Angle of Attack
Angle Of Attack is a staple of military aviation that seems to have been ignored by much of the civilian world. Too bad, AOA can save your life when the chips are down. Most pilots know that their wings stall at a particular angle of attack, depending on flap and other high-lift device settings. But years of simulator training has put the focus on airspeed which is only a by product of AOA.
The Aerodynamics of AOA
As an airfoil cuts through the relative wind, an aerodynamic force is produced. This force can be broken down into two components, lift and drag. The lift produced by an airfoil is the net force produced perpendicular to the relative wind. The drag incurred by an airfoil is the net force produced parallel to the relative wind.
The angle of attack is the angle between the chord line and the relative wind.
AOA Impact on Lift
The coefficient of lift is a measure of how much lift the wing can produce and can only be changed by changing the shape of the wing or the angle of attack at which it cuts through the relative wind. We can change the shape of the wing using flaps, slats, or other similar leading and trailing edge devices. We change the angle of attack using our flight controls and, in some cases, power settings.
For any given wing, an increase in angle of attack leads to an increase in the coefficient of lift up until the point it doesn't. In the graph shown, we see that a typical cambered wing produces a higher coefficient of lift but when it gets to its critical angle of attack, the lift drops off quickly. A symmetrical wing, on the other hand, produces less total lift but when it drops off, it drops off slowly.
[Dole, pg. 36] The importance of AOA in determining aircraft performance cannot be overemphasized. We have discussed stall AOA, but these facts are of equal importance: an aircraft has its maximum climb angle at a certain AOA, will achieve maximum rate of climb at another AOA, and will get maximum range at still another AOA.
Figure: Development of a Boundary Layer on a Smooth Flat Plate, from [ATCM 51-3, pg. 53].
To understand airfoil performance at high angles of attack, one must first consider the airflow at just about any angle of attack. When an airfoil passes through an airstream, the particles of air right next to the skin of the airfoil are pulled along at the same speed of the airfoil. As you get further away from the skin of the airfoil, the particles are less apt to "grab on" to the wing and at a certain distance they do not "grab on" at all. This layer of air, the particles that grab on to the wing completely to those that don't, is known as the boundary layer.
The behavior of the boundary layer determines, in great measure, the maximum lift coefficient and the stalling characteristics of the airfoil.
[Dole, pg. 39] The beginning of airflow at the leading edge of a smooth airfoil surface produces a very thin layer of smooth airflow. This type of airflow is called laminar flow and is characterized by smooth regular streamlines. Fluid particles in this region do not intermingle. As the airflow moves back from the leading edge, the boundary layer thickens and becomes unstable. Small pressure disturbance cause the unstable airflow to tumble, and intermixing of the air particles takes places. This type of airflow is called turbulent flow.
Adverse Pressure Gradient
As we saw in our discussion of lift, the pressure over and under the wing decreases as the velocity of the air increases. The pressure differential over the top and under the bottom of the wing generate the aerodynamic force that becomes lift and drag.
The point of minimum pressure divides the airfoil into two. Forward of that point the pressure gradient is helping to produce lift and, to a lesser degree, a pulling force forward. Aft of that point we have what is called the adverse pressure gradient. The pressure here contributes to drag and a separation of the air flowing over the wing. More on that below.
As the angle of attack is increased, the point of minimum pressure moves forward and the size of the adverse pressure gradient increases. Three things happen as a result:
- The lift component of aerodynamic force increases, up to a point.
- The drag component of aerodynamic force increases.
- The turbulent flow area increases, encouraging separation of the boundary layer.
The friction along the airfoil tends to reduce the velocity of the air particles right next to the surface to zero, forming a thin boundary layer of air. The adverse pressure gradient tends to expand the boundary layer to the point the air particles separate and are neither flowing with the relative wind or sticking to the airfoil.
[Dole, pg. 43] The result of the air slowing creates a stagnated region close to the surface of the object. Airflow from outside the boundary layer will overrun the point of stagnation and cause the the boundary layer to separate from the surface. A flow reversal results, and the airflow moves forward, lift is destroyed, and drag becomes excessively high.
The airflow separation can happen under conditions of slow speed flight, high-G maneuvering, or high speed shock waves. All three were of concern to us in the supersonic T-38, the first two are concerns for all jet aircraft. More about this in the sections Low Speed Flight, and Operating Flight Strength (V-g / V-n Diagrams).
While we are on the subject of AOA, however, it may be helpful to look at two aircraft systems for detecting and displaying AOA to the pilot.
