The center of gravity of an aircraft is the point over which the aircraft would
balance. Its position is calculated after supporting the aircraft on at
least two sets of weighing scales or load cells and noting the weight shown
on each set of scales or load cells. The center of gravity affects the stability
of the aircraft. To ensure the aircraft is safe to fly, the center of gravity
must fall within specified limits established by the aircraft
manufacturer. Terminology
Ballast Ballast is removable or permanently
installed weight in an aircraft used to bring the center of gravity into the
allowable range. Center-of-Gravity Limits
Center of gravity limits are specified longitudinal and/or lateral limits
within which the aircraft's center of gravity must be located during flight.
The CG limits are indicated in the airplane flight manual. The area between
the limits is called the CG range of the aircraft.
Weight and Balance When the weight of the aircraft is at or
below the allowable limit(s) for its configuration and its center of gravity
is within the allowable range, and both will remain so for the duration of the
flight, the aircraft is said to be within weight and balance. Different
maximum weights may be defined for different situations; for example, large
aircraft may have maximum landing weights that are lower than maximum
take-off weights. The center of gravity may change over the duration of the
flight as the aircraft's weight changes due to fuel burn or by passengers moving
forward or aft in the cabin. Reference Datum
The reference datum is a reference plane that allows accurate, and uniform,
measurements to any point on the aircraft. The location of the reference
datum is established by the manufacturer and is defined in the aircraft flight
manual. The horizontal reference datum is an imaginary vertical plane or point,
arbitrarily fixed somewhere along the longitudinal axis of the aircraft, from
which all horizontal distances are measured for weight and balance
purposes. There is no fixed rule for its location, and it may be located forward
of the nose of the aircraft. For helicopters, it may be located at the
rotor mast, the nose of the helicopter, or even at a point in space ahead of the
helicopter. While the horizontal reference datum can be anywhere the
manufacturer chooses, most small training helicopters have the horizontal
reference datum 100 inches forward of the main rotor shaft centerline. This is
to keep all the computed values positive. The lateral reference datum is
usually located at the center of the helicopter.
Arm The arm is the horizontal distance from
the reference datum to the center of gravity of an item. The algebraic sign
is plus if measured aft of the datum or to the right side of the center line
when considering a lateral calculation. The algebraic sign is minus if measured
forward of the datum or the left side of the center line when considering a
lateral calculation. Moment
The moment is the moment of force, or torque, that results from an object’s
weight acting through an arc that is centered on the zero point of the
reference datum distance. Moment is also referred to as the tendency of an object
to rotate or pivot about a point. The further an object is from this point,
the greater the force it exerts. Moment is calculated by multiplying the weight
of an object by its arm. Mean Aerodynamic Chord
A specific chord line of a tapered wing. At the mean aerodynamic chord, the
center of pressure has the same aerodynamic force, position, and area as
it does on the rest of the wing. The MAC represents the width of an equivalent
rectangular wing in given conditions. On some aircraft, the center of gravity is
expressed as a percentage of the length of the MAC. In order to make such a
calculation, the position of the leading edge of the MAC must be known ahead of
time. This position is defined as a distance from the reference datum and is
found in the aircraft's flight manual and also on the aircraft's type
certificate data sheet. If a general MAC is not given but a LeMAC and a TeMAC are
given then your MAC can be found by finding the difference between your
LeMAC and your TeMAC. Calculation
Center of gravity is calculated as follows:
Determine the weights and arms of all mass within the aircraft.
Multiply weights by arms for all mass to calculate moments.
Add the moments of all mass together. Divide the total moment by the total
weight of the aircraft to give an overall arm.
The arm that results from this calculation must be within the center of
gravity limits dictated by the aircraft manufacturer. If it is not, weight in
the aircraft must be removed, added, or redistributed until the center of
gravity falls within the prescribed limits.
Aircraft center of gravity calculations are only performed along a single axis
from the zero point of the reference datum that represents the longitudinal
axis of the aircraft. Some helicopter types utilize lateral CG limits as well
as longitudinal limits. Operation of such helicopters requires calculating CG
along two axes: one calculation for longitudinal CG and another calculation
for lateral CG. The weight, moment and arm values of
fixed items on the aircraft do not change and are provided by the
manufacturer on the Aircraft Equipment List. The manufacturer also provides
information facilitating the calculation of moments for fuel loads. Removable
weight items must be properly accounted for in the weight and CG calculation by
the aircraft operator. = Example =
To find the center of gravity, we divide the total moment by the total mass:
193,193 / 2,055 = 94.01 inches behind the datum plane.
