i
ii
iii
Preface
FAA-H-8083-1, Aircraft Weight and Balance Handbook, has
been prepared in recognition of the importance of weight
and balance technology in conducting safe and efficient
flight. The objective of this handbook is twofold: to provide
the Aviation Maintenance Technician (AMT) with the
method of determining the empty weight and empty-weight
center of gravity (EWCG) of an aircraft, and to furnish the
flight crew with information on loading and operating the
aircraft to ensure its weight is within the allowable limit and
the center of gravity (CG) is within the allowable range.
Any time there is a conflict between the information in this
handbook and specific information issued by an aircraft
manufacturer, the manufacturer’s data takes precedence over
information in this handbook. Occasionally, the word must
or similar language is used where the desired action is
deemed critical. The use of such language is not intended
to add to, interpret, or relieve a duty imposed by Title 14 of
the Code of Federal Regulations (14 CFR).
This handbook supersedes Advisory Circular (AC) 91-23A,
Pilot’s Weight and Balance Handbook, revised in 1977.
Comments regarding this handbook should be sent to U.S.
Department of Transportation, Federal Aviation Administration, Airman Testing Standards Branch, AFS-630, P.O.
Box 25082, Oklahoma City, OK 73125.
This publication may be purchased from the Superintendent of
Documents, P.O. Box 371954, Pittsburgh, PA 15250-7954, or
from the U.S. Government Printing Office bookstores located in
major cities throughout the United States.
AC 00-2, Advisory Circular Checklist, transmits the current
status of Federal Aviation Administration (FAA) advisory
circulars and other flight information publications. This
checklist is free of charge and may be obtained by sending
a request to U.S. Department of Transportation, Subsequent
Distribution Office, SVC-121.23, Ardmore East Business
Center, 3341 Q 75th Avenue, Landover, MD 20785. The
checklist is also available on the Internet at http://www.
faa.gov/abc/ac-chklst/actoc.htm.
Acknowledgments
This book was produced as a combined FAA and industry effort.
iv
v
Introduction
Weight and balance control for large aircraft is discussed,
including cargo management, takeoff and landing conditions,
and the determination of fuel dump time for emergency
conditions. Examples are also given for weight and balance
control of commuter category airplanes in both the passenger
and cargo configuration.
The unique requirements for helicopter weight and balance
control are discussed, including the determination of lateral
CG and the way both lateral and longitudinal CG change as
fuel is consumed.
A chapter is included giving the methods and examples of
solving weight and balance problems, using hand-held
electronic calculators, E6-B flight computers, and a dedicated
electronic flight computer.
This handbook begins with the basic principle of aircraft
weight and balance control, emphasizing its importance and
including examples of documentation furnished by the
aircraft manufacturer and by the FAA to ensure the aircraft
weight and balance records contain the proper data.
Procedures for the preparation and the actual weighing of
an aircraft are described, as are the methods of determining
the location of the empty-weight center of gravity (EWCG)
relative to both the datum and the mean aerodynamic
chord (MAC).
Loading computations for general aviation aircraft are
discussed, using both loading graphs and tables of weight and
moment indexes.
Information is included that allows an Aviation Maintenance
Technician (AMT) to determine the weight and center of gravity
(CG) changes caused by repairs and alterations. This includes
instructions for conducting adverse-loaded CG checks, also
explaining the way to determine the amount and location of
ballast needed to bring the CG within allowable limits.
vi
vii
Contents
Empty-Weight Center of Gravity Formulas ................... 3-5
Datum Forward of the Airplane —
Nose Wheel Landing Gear ................................... 3-5
Datum Aft of the Main Wheels —
Nose Wheel Landing Gear ................................... 3-6
Datum Forward of the Main Wheels —
Tail Wheel Landing Gear ..................................... 3-6
Datum Aft of the Main Wheels —
Tail Wheel Landing Gear ..................................... 3-7
Location with Respect to the
Mean Aerodynamic Chord ................................... 3-7
Chapter 4
General Aviation Aircraft Operational
Weight and Balance Computations ................ 4-1
Determining the Loaded Weight and CG ....................... 4-1
Computational Method............................................. 4-1
Loading Graph Method ............................................ 4-2
Multiengine Airplane Weight and
Balance Computations ................................................. 4-6
Determining the Loaded CG ........................................... 4-6
The Chart Method Using Weight,
Arm, and Moments ............................................... 4-7
Determining the CG in Percent of MAC ................. 4-7
The Chart Method Using Weight
and Moment Indexes ............................................. 4-7
Chapter 5
Center of Gravity Change After
Repair or Alteration .............................................. 5-1
Equipment List ................................................................. 5-1
Weight and Balance Revision Record............................. 5-3
Weight Changes Caused by a Repair or Alteration ........ 5-3
Computations Using Weight, Arm, and Moment ... 5-3
Computations Using Weight and
Moment Indexes .................................................... 5-4
Empty-Weight CG Range ................................................ 5-4
Adverse-Loaded CG Checks ........................................... 5-4
Forward Adverse-Loaded CG Check ...................... 5-5
Aft Adverse-Loaded CG Check ............................... 5-6
Ballast ............................................................................... 5-7
Temporary Ballast ..................................................... 5-7
Permanent Ballast ..................................................... 5-7
Chapter 1
Weight and Balance Control ................................. 1-1
Why is Weight and Balance Important? ......................... 1-1
Weight Control ................................................................. 1-2
Effects of Weight .............................................................. 1-2
Weight Changes ................................................................ 1-3
Stability and Balance Control ......................................... 1-4
Chapter 2
Weight and Balance Theory
and Documentation ...............................................2-1
Weight and Balance Theory ............................................ 2-1
Aircraft Arms, Weights, and Moments .................... 2-1
The Law of the Lever ............................................... 2-2
Determining the CG ................................................. 2-2
Shifting the CG ......................................................... 2-4
Shifting the Airplane CG .......................................... 2-6
Weight and Balance Documentation............................... 2-7
FAA-Furnished Information .................................... 2-7
Manufacturer-Furnished Information .................... 2-12
Chapter 3
Weighing the Aircraft and Determining
the Empty-Weight Center of Gravity .............. 3-1
Requirements .................................................................... 3-1
Equipment for Weighing .................................................. 3-1
Preparation for Weighing ................................................. 3-2
Weigh Clean Aircraft Inside Hangar ....................... 3-2
Equipment List .......................................................... 3-2
Ballast ........................................................................ 3-3
Draining the Fuel ...................................................... 3-3
Oil .............................................................................. 3-3
Other Fluids .............................................................. 3-3
Configuration of the Aircraft ................................... 3-3
Jacking the Aircraft ................................................... 3-3
Leveling the Aircraft ................................................. 3-4
Determining the Center of Gravity ................................. 3-4
viii
Chapter 6
Weight and Balance Control —
Large Aircraft .......................................................... 6-1
Weighing Requirements ................................................... 6-1
Individual Aircraft Weight ........................................ 6-1
Fleet Weights ............................................................. 6-2
Weighing Procedures ................................................ 6-2
Locating and Monitoring Weight and CG Location ...... 6-2
Determining the Empty Weight and EWCG ........... 6-2
Determining the Loaded CG of the Airplane
in Percent MAC .................................................... 6-3
On Board Aircraft Weighing System....................... 6-3
Determining the Correct Stabilizer Trim Setting ........... 6-5
Stabilizer Trim Setting in % MAC .......................... 6-5
Stabilizer Trim Setting in Units ANU
(Airplane Nose Up) ............................................... 6-5
Determining CG Changes Caused by
Modifying the Cargo .................................................... 6-5
Effects of Loading or Offloading Cargo ................. 6-5
Effects of Onloading Cargo ..................................... 6-6
Effects of Shifting Cargo from
One Hold to Another ............................................. 6-8
Determining Cargo Pallet Loads with
Regard to Floor Loading Limits .................................. 6-9
Determining the Maximum Amount of Payload
That Can Be Carried................................................... 6-10
Determining the Landing Weight .................................. 6-10
Determining the Minutes of Fuel Dump Time ............. 6-12
Weight and Balance of Commuter
Category Airplanes ..................................................... 6-13
Determining the Loaded Weight and CG .............. 6-13
Determining the Changes in CG When
Passengers are Shifted ........................................ 6-17
Determining Changes in Weight and CG
When the Airplane is Operated in
its Cargo Configuration ...................................... 6-18
Determining the CG Shift When Cargo is Moved
From One Section to Another ............................ 6-18
Determining the CG Shift When Cargo is
Added or Removed ............................................. 6-19
Determining Which Limits are Exceeded ............. 6-19
Chapter 7
Weight and Balance Control—Helicopters ..... 7-1
Determining the Loaded CG of a Helicopter ................. 7-2
Effects of Offloading Passengers and Using Fuel .. 7-3
Chapter 8
Use of Computers for Weight
and Balance Computations ............................... 8-1
Using an Electronic Calculator to Solve
Weight and Balance Problems ..................................... 8-1
Using an E6-B Flight Computer to Solve
Weight and Balance Problems ..................................... 8-1
Using a Dedicated Electronic Flight Computer to
Solve Weight and Balance Problems ........................... 8-3
Typical Weight and Balance Problems ........................... 8-3
Determining CG in Inches From the Datum ........... 8-3
Determining CG, Given Weights and Arms ............ 8-5
Determining CG, Given Weights and
Moment Indexes .................................................... 8-5
Determining CG in Percent of
Mean Aerodynamic Chord ................................... 8-6
Determining Lateral CG of a Helicopter ................. 8-6
Determining ÐCG Caused by Shifting Weights ..... 8-6
Determining Weight Shifted to Cause
Specified ÐCG ....................................................... 8-7
Determining Distance Weight is Shifted to
Move CG a Specific Distance .............................. 8-7
Determining Total Weight of an Aircraft That Will
Have a Specified ÐCG When Cargo is Moved ... 8-7
Determining Amount of Ballast Needed to
Move CG to a Desired Location .......................... 8-7
Appendix
Supplemental Study Materials
for Aircraft Weight and Balance ..........Appendix-1
Glossary ......................................................... Glossary-1
Index ..................................................................... Index-1
1–1
Chapter 1
Weight and Balance Control
The designers of an aircraft have determined the maximum
weight, based on the amount of lift the wings or rotors can
provide under the operating conditions for which the aircraft
is designed. The structural strength of the aircraft also limits
the maximum weight the aircraft can safely carry. The ideal
location of the center of gravity (CG) was very carefully
determined by the designers, and the maximum deviation
allowed from this specific location has been calculated.
The manufacturer provides the aircraft operator with the
empty weight of the aircraft and the location of its emptyweight center of gravity (EWCG) at the time the aircraft
left the factory. The AMT who maintains the aircraft and
performs the maintenance inspections keeps the weight and
balance records current, recording any changes that have
been made because of repairs or alterations.
The pilot in command of the aircraft has the responsibility
on every flight to know the maximum allowable gross weight
of the aircraft and its CG limits. This allows the pilot to
determine on the preflight inspection that the aircraft is
loaded in such a way that the CG is within the allowable
limits.
Weight and balance technology, like all other aspects of
aviation, has become more complex as the efficiency and
capability of aircraft and engines have increased. Therefore,
this requires all pilots and AMTs to understand weight and
balance control, and to operate and maintain their aircraft
so its weight and CG location are within the limitations
established when the aircraft was designed, manufactured,
and certified by the FAA.
Why is Weight and Balance Important?
Weight and balance is one of the most important factors
affecting safety of flight. An overweight aircraft, or one
whose center of gravity is outside the allowable limits, is
inefficient and dangerous to fly. The responsibility for
proper weight and balance control begins with the engineers
and designers and extends to the pilot who operates and the
Aviation Main-tenance Technician (AMT) who maintains the
aircraft.
Modern aircraft are engineered utilizing state-of-the-art
technology and materials to lift the maximum amount of
weight and carry it the greatest distance at the highest speed.
As much care and expertise must be exercised in operating
and maintaining these efficient aircraft as was taken in their
design and manufacturing.
Various types of aircraft have different load requirements.
Transport aircraft must carry huge loads of passengers and
cargo for long distances at high altitude and high speed.
Military aircraft must be highly maneuverable and extremely
sturdy. Corporate aircraft must carry a reasonable load at a
high speed for long distances. Agricultural aircraft must
carry large loads short distances and be extremely
maneuverable. Trainers and private aircraft must be
lightweight, low cost, simple, and safe to operate.
All aircraft regardless of their function have two characteristics in common: all are sensitive to weight, and the
center of gravity of the aircraft must be maintained within a
specified range.
Maximum weight: The maximum
authorized weight of the aircraft and
all of its equipment as specified in the
Type Certificate Data Sheets (TCDS)
for the aircraft.
Center of gravity (CG): The point at
which an airplane would balance if
suspended. Its distance from the
reference datum is found by dividing
the total moment by the total weight
of the airplane.
Empty weight: The weight of the
airframe, engines, and all items of
operating equipment that have fixed
locations and are permanently installed
in the aircraft.
Empty-weight center of gravity
(EWCG): The center of gravity of an
aircraft, when the aircraft contains
only the items specified in the aircraft
empty weight.
1–2
Weight Control
Weight is a major factor in airplane construction and
operation, and it demands respect from all pilots and
particular diligence by all AMTs. Excessive weight reduces
the efficiency of an aircraft and the safety margin
available if an emergency condition should arise.
When an aircraft is designed, it is made as light as the
required structural strength will allow, and the wings
or rotors are designed to support the maximum allowable
gross weight. When the weight of an aircraft is increased,
the wings or rotors must produce additional lift and the
structure must support not only the additional static loads ,
but also the dynamic loads imposed by flight maneuvers.
For example, the wings of a 3,000-pound airplane must
support 3,000 pounds in level flight, but when the airplane
is turned smoothly and sharply using a bank angle of 60°,
the dynamic load requires the wings to support twice this,
or 6,000 pounds.
Severe uncoordinated maneuvers or flight into turbulence
can impose dynamic loads on the structure great enough to
cause failure. The structure of a normal category airplane
must be strong enough to sustain a load factor of 3.8 times
its weight; that is, every pound of weight added to an aircraft
requires that the structure be strong enough to support an
additional 3.8 pounds. An aircraft operating in the utility
category must sustain a load factor of 4.4, and acrobatic
category aircraft must be strong enough to withstand 6.0
times their weight.
The lift produced by a wing is determined by its airfoil shape,
angle of attack, speed through the air, and the air density.
When an aircraft takes off from an airport with a high density
altitude, it must accelerate to a speed faster than would be
required at sea level to produce enough lift to allow takeoff;
therefore, a longer takeoff run is necessary. The distance
needed may be longer than the available runway. When
operating from a high density altitude airport, the Pilot’s
Operating Handbook (POH) or Airplane Flight Manual
(AFM) must be consulted to determine the maximum weight
allowed for the aircraft under the conditions of altitude,
temperature, wind, and runway conditions.
Effects of Weight
Most modern aircraft are so designed that if all seats are
occupied, all baggage allowed by the baggage compartment
structure is carried, and all of the fuel tanks are full, the
aircraft will be grossly overloaded. This type of design gives
the pilot a great deal of latitude in loading the aircraft for a
particular flight. If maximum range is required, occupants
or baggage must be left behind, or if the maximum load must
be carried, the range, dictated by the amount of fuel on board,
must be reduced.
Some of the problems caused by overloading an aircraft are:
• The aircraft will need a higher takeoff speed, which
results in a longer takeoff run.
• Both the rate and angle of climb will be reduced.
• The service ceiling will be lowered.
• The cruising speed will be reduced.
• The cruising range will be shortened.
• Maneuverability will be decreased.
• A longer landing roll will be required because the landing
speed will be higher.
• Excessive loads will be imposed on the structure,
especially the landing gear.
The POH or AFM includes tables or charts that give the pilot
an indication of the performance expected for any gross
weight. An important part of careful preflight planning
includes a check of these charts to determine the aircraft is
loaded so the proposed flight can be safely made.
Static load: The load imposed on an
aircraft structure due to the weight of
the aircraft and its contents.
Dynamic load: The actual weight of
the aircraft multiplied by the load
factor, or the increase in weight caused
by acceleration.
Load factor: The ratio of the
maximum load an aircraft can sustain
to the total weight of the aircraft.
Normal category aircraft must have a
load factor of at least 3.8, utility
category aircraft 4.4, and acrobatic
category aircraft, 6.0.
Density altitude: Pressure altitude
corrected for nonstandard temperature.
High Density Altitude Airport Operations
Consult the POH or AFM to determine the maximum weight allowed
for the aircraft under the conditions of altitude, temperature, wind, and
runway conditions.
Your preflight planning must include a careful check of gross weight
performance charts to determine the aircraft is loaded properly and the
proposed flight can be safely made.
Pilot’s Operating Handbook (POH):
An FAA-approved document
published by the airframe
manufacturer that lists the operating
conditions for a particular model of
aircraft and its engines.
Airplane Flight Manual (AFM): An
FAA-approved document, prepared
by the holder of a Type Certificate for
an airplane or rotorcraft, that specifies
the operating limitations and contains
the required markings and placards and
other information applicable to the
regulations under which the aircraft
was certificated.
1–3
Weight Changes
The maximum allowable gross weight for an aircraft is
determined by design considerations. However, the
maximum operational weight may be less than the maximum
allowable due to such considerations as high density altitude
or high-drag field conditions caused by wet grass or water
on the runway. The maximum gross weight may also be
limited by the departure or arrival airport’s runway length.
One important preflight consideration is the distribution of
the load in the aircraft. Loading an aircraft so the gross
weight is less than the maximum allowable is not
enough. This weight must be distributed to keep the CG
within the limits specified in the POH or AFM.
If the CG is too far forward, a heavy passenger can be moved
to one of the rear seats or baggage can be shifted from a
forward baggage compartment to a rear compartment. If the
CG is too far aft, passenger weight or baggage can be shifted
forward. The fuel load should be balanced laterally: the
pilot should pay special attention to the POH or AFM
regarding the operation of the fuel system, in order to keep
the aircraft balanced in flight.
Weight and balance of a helicopter is far more critical than
for an airplane. A helicopter may be properly loaded for
takeoff, but near the end of a long flight when the fuel tanks
are almost empty, the CG may have shifted enough for the
helicopter to be out of balance laterally or longitudinally.
Before making any long flight, the CG with the fuel available
for landing must be checked to ensure it will be within the
allowable range.
Airplanes with tandem seating normally have a limitation
requiring solo flight to be made from the front seat in some
airplanes or the rear seat in others. Some of the smaller
helicopters also require solo flight be made from a specific
seat, either the right or the left. These seating limitations will
be noted by a placard, usually on the instrument panel, and
they should be strictly adhered to.
As an aircraft ages, its weight usually increases due to trash
and dirt collecting in hard-to-reach locations, and moisture
absorbed in the cabin insulation. This growth in weight is
normally small, but it can only be determined by accurately
weighing the aircraft.
Changes of fixed equipment may have a major effect upon
the weight of the aircraft. Many aircraft are overloaded by
the installation of extra radios or instruments. Fortunately,
the replacement of older, heavy electronic equipment with
newer, lighter types results in a weight reduction. This weight
change, however helpful, will probably cause the CG to shift
and this must be computed and annotated in the weight and
balance data.
Repairs and alterations are the major sources of weight
changes, and it is the responsibility of the AMT making any
repair or alteration to know the weight and location of these
changes, and to compute the new CG and record the new
empty weight and EWCG in the aircraft weight and balance
data.
The AMT conducting an annual or 100-hour inspection must
ensure the weight and balance data in the aircraft records is
current and accurate. It is the responsibility of the pilot in
command to use the most current weight and balance data
when operating the aircraft.
Service ceiling: The highest altitude
at which an aircraft can maintain a
steady rate of climb of 100 feet per
minute.
Has the Aircraft Gained Weight?
As an aircraft ages, its weight usually increases. Repairs and alterations
are the major sources of weight change.
AMTs conducting an annual or 100-hour inspection must ensure the
weight and balance data in the aircraft records is current and accurate.
The pilot in command’s responsibility is to use the most current weight
and balance data when planning a flight.
Balanced laterally: Balanced in such
a way that the wings tend to remain
level.
