Archer's paradox

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Arrow direction when braced and when at full draw. A = bow riser/grip, B = median plane of the bow, C = arrow aiming line and trajectory Archers-paradox-corrected.png
Arrow direction when braced and when at full draw. A = bow riser/grip, B = median plane of the bow, C = arrow aiming line and trajectory
Arrow flexing both towards and away from the bow handle. Arrow-flexing.png
Arrow flexing both towards and away from the bow handle.

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.

Contents

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, [1] 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, [4] this dynamic flexing has incorrectly become a common usage of the term. This misuse sometimes causes misunderstanding on the part of those only familiar with modern target bows, which often have risers with an eccentrically cutout "arrow window"; being "centre shot", these bows do not exhibit any paradoxical behaviour as the arrow is always pointing visually along its line of flight. [5] [6] [7]

Details

In order to be accurate, an arrow must have the correct stiffness, or "dynamic spine", to flex out of the way of the bow and to return to the correct path as it leaves the bow. [8] Incorrect dynamic spine results in unpredictable contact between the arrow and the bow, therefore unpredictable forces on the arrow as it leaves the bow, and therefore reduced accuracy. [9] Additionally, if an archer shoots several arrows with different dynamic spines, as they clear the bow they will be deflected on launch by different amounts and so will strike in different places. Competition archers therefore strive not only for arrows that have a spine within a suitable range for their bow, but also for highly consistent spine within sets of arrows. [10] This is done using a static spine tester. [11] [12] [13] [14]

Choice of bow and spine

Less powerful bows require arrows with less dynamic spine. (Spine is the stiffness of the arrow. [14] ) Less powerful bows have less effect in deforming the arrow as it is accelerated (see "Euler" buckling, case I) from the bow and the arrow must be "easier" to flex around the riser of the bow before settling to its path. Conversely, powerful bows need stiffer arrows with more spine, as the bow will have a much greater bending effect on the arrow as it is accelerated. [15] An arrow with too much dynamic spine for the bow will not flex and as the string comes closer to the bow stave, the arrow will be forced off to the side. Too little dynamic spine will result in the arrow deforming too much and being propelled off to the other side of the target. In extreme cases, the arrow may break before it can accelerate, which can be a safety hazard. [16] [17] [18]

Calibration

Dynamic spine is largely determined by shaft length, head weight, and static spine. Static spine is the stiffness of the center portion of the shaft under static conditions. [19] The Archery Trade Association (ATA) (formerly the Archery Manufacturers and Merchants Organization (AMO)) static spine test method hangs a 2-pound (0.91 kg) weight from the center of a 26-inch (0.66 m) suspended section of the arrow shaft. [20] [21] The American Society for Testing and Materials (ASTM) F2031-05 ("Standard Test Method for Measurement of Arrow Shaft Static Spine (Stiffness)") hangs an 880-gram (1.94 lb) weight from the center of a 28-inch (0.71 m) suspended section of the arrow shaft. [22] The (obsolete) British Grand National Archery Society (GNAS) system used a 1.5-pound (0.68 kg) weight and a variable length with the arrow supported just behind the head and just in front of the nock.[ citation needed ] Because of this, GNAS cannot be directly converted to ATA or ASTM.

The primary unit of measurement for spine is deflection in thousandths of an inch (a deflection of 500 equals 0.500 in or 12.7 mm) Deflection is sometimes converted to pounds of bow weight by dividing 26 by the deflection in inches. (26 in⋅lb divided by 0.500 in equals a spine of 52 lb) [23]

Solutions

Some modern bows have a cutout in the direct center of the body or riser that the arrow flies through; this allows the arrow to always move with the string.[ citation needed ] However, dynamic spine arrows are still used.

Related Research Articles

<span class="mw-page-title-main">Archery</span> Using a bow to shoot arrows

Archery is the sport, practice, or skill of using a bow to shoot arrows. The word comes from the Latin arcus, meaning bow. Historically, archery has been used for hunting and combat. In modern times, it is mainly a competitive sport and recreational activity. A person who practices archery is typically called an archer, bowman, or toxophilite.

<span class="mw-page-title-main">English longbow</span> Type of ranged weapon

The English longbow was a powerful medieval type of bow, about 6 ft (1.8 m) long. While it is debated whether it originated in England or in Wales from the Welsh bow, by the 14th century the longbow was being used by both the English and the Welsh as a weapon of war and for hunting. English longbows were effective against the French during the Hundred Years' War, particularly in the battles of Sluys (1340), Crécy (1346), Poitiers (1356), and the Battle of Agincourt (1415). They were less successful later on, as longbowmen had their lines broken at the Battle of Verneuil (1424); although the English won a decisive victory there, they were completely routed at the Battle of Patay (1429) when they were charged by the French mounted men-at-arms before they had prepared the terrain and finished defensive arrangements. The Battle of Pontvallain (1370) had also previously shown longbowmen were not particularly effective when not given the time to set up defensive positions.

