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I am creating a flight simulator and I need to implement lateral and longitudinal stability. Roll stability is now working because I am computing the lift of each wing independently. But yaw stability is confusing to me.

What is the main source of yaw stability : is it the weathervaning effect of the tail or is it the sweep angle of the wing ? Which one is the more responsible of stability ?

When I implement weathervaning effect by applying the wind at a certain point of the tail, the problem is that the oscillation will continue and the plane will always overshoot as he is not losing any of its angular velocity. So it will never align into the wind but will keep overshooting from negative to positive angle.

So my other question is : in real life, what does prevent the plane to overshoot wind direction? When I just apply some scaled-angular drag value to the plane, it helps to dampen the oscillations, but the plane is wayyy to slow to align into the wind and thats just aweful to controll and not realistic at all. So I guess angular drag is not the answer why oscillations stops in real life. There must be another force depending on wind speed or I don't know...

And longitudinal stability is also confusing to me. I know that it depends on the position of CG, CL and the downforce generated by the tail horizontal stabilizer. But what about the weathervaning effect ?? Isn't it the main force that explains why the plane align into the wind on its pitch axis ?

As you can see I am a bit confused. I already looked many websites and I mainly understood how stability and flight dynamics work, but as I am working on a simulation, I need some equations to implement, and some concrete values to understand which forces are bigger than others.

Thank you !

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  • $\begingroup$ One thing to consider is that oscillations are an issue in real aircraft and many have yaw-dampers specifically designed to actively combat this situation. Depending on the aircraft you're modeling, you may not get a purely aerodynamic solution to dampening and the plane may continue to oscillate no matter how you model it. $\endgroup$
    – FreeMan
    Apr 23 '20 at 17:26
  • $\begingroup$ Thanks. But as I said, I am making a flight simulator and the plane I am modeling is a Pitts Special. As an aerobatic plane I am waiting for it to stop oscillating, so I am searching for a way to implement this $\endgroup$
    – Anselme
    Apr 23 '20 at 17:29
  • $\begingroup$ Roll and yaw are heavily coupled in conventional aircraft, it makes little sense to discuss roll and yaw stability as separate phenomena. The longitudinal modes can be resolved separately, but roll and yaw share modes. For more information, see here: courses.cit.cornell.edu/mae5070/DynamicStability.pdf $\endgroup$ Apr 23 '20 at 17:55
  • $\begingroup$ Maybe it makes a little sense to discuss them at separate phenomena, but as I said, I am trying to implement a COMPUTER SIMULATION. That means I write code, so I need concrete forces and torque to apply, so I am not searching for some explainations of how we can represent the damper phenomena, I am trying to return to the roots and apply the forces that CAUSES them. We can simplify the problem, and I would like to simply know what causes a weathercock to not overshoot wind direction, and why it dampers pretty quick into wind direction. If I can modelize that I'll be good. $\endgroup$
    – Anselme
    Apr 23 '20 at 18:19
  • $\begingroup$ @Anselme the source I linked has a thorough discussion fo the physics involved, your model should end up looking like that. Implementing it on a computer does not make much of a difference, if anything, it adds complexity due to the discretization, so I suggest you look at the analytical approach first. $\endgroup$ Apr 24 '20 at 13:27
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Wing sweep does affect yaw stability, but all planes with a vertical tail will "weathervane" into the wind. It seems you are on the right track considering angular drag as a mechanism of stability, angular lift works even better. A vertical stabilizer can act as a vertical wing. Symmetrically, it can generate lift against either deflection.

Secondly, the "overshoot" is a real concern in design, but will be a function of weight as well as "angular drag". Much harder to stop a piano on ice compared to a light cardboard box. A tail will typically be light, pivoting around the center of gravity. Ample tail area will make it easier to control.

Finally, as far as "damping" is concerned, one must realize the "viscosity" of air will resist motion as well. Once a force is removed, drag will help it slow to a stop, so the opposite "correcting force" need not be as large.

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  • $\begingroup$ Thank you very much. The problem is when I compute angular drag, it's always the same at high speed and low speed. If I want the tail to align quick into the wind without too much oscillations, then it forbids any quicker rotations even on 0 airpseed, not allowing me to do Lomcevak for examples. That's why angular drag seems not realistic at all and it does not seem to be the way to achieve it. Maybe considering lift could do the trick, I will try it. Yeah, of course overshooting depends on weight but that does not tell me how to compute a realistic weathervane effect $\endgroup$
    – Anselme
    Apr 23 '20 at 15:45
  • $\begingroup$ Here is how I want it to work : get the tail align quick into the wind without too many oscillations, like on a real aircraft, but allow for some realistic aerobatics like Lomcevak for example. Any angular drag value high enough to dampen the yaw oscillations after a perturbation are completely killing the momentum of the plane on its yaw. I don't know if I am clear enough $\endgroup$
    – Anselme
    Apr 23 '20 at 15:48
  • $\begingroup$ @Anselme I'm seeing using lift (from rudder deflection) yawing the tail. "Angular drag" will stop rotation at a certain deflection point. Angular resistance to the yawing force is 0 at first, increasing as more tail area "comes into the wind". So, angular resistance increases and yaw "lift" decreases as tail "weathervanes". Even with rudder still deflected, yaw and resistance to yaw forces reach zero, and yaw stops. $\endgroup$ Apr 24 '20 at 12:27
  • $\begingroup$ The only other consideration is the resistance to movement of the air itself. I would make sure I'm not modelling movement through water, but air "viscosity" will help dampen any movement quickly once forces balance to zero. The "flutter" case should only occur if the tail assembly is elastic enough to bend and store energy as a spring. $\endgroup$ Apr 24 '20 at 12:33
  • $\begingroup$ Thank you. I don't know if what I am doing is right, but I did lilke "quiet flyer" told me to do. See the answer below My simulation works quite well now and the yaw dampens well. What I am doing is computing the lift of the vertical tail, AND the lift of the fuselage side. As they are not on the same 3D point they don't have the same AOA, thus it creates a counter-yaw that helps dampen. $\endgroup$
    – Anselme
    Apr 24 '20 at 13:36
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Rolling is also one of the main source of yawing moment. Because when aircraft is rolling, lift of the wings is not equal to each other. This causes different induced drags for each wing. Drag difference of the wings generates yawing moment. You need to consider that one also.

