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Available in 9 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-9" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">9 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Lukost%C5%99eleck%C3%BD_paradox" title="Lukostřelecký paradox – Czech" lang="cs" hreflang="cs" data-title="Lukostřelecký paradox" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Paradoxe_de_l%27archer" title="Paradoxe de l'archer – French" lang="fr" hreflang="fr" data-title="Paradoxe de l'archer" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B6%81%EC%88%98%EC%9D%98_%EC%97%AD%EC%84%A4" title="궁수의 역설 – Korean" lang="ko" hreflang="ko" data-title="궁수의 역설" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%A8%D7%93%D7%95%D7%A7%D7%A1_%D7%94%D7%A7%D7%A9%D7%AA" title="פרדוקס הקשת – Hebrew" lang="he" hreflang="he" data-title="פרדוקס הקשת" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Boogschuttersparadox" title="Boogschuttersparadox – Dutch" lang="nl" hreflang="nl" data-title="Boogschuttersparadox" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%83%BC%E3%83%81%E3%83%A3%E3%83%BC%E3%81%AE%E3%83%91%E3%83%A9%E3%83%89%E3%83%83%E3%82%AF%E3%82%B9" title="アーチャーのパラドックス – Japanese" lang="ja" hreflang="ja" data-title="アーチャーのパラドックス" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Paradoks_%C5%82ucznika" title="Paradoks łucznika – Polish" lang="pl" hreflang="pl" data-title="Paradoks łucznika" data-language-autonym="Polski" 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Phenomenon in archery</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Zeno%27s_paradoxes#Arrow_paradox" title="Zeno's paradoxes">Zeno's arrow paradox</a>.</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Archers-paradox-corrected.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Archers-paradox-corrected.png/220px-Archers-paradox-corrected.png" decoding="async" width="220" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Archers-paradox-corrected.png/330px-Archers-paradox-corrected.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Archers-paradox-corrected.png/440px-Archers-paradox-corrected.png 2x" data-file-width="467" data-file-height="441" /></a><figcaption>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</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Arrow-flexing.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Arrow-flexing.png/220px-Arrow-flexing.png" decoding="async" width="220" height="145" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Arrow-flexing.png/330px-Arrow-flexing.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Arrow-flexing.png/440px-Arrow-flexing.png 2x" data-file-width="537" data-file-height="353" /></a><figcaption>Arrow flexing both towards and away from the bow handle.</figcaption></figure> <p>The <b>archer's paradox</b> is the phenomenon of an <a href="/wiki/Arrow" title="Arrow">arrow</a> traveling in the direction it is pointed at full <a href="/wiki/Bow_draw" title="Bow draw">draw</a>, 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. </p><p>The bending of the arrow when released is the explanation for why the paradox occurs and should not be confused with the paradox itself. </p><p>Flexing of the arrow when shot from a modern 'centre shot' <a href="/wiki/Bow_and_arrow" title="Bow and arrow">bow</a> 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. </p><p>The term was first used by E. J. Rendtroff in 1913,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> but detailed descriptions of the phenomenon appear in <a href="/wiki/Archery" title="Archery">archery</a> literature as early as <a href="/wiki/Horace_A._Ford" title="Horace A. Ford">Horace A. Ford</a>'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 <a href="/wiki/Clarence_Hickman" class="mw-redirect" title="Clarence Hickman">Clarence Hickman</a>)<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and then experiencing oscillating back-and-forth bending as it travels toward the target,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Details">Details</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Archer%27s_paradox&action=edit&section=1" title="Edit section: Details"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In order to be accurate, an arrow must have the correct <a href="/wiki/Stiffness" title="Stiffness">stiffness</a>, or "<a href="/wiki/Arrow#Shaft" title="Arrow">dynamic spine</a>", to flex out of the way of the bow and to return to the correct path as it leaves the bow.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> This is done using a static spine tester.