David Young
Technical Subject Areas
1. Subject – Weight and Balance.
2. Introduction – The way an aircraft is loaded will strongly affect the way it handles in
flight. Knowing how to properly load an aircraft and check to see whether or not you are
within the limits of the aircraft are very important in the conduction of a safe flight.
Doing this is called weight and balance.
3. Outline –
a. Define all of the weight and balance terms.
b. Discuss the effects of weight distribution on the aircraft.
c. Discuss how to determine if you are within weight and balance limits.
d. Discuss how to compute the center of gravity.
i. Discuss how to account for any weight shifts.
4. Contents –
a. Definitions:
i. Reference Datum – an imaginary vertical plane from which all horizontal
distances are measured from for balance purposes. It may be located
anywhere the manufacturer chooses, but is usually measured from the
nose or the wings.
ii. Station – a location along the airplane fuselage usually given in terms of
distance from the reference datum.
iii. Arm – the horizontal distance, usually measured in inches, from the
reference datum to the center of gravity (CG) of an item.
1. Arms ahead of the datum are negative, and those behind are
positive.
iv. Moment – a force that causes or tries to cause an object to rotate. Moment
is the product of weight (in pounds) of an item multiplied by its arm (in
inches).
1. Moments are usually expressed in lb.-in.
v. Moment Index – the moment divided by a reduction number such as 100
or 1,000 to make the moment value smaller and reduce the chance of math
errors in computing the CG.
vi. Center of Gravity – the point at which an aircraft would balance if it were
possible to suspend it at that point.
1. It is found by dividing the total moment by the total weight of the
aircraft.
vii. CG Limits – the forward and aft limits of the center of gravity in which the
aircraft must be operated at a given weight.
viii. Usable Fuel – the fuel available for flight planning.
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ix. Unusable Fuel – the fuel remaining in the aircraft’s fuel system after a
runout test has been completed in accordance with the FARs.
1. Basically, it is the fuel that cannot be drained by just the operation
of the engine.
x. Standard Empty Weight – the weight of the airframe, engine(s), and all
items that have fixed locations and are permanently installed in the
aircraft.
1. This includes unusable fuel, full operating fluids, and full oil.
xi. Basic Empty Weight – the standard empty weight plus any optional
equipment that has been installed.
xii. Payload – the weight of occupants, cargo, and baggage.
xiii. Useful Load – the difference between takeoff weight and basic empty
weight.
xiv. Maximum Ramp Weight – the maximum weight approved for ground
maneuvers.
1. This includes the weight of start, taxi, and runup fuel.
xv. Maximum Takeoff Weight – the maximum weight approved for the start of
the takeoff run.
xvi. Maximum Landing Weight – the maximum weight approved for the
landing touchdown.
xvii. Maximum Zero Fuel Weight – the maximum weight exclusive of usable
fuel.
xviii. Standard Weights – established weights for numerous item in weigh and
balance calculations.
1. Gasoline – 6 lb/gal
2. Oil – 7.5 lb/gal
3. Water – 8.35/gal
b. Increasing the weight of an aircraft reduces its performance. A heavier aircraft
will have a:
i. Higher takeoff speed.
ii. Longer takeoff roll.
iii. Reduced rate and angle of climb.
iv. Shorter range.
v. Reduced cruising speed.
vi. Reduced maneuverability.
vii. Higher stalling speed.
viii. Higher landing speed.
ix. Longer landing roll.
c. To make sense of this, think of riding a bicycle.
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i. When you are on the bike by yourself, imagine the amount of time it
would take to accelerate to 10 mph.
ii. Then, imagine how easy it is to steer the bike.
iii. Now imagine your friend hopping on the bike with you.
iv. It would take longer for that bike to reach 10 mph because of the increased
weight.
v. Steering the bike would be much more difficult because of the increased
weight.
vi. This is very similar to an airplane’s performance when it gets heavier.
d. If an aircraft respects the manufacturers gross weight and load factor limits, the
aircraft’s structure will not be compromised.
i. However, if either of those limits is exceeded, the aircraft’s structure is not
guaranteed to hold, so flight outside these limits is extremely dangerous.
