I am currently working on a flight simulator and I try to simulate every actions that applies on my plane. As you know, planes tend to orient themselves into the airflow direction, because of the "weathervaning effect". It's the same effect that explains why arrows stay straight in the air. So let's take an arrow for example, with an angle of attack of alpha degrees.
The wind force that applies on the fins of the arrow is :
$$F=\sin\alpha \cdot\ K$$
With $K$ a coefficient changing with air density, airspeed, drag coefficient and so son.
So the torque generated on the arrow is :
$$\tau=\sin\alpha \cdot K \cdot d$$
With $d$ being the distance from the back of the arrow to the center of gravity, on which the arrow will rotate.
When I run this into my simulation, the arrow realign itself onto the wind, but... It overshoots everytime. When it overshooted, then it tries to realign going the opposite direction, but overshoots again, and so on.
And, of course, that's obvious. Because there are no energy loss on that simulation.
My question is :
Why do in real life, arrows will never oscilate so much? What force, linear or angular drag causes it to not overshoot and align into the wind? How can I simulate that to obtain a valid simulation?