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Jim_14-0" class="reference"><a href="#cite_note-Jim-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Choice_of_bow_and_spine">Choice of bow and spine</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Archer%27s_paradox&action=edit&section=2" title="Edit section: Choice of bow and spine"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Less powerful bows require arrows with less dynamic spine. (Spine is the stiffness of the arrow.<sup id="cite_ref-Jim_14-1" class="reference"><a href="#cite_note-Jim-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>) Less powerful bows have less effect in deforming the arrow as it is <a href="/wiki/Accelerate" class="mw-redirect" title="Accelerate">accelerated</a> (see Euler <a href="/wiki/Buckling" title="Buckling">buckling</a>, 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.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Calibration">Calibration</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Archer%27s_paradox&action=edit&section=3" title="Edit section: Calibration"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Archery_Trade_Association" title="Archery Trade Association">Archery Trade Association</a> (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.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> 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.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This is one of those claims where hundreds of blogs that fail WP:RS quote the GNAS page, but the material seems to have disappeared from the GNAS page itself. (February 2013)">citation needed</span></a></i>]</sup> Because of this, GNAS cannot be directly converted to ATA or ASTM. </p><p>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)<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Solutions">Solutions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Archer%27s_paradox&action=edit&section=4" title="Edit section: Solutions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2023)">citation needed</span></a></i>]</sup> However, dynamic spine arrows are still used. </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Archer%27s_paradox&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation journal cs1">"The Toxophilist's Paradox". <i><a href="/wiki/Forest_and_Stream" title="Forest and Stream">Forest and Stream</a></i>. 8 February 1913.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Forest+and+Stream&rft.atitle=The+Toxophilist%27s+Paradox&rft.date=1913-02-08&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRheingans1936" class="citation journal cs1">Rheingans, W. R. (March–April 1936). "Exterior and Interior Ballistics of Bows and Arrows - Review". <i><a href="/w/index.php?title=Archery_Review&action=edit&redlink=1" class="new" title="Archery Review (page does not exist)">Archery Review</a></i>: 236 ff.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archery+Review&rft.atitle=Exterior+and+Interior+Ballistics+of+Bows+and+Arrows+-+Review&rft.pages=236+ff&rft.date=1936-03%2F1936-04&rft.aulast=Rheingans&rft.aufirst=W.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRheingansNagler1937" class="citation journal cs1">Rheingans, W. R.; Nagler, F. (June–August 1937). "Spine and Arrow Design". <i><a href="/w/index.php?title=American_Bowman_Review&action=edit&redlink=1" class="new" title="American Bowman Review (page does not exist)">American Bowman Review</a></i>: <span class="nowrap">226–</span>232.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Bowman+Review&rft.atitle=Spine+and+Arrow+Design&rft.pages=%3Cspan+class%3D%22nowrap%22%3E226-%3C%2Fspan%3E232&rft.date=1937-06%2F1937-08&rft.aulast=Rheingans&rft.aufirst=W.+R.&rft.au=Nagler%2C+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPark2013" class="citation journal cs1">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". <i><a href="/wiki/Proceedings_of_the_Institution_of_Mechanical_Engineers,_Part_P:_Journal_of_Sports_Engineering_and_Technology" class="mw-redirect" title="Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology">Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology</a></i>. <b>227</b> (3): <span class="nowrap">172–</span>183. