aircraft weight
and balance
A.
general
You as pilot are responsible for the safe loading of your airplane and must
ensure that it is not overloaded. The performance of an airplane is influenced
by its weight and overloading it will cause serious problems. The takeoff run
necessary to become airborne will be longer. In some cases, the required
takeoff run may be greater than the available runway. The angle of climb and
the rate of climb will be reduced. Maximum ceiling will be lowered and range
shortened. Landing speed will be higher and the landing roll longer. In
addition, the additional weight may cause structural stresses during manoeuvres
and turbulence that could lead to damage.
The total gross weight authorized for any particular type of airplane must
therefore never be exceeded. A pilot must be capable of estimating the proper
ratio of fuel, oil and payload permissible for a flight of any given duration.
The weight limitations of some general aviation airplanes do not allow for all
seats to be filled, for the baggage compartment to be filled to capacity and for
a full load of fuel as well. It is necessary, in this case, to choose between
passengers, baggage and full fuel tanks.
The distribution of weight is also of vital importance since the position of
the centre of gravity affects the stability of the airplane. In loading an
airplane, the C.G. must be within the permissible range and remain so during the
flight to ensure the stability and manoeuvrability of the airplane during
flight.
Airplane manufacturers publish weight and balance limits for their airplanes.
This information can be found in two sources:
1. The Aircraft Weight and Balance Report.
2. The Airplane Flight Manual.
The information in the Airplane Flight Manual is general for the particular
model of airplane.
The information in the Aircraft Weight and Balance Report is particular to a
specific airplane. The airplane with all equipment installed is weighed and the
C.G. limits calculated and this information is tabulated on the report that
accompanies the airplane logbooks. If alterations or modifications are made or
additional equipment added to the airplane, the weight and balance must be
recalculated and a new report prepared.
B. weight
Various terms are used in the discussion of the weight of an airplane. They
are as follows:
Standard Weight Empty: The weight of the airframe and engine with all
standard equipment installed. It also includes the unusable fuel and oil.
Optional or Extra Equipment: Any and ail additional instruments, radio
equipment, etc., installed but not included as standard equipment, the weight of
which is added to the standard weight empty to get the basic empty weight. It
also includes fixed ballast, full engine coolant, hydraulic and deicing
fluid.
Basic Weight Empty: The weight of the airplane with all optional
equipment included. In most modern airplanes, the manufacturer includes full oil
in the basic empty weight.
Useful load (or Disposable load): The difference between gross takeoff
weight and basic weight empty. It is, in other words, all the load which is
removable, which is not permanently part of the airplane. It includes the usable
fuel, the pilot, crew, passengers, baggage, freight, etc.
Payload: The load available as passengers, baggage, freight, etc., after
the weight of pilot, crew, usable fuel have been deducted from the useful
load.
Operational Weight Empty: The basic empty weight of the airplane plus the
weight of the pilot. It excludes payload and usable fuel.
Usable Fuel: Fuel available for flight planning.
Unusable Fuel: Fuel remaining in the tanks after a runout test has been
completed in accordance with government regulations.
Operational Gross Weight: The weight of the airplane loaded for takeoff.
It includes the basic weight empty plus the useful load.
Maximum Gross Weight: The maximum permissible weight of the
airplane.
Maximum TakeOff Weight: The maximum weight approved for the start of the
takeoff run.
Maximum Ramp Weight: The maximum weight approved for ground
manoeuvring.
It includes the weight of fuel used for start, taxi and run up.
Zero Fuel Weight: The weight of the airplane exclusive of usable
fuel.
Passenger Weights: Actual passenger weights must be used in
computing the weight of an airplane with limited seating capacity. Allowance
must be made for heavy winter clothing when such is worn. Winter clothing may
add as much as 14 lbs to a person's basic weight; summer clothing would add
about 8 lbs. On larger airplanes with quite a number of passenger seats and for
which actual passenger weights would not be available, the following average
passenger weights may be used. The specified weights for males and females
include an allowance for 8 lbs of carryon baggage.

Summer 
Winter 
Males
(12yrs&up) 
182
lbs 
188
lbs 
Females (12yrs&up) 
135 lbs 
141 lbs 
Children (211 yrs) 
75 lbs 
75 lbs 
Infants (0up to 2 yrs) 
30 lbs 
30 lbs 
Fuel and 0il: The Airplane Flight Manuals for airplanes of U.S.
manufacture give fuel and oil quantities in U.S. gallons. Canadian manufactured
airplanes of older vintage may have manuals that give fuel and oil quantities in
Imperial gallons. Some recently printed manuals may give fuel and oil quantities
in litres. At most airports in Canada, fuel is now dispensed in litres. It is
therefore necessary to convert from litres to U.S. or Imperial gallons as
required for your particular airplane. To convert litres to U.S. gallons,
multiply by .264178. To convert litres to Imperial gallons, multiply
by.219975.
