Load factor (aerodynamics)
Encyclopedia
In aeronautics, the load factor is defined as the ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...

 of the lift
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...

 of an aircraft
Aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...

 to its weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...



and represents a global measure of the stress ("load") to which the structure of the aircraft is subjected:
where:
n = Load factor
L = Lift
W = Weight

Since the load factor is the ratio of two forces, it is dimensionless. However, its units are traditionally referred to as g, because of the relation between load factor and apparent acceleration of gravity felt on board the aircraft. A load factor of one, or 1 g, represents conditions in straight and level flight, where the lift is equal to the weight. Load factors greater or less than one (or even negative) are the result of maneuvers or wind gusts.

Load factor and g

The fact that the load factor is commonly expressed in g units does not mean that it is dimensionally the same as the acceleration of gravity
Earth's gravity
The gravity of Earth, denoted g, refers to the acceleration that the Earth imparts to objects on or near its surface. In SI units this acceleration is measured in metres per second per second or equivalently in newtons per kilogram...

, also indicated with g. The load factor is strictly non-dimensional.

The use of g units refers to the fact that an observer on board an aircraft will experience an apparent acceleration of gravity (i.e. relative to his frame of reference) equal to load factor times the acceleration of gravity. For example, an observer on board an aircraft performing a turn with a load factor of 2 (i.e. a 2 g turn) will see objects falling to the floor at twice the normal acceleration of gravity.

In general, whenever the term load factor is used, it is formally correct to express it using numbers only, as in "a maximum load factor of 4". If the term load factor is omitted then g is used instead, as in "pulling a 3 g turn".

Positive and negative load factors

The load factor, and in particular its sign, depends not only on the forces acting on the aircraft, but also on the orientation of its vertical axis.

During straight and level flight, the load factor is +1 if the aircraft is flown "the right way up", whereas it becomes -1 if the aircraft is flown "upside-down" (inverted). In both cases the lift vector is the same (as seen by an observer on the ground), but in the latter the vertical axis of the aircraft points downwards, making the lift vector's sign negative.

In turning flight the load factor is normally greater than +1. For example, in a turn with a 60° angle of bank the load factor is +2. Again, if the same turn is performed with the aircraft inverted, the load factor becomes -2. In general, in a balanced turn in which the angle of bank is θ, the load factor n is related to the cosine
Trigonometric function
In mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle...

 of θ by the formula:
Another way to achieve load factors significantly higher than +1 is to pull on the elevator
Elevator (aircraft)
Elevators are flight control surfaces, usually at the rear of an aircraft, which control the aircraft's orientation by changing the pitch of the aircraft, and so also the angle of attack of the wing. In simplified terms, they make the aircraft nose-up or nose-down...

 control at the bottom of a dive, whereas strongly pushing the stick forward during straight and level flight is likely to produce negative load factors, by causing the lift to act in the opposite direction to normal, i.e. downwards.

Load factor and lift

In the definition of load factor, the lift is not simply that one generated by the aircraft's wing
Wing
A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

, instead it is the vector sum of the lift generated by the wing, by the fuselage and by the tailplane
Tailplane
A tailplane, also known as horizontal stabilizer , is a small lifting surface located on the tail behind the main lifting surfaces of a fixed-wing aircraft as well as other non-fixed wing aircraft such as helicopters and gyroplanes...

, or in other words it is the component perpendicular to the airflow of the sum of all aerodynamic forces acting on the aircraft.

The lift in the load factor is also intended as having a sign, which is positive if the lift vector points in the same direction, or close to, as the aircraft's vertical axis, or negative if it points in the opposite direction, or close to opposite, to the vertical axis.

Design standards

Excessive load factors must be avoided because of the possibility of exceeding the structural strength of the aircraft.

Aviation authorities
National aviation authority
The National Aviation Authority is the government statutory authority in each country that oversees the approval and regulation of civil aviation.-Role:...

 specify the load factor limits within which different classes of aircraft are required to operate without damage. For example, the US Federal Aviation Regulations
Federal Aviation Regulations
The Federal Aviation Regulations, or FARs, are rules prescribed by the Federal Aviation Administration governing all aviation activities in the United States. The FARs are part of Title 14 of the Code of Federal Regulations...

 prescribe the following limits (for the most restrictive case):
  • For commercial transport airplanes, from -1 to +2.5 (or up to +3.8 depending on design takeoff weight)
  • For light airplanes, from -1.5 to +3.8
  • For aerobatic airplanes, from -3 to +6
  • For helicopters, from -1 to +3.5

However, many aircraft types, in particular aerobatic
Aerobatics
Aerobatics is the practice of flying maneuvers involving aircraft attitudes that are not used in normal flight. Aerobatics are performed in airplanes and gliders for training, recreation, entertainment and sport...

 airplanes, are designed so that they can tolerate load factors much higher than the minimum required. For example, the Sukhoi Su-26
Sukhoi Su-26
|-See also:...

 family have load factors limits of -10 to +12.

The maximum load factors, both positive and negative, applicable to an aircraft are usually specified in the pilot's operating handbook.

Human perception of load factor

When the load factor is +1, all occupants of the aircraft feel that their weight is normal. When the load factor is greater than +1 all occupants feel heavier than usual. For example, in a 2 g maneuver all occupants feel that their weight is twice normal. When the load factor is zero, or very small, all occupants feel weightless. When the load factor is negative, all occupants feel they are upside down.

Human beings have limited ability to withstand a load factor significantly greater than 1, both positive and negative. Unmanned aerial vehicles can be designed for much greater load factors, both positive and negative, than conventional aircraft because these vehicles can be used in maneuvers which would be incapacitating for a human pilot.
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