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 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
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 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.
|
|
Summer
|
Winter
|
|
Males (12yrs&up)
|
182
lbs
|
188
lbs
|
|
Females (12yrs&up)
|
135
lbs
|
141
lbs
|
|
Children (2-11 yrs)
|
75
lbs
|
75
lbs
|
|
Infants (0-up 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.
|
|
JP-4
|
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
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.
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 inch-pounds) 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 Inch-Lb.
|
|
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
|
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