What exactly is the “Archers’ Paradox” ?  This question is explored below…

Common assumptions

• Arrows are solid and often very stiff indeed; just trying to bend one with your hands amply demonstrates this fact.
• When release, the string travels straight forward as it pushes the released fingers out of the way. Ergo, the string must push the arrow straight forward towards the target.
• The only thing affected the arrow’s flight once it leaves the bow are its flights, and external influences such as solid obstacles and wind.

All false!

The term “Archer’s Paradox” first appeared in the works of Dr. Robert P. Elmer, a well known archery author of the 1930s.  His personal observations and suspicions were later (largely) confirmed by high speed photography used to scrutinise the behaviour of arrows upon release by the archer.

Elmer’s curiosity lay in why an arrow will succeed in hitting a target even though the arrow is aimed to the side of the target prior to release.  Elmer noted that arrows consistently and accurately aimed to one side of a target (the bullseye) will nevertheless consistently strike the bullseye.

From appearances, when properly placed on the bow of a right-handed archer, the arrow should strike well to the left of the target as it travels in a direct path to the target.  It does not.  This is the paradox.

What his reasoning and much subsequent photography revealed was that the arrow flexes in flight and the string does not travel straight forward upon release. Even though to the naked eye an arrow seems a rigid and unbending shaft, in reality it bends and flexes when placed under the pressures of an accelerating bowstring and the lateral displacement caused by the bowstring sliding sideways from the fingers of the archer, and again to its resting point on the bow after the arrow has left the string.

You will have heard it said that for every action there is an equal and opposite reaction. And this is certainly true in this case. The action is the bowstring sliding sideways and then forward towards the target.  The reaction is the arrow flexing in direct proportion to the force of the bow.

It bends in a ‘balanced’ way to one side, then the opposite way, and back, again and again, decreasing its oscillations slightly each cycle on its path to strike the target.  The shaft bends due to the inertial resistance of the shaft and the (heavier) tip, as well as the side-thrust of the string coming off the fingers, and the manner of the bend is consistently the same because the bowstring slips off the fingertips in the same sideways direction each time. (Assuming the archer is consistent in her/his release technique)

(Watch this beautifully filmed, slow-motion exploration of archery’s greatest conundrum, the “Archers’ Paradox”. Double click anywhere on the footage to enlarge it and view it in your browser. To appreciate this footage fully, make you’re your sound system is switched on.)

The tail of the arrow gets pushed away from the bow at just the same time that the string is suddenly free to push the shaft towards the front of the bow. The tip of the arrow gets no sideways push, but since it has mass it resists the forward motion for an instant while the nock is moving forward, and the shaft bends as a result.

The spine (stiffness) of the shaft together with the weight of the tip, the strength of the bow limbs, the tension of the plunger (see footnotes), and the motion of the fingers,  all serve to determine how much bend will occur.

Practical experience and testing reveals that for maximum accuracy and for bow clearance the spine for a given bow must be neither too stiff nor too weak. If it is either the arrow is deflected when it strikes the riser.  The way the archer releases the string also controls how much bending occurs and that is the primary reason why it is so important that the archer practice release consistency, some would say above all else.

Essentially, prior to release, the arrow must be pointed off target by a distance that proportionately equals the sideways deflection caused by the string sliding off of the fingers.

This offset distance is subject to the sum of a sequence of events (The System) and includes the various parts of the archers setup e.g. the technique of the archer, the material of the finger tab, the spine of the arrow, the weight of the tip of the arrow, the nature of the bowstring (strands, composition, serving, length, twists), the nock and its grip on the string, the plunger button’s resistance, the arrow rest, the settings of brace height, sight, centre-shot etc.    Change any one part of the System and you alter the behaviour of the rest of its constituent parts.  They are all critically interdependent.

The arrow’s flexion, while unavoidable, is beneficial because it actually assists in accuracy.

Due to flexion, the shaft’s trailing end will not strike the arrow rest and the bow.  Were it to hit or graze the bow’s other components as it leaves the bow, the arrow’s flight would be altered causing decreased accuracy and torn or creased fletches. This often happens when the arrow spine is too weak but can also happen if it is too stiff.

The cushion plunger (or button) can be employed on a recurve bow to dampen the reflections of the shaft, so as to absorb some of the energy of the flexion, resulting in oscillations that are considerably smaller.  Fewer/smaller oscillations will keep the arrow closer to the centre of the target during flight, resulting in more efficient flight and a more accurate shot.

The process of tuning the bow uses a series of tests and adjustments to the various components, to arrive at just the right amount that the arrow needs to be aimed off dead centre, thereby decrease the amount of flexion for the System, to get the smallest possible arrow groups.

This, in a nutshell of sorts, is what Archers’ Paradox is all about.

The following studies offer far more detailed advice to the ravenous intellect

The Archer’s Paradox and Modelling, a Review, B.W. Kooi, Faculty of Biology, Amsterdam, and On the Mechanics of the Arrow by B.W. Kooi and J.A. Sparenberg

Footnotes:
(Plunger Button: a fine tuning device with an adjustable spring cushioned tip inside a housing. The plunger button is installed on the riser with the tip protruding above the arrow rest and its purpose is to push the arrow to the left, on a right hand bow, to compensate for archer’s paradox. The side of the arrow is in contact with the plunger button tip when the arrow is sitting on the arrow rest.)

(Flexion: The act of bending a joint, limb or shaft. The condition of the joint, limb or shaft so bent.)