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F1754337112464844">10.1177/1754337112464844</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:111439189">111439189</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Institution+of+Mechanical+Engineers%2C+Part+P%3A+Journal+of+Sports+Engineering+and+Technology&rft.atitle=Arrow+behaviour+in+the+lateral+plane+during+and+immediately+following+the+power+stroke+of+a+recurve+archery+bow&rft.volume=227&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E172-%3C%2Fspan%3E183&rft.date=2013-09-08&rft_id=info%3Adoi%2F10.1177%2F1754337112464844&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A111439189%23id-name%3DS2CID&rft.aulast=Park&rft.aufirst=James+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKooiSparenberg1997" class="citation journal cs1">Kooi, B. W.; Sparenberg, J. A. (1997). <a rel="nofollow" class="external text" href="http://www.bio.vu.nl/thb/users/kooi/kosp97.pdf">"On the Mechanics of the Arrow: Archer's Paradox"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/w/index.php?title=Journal_of_Engineering_Mathematics&action=edit&redlink=1" class="new" title="Journal of Engineering Mathematics (page does not exist)">Journal of Engineering Mathematics</a></i>. <b>31</b> (4): <span class="nowrap">285–</span>306. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997JEnMa..31..285K">1997JEnMa..31..285K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FA%3A1004262424363">10.1023/A:1004262424363</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:122605918">122605918</a><span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Engineering+Mathematics&rft.atitle=On+the+Mechanics+of+the+Arrow%3A+Archer%27s+Paradox&rft.volume=31&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E285-%3C%2Fspan%3E306&rft.date=1997&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122605918%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1023%2FA%3A1004262424363&rft_id=info%3Abibcode%2F1997JEnMa..31..285K&rft.aulast=Kooi&rft.aufirst=B.+W.&rft.au=Sparenberg%2C+J.+A.&rft_id=http%3A%2F%2Fwww.bio.vu.nl%2Fthb%2Fusers%2Fkooi%2Fkosp97.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKooi1998" class="citation book cs1">Kooi, B. W. (1998). <a rel="nofollow" class="external text" href="http://www.bio.vu.nl/thb/users/kooi/kooi98.pdf">"The Archer's Paradox and Modelling, a Review"</a> <span class="cs1-format">(PDF)</span>. In Hollister-Short, Graham (ed.). <i><a href="/wiki/History_of_Technology_(book_series)" title="History of Technology (book series)">History of Technology</a></i>. 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Ron (24 June 2001). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131020213548/http://www.texasarchery.org/Documents/ArchersParadox/Archersparadox.htm">"Archer's Paradox"</a>. <i>texasarchery.org</i>. Texas State Archery Association. Archived from <a rel="nofollow" class="external text" href="http://www.texasarchery.org/Documents/ArchersParadox/Archersparadox.htm">the original</a> on 20 October 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=texasarchery.org&rft.atitle=Archer%27s+Paradox&rft.date=2001-06-24&rft.aulast=Carmichael&rft.aufirst=A.+Ron&rft_id=http%3A%2F%2Fwww.texasarchery.org%2FDocuments%2FArchersParadox%2FArchersparadox.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://begaarchers.com.au/?page_id=2656">"The Archer's Paradox"</a>. Bega Valley Traditional Archers. February 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Archer%27s+Paradox&rft.pub=Bega+Valley+Traditional+Archers&rft.date=2013-02&rft_id=http%3A%2F%2Fbegaarchers.com.au%2F%3Fpage_id%3D2656&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://oakcreekarchery.com/wp-content/uploads/2010/06/Spine-Instructions2.pdf">"Spine-O-Meter Mark II Instruction Manual"</a> <span class="cs1-format">(PDF)</span>. <i>oakcreekarchery.com</i>. Oak Creek Archery. 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=oakcreekarchery.com&rft.atitle=Spine-O-Meter+Mark+II+Instruction+Manual&rft.date=2010&rft_id=http%3A%2F%2Foakcreekarchery.com%2Fwp-content%2Fuploads%2F2010%2F06%2FSpine-Instructions2.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://poorfolkbows.com/spine3.htm">"How To Make a Spine Tester"</a>. poorfolkbows.com<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=How+To+Make+a+Spine+Tester&rft.pub=poorfolkbows.com&rft_id=http%3A%2F%2Fpoorfolkbows.com%2Fspine3.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://oakcreekarchery.com/wp-content/uploads/2010/06/Arrow-Translation.pdf">"Spine-O-Meter Appendix A: Translating Arrow Spine Test Methods"</a> <span class="cs1-format">(PDF)</span>. <i>oakcreekarchery.com</i>. Oak Creek Archery. 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=oakcreekarchery.com&rft.atitle=Spine-O-Meter+Appendix+A%3A+Translating+Arrow+Spine+Test+Methods&rft.date=2010&rft_id=http%3A%2F%2Foakcreekarchery.com%2Fwp-content%2Fuploads%2F2010%2F06%2FArrow-Translation.