Weight and Balance
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 take-off
run necessary to become airborne will be longer. In some cases, the required take-off 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 center 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.
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 de-icing 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 take-off 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 take-off. It includes the basic weight empty plus the
useful load.
Maximum Gross Weight: The maximum permissible weight of the airplane.
Maximum Take-Off Weight: The maximum weight approved for the start of the take-off 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 carry-
on baggage.
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 liters. At most airports in Canada,
fuel is now dispensed in liters. It is therefore necessary to convert from liters to U.S. or Imperial gallons as required
for your particular airplane. To convert liters to U.S. gallons, multiply by .264178. To convert liters 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 liter of aviation gasoline weighs 1.69 lbs.
Maximum Landing Weight: The maximum weight approved for landing touchdown. Most multi-engine 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.
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.
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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 ground speed 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 liters will be required? One U.S. gallon equals 3.785332 liters. The quantity of fuel required
is, therefore, 263.8 liters (69.7 x 3.785332).
Balance limits
The position of the center 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.
Definitions
The center 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 center 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 inch-pounds) by the total weight (in lb.) and is expressed
in inches forward (-) or aft (+) of the balance datum line.
The center 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.
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.
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.
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.
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. Take-off 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 g-forces 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 center 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 take-offs 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.
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