Example AOA System: T-38
We aren't in the business of flying supersonic on razor thin wings, but this illustration from the T-38 manual gives an excellent primer on AOA versus airspeed.
[1T-38A-1, pg. 4-18] The [ARU-26/A AOA] indicator presents AOA as a percentage of maximum lift AOA. The dial is calibrated in unites of .1 counterclockwise from 0 to 1.1. Each unit represents approximately 10% of aircraft lift, from 0% and 0 indication to 100% at 1.0 indication. Three preset fixed indices and two colored arcs on the dial indicate the following:
- .18 White Index — Maximum Range (1-G flight)
- .3 White Index — Maximum Endurance (1-G flight)
- .6 White Index — Optimum Final Approach at 3-o'clock Position (1-G flight)
- .9 to 1.0 Yellow Arc - Buffet Warning
- 1.0 to 1.1 Red Arc - Stall Warning
Normalized Angle of Attack
Gulfstream calls their displayed angle of attack value to be a "normalized angle of attack," which is just a way to confuse things a bit. The normalized AOA is simply the way everyone else refers to AOA on the pilot's meter: 1.0 is stall, 0.0 is zero G. They explained it thusly in a mishap report:
Figure: G650 pitch limit indicator, from NTSB AAR-12/02, figure 2.
[NTSB AAR-12/03, ¶1.1] Normalized AOA is a measure of the usable AOA range of an airplane, with a normalized AOA of 1.0 corresponding to the reference stall AOA in free air and a normalized AOA of 0.0 corresponding to the zero-lift AOA in free air. This figure is presented for information purposes only and is not intended to depict the flight conditions on the day of the accident.
Example AOA System: G450
Not all modern aircraft include an AOA display for pilot use in flight, only using the information for stall warning protection. The CL-604, for example, has an AOA indicator marked "Not for use inflight." The G450, on the other hand, does include an AOA indicator on the Pilot's Flight Display. The manual, however, is silent on the subject of "normalized AOA." It appears to be their term converting the AOA in degrees to the 1.0 scale.
How to Use AOA
Most civilian aircraft seem to be silent on the subject of actually flying by reference to an AOA indicator, so I certainly can't recommend you do that. But I do recommend you keep an eye on it and see what it normally indicates for various phases of flight. I've done that for the G450 and also present findings for Cessna Citations.
- Takeoff Rotation: 0.2 to 0.3
- Cruise (0.80 Mach): 0.15 to 0.20
- Cruise (LRC): 0.30
- Pattern: 0.40
- VREF: 0.50
A reader with considerable experience with the entire line of Cessna Citations offers the following:
- V2 ≈ 0.7
- VREF, best glide, VX, maximum endurance ≈ 0.6
- Maximum Range ≈ 0.35
Armed with this information, you can have a back up plan if the airspeed indicators quit or if there is a disparity you cannot otherwise explain.
Portions of this page can be found in the book Flight Lessons 1: Basic Flight, Chapter 12.
14 CFR 25, Title 14: Aeronautics and Space, Federal Aviation Administration, Department of Transportation
Air Training Command Manual 51-3, Aerodynamics for Pilots, 15 November 1963
Connolly, Thomas F., Dommasch, Daniel 0., and Sheryby, Sydney S., Airplane Aerodynamics, Pitman Publishing Corporation, New York, NY, 1951.
Davies, D. P., Handling the Big Jets, Civil Aviation Authority, Kingsway, London, 1985.
Dole, Charles E., Flight Theory and Aerodynamics, 1981, John Wiley & Sons, Inc, New York, NY, 1981.
FAA-H-8083-15, Instrument Flying Handbook, U.S. Department of Transportation, Flight Standards Service, 2001.
Gulfstream G450 Airplane Flight Manual, Revision 35, April 18, 2013.
Gulfstream G450 Aircraft Operating Manual, Revision 35, April 30, 2013.
Hage, Robert E. and Perkins, Courtland D., Airplane Peformance Stability and Control, John Wiley & Sons, Inc., 1949.
Hurt, H. H., Jr., Aerodynamics for Naval Aviators, Skyhorse Publishing, Inc., New York NY, 2012.
NTSB Aircraft Accident Report, AAR-12/03, Crash During Experimental Test Flight, Gulfstream Aerospace Corporation GVI (G650), N652GD, Roswell, New Mexico, April 2, 2011
Technical Order 1T-38A-1, T-38A/B Flight Manual, USAF Series, 1 July 1978.