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The angle of attack of an aircraft is defined as the angle between the relative wind and the wing's chord line. Since drag is defined as the component of the resultant force parallel to the relative wind, angle of attack is also the angle between the drag and the chord line. In other words, since the relative wind is usually approximately horizontal, if the plane is climbing, the angle of attack is positive, and if it's in a dive, the angle of attack is negative.

Angle of attack is often abbreviated as α or AOA.

Forces and moments on a wing section generally1 vary as functions of angle of attack; airfoils are often identified by the way their coefficients of lift, drag, and moment vary according to angle of attack. All of NACA's voluminous airfoil data archives are presented as graphs in this form.

The angle of attack when lift is zero is defined as the "zero-lift angle of attack" (duh), αL=0. αL=0 is different depending on the shape of the airfoil: for a cambered airfoil (eyebrow-shaped), it is negative, while for a perfectly symmetrical airfoil, αL=0 is identically zero. With the wing sitting at zero lift, a line can be drawn along the line of relative velocity, through the airfoil, and out its trailing edge. This is known as the "zero-lift line". As the airfoil then changes orientation relative to the wind, the angle between the zero-lift line and relative wind is known as absolute angle of attack, and is the sum of the zero-lift angle of attack and the geometric angle of attack: αa = α + αL=0.

At some large value of α, the flow passing over the top of the airfoil will separate, and the sudden increase in drag will make the aircraft stall - i.e., don't try to fly straight up, 'cause it won't work.

A twisted airfoil (see wing divergence, reversal) can cause the angle of attack to vary along the length of a wing.

In practice, airfoils tend to shed vortices from the wingtip, which creates a downwash and deflects the local airflow in the vicinity of the wing downward by an angle of αi. This is the induced angle of attack. 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: αeff = α - αi. This is related to finite wing theory.

You might want to find a website or a book with some diagrams to help you visualize these different types of α; airfoils are generally curvy and not given to ascii art. The book I'm looking at now is Introduction to Flight, fourth edition, by John D. Anderson, Jr.; it's pretty decent. A quick search turns up this site, which doesn't have too many pictures, but does have a spiffy java applet: http://wright.grc.nasa.gov/WWW/K-12/airplane/incline.html.

1About the aerodynamic center, however, moment is a constant.

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