1–4
Stability and Balance Control
Balance control refers to the location of the CG of an
aircraft. This is of primary importance to aircraft stability,
which determines safety in flight.
The CG is the point at which the total weight of the
aircraft is assumed to be concentrated, and the CG must
be located within specific limits for safe flight. Both
lateral and longitudinal balance are important, but the
prime concern is longitudinal balance; that is, the location
of the CG along the longitudinal or lengthwise axis.
An airplane is designed to have stability that allows it to be
trimmed so it will maintain straight and level flight with
hands off of the controls. Longitudinal stability is maintained
by ensuring the CG is slightly ahead of the center of lift. This
produces a fixed nose-down force independent of the
airspeed. This is balanced by a variable nose-up force, which
is produced by a downward aerodynamic force on the
horizontal tail surfaces that varies directly with airspeed.
[Figure 1-1]
As long as the CG is maintained within the allowable limits
for its weight, the airplane will have adequate longitudinal
stability and control. If the CG is too far aft, it will be too
near the center of lift and the airplane will be unstable, and
difficult to recover from a stall. [Figure 1-2] If the unstable
airplane should ever enter a spin, the spin could become flat
and recovery would be difficult or impossible.
Figure 1-3. If the CG is too far forward, there will not be
enough elevator nose-up force to flare the airplane for
landing.
Figure 1-2. If the CG is too far aft, at the low stall airspeed
there might not be enough elevator nose-down force to get the
nose down for recovery.
Figure 1-1. Longitudinal forces acting on an airplane in
flight.
If a rising air current should cause the nose to pitch up, the
airplane will slow down and the downward force on the tail
will decrease. The weight concentrated at the CG will pull
the nose back down. If the nose should drop in flight, the
airspeed will increase and the increased downward tail load
will bring the nose back up to level flight.
If the CG is too far forward, the downward tail load will have
to be increased to maintain level flight. This increased tail
load has the same effect as carrying additional weight — the
aircraft will have to fly at a higher angle of attack, and drag
will increase.
A more serious problem caused by the CG being too far
forward is the lack of sufficient elevator authority. At slow
takeoff speeds, the elevator might not produce enough noseup force to rotate and on landing there may not be enough
elevator force to flare the airplane. [Figure 1-3] Both takeoff
and landing runs will be lengthened if the CG is too far
forward.
Center of lift: The location along the
chord line of an airfoil at which all the
lift forces produced by
the airfoil are considered to be
concentrated.
Longitudinal balance: Balance
around the pitch, or lateral, axis.
Longitudinal axis: An imaginary line
through an aircraft from nose to tail,
passing through its center
of gravity.
1–5
Figure 1-4. Lateral imbalance causes wing heaviness, which
may be corrected by deflecting the aileron. The additional lift
causes additional drag and the airplane flies inefficiently.
The efficiency of some modern high-performance military
fighter airplanes is increased by giving them neutral
longitudinal stability. This is normally a very dangerous
situation; but these aircraft are flown by autopilots which
react far faster than a human pilot, and they are safe for their
special operations.
The basic aircraft design assumes that lateral symmetry
exists. For each item of weight added to the left of the
centerline of the aircraft (also known as buttock line zero,
or BL-0), there is generally an equal weight at a
corresponding location on the right.
The lateral balance can be upset by uneven fuel loading or
burnoff. The position of the lateral CG is not normally
computed for an airplane, but the pilot must be aware of the
adverse effects that will result from a laterally unbalanced
condition. [Figure 1-4] This is corrected by using the aileron
trim tab until enough fuel has been used from the tank on
the heavy side to balance the airplane. The deflected trim tab
deflects the aileron to produce additional lift on the heavy
side, but it also produces additional drag, and the airplane
Figure 1-5. Fuel in the tanks of a sweptwing airplane affects
both lateral and longitudinal balance. As fuel is used from an
outboard tank, the CG shifts forward.
flies inefficiently.
Helicopters are affected by lateral imbalance more than
airplanes. If a helicopter is loaded with heavy occupants and
fuel on the same side, it could be enough out of balance to
make it unsafe to fly. It is also possible that if external loads
are carried in such a position to require large lateral
displacement of the cyclic control to maintain level flight,
the fore-and-aft cyclic control effectiveness will be limited.
Lateral balance: Balance around the
roll, or longitudinal, axis.
Sweptwing airplanes are more critical due to fuel imbalance
because as the fuel is used from the outboard tanks the CG
shifts forward, and as it is used from the inboard tanks the
CG shifts aft. [Figure 1-5] For this reason, fuel-use
scheduling in high-speed jet aircraft operation is critical.
Aircraft can perform safely and achieve their designed
efficiency only when they are operated and maintained in the
way their designers intended. This safety and efficiency is
determined to a large degree by holding the aircraft’s weight
and balance parameters within the limits specified for its
design. The remainder of this book describes the way in
which this is done.
Butt (or buttock) line zero: A line
through the symmetrical center of an
aircraft from nose to tail. It serves as
the datum for measuring the arms used
to find the lateral CG. Lateral moments
that cause the aircraft to rotate
clockwise are positive (+), and those
that cause it to rotate counterclockwise are negative (–).
1–6
2–1
Chapter 2
Weight and Balance Theory
and Documentation
Reference datum (GAMA): An
imaginary vertical plane from which
all horizontal distances are measured
for balance purposes.
Weight and Balance Theory
Two elements are vital in the weight and balance considerations of an aircraft:
• The total weight of the aircraft must be no greater than
the maximum gross weight allowed by the FAA for the
particular make and model of the aircraft.
• The center of gravity, or the point at which all of the
weight of the aircraft is considered to be concentrated,
must be maintained within the allowable range for the
operational weight of the aircraft.
Aircraft Arms, Weights, and Moments
The term arm, usually measured in inches, refers to the
distance between the center of gravity of an item or object
and the reference datum. Arms ahead of, or to the left of
the datum are negative (–), and those behind, or to the right
of the datum are positive (+). When the datum is ahead of
the aircraft, all of the arms are positive and computational
errors are minimized.
Weight is normally measured in pounds. When weight is
removed from an aircraft, it is negative (–), and when added,
it is positive (+).
There are a number of weights that must be considered in
aircraft weight and balance. The following are terms for
various weights as used by the General Aviation Manufacturers Association (GAMA).
• The standard empty weight is the weight of the
airframe, engines and all items of operating weight that
have fixed locations and are permanently installed in the
aircraft. This weight must be recorded in the aircraft
weight and balance records. The basic empty weight
includes the standard empty weight plus any optional
equipment that has been installed.
• Maximum allowable gross weight is the maximum weight
authorized for the aircraft and all of its contents as
specified in the Type Certificate Data Sheets (TCDS) or
Aircraft Specifications for the aircraft.
• Maximum landing weight is the greatest weight that an
aircraft normally is allowed to have when it lands.
• Maximum takeoff weight is the maximum allowable
weight at the start of the takeoff run.
• Maximum ramp weight is the total weight of a loaded
aircraft, and includes all fuel. It is greater than the
takeoff weight due to the fuel that will be burned during
the taxi and runup operations. Ramp weight is also
called taxi weight.
The manufacturer establishes the allowable gross weight and
the range allowed for the CG, as measured in inches from a
reference plane called the datum. In large aircraft, this range
is measured in percentage of the mean aerodynamic chord
(MAC), the leading edge of which is located a specified
distance from the datum.
The datum may be located anywhere the manufacturer
chooses; it is often the leading edge of the wing or some
specific distance from an easily identified location. One
popular location for the datum is a specified distance forward
of the aircraft, measured in inches from some point such as
the leading edge of the wing or the engine firewall.
Arm (GAMA): The horizontal
distance from the reference datum to
the center of gravity (CG) of an item.
Standard empty weight (GAMA):
Weight of a standard airplane
including unusable fuel, full
operating fluids and full oil.
Basic empty weight (GAMA):
Standard empty weight plus optional
equipment.
Maximum landing weight
(GAMA): Maximum weight
approved for the landing touchdown.
Maximum takeoff weight (GAMA):
Maximum weight approved for the
start of the takeoff run.
Maximum ramp weight (GAMA):
Maximum weight approved for
ground maneuver. (It includes weight
of start, taxi, and runup fuel.)
2– 2
The datum of some helicopters is the center of the rotor mast,
but this location causes some arms to be positive and others
negative. To simplify weight and balance computations, most
modern helicopters, like airplanes, have the datum located at
the nose of the aircraft or a specified distance ahead of it.
A moment is a force that tries to cause rotation, and is the
product of the arm, in inches, and the weight, in pounds.
Moments are generally expressed in pound-inches (lb-in) and
may be either positive or negative. Figure 2-1 shows the way
the algebraic sign of a moment is derived. Positive moments
cause an airplane to nose up, while negative moments cause
it to nose down.
Consider these facts about the lever in Figure 2-2: The 100-
pound weight A is located 50 inches to the left of the fulcrum
(the datum, in this instance), and it has a moment of
100°?–50 = –5,000 lb-in. The 200-pound weight B is located
25 inches to the right of the fulcrum, and its moment is 200°
+25 = +5,000 lb-in. The sum of the moments is –5,000
+5,000 = 0, and the lever is balanced. [Figure 2-3] The forces
that try to rotate it clockwise have the same magnitude as
those that try to rotate it counterclockwise.
Figure 2-1. Relationships between the algebraic signs of
weights, arms, and moments.
The Law of the Lever
All weight and balance problems are based on the physical
law of the lever. This law states that a lever is balanced when
the weight on one side of the fulcrum multiplied by its arm
is equal to the weight on the opposite side multiplied by its
arm. In other words, the lever is balanced when the algebraic
sum of the moments about the fulcrum is zero. [Figure
2-2] This is the condition in which the positive moments
(those that try to rotate the lever clockwise) are equal to the
negative moments (those that try to rotate it counterclockwise).
Figure 2-2. The lever is balanced when the algebraic sum of the
moments is zero.
Figure 2-3. When a lever is in balance, the sum of the
moments is zero.
Determining the CG
One of the easiest ways to understand weight and balance
is to consider a board with weights placed at various
locations. We can determine the CG of the board and observe
the way the CG changes as the weights are moved.
The CG of a board like the one in Figure 2-4 may be determined by using these four steps:
1. Measure the arm of each weight in inches from a datum.
2. Multiply each arm by its weight in pounds to determine
the moment in pound-inches of each weight.
3. Determine the total of all the weights and of all the
moments. Disregard the weight of the board.
4. Divide the total moment by the total weight to determine
the CG in inches from the datum.
Fulcrum: The point about which a
lever balances.
Moment: A force that causes or tries
to cause an object to rotate.
The Physical Law of the Lever
A lever is balanced when the algebraic sum of the moments about its
fulcrum is equal to zero.
2–3
To prove this is the correct CG, move the datum to a location
110 inches to the right of the original datum and determine
the arm of each weight from this new datum, as in Figure
2-6. Then make a new chart similar to the one in Figure 2-
7. If the CG is correct, the sum of the moments will be zero.
Figure 2-4. Determining the center of gravity from a datum
located off the board.
In Figure 2-4, the board has three weights, and the datum is
located 50 inches to the left of the CG of weight A. Determine
the CG by making a chart like the one in Figure 2-5.
Figure 2-5. Determining the CG of a board with three weights
and the datum located off the board.
As noted in Figure 2-5, “A” weighs 100 pounds and is
50 inches from the datum; “B” weighs 100 pounds and is 90
inches from the datum; “C” weighs 200 pounds and is
150 inches from the datum. Thus the total of the three weights is
400 pounds, and the total moment is 44,000 lb-in.
Determine the CG by dividing the total moment by the
total weight.
Figure 2-6. Arms from the datum assigned to the CG.
The new arm of weight A is 110 – 50 = 60 inches, and since
this weight is to the left of the datum, its arm is negative, or
–60 inches. The new arm of weight B is 110 – 90 = 20 inches,
and it is also to the left of the datum, so it is –20; the new
arm of weight C is 150 – 110 = 40 inches. It is to the right of
the datum and is therefore positive.
Figure 2-7. The board balances at a point 110 inches to the
right of the original datum. The board is balanced when the sum
of the moments is zero.
The location of the datum used for determining the arms of
the weights is not important; it can be anywhere. But all of
the measurements must be made from the same datum
location.
2– 4
Determining the CG of an airplane is done in the same way
as determining the CG of the board in the example on the
previous page. [Figure 2-8] Prepare the airplane for weighing
(as explained in Chapter 3) and place it on three scales. All
tare weight, the weight of any chocks or devices used to hold
the aircraft on the scales, is subtracted from the scale reading,
and the net weight of the wheels is entered into a chart like
the one in Figure 2-9. The arms of the weighing points are
specified in the TCDS for the airplane in terms of stations,
which are distances in inches from the datum.
Shifting the CG
One common weight and balance problem involves moving
passengers from one seat to another or shifting baggage or
cargo from one compartment to another to move the CG to a
desired location. This also can be visualized by using a board
with three weights and then working out the problem the way
it is actually done on an airplane.
Solution by Chart
The CG of a board can be moved by shifting the weights as
demonstrated in Figure 2-10: As the board is loaded, it
balances at a point 72 inches from the CG of weight A.
[Figure 2-11]
To shift weight B so the board will balance about its center,
50 inches from the CG of weight A, first determine the arm
of weight B that will produce a moment that causes the total
moment of all three weights around this desired balance point
to be zero. The combined moment of weights A and C around
this new balance point is 5,000 lb-in, so the moment of weight
B will have to be –5,000 lb-in in order for the board to
balance. [Figure 2-12]
Figure 2-8. Determining the CG of an airplane whose datum
is ahead of the airplane.
Figure 2-9. Chart for determining the CG of an airplane
whose datum is ahead of the airplane.
Figure 2-10. Moving the CG of a board by shifting the
weights. This is the original configuration.
Figure 2-12. Determining the combined moment of weights A
and C.
The empty weight of this aircraft is 5,862 pounds. Its
EWCG, determined by dividing the total moment by the
total weight, is located at fuselage station 201.1. This is
201.1 inches behind the datum.
Figure 2-11. Shifting the CG of a board by moving one of the
weights. This is the original condition of the board.
Tare weight: The weight of any
chocks or devices used to hold the
aircraft on the scales. Tare weight is
subtracted from the scale reading, to
get the net weight of the aircraft.
Station (GAMA): A location along
the airplane fuselage usually given
in terms of distance from the
reference datum.
2–5
Determine the arm of weight B by dividing its moment,
–5,000 lb-in, by its weight of 200 pounds. Its arm is –25 inches.
To balance the board at its center, weight B will have to be
placed so its CG is 25 inches to the left of the center of the
board, as in Figure 2-13.
Solution by Formula
This same problem can also be solved by using this basic
equation:
Figure 2-13. Placement of weight B to cause the board to
balance about its center.
Rearrange this formula to determine the distance weight B
must be shifted:
The CG of the board in Figure 2-10 was 72 inches from the
datum. This CG can be shifted to the center of the board as
in Figure 2-13 by moving weight B. If the 200-pound weight
B is moved 55 inches to the left, the CG will shift from 72
inches to 50 inches, a distance of 22 inches. The sum of the
moments about the new CG will be zero. [Figure 2-14]
Figure 2-14. Proof that the board balances at its center. The
board is balanced when the sum of the moments is zero.
When the distance the weight is to be shifted is known, the
amount of weight to be shifted to move the CG to any location can be determined by another arrangement of the basic
equation. Use the following arrangement of the formula to
determine the amount of weight that will have to be shifted
from station 80 to station 25, to move the CG from station
72 to station 50.
A Basic Weight and Balance Equation
This equation can be rearranged to find the distance a weight must
be shifted to give a desired change in the CG location:
The equation can also be rearranged to find the amount of weight to
shift to move the CG to a desired location:
It can also be rearranged to find the amount the CG is moved when
a given amount of weight is shifted:
Finally, this equation can be rearranged to find the total weight that
would allow shifting a given amount of weight to move the CG a given
distance:
? : This symbol, Delta, means a
change in something. ÐCG means a
change in the center of gravity
location.
If the 200-pound weight B is shifted from station 80 to
station 25, the CG will move from station 72 to station 50.
2– 6
A third arrangement of this basic equation may be used to
determine the amount the CG is shifted when a given amount
of weight is moved for a specified distance (as it was done
in Figure 2-10). Use this formula to determine the amount
the CG will be shifted when 200-pound weight B is moved
from +80 to +25.
Moving weight B from +80 to +25 will move the CG 22
inches, from its original location at +72 to its new location at
+50 as seen in Figure 2-13.
Shifting the Airplane CG
The same procedures for shifting the CG by moving weights
can be used to change the CG of an airplane by rearranging
passengers or baggage.
Consider this airplane:
Airplane empty weight and EWCG .......1,340 lbs @ +37.0
Maximum gross weight ......................................... 2,300 lbs
CG limits ..................................................... +35.6 to +43.2
Front seats (2) ................................................................. +35
Rear seats (2) ................................................................... +72
Fuel ................................................................. 40 gal @ +48
Baggage (maximum) .......................................60 lbs@ +92
Figure 2-15. Loading diagram for a typical single-engine
airplane.
The pilot has prepared a chart, Figure 2-16, with certain
permanent data filled in and blanks left to be filled in with
information on this particular flight:
Figure 2-16. Blank loading chart.
For this flight, the 140-pound pilot and a 115-pound
passenger are to occupy the front seats, and a 212-pound and
a 97-pound passenger are in the rear seats. There will be 50
pounds of baggage, and the flight is to have maximum range,
so maximum fuel is carried. The loading chart, Figure 2-
17, is filled in using the information from Figure 2-15:
Figure 2-17. This completed loading chart shows the weight is
within limits, but the CG is too far aft.
CG limits (GAMA): The extreme
center of gravity locations within
which the airplane must be operated
at a given weight.
2–7
With this loading, the total weight is less than the maximum
of 2,300 pounds and is within limits, but the CG is 0.9 inch
too far aft.
One possible solution would be to trade places between the
212-pound rear-seat passenger and the 115-pound front-seat
passenger. Use a modification of the basic weight and
balance equation to determine the amount the CG will
change when the passengers swap seats:
Weight and Balance Documentation
FAA-Furnished Information
Before an aircraft can be properly weighed and its emptyweight center of gravity computed, certain information must
be known. This information is furnished by the FAA for every
certificated aircraft in the Type Certificate Data Sheets
(TCDS) or Aircraft Specifications available to all AMTs and
can be accessed via the internet: http://av-info.gov/tc.
When the design of an aircraft is approved by the FAA, an
Approved Type Certificate and TCDS are issued. The TCDS
include all of the pertinent specifications for the aircraft, and
at each annual or 100-hour inspection, it is the responsibility
of the inspecting AMT to ensure that the aircraft adheres to
them. See Pages 2-8 through 2-10, Figure 2-19, for an example
TCDS excerpt.
The weight and balance information on a TCDS includes the
following items.
Data Pertinent to Individual Models
This type of information is determined in the sections
pertinent to each individual model:
CG Range
Normal Category
(+82.0) to (+93.0) at 2,050 pounds
(+87.4) to (+93.0) at 2,450 pounds
Utility Category
(+82.0) to (86.5) at 1,950 pounds
Straight line variations between points given.
The two passengers changing seats moved the CG forward
1.6 inches, which places it within the operating range. This
can be proven correct by making a new chart incorporating
the changes. [Figure 2-18]
Figure 2-18. This loading chart, made after the seat changes,
shows both the weight and balance are within allowable limits.
Aircraft Specifications:
Documentation containing the
pertinent specifications for aircraft
certificated under the CARs.
Approved Type Certificate:
A certificate of approval issued by
the FAA for the design of an
airplane, engine, or propeller.
Type Certificate Data Sheets
(TCDS): The official specifications
issued by the FAA for an aircraft,
engine, or propeller.
About the TCDS
Aircraft certificated before January 1, 1958, were issued Aircraft
Specifications under the Civil Air Regulations (CARs), but when the
Civil Aeronautics Administration (CAA) was replaced by the FAA,
Specifications were replaced by TCDS. TCDS and Aircraft
Specifications are available from the Superintendent of Documents
in six volumes in both paper and Microfiche format. Description of the
volume contents, price, and ordering instructions are found in Advisory
Circular (AC) 00-2, Advisory Circular Checklist.
