Angle of Attack & Lift Coefficient

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Angle of Attack & Lift Coefficient

Angle of attack is a term used in aerodynamics to describe the angle between the airfoil's chord line and the relative airflow, wind, effectively the direction in which the aircraft is currently moving. It can be described as the angle between where the wing is pointing and where it is going.

The lift coefficient (C_L or C_Z) is non-dimensional coefficient that relates the lift generated by an airfoil, the dynamic pressure of the fluid flow around the airfoil, and the planform area of the airfoil. It may also be described as the ratio of lift pressure to dynamic pressure.

Angle of Attack

In this diagram, the black lines represent the flow of the wind. The wing is shown end on. The angle α is the angle of attack.

Angle of attack (AOA, $α$ , Greek letter alpha) is a term used in aerodynamics to describe the angle between the airfoil's chord line and the relative airflow, wind, effectively the direction in which the aircraft is currently moving. It can be described as the angle between where the wing is pointing and where it is going.

The amount of lift generated by a wing is directly related to the angle of attack, with greater angles generating more lift (and more drag). This remains true up to the stall point, where lift starts to decrease again because of flow separation.

Planes flying at high angles of attack can suddenly enter a stall if, for example, a strong wind gust changes the direction of the relative wind. Also, to maintain a given amount of lift, the angle of attack must be increased as speed through the air decreases. This is why stalling is an effect that occurs more frequently at low speeds.

Nonetheless, a wing (or any other airfoil) can stall at any speed. Planes that already have a high angle of attack, for example because they are pulling g or a heavy payload, will stall at a speed well above the normal stall speed, since only a small increase in the angle of attack will take the wing above the critical angle.

The critical angle is typically around 15° for most airfoils. Using a variety of additional aerodynamic surfaces — known as high-lift devices — like leading edge extensions (leading edge wing root extensions), fighter aircraft have increased the potential flyable alpha from about 20° to over 45°, and in some designs, 90° or more. That is, the plane remains flyable when the wing's chord is perpendicular to the direction of motion.

Some aircraft are equipped with a built-in flight computer that automatically prevents the plane from lifting its nose any further when the maximum angle of attack is reached, irrespective of pilot input. This is called the angle of attack limiter or alpha limiter. Modern airliners that limit the angle of attack by means of computers include the Airbus 320, 330, 340, and 380 series.

The pilot may disengage the alpha limiter at any time, thus allowing the plane to perform tighter turns (but with considerably higher risk of going into a stall). A famous military example of this is Pugachev's Cobra. Currently, the highest angle of attack recorded for a duration of 2-3 seconds is 120 degrees, performed in the Russian Su-27 by famous Russian test pilot Viktor Pugatshev at Paris Airshow in 1989.

Sailing

In sailing, the angle of attack is the angle between a mid-sail and the direction of the wind. The physical principles involved are the same as for aircraft. See points of sail.

Lift coefficent may also be used as a characteristic of a particular shape (or cross-section) of an airfoil. In this application it is called the section lift coefficient c_L. It is common to show, for a particular airfoil section, the relationship between lift coefficient and angle of attack. It is also useful to show the relationship between lift coefficient and drag coefficient.

The section lift coefficient is based on the concept of an infinite wing of non-varying cross-section. It is not practical to define the section lift coefficient in terms of total lift and total area because they are infinitely large. Rather, the lift is defined per unit span of the wing. In such a situation, the above formula becomes:

$c_L={L \over \frac{1}{2}\rho v^2c}$

where c is the chord length of the airfoil.

Note that the lift equation does not include terms for angle of attack — that is because there is no mathematical relationship between lift and angle of attack. (In contrast, there is a straight-line relationship between lift and dynamic pressure; and between lift and area.) The relationship between the lift coefficient and angle of attack is complex and can only be determined by experimentation or complex analysis. See the accompanying graph. The graph for section lift coefficient vs. angle of attack follows the same general shape for all airfoils, but the particular numbers will vary. The graph shows an almost linear increase in lift coefficient with increasing angle of attack, up to a maximum point, after which the lift coefficient falls away rapidly. This indicates the lift coefficient at the stall of the airfoil.

The lift coefficient is a dimensionless number.

Note that in the graph here, there is still a small but positive lift coefficient with angles of attack less than zero. This is true of any airfoil with camber (asymmetrical airfoils). The pressures on the upper surface of the airfoil are lower than on the bottom surface, even at zero angle of attack.

Sailing

See also

See also