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

[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!

 

[Skylane81E]

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.

 

[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.)

 

[Skylane81E]

AOA affects airspeed indication as well.

 

[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.

 

[JHW]

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.

A statement from a 100-level fluid mechanics textbook. But not true in real life. That's why you see all sorts of regulatory verbiage around pitot tube accuracy. For example, some aircraft have weight restrictions as part of their RVSM certification to keep the pitot and static ports operating in an acceptable range of angles. It's also why you develop a table of pitot tube correction factors as part of the test flying of a new aircraft type.

 

[MAKG1]

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.)

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.

 

[Skylane81E]

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.

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?

 

[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.

 

[wildwobby]

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?

Because indicated airspeed is not the same thing as true airspeed. Just because the ASI reads zero doesn't mean squawt. Thats the reason why there is calibrated airspeed. The ASI reading (indicated) comes directly from pitot and static pressure differential. At large angles of attack especially, the pressure at the hole of the pitot tube is not stagnation pressure and you are not getting a pressure representing the true velocity of the aircraft.

I'm pretty sure modern airliners have multiple pitot tubes at various angles and a flight computer that compensates for sources of error. As I understand it though, the static error is far greater than the pitot error at different angles of attacks.

 

[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?

 

[skylanerg]

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?

I'm familiar with the 0 KIAS slow flight manuver in the 182. Is that peculiar to the 182? What about the 206 or 210? Or Piper and Beech models?

 

[MAKG1]

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.

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.

 

[Skylane81E]

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?

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:

 

[flyingron]

Not falling vertically. Flying vertically. Thats the error in this line of thinking. Relative wind has nothing to do with the relative angle of flight vs the ground.

I never said it did. However given airspeed and vertical speed you can compute what the relative wind is and knowing the pitch angle and the angle of incidence you can compute the angle of attack.

 

[bqmassey]

I never said it did. However given airspeed and vertical speed you can compute what the relative wind is and knowing the pitch angle and the angle of incidence you can compute the angle of attack.

Only if you had some way to measure vertical speed relative to the air around you.

 

[JHW]

I never said it did. However given airspeed and vertical speed you can compute what the relative wind is and knowing the pitch angle and the angle of incidence you can compute the angle of attack.

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

 

[Skylane81E]

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

 

[flyingron]

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.

I made that observation already.

 

[flyingron]

Not falling vertically. Flying vertically. Thats the error in this line of thinking. Relative wind has nothing to do with the relative angle of flight vs the ground.

No error in my line of thinking. You'll have to define what you mean by "vertical." The statement was the nose pointed at the ground. If the aircraft is also traveling vertical (no horizontal component), then the AOA = AOI and on any aircraft I'm familiar with, that is below the critical angle. If you pull the yoke, something's got to give.

 

[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 VIAS being a function of AoA (basically VIAS(AoA) ) makes the math unsolvable. If the VSI measurements are tabulated with VIAS 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 VS1. It is true that dynamic pressure is proportional to V2 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.

 

[N801BH]

Good god people.........................

Just fly the plane.......

DON'T stare are AOA gauges.....

Glance at the ASI.. if it looks good then keep looking outside, if the ground is coming up TOO fast,, pull back..... if the ground is getting smaller,,, push forward......

 

[Skylane81E]

I used both GPS and ASI data,

The GPS was needed to estimate my speed cuz the ASI quit functioning due to the AOA. Runs both up and downwind were also needed

Anyway given this data can you figure my AOA?

ASI 0
VS 0
Temp any
GS 30kts
Track any
Heading any
Pressure altitude any
Actual altitude any

From what the plane would know it couldn't calculat my TAS and as such would not be able to figgure AOA either. Reliable airspeed data is going to be required. And at high AOA you aren't going to get it

 

[bobmrg]

No. A sudden change in attitude, such as trying to pull out of that dive quickly, will cause a stall. No horizontal motion is necessary.

Something that I read a long time ago fits in here. As I recall, WWII torpedo bomber pilots dove as vertically as possible and pulled many G's after dropping their torpedos. Some stalled at low altitude trying to pull up sharply and sacrificed their lives for us. If true, it's the best argument for "any attitude, any airspeed."

Bob Gardner

 

[wabower]

My uncle Jim's fighter Mustang squadron was based with a P-47 group for a while in Italy. He told the same story about the Jugs mushing into the ground during their bomb runs.

Something that I read a long time ago fits in here. As I recall, WWII torpedo bomber pilots dove as vertically as possible and pulled many G's after dropping their torpedos. Some stalled at low altitude trying to pull up sharply and sacrificed their lives for us. If true, it's the best argument for "any attitude, any airspeed."

Bob Gardner

 

[gismo]

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.

 

[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.