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class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Construction" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Construction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Construction</span> </div> </a> <button aria-controls="toc-Construction-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Construction subsection</span> </button> <ul id="toc-Construction-sublist" class="vector-toc-list"> <li id="toc-Compression_spokes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Compression_spokes"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Compression spokes</span> </div> </a> <ul id="toc-Compression_spokes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tension_spokes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tension_spokes"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Tension spokes</span> </div> </a> <ul id="toc-Tension_spokes-sublist" class="vector-toc-list"> <li id="toc-Types" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Types"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Types</span> </div> </a> <ul id="toc-Types-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tangential_lacing" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Tangential_lacing"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>Tangential lacing</span> </div> </a> <ul id="toc-Tangential_lacing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wheelbuilding" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Wheelbuilding"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.3</span> <span>Wheelbuilding</span> </div> </a> <ul id="toc-Wheelbuilding-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Spoke_length" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Spoke_length"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Spoke length</span> </div> </a> <button aria-controls="toc-Spoke_length-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Spoke length subsection</span> </button> <ul id="toc-Spoke_length-sublist" class="vector-toc-list"> <li id="toc-Calculation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Calculation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Calculation</span> </div> </a> <ul id="toc-Calculation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Derivation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Derivation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Derivation</span> </div> </a> <ul id="toc-Derivation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Spoke</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 33 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-33" 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">33 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B1%D9%85%D9%82_(%D8%B9%D8%AC%D9%84%D8%A7%D8%AA)" title="برمق (عجلات) – Arabic" lang="ar" hreflang="ar" data-title="برمق (عجلات)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Rayo" title="Rayo – Aragonese" lang="an" hreflang="an" data-title="Rayo" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/D%C9%99nd%C9%99n%C9%99" title="Dəndənə – Azerbaijani" lang="az" hreflang="az" data-title="Dəndənə" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%86%D0%B0" title="Спица – Bulgarian" lang="bg" hreflang="bg" data-title="Спица" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%99%C4%95%D0%BF%D1%81%D0%B5" title="Йĕпсе – Chuvash" lang="cv" hreflang="cv" data-title="Йĕпсе" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Paprsek_(kolo)" title="Paprsek (kolo) – Czech" lang="cs" hreflang="cs" data-title="Paprsek (kolo)" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Eger" title="Eger – Danish" lang="da" hreflang="da" data-title="Eger" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Speiche_(Rad)" title="Speiche (Rad) – German" lang="de" hreflang="de" data-title="Speiche (Rad)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kodar" title="Kodar – Estonian" lang="et" hreflang="et" data-title="Kodar" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Radio_(rueda)" title="Radio (rueda) – Spanish" lang="es" hreflang="es" data-title="Radio (rueda)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Spoko" title="Spoko – Esperanto" lang="eo" hreflang="eo" data-title="Spoko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Gurpil-izpi" title="Gurpil-izpi – Basque" lang="eu" hreflang="eu" data-title="Gurpil-izpi" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D8%B1%D9%87" title="پره – Persian" lang="fa" hreflang="fa" data-title="پره" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rayon_(technique)" title="Rayon (technique) – French" lang="fr" hreflang="fr" data-title="Rayon (technique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Gath_(cuibhle)" title="Gath (cuibhle) – Scottish Gaelic" lang="gd" hreflang="gd" data-title="Gath (cuibhle)" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%94%ED%80%B4%EC%82%B4" title="바퀴살 – Korean" lang="ko" hreflang="ko" data-title="바퀴살" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Spoko" title="Spoko – Ido" lang="io" hreflang="io" data-title="Spoko" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kerangka_roda" title="Kerangka roda – Indonesian" lang="id" hreflang="id" data-title="Kerangka roda" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Raggio_(ruota)" title="Raggio (ruota) – Italian" lang="it" hreflang="it" data-title="Raggio (ruota)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%86%E0%B2%B0%E0%B3%86" title="ಆರೆ – Kannada" lang="kn" hreflang="kn" data-title="ಆರೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Speech" title="Speech – Luxembourgish" lang="lb" hreflang="lb" data-title="Speech" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%85%E1%80%95%E1%80%AF%E1%80%90%E1%80%BA%E1%80%90%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA" title="စပုတ်တိုင် – Burmese" lang="my" hreflang="my" data-title="စပုတ်တိုင်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Spaak_(wiel)" title="Spaak (wiel) – Dutch" lang="nl" hreflang="nl" data-title="Spaak (wiel)" 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%B9%E3%83%9D%E3%83%BC%E3%82%AF" title="スポーク – Japanese" lang="ja" hreflang="ja" data-title="スポーク" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Eike_(hjul)" title="Eike (hjul) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Eike (hjul)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Szprycha" title="Szprycha – Polish" lang="pl" hreflang="pl" data-title="Szprycha" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Raio_(roda)" title="Raio (roda) – Portuguese" lang="pt" hreflang="pt" data-title="Raio (roda)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%86%D0%B0" title="Спица – Russian" lang="ru" hreflang="ru" data-title="Спица" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Spoke" title="Spoke – Simple English" lang="en-simple" hreflang="en-simple" data-title="Spoke" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Eker" title="Eker – Swedish" lang="sv" hreflang="sv" data-title="Eker" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%86%D1%8F" title="Спиця – Ukrainian" lang="uk" hreflang="uk" data-title="Спиця" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/%C5%A0p%C4%ABkis" title="Špīkis – Samogitian" lang="sgs" hreflang="sgs" data-title="Špīkis" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%BC%BB%E6%A2%9D" title="輻條 – Chinese" lang="zh" hreflang="zh" data-title="輻條" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q845671#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Part of a wheel extending radially from the hub to the rim</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">For other uses, see <a href="/wiki/Spoke_(disambiguation)" class="mw-disambig" title="Spoke (disambiguation)">Spoke (disambiguation)</a>.</div> <p>A <b>spoke</b> is one of some number of rods radiating from the center of a <a href="/wiki/Wheel" title="Wheel">wheel</a> (the <a href="/wiki/Bicycle_hub" class="mw-redirect" title="Bicycle hub">hub</a> where the <a href="/wiki/Axle" title="Axle">axle</a> connects), connecting the hub with the round traction surface. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Wheel_Iran.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Wheel_Iran.jpg/220px-Wheel_Iran.jpg" decoding="async" width="220" height="244" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e6/Wheel_Iran.jpg 1.5x" data-file-width="275" data-file-height="305" /></a><figcaption>A spoked wheel on display at the <a href="/wiki/National_Museum_of_Iran" title="National Museum of Iran">National Museum of Iran</a>, in <a href="/wiki/Tehran" title="Tehran">Tehran</a>. The wheel is dated to the late 2nd millennium BCE and was excavated at <a href="/wiki/Choqa_Zanbil" class="mw-redirect" title="Choqa Zanbil">Choqa Zanbil</a>.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Cartwheel_and_axle_assembly.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Cartwheel_and_axle_assembly.jpg/220px-Cartwheel_and_axle_assembly.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Cartwheel_and_axle_assembly.jpg/330px-Cartwheel_and_axle_assembly.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Cartwheel_and_axle_assembly.jpg/440px-Cartwheel_and_axle_assembly.jpg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption>The remains of a pair of <a href="/wiki/Cart" title="Cart">cart</a> wheels with metal axle assembly.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ox_wagon_at_Aliwal_North.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Ox_wagon_at_Aliwal_North.jpg/220px-Ox_wagon_at_Aliwal_North.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Ox_wagon_at_Aliwal_North.jpg/330px-Ox_wagon_at_Aliwal_North.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Ox_wagon_at_Aliwal_North.jpg/440px-Ox_wagon_at_Aliwal_North.jpg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption>An <a href="/wiki/Ox-wagon" title="Ox-wagon">ox-wagon</a> in <a href="/wiki/Aliwal_North" title="Aliwal North">Aliwal North</a>, <a href="/wiki/South_Africa" title="South Africa">South Africa</a>. Note the three missing spokes and the metal tire.