Archers paradox is essentially the bending of
the arrow upon release of the bow and the eventual
straightening out of the arrow as it hits the target.
Due to the high force the bow string acting on the arrow and the
friction from the archers fingers slipping off
and releasing the string it causes the arrow to oscillate back and
forth. this is a natural vibration similar to hitting
something with a hammer.This force can be in the range anywhere
from 30-50 lbs which is very large compared
to the mass of the arrow, which is why the acceleration is
so rapid due to newtons
second law F=ma
The line of sight the archer takes when aiming down the arrow when
the bow is drawn to full draw is
different then the expected trajectory of the arrow as seen in the
pictures below.
this is why the stiffness of the arrow is so crucial and is
calculated on the draw weight of the bow.
1.) Immediately after release of the arrow the
arrow
is pointing to the right of the target as the string slides off
the fingers
of the archer and the string moves to the left (right handed
shooter)
2.) The arrow begins to oscillate and the arrow then points
directly at the target.
As the string moves back to the right.
3.) The arrow leaves the bow and begins to fly directly towards
the intended or aimed upon target.