AOA digit 737

Head up display on a 737 "showing" AOA, as the vertical angular distance between the circle on the left just above horizon (speed vector direction) and the 'V' in the middle (longitudinal axis direction). The AOA is also indicated on the upper right side, on the gauge, showing 3°.

The Angle of attack (AOA , α, Greek letter alpha) is a useful concept in aviation, as it is important in determining the aerodynamic forces that act on the vehicle. Most of the airplane’s critical performance characteristics are closely related to angle of attack.

Article created by Jonathan Herault

Definitions Edit

Wing absolute geometric AOAs

Positive cambered wing showing the algebraic definitions of absolute, zero lift and geometric AOA.

For an aircraft, the angle of attack is defined as the angle that exists between the projection of the wind vector (or velocity vector) on the aircraft's plane of symmetry, and an arbitrary reference line on the body. This reference line is usually parallel to the mean aerodynamic chord, or zero lift line of the aircraft, or for passenger airplanes, parallel to the cabin floor.  AOA is always denoted α.[1]

For a wing, AOA is similarly defined by the angle made (in the plane of symmetry of the aircraft) by the wing's chord line and the wind vector (far upstream oncoming flow). Since drag is defined as the component of the resultant force parallel to the relative wind, angle of attack can also be thought of as the angle between the drag and the chord line. One can also define an absolute angle of attack, \alpha_a, that exists between the wing's zero lift line and the wind vector. The angle of attack at zero lift, \alpha_{L=0} is related to \alpha_a and \alpha by \alpha_a=\alpha-\alpha_{L=0}. For a positive cambered wing, \alpha_{L=0}< 0 and therefore, .\alpha_a > \alpha.

The Differences Between AOA & Other Characteristic Aviation Angles Edit

Acft AOAs and wing angle of incidence

Relationships between aircraft and wing geometric, zero-lift AOAs, and wing angle of incidence Failed to parse (unknown function\i): \i_w

The AOA of an aircraft must not be confused with its pitch angle, which is defined by the angle between the horizon and the above mentioned reference line, whereas the angle of attack is the angle from the longitudinal axis to the direction of the arrival of the air to the aircraft. Those two angles are equal only on straight leveled flight, that is to say when and only when the velocity vector is aiming at the horizon.

The angle of incidence , although used instead of AOA by the British, usually refers to the angle, fixed, where the wing is mounted on an aircraft. It is the angle made by the aircraft's body reference line and the chord of the wing.

Finally, the flight path angle refers to the angle between the velocity vector and the horizon, which is in fact the slope of the aircraft's trajectory in reference to the ground.

Induced and Effective AOA for a Wing

Induced effective AOAs

Definitions of induced end effective AOA, respectively \alpha_i and \alpha_e

When a wing passes through the air, it creates a perturbation, which leads to a vertical component on the relative motion on the air over the wing. Consequently the air flow past the wing is inclined in regard of the initial free stream. Then, the wing behaves as thought the flow were coming from a different direction: the local flow direction.

In practice, these perturbations stem from wingtip vortices [2][3], which create downwash and deflects the local airflow in the vicinity of the wing downward by an angle equal to the arctangent of the ratio u/V (where u is the vertical downwash component). This angle is the induced angle of attack \alpha_i. The airfoil section itself is then responding to an effective angle of attack equal to the geometric angle of attack minus the induced angle of attack: \alpha_e=\alpha-\alpha_i. In most cases, the absolute value of the angle of attack is decreased, and so as for the lift force. Then, in order to produce a given lift force, the AOA of the wing must be greater than the AOA that would be given by a theoretical study of the wing section (2D wing). Moreover, the resulting force exerted by the air on the wing, now perpendicular to the local flow direction, is tilted backwards by an angle equal to the induced angle of attack and then is no longer perpendicular to the free stream velocity. This important phenomenon is at the origin of the induced drag (i.e. the component of the resulting force parallel to the free stream velocity), and therefore for a given lift, a greater induced AOA implies a greater drag. For a wing, the value of \alpha_i depends notably on the aspect ratio, the sweep angle, and more generally on the shape. One must bear in mind that because this is a 3-dimentional effect, usual 2D studies of a wing (CFD or wing tunnel) will fail to predict its real performances.