(Continued on Page 2-11)
2– 8
DEPARTMENT OF TRANSPORTATION
FEDERAL AVIATION ADMINISTRATION
2A13
Revision 41
PIPER
PA-28-140 PA-28-151
PA-28-150 PA-28-181
PA-28-160 PA-28-161
PA-28-180 PA-28R-201
PA-28-235 PA-28R-201T
PA-28S-160 PA-28-236
PA-28S-180 PA-28RT-201
PA-28R-180 PA-28RT-201T
PA-28R-200 PA-28-201T
May 12, 1987
TYPE CERTIFICATE DATA SHEET NO. 2A13
This data sheet, which is a part of Type Certificate 2A13, prescribes conditions and limitations under which
the product for which the type certificate was issued meets the airworthiness requirements of the Civil Air
Regulations.
Type Certificate Holder Piper Aircraft Corporation
2926 Piper Drive
Vero Beach, Florida 32960
I. Model PA-28-160, Cherokee, 4 PCLM (Normal Category), Approved October 31, 1960.
Engine Lycoming 0-320-B2B or 0-320-D2a with Carburetor setting 10-3678-32
Fuel 91/96 minimum grade aviation gasoline.
Engine Limits For all operations, 2700 r.p.m. (160 h.p.)
Propeller and Sensenich M74DM or 74DM6 on S/N 1 through 1760 1760A;
Propeller Limits Sensenich M74DMS or 74D6S5 on S/N 1761 and up. Static r.p.m. at
maximum permission throttle setting: Not over 2425, not under 2325.
No additional tolerance permitted.
Diameter: Not over 74", not under 72.5".
See Note 10.
Propeller Spinner Piper P/N 14422-00 on S/N 1 through 1760A;
Piper P/N 63760-04 or 65805 on S/N 1761 and up.
See Note 11.
Page No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Rev. No. 41 36 36 35 35 36 36 35 36 36 35 35 36 35 36 35 36 36 36
Page No. 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
Rev. No. 36 35 36 36 35 37 38 37 39 37 37 38 39 38 41 38 39 38 41
Page No. 39 40 41 42 43 44 45 46
Rev. No. 38 41 38 38 38 38 38 39
Figure 2-19. Excerpts from a Type Certificate Data Sheet.
2–9
Figure 2-19. Excerpts from a Type Certificate Data Sheet (continued).
2A13 –2– March 3, 1981
Revision 37
Airspeed Limits Never exceed 171 m.p.h. (148 knots) CAS
Maximum Structural 140 m.p.h. (121 knots) CAS
cruising 140 m.p.h. (121 knots) CAS
Maneuvering 129 m.p.h. (112 knots) CAS
Flaps extended 115 m.p.h. (100 knots) CAS
Center of Gravity (+84.0) to (+95.9) at 1650 lb. or less
Range (+85.9) to (+95.9) at 1975 lb.
(+88.2) to (+95.9) at 2200 lb.
Straight line variation between points given
Empty Wt. C.G. Range None
Maximum Weight 2200 lb.
No. of Seats 4 (2 at +85.5,2 at +118.1)
Maximum Baggage 125 lbs. (+142.8) (S/N 28-1 through 28-1760A)
See NOTE 8.
200 lbs. (+142.8) (S/N 28-1761 and up)
Fuel Capacity 50 gal. (2 wing tanks) (+95)
See NOTE 1 for data on system fuel.
Oil Capacity 8 qts. (+32.5), 6 qts. useable
See NOTE 1 for data on system oil.
Control Surface Wing flaps (±2°) Up 0° Down 40°
Movements Ailerons (±2°) Up 30° Down 15°
Rudder (±2°) Left 27° Right 27°
Stabilator (±2°) Up 18° Down 2°
Stabilator tab (±1°) Up 3° Down 12°
Nose Wheel Travel (+1°) Left 30° Right 30°
(Effective on S/N 1 through 3377)
Left 22° Right 22°
(Effective on S/N 3378 and up)
Manufacturer’s 28-03, 28-1 and up.
Serial Nos.
II. Model PA-28-150, Cherokee, 4 PCLM (Normal Category), Approved June 2, 1961
Engine Lycoming 0-320-A2B or 0-320-E2A with carburetor setting 10-3678-32
Fuel 80/87 minimum grade aviation gasoline
Engine Limits For all operations, 2700 r.p.m. (150 h.p.)
Propeller and Sensenich M74DM or 74DM6 on S/N 1 through 1760A;
Propeller Limits Sensenich M74DMS or 74DM6S5 on S/N 1761 and up
Static r.p.m. at maximum permissible throttle setting not over 2375,
not under 2275.
No additional tolerance permitted.
Diameter: Not over 74", not under 72.5."
See NOTE 10.
2–10
Figure 2-19. Excerpts from a Type Certificate Data Sheet (continued).
Data Pertinent to All Models:
Datum 78.4" forward of wing leading edge (straight wing only). 78.4" forward of
inboard intersection of straight and tapered sections (semi-tapered wings).
Leveling Means Two screws left side fuselage below window.
Certification Basis Type Certificate No. 2A13 issued October 31, 1960. Date of Application for
Type Certificate, February 14, 1965.
Delegation Option Authorization granted per FAR 21, Subpart J. July 17, 1968.
PA-28-140 and PA-28-151: CAR 3, effective May 15, 1956, including
Amendments 3-1, 3-2, 3-4, and paragraphs 3.304 and 3.705 of Amendment 3-7.
PA-28-150, PA-28-160, PA-28-180, PA-28-235, PA-28S-160, PA-28S-180, PA28R-180, PA-28R-200; CAR 3, effective May 15, 1956, including
Amendments 3-1, 3-2 and paragraphs 3.304 and 3.705.
PA-28-161: CAR 3 effective May 15, 1956, through Amendment 3-2;
paragraph 3.387(d) of Amendment 3-4; paragraphs 3.304 and 3.705 of
Amendment 3-7; FAR 23.959 of Amendment 23-7; FAR 36 effective
December 1, 1969, through Amendment 36-4.
PA-28-181: CAR 3 effective May 15, 1956, through Amendment 3-2,
Amendment 3-4 and paragraphs 3.304 and 3.705 of Amendment 3-7.
Also, FAR 23.207, 23.221 and 23.959 of Amendment 23-7.
PA-28R-201: CAR 3 effective May 15, 1956, through Amendment 3-2; paragraphs 3.304 and 3.705 of Amendment 3-7; paragraphs 23.221, 23.959, 23.965,
23.967(e)(2), 23.1091 and 23.1093 of FAR 23 Amendment 23-16;
FAR 36 effective December 1, 1969, through Amendment 36-4 (no
acoustical change).
PA-28R-201T: CAR 3 effective May 15, 1956, through Amendment 3-2
including paragraphs 3.304 and 3.705 of Amendment 3-7; FAR 23.221, 23.901,
23.909, 23.959, 23.965, 23.967(e)(2), 23.1041, 23.1043, 23.1047, 23.1143,
23.1305, 23.1441 and 23.1527 of Amendment 23-16; FAR 36 effective
December 1, 1969, through Amendment 36-4.
PA-28-236: CAR 3 effective May 15, 1956, through Amendment 3-2, and
paragraphs 3.304 and 3.705 of Amendment 3-7 effective May 3, 1962. FAR
23.221, 23.959, 23.1091, and 23.1093 of FAR Part 23, Amendment 23-17
effective February 1, 1977; FAR 23.1581(b)(2) of FAR 23 Amendment 23-21
effective March 1, 1978; and applicable portions of FAR 36, as amended up to
Amendment 36-9 effective April 3, 1978.
March 3, 1981 – 39– 2A13
Revision 38
2–11
If this information is given, there may be a chart on the TCDS
similar to the one in Figure 2-20. This chart helps visualize the
CG range. Draw a line horizontally from the aircraft weight and
a line vertically from the fuselage station on which the CG is
located. If these lines cross inside the enclosed area, the CG is
within the allowable range for the weight.
Note that there are two enclosed areas; the larger is the CG
range when operating the Normal category only, and the
smaller range is for operation in both the Normal and Utility
categories. When operating with the weight and CG limitations shown for the Utility category, the aircraft is approved
for limited acrobatics such as spins, lazy eights, chandelles,
and steep turns in which the bank angle exceeds 60°. When
operating outside of the smaller enclosure but within the
larger, the aircraft is restricted from these maneuvers.
Figure 2-20. CG range chart.
If the aircraft has retractable landing gear, a note may be
added, for example:
“Moment due to retracting of landing gear (+819 lb-in)”
Empty Weight CG Range
When all of the seats and baggage compartments are located
close together, it is not possible, as long as the EWCG is
located within the EWCG range, to legally load the aircraft
so that its operational CG falls outside this allowable range.
If the seats and baggage areas extend over a wide range, the
EWCG range will be listed as “None.”
Maximum Weight
The maximum allowable takeoff and landing weight and the
maximum allowable ramp weight are given. This basic
information may be altered by a note such as the following:
“NOTE 5. A landing weight of 6,435 lbs must be observed if
10 PR tires are installed on aircraft not equipped with 60-
810012-15 (LH) or 60-810012-16 (RH) shock struts.”
Number of Seats
The number of seats and their arms are given in such terms as:
“4 (2 at +141, 2 at +173)”
Maximum Baggage (Structural Limit)
This is given as:
“500 lbs at +75 (nose compartment)
655 lbs at +212 (aft area of cabin)”
Fuel Capacity
This important information is given in such terms as:
“142 gal (+138) comprising two interconnected cells in each
wing”
—or,
“204 gal (+139) comprising three cells in each wing and one
cell in each nacelle (four cells interconnected) See NOTE 1
for data on fuel system.”
“NOTE 1” will read similar to this example:
“NOTE 1. Current weight and balance data, including list of
equipment included in standard empty weight and loading
instructions when necessary, must be provided for each
aircraft at the time of original certification.
The standard empty weight and corresponding center of
gravity locations must include unusable fuel of 24 lbs at
(+135).”
Normal category: A category of
aircraft certificated under 14 CFR,
Part 23 and CAR, Part 3 that allows
the maximum weight and CG range
while restricting the maneuvers that
are permitted.
Utility category: A category of
aircraft certificated under 14 CFR,
Part 23 and CAR, Part 3 that permits
limited acrobatic maneuvers but
restricts the weight and the
CG range.
2–12
Oil Capacity (Wet Sump)
The quantity of the full oil supply and its arm are given in
such terms as:
“26 qt (+88)”
Data Pertinent to All Models
Datum
The location of the datum may be described, for example, as:
“Front face of firewall”
—or,
“78.4" forward of wing leading edge (straight wing only).
78.4" forward of inboard intersection of straight and tapered
sections (semi-tapered wings).”
Leveling Means
A typical method is:
“Upper door sill.”
This means that a spirit level is held against the upper door
sill and the aircraft is level when the bubble is centered.
Other methods require a spirit level to be placed across
leveling screws or leveling lugs in the primary aircraft
structure or dropping a plumb line between specified
leveling points.
TCDS are issued for aircraft that have been certificated since
January 1, 1958, when the FAA came into being. For aircraft
certificated before this date, basically the same data is
included in Aircraft, Engine, or Propeller Specifications that
were issued by the Civil Aeronautics Administration.
The book, Aircraft Listings, Volume VI of the Type Certificate
Data Sheets Specifications and Listings, includes weight and
balance information on aircraft of which there are fewer than
50 listed as being certificated.
Manufacturer-Furnished Information
When an aircraft is initially certificated, its empty weight and
EWCG are determined and recorded in the weight and
balance record such as the one in Figure 2-21. Notice in this
figure that the moment is expressed as “Moment (lb-in/
1000).” This is a moment index which means that the
moment, a very large number, has been divided by 1,000 to
make it more manageable. Chapter 4 discusses moment
indexes in more detail.
Figure 2-21. Typical weight and balance data for a 14 CFR, Part 23 airplane.
2–13
Dealing with Large Moments
Moments are the product of the arm in inches and the weight in
pounds, and for large aircraft this produces very large numbers. To
reduce the likelihood of mathematical errors, the manufacturers often
divide these large numbers by a reduction factor of 100 or 1,000 to
get a moment index which is easier to handle. To change a moment
index to a moment, just multiply it by the reduction factor.
Equipment list: A list of items
approved by the FAA for installation
in a particular aircraft. The list
includes the name, part number,
weight, and arm of the component.
Installation of an item in the
equipment list is considered to be a
minor alteration.
An equipment list is furnished with the aircraft which specifies all the required equipment, and all equipment approved
for installation in the aircraft. The weight and arm of each
item is included on the list, and all equipment installed when
the aircraft left the factory is checked.
When an AMT adds or removes any item on the equipment
list, he or she must change the weight and balance record to
indicate the new empty weight and EWCG, and the
equipment list is revised to show which equipment is actually
installed. Figure 2-22 is an excerpt from a comprehensive
equipment list which includes all of the items of equipment
approved for this particular model of aircraft. The POH for
each individual aircraft includes an aircraft specific equipment list of the items from this master list. When any item is
added to or removed from the aircraft, its weight and arm are
determined in the equipment list and used to update the
weight and balance record.
The POH/AFM also contains CG moment envelopes and
loading graphs. Examples of the use of these handy graphs
are given in Chapter 4.
Figure 2-22. Excerpt from a typical comprehensive equipment list (continued on next page).
2–14
Figure 2-22. Excerpt from a typical comprehensive equipment list (continued).
3–1
Chapter 3
Weighing the Aircraft and
Determining the Empty-Weight
Center of Gravity
Chapter 2 explained the theory of weight and balance and
gave examples of the way the center of gravity could be
found for a board loaded with several weights. In this
chapter, the practical aspects of weighing an airplane and
locating its center of gravity are discussed. Formulas are
introduced that allow the CG location to be measured in
inches from various datum locations and in percentage of
the mean aerodynamic chord.
Requirements
Weight and balance is of such vital importance that each AMT
maintaining an aircraft must be fully aware of his or her
responsibility to provide the pilot with current and accurate
information for the actual weight of the aircraft and the
location of the center of gravity. The pilot in command has
the responsibility to know the weight of the load, CG,
maximum allowable gross weight, and CG limits of
the aircraft.
The weight and balance report must include an equipment
list showing weights and moment arms of all required and
optional items of equipment included in the certificated
empty weight.
When an aircraft has undergone extensive repair or major
alteration, it should be reweighed and a new weight and
balance record started.
Equipment for Weighing
There are two basic types of scales used to weigh aircraft:
scales on which the aircraft is rolled so the weight is taken
from the wheels, and electronic load cells placed between the
aircraft jack and the jack pads on the aircraft.
Some aircraft are weighed with mechanical scales of the low
profile type similar to those shown in Figure 3-1.
Large aircraft, including heavy transports, are weighed by
rolling them onto weighing platforms with electronic
weighing cells that accurately measure the force applied by
the weight of the aircraft. [Figure 3-2]
Electronic load cells are used when the aircraft is weighed
by raising it on jacks. The cells are placed between the jack
and the jack pad on the aircraft, and the aircraft is raised on
the jacks until the wheels are off the floor and the aircraft is
in a level flight attitude. The weight measured by each load
cell is indicated on the control panel.
Mechanical scales should be protected when they are not
in use, and they must be periodically checked for accuracy
by measuring a known weight and noting any errors detected.
Electronic load cells normally have a built-in calibration that
allows them to be accurately zeroed before any load
is applied.
Who’s responsible?
AMTs must provide the pilot with current and accurate aircraft weight
information and where its EWCG is located.
The pilot in command has the responsibility to know the weight of the
load, CG, maximum allowable gross weight, and CG limits of
the aircraft.
Load cell: A component in an
electronic weighing system placed
between the jack and the jack pad on
the aircraft. The load cell contains
strain gauges whose resistance
changes with the weight on the cell.
3– 2
Bilge area: The lowest part of an
aircraft structure in which water and
contaminants collect.
Figure 3-1. Low profile platform scales are used to weigh some aircraft. One scale is placed under each wheel. (Photo courtesy
General Electrodynamics Corp.)
Figure 3-2. Weighing platforms accurately measure the weight of
large aircraft without having to raise the aircraft off the ground.
(Photo courtesy General Electrodynamics Corp.)
Specific Gravity
Both the heat energy available and the weight of the fuel are
determined by its specific gravity (s.g.), and this in turn is affected by
its temperature. Cold fuel has a higher s.g. and therefore weighs more
per gallon than warm fuel, and since the heat energy content is
measured in Btu or Calories per pound or kilogram, cold fuel has more
heat energy per gallon than warm fuel.
Preparation for Weighing
The major considerations in preparing an aircraft for weighing are discussed below.
Weigh Clean Aircraft Inside Hangar
The aircraft should be weighed inside a hangar where wind
cannot blow over the surface and cause fluctuating or false
scale readings.
The aircraft should be clean inside and out, with special
attention paid to the bilge area to be sure no water or debris
is trapped there, and the outside of the aircraft should be as
free as possible of all mud and dirt.
Equipment List
All of the required equipment must be properly installed, and
there should be no equipment installed that is not included
in the equipment list. If such equipment is installed, the
weight and balance record must be corrected to indicate it.
3–3
Ballast
All required permanent ballast must be properly secured
in place and all temporary ballast must be removed.
Draining the Fuel
Drain fuel from the tanks in the manner specified by the
aircraft manufacturer. If there are no specific instructions,
drain the fuel until the fuel quantity gauges read empty when
the aircraft is in level flight attitude. Any fuel remaining in
the system is called residual, or unusable fuel and is part of
the aircraft empty weight.
If it is not feasible to drain the fuel, the tanks can be topped
off to be sure of the quantity they contain and the aircraft
weighed with full fuel. After the weighing is complete, the
weight of the fuel and its moment are subtracted from those
of the aircraft as weighed. To correct the empty weight for
the residual fuel, add its weight and moment. The amount
of residual fuel and its arm are normally found in NOTE 1 in
the section of the TCDS, “Data Pertaining to All Models.”
See “Fuel Capacity” on Page 2-11.
When computing the weight of the fuel, for example a tank
full of jet fuel, measure its specific gravity (s.g.) with a
hydrometer and multiply it by 8.345 (the nominal weight of
1 gallon of pure water whose s.g. is 1.0). If the ambient
temperature is high and the jet fuel in the tank is hot enough
for its specific gravity to reach 0.81, rather than its nominal
s.g. of 0.82, the fuel will actually weigh 6.76 pounds per
gallon rather than its nominal weight of 6.84 pounds
per gallon. The standard weight of aviation gasoline (Avgas)
is 6 pounds per gallon.
Oil
The empty weight of aircraft certificated under the CAR, Part
3 does not include the engine lubricating oil. The oil must
either be drained before the aircraft is weighed, or its weight
must be subtracted from the scale readings to determine the
empty weight. To weigh an aircraft that does not include the
engine lubricating oil as part of the empty weight, place it in
level flight attitude, then open the drain valves and allow all
of the oil that is able to, to drain out. Any oil remaining is
undrainable oil and is part of the empty weight. Aircraft
certificated under 14 CFR, Parts 23 and 25 include full oil as
part of the empty weight.
If it is impractical to drain the oil, the reservoir can be filled
to the specified level and the weight of the oil computed at
7.5 pounds per gallon. Then its weight and moment are
subtracted from the weight and moment of the aircraft
as weighed. The amount and arm of the undrainable oil are
found in NOTE 1 of the TCDS, and this must be added to the
empty weight.
Other Fluids
The hydraulic fluid reservoir and all other reservoirs containing fluids required for normal operation of the aircraft should
be full. Fluids not considered to be part of the empty weight
of the aircraft are potable (drinkable) water, lavatory
precharge water, and water for injection into the engines.
Configuration of the Aircraft
Consult the aircraft service manual regarding the position of
the landing gear shock struts and the control surfaces for
weighing; when weighing a helicopter, the main rotor must
be in its correct position.
Jacking the Aircraft
Large aircraft are often weighed by rolling them onto ramps
in which load cells are embedded. This eliminates the
problems associated with jacking the aircraft off the ground.
