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I am trying to learn airplane dynamics. I made a 3D rigid body simulator using lift and drag equations but it does not behave the way I expect.

When I deflect the ailerons, it causes the lift forces from the left and right wings to differ, causing a net moment on the aircraft. This starts a rolling motion. When I return the ailerons back to the neutral position, the lift forces balance and the net moment is back to zero. The plane keeps rolling at a constant speed and does not stop. This makes sense from a physics perspective.

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However, when I am flying in a commercial simulator (RealFlight RC Flight Simulator) the plane stops rolling immediately after the aileron control sticks are released. I believe this is also how a real plane behaves.

What stops the plane from rolling? There should be a counter-torque applied to stop a rigid body from rotating. Where does this torque come from? Is it angular air resistance?

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    $\begingroup$ See aerodynamic damping $\endgroup$
    – Aditya Sharma
    Commented Jun 28 at 10:50
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    $\begingroup$ FYI, physical behavior much more accurate than RealFlight's, especially post-stall, is found in Michael Selig's seligsim.com. $\endgroup$
    – Camille Goudeseune
    Commented Jun 28 at 21:58
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    $\begingroup$ As noted in other peoples comments and answers, part of the answer is your simulator probably does not include Clp, also known as rolling moment coefficient due to roll rate. In addition to that, check to make sure Ixx is realistic (moment of inertia about the longitudinal axis) AND the commercial sim might have a roll rate command flight control system modelled. $\endgroup$
    – AeroAndy
    Commented Jun 29 at 1:13
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    $\begingroup$ This answer by @PeterKämpf should answer your question. It would also be helpful if you show how you calculate the increase/decrease of lift: without that it's impossible to find the errors in your model (if any)... $\endgroup$
    – sophit
    Commented Jun 29 at 6:31

2 Answers 2

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Consider the relative wind on each wing. The falling wing has the relative wind coming from in front and below and the rising wing has the relative wind coming from in front and above. In other words, the falling wing is at a greater angle of attack and so produces more lift, arresting the roll.

Note that a real plane has various other tendencies affecting roll. For instance, at high degrees of bank many planes will continue rolling into the bank even with neutral ailerons.

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    $\begingroup$ Yes, this is the answer. OP should modify his simulator to calculate lift separately for the left and right wing and for the tail. If roll or pitch rates are nonzero, taking the fuselage's velocity vector for lift calculations is simply incorrect. $\endgroup$
    – Rainer P.
    Commented Jun 29 at 13:46
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    $\begingroup$ This answer helped me pinpoint the problem. It was a bug in my simulation code. I was calculating the velocities at each wing but I unintentionally used the fuselage velocity to do the rest of the calculation. When I corrected this, the rolling stopped when the ailerons were back! $\endgroup$
    – takfuruya
    Commented Jul 1 at 12:23
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Even ignoring the airfoil, you can consider the wings to act like "fins" in that they resist rotation. Consider the case of an airplane-shaped object, with no forward speed, rolling. There will be air pressure applied to the top or bottom of the wing from the direction it is rolling, which slows it down. In your case the airplane has forward airspeed, but the "cross wind" being applied to the fins from their rotation still applies.

This effect on its own won't slow down the roll as much as the commercial flight simulator will, because there are other wing effects in practice (airfoil, angle of attack, wing sweep, wing dihedral, other control surfaces, fuselage shape) but this basic effect will at least get your plane to stop rolling... eventually.

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    $\begingroup$ Yes. See Aditya's comment+link about aerodynamic damping. $\endgroup$
    – Camille Goudeseune
    Commented Jun 28 at 21:59

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