by supplying the engine(s) unevenly from tanks on one side of the airplane. The pilot can compensate for the resulting wingheavy condition by adjusting the aileron trim tab or by holding a constant aileron control pressure. However, this places the airplane controls in an outofstreamline condition, increases drag, and results in decreased operating efficiency. Since lateral balance is relatively easy to control and longitudinal balance is more critical, further reference to balance in this handbook will mean longitudinal location of the center of gravity.
In any event, flying an airplane that is out of balance can produce increased pilot fatigue with obvious effects on the safety and efficiency of flight. The pilot’s natural correction for longitudinal unbalance is a change of trim to remove the excessive control pressure. Excessive trim, however, has the effect of not only reducing aerodynamic efficiency but also reducing primary control travel distance in the direction the trim is applied.
Adverse balance conditions affect airplane flight characteristics in much the same manner as those mentioned for an excess weight condition. In addition, there are two essential airplane characteristics that may be seriously affected by improper balance; these are stability and control. Loading in a noseheavy condition causes problems in controlling and raising the nose, especially during takeoff and landing. Loading in a tailheavy condition has a most serious effect upon longitudinal stability, and can reduce the airplane’s capability to recover from stalls and spins. Another undesirable characteristic produced from tailheavy loading is that it produces very light control forces. This makes it easy for the pilot to inadvertently overstress the airplane.
Limits for the location of the airplane’s center of gravity are established by the manufacturer. These are the fore and aft limits beyond which the CG should not be located for flight. These limits are published for each airplane in the Type Certificate Data Sheet, or Aircraft Specification and the Airplane Flight Manual or Pilot’s Operating Handbook (AFM/POH). If, after loading, the CG is not within the allowable limits, it will be necessary to relocate some items within the airplane before flight is attempted.
The forward centerofgravity limit is often established at a location that is determined by the landing characteristics of the airplane. During landing, which is one of the most critical phases of flight, exceeding the forward CG limit may result in excessive loads on the nosewheel; a tendency to nose over on tailwheeltype airplanes; decreased performance; higher stalling speeds; and higher control forces. In extreme cases, a CG location that is forward of the forward limit may result in nose heaviness to the extent that it may be difficult or impossible to flare for landing. Manufacturers purposely place the forward CG limit as far rearward as possible to aid pilots in avoiding damage to the airplane when landing. In addition to decreased static and dynamic longitudinal stability, other undesirable effects caused by a CG location aft of the allowable range may include extreme control difficulty, violent stall characteristics, and very light stick forces that make it easy to overstress the airplane inadvertently.
A restricted forward centerofgravity limit is also specified to assure that sufficient elevator deflection is available at minimum airspeed. When structural limitations or large stick forces do not limit the forward CG position, it is located at the position where fullup elevator is required to obtain a high angle of attack for landing.
The aft centerofgravity limit is the most rearward position at which the CG can be located for the most critical maneuver or operation. As the CG moves aft, a less stable condition occurs, which decreases the ability of the airplane to right itself after maneuvering or turbulence.
For some airplanes the CG limits, both fore and aft, may be specified to vary as gross weight changes. They may also be changed for certain operations such as acrobatic flight, retraction of the landing gear, or the installation of special loads and devices that change the flight characteristics.
The actual location of the CG can be altered by many variable factors and is usually controlled by the pilot. Placement of baggage and cargo items determines the CG location. The assignment of seats to passengers can also be used as a means of obtaining a favorable balance. If the airplane is tailheavy, it is only logical to place heavy passengers in forward seats. Also, fuel burn can affect the CG based on the location of the fuel tanks.
Would you like to purchase a hard copy of the Pilot's Handbook of Aeronautical Knowledge? Click here for the American Flyers Pilot Shop. 
Weight and balance control should be a matter of concern to all pilots. The pilot has control over loading and fuel management (the two variable factors that can change both total weight and CG location) of a particular airplane.
The airplane owner or operator should make certain that uptodate information is available in the airplane for the pilot’s use, and should ensure that appropriate entries are made in the airplane records when repairs or modifications have been accomplished. Weight changes must be accounted for and the proper notations made in weight and balance records. The equipment list must be updated, if appropriate. Without such information, the pilot has no foundation upon which to base the necessary calculations and decisions.