In larger aircraft, weight and balance is often expressed as a percentage of
mean aerodynamic chord, or MAC. For example, assume the leading edge of the
MAC is 62 inches aft of the datum. Therefore, the CG calculated above lies
32 inches aft of the leading edge of the MAC. If the MAC is 80 inches in length,
the percentage of MAC is 32 / 80 = 40%. If the allowable limits were 15% to 35%,
the aircraft would not be properly loaded.
Incorrect weight and balance in fixed-wing aircraft
When the center of gravity or weight of an aircraft is outside the acceptable
range, the aircraft may not be able to sustain flight, or it may be impossible
to maintain the aircraft in level flight in some or all circumstances. Placing
the CG or weight of an aircraft outside the allowed range can lead to an
unavoidable crash of the aircraft. = Center of gravity out of range =
When the fore-aft center of gravity is out of range serious aircraft control
problems occur. The fore-aft CG affects longitudinal stability of the aircraft,
with the stability increasing as the CG moves forward, and stability decreasing
as the CG moves aft. With a forward CG position, although the stability of the
aircraft increases, the elevator control authority is reduced in the capability
of raising the nose of the aircraft. This can cause a serious condition
during the landing flare when the nose cannot be raised sufficiently to slow
the aircraft. An aft CG position creates severe handling problems due to the
reduced pitch stability and increased elevator control sensitivity, with
potential loss of aircraft control. Because the burning of fuel gradually
produces a loss of weight and possibly a shift in the CG, it is possible for an
aircraft to take off with the CG within normal operating range, and yet later
develop an imbalance that results in control problems. Calculations of CG
must take this into account. Here's an example of a Piper Mirage with
too much weight in the back of the aircraft that results in the Takeoff CG
within limits but the Landing CG is aft of the CG Envelope limits.
= Weight out of range = Few aircraft impose a minimum weight for
flight, but all impose a maximum weight. If the maximum weight is exceeded, the
aircraft may not be able to achieve or sustain controlled, level flight.
Excessive take-off weight may make it impossible to take off within available
runway lengths, or it may completely prevent take-off. Excessive weight in
flight may make climbing beyond a certain altitude difficult or
impossible, or it may make it impossible to maintain an altitude.
Incorrect weight and balance in helicopters
The center of gravity is even more critical for helicopters than it is for
fixed-wing aircraft. As with fixed-wing aircraft, 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. For helicopters with a single main rotor,
the CG is usually close to the main rotor mast. Improper balance of a
helicopter’s load can result in serious control problems. In addition to making
a helicopter difficult to control, an out-of-balance loading condition also
decreases maneuverability since cyclic control is less effective in the
direction opposite to the CG location. The pilot tries to perfectly balance a
helicopter so that the fuselage remains horizontal in hovering flight, with no
cyclic pitch control needed except for wind correction. Since the fuselage acts
as a pendulum suspended from the rotor, changing the center of gravity changes
the angle at which the aircraft hangs from the rotor. When the center of
gravity is directly under the rotor mast, the helicopter hangs horizontal;
if the CG is too far forward of the mast, the helicopter hangs with its nose
tilted down; if the CG is too far aft of the mast, the nose tilts up.
= CG forward of forward limit = A forward CG may occur when a heavy
pilot and passenger take off without baggage or proper ballast located aft of
the rotor mast. This situation becomes worse if the fuel tanks are located aft
of the rotor mast because as fuel burns the weight located aft of the rotor mast
becomes less. This condition is recognizable when
coming to a hover following a vertical takeoff. The helicopter will have a
nose-low attitude, and the pilot will need excessive rearward displacement of
the cyclic control to maintain a hover in a no-wind condition. In this
condition, the pilot could rapidly run out of rearward cyclic control as the
helicopter consumes fuel. The pilot may also find it impossible to decelerate
sufficiently to bring the helicopter to a stop. In the event of engine failure
and the resulting autorotation, the pilot may not have enough cyclic control
to flare properly for the landing. A forward CG will not be as obvious when
hovering into a strong wind, since less rearward cyclic displacement is required
than when hovering with no wind. When determining whether a critical balance
condition exists, it is essential to consider the wind velocity and its
relation to the rearward displacement of the cyclic control.
