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Load Factor


Load factor is the ratio of the total load supported by the airplane’s wing to the total weight of the airplane. In still air flight, the load on the wing equals the lift it generates. The load factor is expressed in G units. In an unaccelerated level flight the load on the wings is equal to lift and to the weight. Consequently, the load factor equals 1G. If Lift = Weight then Lift / Weight = 1G.

The load factor may be POSITIVE or NEGATIVE.

POSITIVE LOAD FACTOR - During normal flight, the load factor is 1 G or greater than 1 G. Whenever the load factor is one or greater the load factor is defined as positive.

NEGATIVE LOAD FACTOR - Under certain conditions, an abrupt deviation from the airplane's equilibrium can cause an inertial acceleration that in turn will cause the weight to become greater than the lift. For example, during a stall, the load factor may be reduced towards zero. This will cause the pilot to feel "weightless". A sudden and forceful elevator control movement forward can cause the load factor to move into a negative region.

Both excessive deviation from positive and negative load factor limits must be avoided because of the possibility of exceeding the structural load limits of the airplane.

Effect of Turns on Load Factor
As an airplane is banked, more lift is required to maintain level flight. As illustrated below, a greater bank angle is required to produce sufficient lift to support level turn under the same weight conditions. At a 60° bank, the lift must be twice larger than the weight to support a level turn. In other words, the Load Factor with a bank angle of 60° is 2 G's.

Load Factor

The following demonstrates the increased wing load as the angle of bank increases. The increase is shown by the relative lengths of the red arrows. Figures below the arrows indicate the increase in load factor (G units).

Load Factor

Load Factor

It should also be noted how rapidly load factor increases as the angle of bank approaches 90°. The 90° banked, constant altitude turn is not mathematically possible. An airplane can be banked to 90°, but a continued coordinated turn is impossible at this bank angle without losing altitude. Although the load factor could be mathematically calculated for every bank angle, it has very little importance on a day to day operation. However, the understanding of the effects of an increased bank is fundamental to an operation of an airplane. The adjacent graph illustrates the load factor changes with the change of angle of bank.


Effect of Load Factor on Stalling Speed
A stall occurs when the angle of attack is increased to such a value where the smooth flow of air over the airfoil breaks up and tears away, producing an abrupt change of characteristics and loss of lift. In other words, a stall is a condition where the lift generated by the airplane's wing can no longer support its weight.
In an unaccelerated flight a stall will occur at a certain angle of attack. In an absence of angle of attack indicator, the approaching stall can be derived from the airplane's airspeed. Manipulating the lift formula gives us the relationship between the airspeed and the angle of attack.

     

Where
    L = Lift           D = Drag             = Air density          V = Velocity 
    S = Wing area*         CL = Lift coefficient       CD = Drag coefficient
It should be noted that the wing area (S) and the air density () are constant for any given altitude while both CL/ CD and the velocity (V }are variables. The air velocity is a major contributor to lift and drag because both are proportional to the square of the velocity. From the lift and drag formulas, it follows that the velocity and the angle of attack (represented by either CL or CD) are inversely proportional. For example, an increase in the angle of attack at a constant power will decrease the speed. Conversely, high speed at a constant power will require lower angle of attack.

From


The following holds

The last formula demonstrates the speed (V) as a function of the angle of attack (CL). It also demonstrates a direct relationship between the airspeed V, the weight of the airplane W and the lift coefficient  CL.
Increasing the load factor to a value where the generated lift can no longer support its weight will result in a stall. The following formula demonstrates the relationship of the load factor and the stalling speed.

    Where: VSA is accelerated stall speed
        VS is unaccelerated stall speed
       N is the Load Factor ( In G's)

Load Factor
In the following example, an airplane with an stall speed of 55Kts is flown in a sixty degrees bank. As mentioned earlier, a sixty degrees bank results in a 2 G's load factor.

The result shows that an airplane with unaccelerated stall speed of 55kts will actually stall at 77kst at a 60 degrees bank.
The graph to the right is regularly used to determine the increase in stalling speed (in percent) in a given angle of bank.




Effect of Speed on Load Factor
The amount of excess load that can be imposed on the wing depends on how fast the airplane is flying. At slow speeds, the maximum available lifting force of the wing is only slightly greater than the amount necessary to support the weight of the airplane. Consequently, the load factor should not become excessive even if the controls are moved abruptly or the airplane encounters severe gusts, as previously stated. The reason for this is that the airplane will stall before the load can become excessive. However, at high speeds, the lifting capacity of the wing is so great that a sudden movement of the elevator controls or a strong gust may increase the load factor beyond safe limits. Because of this relationship between speed and safety, certain maximum speeds have been established. Each airplane is restricted in the speed at which it can safely execute maneuvers, withstand abrupt application of the controls, or fly in rough air. This speed is referred to as the design maneuvering speed.

Effect of Flight Maneuvers on Load Factor

Load factors apply to all flight maneuvers. In a straight-and-level unaccelerated flight, a load factor of 1G is always present, but certain maneuvers are known to involve relatively high load factors.

Turns - As previously discussed, increased load factors are a characteristic of all banked turns. Load factors become significant both to flight performance and to the load on wing structure as the bank increases beyond approximately 45°.

Stalls - The normal stall entered from straight-and-level flight, or an unaccelerated straight climb, should not produce added load factors beyond the 1G of straight-and-level flight. During the pullup following stall recovery, however, significant load factors are often encountered. These may be increased by excessively steep diving, high airspeed, and abrupt pullups to level flight. One usually leads to the other, thus increasing the resultant load factor. The abrupt pullup at a high diving speed may easily produce critical loads on structures, and may produce recurrent or secondary stalls by building up the load factor to the point that the speed of the airplane reaches the stalling airspeed during the pullup.

Advanced Maneuvers - Spins, chandelles, lazy eights, and aerobatic maneuvers are not be covered here. However, before attempting these maneuvers, pilots should be familiar with the airplane being flown, and know whether or not these maneuvers can be safely performed.

Effect of Turbulence on Load Factor - Turbulence in the form of vertical air currents can, under certain conditions, cause severe load stress on an airplane wing.
When an airplane is flying at a high speed with a low angle of attack, and suddenly encounters a vertical current of air moving upward, the relative wind changes to an upward direction as it meets the airfoil. This increases the angle of attack of the wing.
If the air current is well defined and travels at a significant rate of speed upward (15 to 30 feet per second), a sharp vertical gust is produced which will have the same effect on the wing as applying sudden sharp back pressure on the elevator control.
All certificated airplanes are designed to withstand loads imposed by turbulence of considerable intensity. Nevertheless, gust load factors increase with increasing airspeed. Therefore it is wise, in extremely rough air, as in thunderstorm or frontal conditions, to reduce the speed to the design maneuvering speed. As a general rule, when severe turbulence is encountered, the airplane should be flown at the maneuvering speed shown in the approved Airplane Flight Manual, Pilot’s Operating Handbook, or placard in the airplane. This is the speed least likely to result in structural damage to the airplane, even if full control travel is used, and yet allows a sufficient margin of safety above stalling speed in turbulent air.
Placarded never exceed speeds are determined for smooth air only. High dive speeds or abrupt maneuvering in gusty air at airspeeds above the maneuvering speed may place damaging stress on the whole structure of an airplane. Stress on the structure means stress on any vital part of the airplane.

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Last update May 17, 2005
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