Weight and Balance
A pilot cannot legally fly an aircraft unless:
 the aircraft is operated in accordance with the requirements of the Pilot Operating Handbook—including weight and loading limitations;1
 the load is properly disposed in the aircraft;2
 the cargo and equipment is secured to prevent shifting and the passenger exits are not blocked.3
There are various terms associated with weight and balance:
 Standard Weight Empty (Standard Empty Weight) is the weight of the airframe and engines with standard equipment, including unusable fuel and oil. Essentially, this is the weight of the aircraft when it came out of the factory, before optional equipment was added.
 Basic Empty Weight is the weight of the aeroplane with the current equipment options (instruments, radios, interior features), excluding passengers, cargo and usable fuel; depending on the aircraft manufacturer, basic empty weight sometimes includes full oil weight, and the pilot must examine the aircraft weight and balance list to determine if oil weight is included.
 Usable Fuel is aircraft fuel available for flight, while Unusable Fuel is fuel remaining in the tanks that is unreliable and cannot be used.
 Maximum Gross Weight is the maximum permissible weight of the aeroplane.
 Useful (Disposable) Load is gross takeoff weight, less basic empty weight.
 Operation Gross Weight is the weight of the aircraft loaded for takeoff (Basic Empty Weight plus Payload Weight).
Requirements
Before each flight, the pilot must ensure that the aircraft does not exceed the maximum gross weight. The pilot must also determine the Centre of Gravity (C of G) of an aircraft before each flight to ensure it is between the maximum rearward and maximum forward positions (the C of G Range).
The C of G is the central balance of the aircraft—the point at which it could be suspended and remain balanced— and is calculated using the load “positions” or “stations” prescribed in the Pilot Operating Handbook and the actual load anticipated for an intended flight.
Aeroplane manufacturers publish weight and balance limits, including the Standard Empty Weight in the aircraft’s Pilot Operating Handbook. In addition, each aircraft has an Aircraft Weight and Balance Report which is kept with the aircraft documents; it provides the actual Basic Empty Weight (BEW) and C of G information for the specific aircraft, including changes in radio equipment and any other equipment or airframe changes since manufacture. Typically, the aircraft documents will include a series of superseded reports, but only the latest report must be used for calculation purposes.
In the Weight and Balance section of the Pilot Operating Handbook, data is provided for each “position” or “station” in the aircraft. Specifically, the Pilot Operating Handbook data provides an arm for each station, which is the distance in inches from a predetermined balance datum line (the datum line is simply a reference line that allows measurement of longitudinal position of the stations). Typically, station arms are provided for the front passengers, the second row passengers, the rear cargo hold, the forward cargo hold, and the fuel. The weight and balance is calculated by using the station information and anticipated weight at each station, as well as the aircraft BEW and its corresponding C of G as derived from the Aircraft Weight and Balance Report.
Procedure
For each station item, the weight is multiplied by the arm to establish (for each position) a moment. To determine the aircraft C of G, the total moment (all station moments added together, including the BEW moment) is divided by the total weight. The sum, in inches, provides the C of G for the aircraft and is compared with the aircraft C of G “envelope” found in the Pilot Operating Handbook to determine if it is within limits.
Item 
Weight (pounds) 
Arm (inches) 
Moment 

Basic Empty Weight 
1380 
85.0 
117,3004 
Pilot and Front Passengers 
320 
85.5 
27,360 
Rear Passengers 
90 
117 
10,530 
Fuel (usable) 
180 
95 
17,100 
Baggage Area #1 
25 
133 
3,325 
Totals 
1995 

175,615 
C of G: 
175,615 1995 
= 88.0 
A computation table, such as appears above, helps simplify the calculations. In this example, the total weight (1995 lbs.) is added up to ensure it is within the permissible limit; then the total moment (175,615) is divided by the total weight to provide the centre of gravity (88.0 inches); finally, this C of G number, along with the total takeoff weight of the aircraft, is checked against graphs found in the Pilot Operating Handbook to determine if the aircraft is within permissible limits.
These graphs commonly depict the maximum aft C of G and the maximum forward C of G in relation to various takeoff weights. In the sample graph that appears to the right, the maximum forward limit is 84 inches aft datum, and the maximum rearward limit is 96 inches. To conduct a takeoff beyond these limits would be deadly. Note also that the maximum takeoff weight—for this aircraft, 2150 lbs.—could only be used when the C of G is between 88.5 inches and 96 inches; as the weight is reduced, the C of G must migrate forward of 88.5 to remain within the graph limits. Finally, note how this graph sets the legal limits for utility category manoeuvres, such as spins, or steep turns in excess of 45° bank (see discussions on P. 27).
While the format of the above weight and balance graphic is typical of many aircraft such as the Piper Cherokee, there is a second format commonly used. In the Pilot Operating Handbook of Cessna aircraft, for example, the determination of the aircraft’s balance point does not include the calculation of the C of G directly; instead the pilot determines the balance point by calculating the total moment of the aircraft—i.e., simply adding all the moments together—and then comparing this number with the aircraft’s total weight.
In the above example we have used, the total moment was of course 175,615, a unit referred to as poundinches. Since this figure is commonly large and cumbersome, the number is typically divided by 1000; so 175,615 lbin. would become 175.615 lbin/1000. (The unit names have the appearance of rocket science, but in fact it is all real simple stuff.) It is the 175.6 figure, along with the total weight of the aircraft (1995 lbs.), which is checked against graphs in the aircraft’s Pilot Operating Handbook. As show in the graph that appears below, the information presented is more or less identical to that which appears in the previous weight and balance graph.
To determine the poundinches/1000 a second specialized graph is used which makes this format of weight and balance quite easy to calculate. This second graph appears above, and you can see that each station—pilot and front passenger, Rear passenger, fuel, etc.—has its own reference line. The weight for each station establishes a point on the reference line, and the station moment (lbin/1000) is determined by extension of a downward vertical line. These can then be entered on a table, as shown below.
Item 
Moment (lb.inches/1000) 