Before any flight, the pilot should determine the weight and balance condition of the airplane. Simple and orderly procedures, based on sound principles, have been devised by airplane manufacturers for the determination of loading conditions. The pilot must use these procedures and exercise good judgment. In many modern airplanes, it is not possible to fill all seats, baggage compartments, and fuel tanks, and still remain within the approved weight and balance limits. If the maximum passenger load is carried, the pilot must often reduce the fuel load or reduce the amount of baggage.
The pilot should be familiar with terms used in working the problems related to weight and balance. The following list of terms and their definitions is well standardized, and knowledge of these terms will aid the pilot to better understand weight and balance calculations of any airplane. Terms defined by the General Aviation Manufacturers Association as an industry standard are marked in the titles with GAMA.
the reference datum, or in percent of mean aerodynamic chord (MAC).
Gasoline . . . . . . . . . . . . . . . . . . . . . 6 lb/US gal Jet A, Jet A1 . . . . . . . . . . . . . . . . 6.8 lb/US gal Jet B . . . . . . . . . . . . . . . . . . . . . . . 6.5 lb/US gal Oil . . . . . . . . . . . . . . . . . . . . . . . . 7.5 lb/US gal Water . . . . . . . . . . . . . . . . . . . . . 8.35 lb/US gal
It might be advantageous at this point to review and discuss some of the basic principles of how weight and balance can be determined. The following method of computation can be applied to any object or vehicle where weight and balance information is essential; but to fulfill the purpose of this handbook, it is directed primarily toward the airplane.
By determining the weight of the empty airplane and adding the weight of everything loaded on the airplane, a total weight can be determined. This is quite simple; but to distribute this weight in such a manner that the entire mass of the loaded airplane is balanced around a point (CG), which must be located within specified limits, presents a greater problem, particularly if the basic principles of weight and balance are not understood.
The point where the airplane will balance can be determined by locating the center of gravity, which is, as stated in the definitions of terms, the imaginary point where all the weight is concentrated. To provide the necessary balance between longitudinal stability and elevator control, the center of gravity is usually located slightly forward of the center of lift. This loading condition causes a nosedown tendency in flight, which is desirable during flight at a high angle of attack and slow speeds.
A safe zone within which the balance point (CG) must fall is called the CG range. The extremities of the range are called the forward CG limits and aft CG limits. These limits are usually specified in inches, along the longitudinal axis of the airplane, measured from a datum reference. The datum is an arbitrary point, established by airplane designers, which may vary in location between different airplanes. [Figure 82]
The distance from the datum to any component part of the airplane, or any object loaded on the airplane, is called the arm. When the object or component is located aft of the datum, it is measured in positive inches; if located forward of the datum, it is measured as negative inches, or minus inches. The location of the object or part is often referred to as the station. If the weight of any object or component is multiplied by the distance from the datum (arm), the product is the moment. The moment is the measurement of the gravitational force that causes a tendency of the weight to rotate about a point or axis and is expressed in poundinches.
To illustrate, assume a weight of 50 pounds is placed on the board at a station or point 100 inches from the datum. The downward force of the weight can be determined by multiplying 50 pounds by 100 inches, which produces a moment of 5,000 lbin. [Figure 83]
To establish a balance, a total of 5,000 lbin must be applied to the other end of the board. Any combination of weight and distance which, when multiplied, produces a 5,000 lbin moment will balance the board. For example, as illustrated in figure 84, if a 100pound weight is placed at a point (station) 25 inches from the datum, and another 50pound weight is placed at a point (station) 50 inches from the datum, the sum of the product of the two weights and their distances will total a moment of 5,000 lbin, which will balance the board.
The airplane’s weight and balance restrictions should be closely followed. The loading conditions and empty weight of a particular airplane may differ from that found in the AFM/POH because modifications or equipment changes may have been made. Sample loading problems in the AFM/POH are intended for guidance only; therefore, each airplane must be treated separately. Although an airplane is certified for a specified maximum gross takeoff weight, it will not safely take off with this load under all conditions. Conditions that affect takeoff and climb performance such as high elevations, high temperatures, and high humidity (highdensity altitudes) may require a reduction in weight before flight is attempted. Other factors to consider prior to takeoff are runway length, runway surface, runway slope, surface wind, and the presence of obstacles. These factors may require a reduction in weight prior to flight.
