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?