Importance of AOA Edit

For pilots Edit


Evolution on the lift coefficient with AOA, and notably the stall AOA reached at the top of the curve. Here about 16°

Due to the dependence of the lift equation on α, the main aerodynamic forces (i.e. lift and drag), the performances of the aircraft in terms of best gliding speed, minimum speed etc. are directly impacted by AOA. In fact, the low-speed limits and most of the “optimum” numbers (including the stall, best rate of climb, best lift/drag ratio, best endurance, normal approach, short field approach, etc.) involve angle of attack. The corresponding airspeeds vary in proportion to the square root of the weight times load factor, whereas the high-speed limits (including never-exceed speed, the normal-operations limit, the landing-gear operation limit etc.) are, for all practical purposes, definite indicated airspeeds.

A reliable way to measure angle of attack, and a convenient display system to the pilots, such as HUD, enables direct "AOA flying". For example, the landing is made at a particular angle of attack, as well as the best climb speed, or the best endurance speed. In most of the case, this angle of attack is achieved by reaching the corresponding speed given the loading of the aircraft. For a pilot, the flying of the aircraft is achieved by directly controlling thrust and control surfaces. Any input change in those parameters affects the mechanical equilibrium of the aircraft, and all the variables that defines it which falls out in a consequence of equilibrium. Speed and AOA are part of them. At last, because of AOA stability, an aircraft is trimmed for a particular AOA [4], i.e. trimming allows AOA control. However, except in a few aforementioned cases, AOA control is not an end in itself.

During the design process Edit

Swept back wing with twisted tips Etkin

Swept back wing with twisted wingtips. [5]

Lift generated by the wing is mainly a function of angle of attack, through the lift coefficient which is only a function of AOA. For stability purposes, for example, a positive pitch stiffness can be obtained for a tailless aircraft with a swept back wing by decreasing the wing's angle of incidence when moving away from the body. This is called wing twist or washout. Because of the change of AOA, when the net lift is zero, the forward part of the wing has a positive lift whereas the rear part of the wing has a negative one. The result is a net positive couple, as desired.[6] Moreover, when approaching stall speed, the washout leads the part of the wing near the root to stall first because of its greater AOA, whilst the rest still generates lift. That moves the pressure center backwards, creating a pitch down moment allowing the wing root to recover from stall. Also, since the aircraft's flight control surfaces are often located at the wingtip, the washout alert the pilot to the advancing stall while still allowing the control surfaces to remain effective, meaning the pilot can usually prevent the aircraft from stalling fully before control is completely lost.

Footnotes Edit

  1. Etkin 1972, p. 114.
  2. Katz & Plotkin 1972, pp. 171-172.
  3. Munk 1929, pp. 1.
  4. Etkin 1972, p. 202-211.
  5. Etkin 1972, p. 201.
  6. Etkin 1972, p. 201.

References Edit

  • Etkin, B. (1972), Dynamics of Atmospheric Flight, p.114&pp.201-211, Wiley, New York.
  • Hull, D.G. (2007), Fundamentals of Airplanes Mechanics, Springer, Berlin.
  • Katz, J.&Plotkin, A. Low speed aerodynamics, pp.171-172 Cambridge University press, Cambridge.
  • Munk, M.M. (1929) Theory of the complete wing, pp.89-93 in Fundamentals of fluid dynamics for aircraft enginers, Ronald Press Company, New York.

Further readings Edit

Gracey, William (1958)."Summary of Methods of Measuring Angle of Attack on Aircraft"NACA Technical Note (NASA Technical Reports) (NACA-TN-4351)

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