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Wooden_Spokes.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Wooden_Spokes.JPG/220px-Wooden_Spokes.JPG" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Wooden_Spokes.JPG/330px-Wooden_Spokes.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Wooden_Spokes.JPG/440px-Wooden_Spokes.JPG 2x" data-file-width="1262" data-file-height="1200" /></a><figcaption>Wooden spoke wheel with metal rim from antique truck on display in <a href="/wiki/Underground_Atlanta" title="Underground Atlanta">Underground Atlanta</a>.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Bicycle_wheel.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Bicycle_wheel.jpg/220px-Bicycle_wheel.jpg" decoding="async" width="220" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Bicycle_wheel.jpg/330px-Bicycle_wheel.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Bicycle_wheel.jpg/440px-Bicycle_wheel.jpg 2x" data-file-width="1405" data-file-height="1917" /></a><figcaption>Metal <a href="/wiki/Tension-spoked_wheel" class="mw-redirect" title="Tension-spoked wheel">tension-spoked wheel</a> from a bicycle.</figcaption></figure> <p>The term originally referred to portions of a log that had been <a href="/wiki/Riving" class="mw-redirect" title="Riving">riven</a> (split lengthwise) into four or six sections. The radial members of a wagon wheel were made by carving a spoke (from a log) into their finished shape. A <a href="/wiki/Spokeshave" title="Spokeshave">spokeshave</a> is a <a href="/wiki/Tool" title="Tool">tool</a> originally developed for this purpose. Eventually, the term spoke was more commonly applied to the finished product of the <a href="/wiki/Wheelwright" title="Wheelwright">wheelwright</a>'s work than to the materials they used. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The spoked <a href="/wiki/Wheel" title="Wheel">wheel</a> was invented to allow the construction of lighter and swifter vehicles. The earliest physical evidence for spoked wheels were found in the <a href="/wiki/Sintashta_culture" title="Sintashta culture">Sintashta culture</a>, dating to <abbr title="circa">c.</abbr> 2000 BCE.<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> Soon after this, horse cultures of the <a href="/wiki/Caucasus" title="Caucasus">Caucasus</a> region used horse-drawn spoked-wheel war <a href="/wiki/Chariots" class="mw-redirect" title="Chariots">chariots</a> for the greater part of three centuries. They moved deep into the <a href="/wiki/Greek_peninsula" class="mw-redirect" title="Greek peninsula">Greek peninsula</a>, where they joined with the existing Mediterranean peoples to give rise, eventually, to <a href="/wiki/Classical_Greece" title="Classical Greece">classical Greece</a> after the breaking of <a href="/wiki/Minoan_civilization" title="Minoan civilization">Minoan</a> dominance and consolidations led by pre-classical <a href="/wiki/Sparta" title="Sparta">Sparta</a> and <a href="/wiki/Athens" title="Athens">Athens</a>. </p><p>Neo-<a href="/wiki/Chalcolithic" title="Chalcolithic">Chalcolithic</a>/proto-historic period (1800-1200 BCE)<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> paintings in various regions of India such as Chibbar Nulla, Chhatur Bhoj Nath Nulla, Kathotia, etc. depict the usage of chariots with spoked wheels.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Celt" class="mw-redirect" title="Celt">Celtic</a> chariots introduced an <a href="/wiki/Iron" title="Iron">iron</a> rim around the wheel in the 1st millennium BCE. The spoked wheel was in continued use without major modification until the 1870s, when <a href="/wiki/Wire_wheel" title="Wire wheel">wire wheels</a> and rubber <a href="/wiki/Tire" title="Tire">tires</a> were invented.<sup id="cite_ref-Herlihy_8-0" class="reference"><a href="#cite_note-Herlihy-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Construction">Construction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=2" title="Edit section: Construction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Spokes can be made of wood, metal, or synthetic fiber depending on whether they will be in <a href="/wiki/Tension_(mechanics)" class="mw-redirect" title="Tension (mechanics)">tension</a> or <a href="/wiki/Physical_compression" class="mw-redirect" title="Physical compression">compression</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Compression_spokes">Compression spokes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=3" title="Edit section: Compression spokes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The original type of spoked wheel with wooden spokes was used for <a href="/wiki/Horse" title="Horse">horse</a>-drawn <a href="/wiki/Carriage" title="Carriage">carriages</a> and <a href="/wiki/Wagon" title="Wagon">wagons</a>. In early motor cars, wooden spoked wheels of the <a href="/wiki/Artillery_wheel" title="Artillery wheel">artillery</a> type were normally used. </p><p>In a simple wooden wheel, a load on the hub causes the wheel rim to flatten slightly against the ground as the lowermost wooden spoke shortens and compresses. The other wooden spokes show no significant change. </p><p>Wooden spokes are mounted <a href="/wiki/Radius" title="Radius">radially</a>. They are also dished, usually to the outside of the vehicle, to prevent wobbling. Also, the dishing allows the wheel to compensate for expansion of the spokes due to absorbed moisture by dishing more.