Several years ago, I posted a question about Why do archery arrows tilt downwards in their descent?. An answer was given that a torque arises from the difference in location of net force of gravity (center of mass) vs net force of drag (center of arrow). This answer makes sense to me.
Now I'm wondering why arrows always seem to point tangential to their path. I have never shot a real arrow, but it is my perception that arrows points horizontally at the top of their arc, regardless of initial velocity. This idea seems in conflict with the idea that rotating objects rotate more if they have more time to rotate. An arrow show with more initial velocity would seem to have more time to rotate.
I have a suspicion that as the arrow starts to rotate after initial launch, the increasing air resistance on the arrow from above slows the rotation exponentially. First the arrow is burrowing through the air point-first, but later it is horizontal and experiencing much more drag until it comes to a momentary pause. Thus I suspect that the maximum height an arrow reaches is highly dependent on the amount of drag, even though superficially arrows may appear to cut through the air. Is it naive to treat a rotating arrow as an ordinary projectile, since at maximum height, it is experiencing drag forces much larger than were present at the time of launch?
Best Answer
Gravity can't apply a torque to an object in freefall.
Drag/air pressure always acts in the opposite direction to the object's path through the air. For still air, this will be the opposite direction to the object's path relative to the ground.
The object will be designed so the center of pressure is behind the center of mass. The drag from the air will provide a torque so the center of pressure trails the object as it moves through the air. Since the arrow is moving horizontally at the top of the arc, it is also aligned horizontally.
The rotational moment of inertia of an arrow is easily overcome by the aerodynamic forces. I don't see any reason to assume the drag forces are greater at the top of the arc.
It might be introduced. The arrow is basically a weathervane. If it's pointed into the wind, it stays there. If it's not pointed into the wind, the pressure from the wind creates a torque that turns it that way.
As the arrow moves through the air, if it's not aligned with the velocity vector, it will experience a torque that tends to align it.
Given you specify "top of arc", then initial velocity is irrelevant. The top of the arc is when the arrow has no vertical velocity. The amount of drag is irrelevant, just the direction (which given the description must be horizontal).