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What is the Archer's Paradox?



Archer's paradox - Wikipedia
The archer's paradox is the phenomenon of an arrow traveling in the direction it is pointed at full draw, when it seems that the arrow would have to pass through the starting position it was in before being drawn, where it was pointed to the side of the target. The bending of the arrow when released is the explanation for why the paradox occurs and should not be confused with the paradox itself. Flexing of the arrow when shot from a modern 'centre shot' bow is still present and is caused by a variety of factors, mainly the way the string is deflected from the fingers as the arrow is released.

The term was first used by E.J. Rendtroff in 1913, but detailed descriptions of the phenomenon appear in archery literature as early as Horace A. Ford's 1859 text "Archery: Its Theory and Practice". As understanding was gained about the arrow flexing around and out of the way of the bow as it is shot (as first filmed by Clarence Hickman)[2][3] and then experiencing oscillating back-and-forth bending as it travels toward the target, this dynamic flexing has incorrectly become a common usage of the term, causing misunderstanding by those only familiar with modern target bows, which often have risers with an eccentrically cutout "arrow window" and being "centre shot" do not actually show any paradoxical behaviour as the arrow is always pointing visually along its line of flight. [...]

SmarterEveryDay
The Archer's Paradox in SLOW MOTION - Smarter Every Day 136



Spine and Archer's Paradox - Bowhunter-ed.com
Every arrow shaft has a degree of stiffness called spine, which is its resistance to bending. Bending, known as “archer’s paradox,” occurs when an arrow is released from the bow. The forward thrust of the string causes the shaft to bend in one direction and then react in the opposite direction as it speeds downrange.

Spine strength must be matched to bow draw weight. If your arrows are too lightly or heavily spined for your bow, the “archer’s paradox” movements will be extreme, resulting in poor arrow flight and loss of accuracy. (It’s better to err on the stiff, or too heavily spined, side.) Arrow manufacturers publish selection charts that match bow weights to proper arrow spine. Your local archery shop will help you match your gear. [...]

What Is The Archers Paradox? - My Archery Corner
I think you know that “paradox” means that two or more things that can never be true at the same time, suddenly are true at the same time. So a paradox contradicts itself and defies any logic. An example would be “a wise fool”. A fool is supposed to be silly or stupid, but wisdom can be found in what they say nevertheless.

Now, what is that archers paradox all about? When you look at the bow and arrow and give it some thought you will notice that it should be impossible to hit any target with an arrow. The arrow should not be able to pass the riser (grip) of the bow and hit the target behind it. Instead it should deflect from the riser and fly either to the right or the left, depending on which side of the bow you are holding the arrow. [...]

The Archer's Paradox and modern bows | Bow International
The definition of a paradox is that it is a seemingly true statement, or group of statements, that leads to a contradiction or a situation which seems to defy logic or intuition. The paradox relating to archery is “that an arrow will fly in a straight line to a target when it starts off pointing away from the target.”

A complete understanding of the archer’s paradox did not occur until the late 1920s and early 1930s, when work by Robert P Elmer, Paul E Klopsteg, ES Hodgson and Clarence N Hickman was published. Elmer and Klopsteg had developed a working theory by the end of the 1920s and early 1930s, but it took proper slow-motion filming by Hickman to finally determine what actually happens. [...]

What is archers paradox? - Quora
The archer’s paradox is fascinating (to me, anyway), but it is one of the more confusing paradoxes out there, made doubly so because it’s not actually a paradox, only a seeming one. Of the two answers here on Quora, one is wrong, and the other is too terse (IMO). Let me see if I can illuminate:

First, picture the simplest possible bow, a big thick piece of wood with tapered ends, bent into a “C” by a taught string. Pull it back until it feels really tight, then let it release with a big twang. What just happened? Well, the string was forced back towards the wood by the uncurling of that wood, with a decent amount of force (also, you just damaged your bow by firing it without an arrow, but that’s a separate topic). That force is very linear; the string is pulled straight towards the center of the bow. We are going to call that direction “A”, and it runs right through the middle of the bow, and we can imagine it continuing forward away from you and into some distant medieval soldier (let’s call him Ser Robyn). [...]

The Archer's Paradox - The Physics Behind Archery
It 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,
1. The arrow is pointing to the right of the target. There is a force and a moment at this point.
2. 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.
3. The arrow leaves bow and flies directly to the target. It is fully oscillating at this moment. [...]




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