Pilot's Handbook of Aeronautical Knowledge
Chapter 10: Weight and Balance
Operating an aircraft within the weight and balance limits is critical to flight safety. Pilots must ensure that the center of gravity (CG) is and remains within approved limits throughout all phases of a flight.
If an aircraft's CG is outside the approved limits, positive control will be difficult or impossible, resulting in a hazardous flight condition. In addition, operating above the aircraft's maximum weight limitation compromises its structural integrity and adversely affects performance.
Weight Control
Weight attracts all bodies to the earth. It is a product of the mass of a body. Weight also is the result of acceleration acting on the body.
Loading an aircraft beyond the manufacturer's recommended weight must be avoided. The force of lift, created by the wings, counteracts weight and sustains an aircraft in flight. However, lift is limited by several factors, including airfoil design, angle of attack (AOA), airspeed, and air density. Pilots must understand and respect these limits.
Manufacturers attempt to make aircraft as light as possible without sacrificing strength or safety. Therefore, any item aboard an aircraft that increases the total weight is undesirable for performance.
If an aircraft is not properly loaded, the initial indication of poor performance usually takes place during takeoff. An overloaded aircraft may not be able to leave the ground. If it does become airborne, it may exhibit unexpected and hazardous flight characteristics.
Preflight planning should include a check of performance charts to determine if the aircraft's weight may contribute to hazardous flight operations.
Pilots who manage to depart in an aircraft loaded beyond its gross weight limit can expect:
The operating weight of an aircraft can be changed by simply altering the fuel load. Gasoline weighs six (6) pounds per gallon, which is considerable. The weight of one passenger can range from 20 to 40 gallons of fuel. When taking passengers and cargo, reducing total fuel on board can keep the aircraft within gross weight limits. Flight planning should factor the total range or flight time available based on the reduced amount of total fuel.
During routine flight, fuel burn is the only weight change that takes place. As fuel is used, an aircraft becomes lighter and performance is improved.
Balance, Stability, and Center of Gravity
Balance refers to the location of the center of gravity (CG) of an aircraft. It is critical to stability and safety in flight.
The CG is a point at which the aircraft would balance if it were suspended at that point.
The CG can be moved along the aircraft's longitudinal axis, based on the distribution of weight in the aircraft. The fore and aft location of the CG is the primary concern when determining an aircraft's balance.
The distance between CG's forward and back limits — called the CG range — is certified for an aircraft by the manufacturer.
if the CG is displaced too far forward on the longitudinal axis, a noseheavy condition will result. If the CG is displaced too far aft on the longitudinal axis, a tailheavy condition results. A center of gravity outside of the permissible CG range can result in an unstable or hazardous flight condition.
The position of the lateral CG is not computed in all aircraft. However, pilots must be aware that adverse effects arise as a result of a laterally unbalanced condition. A lateral unbalance occurs if the fuel load is mismanaged by supplying the engine(s) unevenly from tanks on one side of the airplane. This can be offset with rudder trim or constant control pressure. The result will be an outofstreamline aircraft with more drag and decreased efficiency.
Adverse Balance
Just as excess weight affects flight characteristics, adverse balance conditions operate in much the same manner. Stability and positive control are impacted by improper balance.
Loading in a noseheavy condition causes problems in controlling and raising the nose, especially during takeoff and landing.
Loading in a tailheavy condition impacts longitudinal stability and reduces the pilot's ability to recover from stalls and spins. Tailheavy loading also produces very light control forces.
The CG's fore and aft limits are published for each aircraft in the Type Certificate Data Sheet (TCDS), or aircraft specification and the AFM or POH. The CG should not exist beyond these limits before flight. If the CG is beyond the CG range, reloading the aircraft or removing items may be necessary before flight.
