# Why do arrows not oscilate so much?

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?

Thank you.

• If you search the web for "physics of arrows" you'll get a lot of information. I get the impression you're talking about what is known as "The Archer's Paradox". – StephenG Apr 23 at 13:14
• Thanks, but I'm not talking about the Archer's Paradox at all. I am considering the arrow straight and that cannot bend. I am talking about the aerodynamics of the arrow. My example works as well with a weathercock but I cannot find deep explainations rather than "wind strikes the tail of the weathercock, and it aligns on wind." Ok, but using this model the weathercock will accelerate toward wind direction, and would overshoot as there are no energy loss. So something is missing – Anselme Apr 23 at 13:20