Can AOA be derived from pitch and FPV?

The presence of the Flight Path Vector (FPV) symbol on primary flight displays has been standard for decades by now. It adds to the pilot´s situational awareness, by showing “where the aircraft is going”. It can be a great help to fly a precise trajectory. Over the years, it has become entangled in some oversimplified explanations. One of them: The idea that the difference between pitch and FPV is equal to the angle of attack (AOA). In this article, we are going to digest the axes conventions and understand that the world is not so simple.

The famous picture (to be used with caution)

The picture below is straight from the ICAO Aircraft Upset Prevention and Recovery Training Aid (AUPRTA). It contains a very important limitation: The wind is assumed to be zero. Any pilot will know that the wind is rarely zero, so the natural question will be: What happens, if the wind is not zero? This is exactly what we are going to investigate.

Figure 1: ICAO AUPRTA picture. Note the critical assumption (top left): No wind. [1]

The picture is correct, as it assumes no wind. Unfortunately, this limitation is often overlooked. For completeness, it should be noted that the wing incidence is ignored too, as many manufacturers define AOA with respect to the longitudinal axis (see below).

The aircraft frames of reference

All physics and engineering students undergo some form of “drill program” to fully understand “frames of reference”. And for good reason: Any velocity, force etc. is only meaningful when expressed in the proper reference frame. Let us look at some typical aerospace conventions:

Ignore incidence angle: AOA against body x-axis

It will be clear to most readers, that the wing can have an angle of incidence (chord-offset from the aircraft´s longitudinal axis) and the chord may even vary span-wise. For this reason, many aircraft manufacturers simply define the AOA with respect to the body x-axis to establish a common reference.

The body frame

With its origin in the aircraft´s center of gravity, the body frame consists of the longitudinal (x), lateral (y) and vertical (z) axes [2]. It is shown red in Figure 2 below.

Figure 2: Aircraft body and wind axes with alpha and beta

The wind frame

Looking at the body frame, if we rotate the aircraft so that the oncoming wind is no longer “head-on”, we see two important angles: the angle of attack (AOA or alpha) and the angle of sideslip (AOS or beta) [2] [3]. This new frame of reference, which is oriented to match the oncoming wind, is called wind axes system. It is shown in yellow in Figure 2 above.

The path frame

If the airmass is not stationary, there will be a further displacement caused by the movement of the air mass and the resulting path will be different [2] [3] [4]. See Figure 3 below. Sometimes, a path-referenced axes system is defined. In German literature this is typically denoted with index “k”. We will call it “path frame”.

The local ground frame

If we want to relate to the local ground reference frame (for navigation), we can define another axes system (green in Figure 3), which will allow us to measure ground speed and vertical speed, as well as pitch and roll angles etc. [2] [3]. With the frames of reference sorted, we can now look at the calculation of the FPV.

How is the FPV calculated?

In most aircraft, the FPV is simply derived from ground speed and vertical speed, usually baro-inertial vertical speed [2]. It thus represents, where the aircraft is moving with respect to the ground. This is what it was invented for after all. The angle of the FPV with respect to the ground is called Flight Path Angle (FPA). Some aircraft displays incorporate a “reference-FPA” line to show the default approach angle.

Steady or maneuvering?

A further complication comes into play when we look at dynamic maneuvers. As the calculation of the FPV symbol takes some time, there will always be a “lag” during highly dynamic situations. The FPV is thus not meaningful in a highly dynamic situation.

Bringing it all together

Imagine now a situation, where an aircraft is climbing while experiencing a downdraft and a tailwind. This combination will make it obvious how all the “ingredients” come together. Figure 3 shows such a situation.

Figure 3: Bringing all together: Pitch, FPA, AOA and wind, based on [2] (aircraft symbol credit: [5])

Evidently, the difference between pitch and FPA is not equal to the AOA. It is only when the wind velocity is very small or oriented in a certain way, that the AOA can be approximated like this [2] [3] [4] [6]. This can further be understood by a simple example: Imagine, flying at your aircraft´s typical “minimum clean” speed in level flight. You will know the airspeed values for a typical weight and the corresponding AOA and pitch/N1 settings. Now imagine the same level flight, but in a downdraft. It will be clear that the airspeed will be the same, the AOA and load factor will be nearly the same for all practical purposes. The pitch/N1 however, will be higher.

Use cases of the “simplified” version

With the “full picture” in mind, we can now see under what conditions the “pitch-FPA” concept might be useful: If we are in steady horizontal flight (i.e. in cruise, no bank) and the wind consists of only a horizontal component. Under these conditions, the difference between pitch and FPA is indeed the AOA (again, ignoring incidence). This is often used during maintenance check flights and flight tests to cross-check AOA readings. A bank angle or a vertical wind component is enough to invalidate the concept. Knowing these limitations, it can still be useful to keep an eye on the difference between pitch and FPV for situational awareness.

References

[1]	ICAO, «AUPRTA,» 2025. [Online]. Available: https://www.icao.int/safety/loci/auprta/index.html.
[2]	R. Brockhaus, W. Alles und R. Luckner, Flugregelung, 3. Auflage, Springer, 2011.
[3]	J. Zeis, «Angle of attack and sideslip estimation using an inertial reference platform,» USAF Institute of technology, Ohio, 1988.
[4]	V. Véras und L. Góes, «SYNTHETIC AIR DATA - A COMPARATIVE PRACTICAL STUDY,» ICAS Congress , 2022.
[5]	Vecteezy, «Aircraft silhouette,» [Online]. Available: https://www.vecteezy.com/free-vector/airplane-silhouette. [Zugriff am 2025].
[6]	C. Raab und N. Fezans, «MEASURING THE ANGLE OF ATTACK – PRACTICAL CONSIDERATIONS FOR THE DEVELOPMENT OF FAULT DETECTION RESIDUALS,» ICAS Congress, 2024.