# Relativ Wind & Angle of Attack?

## Main Question or Discussion Point

Hi, im again toying with programming and simple flight movements and whilst researching ive read that the angle of attack is perpendicular to the relative wind or flow and NOT an aeroplane wing.

But isnt relative flow always in the oppostive direction of the planes direction vector? Meaning it is perpendicular to the wing?

Im struggerling with the CL and AoA.

Is the Angle of attack of a plane simply the angle of the wings?

Or is AoA the angle of the wing in relation to the relative wind, until the planes back in a state of equilibrium where its now heading in a new direction but the AoA is back at 0?

Or am i completly off target here?

Thanks
Andy

## Answers and Replies

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rcgldr
Homework Helper
Relative wind is the air speed using the velocity of the plane as a frame of reference. It's just as valid to consider relative plane velocity using the ambient air as a frame of reference.

Angle of attack is usually defined as the angle of the line from wing's leading edge surface to the wings trailing edge surface, relative to the direction of the plane with respect to the surrounding and unaffected ambient air.

Because of air foil shapes, some will produce positive lift with a "negative" AOA. To make it easier to compare air foils, sometimes "effective angle of attack" is used, which is defined so that zero angle of attack corresponds to zero lift.

By definition, lift is the component of aerodynamic force perpenicular to the direction of travel of the plane (using an air based frame of reference), and drag is the component in the direction of travel. Thrust may also have an offset angle relative to the direction of travel of a plane.

K^2
Science Advisor
Is the Angle of attack of a plane simply the angle of the wings?
No, the airplane rarely flies "straight forward". It's usually pitched slightly up or down. So the angle of relative wind to chord line of the wing varies. The chord itself can also have an angle relative to the airplane's body.

If you are actually interested in writing a flight simulation, you need to understand how the forces acting on the airplane produce an equilibrium pitch, and therefore equilibrium AoA for the airplane, and how the pilot can control this, because this is how the airspeed for the aircraft is actually adjusted. (Throttle is used in uniform flight to adjust rate of descent/ascent.)

At a minimum, you need to consider 4 aerodynamic surfaces. Left wing, right wing, horizontal stabilizer, and vertical stabilizer. That last one is fairly straight forward, but the first 3 play very important role in balancing the aircraft. The center of pressure of the wings is located behind center of mass and generate drag (against relative wind) and positive lift (perpendicular to relative wind). Because the force vector points up, the torque from wing lift tries to pitch the plane forward. To prevent that from happening, the horizontal stabilizer provides negative lift. It pulls the tail down. It also generates drag, same as any other surface.

If an airplane is traveling at target air speed, the torques from wings and horizontal stabilizer balance each other out, and the airplane continues at whatever angle of attack it currently has. If the airplane travels faster, the lift exceeds weight, airplane gets some positive vertical velocity, which means relative wind gets some negative vertical velocity. The angle of attack reduces, which means less positive lift on wings and more negative lift on tail. The aircraft pitches up and slows down. If the aircraft is traveling too slow, it begins to descend, pitches down, and speeds up.

So how do you adjust the target speed? That's where control surfaces come in. You don't just have a fixed wing. You also have ailerons, elevators, rudder, flaps, slats, and numerous tabs. If you do not need extreme precision, there is a very simple way to simulate control surfaces. You can simulate them as the entire surface rotating slightly, changing angle of attack. For small deflections, it's actually fairly accurate, so it will work for ailerons, elevators, and rudder at least. Also, for the basic simulation, you can forget about the fact that you have other control surfaces, and pretend that ailerons run the length of the wing. This way, you still have just the 4 surfaces mentioned earlier, each of which you can control the AoA slightly.

So what do you do? Well, if you want to reduce target speed, you need to make equilibrium position slightly pitched up. For that, you reduce AoA of horizontal stabilizer, increasing its negative lift. This corresponds to pulling on the yoke/stick slightly or adjusting the trim tab accordingly. And vice versa. If you want to speed up, you increase AoA of horizontal stabilizer reducing its negative lift.