The following weights are for average density at the standard air temperature
of 15° C. At colder temperatures, the weights increase slightly. For example, at
40° C, one litre of aviation gasoline weighs 1.69 lbs.

Litre

U.S. Gallon 
Imp. Gallon 
Aviation Gas 
1.58 lb. 
6.0 lb. 
7.20 lb. 
JP4 
1.76 lb. 
6.6 lb. 
8.01 lb. 
Kerosene 
1.85 lb. 
7.0
lb. 
8.39 lb. 
Oil 
1.95 lb. 
7.5 lb. 
8.5 lb. 
Maximum Landing Weight: The maximum weight approved for
landing touchdown. Most multiengine airplanes which operate over long stage
lengths consume considerable weights of fuel. As a result, their weight is
appreciably less on landing than at takeoff. Designers take advantage of this
condition to stress the airplane for the lighter landing loads, thus saving
structural weight. If the flight has been of short duration, fuel or payload may
have to be jettisoned reduce the gross weight maximum or maximum landing weight.
Maximum Weight  Zero Fuel: Some transport planes carry fuel
in their wings, the weight of which relieves; the bending moments imposed on the
wings by the lift. The maximum weight  zero fuel limits the load which may be
carried in the fuselage. Any increase in weight in the form of load carried
fuselage must be counterbalanced by adding weight in the form of fuel in the
wings.
Float Buoyancy: The maximum permissible gross weight of a
seaplane is governed by the buoyancy of the floats. The buoyancy of a seaplane
float is equal to the weight of water displaced by the immersed part of the
float. This is equal to the weight the float will support without sinking beyond
a predetermined level (draught line).
The buoyancy of a seaplane float is designated by its model
number. A 4580 float has a buoyancy of 4580 lb. A seaplane fitted with a pair of
4580 floats has a buoyancy of 9160 lbs.
Regulations require an 80% reserve float buoyancy. The floats
must, therefore, have a buoyancy equal to 180% of the weight of the airplane.
To find the maximum gross weight of a seaplane fitted with,
say 7170 model floats, multiply the float buoyancy by 2 and divide by 1.8 (7170
x 2)/1.8 = 7966 lb.
C. computing the load
A typical light airplane has a basic weight of 1008 lb. and
an authorized maximum gross weight of 1600 lb. An acceptable loading of this
airplane would be as follows:
Basic Empty Weight . . . . . . . . . . . . . .1008 lb.
Consisting of Weight Empty . . . . . . . . . . 973 lb.
Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 15 lb.
Extra Equipment . . . . . . . . . . . . . . . . . . . .20 lb
Useful Load . . . . . . . . . . . . . . .. . . . . . . . 592
lb.
Consisting of Pilot . . . . . . . . . . . . . . . . . . .150
lb.
Fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 146 lb.
Payload: Passenger . . . . . . . . . . . . . . . . . .175 lb.
Baggage . . . .. . . . . . . . . . . . . . . . . . . . . . .
121 lb.
Problem
To find the maximum payload that can be transported a given
distance and the amount of fuel required.
A seaplane on contract with a mining company is required to
transport a maximum load of freight a distance of 300 nautical miles to a bush
operation. The estimated groundspeed is 110 knots. The useful load for this
airplane is 1836
pounds. Fuel capacity is 86 U.S. gallons. Fuel consumption is
20 gallons per hour or 120 lb of fuel per hour.
The time to fly 300 nautical miles is 164 minutes ((300/110)
x 60). Add to that the 45 minutes required for reserve and the amount of fuel
required must be sufficient for 209 minutes of flying time.
The amount of fuel required at 20 gallons per hour is 69.7
U.S. gallons ((20/60) x 209). That quantity of fuel weighs 418 lb (69.7 x 61b.).
The fuel calculations can also be computed by using the
weight of fuel consumed per hour. The weight of fuel necessary for the flight is
418 lb. ((120/60) x 209).
The useful load is 1836 lb. The weight of the pilot (170 lb.)
and fuel (418 lb.) is 588 lb. Therefore, the maximum payload permissible is 1248
lb.
