What is the archer's paradox?
The archer's paradox is the bending of the arrow upon the release of the bow and the eventual straightening out of the arrow when it hits the target. The archer's paradox causes 'fishtailing' which occurs due to the friction between the fingers and the strings as it slips off. As the fingers slide to the right, there is a friction force acting to the right as well. This force leaves upon release and the draw string accelerates to the plane of the bow (to the left). To control this, tab releases, in place of bare fingers, are used which reduce the friction but do not eliminate it entirely.
Essentially,
The archer's paradox is the bending of the arrow upon the release of the bow and the eventual straightening out of the arrow when it hits the target. The archer's paradox causes 'fishtailing' which occurs due to the friction between the fingers and the strings as it slips off. As the fingers slide to the right, there is a friction force acting to the right as well. This force leaves upon release and the draw string accelerates to the plane of the bow (to the left). To control this, tab releases, in place of bare fingers, are used which reduce the friction but do not eliminate it entirely.
Essentially,
- The arrow is pointing to the right of the target. There is a force and a moment at this point.
- The arrow is now in line with the target, and then moves slightly to the left. There is a moment at the center of mass of the arrow and the equation used is the rigid body equation, which equals I α. I is the inertia and α is the angular acceleration.
- The arrow leaves bow and flies directly to the target. It is fully oscillating at this moment.
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