<span class="mw-page-title-main">Arrow</span> Shafted projectile that is shot with a bow

An arrow is a fin-stabilized projectile launched by a bow. A typical arrow usually consists of a long, stiff, straight shaft with a weighty arrowhead attached to the front end, multiple fin-like stabilizers called fletchings mounted near the rear, and a slot at the rear end called a nock for engaging the bowstring. A container or bag carrying additional arrows for convenient reloading is called a quiver.

<span class="mw-page-title-main">Compound bow</span> Type of bow for archery

In modern archery, a compound bow is a bow that uses a levering system, usually of cables and pulleys, to bend the limbs.

<i>Kyūdō</i> Japanese archery based martial art

Kyūdō is the Japanese martial art of archery. Kyūdō is based on kyūjutsu, which originated with the samurai class of feudal Japan. In 1919, the name of kyūjutsu was officially changed to kyūdō, and following the example of other martial arts that have been systematizing for educational purposes, kyūdō also reorganized and integrated various forms of shooting that had been used up until then. High level experts in kyūdō may be referred to as kyūdōka (弓道家)(Kyudo Master) and some practitioners may refer to themselves as yumihiki (弓引き), or 'bow puller'. Kyūdō is practised by thousands of people worldwide. The bow they use is called a yumi (弓), and the most common one has an asymmetrical shape of more than 2.0 metres, and is characterized by the archer holding the part of the bow below the center to shoot the arrow.

<span class="mw-page-title-main">Bow and arrow</span> Pre-gunpowder ranged weapon system

The bow and arrow is a ranged weapon system consisting of an elastic launching device (bow) and long-shafted projectiles (arrows). Humans used bows and arrows for hunting and aggression long before recorded history, and the practice was common to many prehistoric cultures. They were important weapons of war from ancient history until the early modern period, where they were rendered increasingly obsolete by the development of the more powerful and accurate firearms. Today, bows and arrows are mostly used for hunting and sports.

<span class="mw-page-title-main">Bow shape</span> Important aspect of archery

In archery, the shape of the bow is usually taken to be the view from the side. It is the product of the complex relationship of material stresses, designed by a bowyer. This shape, viewing the limbs, is designed to take into account the construction materials, the performance required, and the intended use of the bow.

<span class="mw-page-title-main">Composite bow</span> Bow made from horn, wood, and sinew laminated together

A composite bow is a traditional bow made from horn, wood, and sinew laminated together, a form of laminated bow. The horn is on the belly, facing the archer, and sinew on the outer side of a wooden core. When the bow is drawn, the sinew and horn store more energy than wood for the same length of bow. The strength can be made similar to that of all-wood "self" bows, with similar draw-length and therefore a similar amount of energy delivered to the arrow from a much shorter bow. However, making a composite bow requires more varieties of material than a self bow, its construction takes much more time, and the finished bow is more sensitive to moisture.

<span class="mw-page-title-main">Arrowhead</span> Sharpened tip of an arrow

An arrowhead or point is the usually sharpened and hardened tip of an arrow, which contributes a majority of the projectile mass and is responsible for impacting and penetrating a target, as well as to fulfill some special purposes such as signaling.

<span class="mw-page-title-main">Fletching</span> Aerodynamic stabilization of arrows, etc.

Fletching is the fin-shaped aerodynamic stabilization device attached on arrows, bolts, darts, or javelins, and are typically made from light semi-flexible materials such as feathers or bark. Each piece of such fin is a fletch, also known as a flight or feather. A fletcher is a person who attaches fletchings to the shaft of arrows.

<span class="mw-page-title-main">Bowhunting</span>

Bowhunting is the practice of hunting game animals by archery. Many indigenous peoples have employed the technique as their primary hunting method for thousands of years, and it has survived into contemporary use for sport and hunting.

<span class="mw-page-title-main">Self bow</span>

A self bow or simple bow is a bow made from a single piece of wood. Extra material such as horn nocks on the ends, or built-up handles, would normally be accepted as part of a self bow. Some modern authorities would also accept a bow spliced together in the handle from two pieces of wood.