What quantity of fuel in litres will be required? One U.S.
gallon equals 3.785332 litres. The quantity of fuel required is, therefore,
263.8 litres (69.7 x 3.785332).
D. balance limits
The position of the centre of gravity along its longitudinal
axis affects the stability of the airplane. There are forward and aft limits
established by the aircraft design engineers beyond which the C.G. should not be
located for flight. These limits are set to assure that sufficient elevator
deflection is available for all phases of flight. If the C.G. is too far
forward, the airplane will be nose heavy, if too far aft, tail heavy. An
airplane whose centre of gravity is too far aft may be dangerously unstable and
will possess abnormal stall and spin characteristics. Recovery may be difficult
if not impossible because the pilot is running out of elevator control. It is,
therefore, the pilot's responsibility when loading an airplane to see that the
C.G. lies within the recommended limits.
If the C.G. is too far forward, the airplane will be nose
heavy, if too far aft, tail heavy. An airplane whose centre of gravity is too
far aft may be dangerously unstable and will possess abnormal stall and spin
characteristics. Recovery may be difficult if not impossible because the pilot
is running out of elevator control. It is, therefore, the pilot’s responsibility
when loading an airplane to see that the C.G. lies within the recommended
limits.
Usually the Airplane Owner's Manual lists a separate weight
limitation for the baggage compartment in addition to the gross weight
limitation of the whole airplane. This is a factor to which the pilot must pay
close attention, for overloading the baggage compartment (even if the plane
itself is not overloaded) may move the C.G. too far aft and affect longitudinal
control.
The Airplane Owner's Manual may also specify such things as
the seat to be occupied in solo flight (in a tandem seating arrangement) or
which fuel tank is to be emptied first. Such instructions should be carefully
complied with.
As the flight of the airplane progresses and fuel is
consumed, the weight of the airplane decreases. Its distribution of weight also
changes and hence the C.G. changes. The pilot must take into account this
situation and calculate the weight and balance not only for the beginning of the
flight but also for the end of it.
E. definitions
The centre of gravity (C.G.) is the point through which the
weights of all the various parts of an airplane pass. It is, in effect, the
imaginary point from which the airplane could be suspended and remain balanced.
The C.G. can move within certain limits without upsetting the balance of the
airplane. The distance between the forward and aft C.G. limits is called the
centre of gravity range.
The balance datum line is a suitable line selected
arbitrarily by the manufacturer from which horizontal distances are measured for
balance purposes. It may be the nose of the airplane, the firewall or any other
convenient point .
The moment arm is the horizontal distance in inches from the
balance datum line to the C.G. The distance from the balance datum line to any
item, such as a passenger, cargo, fuel tank, etc. is the arm of that item.
The balance moment of the airplane is determined by
multiplying the weight of the airplane by the moment arm of the airplane. It is
expressed in inch pounds. The balance moment of any item is the weight of that
item multiplied by its distance from the balance datum line. It is, therefore,
obvious that a heavy object loaded in a rearward position will have a much
greater balance moment than the same object loaded in a position nearer to the
balance datum line.
The moment index is the balance moment of any item or of the
total airplane divided by a constant such as 100, 1000, or 10,000. It is used to
simplify computations of weight and balance especially on large airplanes where
heavy items and long arms result in large unmanageable numbers.
If loads are forward of the balance datum line their moment
arms are usually considered negative (). Loads behind the balance datum line
are considered positive (+)*. The total balance moment is the algebraic sum of
the balance moments of the airplane and each item composing the disposable load.
*In many cases the positive (+) sign is omitted, but the
negative () sign is always shown. To simplify matters, both are included in our
example
The C.G. is found by dividing the total balance moment (in
inchpounds) by the total weight (in lb.) and is expressed in inches forward ()
or aft (+) of the balance datum line.
The centre of gravity range is usually expressed in inches
from the balance datum line (i.e. +39.5" to +45.8"). In some airplanes, it may
be expressed as a percentage of the mean aerodynamic chord (25% to 35%). The MAC
is the mean aerodynamic chord of the wing.
To calculate the position of the C.G. in percent of MAC. Let
us assume that the weight and balance calculations have found the C.G. to be 66
inches aft of the balance datum line and the leading edge of the MAC to be 55
inches aft of the same reference (Fig. 3). The C.G. will, therefore, lie 11
inches aft of the leading edge of the MAC. If the MAC is 40 inches in length,
the position of the C.G. will be at a position (11 ~ 40) 27% of the MAC. If the
calculated C.G. position is within the recommended range (for example, 25% to
35%), the airplane is properly loaded.
