The center of gravity (CG) of an aircraft is the point over which the aircraft would balance.[1] 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.
Center of gravity (CG) is calculated as follows:
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 (rarely), 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 (to calculate fore-to-aft balance). 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 (fore-to-aft balance) and another calculation for lateral CG (left-to-right balance).
The weight, arm, and moment values of the fixed items on the aircraft (i.e. engines, wings, electronic components) 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 (i.e. crew members, passengers, baggage) must be properly accounted for in the weight and CG calculation by the aircraft operator.
| Weight (lb) | Arm (in) | Moment (lb-in) | ||
|---|---|---|---|---|
| Empty aircraft | 1,495.0 | 101.4 | 151,593.0 | |
| Pilot and passengers | 380.0 | 64.0 | 24,320.0 | |
| Fuel (30 gallons @ 6 lb/gal) | 180.0 | 96.0 | 17,280.0 | |
| Totals | 2,055.0 | 94.0 | 193,193.0 |
To find the center of gravity, we divide the total moment by the total weight: 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.
When the weight or center of gravity 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, in some events resulting in load shifting. Placing the CG or weight of an aircraft outside the allowed range can lead to an unavoidable crash of the aircraft.
When the fore-aft center of gravity (CG) is out of range, serious aircraft control problems can occur. The fore-aft CG affects the longitudinal stability of the aircraft, with the stability increasing as the CG moves forward and 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 can cause 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 (often part of this is calculated in advance by the manufacturer and incorporated into CG limits).
The amount a weight must be moved can be found by using the following formula shift distance = (total weight * cg change) / weight shifted
Example: 1500 lb * 33.9 in = 50,850 moment (airplane) 100 lb * 68 in = 8,400 moment (baggage) cg = 37 in = (50,850 + 8,400) / 1600 lb (1/2 in out of cg limit)
We want to move the CG 1 in using a 100 lb bag in the baggage compartment.
shift dist = (total weight * cg change) / weight shifted 16 in = (1600 lb * 1 in) / 100 lb
Reworking the problem with 100 lb moved 16 in forward to 68 in moves CG 1 in. 1500 lb * 33.9 in = 50,850 moment (airplane) 100 lb * 84in = 6,800 moment (baggage) cg = 36 in = (50,850 + 6,800) / 1600 lb new cg = 36 in
Few aircraft impose a minimum weight for flight (although a minimum pilot weight is often specified), but all impose a maximum weight. If the maximum weight is exceeded, the aircraft may not be able to achieve or sustain controlled 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.
The center of gravity is even more critical for helicopters than it is for fixed-wing aircraft (weight issues remain the same). 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.[4] 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 hangswith its nose tilted down; if the CG is too far aft of the mast, the nose tilts up.
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.
Without proper ballast in the cockpit, exceeding the aft CG may occur when:
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.
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 (in the case of small aircraft) when passengers are predominantly on one side of the aircraft (such as a pilot flying alone in a small 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.
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 (but falls within the maximum take-off 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 (by flying in a holding pattern) or dump it (if the aircraft is equipped to do this) 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.
This section shows data obtained from a NASA Ames research grant for large commercial transport aircraft.[5] [6]
The Operational CG Range is utilized during takeoff and landing phases of flight, and the Permissible CG Range is utilized during ground operations (i.e. while loading the aircraft with passengers, baggage and fuel).