But most smaller aircraft are actually lifted off the ground
onto scales or load cells.
You must exercise special care when raising an aircraft on
jacks for weighing. If the aircraft has spring steel landing gear
and it is jacked at the wheel, the landing gear will slide inward
as the weight is taken off of the tire, and care must be taken
to prevent the jack from tipping over.
For some aircraft, stress panels or plates must be installed
before they are raised with wing jacks, to distribute the weight
over the jack pad. Be sure to follow the recommendations
of the aircraft manufacturer in detail anytime an aircraft is
jacked. When using two wing jacks, take special care to
raise them simultaneously, keeping the aircraft level so it
will not slip off the jacks. As the jacks are raised, keep the
safety collars screwed down against the jack cylinder
to prevent the aircraft from tilting if one of the jacks should
lose hydraulic pressure.
Permanent ballast: A weight
permanently installed in an aircraft
to bring its center of gravity into
allowable limits. Permanent ballast is
part of the aircraft empty weight.
Temporary ballast: Weights that
can be carried in a cargo
compartment to move the location of
the CG for a specific flight condition.
Temporary ballast must be removed
when the aircraft is weighed.
Undrainable oil: Oil that does not
drain from an engine lubricating
system when the aircraft is in the
normal ground attitude and the drain
valve is left open. The weight of the
undrainable oil is part of the empty
weight of the aircraft.
Residual fuel: Fuel that remains in
the sumps and fuel lines when the
fuel system is drained from the inlet
to the fuel metering system, with the
aircraft in level flight attitude. The
weight of the residual fuel is part of
the empty weight of the aircraft.
Unusable fuel (GAMA): Fuel
remaining after a runout test has
been completed in accordance with
governmental regulations.
3– 4
Leveling the Aircraft
When an aircraft is weighed, it must be in its level flight
attitude so that all of the components will be at their correct
distance from the datum. This attitude is determined by
information in the TCDS. Some aircraft require a plumb line
to be dropped from a specified location so that the point of
the weight, the bob, hangs directly above an identifiable point.
Others specify that a spirit level be placed across two leveling
lugs, often special screws on the outside of the fuselage.
Other aircraft call for a spirit level to be placed on the upper
door sill.
Lateral level is not specified for all general aviation (GA)
airplanes, but provisions are normally made on transport
airplanes and helicopters for determining both longitudinal
and lateral level. This may be done by built-in leveling
indicators, or by a plumb bob that shows the conditions of
both longitudinal and lateral level.
The actual adjustments to level the aircraft using load cells
are made with the jacks. When weighing from the wheels,
leveling is normally done by adjusting the air pressure in the
nose wheel shock strut.
Determining the Center of Gravity
When the aircraft is in its level flight attitude, drop a plumb
line from the datum and make a mark on the hangar floor
below the tip of the bob. Draw a chalk line through this point
parallel to the longitudinal axis of the aircraft. Then draw
lateral lines between the actual weighing points for the main
wheels, and make a mark along the longitudinal line at the
weighing point for the nose wheel or the tail wheel. These
lines and marks on the floor allow you to make accurate
measurements between the datum and the weighing points
to determine their arms.
Two Ways to Express CG Location
The location of the CG may be expressed in terms of inches from a
datum specified by the aircraft manufacturer, or as a percentage of
the MAC. The location of the leading edge of the MAC, the LEMAC,
is a specified number of inches from the datum.
Safety Considerations
Special precautions must be taken when raising an aircraft on jacks.
1. Stress plates must be installed under the jack pads if the manufacturer specifies them.
2. If anyone is required to be in the aircraft while it is being jacked,
there must be no movement.
3. The jacks must be straight under the jack pads before beginning
to raise the aircraft.
4. All jacks must be raised simultaneously and the safety collars
screwed down against the jack cylinder to prevent the aircraft tipping if any jack should lose pressure.
Determine the CG by adding the weight and moment of each
weighing point to determine the total weight and total
moment. Then divide the total moment by the total weight to
determine the CG relative to the datum.
As an example of locating the CG with respect to the datum,
which in this case is the firewall, consider the tricycle landing
gear airplane in Figures 3-3 and 3-4.
When the airplane is on the scales with the parking brakes
off, place chocks around the wheels to keep the airplane from
rolling. Subtract the weight of the chocks, called tare weight,
from the scale reading to determine the net weight at each
weighing point. Multiply each net weight by its arm to
determine its moment, then determine the total weight and
total moment. The CG is determined by dividing the total
moment by the total weight.
Tare weight: The weight of any
chocks or devices used to hold an
aircraft on the scales when it is
weighed. The tare weight must be
subtracted from the scale reading to
obtain the net weight of the aircraft.
Figure 3-3. The datum is located at the firewall.
The airplane in Figures 3-3 and 3-4 has a net weight of 2,006
pounds, and its CG is 32.8 inches behind the datum.
3–5
Empty-Weight Center
of Gravity Formulas
A chart like the one in Figure 3-4 helps visualize the weights,
arms, and moments when solving an EWCG problem, but it
is quicker to determine the EWCG by using formulas and an
electronic calculator. The use of a calculator for solving these
problems is described in Chapter 8.
There are four possible conditions and their formulas that
relate the location of the CG to the datum. Notice that the
formula for each condition first determines the moment
of the nose wheel or tail wheel and then
divides it by the total weight of the airplane. The arm thus
determined is then added to or subtracted from the distance
between the main wheels and the datum, distance D.
Nose wheel airplanes with the datum forward of the main wheels
Figure 3-4. Locating the CG of an airplane relative to the datum which is located at the firewall. See Figure 3-3.
Datum Forward of the Airplane—
Nose Wheel Landing Gear
The datum of the airplane in Figure 3-5 is 100 inches forward
of the leading edge of the wing root, or 128 inches forward
of the main-wheel weighing points. This is distance (D). The
weight of the nose wheel (F) is 340 pounds, and the distance
between main wheels and nose wheel (L) is 78 inches. The
total weight of the airplane (W) is 2,006 pounds.
Nose wheel airplanes with the datum aft of the main wheels
Tail wheel airplanes with the datum forward of the main wheels
Tail wheel airplanes with the datum aft of the main wheels
Figure 3-5. The datum is 100 inches forward of the wing root
leading edge.
Determine the CG by using this formula:
The CG is 114.8 inches aft of the datum. This is 13.2 inches
forward of the main-wheel weighing points which proves the
location of the datum has no effect on the location of the CG
so long as all measurements are made from the same location.
Determining the Location of the CG
1. Determine the location of the CG relative to the main-wheel weighing points. This is the or part of the formula.
2. Convert the location of the CG measured from the main-wheel
weighing points to the location measured from the datum or the
LEMAC.
3– 6
Datum Aft of the Main Wheels—
Nose Wheel Landing Gear
The datum of some aircraft may be located aft of the main
wheels. The airplane in this example is the same one just
discussed, but the datum is at the intersection of the trailing
edge of the wing with the fuselage.
The distance (D) between the datum of the airplane in Figure
3-6 and the main-wheel weighing points is 75 inches, the
weight of the nose wheel (F) is 340 pounds, and the distance
between main wheels and nose wheel (L) is 78 inches. The
total net weight of the airplane (W) is 2,006 pounds.
Datum Forward of the Main Wheels—
Tail Wheel Landing Gear
Locating the CG of a tail wheel airplane is done in the same
way as locating it for a nose wheel airplane except the
formulas use rather than .
The distance (D) between the datum of the airplane in Figure
3-7 and the main-gear weighing points is 7.5 inches, the
weight of the tail wheel (R) is 67 pounds, and the distance
(L) between the main-wheel and the tail wheel weighing
points is 222 inches. The total net weight of the airplane (W)
is 1,218 pounds.
Figure 3-6. The datum is aft of the main wheels at the wing
trailing edge.
The location of the CG may be determined by using this
formula:
The CG location is a negative value, which means it is 88.2
inches forward of the datum. This places it 13.2 inches
forward of the main wheels, exactly the same location as it
was when it was measured from other datum locations.
Figure 3-7. The datum of this tail wheel airplane is 7.5 inches
forward of the wing root leading edge.
Determine the CG by using this formula:
The CG is 19.7 inches behind the datum.
Location of Datum
It makes no difference where the datum is located as long as all
measurements are made from the same location.
3–7
Datum Aft of the Main Wheels—
Tail Wheel Landing Gear
The datum of the airplane in Figure 3-8 is located at the
intersection of the wing root trailing edge and the fuselage.
This places the arm of the main gear (D) at –80 inches. The
net weight of the tail wheel (R) is 67 pounds, the distance
between the main wheels and the tail wheel (L) is 222 inches,
and the total net weight (W) of the airplane is 1,218 pounds.
The MAC, as seen in Figure 3-9, is the chord of an imaginary
airfoil that has all of the aerodynamic characteristics of the
actual airfoil. It can also be thought of as the chord drawn
through the geographic center of the plan area of the wing.
Figure 3-8. The datum is aft of the main wheels, at the
intersection of the wing trailing edge and the fuselage.
Since the datum is aft of the main wheels, use this formula:
The CG is 67.8 inches forward of the datum, or 12.2 inches
aft of the main-gear weighing points. The CG is in exactly
the same location relative to the main wheels, regardless of
where the datum is located.
Location with Respect to the
Mean Aerodynamic Chord
AMTs are primarily concerned with the location of the CG
relative to the datum, an identifiable physical location from
which measurements can be made. But because the aerodynamic characteristics of a wing relate to its chord length,
pilots and flight engineers are more concerned with the
location of the CG relative to the chord; and because the mean,
or average, physical chord of a tapered wing is difficult to
measure, the mean aerodynamic chord (MAC) is used. The
allowable CG range is expressed in percentages of the MAC.
Figure 3-9. The MAC is the chord drawn through the
geographic center of the plan area of the wing.
Chord: A straight-line distance
across a wing from leading edge to
trailing edge.
MAC and CG
The location of the CG with respect to the mean aerodynamic chord
is important to the flight crew because it predicts the handling
characteristics of the aircraft.
Mean aerodynamic chord (MAC):
The chord of an imaginary airfoil
that has the same aerodynamic
characteristics as the actual airfoil.
The relative positions of the CG and the aerodynamic center
of lift of the wing have critical effects on the flight characteristics of the aircraft. Consequently, relating the CG location
to the chord of the wing is convenient from a design and
operations standpoint. Normally, an aircraft will have
acceptable flight characteristics if the CG is located
somewhere near the 25% average chord point. This means the
CG is located one-fourth of the total distance back from the
leading edge of the wing section. Such a location will place
the CG forward of the aerodynamic center for most airfoils.
3– 8
In order to relate the percent MAC to the datum, all weight
and balance information includes two items: the length of
MAC in inches and the location of the leading edge of MAC
(LEMAC) in inches from the datum.
The weight and balance data of the airplane in Figure 3-10
states that the MAC is from stations 1022 to 1198 and the
CG is located at station 1070.
MAC = 1198 – 1022 = 176 inches
LEMAC = station 1022
CG is 48 inches behind LEMAC (1070 – 1022 =
48 inches)
The location of the CG expressed in percentage of MAC is
determined using this formula:
It is sometimes necessary to determine the location of the CG
in inches from the datum when its location in % MAC is known.
The CG of the airplane is located at 27.3% MAC
MAC = 1198 – 1022 = 176 inches
LEMAC = station 1022
Determine the location of the CG in inches from the datum
by using this formula:
Figure 3-10. Large aircraft weight and balance calculation diagram.
Leading edge of MAC (LEMAC):
Leading Edge of the Mean
Aerodynamic Chord.
TEMAC: Trailing Edge of the Mean
Aerodynamic Chord.
The CG of the airplane is located at 27.3% MAC.
The CG of this airplane is located at station 1070 which is
1,070 inches aft of the datum.
It is important for longitudinal stability that the CG be located
ahead of the center of lift of a wing. Since the center of lift is
expressed as a percentage of the MAC, the location of the
CG is expressed in the same terms. See Chapter 6 for more
about using % MAC in weight and balance technology, in
“Weight and Balance Control —Large 䅩牣牡晴⸠
4– 1
Chapter 4
General Aviation Aircraft Operational
Weight and Balance Computations
Weight and balance data allows the pilot to determine the
loaded weight of the aircraft and determine whether or not
the loaded CG is within the allowable range for the weight.
See Figure 4-1 for an example of the data necessary for these
calculations.
Determining the Loaded Weight and CG
An important part of preflight planning is to determine that
the aircraft is loaded so its weight and CG location are within
the allowable limits. [Figure 4-2] There are two ways of
doing this: by the computational method using weights,
arms, and moments; and by the loading graph method,
using weight and moment indexes.
Figure 4-1. Weight and balance data needed to determine
proper loading of a 14 CFR, Part 23 airplane.
Figure 4-2. Airplane loading diagram.
Computational Method
The computational method uses weights, arms, and moments
and relates the total weight and CG location to a CG limits
chart similar to those included in the TCDS and the POH/
AFM.
A worksheet such as the one in Figure 4-3 provides space for
all of the pertinent weight and balance data. Data is included
for the airplane weight, CG, and moment along with the arms
of the seats, fuel, and baggage areas.
4–2
Figure 4-3. Blank weight and balance worksheet.
To determine that the airplane is properly loaded for this
flight, use the CG limits envelope in Figure 4-5 (which is
typical of those found in the POH/AFM). Draw a line
vertically upward from the CG of 43.54 inches, and one
horizontally to the right from the loaded weight of 3,027
pounds. These lines cross inside the envelope, which shows
the airplane is properly loaded for takeoff, but 77 pounds
overweight for landing.
Loading Graph Method
Everything possible is done to make flying safe, and one
expedient method is the use of charts and graphs from the
POH/AFM to simplify and speed up the preflight weight
and balance computations. Some use a loading graph and
moment indexes rather than the arms and moments. These
charts eliminate the need for calculating the moments and
thus make computations quicker and easier. [Figure 4-5]
When planning the flight, fill in the blanks in the worksheet
with the specific data for the flight. [Figure 4-4]
Pilot ............................................................................ 120 lbs
Front seat passenger .................................................. 180 lbs
Rear seat passengers ................................................. 175 lbs
Fuel 88 gal ................................................................. 528 lbs
Baggage A.................................................................. 100 lbs
Baggage B.................................................................... 50 lbs
Determine the moment of each item by multiplying its weight
by its arm. Then determine the total weight and the sum of
the moments. Divide the total moment by the total weight to
determine the CG in inches from the datum. The total weight
is 3,027 pounds and the CG is 43.54 inches aft of the datum.
Figure 4-4. Completed weight and balance worksheet.
CG limits envelope: An enclosed
area on a graph of the airplane
loaded weight and the CG location.
If lines drawn from the weight and
CG cross within this envelope, the
airplane is properly loaded.
Loading Graph Method
Loading graphs simplify weight and balance computations because
they eliminate the need for multiplication when computing a loaded CG.
Moment index: A moment that has
been divided by a reduction factor to
obtain a smaller number to make
computations easier and reduce the
likelihood of mathematical errors.
Loading graph: A graph of load
weight and load moment indexes.
Diagonal lines for each item relate
the weight to the moment index
without having to use mathematics.
4– 3
Figure 4-5. Center of gravity limits chart from a typical POH.
Moment Indexes
Moments determined by multiplying the weight of each
component by its arm result in large numbers that are
awkward to handle and can become a source of mathematical
error. To eliminate these large numbers, moment indexes are
used. The moment is divided by a reduction factor such as
100 or 1,000 to get the moment index. The loading graph
provides the moment index for each component, so you can
avoid mathematical calculation. The CG envelope uses
moment indexes rather than arms and moments.
Loading Graph
Figure 4-6 (see Page 4-4) is a typical loading graph taken from
the POH of a modern four-place GA airplane. To compute
the weight and balance, using the loading graph in Figure 4-
6, make a loading schedule chart like the one in Figure 4-7.
In Figure 4-6, follow the horizontal line for 300 pounds load
weight to the right until it intersects the diagonal line for pilot
and front passenger. From this point, drop a line vertically to
the load moment index along the bottom to determine the load
moment for the front seat occupants. This is 11.1 lb-in/1,000.
Record it in the loading schedule chart.
Determine the load moment for the 175 pounds of rear seat
occupants along the diagonal for 2nd row passengers or cargo.
This is 12.9; record it in the loading schedule chart.
Reduction factor: The number,
usually 100 or 1,000, that is used to
divide the moment to get the
moment index.
Loading schedule: A chart filled in
by the pilot during preflight planning
that lists the weight and moment
indexes of all occupants, fuel, and
baggage.
Figure 4-7. Loading schedule chart.
4–4
Figure 4-6. Loading graph.
4– 5
CG moment envelope: An enclosed
area on a graph of the airplane
loaded weight and loaded moment.
If lines drawn from the weight and
loaded moment cross within this
envelope, the airplane is properly
loaded.
Determine the load moment for the fuel and the baggage in
areas A and B in the same way and enter them all in the
loading schedule chart. The maximum fuel is marked on the
diagonal line for fuel in terms of gallons and liters. The
maximum is 88 gallons of usable fuel. The total capacity is
92 gallons, but 4 gallons are unusable and have already been
included in the empty weight of the aircraft. The weight of
88 gallons of gasoline is 528 pounds and its moment index
is 24.6. The 100 pounds of baggage in area A has a moment
index of 9.7 and the 50 pounds in area B has an index of 5.8.
Enter all of these weights and moment indexes in the loading
schedule chart and add all of the weights and moment
indexes to determine the totals. Transfer these values to the
CG moment envelope in Figure 4-8.
The loading schedule shows that the total weight of the loaded
aircraft is 3,027 pounds, and the loaded airplane moment/
1,000 is 131.8.
Draw a line vertically upward from 131.8 on the horizontal
index at the bottom of the chart, and a horizontal line from
3,027 pounds in the left-hand vertical index. These lines
intersect within the dashed area which shows that the aircraft
is loaded properly for takeoff but it is too heavy for landing.
If the aircraft had to return for landing, it would have to fly
long enough to burn off 77 pounds (slightly less than 13
gallons) of fuel to reduce its weight to the amount allowed
for landing.
Figure 4-8. CG moment envelope.
Usable fuel (GAMA): Fuel available
for flight planning.
4–6
Multiengine Airplane Weight
and Balance Computations
Weight and balance computations for general aviation
multiengine airplanes are similar to those discussed for singleengine airplanes. Computations for large airline and cargo
airplanes are discussed in Chapter 6. See Figure 4-9 for an
example of weight and balance data for a typical twin-engine
general aviation airplane.
The airplane in this example was weighed to determine its
basic empty weight and EWCG. The weighing conditions and
results are:
Fuel drained —
Oil full —
Right wheel scales — 1,084 lbs, tare 8 lbs
Left wheel scales — 1,148 lbs, tare 8 lbs
Nose wheel scales — 1,202 lbs, tare 14 lbs
Determining the Loaded CG
Beginning with the basic empty weight and EWCG and using a
chart such as the one in Figure 4-11, the loaded weight and CG
of the aircraft can be determined. [Figure 4-10]
The aircraft is loaded as shown here:
Fuel (140 gal) ............................................................ 840 lbs
Front seat ................................................................... 320 lbs
Row 2 seats ................................................................ 310 lbs
Fwd. baggage ............................................................. 100 lbs
Aft baggage ................................................................. 90 lbs
Figure 4-9. Typical weight and balance data for a twin-engine
general aviation airplane.
Figure 4-10. Twin-engine airplane weight and balance diagram.
4– 7
The Chart Method Using Weight, Arm,
and Moments
Make a chart showing the weights, arms, and moments of
the airplane and its load.
Figure 4-11. Determining the loaded center of gravity of the
airplane in Figure 4-10.
Determining the CG in Percent of MAC
Refer again to Figures 4-10 and 4-11.
The loaded CG is 42.47 inches aft of the datum.
The MAC is 61.6 inches long.
The LEMAC is located at station 20.1.
The CG is 42.47 – 20.1 = 22.37 inches aft of LEMAC.
Use this formula:
The loaded weight for this flight is 5,064 pounds, and the
CG is located at 42.47 inches aft of the datum.