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-Jim-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-Jim_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Jim_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20131020212920/http://www.texasarchery.org/Documents/ArcheryLore/SpineTester/Spine_Tester.html">"Jim Hill's Spine Tester"</a>. <i>texasarchery.org</i>. Texas State Archery Association. Archived from <a rel="nofollow" class="external text" href="http://www.texasarchery.org/Documents/ArcheryLore/SpineTester/Spine_Tester.html">the original</a> on 20 October 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=texasarchery.org&rft.atitle=Jim+Hill%27s+Spine+Tester&rft_id=http%3A%2F%2Fwww.texasarchery.org%2FDocuments%2FArcheryLore%2FSpineTester%2FSpine_Tester.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.huntersfriend.com/carbon_arrows/hunting_arrows_selection_guide_chapter_3.htm">"Carbon Arrow University"</a>. Hunter's Friend LLC. 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Carbon+Arrow+University&rft.pub=Hunter%27s+Friend+LLC&rft.date=2011&rft_id=http%3A%2F%2Fwww.huntersfriend.com%2Fcarbon_arrows%2Fhunting_arrows_selection_guide_chapter_3.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20131021030807/http://arrowtrademagazine.com/articles/july_06/ControllingDynamicArrowSpine-July2006.pdf">"Controlling Dynamic Arrow Spine"</a> <span class="cs1-format">(PDF)</span>. <i>Arrow Trade Magazine</i>. July 2006. Archived from <a rel="nofollow" class="external text" href="http://arrowtrademagazine.com/articles/july_06/ControllingDynamicArrowSpine-July2006.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 21 October 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Arrow+Trade+Magazine&rft.atitle=Controlling+Dynamic+Arrow+Spine&rft.date=2006-07&rft_id=http%3A%2F%2Farrowtrademagazine.com%2Farticles%2Fjuly_06%2FControllingDynamicArrowSpine-July2006.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRieckmannParkCodringtonCazzolato2012" class="citation journal cs1">Rieckmann, Marianne; Park, James L.; Codrington, John; Cazzolato, Ben (June 2012) [3 April 2012]. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210301063607/http://data.mecheng.adelaide.edu.au/avc/publications/public_papers/2012/Rieckmann_JSportsEngTech_2011_Fmanuscript.pdf">"Modelling the three-dimensional vibration of composite archery arrows under free–free boundary conditions"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Proceedings_of_the_Institution_of_Mechanical_Engineers,_Part_P:_Journal_of_Sports_Engineering_and_Technology" class="mw-redirect" title="Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology">Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology</a></i>. <b>226</b> (2): <span class="nowrap">114–</span>122. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F1754337112442273">10.1177/1754337112442273</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:110116671">110116671</a>. Archived from <a rel="nofollow" class="external text" href="http://data.mecheng.adelaide.edu.au/avc/publications/public_papers/2012/Rieckmann_JSportsEngTech_2011_Fmanuscript.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 1 March 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Institution+of+Mechanical+Engineers%2C+Part+P%3A+Journal+of+Sports+Engineering+and+Technology&rft.atitle=Modelling+the+three-dimensional+vibration+of+composite+archery+arrows+under+free%E2%80%93free+boundary+conditions&rft.volume=226&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E114-%3C%2Fspan%3E122&rft.date=2012-06&rft_id=info%3Adoi%2F10.1177%2F1754337112442273&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A110116671%23id-name%3DS2CID&rft.aulast=Rieckmann&rft.aufirst=Marianne&rft.au=Park%2C+James+L.&rft.au=Codrington%2C+John&rft.au=Cazzolato%2C+Ben&rft_id=http%3A%2F%2Fdata.mecheng.adelaide.edu.au%2Favc%2Fpublications%2Fpublic_papers%2F2012%2FRieckmann_JSportsEngTech_2011_Fmanuscript.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYononindo2012" class="citation audio-visual cs1">Yononindo, Daniel (2 February 2012). <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=96KGWC0PB6s&t=6m15s"><i>Archers Paradox up to the Limit !!! Extended Version</i></a>. Event occurs at 6m15s – via <a href="/wiki/YouTube" title="YouTube">YouTube</a>. <q>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 !!!</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Archers+Paradox+up+to+the+Limit+%21%21%21+Extended+Version&rft.date=2012-02-02&rft.aulast=Yononindo&rft.aufirst=Daniel&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D96KGWC0PB6s%26t%3D6m15s&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20131020215448/http://yeoldedelphbowmen.com/wp-content/uploads/2012/12/Arrow-Spine-Information.pdf">"Arrow Spine Information"</a> <span class="cs1-format">(PDF)</span>. yeoldedelphbowmen.com. December 2012. Archived from <a rel="nofollow" class="external text" href="http://yeoldedelphbowmen.com/wp-content/uploads/2012/12/Arrow-Spine-Information.