top of page
  • Andreas

The alpha-beta trap

Updated: Apr 27, 2020

As pilots we have to ensure many things, but in particular we have to ensure the proper attitude (our own and the one of the aircraft we fly). Accurate attitude flying is key to successful instrument flight and so we care a lot about pitch and roll angles. We maneuver the aircraft with respect to a certain frame of reference (e.g. the local horizon), on some days more accurate than on others.

With all the great emphasis on pitch and roll control, it is important to realize that the aircraft stability and control properties are governed primarily by the relative relationship between the aircraft axis and the wind axis [1]. In aerospace engineering, these two coordinate systems are widely used and their relationship is often characterized through so-called Euler-Angles [2]. Engineers use these to transform quantities from one frame to the another. This is quite an essential operation, as many quantities are measured in one frame and need to be known in a different one. The mental picture of two frames that change their relative relationship can be very helpful in understanding the aircraft reaction to certain flight conditions.

Euler angles and coordinate transformations are usually not part of pilot training, so it is helpful to think of the two frames as being related though alpha (the angle of attack) and beta (the angle of sideslip). The following Figure 1 aims to visualize this:

Figure 1: Relation of aircraft axis and wind axis through alpha and beta

The red axis represent the aircraft frame of reference, the yellow axis are the wind axis. They are related through alpha and beta. Obviously a proficient pilot will keep track of these two angles, even when some flight deck designers make it really hard to do so….

And here it comes, the trap that the title is advertising: Not only are alpha and beta important on their own, their combination is equally important. The flight test envelope is probably smaller than one would tend to think, and many combinations of alpha and beta are either only examined in the wind tunnel, CFD simulation or simply extrapolated [5] [6].

Figure 2: Example of alpha (angle of attack) and beta (sideslip) envelope [3]

Fairly small is the range that has been flown with the real aircraft during type certification. There is a great deal of information available on the dangers of using large rudder inputs at high angles of attack, as this produces a combination of high alpha and beta [4] [7] [8]. Apart from the real world, this is equally important when drawing conclusions from a simulator session. With the advent of Upset Prevention and Recovery Training (UPRT), many airline pilots are going through “unusual phases of flight” in the simulator. This is of course a vital piece of training, but we should keep in mind the significant limitations of simulator training in that context. The physical feedback is often not realistic, as most flight simulators cannot provide sustained acceleration [3]. Likewise, the simulation model can generally be divided into three areas of confidence [3] [5]:

High: Model has been compared with flight test data

Medium: Model is based on wind tunnel/CFD data

Low: Extrapolation of wind tunnel/CFD data

Compare these three areas of confidence with Figure 2. This makes it quite clear that the simulator model may be significantly inaccurate if simultaneous high alpha and beta are encountered. It is worth noting that the confidence of the model is generally not degraded for roll or pitch excursions alone, as long as alpha and beta remain within limits [3]. This is why the frame-of-reference mindset is important.

Figure 3: Full-Flight simulator: Excellent tool, if it's limitations are well-understood.

State-of-the-art simulators provide a nice alpha-beta plot and make it obvious if the respective envelope has been exceeded [3] [6] [7]. Some regulatory agencies require this very capability for UPRT [5]. It is certainly good practice, to keep an eye on the alpha-beta plot, even when not performing UPRT.

So the best way to avoid the alpha-beta trap is to be aware. Be aware of the relationship between the aircraft axis and the wind axis and having Figure 1 and 2 in mind. If someone is proposing a new “recovery method” and claiming that “it worked in the simulator”, the alpha-beta plot is probably a good place to start the critical analysis…



[1] Torenbeek & Wittenberg, Flight Physics, Springer, 2009

[2] M. V. Cook, Flight Dynamics Principles, Elsevier, 2007

[3] Upset Recovery Industry Team, Airplane Upset Recovery Training Aid, Rev 2, 2008

[4] Wainwright, Airplane Upset Recovery – A test pilot’s point of view, Airbus FAST ed. 24, 1999

[5] FAA, National Simulator Program, FSTD Qualification Guidance Bulletin 11-05, Feb 2018

[6] Samani, presentation at the ICAO LOC-I Symposium, Nairobi, 2015

[7] Ransbury, Technology in Airline Jet Upset Training, Skiesmag, 06/2015

[8] Bolds-Moorehead et al., Stalling Transport Aircraft, The Aeronautical Journal vol. 117, issue 1198, Cambridge University Press, 2016

bottom of page