To determine that the weight and CG are within the allowable
range, refer to the CG range chart of Figure 4-12. Draw a line
vertically upward from 42.47 inches from the datum and one
horizontally from 5,064 pounds. These lines cross inside the
envelope, showing that the airplane is properly loaded.
Figure 4-12. Center of gravity range chart.
The loaded CG is located at 36.3% of the mean aerodynamic
chord.
The Chart Method Using Weight
and Moment Indexes
As mentioned in the previous chapter, anything that can be
done to make careful preflight planning easier makes flying
safer. Many manufacturers furnish charts in the POH/AFM
that use weight and moment indexes rather than weight, arm,
and moments. They further help reduce errors by including
tables of moment indexes for the various weights.
Consider the loading for this particular flight:
Cruise fuel flow = 16 gallons per hour
Estimated time en route = 2 hours 10 minutes
Reserve fuel = 45 minutes = 12 gallons
Total required fuel = 47 gallons
The pilot completes a chart like the one in Figure 4-13 using
moment indexes from the tables in Figures 4-14 through 4-16.
4–8
Figure 4-13. Typical weight and balance loading form.
Takeoff — 3,781 lbs and 4,310 moment/100
Landing — 3,571 lbs and 4,064 moment/100
Locate the moment/100 diagonal line for 4,310 and follow it
down until it crosses the horizontal line for 3,781 pounds.
These lines cross inside the envelope at the vertical line for a
CG location of 114 inches aft of the datum.
The maximum allowable takeoff weight is 3,900 pounds, and
this airplane weighs 3,781 pounds. The CG limits for 3,781
pounds are 109.8 to 117.5. The CG of 114 inches falls within
these allowable limits.
The moments/100 in the index column are found in the
charts in Figures 4-14 through 4-16. If the exact weight is
not in the chart, interpolate between the weights that are
included. When a weight is greater than any of those shown
in the charts, add the moment indexes for a combination of
weights to get that which is desired. For example, to get the
moments/100 for the 320 pounds in the front seat, add the
moment indexes for 100 pounds (105) to that for 220 pounds
(231). This gives the moment index of 336 for 320 pounds
in the front seat.
Use the moment limits vs. weight envelope in Figure 4-17
on Page 4-10 to determine if the weight and balance conditions will be within allowable limits for both takeoff and
landing at the destination.
Interpolate: To determine a value in
a series between two known values.
Moment limits vs. weight envelope:
An enclosed area on a graph of three
parameters. The diagonal line
representing the moment/100 crosses
the horizontal line representing the
weight at the vertical line representing the CG location in inches aft
of the datum. When the lines cross
inside the envelope, the aircraft
is loaded within its weight and
CG limits.
4– 9
Interpolation
Determine the weight and moment index of 55 gallons of fuel
55 is 50% of the way between 50 and 60. The weight and moment
index of 55 gallons is 50% of the difference between the weights and
moment indexes for 50 gallons and 60 gallons.
Weight Moment index
360 – 300 = 60. 421 – 351 = 70.
50% of 60 = 30. 50% of 70 = 35.
300 + 30 = 330. 351 + 35 = 386.
Figure 4-16. Weight and moment index for fuel.
Figure 4-14. Weight and moment index for occupants.
Figure 4-15. Weight and moment index for baggage.
4–10
Figure 4-17. Moment limits vs. weight envelope.
5– 1
Chapter 5
Center of Gravity Change
After Repair or Alteration
The largest weight changes that occur during the lifetime of
an aircraft are those caused by alterations and repairs. It is
the responsibility of the AMT doing the work to accurately
document the weight change and record it in both the
maintenance records and the POH/AFM.
Equipment List
A typical comprehensive equipment list is shown in Figure
2-22 on Page 2-13. Addition or removal of equipment
included in this list is considered by the FAA to be a minor
alteration. The weights and arms are included with the items
in the equipment list, and these minor alterations can be done
and the aircraft approved for return to service by an
appropriately rated AMT. The only documentation required
Minor alteration: An alteration
other than a major alteration. This
includes alterations that are listed in
the aircraft, aircraft engine, or
propeller specifications.
is an entry in the aircraft maintenance records and the
appropriate change to the weight and balance record in the
POH/AFM. [Figure 5-1]
Any major alteration or repair requires the work to be done
by an appropriately rated AMT or facility. The work must be
checked for conformity to FAA-approved data and signed off
by an AMT holding an Inspection Authorization, or by an
authorized agent of an appropriately rated FAA-approved
repair station. A repair station record or an FAA Form 337,
Major Repair and Alteration, must be completed which
describes the work. A dated and signed revision to
the weight and balance record is made and kept with the
maintenance records, and the airplane’s new empty weight
and empty weight arm or moment index are entered in
the POH/AFM.
Major alteration: An alteration not
listed in the aircraft, aircraft engine,
or propeller specifications —
(1) That might appreciably affect
weight, balance, structural strength,
performance, powerplant operation,
flight characteristics, or other
qualities affecting airworthiness; or
(2) That is not done according to
accepted practices or cannot be done
by elementary operations.
Figure 5-1. Typical Part 23 weight and balance record.
5– 2
Figure 5-2. A typical CAR 3 airplane weight and balance revision record.
5– 3
Weight and Balance Revision Record
Aircraft manufacturers use different formats for their weight
and balance data, but Figure 5-2 is typical of a weight and
balance revision record. All weight and balance records
should be kept with the other aircraft records. Each revision
record should be identified by the date and the aircraft make,
model, and serial number. The pages should be signed by the
person making the revision and his or her certificate type and
number must be included.
The computations for a weight and balance revision are
included on a weight and balance revision form. The date
these computations were made is shown in the upper righthand corner of Figure 5-2. When this work is superseded, a
notation must be made on the new weight and balance
revision form, including a statement that these computations
supersede the computations dated “xx/xx/xx.”
Appropriate fore and aft extreme loading conditions should
be investigated and the computations shown.
The weight and balance revision sheet should clearly show
the revised empty weight, empty weight arm and/or moment index, and the new useful load.
Weight Changes Caused by
a Repair or Alteration
A typical alteration might consist of removing two pieces of
radio equipment from the instrument panel, and a power
supply that was located in the baggage compartment behind
the rear seat. In this example, these two pieces are replaced
with a single lightweight, self-contained radio. At the same
time, an old emergency locator transmitter (ELT) is removed
from its mount near the tail, and a lighter weight unit is
installed. A passenger seat is installed in the baggage
compartment.
Computations Using Weight, Arm, and Moment
The first step in the weight and balance computation is to
make a chart like the one in Figure 5-3, listing all of the items
that are involved.
The new CG of 36.4 inches aft of the datum is determined
by dividing the new moment by the new weight.
Figure 5-3. Weight, arm, and moment changes caused by a typical alteration.
After an Alteration
When determining the new weight and CG after an alteration, take
these steps:
1. Subtract the weights and moments of all items removed.
2. Add the weights and moments of all items added.
3. Determine the new total weight and total moment.
4. Divide the total moment by the total weight and the new CG in
inches from the datum.
Useful load (GAMA): Difference
between takeoff weight, or ramp
weight if applicable, and basic
empty weight.
5– 4
Computations Using Weight and Moment Indexes
If the weight and balance data uses moment indexes rather
than arms and moments, this same alteration can be computed
using a chart like the one shown in Figure 5-4.
Subtract the weight and moment indexes of all the removed
equipment from the empty weight and moment index of the
airplane. Add the weight and moment indexes of all
equipment installed and determine the total weight and the
total moment index. To determine the position of the new CG
in inches aft of the datum, multiply the total moment index
by 100 to get the moment, and divide this by the total weight
to get the new CG.
Empty-Weight CG Range
The fuel tanks, seats, and baggage compartments of some
aircraft are so located that changes in the fuel or occupant
load have a very limited effect on the balance of the aircraft.
Aircraft of such a configuration show an EWCG range in the
TCDS. [Figure 5-5] If the EWCG is located within this range,
it is impossible to legally load the aircraft so that its loaded
CG will fall outside of its allowable range.
Figure 5-4. Weight and moment index changes caused by a typical alteration.
If the TCDS lists an empty-weight CG range, and after the
alteration is completed the EWCG falls within this range,
then there is no need to compute a fore and aft check for
adverse loading. But if the TCDS lists the EWCG range as
“none” (and most of them do), a check must be made to
determine whether or not it is possible by any combination
of legal loading to cause the aircraft CG to move outside
of either its forward or aft limits.
Adverse-Loaded CG Checks
Most modern aircraft have multiple rows of seats and often
more than one baggage compartment. After any repair or
alteration that changes the weight and balance, the AMT must
ensure that no legal condition of loading can move the CG
outside of its allowable limits. To determine this, adverseloaded CG checks must be performed and the results noted
in the weight and balance revision sheet.
Figure 5-5. Typical notation in a TCDS when an aircraft has an
empty-weight CG range.
Steps for Using Weight and Moment Indexes
When determining the new weight and CG using weight and moment
indexes, take these steps:
1. Subtract the weights and moment indexes of all items removed.
2. Add the weights and moment indexes of all items added.
3. Determine the new total weight and total moment index.
4. Divide the total moment index by the total weight and multiply this
by the reduction factor (in this case 100) to determine the new CG
in inches from the datum.
5– 5
For examples of adverse-loaded CG checks, use the information in Figure 5-6:
Figure 5-7. Loading diagram for adverse-loaded CG checks.
Figure 5-6. Weight and balance information used for adverseloaded CG checks.
Forward Adverse-Loaded CG Check
To conduct a forward CG check, make a chart that includes
the airplane and any occupants and items of the load located
in front of the forward CG limit . [Figure 5-7] Include only
those items behind the forward limit that are essential to flight.
This is the pilot and the minimum fuel.
In this example, the pilot, whose nominal weight is 170
pounds, is behind the forward CG limit. The fuel is also
behind the forward limit, so the minimum fuel is used. For
weight and balance purposes, the minimum fuel is no more
than the quantity needed for one-half-hour of operation at
rated maximum continuous power. This is considered to be
1¦12 gallon for each maximum except takeoff (METO)
horsepower. Because aviation gasoline weighs 6 pounds
per gallon, determine the number of pounds of the minimum
fuel by dividing the METO horsepower by 2; in this example,
minimum fuel is 115 pounds.
The front and rear seats and the baggage are all behind the
forward CG limit so no passengers or baggage are considered.
Make a chart like the one in Figure 5-8 to determine the CG
with the aircraft loaded for its most forward CG. With the load
consisting of only the pilot and the minimum fuel, the CG is
+36.6, which is behind the most forward allowable limit for
this weight of +33.0.
Maximum except takeoff (METO)
horsepower: The maximum power
allowed to be continuously produced
by an engine. Takeoff power is
usually limited to a given amount of
time, such as 1 minute or 5 minutes.
5– 6
Figure 5-8. Load conditions for forward adverse-loaded CG check.
Aft Adverse-Loaded CG Check
To conduct an aft, or rearward, CG check, make a chart that
includes the empty weight and EWCG of the aircraft after
the alteration, and all occupants and items of the load behind
the aft CG limit of 46.0. The pilot is in front of this limit, but
is essential for flight and must be included. In this example,
only the pilot will occupy the front seat. Since the CG of the
fuel is behind the aft limit, full fuel will be used as well as
the nominal weight for both rear seat passengers and the
maximum allowable baggage.
Under these loading conditions, the CG is located at +45.8,
which is ahead of the aft limit of +46.0. [Figure 5-9]
With only the pilot in front of the aft CG limit and the maximum of all items behind the aft limit, the CG will be at
+45.8 inches, which is ahead of the aft limit of +46.0 inches.
Figure 5-9. Load conditions for aft adverse-loaded CG check.
Adverse-loaded CG check:
A weight and balance check to
determine that no condition of legal
loading can move the CG outside of
its allowable limits.
Minimum Fuel
Minimum fuel for weight and balance purposes is no more than the
quantity needed for one-half-hour of operation at rated maximum
continuous power. This is considered to be 1¦12 gallon for each METO
horsepower. The weight of the minimum fuel is determined by dividing
the METO horsepower by 2.
Adverse-Loaded CG Checks
Adverse-loaded CG checks are made to determine that no legal
loading condition can cause the CG to fall outside of the allowable
limits. Use these loading conditions for each check:
Forward Adverse-Loaded CG Check:
• All items of load ahead of the forward CG limit.
• Only the pilot and minimum fuel if they are behind the forward CG
limit.
Aft Adverse-Loaded CG Check:
• All items of load behind the aft CG limit.
• Only the pilot and minimum fuel if they are ahead of the aft CG limit.
5– 7
Ballast
It is possible to load most modern airplanes so the center of
gravity shifts outside of the allowable limits. Placards and
loading instructions in the Weight and Balance Data inform
the pilot of the restrictions that will prevent such a shift from
occurring. A typical placard in the baggage compartment of
an airplane might read:
When the CG of an aircraft falls outside of the limits, it can
usually be brought back by using ballast.
Temporary Ballast
Temporary ballast, in the form of lead bars or heavy canvas
bags of sand or lead shot, is often carried in the baggage
compartments to adjust the balance for certain flight
conditions. The bags are marked “Ballast XX Pounds —
Removal Requires Weight and Balance Check.” Temporary
ballast must be secured so it cannot shift its location in flight,
and the structural limits of the baggage compartment must
not be exceeded. All temporary ballast must be removed
before the aircraft is weighed.
Permanent Ballast
If a repair or alteration causes the aircraft CG to fall outside
of its limits, permanent ballast can be installed. Usually,
permanent ballast is made of blocks of lead painted red and
marked “Permanent Ballast — Do Not Remove.” It should
be attached to the structure so that it does not interfere with
any control action, and attached rigidly enough that it cannot
be dislodged by any flight maneuvers or rough landing.
Ballast: A weight installed or carried
in an aircraft to move the center of
gravity to a location within its
allowable limits.
Two things must first be known to determine the amount of
ballast needed to bring the CG within limits: the amount the
CG is out of limits, and the distance between the location of
the ballast and the limit that is affected.
If an airplane with an empty weight of 1,876 pounds has
been altered so its EWCG is +32.2, and the CG range for
weights up to 2,250 pounds is +33.0 to +46.0, permanent
ballast must be installed to move the EWCG from + 32.2
to +33.0. There is a bulkhead at fuselage station 228 strong
enough to support the ballast.
To determine the amount of ballast needed, use this formula:
When rear row of seats is occupied, 120 pounds of baggage or ballast must be carried in forward baggage
compartment. For additional loading instructions, see
Weight and Balance Data.
A block of lead weighing 7.7 pounds attached to the bulkhead
at fuselage station 228, will move the EWCG back to its
proper forward limit of +33. This block should be painted red
and marked “Permanent Ballast — Do Not Remove.”
Temporary Ballast Formula
The CG of a loaded airplane can be moved into its allowable range
by shifting passengers or cargo, or by adding temporary ballast.
To determine the amount of temporary ballast needed, use this
formula:
5– 8
6– 1
Chapter 6
Weight and Balance Control—
Large Aircraft
Loading schedule: A method and
procedure used to show that an
aircraft is properly loaded and will
not exceed approved weight and
balance limitations during operation.
Takeoff weight: The weight of an
aircraft just before lift-off. It is the
ramp weight less the fuel burned
during start, taxi, and ground run.
Landing weight: The takeoff weight
of an aircraft less the fuel burned
and/or dumped en route.
Empty weight: The weight of the
airframe, engines, all permanently
installed equipment, and unusable
fuel. 14 CFR, Part 25 includes full
oil and CAR 4B requires the oil to
be drained.
Fleet weight: The average weight of
aircraft of the same model and
configuration that have the same
equipment installed.
Weight and balance control for large aircraft consists of
the following:
• Establishing and monitoring the empty weight and
EWCG of the aircraft either individually, or as part of a
fleet. This includes both the initial weighing and the
required periodic reweighing of the aircraft.
• Maintaining a loading schedule that allows the aircraft
to be loaded in such a way that the weight and balance
remain within the approved limits. Provisions are made
to track the weight and CG changes as occupants and
cargo are loaded or deplaned, and as the CG is shifted by
moving cargo from one bin to another. The cargo loading
schedule takes into consideration the floor loading limits
so the structure will not be damaged by an overweight
cargo pallet.
• Providing information to the flight crew that allows them
to fuel and load the aircraft to carry the maximum
payload without exceeding either the maximum takeoff
or landing weights.
This handbook contains information about the adjustment of
the elevator trim for takeoff based on the takeoff weight and
CG location, as well as information regarding the fuel
dumping time needed to reduce the weight of the airplane to
its allowable landing weight in an emergency situation.
Weighing Requirements
FAA-approved operating manuals describe the requirements
for weighing the aircraft. These manuals may specify that
each individual aircraft be weighed, or they may allow fleet
weight to be used if the operator has several aircraft of the
same model and configuration, with the same equipment
installed on each.
Individual Aircraft Weight
Before an aircraft is placed into service, it should be weighed
and the empty weight and CG location established. New
aircraft are normally weighed at the factory and may be placed
in service without reweighing, if the weight and balance
records have been adjusted for alterations or modifications
to the aircraft.
However, the Operation Specifications under which some
large aircraft are operated mandate that the aircraft be reweighed at specified intervals, and it is important when an
aircraft is transferred from one operator to another that the
regulations regarding reweighing be observed.
Large aircraft: An aircraft of more
than 12,500 pounds, maximum
certificated takeoff weight.
6– 2
Locating and Monitoring Weight
and CG Location
It is important that the flight crew have access to the most
current weight and balance records containing the empty
weight and the EWCG. Without this basic information, loaded
weight and balance computations cannot produce accurate
results.
Determining the Empty Weight and EWCG
When the aircraft is properly prepared for weighing ( see Page
3-2), roll it onto the scales and level it. The weights are
measured at three weighing points: the two main wheel points
and the nose wheel point.
The empty weight and EWCG are determined by using the
following steps, and the results are recorded in the weight and
balance record for use in all future weight and balance
computations.
1. Determine the moment index of each of the main-wheel
weighing points by multiplying the net weight (scale
reading less tare weight), in pounds, at these points by
the distance from the datum, in inches. Divide these
numbers by the appropriate reduction factor.
2. Determine the moment index of the nose wheel weighing
point by multiplying its net weight, in pounds, by its distance from the datum, in inches. Divide this by the
reduction factor.
3. Determine the total weight by adding the net weight of
the three weighing points and the total moment index by
adding the moment indexes of each point.
4. Divide the total moment index by the total weight, and
multiply this by the reduction factor. This gives the CG
in inches from the datum.
5. Determine the distance of the CG behind the leading edge
of the mean aerodynamic chord (LEMAC) by subtracting
the distance between the datum and LEMAC from the
distance between the datum and the CG.
Distance CG to LEMAC = Datum to CG – Datum to
LEMAC
6. Determine the EWCG in % MAC by using this formula:
Tare weight: The weight of all
chocks and other items used to
secure an aircraft on the scales for
weighing.
Net weight: The scale readings taken
when weighing an aircraft less the
weight of any chocks or other
devices used to hold the aircraft on
the scales.
Reduction factor: A number,
usually 100 or 1,000 by which a
moment is divided to produce a
smaller number that is less likely to
cause mathematical errors when
computing the center of gravity.
Moment index: The moment
(weight times arm) divided by a
reduction factor such as 100 or 1,000
to make the number smaller and
reduce the chance of mathematical
errors in computing the center
of gravity.
Fleet Weights
To establish a fleet weight for a group of aircraft of the same
model and configuration, with the same equipment installed
in each, several aircraft must be weighed and an average
operating weight determined. The number of aircraft weighed
depends upon the size of the fleet. The FAA recommends in
AC 120-27, Aircraft Weight and Balance Control, that these
numbers range from all the aircraft in a fleet of three or less
to more than six aircraft in fleets of more than nine. The
aircraft chosen to be weighed are those having the highest
time since last weighing.
Weighing to reestablish fleet weights is normally conducted
on a 3-year basis unless changes in aircraft configuration
make it necessary to reweigh and/or recalculate the CG sooner
than called for by this schedule.