A bow draw in archery is the method or technique of pulling back the bowstring to store energy for the bow to shoot an arrow. The most common method in modern target archery is the Mediterranean draw, which has long been the usual method in European archery. Other methods include the pinch draw and the Mongolian or "thumb" draw. In traditional archery practice outside Western Europe the variations of the thumb draw are by far the most dominant draw types, with the Mediterranean draw restricted to the Olympic style of target archery.

<span class="mw-page-title-main">Archery Trade Association</span>

The Archery Trade Association (ATA), is the trade group representing manufacturers, retailers, distributors, sales representatives and others working in the archery and bowhunting industry. The ATA has served its members since 1953. It is dedicated to making the industry profitable by decreasing business overhead, reducing taxes and government regulation, and increasing participation in archery and bowhunting.

This is a list of archery terms, including both the equipment and the practice. A brief description for each word or phrase is also included.

<span class="mw-page-title-main">Recurve bow</span> Type of bow shape in archery

In archery, a recurve bow is one of the main shapes a bow can take, with limbs that curve away from the archer when unstrung. A recurve bow stores more energy and delivers energy more efficiently than the equivalent straight-limbed bow, giving a greater amount of energy and speed to the arrow. A recurve will permit a shorter bow than the simple straight limb bow for given arrow energy, and this form was often preferred by archers in environments where long weapons could be cumbersome, such as in brush and forest terrain, or while on horseback.

Modern competitive archery involves shooting arrows at a target for accuracy and precision from a set distance or distances. This is the most popular form of competitive archery worldwide and is called target archery. A form particularly popular in Europe, North America, and South America is field archery, shot at targets generally set at various distances in a wooded setting. There are also several other lesser-known and historical forms, as well as archery novelty games.

In archery, a release aid, mechanical release, or release is a device that helps to fire arrows more precisely, by using a trigger to release the bowstring, rather than the archer's fingers. It is used to make the release of the bowstring quicker and reducing the amount of torque put onto the bowstring from the archer's fingers.

<span class="mw-page-title-main">Stabiliser (archery)</span>

In archery, a stabiliser is a general term for various types of weights, usually on rods, mounted on the bow to increase stability i.e. lessen movement on release, thereby increasing precision. Stabilisers help reduce inconsistency in the archer's release by increasing the moment of inertia of the bow. If the shooting technique of the archer were perfect, no stabilisers would be required.

<span class="mw-page-title-main">Takedown bow</span> Bow assembled out of a riser and two limbs

A takedown bow is a bow assembled out of a riser and two limbs to make a working bow when strung.

References

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  2. Rheingans, W. R. (March–April 1936). "Exterior and Interior Ballistics of Bows and Arrows - Review". Archery Review : 236 ff.
  3. Rheingans, W. R.; Nagler, F. (June–August 1937). "Spine and Arrow Design". American Bowman Review : 226–232.
  4. Park, James L. (8 September 2013) [9 November 2012]. "Arrow behaviour in the lateral plane during and immediately following the power stroke of a recurve archery bow". Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology . 227 (3): 172–183. doi:10.1177/1754337112464844. S2CID   111439189.
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  6. Kooi, B. W. (1998). "The Archer's Paradox and Modelling, a Review" (PDF). In Hollister-Short, Graham (ed.). History of Technology . Vol. 20. pp. 125–137. ISBN   9780720123760.
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  10. "The Archer's Paradox". Bega Valley Traditional Archers. February 2013. Retrieved 13 February 2013.
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  12. "How To Make a Spine Tester". poorfolkbows.com. Retrieved 13 February 2013.
  13. "Spine-O-Meter Appendix A: Translating Arrow Spine Test Methods" (PDF). oakcreekarchery.com. Oak Creek Archery. 2010. Retrieved 13 February 2013.
  14. 1 2 "Jim Hill's Spine Tester". texasarchery.org. Texas State Archery Association. Archived from the original on 20 October 2013. Retrieved 13 February 2013.
  15. "Carbon Arrow University". Hunter's Friend LLC. 2011. Retrieved 13 February 2013.
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  17. Rieckmann, Marianne; Park, James L.; Codrington, John; Cazzolato, Ben (June 2012) [3 April 2012]. "Modelling the three-dimensional vibration of composite archery arrows under free–free boundary conditions" (PDF). Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology . 226 (2): 114–122. doi:10.1177/1754337112442273. S2CID   110116671. Archived from the original (PDF) on 1 March 2021. Retrieved 13 February 2013.
  18. Yononindo, Daniel (2 February 2012). Archers Paradox up to the Limit !!! Extended Version. Event occurs at 6m15s via YouTube. The breaking of the arrow at the end of the video was NOT due to a lack of knowledge on my part !!! IT WAS QUITE DELIBERATE !!!
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