= CG aft of aft limit = Without proper ballast in the cockpit,
exceeding the aft CG may occur when: A lightweight pilot takes off solo with
a full load of fuel located aft of the rotor mast.
A lightweight pilot takes off with maximum baggage allowed in a baggage
compartment located aft of the rotor mast.
A lightweight pilot takes off with a combination of baggage and substantial
fuel where both are aft of the rotor mast.
An aft CG condition can be recognized by the pilot when coming to a hover
following a vertical takeoff. The helicopter will have a tail-low
attitude, and the pilot will need excessive forward displacement of cyclic
control to maintain a hover in a no-wind condition. If there is a wind, the pilot
needs even greater forward cyclic. If flight is continued in this condition,
the pilot may find it impossible to fly in the upper allowable airspeed range
due to inadequate forward cyclic authority to maintain a nose-low
attitude. In addition, with an extreme aft CG, gusty or rough air could
accelerate the helicopter to a speed faster than that produced with full
forward cyclic control. In this case, dissymmetry of lift and blade flapping
could cause the rotor disc to tilt aft. With full forward cyclic control already
applied, the rotor disc might not be able to be lowered, resulting in
possible loss of control, or the rotor blades striking the tail boom.
Lateral balance In fixed-wing aircraft, lateral balance
is often much less critical than fore-aft balance, simply because most
mass in the aircraft is located very close to its center. An exception is
fuel, which may be loaded into the wings, but since fuel loads are usually
symmetrical about the axis of the aircraft, lateral balance is not usually
affected. The lateral center of gravity may become important if the fuel is not
loaded evenly into tanks on both sides of the aircraft, or when passengers are
predominantly on one side of the aircraft. Small lateral deviations of CG
that are within limits may cause an annoying roll tendency that pilots must
compensate for, but they are not dangerous as long as the CG remains
within limits for the duration of the flight.
For most helicopters, it is usually not necessary to determine the lateral CG
for normal flight instruction and passenger flights. This is because
helicopter cabins are relatively narrow and most optional equipment is located
near the center line. However, some helicopter manuals specify the seat from
which solo flight must be conducted. In addition, if there is an unusual
situation, such as a heavy pilot and a full load of fuel on one side of the
helicopter, which could affect the lateral CG, its position should be
checked against the CG envelope. If carrying external loads in a position
that requires large lateral cyclic control displacement to maintain level
flight, fore and aft cyclic effectiveness could be dramatically
limited. Fuel dumping and overweight operations
Many large transport-category aircraft are able to take-off at a greater weight
than they can land. This is possible because the weight of fuel that the
wings can support along their span in flight, or when parked or taxiing on the
ground, is greater than they can tolerate during the stress of landing
and touchdown, when the support is not distributed along the span of the wing.
Normally the portion of the aircraft's weight that exceeds the maximum landing
weight is entirely composed of fuel. As the aircraft flies, the fuel burns off,
and by the time the aircraft is ready to land, it is below its maximum landing
weight. However, if an aircraft must land early, sometimes the fuel that
remains aboard still keeps the aircraft over the maximum landing weight. When
this happens, the aircraft must either burn off the fuel or dump it before
landing to avoid damage to the aircraft. In an emergency, an aircraft may choose
to land overweight, but this may damage it, and at the very least an overweight
landing will mandate a thorough inspection to check for any damage.
In some cases, an aircraft may take off overweight deliberately. An example
might be an aircraft being ferried over a very long distance with extra fuel
aboard. An overweight take-off typically requires an exceptionally long runway.
Overweight operations are not permitted with passengers aboard.
Many smaller aircraft have a maximum landing weight that is the same as the
maximum take-off weight, in which case issues of overweight landing due to
excess fuel being on board cannot arise. CG of Large Commercial Transport
Aircraft This section shows data obtained from a
NASA Ames research grant for large commercial transport aircraft.
The Operational CG Range is utilized during take off and landing phases of
flight and the Permissible CG Range is utilized during ground operations.
See also List of aviation topics
References