Weighing Procedures
Required operating practices must be followed when
weighing large aircraft. Check the aircraft to be sure all the
required equipment items are installed and all the fluids are
properly accounted for. The aircraft must be clean, and the
weighing must be done in an enclosed building.
Large aircraft are not usually raised off the floor on jacks for
weighing. Rather, they are weighed on ramp-type scales
similar to those in Figure 3-2 on Page 3-2. The scales must
be properly calibrated, zeroed, and used in accordance with
the manufacturer’s instructions. Each scale should be
periodically checked for accuracy as recommended in the
manufacturer’s calibration schedule either by the manufacturer, or by a recognized facility such as a civil department
of weights and measures. If no manufacturer’s schedule is
available, the period between calibrations should not exceed
1 year.
For Large Aircraft
Weight and balance control consists of:
• Establishing and monitoring the empty weight and EWCG.
• Maintaining a loading schedule to keep the weight and CG
within limits.
• Providing information to the flight crew that allows them to load
the aircraft in such a way that the maximum payload may be
safely carried.
6– 3
Determine the location of the CG in inches aft of the datum
by using this formula:
Basic operating index: The
moment of the airplane at its basic
operating weight divided by the
appropriate reduction factor.
PAX: Passengers.
Figure 6-1. Loading tables.
Determining the Loaded CG of the
Airplane in Percent MAC
It is the responsibility of the flight crew to know that both
the weight of the airplane and the location of the CG are
within the allowable limits for both takeoff and landing.
The basic operating weight (BOW) and the basic operating
index are entered into a loading schedule like the one in
Figure 6-1 and the variables for the specific flight are entered
as are appropriate to determine the loaded weight and CG.
Use the data in this example:
Basic operating weight (BOW) ......................... 105,500 lbs
Basic operating index (total moment/1,000) ......... 92,837.0
MAC .......................................................................... 180.9 in
LEMAC ........................................................................ 860.5
Determine the distance from the CG to the LEMAC by
subtracting the distance between the datum and LEMAC from
the distance between the datum and the CG:
The location of the CG in percent of MAC must be known in
order to set the stabilizer trim for takeoff. Use this formula:
On Board Aircraft Weighing System
Some large transport airplanes have an on board aircraft
weighing system (OBAWS) that, when the aircraft is on the
ground, gives the flight crew a continuous indication of the
aircraft gross weight and the location of the CG in % MAC.
The system consists of strain sensing transducers in each
main wheel and nose wheel axle, a weight and balance
computer, and indicators that show the gross weight, the CG
location in % MAC, and an indicator of the ground attitude
of the aircraft.
The strain sensors measure the amount each axle deflects
and send this data into the computer, where signals from all
of the transducers and the ground attitude sensor are
integrated. The results are displayed on the indicators for the
flight crew.
Strain sensor: A device that
converts a physical phenomenon into
an electrical signal. Strain sensors in
a wheel axle sense the amount the
axle deflects and create an electrical
signal proportional to the force that
caused the deflection.
Use Figure 6-2 to determine the moment indexes for the
passengers (PAX), cargo, and fuel.
The airplane is loaded in this way:
Passengers (nominal weight 170 pounds each)
Forward compartment ............................................... 18
Aft compartment ........................................................ 95
Cargo
Forward hold ................................................... 1,500 lbs
Aft hold ........................................................... 2,500 lbs
Fuel
Tanks 1 & 3 ...........................................10,500 lbs each
Tank 2 ............................................................ 28,000 lbs
Basic operating weight (BOW):
The empty weight of the aircraft plus
the weight of the required crew, their
baggage and other standard items
such as meals and potable water.
6– 4
Figure 6-2. Loading schedule for determining weight and CG.
6– 5
Determining the Correct Stabilizer
Trim Setting
It is important before takeoff to set the stabilizer trim for the
existing CG location. There are two ways the stabilizer trim
setting systems may be calibrated: in % MAC, and in Units
ANU (Airplane Nose Up).
Stabilizer Trim Setting in % MAC
If the stabilizer trim is calibrated in units of % MAC, determine
the CG location in % MAC as has just been described, then
set the stabilizer trim on the percentage figure thus determined.
Stabilizer Trim Setting in Units ANU
(Airplane Nose Up)
Some aircraft give the stabilizer trim setting in Units ANU
(Airplane Nose Up) that correspond with the location of the
CG in % MAC. When preparing for takeoff in an aircraft
equipped with this system, first determine the CG in % MAC
in the way described above, then refer to the Stabilizer Trim
Setting Chart on the Takeoff Performance page of the AFM.
Figure 6-3 is an excerpt from such a page from the AFM of a
Boeing 737.
Consider an airplane with these specifications:
CG location ....................................................... station 635.7
LEMAC ............................................................... station 625
MAC .......................................................................... 134.0 in
First determine the distance from the CG to the LEMAC by
using this formula:
Figure 6-3. Stabilizer trim setting in ANU units.
Determining CG Changes Caused
by Modifying the Cargo
Large aircraft carry so much cargo that adding, subtracting,
or moving any of it from one hold to another can cause large
shifts in the CG.
Effects of Loading or Offloading Cargo
Both the weight and CG of an aircraft are changed when cargo
is offloaded or onloaded. This example shows the way to
determine the new weight and CG after 2,500 pounds of cargo
is offloaded from the forward cargo hold.
Consider these specifications:
Loaded weight ...................................................... 90,000 lbs
Loaded CG ........................................................ 22.5% MAC
Weight change ..................................................... –2,500 lbs
Fwd. cargo hold centroid ................................ station 352.1
MAC .......................................................................... 141.5 in
LEMAC .......................................................... station 549.13
Then determine the location of the CG in percent of MAC
by using this formula:
Refer to Figure 6-3. For all flap settings and a CG located at
8% MAC, the stabilizer setting is 73/4 Units ANU.
Centroid: The distance in inches aft
of the datum of the center of a
compartment or a fuel tank for
weight and balance purposes.
6– 6
1. Determine the CG location in inches from the datum
before the cargo is removed. Do this by first determining
the distance of the CG aft of the LEMAC:
6. Determine the location of the new CG by dividing the
total moment/1,000 by the total weight and multiplying
this by the reduction factor of 1,000.
2. Determine the distance between the CG and the datum
by adding the CG in inches aft of LEMAC to the distance
from the datum to LEMAC:
3. Determine the moment/1,000 for the original weight:
4. Determine the new weight and new CG by first
determining the moment/1,000 of the removed weight.
Multiply the amount of weight removed (–2,500 pounds)
by the centroid of the forward cargo hold (352.1 inches),
and then divide this by 1,000.
5. Subtract the removed weight and its moment/1,000 from
the original weight and moment/1,000.
7. Convert the new CG location to % MAC. First, determine
the distance between the CG location and LEMAC:
8. Then, determine new CG in % MAC:
Offloading 2,500 pounds of cargo from the forward cargo
hold moves the CG from 22.5% MAC to 27.1% MAC.
Effects of Onloading Cargo
The previous example showed the way the weight and CG
changed when cargo was offloaded. This example shows the
way both parameters change when cargo is onloaded.
The same basic airplane is used in the example, but 3,000
pounds of cargo is onloaded in the forward cargo hold.
Weight before cargo is loaded ............................. 87,500 lbs
CG before cargo is loaded ............................... 27.1% MAC
Weight change ..................................................... + 3,000 lbs
Fwd. cargo hold centroid ................................. station 352.1
MAC .......................................................................... 141.5 in
LEMAC .......................................................... station 549.13
CG Shift
When the CG moves aft, ? CG is positive; when it moves forward,
? CG is negative.
6– 7
1. Determine the CG location in inches from the datum
before the cargo is onloaded. Do this by first determining
the distance of the CG aft of the LEMAC:
2. Determine the distance between the CG and the datum
by adding the CG in inches aft of LEMAC to the distance
from the datum to LEMAC:
3. Determine the moment/1,000 for the original weight:
4. Determine the new weight and new CG by first determining the moment/1,000 of the added weight. Multiply
the amount of weight added (3,000 pounds) by the
centroid of the forward cargo hold (352.1 inches), and then
divide this by 1,000.
5. Add the onloaded cargo weight and its moment/1,000
to the original weight and moment/1,000.
6. Determine the location of the new CG by dividing the
total moment/1,000 by the total weight and multiplying
this by the reduction factor of 1,000.
7. Convert the new CG location to % MAC. First, determine
the distance between the CG location and LEMAC:
8. Then, determine new CG in % MAC:
Onloading 3,000 pounds of cargo into the forward cargo hold
moves the CG forward 5.51 inches, from 27.1% MAC to
21.59% MAC.
6– 8
Effects of Shifting Cargo from
One Hold to Another
When cargo is shifted from one cargo hold to another, the CG
changes, but the total weight of the aircraft remains the same.
As an example, use this data:
Loaded weight ...................................................... 90,000 lbs
Loaded CG .............. station 580.97 (which is 22.5% MAC)
Fwd. cargo hold centroid .................................... station 352
Aft cargo hold centroid .................................... station 724.9
MAC .......................................................................... 141.5 in
LEMAC ............................................................... station 549
To determine the change in CG, or ? CG, caused by shifting
2,500 pounds of cargo from the forward cargo hold to the aft
cargo hold, use this formula:
The new CG in % MAC caused by shifting the cargo is the
sum of the old CG plus the change in CG:
Index point: A location specified by
the aircraft manufacturer from which
arms used in weight and balance
computations are measured. Arms
measured from the index point are
called index arms.
Since the weight was shifted aft, the CG moved aft, and the
CG change is positive. If the shift were forward, the CG
change would be negative.
Before the cargo was shifted, the CG was located at station
580.97, which is 22.5% MAC. The CG moved aft 10.36
inches, so the new CG is:
Convert the location of the CG in inches aft of the datum to
percent MAC by using this formula:
Some aircraft AFMs locate the CG relative to an index point
rather than the datum or the MAC. An index point is a location
specified by the aircraft manufacturer from which arms used in
weight and balance computations are measured. Arms measured
from the index point are called index arms, and objects ahead of
the index point have negative index arms, while those behind the
index point have positive index arms.
Use the same data as in the previous example, except for
these changes:
Loaded CG ..........index arm of 0.97, which is 22.5% MAC
Index point ......................................... fuselage station 580.0
Fwd. cargo hold centroid ........................ –227.9 index arm
Aft cargo hold centroid ........................... +144.9 index arm
MAC .......................................................................... 141.5 in
LEMAC ................................................... –30.87 index arm
The weight was shifted 372.8 inches (–227.9 to +144.9 =
372.8).
The change in CG can be calculated by using this formula:
Since the weight was shifted aft, the CG moved aft, and the
CG change is positive. If the shift were forward, the CG
change would be negative.
6– 9
Then determine the total weight of the loaded pallet:
Pallet 44.0 lbs
Tiedown devices 27.0 lbs
Cargo 786.5 lbs
857.5 lbs
Determine the load imposed on the floor by the loaded pallet:
The floor must have a minimum load limit of 76 pounds per
square foot.
Before the cargo was shifted, the CG was located at 0.97
index arm, which is 22.5% MAC. The CG moved aft 10.36
inches, and the new CG is:
The pallet has an area of 36 inches (3 feet) by 48 inches (4
feet). This is equal to 12 square feet. The floor has a load
limit of 169 pounds per square foot; therefore, the total
weight of the loaded pallet can be 169° 12 = 2,028 pounds.
Subtracting the weight of the pallet and the tiedown devices
gives an allowable load of 1,948 pounds (2,028 – [47 + 33]).
Determine the floor load limit that is needed to carry a loaded
cargo pallet having these dimensions and weights:
Pallet dimensions ......................................... 48.5 by 33.5 in
Pallet weight .................................................................44 lbs
Tiedown devices ...........................................................27 lbs
Cargo weight .......................................................... 786.5 lbs
First determine the number of square feet of pallet area:
Floor Load —Caution
Loaded cargo pallets must be checked to be sure they do not impose
a load on the floor that is greater than the floor load limit.
The change in the CG in % MAC is determined by using
this formula:
The new CG in % MAC is the sum of the old CG plus the
change in CG:
Notice that the new CG is in the same location whether the distances are measured from the datum or from the index point.
Determining Cargo Pallet Loads with
Regard to Floor Loading Limits
Each cargo hold has a structural floor loading limit based on
the weight of the load and the area over which this weight is
distributed. To determine the maximum weight of a loaded
cargo pallet that can be carried in a cargo hold, divide its total
weight, which includes the weight of the empty pallet and
its tiedown devices, by its area in square feet. This load per
square foot must be equal to or less than the floor load limit.
In this example, determine the maximum load that can be
placed on this pallet without exceeding the floor load limit.
Pallet dimensions ................................................36 by 48 in
Empty pallet weight .....................................................47 lbs
Tiedown devices ...........................................................33 lbs
Floor load limit ........................169 pounds per square foot
6 – 10
Determining the Maximum Amount of
Payload That Can Be Carried
The primary function of a transport or cargo aircraft is to carry
payload. This is the portion of the useful load, passengers or
cargo, that produces revenue. To determine the maximum
amount of payload that can be carried, follow a series of steps,
considering both the maximum limits for the aircraft and the
trip limits imposed by the particular trip. In each step, the trip
limit must be less than the maximum limit. If it is not, the
maximum limit must be used.
These are the specifications for the aircraft in this example:
Basic operating weight (BOW) ......................... 100,500 lbs
Maximum zero fuel weight ............................. 138,000 lbs
Maximum landing weight .................................. 142,000 lbs
Maximum takeoff weight .................................. 184,200 lbs
Fuel tank load ....................................................... 54,000 lbs
Est. fuel burn en route .......................................... 40,000 lbs
1. Compute the maximum takeoff weight for this trip. This
is the maximum landing weight plus the trip fuel.
Max. Limit Trip Limit
142,000 Landing weight 142,000
+ trip fuel + 40,000
184,200 Takeoff weight 182,000
2. The trip limit is the lower, so it is used to determine the
zero fuel weight.
Max. Limit Trip Limit
184,200 Takeoff weight 182,000
– fuel load – 54,000
138,000 Zero fuel weight 128,000
3. The trip limit is again lower, so use it to compute the
maximum payload for this trip.
Max. Limit Trip Limit
138,000 Zero fuel weight 128,000
– BOW – 100,500
Payload (pounds) 27,500
Under these conditions 27,500 pounds of payload may
be carried.
Determining the Landing Weight
It is important to know the landing weight of the airplane
in order to set up the landing parameters, and to be certain
the airplane will be able to land at the intended destination.
In this example of a four-engine turboprop airplane, determine the airplane weight at the end of 4.0 hours of cruise
under these conditions:
Takeoff weight .................................................... 140,000 lbs
Pressure altitude during cruise ........................... 16,000 feet
Ambient temperature during cruise ........................... -32°C
Fuel burned during descent and landing ............... 1,350 lbs
Determine the weight at the end of cruise by using the Gross
Weight Table of Figure 6-4 and following these steps:
1. Use the U.S. Standard Atmosphere Table in Figure 6-5
to determine the standard temperature for 16,000. This
is -16.7°C.
2. The ambient temperature is -32°C, which is a deviation
from standard of 15.3°C. (-32° – -16.7° = 15.3°). It is
below standard.
3. In Figure 6-4, follow the vertical line representing 140,000
pounds gross weight upward until it intersects the diagonal
line for 16,000 feet pressure altitude.
4. From this intersection, draw a horizontal line to the left
to the temperature deviation index (0°C deviation).
5. Draw a diagonal line parallel to the dashed lines for
“Below Standard” from the intersection of the horizontal
line and the Temperature Deviation Index.
6. Draw a vertical line upward from the 15.3°C Temperature
Deviation From Standard.
7. Draw a horizontal line to the left from the intersection of
the “Below Standard” diagonal and the 15.3°C
temperature deviation vertical line. This line crosses the
“Fuel Flow—100 Pounds per Hour per Engine” index at
11.35. This indicates that each of the four engines burns
1,135 (100? 11.35) pounds of fuel per hour. The total fuel
burn for the 4-hour cruise is:
8. The airplane gross weight was 140,000 pounds at takeoff,
and since 18,160 pounds of fuel was burned during cruise
and 1,350 pounds was burned during the approach and
landing phase, the landing weight is:
140,000 – (18,160 + 1,350) = 120,490 pounds
Maximum zero fuel weight: The
maximum authorized weight of an
aircraft without fuel. This is the sum
of the BOW and payload.
Payload: The weight of the
passengers, baggage, and cargo that
produces revenue.
6 – 11
Figure 6-4. Gross weight table.
6 – 12
Figure 6-5. Standard atmosphere table.
Determining the Minutes
of Fuel Dump Time
Most large aircraft are approved for a greater weight for
takeoff than for landing, and to make it possible for them to
return to landing soon after takeoff, a fuel jettison system
is sometimes installed.
It is important in an emergency situation that the flight crew
be able to dump enough fuel to lower the weight to its allowed
landing weight. This is done by timing the dumping process.
In this example, the aircraft has three engines operating and
these specifications apply:
Cruise weight ...................................................... 171,000 lbs
Maximum landing weight .................................. 142,500 lbs
Time from start of dump to landing ................... 19 minutes
Average fuel flow
during dumping and descent ................ 3,170 lb/hr/eng
Fuel dump rate .............................. 2,300 pounds per minute
Follow these steps to determine the number of minutes of
fuel dump time:
1. Determine the amount the weight of the aircraft must be
reduced to reach the maximum allowable landing weight:
171,000 lbs cruise weight
– 142,500 lbs maximum landing weight
28,500 lbs required reduction
2. Determine the amount of fuel burned from the beginning
of the dump to touchdown:
Fuel jettison system: A fuel subsystem that allows the dumping of
fuel in an emergency to lower the
weight of an aircraft to the maximum
landing weight. This system must
allow enough fuel to be jettisoned that
the aircraft can still meet the climb
requirements in 14 CFR Part 25.
For all three engines, this is 52.83° 3 = 158.5 lbs/min.
The three engines will burn 158.5° 19 = 3,011.5 pounds
of fuel between the beginning of dumping and touchdown.
6 – 13
3. Determine the amount of fuel needed to dump by
subtracting the amount of fuel burned during the dumping
from the required weight reduction:
28,500.0 lbs required weight reduction
– 3,011.5 lbs fuel burned after start of dumping
25,488.5 lbs fuel to be dumped
4. Determine the time needed to dump this amount of fuel
by dividing the number of pounds of fuel to dump by the
dump rate:
Weight and Balance of Commuter
Category Airplanes
The Beech 1900 is a typical commuter category airplane that
can be configured to carry passengers or cargo. Figure 6-6
shows the loading data of this type of airplane in the passenger
configuration, and Figure 6-14 on Page 6-18 shows the cargo
configuration.
Determining the Loaded Weight and CG
As this airplane is prepared for flight, a manifest like the
one in Figure 6-7 is prepared.
1. The crew weight and the weight of each passenger is
entered into the manifest, and the moment/100 for each
occupant is determined by multiplying the weight by the
arm and dividing by 100. This data is available in the AFM
and is shown in the Weight and Moments— Occupants
table in Figure 6-8 on Page 6-14.
2. The weight of the baggage in each compartment that is
used is entered with its moment/100. This is determined
in the Weights and Moments— Baggage table in Figure
6-9 on Page 6-14.
3. Determine the weight of the fuel. Jet A fuel has a nominal
specific gravity at +15°C of 0.812 and weighs 6.8 pounds
per gallon, but at +25°C, according to the chart in Figure
6-10 on Page 6-15, it weighs 6.75 lbs/gal.
Using Figure 6-11 on Page 6-16, determine the weights
and moment/100 for 390 gallons of Jet A fuel by
interpolating between those for 6.7 lbs/gal and 6.8 lbs/gal.
The 390 gallons of fuel at this temperature weighs 2,633
pounds, and its moment index is 7,866 lb-in/100.
Figure 6-6. Loading data for passenger configuration.
Jet Fuel Weight Affected by Temperature
The colder the fuel, the more dense and therefore the more pounds
of fuel per gallon.
(Continued on Page 6-17)
6 – 14
Figure 6-7. Determining the loaded weight and CG of a Beech 1900 in the passenger configuration.
