Definitions
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 is a nondimensional 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
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 highlift 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 builtin 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 23 seconds is 120 degrees, performed in the Russian Su27 by famous Russian test pilot Viktor Pugatshev at Paris Airshow in 1989.
In sailing, the angle of attack is the angle between a midsail and the direction of the wind. The physical principles involved are the same as for aircraft. See points of sail.
Lift coefficient
The lift coefficient (C_{L} or C_{Z}) is nondimensional 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.
 Lift coefficient may be used to relate the total lift generated by an aircraft to the total area of the wing of the aircraft. In this application it is called the aircraft lift coefficient C_{L}.
The lift coefficient C_{L} is equal to:
where L is the lift force, ρ is fluid density, v is true airspeed, q is , and A is area.
 Lift coefficent may also be used as a characteristic of a particular shape (or crosssection) 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 nonvarying crosssection. 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:
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 straightline 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.
Source: Wikipedia (All text is available under the terms of the GNU Free Documentation License and Creative Commons AttributionShareAlike License.)