Basic Empty Weight 
175.6 
Pilot and Front Passengers 
27.3 
Rear Passengers 
10.5 
Fuel (usable) 
17.1 
Baggage Area #1 
3.3 
Totals 
175.8 
There may be some confusion over the fact that 175.8 value appears in the above table instead of the 175.8 figure that is plugged into the graph above; the reason for this is that the last two digits are dropped when using the loadweight graph to the right—the difference is inconsequential.
Actual passenger weights must be used in calculating weight and balance, but if these are not available, the following average passenger weights (published in the Aeronautical Information Publication) can be used:
Type of Passenger 
Summer Weight 
Winter Weight 

MALES (12 years and up) 
200 lbs. (90.7 kg.) 
206 lbs. (93.4 kg.) 
FEMALES (12 years and up) 
165 lbs. (74.8 kg.) 
171 lbs. (77.5 kg. ) 
CHILDREN (2 – 11 years) 
75 lbs. (34.0 kg.) 
75 lbs. (34.0 kg.) 
INFANTS (less than 2 years) 
30 lbs. (13.6 kg.) 
30 lbs. (13.6 kg.) 
NOTE:
 On any flight involving a number of passengers whose weights, including carryon baggage, will exceed the average weights listed above, the actual weights of such passengers are to be used.
 The weight of infants must be added separately when the infant’s weight exceeds 10% of the adult responsible.
 Where carryon baggage is not involved or permitted, the weights for males and females may be reduced by 13 lbs (5.9 kg.).
In calculating fuel, aviation fuel weighs approximately 6 lbs. per US Gallon and oil weighs 1.95 lbs. per litre. One US Gallon contains 3.79 litres.
Note that the Aircraft Weight and Balance Report for some aircraft includes oil, while others do not; where oil is not included, the oil station (including weight, arm, and moment) must be added to the preflight calculations. This can only be determined by examining the actual report, including the equipment/weight list included in the Report. Oil weights are published in the Canada Flight Supplement. On occasion, oil is presented as a negative value in the weight and balance calculations (this appears in the table below), and this is because the location of oil is sometimes behind the datum line. Not to worry, here, as the negative moment value for oil (333 lb.inches in the case above) is simply subtracted in reckoning the total moment value. Negative values appear typically when the reference datum line is configured at the firewall (separating the engine and cabin compartments), but it is more common for designers to place the reference datum line at or near the spinner.
Item 
Weight (pounds) 
Arm (inches) 
Moment 
Basic Empty Weight 
1380 
85.0 
117,3005 
Pilot and Front Passengers 
320 
85.5 
27,360 
Rear Passengers 
90 
117 
10,530 
Oil 
22 
15 
333 
Fuel 
180 
95 
17,100 
Baggage Area #1 
25 
133 
3,325 
Totals 
2017 
C of G 
174,949 
.
C of G: 
174,949 2017 
= 86.7 
Weight, Balance and Performance
The heavier the aircraft, the greater the lift required from the wing throughout the speed range. Consider, for example, two identical aircraft, one lightly loaded and the second heavily loaded. If both are flying at the same indicated airspeed, it is clear that the heavier aircraft must have a higher angle of attack (to produce the extra lift) than the lighter aircraft. For a given speed, including speed just above the stall, it must be that the angle of attack of the heavier aircraft is closer to the critical stall angle of attack than the light aircraft—it follows, therefore, that the lighter an aircraft, the slower its stall speed.
The same argument as above can be applied to fuel economy. That is, the aircraft with a lower angle of attack for a given speed must have less induced drag and therefore less thrust (fuel burn) will be required.
The location of the Centre of Gravity (C of G) with respect to whether it is forward or rearward also affects aircraft performance. While an aircraft takes off with a specific ramp weight, once it leaves the ground the effective “negative” lift of the horizontal stabilizer has the effect of increasing the aircraft’s “aerodynamic weight.” If a C of G is located forward, the negative lift of the tail will have to be increased to balance the forward weight, and as the negative lift is increased, the aerodynamic weight, overall, is increased. Using the same reasoning as applied above with respect to weight in general, an aircraft with a forward C of G will have a higher stall speed than the aircraft with a rearward C of G. A forward C of G loading, however, has an positive effect with respect to stability—an aircraft with heavy tail loading will be more stable in recovering from a pitchdown attitude as the associated acceleration will activate a greater amount of horizontal stabilizer weight, thereby making it easier to raise the nose. Also, at the point of stall, a forward C of G will make recovery easier (the pilot has more pitch authority on the control column than is the case with a rearward C of G).6
These features, of course, are related to loading variations within limits. An aircraft loaded outside limits is simply dangerous. Always ensure weight and balance is within limits—if it is not and you have an accident, your insurance will not cover property or personal liability.
Further Readings:
Transport Canada's The Importance of Proper Weight and Balance
Transport Canada's Take Five: Overloading
References
1 CAR 602.07,
2 CAR 602.86 (1).
3 CAR 602.86(2).
4 This calculation of the moment is based on weight times arm—1380 × 85.0 = 117,300. The unit of the moment is commonly referred to as poundinches—e.g., 117,300 poundinches.
5 This calculation of the moment is based on weight times arm—1380 × 85.0 = 117,300. The unit of the moment is commonly referred to as poundinches—e.g., 117,300 poundinches.
6 See also discussion regarding the effects of C of G on the stall speed that appears on P. 1.