Definitions:  

    Archer (är-ch&r ) noun - one who uses a bow and arrow
    Par·a·dox (pr-dks)  noun

1.A seemingly contradictory statement that may nonetheless be true: the paradox that standing is more tiring than walking.
2.One exhibiting inexplicable or contradictory aspects: “The silence of midnight, to speak truly, though apparently a paradox, rung in my ears” (Mary Shelley).
3.An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises.
4.A statement contrary to received opinion.
 

[Latin paradoxum, from Greek paradoxon, from neuter singular of paradoxos, conflicting with expectation : para-, beyond; see para-1 + doxa, opinion (from dokein, to think.]

Layperson "logic" dictates that a straight and balanced arrow must be shot straight at a target in order to hit it.   In reality, the arrow must be aimed OFF of the target by a traditional archer in order to hit the target.  You do not point the arrow at the target, this is THE paradox.  Thus the 4th definition above seems to me to fit the phrase most closely. ("archer's paradox").

Flaws of logical assumption

1. The arrow is obviously stiff and rigid, just hold it in your hands and try to bend it!  It doesn't bend much, if at all.
2. The string travels straight forward when released by the fingers because it pushes the fingers out of the way!  It must push the arrow STRAIGHT to the target!
Wrong!
Discussion:

The term "Archer's Paradox" was coined by Dr. Robert P. Elmer, a well-known archery author in the 1930s.  His observations were confirmed by others who used high speed photography to scrutinize the behavior of an arrow upon release by the archer to answer a paradoxical situation.  

His concern was the question as to why an arrow will succeed in hitting a target even though the arrow is placed at an angle to the side of the target prior to shooting.  It is actually pointing away, off of the target to the side away from the bow. 

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 a paradoxical situation!  (And is also present for left-handed archers, only to the opposite/right side of the target.)

What his reasoning and much subsequent photography revealed was that the arrow flexes and the string does not travel straight forward upon loosing!  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.   Even the string slides sideways from the fingers on it's way to the resting position after the arrow has flown.

It is said for every action there is an equal and opposite reaction and it 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.  It bends in a balanced way to one side, and then bends the opposite way, and back, again and again, decreasing its oscillations slightly each cycle as it flies until it strikes the target.  The shaft bends due to the inertial resistance of the shaft and the (heavier) tip as well as the sidethrust of the string coming off of the fingers, and the manner of the bend is consistently the same because the bowstring slips off of the fingertips in the same sideways direction each time. (Assuming the archer is consistent in her/his release technique!)  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 and the strength of the bow limbs, the tension of the plunger, and the fingers motion  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. Otherwise the arrow strikes the bow and is deflected.  The way the archer releases the string also controls how much bending occurs and that is one reason why it is so important that the archer be consistent  in how the arrow is "loosed" or released. 

Back to defining Archers' Paradox:  Essentially, prior to release, the arrow must be pointed OFF of the target by a distance that equals proportionately the sideways deflection caused by the string sliding off of the fingers of the archer.  This Offset Distance, aka "Center-Shot" is subject to the SYSTEM.  let's define the SYSTEM as a combination of all the varying parts of the setup: 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, center-shot.    Change any one part of the SYSTEM and you alter the behavior of the rest of the parts.  They are all inter-dependent, in other words.

The arrow 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 then the arrow's flight would be altered causing decreased accuracy (and torn or creased fletchings). This often happens when the arrow spine is too weak but can also happen if it is too stiff.  The spine must be ahhhhhh, just right.

The cushion plunger or button is employed on a recurve bow to dampen the reflections of the shaft, to absorb some of the energy of the flexion so the oscillations will be smaller.  Fewer/smaller oscillations will keep the arrow closer to the center of the target during flight, resulting in more efficient flight and a more accurate shot.  The process of TUNING the recurve bow is making a series of tests and adjustments to the various components to arrive at just the right amount that the arrow need be aimed "off" of dead center and decrease the amount of flexion, for the system, to get the smallest groups of arrows at the target as possible.

THAT , in my opinion, is archer's paradox.  I'm amazed that people were able to deduce the causes prior to having ultra-high speed photography, and am amused that people today are unable to accept certain verifiable facts even with such photography. 

To see this flexion and paradox, you can check the various slow motion videos on the TSAA's High Speed Video Library page.

A.Ron Carmichael, 6/24/2001

For a more scientifically rigorous explanation, though emotionally less satisfying<G> please view Joe Tapley's page.

A related erroneous assumption:  ROTATION of the arrow causes the arrow to hit the rest

It is likely impossible for an arrow to ROTATE sufficiently between the time the nock leaves the string and the nock passes the plunger/riser of the bow for this rotation to be worthy of concern.  If an arrow hits a rest or plunger then it is due to OTHER causes, such as being too weak/stiff of a spine, or improperly set to center-shot (see paradox above<G>).  Rotation of a shaft is so miniscule during the first 8 or 10 inches of arrow flight that it can only be estimated and calculated using advanced math, not through empiric measurements such as high-speed photography offer. Though it DOES rotate, and it is noticeable at times using high speed photography, but only a tiny amount of rotation can be seen some of the time.

Lacking a true airfoil, vanes of an arrow will cause rotation ONLY due to compression of air against an angular/curved surface of the vane.  This air compression can only come about by the arrow system traveling through air.   As the arrow starts moving forward the vanes will come under pressure.  Being flexible, they will "give" first, since the nock prevents the arrow from rotating while attached to the string.   Once the nock separates from the string, the mass of arrow begins to be overcome and rotation should begin, albeit slowly at first.  There is the inertia of arrow mass at rest (rotationally speaking) to be overcome.

The arrow system (point/insert/shaft/vanes/adhesive/nock) together all have mass of many grams.  This mass is rotationally at rest at the instant of release from the string, and cannot begin to change until acted on by the resistance of air, which will be compressed by the vanes.

During the initial milliseconds of acceleration, the vanes will begin to be pushed back by the air until compression equals their resistance to bending, and then the compressive force of the air will begin to be transferred to the mass of the shaft.  Once the compressive force begins to exceed the resistance of the mass THEN and ONLY then will the arrow begin to rotate.  It's like trying to push a car on flat ground.  Initially you push and you push,  it doesn't move right away, but eventually the car begins to budge a little, then more, then more.  

I reckon that the bowstring will travel forward of the brace height during release by perhaps an inch or two, making the distance from the point of nock release to the arrow rest/plunger perhaps 7 inches.  So the vanes would have to be compressed during this 7 inches AND reach maximum flexion AND overcome 90 to 100 grams of resistance AND rotate the shaft "significantly" in order for the vanes to be in danger of striking the bow DUE TO ROTATION.

Does the arrow rotate in that first 7 or 8 inches?   Possibly.   Even probably.  Is it a significantly large enough amount of rotation to cause contact in and of itself?  Probably not.  The rotation could only be measured in nano- or micro-meters, if it could be empirically measured at all.

For some pictures that help view the  behavior of the arrow during acceleration at the bow, click here.  In particular, this AVI file (alt) clearly shows the lateral displacement of the bowstring coming off of the fingers AND it shows that the spinwing does NOT rotate noticeably prior to clearing the riser.  You can use your right and left arrow keys to step through the video ONE FRAME at a time to see it more clearly.