# What are the relations between Angle of attack and Calibrated Airspeed?

I would like to estimate Angle of Attack using trigonometric relations i.e AoA = arctan (w/u) airspeed components (i.e u, v, w). When I am considering body 'x' velocity ('u' component), is it necessary to use the Indicated Airspeed? Instead I would like to use Calibrated Airspeed. Is it acceptable? Could anyone please clear my doubt?

• Your title is misleading. The question is fairly clear and valid, but what most people will assume from the title is something like "In normal flight, how will change of CAS affect AoA?"
– Zeus
Commented Aug 24, 2021 at 1:14

You must use the same quantities for both speeds. Usually, this will be TAS.

As you see, you are going to use a ratio of speeds: w/u. This ratio must be dimensionless, and furthermore, the quantities must be "compatible". For such purposes, you can't meaningfully divide IAS by TAS (or CAS), or, say, altitude by flight level, even though they are both expressed in kt (or ft). They are just different physical quantities.

So, if you "would like" to use CAS for u, you must use CAS for w. How do you get it?

If you are trying to ascertain AoA that way on a real airplane in flight, you'll have difficulties measuring w (body normal airspeed). There is no sensor for it.1 And if you were to imagine some sort of a vertical Pitot tube, its IAS would have very different instrumental errors to the "normal" forward IAS, making these two IASes "incompatible", and you'd need to calibrate it extensively (and thus use CAS).

But the next catch is to check what CAS actually tries to express. Normally, the pilot (as well as the aerodynamicist) is interested in the "flight path" (total) airspeed rather than in the "body forward" airspeed. IAS measures the latter, but the standard CAS conversion may include correction for the AoA, amongst other things. If this is the case, you'd need to use arcsin instead of arctan (assuming you can get "CAS w").

In practice, one uses this formula to obtain AoA when solving equations of motion numerically. In this case, naturally, you have TAS everywhere as the primary quantity. You don't even need CAS nor IAS except for indication to the pilot, and perhaps as an input to autopilot or other equipment if you are simulating it.

1 Note the VSI measures vertical speed (in ground, not body frame), and it's not airspeed at all.

• Fine. I have few more doubts. 1) Are true airspeed expressed in x, y, z axis displayed/available on an airplane's computer? If I want to use both the u & w component from TAS, is it readily available during flight? 2) Suppose in the absence/failure of Pitot tube(s), what may be the other way to estimate AoA/AoS? Commented Aug 24, 2021 at 5:03
• @S.Prabhu, whether it is an air computer or old-fashioned gauges, you need to start from the sensors: what is actually measured? For most GA airplanes, you only have a Pitot tube and a static port (there are often more than one of the latter, but they are usually plumbed together as one input). This implies that you can only have something closest to "u component of IAS", which you (or the computer) can correct to "u component of CAS", and then with some assumptions about AoA, to "total CAS", and then considering the static data to "total TAS". You can't reliably have AoA from here.
– Zeus
Commented Aug 24, 2021 at 7:24
• As for your (2), it deserves a separate question. Generally, estimating data from incomplete observations is a big topic in itself. You can't have AoA in this case, but you can estimate it if you make some assumptions, the first of which is your aircraft performance. Say, if you know current weight and power setting, and flying straight & level, you can fairly reliably deduce AoA and CAS for this specific aircraft.
– Zeus
Commented Aug 24, 2021 at 7:33
• 1) I have seen in some articles that they estimated AOA using gps 'z' & 'x' velocities (represented in body frame). Will it work in real-time applications? 2) I noticed some aircrafts with multiple static holes on the fuselage. In general, how the static pressure input fed to adc? By taking average of all holes or individual/selected inputs considered? Commented Aug 24, 2021 at 8:08
• @S.Prabhu, these are all worthy questions that deserve better than be discussed in 500-char comments. For (1), it will be valid only in still air (and that's before we start on the question of accuracy). For (2), differently (I already mentioned the most common arrangement), but if you think you could use the difference between left and right to estimate sideslip, you are right.
– Zeus
Commented Aug 24, 2021 at 8:19

Calibrated airspeed is essentially Indicated airspeed with corrections applied, so that should be fine for what it sounds like you're doing.