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  • $\begingroup$ Do you have any sources to back up your claims? $\endgroup$
    – dalearn
    Apr 23 '20 at 15:23
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    $\begingroup$ It is not a claim. It is pure aerodynamics. You can refer any aerodynamics text book or faa flight manuels for beginner pilots. $\endgroup$ Apr 23 '20 at 15:25
  • $\begingroup$ Thank you for your answer, yeah I am already taking into account this effect as I said, each wing lift is computed separatly. But that does not answer my question $\endgroup$
    – Anselme
    Apr 23 '20 at 15:40
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There is an aerodynamic damping effect in yaw just as there is in roll. Imagine that the whole aircraft has somehow become yawed 10 degrees to the flight path, and then whatever torque has caused this to happen has vanished. The fin will generate a yaw torque that makes the plane start to yaw back toward the flight path, but as it yaws, the rotational velocity changes the local linear velocity of different points on the fuselage, which changes in the "sideways angle-of-attack" of the forward parts of the fuselage in a way that decreases the net yaw torque on the aircraft. Specifically, the yaw rotation will increase the "sideways angle-of-attack" of the forward parts of the aircraft and decrease the "sideways angle-of-attack" of the aft parts of the aircraft, including the vertical fin. At some high enough rotation rate, the net yaw torque would be zero even though the fin is still "feeling" a sideways component in the airflow.

One way to envision is this is to understand that in steady turning flight, whenever the aircraft's yaw and pitch rotation rates are stable and fully synchronized to the turn rate, we can envision the "relative wind" or free-stream airflow to actually be curved to follow the path of the turn, so that different points on the fuselage cannot all have zero "sideways" angle-of-attack, nor can they all have the identical pitch-wise angle-of-attack.

In short, the rotation of the aircraft in the yaw axis causes different parts of the aircraft to be moving through the airmass in different directions at any given instant in time, so that "yaw strings" attached to different points on the aircraft would be angled in slightly different directions. To read about how one pilot takes this into account in actual practice, see the Soaring magazine article Circling the Holghaus way by Richard H. Johnson. Links to some other articles discussing the curvature of the relative wind in turning flight are embedded in this ASE answer.

As for your question about the "weathervane effect" in the pitch axis, you could say that the balancing act between the wing and the horizontal tail is sort of like a "weathervane effect". Airfoils generally generate a nose-down pitching moment. Since apparent "center of lift" of the wing (including the effect of this nose-down pitching moment) is usually not at the CG of the aircraft, the point where everything comes into balance will usually not be the point where the horizontal tail is generating exactly zero lift.

Naturally, there is an aerodynamic damping effect for pitch rotations as well. The difference in angle-of-attack between the wing and the tail required to command a given angle-of-attack of the wing in turning flight will be different than in linear flight, especially at steep bank angles where the turn mostly involves pitch rotation. Again this is due to the fact the pitch rotation creates a local change in angle-of-attack that varies from one point along the fuselage to another. Generally we have to have the stick further aft to command a given angle-of-attack of the wing in turning flight than in linear flight. This is effect is especially pronounced in slow-flying aircraft like sailplanes. If the fuselage could "bend like a banana" to match the curving relative wind in the turn, this effect would vanish.

The idea of a "curvature" in the free-stream "relative wind" is really just another way to look at aerodynamic damping due to rotation about the pitch or yaw axes, while aerodynamic damping due to rotation about the roll axis can be viewed as a being due to a "twist" in the free-stream "relative wind".

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  • $\begingroup$ Thank you again. "There is an aerodynamic damping effect in yaw just as there is in roll." I managed to get this roll damping effect by computing and applying lift on each wing independently. And that worked perfectly showing the simulation is accurate. However I am not understanding your explaination. Or maybe I did... Are you saying that when I am yawing RIGHT, the right wing looses speed, so looses lift, so looses drag, so get quicker, while its the opposite onthe LEFT wing ? Is that supposed to dampen my yaw perturbations ? $\endgroup$
    – Anselme
    Apr 23 '20 at 16:00
  • $\begingroup$ I am thinking of an effect coming from the fuselage itself, but the change in drag from each wing might also play a role. $\endgroup$ Apr 23 '20 at 16:01
  • $\begingroup$ I am not sure to understand why those different yaw directions on different points of the fuselage would help damper the yaw moment... I am reading the link you gave me but still... $\endgroup$
    – Anselme
    Apr 23 '20 at 16:31
  • $\begingroup$ Added fourth sentence in first paragraph, may help. $\endgroup$ Apr 23 '20 at 16:35

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