Figure 6-8. Weights and moments —occupants.
Figure 6-9. Weights and moments—baggage.
6 – 15
Figure 6-10. Density variation of aviation fuel.
6 – 16
Figure 6-11. Weights and moments —usable fuel.
Figure 6-12. Weight and balance diagram.
6 – 17
This type of problem is usually solved by using these two
formulas (below). The total amount of weight shifted is 550
pounds (300 + 250) and both rows of passengers have moved
aft by 210 inches (410 – 200 and 440 – 230).
4. Add all of the weights and all of the moment indexes.
Divide the total moment index by the total weight, and
multiply this by the reduction factor of 100. The total
weight is 14,729 pounds, the total moment index is 43,139
lb-in/100. The CG is located at fuselage station 292.9.
5. Check to determine that the CG is within limits for this
weight. Refer to the Weight and Balance Diagram in
Figure 6-12 on Page 6-16. Draw a horizontal line across
the envelope at 14,729 pounds of weight and a vertical
line from the CG of 292.9 inches aft of datum. These lines
cross inside the envelope verifying the CG is within limits
for this weight.
Determining the Changes in CG When
Passengers are Shifted
Consider the airplane above for which the loaded weight and
CG have just been determined, and determine the change in
CG when the passengers in rows 1 and 2 are moved to rows
8 and 9. Figure 6-13 shows the changes from the conditions
shown in Figure 6-7. There is no weight change, but the
moment index has been increased by 1,155 pound-inches/100
to 44,294. The new CG is at fuselage station 300.7.
The CG has been shifted aft 7.8 inches and the new CG is
at station 300.7.
Figure 6-13. Change in CG caused by shifting passenger seats.
6 – 18
Figure 6-14. Loading data for cargo configuration.
Determining Changes in Weight and CG When
the Airplane is Operated in its Cargo
Configuration
Consider the airplane configuration shown in Figure 6-14.
The airplane is loaded as recorded in the table in Figure
6-15. The basic operating weight (BOW) includes the pilots
and their baggage so there is no separate item for them.
The arm of each cargo section is the centroid of that section,
as is shown in Figure 6-14.
The fuel, at the standard temperature of 15°C weighs 6.8
pounds per gallon. Refer to the Weights and Moments—
Usable Fuel in Figure 6-11 on Page 6-16 to determine the
weight and moment index of 370 gallons of Jet A fuel.
The CG under these loading conditions is located at station 296.2.
Determining the CG Shift When Cargo is Moved
From One Section to Another
When cargo is shifted from one section to another, use this
formula:
Figure 6-15. Flight manifest of a Beech 1900 in the cargo configuration.
If the cargo is moved forward, the ? CG is subtracted from
the original CG. If it is shifted aft, add the ? CG to the
original.
6 – 19
Determining the CG Shift When Cargo
is Added or Removed
When cargo is added or removed, add or subtract the weight
and moment index of the affected cargo to the original
loading chart. Determine the new CG by dividing the new
moment index by the new total weight, and multiply this by
the reduction factor.
Determining Which Limits are Exceeded
When preparing an aircraft for flight, you must consider all
parameters and check to determine that no limit has been
exceeded.
Consider the parameters below, and determine which limit,
if any, has been exceeded.
• The airplane in this example has a basic empty weight of
9,005 pounds and a moment index of 25,934 poundinches/100.
• The crew weight is 340 pounds, and its moment/100
is 439.
• The passengers and baggage have a weight of 3,950
pounds and a moment/100 of 13,221.
• The fuel is computed at 6.8 lbs/gal:
The ramp load is 340 gallons, or 2,312 pounds.
Fuel used for start and taxi is 20 gallons, or 136 pounds.
Fuel remaining at landing is 100 gallons, or 680 pounds.
• Maximum takeoff weight is 16,600 pounds.
• Maximum zero fuel weight is 14,000 pounds.
• Maximum landing weight is 16,000 pounds.
Take these steps to determine which limit, if any, is exceeded:
1. Determine the zero fuel weight, which is the weight of the
aircraft with all of the useful load except the fuel on board.
The zero fuel weight of 13,295 pounds is less than the
maximum of 14,000 pounds, so this parameter is
acceptable.
2. Determine the takeoff weight and CG. The takeoff weight
is the zero fuel weight plus the ramp load of fuel, less
the fuel used for start and taxi. The takeoff CG is the
(moment/100 ÷ weight)°?100.
The takeoff weight of 15,471 pounds is below the
maximum takeoff weight of 16,600 pounds, and a check
of Figure 6-12 on Page 6-16 shows that the CG at station
298.0 is also within limits.
3. Determine the landing weight and CG. This is the zero
fuel weight plus the weight of fuel at landing.
The landing weight of 13,975 pounds is less than the
maximum landing weight, of 14,000 pounds. According
to Figure 6-12, the landing CG at station 297.5 is also
within limits.
6 – 20
7– 1
Chapter 7
Weight and Balance Control—
Helicopters
Weight and balance considerations of a helicopter are similar
to those of an airplane, except they are far more critical, and
the CG range is much more limited. [Figure 7-1] The engineers who design a helicopter determine the amount of
cyclic control power that is available, and establish both the
longitudinal and lateral CG envelopes that allow the pilot to
load the helicopter so there is sufficient cyclic control for all
flight conditions.
If the CG is ahead of the forward limit, the helicopter will
tilt, and the rotor disk will have a forward pull. To counteract
this, rearward cyclic is required. If the CG is too far forward,
there may not be enough cyclic authority to allow the
helicopter to flare for a landing, and it will consequently
require an excessive landing distance.
If the CG is aft of the allowable limits, the helicopter will fly
with a tail-low attitude and may need more forward cyclic
stick displacement than is available to maintain a hover in a
no-wind condition. There might not be enough cyclic power
to prevent the tail boom striking the ground. If gusty winds
should cause the helicopter to pitch up during high speed
flight, there might not be enough forward cyclic control to
lower the nose.
Helicopters are approved for a specific maximum gross
weight, but it is not safe to operate them at this weight under
all conditions. High density altitude decreases the safe
maximum weight as it affects the hovering, takeoff, climb,
autorotation, and landing performance.
The fuel tanks on some helicopters are behind the CG,
causing it to shift forward as fuel is used. Under some flight
conditions, the balance may shift enough that there will not
be sufficient cyclic authority to flare for landing. For these
helicopters, the loaded CG should be computed for both
takeoff and landing weights.
Figure 7-1. Typical helicopter datum, flight stations, and butt
line locations.
7– 2
Lateral balance of an airplane is usually of little concern and
is not normally calculated. But some helicopters, especially
those equipped for hoist operations, are sensitive to the lateral
position of the CG, and their POHs include both longitudinal
and lateral CG envelopes as well as information on the
maximum permissible hoist load. Figure 7-2 is an example
of such CG envelopes.
Determining the Loaded
CG of a Helicopter
The empty weight and empty-weight center of gravity of a
helicopter are determined in the same way as for an airplane.
The weights recorded on the scales supporting the helicopter
are added and their distance from the datum are used to
compute the moments at each weighing point. The total
moment is divided by the total weight to determine the
location of the CG in inches from the datum. The datum of
some helicopters is located at the center of the rotor mast,
but since this causes some arms to be positive (behind the
datum) and others negative (ahead of the datum), most
modern helicopters have the datum located ahead of the
aircraft as do most airplanes. When the datum is ahead of the
aircraft, all arms are positive.
The lateral CG is determined in the same way as the
longitudinal CG, except the distances between the scales and
butt line zero (BL 0) are used as the arms. Arms to the right
of BL 0 are positive and those to the left are negative.
Butt (or buttock) line zero: A line
through the symmetrical center of an
aircraft from nose to tail. It serves as
the datum for measuring the arms
used to find the lateral CG. Lateral
moments that cause the aircraft to
rotate clockwise are positive (+), and
those that cause it to rotate counterclockwise are negative (–).
Figure 7-2. Typical helicopter CG envelopes.
Figure 7-3. Determining the longitudinal CG and the lateral offset moment.
Maximum permissible hoist load:
The maximum external load that is
permitted for a helicopter to carry.
This load is specified in the POH.
7– 3
Determine whether or not a helicopter with these specifica-tions
is within both longitudinal and lateral weight and balance limits
by constructing a chart like the one in Figure 7-3:
Empty weight ......................................................... 1,545 lbs
Empty-weight CG ....................... 101.4 in. aft of the datum
Lateral balance arm .............................. 0.2 in. right of BL 0
Maximum allowable gross weight ........................ 2,250 lbs
Pilot ........................................170 lbs @ 64 in. aft of datum
and 13.5 in. left of BL 0
Passenger ...............................200 lbs @ 64 in. aft of datum
and 13.5 in. right of BL 0
Fuel 48 gal .............................288 lbs @ 96 in. aft of datum
and 8.4 in. left of BL 0
Check the helicopter CG envelopes in Figure 7-2 to determine
whether or not the CG is within limits both longitudinally
and laterally.
In the longitudinal CG envelope, draw a line vertically upward
from the CG of 94.4 inches aft of datum and a horizontal line
from the weight of 2,203 pounds gross weight. These lines
cross within the approved area.
Lateral offset moment: The
moment, in lb-in, of a force that
tends to rotate a helicopter about its
longitudinal axis. The lateral offset
moment is the product of the weight
of the object and its distance from
butt line zero. Lateral offset
moments that tend to rotate the
aircraft clockwise are positive, and
those that tend to rotate it
counterclockwise are negative.
Figure 7-4. Determining the longitudinal CG and the lateral offset moment for the second leg of the flight.
Figure 7-5. Determining the longitudinal CG and the lateral offset moment for the second leg of the flight with the pilot flying
from the right seat.
In the lateral offset moment envelope, draw a line vertically
upward from left, or –1,705 lb-in, and a line horizontally
from 2,203 pounds on the gross weight index. These lines
cross within the envelope, showing the lateral balance is also
within limits.
Effects of Offloading Passengers and Using Fuel
Consider the helicopter in Figure 7-3. The first leg of the flight
consumes 22 gallons of fuel, and at the end of this leg, the
passenger deplanes. Is the helicopter still within allowable
CG limits for takeoff?
To find out, make a new chart like the one in Figure 7-4 to
show the new loading conditions of the helicopter at the
beginning of the second leg of the flight.
Under these conditions, according to the helicopter CG
envelopes in Figure 7-2, the longitudinal CG is within limits.
However, the lateral offset moment is excessive since both
the pilot and the fuel are on the left side of the aircraft. If the
POH allows it, the pilot may fly the aircraft on its second leg
from the right-hand seat. According to Figures 7-5 and 7-2,
this will bring the lateral balance into limits.
7– 4
8– 1
Chapter 8
Use of Computers for Weight
and Balance Computations
Almost all weight and balance problems involve only simple
math. This allows slide rules and hand-held electronic
calculators to relieve us of much of the tedium involved with
these problems. This chapter gives a comparison of the
methods of determining the CG of an airplane while it is being
weighed. First, determine the CG using a simple electronic
calculator, then solve the same problem using an E6-B flight
computer. Then, finally, solve it using a dedicated electronic
flight computer.
Later in this chapter are examples of typical weight and
balance problems (solved with an electronic calculator) of the
kind that pilots and AMTs will encounter throughout their
aviation endeavors.
Using an Electronic Calculator to Solve
Weight and Balance Problems
Determining the CG of an airplane in inches from the mainwheel weighing points can be done with any simple electronic
calculator that has addition (+), subtraction (–),
multiplication (?), and division (÷) functions. Scientific
calculators with such additional functions as memory (M),
parentheses (( )), plus or minus (+/–), exponential (yx ),
reciprocal (1/?), and percentage (%) functions allow you to
solve more complex problems or to solve simple problems
using fewer steps.
The chart in Figure 8-1 includes data on the airplane used in
this example problem.
Figure 8-1. Weight and balance data of a typical nose
wheel airplane.
Positive/Negative Key
The (+/–) key changes the number just keyed in from a positive to a
negative number.
According to Figure 8-1, the weight of the nose wheel (F) is
340 pounds, the distance between main wheels and nose
wheel (L) is –78 inches, and the total weight (W) of the
airplane is 2,006 pounds. (L is negative because the nose
wheel is ahead of the main wheels.)
To determine the CG, use this formula:
Key the data into the calculator as shown in red, and when
the equal (=) key is pressed, the answer (shown here in blue)
will appear.
(340)(?)(78)(+/–)(÷)(2006)(=) –13.2
The arm of the nose wheel is negative, so the CG is –13.2, or
13.2 inches ahead of the main-wheel weighing points.
Using an E6-B Flight Computer to Solve
Weight and Balance Problems
The E6-B uses a special kind of slide rule. Instead of its scales
going from 1 to 10, as on a normal slide rule, both scales go
from 10 to 100. The E6-B cannot be used for addition or
subtraction, but it is useful for making calculations involving
multiplication and division. Its accuracy is limited, but it is
sufficiently accurate for most weight and balance problems.
8 –2
The same problem that was just solved with the electronic
calculator can be solved on an E6-B by following these steps:
Then, divide 26,500 by 2,006: [Figure 8-2b]
• On the inner scale, place 20, which represents 2,006,
opposite 26.5 on the outer scale. (26.5 represents 26,500)
(Step 3).
• Opposite the index, 10, on the inner scale, read 13.2 on
the outer scale (Step 4).
• Determine the value of 13.2 by estimating: 20,000 ÷ 2000
= 10, so 26,500 ÷ 2,006 = 13.2.
• The arm (–78) is negative, so the CG is also negative.
The CG is –13.2 inches, or 13.2 inches ahead of the datum.
Figure 8-2a. E6-B computer set up to multiply 340 by 78. Figure 8-2b. E6-B computer set up to divide 26,500 by 2,006.
First, multiply 340 by 78 (disregard the – sign): [Figure 8-2a]
• Place 10 on the inner scale (this is the index) opposite 34
on the outer scale (this represents 340) (Step 1).
• Opposite 78 on the inner scale, read 26.5 on the outer scale
(Step 2).
• Determine the value of these digits by estimating:
300 ? 80 = 24,000, so 340 ? 78 = 26,500.
8– 3
Using a Dedicated Electronic
Flight Computer to Solve Weight
and Balance Problems
Dedicated electronic flight computers like the one in Figure
8-3 are programmed to solve many flight problems, such as
wind correction, heading and ground speed, endurance, and
true airspeed (TAS), as well as weight and balance problems.
Typical Weight and Balance Problems
A hand-held electronic calculator like the one in Figure
8-4 is a valuable tool for solving weight and balance problems. It can be used for a variety of problems and has a high
degree of accuracy. The examples given here are solved with
a calculator using only the (? ), (÷), (+), (–), and (+/–)
functions. If other functions are available on your calculator,
some of the steps may be simplified.
Figure 8-3. Dedicated electronic flight computers are
programmed to solve weight and balance problems as well as
flight problems.
The problem just solved with an electronic calculator and
an E6-B can also be solved with a dedicated flight computer
using the information in Figure 8-1.
Each flight computer handles the problems in slightly
different ways, but all are programmed with prompts that
solicit you to input the required data so you do not need to
memorize any formulas. Weights and arms are input as
called for, and a running total of the weight, moment, and
CG are displayed.
Figure 8-4. A typical electronic calculator is useful for solving
most types of weight and balance problems.
Determining CG in Inches From the Datum
This type of problem is solved by first determining the
location of the CG in inches from the main-wheel weighing
points, then measuring this location in inches from the datum.
There are four types of problems involving the location of
the CG relative to the datum.
8 –4
Nose Wheel Airplane with Datum
Ahead of the Main Wheels
The datum (D) is 128 inches ahead of the main-wheel
weighing points, the weight of the nose wheel (F) is 340
pounds, and the distance between main wheels and nose
wheel (L) is 78 inches. The total weight (W) of the airplane
is 2,006 pounds. Refer to Figure 3-5 on Page 3-5.
Use this formula:
Tail Wheel Airplane with Datum
Ahead of the Main Wheels
The datum (D) is 7.5 inches ahead of the main-wheel
weighing points, the weight of the tail wheel (R) is 67 pounds,
and the distance between main wheels and tail wheel (L) is
222 inches. The total weight (W) of the airplane is 1,218
pounds. Refer to Figure 3-7 on Page 3-6.
Use this formula:
1. Determine the CG in inches from the main wheels:
(340)(?)(78)(÷)(2006)(=) 13.2
2. Determine the CG in inches from the datum:
(128)(–)(13.2)(=) 114.8
The CG is 114.8 inches behind the datum.
Nose Wheel Airplane with Datum
Behind the Main Wheels
The datum (D) is 75 inches behind the main-wheel weighing
points, the weight of the nose wheel (F) is 340 pounds, and
the distance between main wheels and nose wheel (L) is 78
inches. The total weight (W) of the airplane is 2,006 pounds.
Refer to Figure 3-6 on Page 3-6.
Use this formula:
1. Determine the CG in inches from the main wheels:
(340)(?)(78)(÷)(2006)(=) 13.2
2. Determine the CG in inches from the datum:
(75)(+)(13.2)(=) 88.2
The minus sign before the parenthesis in the formula means
the answer is negative. The CG is 88.2 inches ahead of the
datum (–88.2).
1. Determine the CG in inches from the main wheels:
(67)(?)(222)(÷)(1218)(=) 12.2
2. Determine the CG in inches from the datum:
(7.5)(+)(12.2)(=) 19.7
The CG is 19.7 inches behind the datum.
Tail Wheel Airplane with Datum
Behind the Main Wheels
The datum (D) is 80 inches behind the main-wheel weighing
points, the weight of the tail wheel (R) is 67 pounds, and the
distance between main wheels and tail wheel (L) is 222
inches. The total weight (W) of the airplane is 1,218 pounds.
Refer to Figure 3-8 on Page 3-7.
Use this formula:
1. Determine the CG in inches from the main wheels:
(67)(?)(222)(÷)(1218)(=) 12.2
2. Determine the CG in inches from the datum:
(80)(+/–)(+)(12.2)(=) –67.8
The CG is 67.8 inches ahead of the datum.
8– 5
Determining CG, Given Weights and Arms
Some weight and balance problems involve weights and
arms to determine the moments. Divide the total moment
by the total weight to determine the CG. Figure 8-5 contains
the specifications for determining the CG using weights and
arms.
Determine the CG by using the data in Figure 8-5 and
following these steps:
1. Determine the total weight and record this number:
(830)(+)(836)(+)(340)(=) 2006
2. Determine the moment of each weighing point and record
them:
(830)(?)(128)(=) 106240
(836)(?)(128)(=) 107008
(340)(?)(50)(=) 17000
3. Determine the total moment and divide this by the
total weight:
(106240)(+)(107008)(+)(17000)(=)(÷)(2006)(=) 114.8
This airplane weighs 2,006 pounds and its CG is 114.8 inches
from the datum.
Determining CG, Given Weights
and Moment Indexes
Other weight and balance problems involve weights and
moment indexes, such as moment/100, or moment/1,000. To
determine the CG, add all the weights and all the moment
indexes. Then divide the total moment index by the total
weight and multiply the answer by the reduction factor. Figure
8-6 contains the specifications for determining the CG using
weights and moment indexes.
Determine the CG by using the data in Figure 8-6 and
following these steps:
1. Determine the total weight and record this number:
(830)(+)(836)(+)(340)(=) 2006
2. Determine the total moment index, divide this by the total
weight, and multiply it by the reduction factor of 100:
(1,062.4)(+)(1,070.1)(+)(170)(=)(2302.5)(÷)(2006)(=)
(1.148)(?)(100)(=) 114.8
This airplane weighs 2,006 pounds and its CG is 114.8 inches
from the datum.
Figure 8-5. Specifications for determining the CG of an airplane using weights and arms.
Figure 8-6. Specifications for determining the CG of an
airplane using weights and moment indexes.
8 –6
Determining CG in Percent of
Mean Aerodynamic Chord
• The loaded CG is 42.47 inches aft of the datum.
• MAC is 61.6 inches long.
• LEMAC is at station 20.1.