Manufacturers purposely place the forward CG limit as far rearward as possible to aid pilots in avoiding damage when landing. This also permits sufficient elevator/control deflection at minimum airspeed.
As the CG moves aft, a less stable condition occurs, which decreases the ability of the aircraft to right itself after maneuvering or turbulence.
For some aircraft, both fore and aft CG limits may be specified to vary as gross weight changes.
Pilots can undertake several actions to relocate the CG before flight, including relocating baggage and cargo items, and placing heavier passengers in forward seats.
While fuel burn can affect the CG, this is based on the location of the fuel tanks. Most small aircraft carry fuel in the wings very near the CG. Therefore, while fuel burn will reduce the aircraft's gross weight, it will have little effect on the loaded CG.
Before any flight, the pilot should determine the weight and balance condition of the aircraft. Charts and graphs are provided in the approved AFM/POH to enable pilots to make weight and balance computations.
A typical generalaviation aircraft (two or four seats) cannot remain within the approved weight and balance limits with full passengers, fuel, and baggage compartments. If the maximum passenger load is carried, the pilot typically will need to reduce the fuel load or baggage.
Weight and Balance Computations
Determining the total weight of a loaded aircraft simply requires totalling the aircraft's empty weight, the fuel and oil, and everything loaded on the aircraft.
Determining the distribution of mass around the CG requires additional calculations.
The point at which an aircraft balances can be determined by locating the CG — the imaginary point at which all the weight is concentrated. To provide the necessary balance between longitudinal stability and elevator control, the CG 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 AOA and slow speeds.
The CG range limits are usually specified in inches, along the longitudinal axis of the airplane, measured from a reference point called a datum. The datum reference is an arbitrary point, established by aircraft designers that may vary in location between different aircraft.
The fulcrum is where the airplane would balance were it placed on a single, raised point. For sample illustrations, the datum can be located at the fulcrum. However, in many aircraft it's at a different location along the longitudinal axis, and it's only used for reference.
The arm is the distance from the datum to any component part or any object loaded on the aircraft. 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 station is the location of passengers, fuel, oil, baggage, and additional items.
The moment is the weight of a station multiplied by the arm. Each occupied station has a calculated moment.
The moment is is expressed in inchpounds (inlb). It is the measurement of the gravitational force that causes a tendency of the weight to rotate about a point or axis.
A classic example of moment weight (or moment effectiveness) is a 50lb weight and a 100lb weight on a playground seesaw — a long board balanced on a fulcrum. The large weight is placed closer to the fulcrum, while the smaller weight is more distant from the fulcrum. The lesser weight has a greater arm. It exhibits as much potential energy as the greater weight because of this greater arm.
In classical physics, this mechanical advantage is called leverage, proven as "the law of the lever" by Archimedes. The further a weight is from the fulcrum, the farther it travels when it is moved around the axis. Objects closer to the fulcrum do not travel as far around the axis. Thus, an object farther from the fulcrum has a greater mechanical advantage — less force is required to change its position.
If small weight's station is 100 inches from the fulcrum, the moment (downward force of the station) can be determined by multiplying 50 pounds (weight) by 100 inches (station). The specific location on the board produces a moment of 5,000 inchpounds.
In order to balance the board, the large weight's moment also should be 5,000 inchpounds. The weight of the object cannot be adjusted, but the station is variable. Thus, in order for the large weight to produce 5,000 inlb of downward force, the station will need to be 50 inches from the fulcrum.
Weight  Arm  Moment  