Some airplanes are designed so that it is difficult to load them in a manner that will place the CG out of limits. These are usually small airplanes with the seats, fuel, and baggage areas located near the CG limit. These airplanes, however, can be overloaded in weight.
Other airplanes can be loaded in such a manner that they will be out of CG limits even though the useful load has not been exceeded.
Because of the effects of an outofbalance or overweight condition, a pilot should always be sure that an airplane is properly loaded.
There are various methods for determining the loaded weight and center of gravity of an aircraft. There is the computation method, as well as methods that utilize graphs and tables provided by the aircraft manufacturer.
The computational method involves the application of basic math functions. The following is an example of the computational method.
Given:
Maximum Gross Weight . . . . . . . . . . . . . .3400 lb CenterofGravity Range . . . . . . . . . . . . . 7886 in Front Seat Occupants . . . . . . . . . . . . . . . . . .340 lb Rear Seat Occupants . . . . . . . . . . . . . . . . . .350 lb Fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 gal Baggage Area 1 . . . . . . . . . . . . . . . . . . . . . . .80 lb To determine the loaded weight and CG, follow these steps.
Step 1—List the weight of the airplane, occupants, fuel, and baggage. Remember that fuel weighs 6 pounds per gallon.
Step 2—Enter the moment for each item listed. Remember “weight x arm = moment.”
Step 3—Total the weight and moments.
Step 4—To determine the CG, divide the total moment by the total weight.
NOTE: The weight and balance records for a particular airplane will provide the empty weight and moment as well as the information on the arm distance.
������������������  ������  ���  �������� 
�����������������������  �����  ������  ������������ 
��������������������  �����  ������  ������������� 
�������������������  �����  �����  ������������� 
����  �����  ������  ������������� 
��������������  ������  �����  ������������� 
�������������������������  �����  �������  
�������������������������� 
The total loaded weight of 3,320 pounds does not exceed the maximum gross weight of 3,400 pounds and the CG of 84.8 is within the 7886 inch range; therefore, the airplane is loaded within limits.
The table method applies the same principles as the computational and graph methods. The information and limitations are contained in tables provided by the manufacturer. Figure 87 is an example of a table and a weight and balance calculation based on that table. In this problem, the total weight of 2,799 pounds and moment of 2,278/100 are within the limits of the table.
Figure 89 is a sample of weight and balance computation using an airplane with a zero fuel weight. In this example, the total weight of the airplane less fuel is 4,240 pounds, which is under the zero fuel weight of 4,400 pounds. If the total weight of the airplane without fuel had exceeded 4,400 pounds, passengers or cargo would have to be reduced to bring the weight at or below the max zero fuel weight.
A pilot must be able to accurately and rapidly solve any problems that involve the shift, addition, or removal of weight. For example, the pilot may load the aircraft within the allowable takeoff weight limit, then find a CG limit has been exceeded. The most satisfactory solution to this problem is to shift baggage, passengers, or both. The pilot should be able to determine the minimum load shift needed to make the aircraft safe for flight. Pilots should be able to determine if shifting a load to a new location will correct an outoflimit condition. There are some standardized calculations that can help make these determinations.
When weight is shifted from one location to another, the total weight of the aircraft is unchanged. The total moments, however, do change in relation and proportion to the direction and distance the weight is moved. When weight is moved forward, the total moments decrease; when weight is moved aft, total moments increase. The moment change is proportional to the amount of weight moved. Since many aircraft have forward and aft baggage compartments, weight may be shifted from one to the other to change the CG. If starting with a known aircraft weight, CG, and total moments, calculate the new CG (after the weight shift) by dividing the new total moments by the total aircraft weight.
To determine the new total moments, find out how many moments are gained or lost when the weight is shifted. Assume that 100 pounds has been shifted from station 30 to station 150. This movement increases the total moments of the aircraft by 12,000 lbin.