1. Determine the distance between the CG and LEMAC:
(42.47)(–)(20.1)(=) 22.37
2. Then, use this formula:
2. Multiply the lateral arm (the distance between butt line
zero and the CG of each item) by its weight to get the
lateral offset moment of each item. Moments to the right
of BL 0 are positive and those to the left are negative.
(1545)(?)(.2)(=) 309
(170)(?)(13.5)(+/–)(=) –2295
(200)(?)(13.5)(=) 2700
(288)(?)(8.4)(+/–)(=) –2419
3. Determine the algebraic sum of the lateral offset moments.
(309)(+)(2295)(+/–)(+)(2700)(+)(2419)(+/–)(=) –1705
4. Divide the sum of the moments by the total weight to
determine the lateral CG.
(1705)(+/–)(÷)(2203)(=) – 0.77
The lateral CG is 0.77 inch to the left of butt line zero.
Determining ? CG Caused by Shifting Weights
Fifty pounds of baggage is shifted from the aft baggage
compartment at station 246 to the forward compartment at
station 118. The total airplane weight is 4,709 pounds. How
much does the CG shift?
1. Determine the number of inches the baggage is shifted:
(246)(–)(118)(=) 128
2. Use this formula:
Figure 8-7. Specifications for determining the lateral CG of a helicopter.
(22.37)(?)(100)(÷)(61.6)(=) 36.3
The CG of this airplane is located at 36.3% of the mean
aerodynamic chord.
Determining Lateral CG of a Helicopter
It is often necessary when working weight and balance of
a helicopter to determine not only the longitudinal CG, but
the lateral CG as well. Lateral CG is measured from butt
line zero (BL 0). All items and moments to the left of BL 0
are negative, and those to the right of BL 0 are positive.
Figure 8-7 contains the specifications for determining the
lateral CG of a typical helicopter.
Determine the lateral CG by using the data in Figure 8-7 and
following these steps:
1. Add all of the weights:
(1545)(+)(170)(+)(200)(+)(288)(=) 2203
(50)(?)(128)(÷)(4709)(=) 1.36
The CG is shifted forward 1.36 inches.
8– 7
Determining Weight Shifted to
Cause Specified ? CG
How much weight must be shifted from the aft baggage
compartment at station 246 to the forward compartment at
station 118, to move the CG forward 2 inches? The total
weight of the airplane is 4,709 pounds.
1. Determine the number of inches the baggage is shifted:
Determining Total Weight of an
Aircraft That Will Have a Specified
? CG When Cargo is Moved
What is the total weight of an airplane if moving 500 pounds
of cargo 96 inches forward shifts the CG 2.0 inches?
Use this formula:
(500)(???????÷)(2)(=) 24000
Moving 500 pounds of cargo 96 inches forward will cause a
2.0-inch shift in CG of a 24,000-pound airplane.
Determining Amount of Ballast Needed
to Move CG to a Desired Location
How much ballast must be mounted at station 228 to move
the CG to its forward limit of +33? The airplane weighs
1,876 pounds and the CG is at +32.2, a distance of 0.8 inch
out of limit.
Use this formula:
(246)(–)(118)(=) 128
2. Use this formula:
(2)(?)(4709)(÷)(128)(=) 73.6
Moving 73.6 pounds of baggage from the aft compartment to
the forward compartment will shift the CG forward 2 inches.
Determining Distance Weight is Shifted
to Move CG a Specific Distance
How many inches aft will a 56-pound battery have to be
moved to shift the CG aft by 1.5 inches? The total weight of
the airplane is 4,026 pounds.
Use this formula:
(1.5)(?????????÷)(56)(=) 107.8
Moving the battery aft by 107.8 inches will shift the CG aft
1.5 inches.
(1876)(?)(.8)(÷)(195)(=) 7.7
Attaching 7.7 pounds of ballast to the bulkhead at station 228
will move the CG to +33.0.
8 –8
Glossary– 1
Glossary
14 CFR, Part 121. The Federal regulations governing
domestic, flag, and supplemental operations.
14 CFR, Part 135. The Federal regulations governing
Commuter and On-Demand Operations.
adverse loaded CG check. A weight and balance check to
determine that no condition of legal loading of an aircraft can
move the CG outside of its allowable limits.
Aircraft Specifications. Documentation containing the
pertinent specifications for aircraft certificated under the
CARs.
Airplane Flight Manual (AFM). An FAA-approved
document, prepared by the holder of a Type Certificate for
an airplane or rotorcraft, that specifies the operating
limitations and contains the required markings and placards
and other information applicable to the regulations under
which the aircraft was certificated.
Approved Type Certificate. A certificate of approval issued
by the FAA for the design of an airplane, engine, or propeller.
arm (GAMA). The horizontal distance from the reference
datum to the center of gravity (CG) of an item.
balanced laterally. Balanced in such a way that the wings
tend to remain level.
ballast. A weight installed or carried in an aircraft to move
the center of gravity to a location within its allowable limits.
permanent ballast (fixed ballast). A weight
permanently installed in an aircraft to bring its center of
gravity into allowable limits. Permanent ballast is part of the
aircraft empty weight.
temporary ballast. Weights that can be carried in a cargo
compartment of an aircraft to move the location of the CG
for a specific flight condition. Temporary ballast must be
removed when the aircraft is weighed.
basic empty weight (GAMA). Standard empty weight plus
optional equipment.
basic operating index. The moment of the airplane at its
basic operating weight divided by the appropriate reduction
factor.
basic operating weight (BOW). The empty weight of the
aircraft plus the weight of the required crew, their baggage
and other standard items such as meals and potable water.
bilge area. The lowest part of an aircraft structure in which
water and contaminants collect.
butt (or buttock) line zero. A line through the symmetrical
center of an aircraft from nose to tail. It serves as the datum
for measuring the arms used to determine the lateral CG.
Lateral moments that cause the aircraft to rotate clockwise
are positive (+), and those that cause it to rotate
counterclockwise are negative (–).
calendar month. A time period used by the FAA for
certification and currency purposes. A calendar month
extends from a given day until midnight of the last day of that
month.
center of gravity (CG) (GAMA). The point at which an
airplane would balance if suspended. Its distance from the
reference datum is determined by dividing the total moment
by the total weight of the airplane.
center of lift. The location along the chord line of an airfoil
at which all the lift forces produced by the airfoil are
considered to be concentrated.
centroid. The distance in inches aft of the datum of the center
of a compartment or a fuel tank for weight and balance
purposes.
CG arm (GAMA) . The arm obtained by adding the
airplane’s individual moments and dividing the sum by the
total weight.
General Aviation Manufacturers Association (GAMA)
Glossary– 2
CG limits (GAMA). The extreme center of gravity locations
within which the airplane must be operated at a given weight.
CG limits envelope. An enclosed area on a graph of the
airplane loaded weight and the CG location. If lines drawn
from the weight and CG cross within this envelope, the
airplane is properly loaded.
CG moment envelope. An enclosed area on a graph of the
airplane loaded weight and loaded moment. If lines drawn
from the weight and loaded moment cross within this
envelope, the airplane is properly loaded.
chord. A straight-line distance across a wing from leading
edge to trailing edge.
delta (? ). This symbol, Ð, means a change in something.
ÐCG means a change in the center of gravity location.
dynamic load. The actual weight of the aircraft multiplied
by the load factor, or the increase in weight caused by
acceleration.
empty weight. The weight of the airframe, engines, all
permanently installed equipment and unusable fuel.
Depending upon the part of the Federal regulations under
which the aircraft was certificated, either the undrainable oil
or full reservoir of oil is included.
empty-weight center of gravity (EWCG). The center of
gravity of an aircraft when it contains only the items specified
in the aircraft empty weight.
empty-weight center of gravity range. The distance between
the allowable forward and aft empty-weight CG limits.
equipment list. A list of items approved by the FAA for
installation in a particular aircraft. The list includes the name,
part number, weight, and arm of the component. Installation
or removal of an item in the equipment list is considered to
be a minor alteration.
fleet weight. An average weight accepted by the FAA for
aircraft of identical make and model that have the same
equipment installed. When a fleet weight control program is
in effect, the fleet weight of the aircraft can be used rather
than every individual aircraft having to be weighed.
fuel jettison system. A fuel subsystem that allows the flight
crew to dump fuel in an emergency to lower the weight of an
aircraft to the maximum landing weight if a return to landing
is required before sufficient fuel is burned off. This system must
allow enough fuel to be jettisoned that the aircraft can still
meet the climb requirements specified in 14 CFR, Part 25.
fulcrum. The point about which a lever balances.
index point. A location specified by the aircraft manufacturer
from which arms used in weight and balance computations
are measured. Arms measured from the index point are called
index arms.
interpolate. To determine a value in a series between two
known values.
landing weight. The takeoff weight of an aircraft less the fuel
burned and/or dumped en route.
large aircraft (14 CFR, Part 1). An aircraft of more than
12,500 pounds, maximum certificated takeoff weight.
lateral balance. Balance around the roll, or longitudinal, axis.
lateral offset moment. The moment, in lb-in, of a force that
tends to rotate a helicopter about its longitudinal axis. The
lateral offset moment is the product of the weight of the object
and its distance from butt line zero. Lateral offset moments
that tend to rotate the aircraft clockwise are positive, and those
that tend to rotate it counterclockwise are negative.
LEMAC. Leading Edge of the Mean Aerodynamic Chord.
load cell. A component in an electronic weighing system that
is placed between the jack and the jack pad on the aircraft.
The load cell contains strain gauges whose resistance changes
with the weight on the cell.
load factor. The ratio of the maximum load an aircraft can
sustain to the total weight of the aircraft. Normal category
aircraft must have a load factor of at least 3.8, utility category
aircraft 4.4, and acrobatic category aircraft, 6.0.
loading graph. A graph of load weight and load moment
indexes. Diagonal lines for each item relate the weight to the
moment index without having to use mathematics.
loading schedule. A method and procedure used to show that
an aircraft is properly loaded and will not exceed approved
weight and balance limitations during operation.
Glossary– 3
longitudinal axis. An imaginary line through an aircraft
from nose to tail, passing through its center of gravity.
longitudinal balance. Balance around the pitch, or lateral,
axis.
MAC. Mean Aerodynamic Chord.
major alteration. An alteration not listed in the aircraft,
aircraft engine, or propeller specifications, (1) that might
appreciably affect weight, balance, structural strength,
performance, powerplant operation, flight characteristics, or
other qualities affecting airworthiness; or (2) that is not done
according to accepted practices or cannot be done by
elementary operations.
maximum landing weight (GAMA). Maximum weight
approved for the landing touchdown.
maximum permissible hoist load. The maximum external
load that is permitted for a helicopter to carry. This load is
specified in the POH.
maximum ramp weight (GAMA) . Maximum weight
approved for ground maneuver. It includes weight of start,
taxi, and runup fuel.
maximum takeoff weight (GAMA). Maximum weight
approved for the start of the takeoff run.
maximum taxi weight. Maximum weight approved for
ground maneuvers. This is the same as maximum ramp
weight.
maximum weight. The maximum authorized weight of the
aircraft and all of its equipment as specified in the Type
Certificate Data Sheets (TCDS) for the aircraft.
Glossary– 4
maximum zero fuel weight. The maximum authorized
weight of an aircraft without fuel. This is the sum of the BOW
and payload.
maximum zero fuel weight (GAMA). Maximum weight,
exclusive of usable fuel.
METO horsepower (maximum except takeoff). The
maximum power allowed to be continuously produced by an
engine. Takeoff power is usually limited to a given amount
of time, such as 1 minute or 5 minutes.
minimum fuel. The amount of fuel necessary for one-half
hour of operation at the rated maximum-continuous power
setting of the engine, which, for weight and balance purposes,
is
1
¦12 gallon per maximum-except-takeoff (METO) horsepower. It is the maximum amount of fuel that could be used
in weight and balance computations when low fuel might
adversely affect the most critical balance conditions. To
determine the weight of the minimum fuel in pounds, divide
the METO horsepower by 2.
minor alteration. An alteration other than a major alteration.
This includes alterations that are listed in the aircraft, aircraft
engine, or propeller specifications.
moment. A force that causes or tries to cause an object to
rotate.
moment (GAMA). The product of the weight of an item
multiplied by its arm. (Moment divided by a constant is used
to simplify balance calculations by reducing the number of
digits; see reduction factor.)
moment index. The moment (weight times arm) divided by
a reduction factor such as 100 or 1,000 to make the number
smaller and reduce the chance of mathematical errors in
computing the center of gravity.
moment limits vs. weight envelope. An enclosed area on a
graph of three parameters. The diagonal line representing the
moment/100 crosses the horizontal line representing the
weight at the vertical line representing the CG location in
inches aft of the datum. When the lines cross inside the
envelope, the aircraft is loaded within its weight and CG
limits.
net weight. The weight of the aircraft less the weight of any
chocks or other devices used to hold the aircraft on the scales.
normal category. A category of aircraft certificated under
14 CFR, Part 23 and CAR, Part 3 that allows the maximum
weight and CG range while restricting the maneuvers that are
permitted.
PAX. Passengers.
payload (GAMA). Weight of occupants, cargo, and baggage.
Pilot’s Operating Handbook (POH). An FAA-approved
document published by the airframe manufacturer that lists
the operating conditions for a particular model of aircraft and
its engines.
potable water. Water carried in an aircraft for the purpose
of drinking.
ramp weight. The zero fuel weight plus all of the usable fuel
on board.
reference datum (GAMA). An imaginary vertical plane
from which all horizontal distances are measured for balance
purposes.
reduction factor. A number, usually 100 or 1,000 by which
a moment is divided to produce a smaller number that is less
likely to cause mathematical errors when computing the
center of gravity.
residual fuel. Fuel that remains in the sumps and fuel lines
when the fuel system is drained from the inlet to the fuel
metering system, with the aircraft in level flight attitude. The
weight of the residual fuel is part of the empty weight of the
aircraft.
service ceiling. The highest altitude at which an aircraft can
maintain a steady rate of climb of 100 feet per minute.
small aircraft (14 CFR, Part 1). An aircraft of 12,500
pounds or less, maximum certificated takeoff weight.
Glossary– 5
standard average passenger weight. This includes 20
pounds of carry-on baggage for adult passengers.
summer (May 1 through October 31)
average (60% M, 40% F) ................180 lbs
male ..................................................195 lbs
female ...............................................155 lbs
winter (November 1 through April 30)
average (60% M, 40% F) ................185 lbs
male ..................................................200 lbs
female ...............................................160 lbs
children between ages 2 and 12 years
summer and winter ............................80 lbs
(Children under 2 are considered “babes in arms” and
their weight has been factored into the weight of the adult
passengers.)
standard empty weight (GAMA). Weight of a standard
airplane including unusable fuel, full operating fluids, and
full oil.
static load. The load imposed on an aircraft structure due to
the weight of the aircraft and its contents.
station (GAMA). A location along the airplane fuselage
usually given in terms of distance from the reference datum.
strain sensor. A device that converts a physical phenomenon
into an electrical signal. Strain sensors in a wheel axle sense
the amount the axle deflects and create an electrical signal
that is proportional to the force that caused the deflection.
takeoff weight. The weight of an aircraft just before brake
release. It is the ramp weight less the weight of the fuel burned
during start and taxi.
tare weight. The weight of any chocks or devices that are
used to hold an aircraft on the scales when it is weighed. The
tare weight must be subtracted from the scale reading to get
the net weight of the aircraft.
TEMAC. Trailing Edge of the Mean Aerodynamic Chord.
Type Certificate Data Sheets (TCDS). The official
specifications issued by the FAA for an aircraft, engine, or
propeller.
undrainable oil. Oil that does not drain from an engine
lubricating system when the aircraft is in the normal ground
attitude and the drain valve is left open. The weight of the
undrainable oil is part of the empty weight of the aircraft.
unusable fuel (GAMA). Fuel remaining after a runout test
has been completed in accordance with governmental
regulations.
usable fuel (GAMA). Fuel available for flight planning.
useful load (GAMA). Difference between takeoff weight, or
ramp weight if applicable, and basic empty weight.
utility category. A category of aircraft certificated under 14
CFR, Part 23 and CAR, Part 3 that permits limited acrobatic
maneuvers but restricts the weight and the CG range.
wing chord. A straight-line distance across a wing from
leading edge to trailing edge.
zero fuel weight. The weight of an aircraft without fuel.
Glossary– 6
Index– 1
Index
A
adverse-loaded CG checks ............................................... 5-4
aircraft specifications ....................................................... 2-7
arm .................................................................................... 2-1
B
balance control ................................................................. 1-4
ballast ....................................................................... 3-3, 5-7
bilge area ........................................................................... 3-2
C
cargo .................................................................................. 6-5
cargo changes— effects of ............................................... 6-5
cargo configuration ........................................................ 6-18
cargo pallet ....................................................................... 6-9
center of gravity (CG) ...................................................... 1-1
CG
determining ..................................................2-2, 3-4, 4-1
shifting ................................................................. 2-4 –2-6
CG limits envelope .................................................. 4-2– 4-3
CG moment envelope ....................................................... 4-5
CG range chart ............................................................... 2-11
chart method ..................................................................... 4-7
chord ................................................................................. 3-7
computational method ..................................................... 4-1
D
datum, location of ................................................... 3-5– 3-6
density altitude, high ........................................................ 1-2
draining of fuel and oil .................................................... 3-3
dynamic loads ................................................................... 1-2
E
E6-B flight computer ....................................................... 8-1
electronic calculators ....................................................... 8-1
electronic flight computers .............................................. 8-3
empty weight .................................................................... 1-1
basic ............................................................................... 2-1
standard ......................................................................... 2-1
empty-weight center of gravity (EWCG) .............. 1-1, 3-5
helicopter ...................................................................... 7-2
range .............................................................................. 5-4
equipment list ........................................................ 2-13, 5-1
F
fleet weight .......................................................6-1–6-2, 6-2
floor loading limits ........................................................... 6-9
fuel jettison system ........................................................ 6-12
I
interpolation............................................................. 4-8– 4-9
L
landing weight ................................................................ 6-10
law of the lever ................................................................. 2-2
leading edge of MAC (LEMAC) ..................................... 3-8
lift, center of ..................................................................... 1-4
load factor ......................................................................... 1-2
loading graph ........................................................... 4-2, 4-4
loading schedule ............................................................... 6-1
Index– 2
M
major alteration ................................................................ 5-1
maximum weight .............................................................. 1-1
mean aerodynamic chord (MAC) .................................... 3-7
minor alteration ................................................................ 5-1
moment ............................................................................. 2-2
large ............................................................................. 2-13
moment index ................................................................... 4-2
moment limits vs. weight envelope ...................... 4-8, 4-10
N
normal category .............................................................. 2-11
P
passenger configuration ................................................. 6-13
payload—maximum ...................................................... 6-10
R
reference datum ................................................................ 2-1
S
service ceiling .......................................................... 1-2, 1-3
specific gravity ................................................................. 3-2
stability ............................................................................. 1-4
stabilizer trim setting ....................................................... 6-5
static loads ........................................................................ 1-2
stations .............................................................................. 2-4
T
tare weight ............................................................... 2-4, 3-4
Type Certificate Data Sheets (TCDS) ............................. 2-7
U
utility category................................................................ 2-11
W
weighing
equipment for ................................................................ 3-1
jacking aircraft .............................................................. 3-3
platforms ....................................................................... 3-2
preparation for .............................................................. 3-2
requirements ................................................................. 6-1
weight
changes ................................................................. 1-3, 5-1
control ........................................................................... 1-2
effects of ........................................................................ 1-2
individual aircraft ......................................................... 6-1
weight and balance ........................................................... 1-1
basic equation ............................................................... 2-5
data ................................................................................ 4-1
definitions ........................................................ Glossary-3
documentation .............................................................. 2-7
helicopter ...................................................................... 7-1
importance .................................................................... 1-1
large aircraft .................................................................. 6-1
monitoring ..................................................................... 6-2
multiengine airplane ..................................................... 4-6
Part 135 aircraft .......................................................... 6-13
Part 23 airplane ............................................................. 4-1
requirements ................................................................. 3-1
revision .......................................................................... 5-3
theory ............................................................................ 2-1
typical problems ........................................................... 8-3
worksheet ...................................................................... 4-2