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 20 October 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Arrow+Spine+Information&rft.pub=yeoldedelphbowmen.com&rft.date=2012-12&rft_id=http%3A%2F%2Fyeoldedelphbowmen.com%2Fwp-content%2Fuploads%2F2012%2F12%2FArrow-Spine-Information.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.outlab.it/doc/amostd.pdf">"AMO Standards (1987)"</a> <span class="cs1-format">(PDF)</span>. Archery Manufacturers and Merchants Organization. 1987<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=AMO+Standards+%281987%29&rft.pub=Archery+Manufacturers+and+Merchants+Organization&rft.date=1987&rft_id=http%3A%2F%2Fwww.outlab.it%2Fdoc%2Famostd.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://peteward.com/AMOStandards.pdf">"AMO Standards (2001)"</a> <span class="cs1-format">(PDF)</span>. Archery Manufacturers and Merchants Organization. 2001<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=AMO+Standards+%282001%29&rft.pub=Archery+Manufacturers+and+Merchants+Organization&rft.date=2001&rft_id=http%3A%2F%2Fpeteward.com%2FAMOStandards.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.astm.org/Standards/F2031.htm">"ASTM F2031 - 05(2010) Standard Test Method for Measurement of Arrow Shaft Static Spine (Stiffness)"</a>. American Society for Testing and Materials. 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=ASTM+F2031+-+05%282010%29+Standard+Test+Method+for+Measurement+of+Arrow+Shaft+Static+Spine+%28Stiffness%29&rft.pub=American+Society+for+Testing+and+Materials&rft.date=2010&rft_id=http%3A%2F%2Fwww.astm.org%2FStandards%2FF2031.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCosgrove1994" class="citation book cs1 cs1-prop-long-vol">Cosgrove, Gabriela (1994). "Wooden Arrows". <i>The Traditional Bowyer's Bible</i>. Vol. Three. Guilford: The Lyons Press. p. 228. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-58574-087-X" title="Special:BookSources/1-58574-087-X"><bdi>1-58574-087-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Wooden+Arrows&rft.btitle=The+Traditional+Bowyer%27s+Bible&rft.place=Guilford&rft.pages=228&rft.pub=The+Lyons+Press&rft.date=1994&rft.isbn=1-58574-087-X&rft.aulast=Cosgrove&rft.aufirst=Gabriela&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArcher%27s+paradox" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Archer%27s_paradox&action=edit&section=6" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Archer%27s_paradox" class="extiw" title="commons:Category:Archer's paradox">Archer's paradox</a> at Wikimedia Commons</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=O7zewtuUM_0">The Archer's Paradox in SLOW MOTION</a> - video</li></ul> <div class="navbox-styles"><style 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abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Archery" title="Template:Archery"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Archery" title="Template talk:Archery"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Archery" title="Special:EditPage/Template:Archery"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Archery634" style="font-size:114%;margin:0 4em"><a href="/wiki/Archery" title="Archery">Archery</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/History_of_archery" title="History of archery">History</a> <ul><li><a href="/wiki/Chinese_archery" title="Chinese archery">Chinese</a></li> <li><a href="/wiki/Ky%C5%ABd%C5%8D" title="Kyūdō">Japanese</a></li> <li><a href="/wiki/Turkish_archery" title="Turkish archery">Turkish</a></li></ul></li> <li><a href="/wiki/History_of_crossbows" title="History of crossbows">History of crossbows</a></li> <li><a href="/wiki/Modern_competitive_archery" title="Modern competitive archery">Modern competitive archery</a></li> <li><a href="/wiki/World_Archery" title="World Archery">World Archery Federation</a></li> <li><a href="/wiki/World_Archery_Rankings" title="World Archery Rankings">World Archery Rankings</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Archer's paradox</a></li> <li><a href="/wiki/Mounted_archery" title="Mounted archery">Mounted archery</a> <ul><li><a href="/wiki/Ballista_elephant" title="Ballista elephant">Ballista elephant</a></li> <li><a href="/wiki/Yabusame" title="Yabusame">Yabusame</a></li></ul></li> <li><a href="/wiki/Run_archery" title="Run archery">Run archery</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bow_and_arrow" title="Bow and arrow">Bows</a> (<a href="/wiki/Yumi" title="Yumi">yumi</a>)<br /><a href="/wiki/Bow_shape" title="Bow shape">Bow shape</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arbalest" title="Arbalest">Arbalest</a></li> <li><a