Estimation of angle of attack / sideslip from flight test data

[kguthrie]

I'm working on doing some parameter identification for a small UAV model, but unfortunately due to the size of the aircraft, we are unable to measure alpha and beta directly. What we do have are X/Y/Z position and acceleration, velocity, roll/pitch/yaw angles, and roll/pitch/yaw rates. Is there an easy way to estimate the AoA and sideslip angle from these parameters? In my searches, I'm under the impression that since I don't have any measurement of the wind relative to the inertial frame, then I can't use any of my inertial frame or body frame measurements relative to each other to determine these angles. Is my thinking correct?

 

[boneh3ad]

How small is the UAV?

 

[kguthrie]

I'd say on the order of 5' wingspan. Maybe a bit more or less, but around there.

 

[boneh3ad]

So why not just install a small 5-hole probe on your UAV and measure directly? You can get/build some really tiny 5-hole probes.

 

[kguthrie]

That would obviously be ideal, but my understanding (with incomplete information about the issue) is that is not a preferred option. If it is possible to do without, even with the possibility of larger error margins, that would be preferred for this application. My thinking is that we will have to have some sort of probe to measure the angles due to my deduction in the first post, but I was hoping someone would be able to confirm (or disprove) that line of thought.

 

[enigma]

Do you have lift & drag vs. A of A curves for the UAV? If you did you could compare your acceleration vector with your attitude and fudge a lookup table to get an approximation, I think.

 

[Ignea_unda]

If I'm understanding what you have here, I believe that it would be a very simple problem to solve, though you would need 2 data points to calculate the AoA between.

DISCLAIMER: The main assumption I use from here on out is that you are flying through still air. If this is not the case, then my solution does not apply.

If you know your Pitch angle, and you know your positions between 2 locations, say position x1 and x2, where the corresponding world coordinates are (x1, y1, z1) and (x2, y2, z2) respectively, you can calculate the movement of your UAV. (y2-y1)/(x2-x1) will give you the slope of the longitudinal movement, aka the flight angle. Call this F_12. If the pitch stays relatively the same, then the average of Pitch at x1 and x2 can be used. Call this P_12 Then subtract the flight angle, from this. Then simply F_12 - P_12 = AoA_12.

If you apply a similar argument to your Sideslip problem, the solution should be very similar.

Please feel free to make not of any errors in this solution and let me know.

EDIT:

If you know your accelerations you can increase the accuracy of this solution by adding in an integration technique over the accelerations to get more accurate velocity measurements. If, however, you are in steady flight (for the most part) and are looking for approximate AoA and sideslip angles, this would be superfluous.

 

[kguthrie]

Yes, unfortunately it will be flown in a very windy environment.

 

[Ignea_unda]

In that case, enigma's idea might be the best. If the weight is constant (aka battery powered) then I can see this being a reasonable problem to solve. Otherwise, you will have to couple a calculation for fuel burn in as well, since that will change your lift required

Do you have lift & drag vs. A of A curves for the UAV? If you did you could compare your acceleration vector with your attitude and fudge a lookup table to get an approximation, I think.

So, if I understand correctly, it would be an application of
L = W + (W*a)/g

Where:
L is lift
W is weight
a is acceleration
g is gravity

Then knowing your velocity you would have the means to calculate the dynamic pressure, from which CL is easily obtained. An elegant solution, if I've understood it correctly, though I wonder how much error could be in such an approximation. I should think it would be a reasonably accurate method.