Small item  50 pounds  100 inches  5,000 inchpounds 
Large item  100 pounds  50 inches  5,000 inchpounds 
These objects in these locations create equal downward forces.
If additional objects are added to the board, the stations of each object can be adjusted so that the total moments on either side of the fulcrum are equal.
Determining Loaded Weight and CG
There are various methods for determining the loaded weight and CG of an aircraft. There is the computational method as well as methods that utilize graphs and tables provided by the aircraft manufacturer.
Computational Method
A simple computational method, using a table format, can be used to determine total weight and center of gravity.
Item  Weight  Arm  Moment  

Aircraft Empty Weight  2,100  x  78.3  =  164,430 
Front Seat Occupants  340  x  85.0  =  28,900 
Rear Seat Occupants  350  x  121.0  =  42,350 
Fuel  450  x  75.0  =  33,750 
Baggage Area 1  80  x  150.0  =  12,000 
Total  3,320  281,430  
Calculate CG:  281,430 ÷ 3,320 = 84.8 
The result is the total arm. This is the location of the CG, as referenced from the datum.
Consult the AFM/POH to determine if the aircraft is at or under the gross weight. In the above example, total aircraft weight is 3,320 pounds.
Also consult the AFM/POH to determine if the CG is within the allowable CG range. In the above example, the CG is 84.8 inches aft of the datum.
If either figure does not permit safe flight operations, the aircraft may need to be loaded differently, and/or some items may need to be removed from the aircraft.
Graph Method
For some aircraft, loaded weight and CG can be determined using graphs provided by the manufacturers. These will be in the AFM/POH. Because moment values can be large numbers, the moment may sometimes be divided by 100, 1,000, or 10,000 to simplify calculations.
To determine the moment using the loading graph, find the weight (along the leftside metric) and draw a line straight across until it intercepts the item for which the moment is to be calculated. These diagonal lines represent stations. Then draw a line straight down to determine the moment.
In the example below, the red line depicts a pilot and passenger weighing a combined 340 pounds, which has a total moment of 127,000 — or 12.7 for purposes of calculation.
Once this has been done for each item, total all weights and all moments. Draw a line for both weight and moment on the CG envelope graph. If the lines intersect within the envelope, the aircraft is loaded within limits.
In the example below, the red line depicts an airplane with a loaded aircraft weight of 2,367 pounds and a total moment of 105.2. The aircraft's CG is within the permissible CG range.
Table Method
The table method uses information and limitations are contained in tables provided by the manufacturer. It applies the same principles as the computational and graph methods. For each station, a range of moments are provided for a range of weights. Minimum and maximum moments are then provided for the aircraft's gross weight.
WeightShift Calculations
The Pilot's Handbook of Aeronautical Knowledge covers "Shifting, Adding, and Removing Weight," while the FAA's Weight and Balance Handbook discusses CG shifts and weight changes in more detail. Questions regarding this subject matter are found on the Commercial Pilot, Ground Instructor, and Flight Instructor written tests.
The proof for all weightchange and weightshift problems is presented as three equations on a grid. The left column is the weight ratio, while the right column is the distance ratio. The quotients of both ratios are equal.
Weight to be shifted  Δ CG  
÷  =  ÷ 

Total weight  Distance weight is shifted 
One simple mnemonic for this grid is "CACS," for "Cargo, Airplane, CG (change), Shift (distance)." Note that Δ stands for "change" and does not represent the aircraft's initial CG, nor its resultant CG. Both values in the distance ratio are transit lengths, not a specific station or CG.
This table permits identifying any missing value, simply by multiplying two corresponding values, and then dividing the result by the third known value. However, typically the weight of the aircraft is known, so this is not a common aviation problem. Pilots are concerned with:
I know. You were told there would be no math…
Each question above can be solved with a twostep equation.
To illustrate, let's start with an aircraft with a loaded gross weight of 4,800 lbs. The aft limit of the CG is 97 inches. However, the loaded aircraft has a CG of 99 inches aft of the datum, or two (2) inches beyond the aft CG limit. The aircraft has luggage at the rear station (130 inches), which weighs 150 pounds. All of this luggage can be relocated to a forward station (45 inches).
If the distance between the current station of the luggage and the proposed new station is known, how much weight should be transferred to the new station?
The aircraft weight (4,800 lbs.), distance between the arms (85 inches), and desired CG change (2 inches) are known. Start with the aircraft weight and multiply by the inches the CG must transit. Then, divide the result by the third known factor, which is the distance between the stations.
4800 x 2 = 9600.
9600 ÷ 85 = 112.94.
About 113 lbs. of luggage must move to the forward station to move the CG forward two (2) inches. Moving all 150 lbs to the forward station will move the CG even closer to the datum.
Weight to be shifted
112.94 lbs. 
Δ CG
2 inches 

x ↗  ÷ ↓  

Total weight
4,800 lbs. 
Distance weight is shifted
85 inches 
Confirm that both quotients are equal to prove the result:
4800 ÷ 112.94 = 42.5
90 ÷ 2.25 = 42.5
If the weight of the luggage that is to be moved is known, by what distance should be relocated?
In this case, let's again use 150 pounds of luggage. The aircraft still weighs 4,800 lbs, and the CG is two (2) inches beyond the aft limit. Again, we will multiply the total weight by the Δ CG and divide the result by the third known factor — this time, the weight of the luggage.
4800 x 2 = 9600.
9600 ÷ 150 = 64
The luggage must move 64 inches forward to move the CG forward two (2) inches.
Weight to be shifted
150 lbs. 
← ÷  Δ CG
2 inches 