href="/wiki/Austroasiatic_crossbow" title="Austroasiatic crossbow">Austroasiatic crossbow</a></li> <li><a href="/wiki/Cable-backed_bow" title="Cable-backed bow">Cable-backed bow</a></li> <li><a href="/wiki/Composite_bow" title="Composite bow">Composite bow</a></li> <li><a href="/wiki/Compound_bow" title="Compound bow">Compound bow</a></li> <li><a href="/wiki/Crossbow" title="Crossbow">Crossbow</a></li> <li><a href="/wiki/English_longbow" title="English longbow">English longbow</a></li> <li><a href="/wiki/Flatbow" title="Flatbow">Flatbow</a></li> <li><a href="/wiki/Gakgung" title="Gakgung">Gakgung</a></li> <li><a href="/wiki/Holmegaard_bow" title="Holmegaard bow">Holmegaard bow</a></li> <li><a href="/wiki/Laminated_bow" title="Laminated bow">Laminated bow</a></li> <li><a href="/wiki/Longbow" title="Longbow">Longbow</a></li> <li><a href="/wiki/Mongol_bow" title="Mongol bow">Mongol bow</a></li> <li><a href="/wiki/Recurve_bow" title="Recurve bow">Recurve bow</a></li> <li><a href="/wiki/Self_bow" title="Self bow">Self bow</a></li> <li><a href="/wiki/Takedown_bow" title="Takedown bow">Takedown bow</a></li> <li><a href="/wiki/Welsh_bow" title="Welsh bow">Welsh bow</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Equipment</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arrow" title="Arrow">Arrow</a> <ul><li><a href="/wiki/Ya_(arrow)" title="Ya (arrow)">Ya</a></li></ul></li> <li><a href="/wiki/Arrowhead" title="Arrowhead">Arrowhead</a></li> <li><a href="/wiki/Bowstring" title="Bowstring">Bowstring</a></li> <li><a href="/wiki/Bracer" title="Bracer">Bracer</a></li> <li><a href="/wiki/Arrow_cresting" title="Arrow cresting">Cresting machine</a></li> <li><a href="/wiki/Finger_tab" title="Finger tab">Finger tab</a></li> <li><a href="/wiki/Fletching" title="Fletching">Fletching</a></li> <li><a href="/wiki/Flu-flu_arrow" title="Flu-flu arrow">Flu-flu arrow</a></li> <li><a href="/wiki/Release_aid" title="Release aid">Release aid</a></li> <li><a href="/wiki/Crossbow_bolt" title="Crossbow bolt">Quarrel</a></li> <li><a href="/wiki/Quiver" title="Quiver">Quiver</a></li> <li><a href="/wiki/Shooting_target#Archery_sports" title="Shooting target">Target</a></li> <li><a href="/wiki/Thumb_ring" title="Thumb ring">Thumb ring</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Activities</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bowfishing" title="Bowfishing">Bowfishing</a></li> <li><a href="/wiki/Bowhunting" title="Bowhunting">Bowhunting</a></li> <li><a href="/wiki/Bowyer" title="Bowyer">Bowyer</a></li> <li><a href="/wiki/Clout_archery" title="Clout archery">Clout archery</a></li> <li><a href="/wiki/Field_archery" title="Field archery">Field archery</a></li> <li><a href="/wiki/Popinjay_(sport)" title="Popinjay (sport)">Popinjay</a></li> <li><a href="/wiki/Target_archery" title="Target archery">Target archery</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Competitions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Archery_at_the_Summer_Olympics" title="Archery at the Summer Olympics">Olympics</a> <ul><li><a href="/wiki/Archery_at_the_Summer_Youth_Olympics" title="Archery at the Summer Youth Olympics">Youth</a></li></ul></li> <li><a href="/wiki/World_Archery_Championships" title="World Archery Championships">World Championships</a> <ul><li><a href="/wiki/World_Archery_Youth_Championships" title="World Archery Youth Championships">Youth</a></li></ul></li> <li><a href="/wiki/Archery_World_Cup" title="Archery World Cup">World Cup</a></li> <li><a href="/wiki/Archery_at_the_Summer_Paralympics" title="Archery at the Summer Paralympics">Paralympics</a></li> <li><a href="/wiki/Archery_at_the_Summer_World_University_Games" title="Archery at the Summer World University Games">Universiade</a></li> <li><a href="/wiki/World_University_Archery_Championships" title="World University Archery Championships">World University Archery Championships</a></li> <li><a href="/wiki/Archery_at_the_Military_World_Games" title="Archery at the Military World Games">Military World Games</a></li> <li>Continental <ul><li><a href="/wiki/African_Archery_Championships" title="African Archery Championships">Africa</a></li> <li><a href="/wiki/Pan_American_Archery_Championships" title="Pan American Archery Championships">Americas</a></li> <li><a href="/wiki/Asian_Archery_Championships" title="Asian Archery Championships">Asia</a></li> <li><a href="/wiki/European_Archery_Championships" title="European Archery Championships">Europe</a></li></ul></li> <li><a href="/wiki/Naadam#Archery" title="Naadam">Naadam</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" 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