There are several methods by which weight and balance calculations may be
made for any loading situation.
A. finding balance by computation method
For this example, an airplane with a basic weight of 1575 lb. and an
authorized gross weight of 2600 lb. has been selected. The balance datum line
for the airplane, selected by the manufacturer, is the firewall. The recommended
C.G. limits are 35.5" to 44.8".
List in table form the airplane (basic weight), pilot, passengers, fuel, oil,
baggage, cargo, etc., their respective weights and arms. Calculate the balance
moment of each. Total the weights. Total the balance moments. Divide the total
balance moment by the total weight to find the moment arm (i.e. the position of
the C.G.).
(Note: In this example, the oil is listed as a separate item and the balance
datum line is the firewall in order to give an example of a negative moment
arm.)
The moment arm for this loading of the airplane is 42.52" (110,270 2593).
The total weight (2593 lb.) of the loaded airplane is less than the authorized
gross weight (2600 lb.). The moment arm falls within the C.G. range (35.5" to
44.8"). The airplane is, therefore, properly loaded.
Item 
Weight Lb. 
Item Moment Arm Inches

Balance Moment InchLb.

Basic
Airplane 
1575 
+36 
+56,700 
Pilot 
165 
+37 
+6,105 
Passenger (front
seat) 
143 
+37 
+5,291 
Passenger (rear
seat) 
165 
+72 
+11,880 
Child (rear
seat) 
77 
+72 
+5,544 
Baggage 
90 
+98 
+8,820 
Fuel 
360 
+45 
+16,200 
Oil 
18 
15 
 270 
Total 
2593 
42.53 
110,270 
The above example examines the situation of an airplane almost at gross
weight with the C.G. in a rearward position but within the C.G. range. If this
calculation had resulted in a C.G. position that was aft of the C.G. limits,
even though the total weight of the airplane was under the authorized gross
weight, it would be necessary either to lighten the load or to shift the load
by, for example, having the passengers change seats.
A lightly loaded airplane at the end of a flight when the fuel is almost all
consumed may experience the situation that the C.G. moves forward beyond the
permissible C.G. range. In some airplanes, when flying with only the pilot on
board and no passengers or baggage, it is necessary to carry some suitable type
of ballast to compensate for a too far forward C.G. Every pilot should,
therefore, calculate the moment arm for the lightest possible loading of his
airplane to determine if it is acceptable.
B. finding balance by graph method
Most Airplane Flight Manuals include tables and graphs for calculating weight
and balance. They are very easy to use and eliminate the time consuming
mathematical steps of the computation.
C. weight and balance and flight performance
The flight characteristics of an airplane at gross weight with the C.G. very
near its most aft limits are very different from those of the same airplane
lightly loaded.
For lift and weight to be in equilibrium in order to maintain
any desired attitude of flight, more lift must be
produced to balance the heavy weight. To achieve this, the airplane must be
flown at an increased angle of attack. As a result, the wing will stall sooner
(i.e. at a higher airspeed) when the airplane is fully loaded than when it is
light. Stalling speed in turns (that is, at increased load factors) will also be
higher. In fact, everything connected with lift will be affected. Takeoff runs
will be longer, angle of climb and rate of climb will be reduced and, because of
the increased drag generated by the higher angle of attack, fuel consumption
will be higher than normal for any given airspeed. Severe gforces are more
likely to cause stress to the airframe supporting a heavy payload.
An aft C.G. makes the airplane less stable, making recovery from
manoeuvres
more difficult. The airplane is more easily upset gusts. However, with an aft
C.G., the airplane stalls at a slightly lower airspeed. To counteract the tail
heaviness of the aft C.G., the elevator must be trimmed for an up load. The
horizontal stabilizer, as a result, produces extra lift and the wings,
correspondingly, hold a slightly lower angle of attack.
An airplane with a forward centre of gravity, being nose heavy, is more
stable but more pressure on the elevator controls will be necessary to raise the
nose  a fact to remember on the landing flare. The forward C.G. means a
somewhat higher stalling speed another fact to remember during takeoffs and
landings.
Every pilot should be aware of these general characteristics, shared by most
airplanes, when they are loaded to their weight and balance limits. The
important thing to remember is that these characteristics are more pronounced as
the limits are approached and may become dangerous if they are exceeded.
Overloading, as well as the immediate degradation of performance, subjects the
airplane to unseen stresses and precipitates component fatigue.
A free weight and balance
calculator can be downloaded
here