Moment when
at station 150 = 100 lb x 150 in = 15,000 lbin
Moment when
at station 30 = 100 lb x 30 in = 3,000 lbin
Moment change = 12,000 lbin
By adding the moment change to the original moment (or subtracting if the weight has been moved forward instead of aft), the new total moments are obtained. Then determine the new CG by dividing the new moments by the total weight:
Total moments = 616,000 + 12,000 = 628,000 _{CG =} 628,000 _{= 78.5 in }8,000 (Total weight)
The shift has caused the CG to shift to station 78.5
A simpler solution may be obtained by using a computer or calculator and a proportional formula. This can be done because the CG will shift a distance that is proportional to the distance the weight is shifted.
Weight Shifted ∆CG (change of CG)_ _
= Total Weight Distance weight is shifted
100 _{= }∆CG8,000 120
∆CG = 1.5 in
The change of CG is added to (or subtracted from when appropriate) the original CG to determine the new CG:
77 + 1.5 = 78.5 inches aft of datum
The shifting weight proportion formula can also be used to determine how much weight must be shifted to achieve a particular shift of the CG. The following problem illustrates a solution of this type.
Given: Aircraft Total Weight . . . . . . . . . . . . . . . . .7,800 lb CG . . . . . . . . . . . . . . . . . . . . . . . . . . . .Station 81.5 Aft CG Limit . . . . . . . . . . . . . . . . . . . . . . . . . .80.5
Given: Aircraft Total Weight . . . . . . . . . . . . . . . . .6,860 lb CG Station . . . . . . . . . . . . . . . . . . . . . . . . . . . .80.0
Determine the location of the CG if 140 pounds of baggage is added to station 150.
Solution:  

Added Weight New Total Weight  =  ∆CG Distance between weight and old CG 
140 6,860 + 140  =  ∆CG 150–80 
140 7,000  =  ∆CG 70 
CG  =  1.4 in aft 
Add ∆CG to old CG 
New CG = 80.0 in + 1.4 in = 81.4 in
Determine how much cargo must be shifted from the aft cargo compartment at station 150 to the forward cargo compartment at station 30 to move the CG to
exactly the aft limit.  

Solution:  
Weight to be Shifted Total Weight  =  ∆CG Distance weight is shifted 
Weight to be Shifted 7,800  =  1.0 in 120 in 
Weight to be Shifted  =  65 lb 
In many instances, the weight and balance of the aircraft will be changed by the addition or removal of weight. When this happens, a new CG must be calculated and checked against the limitations to see if the location is acceptable. This type of weight and balance problem is commonly encountered when the aircraft burns fuel in flight, thereby reducing the weight located at the fuel tanks. Most small aircraft are designed with the fuel tanks positioned close to the CG; therefore, the consumption of fuel does not affect the CG to any great extent.
The addition or removal of cargo presents a CG change problem that must be calculated before flight. The problem may always be solved by calculations involving total moments. A typical problem may involve the calculation of a new CG for an aircraft which, when loaded and ready for flight, receives some additional cargo or passengers just before departure time.
810
Given: Aircraft Total Weight . . . . . . . . . . . . . . . . .6,100 lb CG Station . . . . . . . . . . . . . . . . . . . . . . . . . . . .80.0
Determine the location of the CG if 100 pounds is removed from station 150.
Solution:  

Weight Removed New Total Weight  =  ∆CG Distance between weight and old CG 
100 6,100 – 100  =  ∆CG 150 – 80 
100 6,000  =  ∆CG 70 
CG  =  1.2 in forward 
Subtract ∆CG from old CG New CG = 80 in  1.2 in = 78.8 in
In the previous examples, the ∆CG is either added or subtracted from the old CG. Deciding which to accomplish is best handled by mentally calculating which way the CG will shift for the particular weight change. If the CG is shifting aft, the ∆CG is added to the old CG; if the CG is shifting forward, the ∆CG is subtracted from the old CG.
American Flyers is happy to provide Chapter 8 from the Pilot's Handbook of Aeronautical Knowledge , an FAA Publication Would you like to purchase a hard copy of the Pilot's Handbook of Aeronautical Knowledge? Click here for the American Flyers Pilot Shop. Chapter 1 • Chapter 2 • Chapter 3 • Chapter 4 • Chapter 5 • Chapter 6 • Chapter 7 • Chapter 8 • Chapter 9 • Chapter 10 