1. Usually, overloading the aircraft results in slow, gradual wearing
down of the structure instead of a catastrophic failure i.e.
separation of the wings.
e. The CG can affect the load imposed on the wings.
i. With a forward CG, more tail-down force is needed to maintain level
flight.
1. The lift required on the wings is increased.
2. Therefore, the wings must fly at a higher angle of attack, which
creates more drag and a higher indicated stall speed.
3. A CG beyond the forward limit may make it difficult, if not
impossible, to keep the aircraft from pitching down as it feels noseheavy.
a. This could be catastrophic during takeoff and landing when
the aircraft is slow.
ii. Think of this as a seesaw that is too heavy on one side (the nose).
1. The tendency of the seesaw will be to fall towards the heavy end.
2. Therefore, the other side (the tail) must somehow create more
force to re-establish balance on the seesaw.
3. This force comes in the form of tail-down force.
iii. With an aft CG, less tail-down force is needed to maintain level flight, and
the aircraft becomes less stable.
1. As the CG moves aft, there is less arm between the CG and the
elevator.
a. The greater the arm, the greater the effectiveness of the
control surface.
2. If the elevator is less effective, it will much harder to recover from
a stall.
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3. If the CG is beyond the aft limit, recovery from a spin may be
impossible because of the reduced elevator and rudder authority.
iv. Think of this as a seesaw that is too heavy on the other side (the tail).
1. The tendency of the seesaw will be to fall towards the tail end.
2. Therefore, the other side (the nose) must somehow create more
force to re-establish balance on the seesaw.
3. This force comes in the form of reduced tail-down force.
f. To control your weight and balance, calculate your center of gravity and check the
POH Weight and Balance section to see if you are within the “Normal” limits of
the aircraft.
i. To calculate the CG, use a weight and balance sheet available in the
dispatch office or on the internet.
ii. To calculate the takeoff CG of the aircraft, fill out the weights on the left
side of the sheet, and write the corresponding arms (found in the W & B
section of the POH) for each weight.
iii. Multiply each weight with its corresponding arm to obtain each
corresponding moment.
iv. To calculate the arm (or CG) of the aircraft, add up all of the moments
(subtracting those for fuel), and divide them by the sum of all the weights
of the aircraft (subtracting the weight of fuel burnt).
v. Check to see if this CG for that particular weight is acceptable.
vi. In Figure A, there is an example of a CG envelope graph similar to what
you might see in the POH.
1. In this example, we are trying to determine if an aircraft weighing
2367 lbs. with a moment of 105200 lb-in. is within the CG limits.
g. You may find that some weight either needs to be shifted, removed, or added to
get the aircraft within limits. Use the following equation to determine the new
CG of the aircraft:
i. CG =
M±ΔM
, where M = current moment, ΔM = change in moment, W =
W±ΔW
current weight, and ΔW = change in weight.
ii. If removing weight, the ± becomes (-).
iii. If adding weight, the ± becomes (+).
iv. For example, if you are flying at a gross weight of 2,200 lbs with a CG
location of 88.0. The location of the CG after 20 gal. of fuel (120 lbs) at
station 70.0 has been consumed is
2,200(88)−120(70)
2,200−120
= 89.03 in.
v. For example, if you are flying at a gross weight of 1,900 lbs and 100 lbs of
cargo is shifted 20 inches, the amount the CG shifted is given by
1.05 in.
5. Evaluation –
100 x 20
1,900
=
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a.
b.
c.
d.
The student can recite the definitions listed.
The student can explain the effects weight has on the aircraft’s performance.
The student can explain the effects CG has on the aircraft’s performance.
The student can figure out a weight and balance for an aircraft as well find a new
CG for weight shifted/removed/added.
6. References –
a. PHAK, Ch. 8
b. Gleim’s Flight Instructor Flight Maneuvers, Part II, Unit II
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Figure A