x ↗  
Total weight
4,800 lbs. 
Distance weight is shifted
64 inches 
Confirm that both quotients are equal to prove the result:
4800 ÷ 150 = 32
64 ÷ 2 = 32
If the weight and transit of the cargo is known, how much will the new loading shift the CG?
Let's move 120 pounds of luggage to a station 90 inches closer to the datum. The aircraft still weighs 4,800 lbs. For this problem, we will multiply the weight shifted by the inches of transit, and then divide the result by the aircraft's weight:
120 x 90 = 10800
10800 ÷ 4800 = 2.25
The aircraft's CG will move 2.25 inches.
Weight to be shifted
120 lbs. 
Δ CG
2.25 

x ↘  

Total weight
4,800 lbs. 
← ÷  Distance weight is shifted
90 inches 
Confirm that both quotients are equal to prove the result:
4800 ÷ 120 = 40
90 ÷ 2.25 = 40
While this may not seem deadsimple at first, note that each formula begins with either the numerator or denominator of the weight ratio multiplied by the the crossfactor of the distance ratio (if using the denominator, multiply by the numerator). The result is then divided by the final known factor. Which is to say:
"Divide Twice": An alternate pattern is to divide the known ratio to get a positive integer, and then divide that result by the remaining known factor. It's just as reliable, and for some pilots it might be easier to remember. However, the FAA doesn't present this pattern in their texts.
WeightAdd Calculations
To calculate how additional weight affects the CG, we have to adjust the formula slightly. Now, the "distance traveled" becomes the distance from the station where weight is added and the aft limit of the CG range.
The weight of the aircraft is the loaded weight before the additional cargo is added.
Weight to be added  Δ CG (to reach limit)  
÷  =  ÷ 

Total weight  Distance between station and CG limit 
If luggage were added to a compartment with a station in front of the CG, then we'd compare the new station to the CG's fore limit. Baggage compartments in the nose section are typically found on large turboprop aircraft.
What is the maximum weight that can be added at a given station while keeping the CG within limits?
In a 2,800pound loaded aircraft, let's say a passenger wants to add luggage to a station 112 inches from the datum. The current CG is 80.5, and the aft CG limit is 82, which permits 1.5 inches of aft CG transit. The station is 30 inches from the CG limit. How much weight can be added at the station?
2800 x 1.5 = 4200
4200 ÷ 30 = 140
Weight to be added
150 lbs. 
Δ CG (maximum)
1.5 

x ↗  ↓ ÷  

Total weight
2,800 lbs. 
Distance between station and CG limit
30 inches 
Any weight beyond 140 pounds at the 112inch station will place the CG beyond the aft limit.
Confirm that both quotients are equal to prove the result:
2800 ÷ 140 = 20
30 ÷ 1.5 = 20
How will a change in known weight at a given station affect the CG? And will the CG remain in limits?
In our 2,800pound loaded aircraft, let's say a passenger wants to add 290 pounds of luggage to a station 108 inches from the datum. The current CG is 80.5, and the aft CG limit is 82, which permits 1.5 inches of aft CG transit. The station is 26 inches from the CG limit. How far will the CG shift when the new cargo is added to the station?
290 x 26 = 7540
7540 ÷ 2800 = 2.69
Weight to be added
290 lbs. 
Δ CG
2.69 

x ↘  

Total weight
2,800 lbs. 
← ÷  Distance between station and CG limit
26 inches 
290 pounds of additional weight at the 108inch station will shift the CG 2.69 inches, to a new location of 83.19 inches. This is greater than 82 inches, i.e. the 1.5 inches that's available between the current CG and the aft limit.
Confirm that both quotients are equal to prove the result:
2800 ÷ 290 = 9.655
26 ÷ 2.69 = 9.66
Computation Method
This problem also can be solved with the computation method, for both adding and removing weight.
Item  Weight  Arm  Moment  

