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# Physics of flight: turning

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I've got my lift, gravity, thrust and drag equations sorted out. Now I'd like to be able to turn my plane. Could someone please explain to me how a plane changes its heading? I'm under the impression that the rudder is only used to make minor adjustments, but turning is handled by other control surfaces. I can see how raising and lowering opposite ailerons changes the roll of the plane, and I can see how if the plane had rolled to the left by, say, 45 degrees, the lift now has a sideways component. But what I'm missing is how the plane actually changes its heading. The only things I can think of are you either have to use the rudder, or "pull back on the stick" to "climb" at your 45 degree angle. But I don't think either of those are correct. Any help appreciated.

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I think that's correct. The lift generated by the wings is perpendicular to the surface. If you bank the plane, the lift force wont be vertical, but also pulling towards the side.

If you want to turn really sharp, you roll the plane 90 degrees, and pull hard on the stick. If you want to increase the rate of turn while not banking so much, use the rudder to make corrections in the horizontal plane.

Also, rolling 90 degrees means, you no longer have vertical lift, so you'll loose altitude. Rudder can compensate for that in a way.

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Ok, thinking of it a different way...

In the plane, pedals control the rudder, pulling back on the stick changes the pitch of the plane, and moving the stick side-to-side rolls the plane.

If I disabled the rudder, and locked the stick so it could only go left or right (no adjustment in pitch from the cockpit allowed) and while facing due North I rolled 45 degrees to the left, would the plane start to turn West, or would it continue to face North while drifting North-West?

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If you want to make it really nasty look for the gyroscopic effect (pitching an airplane with a spinning propellor creates a roll moment). That's just kind of annoying/stupid for most practical flight simulators though (but something I wasn't even aware of until recently).

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>> If you want to make it really nasty...

Nope. Not trying to make it nasty. Just trying to make my flight sim work.

I can make the plane roll but that doesn't change its heading (in my flight sim). I was wondering if that was correct behaviour or if I've missed some vital force or effect that would make the plane change its heading. Hence my question involving disabling rudders etc.

I just want to know if my flight sim is behaving correctly, or if it's possible to change heading by banking the plane - does physics / gravity / lift / something else change the heading if I'm flying along with my wings in 45 degrees away from horizontal because I rolled to get there, or do I continue facing due North (while drifting North West due to the horizontal component of lift)?

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When the plane is rolled to the side, the pitch axis also is no longer horizontal. So, move the elevator to cause the airplane to pitch about the pitch axis, and the pitch changes causes the nose to move to the left or right, effectively changing the heading. The more you pitch, the faster the turn. The more you roll, the more effective the pitch. Gradual turns require only a small amount of elevator deflection to generate a small amount of pitching motion. If the a/c pitches rapidly to a new direction, it still takes a while before the a/c will be moving in the new direction. The new thrust axis has to accelerate the a/c to change the velocity to be aligned with the new orientation of the fuselage.

Turning can be accomplished with the rudder also. It just might take longer....the rudder is not as efficient at turning as using ailerons to bank and elevator to pitch are. When the rudder is deflected, the fuselage is yawed to one side, and if you hold the rudder in place, the thrust (which is aligned with the fuselage) will be pulling in the direction the fuselage was yawed to. Eventually, the aircraft will become moving in that new direction. Turning with the rudder alone can be annoying. The aircraft is directionally stable. When the rudder is deflected, the a/c will, to begin with, stabilize roughly in the starting direction of travel...it'll find equilibrium in the direction it is already moving in...and will slide sideways for a while. This is called "sideslip." But, eventually, it's direction of motion will align with the thrust axis.

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Quote:
 Original post by timgradwellIf I disabled the rudder, and locked the stick so it could only go left or right (no adjustment in pitch from the cockpit allowed) and while facing due North I rolled 45 degrees to the left, would the plane start to turn West, or would it continue to face North while drifting North-West?

You would drift to the west (and loose altitude), but I'd say you would not incur a change of heading, unless there is some weird effect taking place that would generate a yaw effect. Maybe the interaction with gravity (not being aligned with the plane down axis anymore generate some instability) changes the plane's heading, but dont quote me on that.

If you pull on the stick, your heading will definitely change. I suppose it would be interesting to find out for real, or with someone who has practical knowledge.

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I achieved what I think you're looking for in my game by ensuring the wing forces are applied just in front of the aircraft centre-of-mass. This gives me a torque which when the aircraft is rolling leads to a change in heading. May need to 'trim' it in normal flight to remain level though.

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Basically it is just like you say. Rudder is only used for minor corrections or to fight crosswind in landing and take off situations.

By deflecting the ailerons you roll your plane. As soon as the wings are no longer horizontal you experience a lift force that is no longer directly opposing the gravity. Instead it points to the left or right as well as up. That is why you begin to drift sidewards and start falling as Oliii said.

Now put that in combination with what Aph3x said: The layout of the plane decides if this causes the plane to have remarkable changes in heading. The inertia tensor of the plane when viewed as rigid body decides how it reacts to the torque.

Finally, keep in mind that other flight sims you might yours comparing with use simplifications of the flight model to make their sim feel like what most players would think how an aircraft acts [grin]

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Quote:
 Original post by Aph3xMay need to 'trim' it in normal flight to remain level though.

That should be quite ok since all aircrafts need trimming depending on their current weight, velocity, winds, and maybe a hell of lot more influencing forces.

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