Angle of Attack from pitch, TAS, and vertical speed?

[wildwobby]

I had an idea recently that angle of attack can be calculated from the pitch angle minus the the climb angle. Since the pitch angle can be given by the AHRS in an aircraft with a G1000 or similar, and the climb angle can be calculated from TAS and vertical speed which the G1000 also knows... why can't the G1000 display angle of attack information (or can it?).

It seems it would be not require any additional equipment if it is calculated in this manner rather than measured with a separate AoA probe. What is the reason this is not done? I understand that the AoA is not very important in most GA aircraft where stalls are pretty easily predicted based on flying characteristics, stall horn, and speeds at various known configurations, but if the information is there, why not have the ability to display it?

Maybe because this wouldn't be measuring AoA directly, the error in the calculations to the AoA reading wouldn't be accurate enough to provide any meaningful information, but has it even been tried? It seems obvious enough that it would have been done before but I can't find anything online about it.

Anyone have any insight that cares to explain?

 

[Jim Logajan]

I see what the OP was thinking,

If you know exactly where the nose is pointed, and exactly where the plane is actually going you could figure out what angle the relative wind is coming from, at least in still air.

However here is another scenario where the calculating AOA would be difficult. I can hang on my prop behind the curve and get the ASI to indicate zero. That would sure throw a wrench at the computer trying to figure out TAS.

If your indicated speed is zero then AOA is pretty much a pointless value. Below is my quick attempt to work out the math. I was going to use Mathcad so it would look pretty, but my copy is on another computer. I think faster anyway with paper and pencil. Easy to scan this in, crop and shrink and upload the image. If you can't read my writing, basically the equation seems to be:

Theta_aoa = Theta_pitch - arcsin(vertical_speed/indicated_airspeed)

The "zero" for Theta_pitch can be any angle in space, really. But then the "safe" maximum value for Theta_aoa needs to be adjusted accordingly.

If there are mistakes in my math or assumptions I'm sure I'll hear about them!

 

[Jim Logajan]

I think what the OP was thinking is taking the wind calculations of the avionics does and turning the axis 90*

Thing is I bet if I slipped the plane the wind calculations would be wrong.

If my math in post 41 is correct, then AoA can be determined from three intruments most airplanes already have: pitch from artificial horizon, vertical speed indicator, and airspeed indicator. VSI is probably too laggy to make it viable.

(A slip would affect the airspeed indication.)

 

[Jim Logajan]

AOA affects airspeed indication as well.

Unless you are referring to some secondary affect (e.g. venturi affect), a pitot tube, being a dynamic pressure measuring device, would be affected only by the component of fluid velocity parallel to the tube. That is the only component we want or need, so I don't think there is any change needed in the computation.

 

[Jim Logajan]

Sorry, it's not correct. You're looking for true airspeed, not indicated. You'll also need pressure altitude and outside air temperature. The VSI measures rate of change of pressure altitude.

Each of these measurements introduces error. You are almost always better off making a direct measurement. That means a vane.

The wing, the pitot, and the vsi will be affected by those factors in close proportionate measure. So the ratios should remain the same roughly independent of pressure or temperature. That is why students are instructed to fly the same V speeds during landing regardless of altitude. If you use true airspeed instead, then you would need to know all the details you list. True airspeed just complicates things. If your airspeed indicator showed true airspeed your POH would need to show Vso, Vx, and Vy for different altitudes.

The OP posed a question of theory. That a vane can do AoA doesn't really address the question asked. I always find such questions interesting because it is intriguing to work out what would be needed to realize a new mechanism. For the objections listed, for example, calibrated lookup table and a simple program could probably be put together to provide the needed corrections.

 

[Jim Logajan]

Then why can I get a dead zero on my fixed wing airplanes ASI while in sustained strait and level flight if I crank my AOA up sufficiently?

What are you flying? For certified airplanes I didn't know the FAA allowed operation with an airspeed indicator showing an error over 3% or 5 knots in a level flight regime. Are you flying under 20 knots at high AoA?

 

[Jim Logajan]

Yes, the wing, pitot tube, control surfaces, etc., respond to calibrated (not indicated) airspeed. But the VSI does not, and neither does the altimeter. It directly measures the rate of change of pressure, that is, the true vertical speed in terms of pressure altitude. Not terribly accurately, either.

You are correct about VSI being a true airspeed indicator. My post was wrong on that point.

Then why can I get a dead zero on my fixed wing airplanes ASI while in sustained strait and level flight if I crank my AOA up sufficiently?

182, based on GPS GSs run both up wind and down I think my TAS is in the area of 25-30kts but that is only a guess.

Now, how would a computer figure out my AOA from that if it needs my TAS, and needs my IAS to figure that out?

Also while I am neither climbing or descending, calling that maneuver "level flight" is a bit of a misnomer:wink2:

In the first post you said the value came from an ASI, in the second you reference GPS ground speed. It is impossible for me to address your questions or scenarios since I am unclear at any given moment what measurement tools you are referring to.

how are you "given" airspeed and vertical speed when both pitot and static corrections are often a function of AOA ?

I'm not sure why having V[sub]IAS[/sub] being a function of AoA (basically V[sub]IAS[/sub](AoA) ) makes the math unsolvable. If the VSI measurements are tabulated with V[sub]IAS[/sub] and AoA is independently measured during calibration runs, a manufacturer of such a device should be able to construct a lookup table that a simple program could use - along with interpolation - to show your AoA.

That is basically my point, in my case just when AOA would be most useful the reliability of my airspeed data goes out the window

I believe Part 23 regs require accuracy to with 3% or 5 knots down to at least V[sub]S1[/sub]. It is true that dynamic pressure is proportional to V[sup]2[/sup] so low speeds often register as zero, but if you have any non-zero indications at all, they should at least be consistent.

Pragmatically speaking I think the concept of deriving AoA from the proposed values is unlikely to be viable, but it appears to my thumb-fingered math to be theoretically plausible.

For the record, Dynon AoA measurement equipment uses two pitot tubes mounted at different angles so different AoAs produce consistent differences in the pressures the two tubes see.

 

[Jim Logajan]

I took another look at the concept of computing AoA from TAS, and pitch attitude and this time I considered an extreme scenario. Consider an airplane with a 25 KIAS stall speed flying level (no altitude change) at 100 AGL and 50 KTAS with a vertical air current of 50 Kt. The airplane's pitch attitude would be something like 45° nose down yet the AoA would be the same +3° to +5° that it would have flying level at 50 KTAS without the vertical air movement.

So we have two situations where the AoA, TAS, altitude, VSI, etc are identical but the pitch attitude is radically different. This tells me that more information is needed to compute AoA.

Good point - as I understand the method, it needs to assume the air is at zero vertical velocity relative to the pressure altitude. The more the vertical air flow deviates from zero, the greater the error in computed AoA. I can't think of any simple way of correcting for that affect.