What exactly do you mean by angle of attack?
 

Since a wing stalls at high angles of attack, how is it possible for an airplane to perform a loop or similar maneuver without stalling?
 

We are often asked questions about the meaning of angle of attack, and I think the biggest reason for confusion relates to how the concept is typically presented in books. Many of you have probably seen a picture like the following, illustrating an airfoil cross-section of a wing at some angle of attack.

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Typical airfoil at an angle of attack

Note that the direction of the air stream is drawn as being level while the airfoil is tilted upward. Illustrations like these often lead people to believe that angle of attack is the attitude of the vehicle with respect to a level surface. However, it would be just as valid to draw the same image with the airfoil level and the direction of airflow inclined at some angle.

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Typical airfoil at an angle of attack

In addition, the same situation could be presented with neither the airfoil nor the airflow level, but both at some arbitrary angle.

Nevertheless, the airfoil remains at the same angle of attack in each of the three cases shown above. Why? The explanation is that angle of attack is not measured from a level plane but is defined as the angle between the airfoil chord line and the relative wind. The relative wind is a term often used in aerodynamics describing the direction at which a vehicle in flight meets the oncoming air stream.

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Typical airfoil at an angle of attack

A more technically correct term we can use in place of the relative wind is freestream velocity, often represented by the symbol V_¥ (pronounced "V infinity"). Freestream velocity is defined as the velocity of the airflow far ahead of the aircraft such that the air is not affected by the motion of the vehicle through it. Angle of attack, denoted by the Greek letter a (pronounced "alpha"), is defined as the angle between the chord line of the aircraft's airfoil and the freestream velocity vector, as illustrated below.

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Definition of angle of attack on an airfoil

It is very important not to confuse angle of attack with other commonly used angles in aviation. One of these common misconceptions is the confusion between angle of attack and angle of incidence. On many aircraft, like that drawn below, the wing is inclined at some angle to the plane's fuselage.

 

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Definition of angle of incidence on an airplane wing

We measure this angle between an axis running the length of the aircraft, called the longitudinal or x-axis, and the chord line of the wing airfoil and call this value the angle of incidence. The angle of incidence is usually fixed for any given aircraft and never changes.

Another key angle that is most often confused with angle of attack is called the aircraft pitch angle. Pitch angle is one of three angles that are called Euler angles. These three angles define the orientation of the aircraft in roll, pitch, and yaw with respect to a fixed reference coordinate system.

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Aircraft axes of motion

Most often, the angles are referenced to the surface of the Earth. The pitch angle is defined as the angle between the longitudinal axis of the aircraft and the horizon. Pitch is usually represented by the Greek letter q (pronounced "theta"). The following picture illustrates the definitions of angle of attack a, measured with respect to the velocity vector, and pitch angle q, measured with respect to the horizon.

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Definition of angle of attack and pitch angle on an airplane

Some further examples are also provided illustrating the key differences between these two important angles. The first set of examples shows three airfoils all at the same angle of attack but at different pitch angles. This situation demonstrates that a wing can easily be at the same angle of attack even when flying much different maneuvers, such as climbing or descending through a loop.

 

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Airfoil at constant angle of attack but different pitch angles

The second set of examples shows an airfoil at different angles of attack that are always equal to the pitch angle. This scenario is also quite common. During level flight, for example, an aircraft may cruise at different speeds. Lift varies with both speed and angle of attack, as demonstrated by the lift equation (Below). As speed decreases, therefore, angle of attack must increase to maintain the same lift and the same cruising altitude.

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Airfoil at constant pitch angle but different angles of attack

We hope that this explanation has cleared up any misconceptions you may have about angle of attack because understanding this subject is vital to understanding aerodynamics. Angle of attack is one of the most fundamental and important quantities in aerodynamics, if not the most important. Other values like lift and drag depend on angle of attack, as demonstrated by many of the topics we have previously written about. If you understand and can appreciate the significance of angle of attack, you will be well equipped to comprehend many of the other fundamental concepts of aerodynamics.

 by Jeff Scott,

 

 

The Lift Equation

 

The equation for lift is:

 

where

Variable	Units	Description
L	English: lb Metric: N	lift force
	English: slugs/ft3 Metric: kg/m3	air density Air density changes as a function of altitude, so the value of this variable depends on the height you want to find the lift at. You can find tables of the air properties at different altitudes in the appendices of any elementary aerodynamics book, and you can also compute these properties at the  Atmospheric Properties Calculator. All you need to do is enter the altitude you want and the script will compute the temperature, density, pressure, speed of sound, and other properties at that height. The other input values, like velocity and reference length, are not necessary unless you want to perform the rest of the calculations available.
V	English: ft/s Metric: m/s	aircraft velocity
Sref	English: ft2 Metric: m2	reference area For an airplane, the reference area is the area of the wing when viewed from overhead. This can be somewhat confusing because it includes the area of the wing if it were extended through the fuselage: For a helicopter, reference area is the rotor disk area, or the area of the circle through which the rotor blades turn:
CL	-	coefficient of lift This variable is a non-dimensional value that changes with speed as well as angle of attack and is dependent on the aircraft. Although CL is usually determined from wind tunnel experiments (or from computational methods that are beyond the scope of this page), the lift coefficient can be estimated fairly accurately for most aircraft. The following graph compares wind tunnel data for two actual aircraft. One set of is based on the Cessna 172, a low-speed plane with a single piston engine. The other set of data is for the BAC Lightning, a Mach 2 jet-powered British fighter with a wing sweep of 60°. Platforms of these aircraft are shown along with their lift coefficient results. Most aircraft will be behave similarly to the Cessna 172 while high-speed planes with short wingspans, like fighters, will more closely resemble the Lightning data. Unfortunately, I haven't been able to find any comparable results for helicopters.

 by Jeff Scott,