Aircraft Loaded Weight  2,800  x  80.5  =  225,400 
Δ Weight  290  x  108  =  31320 
Total  3,090  256720  
Calculate CG:  256200 ÷ 3,080 = 83.08 
83.08  80.5 = 2.58 inches of CG transit. This represents a 0.11inch differential from the algebraic method. When the aircraft weight in that forumula is increased to 3,090 pounds, the result is 2.44, which is a 0.25inch differential (with a new CG of 82.94). Therefore, the results do not converge when the aircraft weight is increased in the algebraic method. FAA test questions suggest using the "old" aircraft weight for the equations and not increasing the weight.
For testing purposes, if adding or removing weight does not seem to provide the best answer via the algebraic method, try the same problem with the computational method.
When using the computation method for removing weight, use a negative value at the Δ station. The corresponding moment also will deducted from the sum of all moments.
Terms and Definitions
For additional information on weight, balance, CG, and aircraft stability refer to the FAA handbook appropriate to the specific aircraft category.
Commercial Pilot & Flight Instructor Test Questions
The center of gravity of an aircraft is computed along the longitudinal axis.
The center of gravity of an aircraft can be determined by dividing the total moment by the total weight.
With respect to using the weight information given in a typical aircraft owner's manual for computing gross weight, it is important to know that if items have been installed ni the aircraft in addition to the original equipment, the allowable useful load is decreased.
If the nosewheel of an airplane moves aft during gear retraction, how would this aft movement affect the CG location of that airplane? It would cause the CG location to move aft.
If the landing gear on an airplane moves forward during retraction, the total moment will decrease.
— The forward movement along the longitudinal axis decreases the landing gear's arm, and thus its moment, and thus the aircraft's total moment.
How does increased weight affect the takeoff distance of the airplane? The airplane will accelerate more slowly with the same power output, and a higher airspeed is required to generate necessary lift for takeoff.
To maintain level flight in an airplane which is loaded with the CG at the forward limit, an additional download must be imposed on the horizontal stabilizer. This in turn produces an additional load which the wing must support.
An aircraft is loaded with the CG aft of the aft limit. What effect will this have on controllability? Stall and spin recovery may be impossible.
An aircraft is loaded with the CG at the aft limit. What are the performance characteristics compared with the CG at the forward limit? The aft CG provides the lowest stalling speed, the highest cruising speed, and least stability.
— The CG at the aft limit relieves the tail surfaces from imposing the normal downloading force. The wing is then relieved of load. The wing flies at a lower angle of attack, reducing stall speed and drag while increasing cruising speed. However, longitudinal stability is decreased.
As the CG moves aft, the aircraft becomes less stable and less controllable.
As the CG location is changed, recovery from a stall becomes progressively more difficult as the CG moves rearward.
What is the effect of center of gravity on the spin characteristics of a fixedwing aircraft? If the CG is too far a flat spin may develop.
The stalling speed of an aircraft will be highest when the aircraft is loaded with a high gross weight and forward CG.
— The horizontal tail surfaces must provide increased downward force to counter a forward CG, which increases the load imposed on the wing. Stall speed is increased.
If the CG of an aircraft is moved from the aft limit to beyond the forward limit, how will it affect the cruising and stalling speed? Decrease in the cruising speed and increase in the stalling speed.
— Forward CG increases load factor, due to the increased downforce required from the horizontal tail surfaces. Crusising flight will require a higher angle of attack than normal, which will reduce the cruising speed.
When an aircraft's forward CG limit is exceeded, it will affect the flight characteristics of the aircraft by producing higher stalling speeds and more longitudinal stability.
— An advantage of forward CG is greater longitudinal stability. As airspeed decreases, the nose will tend to drop.
What is a characteristic of the indicated airspeed if the CG is at the most forward allowable position and constant power and altitude are maintained? The indicated airspeed will be less than it would be with the CG in the most rearward allowable position.
— With the CG at the mostforward position, the wing will fly at a higher angle of attack and generate more induced drag. Indicated airspeed will be lower, compared to the same airplane with the CG at the maximum aft position.
Under which condition is a forward CG most critical? On landing.
— The landing flare requires enough elevator authority to raise the nosewheel.
Calcuations
What is the location of the CG if 60 pounds are removed from Station 70?
Total weight: 8,420 lb
CG location: Station 85
Answer: 85.1
Could 100 pounds of weight be shifted from Station 30.0 to Station 120.0 without exceeding the aft CG limit?
Total weight: 4,750 lb
CG location: Station 115.8
Aft CG limit: Station 118.0
Answer: Yes; the new CG would be located at Station 117.69.