The rest is straight forward. You adjust AoAs of wings to get rolls, and you can adjust AoA of rudder to make small corrections or to get coordinated turns. If you program drag correctly, that is, make sure it's related to AoA and lift, you should get all of the associated effects gratis. All in all, such simple consideration gives you a fairly descent flight sim. (I've written a few implementations of this, it works.)

Hi, thank you for you replies, i really do envy you guys who can have all the information like that on hand. I wish i did.

I for some reason am missing just that "thing" thats preventing me from my goal, im a computer programmer and ive been a apart of aviation from childhood till now (26! :) ) mainly with paragliding, flying lessons and RC plane and heli flying all my life.

But i just struggle to put the two together, thats the fustrating part.

More annoyingly, withing my programming im using a physics library, where all the complex physics are done, all you have are "bodies" of masses that you apply forces too and the rest sorts its self out.

But still, i cannot seem to forumulate the correct forces to apply to my bodies (wings, tail etc...)

Ill keep trying though.

If you have any more information please please throw it at me! :)

Andy

Hey Gibbon, how are you going with this project?

I'm attempting a similar thing using Cinema 4D and it's built-in dynamics engine. And like you I'm having a hard time calculating the correct forces on different parts of the plane. My plane seems to explode apart when it reaches a certain speed down the runway, lol.

One thing I can't get my head around is when calculating the forces on the tailplane, what velocity to use. I mean if the elevator pitch is changed, causing the tail to rotate around the cg, doesn't the tail have a higher relative airspeed than the cg of the plane? Sort of in the same way the moon is "dragged" through space by earth but is rotating around it at the same time? The flight equations I have don't seem to take this into account.

Anyway, here's one document linked from the JSBSim site that explained a few things I was stuck on, and notes the majority of the required forces and coefficient calculations:
http://www.dcs.shef.ac.uk/intranet/teaching/projects/archive/msc2006/pdf/acq05taa.pdf" [Broken]

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K^2
Science Advisor
Yeah, you are supposed to compute relative wind at the surface, so when an aircraft performs a roll, for example, the angle of attack for left and right wings will be different. Of course, the problem is that each surface is an extended object, so different parts of it might hit different relative wind. A good approximation, usually, is to simply compute relative wind at center of pressure of the surface. For better simulation, this approach would require you to break up large surfaces, like wings, into sections. But again, simple simulation with just one surface per wing wills till give you good enough results to test your system and make sure it works right before going to more complex geometries.

A while ago, I wrote aerodynamics for Grit Engine. You can try downloading it, and looking at the Lua scripts for the airplanes. It's not very clean, but it has everything I've mentioned in it. Might help you get unstuck on some of the issues.

Grit Engine.

K^2, thanks for you information.

The problem im having is calculating the relative wind vector, im having a hard time trying to find a solution to this.
I have my wing chord angle, but im not sure how to get the wings moving angle in order to find the angle between them.

Ill take a look at grit for your scripts, i presume they just come with the engine?

Edit:

Just taken a look over your code and it looks good. Althought, im still unsure how AoA is calculated?

Could you take the time to explain it to me? I get confused when it comes to the coords system i think.

Thanks
Andy

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K^2, do you know which Grit file your code is in? I looked through the SVN but couldn't find it.

Also, what about if the plane is in sideslip or even a turn? Am I correct in thinking you just use the relative wind components that are perpendicular to the wing's leading edge? So say the wing cord points in the Z-axis direction and the velocity vector of the wing is <-10, -20, 100>, relative to the wing. Do you just "zero out" the x-component and use <0, -20, 100> to calculate the speed of air over the wing, and the AoA?

This seems to make sense since if the wind was coming from the front (no side component) it would give the same result, and if the wind was directly from the side their would be no vector component in the "forward" direction and hence no lift generated.

Is this right?

Edit: I just found the code and it has these lines:
Code:
pvel = speedx * (body.worldOrientation * vector3(0,-1,0)) + speedy * (body.worldOrientation * self.actionVectors[s])
speed2 = speedx*speedx + speedy*speedy
It's only using the x & y vector components. So does that mean I was correct with the above mumbo jumbo?

Also, the line:
Code:
aoa = -dot(norm(pvel), body.worldOrientation * self.actionVectors[s])
How does this give you the signed AoA? Doesn't the dot product give only the magnitude of the angle?

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