<sup id="cite_ref-Hansen_9-0" class="reference"><a href="#cite_note-Hansen-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Tension_spokes">Tension spokes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=4" title="Edit section: Tension spokes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Wire_wheel" title="Wire wheel">Wire wheel</a></div> <p>For use in <a href="/wiki/Bicycle" title="Bicycle">bicycles</a>, heavy wooden-spoked wheels were replaced by lighter wheels with spokes made of tensioned, adjustable metal wires, called <a href="/wiki/Wire_wheels" class="mw-redirect" title="Wire wheels">wire wheels</a>. These are also used in <a href="/wiki/Wheelchair" title="Wheelchair">wheelchairs</a>, <a href="/wiki/Motorcycle" title="Motorcycle">motorcycles</a>, <a href="/wiki/Automobile" class="mw-redirect" title="Automobile">automobiles</a>, and early <a href="/wiki/Aircraft" title="Aircraft">aircraft</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Types">Types</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=5" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some types of wheels have removable spokes that can be replaced individually if they break or bend. These include bicycle and wheelchair wheels. High quality bicycles with conventional wheels use spokes of <a href="/wiki/Stainless_steel" title="Stainless steel">stainless steel</a>, while cheaper bicycles may use <a href="/wiki/Galvanized" class="mw-redirect" title="Galvanized">galvanized</a> (also called "rustless") or <a href="/wiki/Chrome_plated" class="mw-redirect" title="Chrome plated">chrome plated</a> spokes. While a good quality spoke is capable of supporting about 225 <a href="/wiki/Kgf" class="mw-redirect" title="Kgf">kgf</a> (c. 500 <a href="/wiki/Pounds-force" class="mw-redirect" title="Pounds-force">pounds-force</a> or 2,200 <a href="/wiki/Newton_(unit)" title="Newton (unit)">newtons</a>) of tension, they are used at a fraction of this load to avoid suffering fatigue failures. Since bicycle and wheelchair wheel spokes are only in tension, flexible and strong materials such as synthetic fibers, are also occasionally used.<sup id="cite_ref-spinergy_10-0" class="reference"><a href="#cite_note-spinergy-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Metal spokes can also be ovalized or bladed to reduce aerodynamic drag, and butted (double or even triple) to reduce weight while maintaining strength. </p><p>A variation on the wire-spoked wheel was Tioga's "Tension Disk", which appeared superficially to be a solid disk but was in fact constructed using the same principles as a normal tension-spoked wheel. Instead of individual wire spokes, a continuous thread of Kevlar (<a href="/wiki/Aramid" title="Aramid">aramid</a>) was used to lace the hub to the rim under high tension. The threads were encased in a translucent disk for protection and some aerodynamic benefit, but this was not a structural component. </p> <table class="wikitable"> <caption>usual spoke diameters<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <th><a href="/wiki/Wire_gauge" title="Wire gauge">wire gauge</a></th> <th>diameter</th> <th>section area </th></tr> <tr> <td>15G</td> <td>1.8 mm</td> <td>3.24 mm<sup>2</sup> </td></tr> <tr> <td>14G</td> <td>2.0 mm</td> <td>4 mm<sup>2</sup> </td></tr> <tr> <td>13G</td> <td>2.3 mm</td> <td>5.29 mm<sup>2</sup> </td></tr> <tr> <td>12G</td> <td>2.6 mm</td> <td>6.76 mm<sup>2</sup> </td></tr> <tr> <td>11G</td> <td>2.9 mm</td> <td>8.41 mm<sup>2</sup> </td></tr> <tr> <td>10G</td> <td>3.2 mm</td> <td>10.24 mm<sup>2</sup> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Tangential_lacing">Tangential lacing</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=6" title="Edit section: Tangential lacing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Wire spokes can be radial to the hub but are more often mounted <a href="/wiki/Tangent" title="Tangent">tangentially</a> to the hub. Tangential spoking allows for the transfer of torque between the rim and the hub. Tangential spokes are thus necessary for the drive wheel, which has torque at the hub from pedalling, and any wheels using hub-mounted brakes such as disk or band brakes, which transfer torque from the rim to the brake in the opposite direction—(via the hub) when braking. </p> <div class="mw-heading mw-heading4"><h4 id="Wheelbuilding">Wheelbuilding</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=7" title="Edit section: Wheelbuilding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Constructing a tension-spoked wheel from its constituent parts is called <a href="/wiki/Wheelbuilding" title="Wheelbuilding">wheelbuilding</a> and requires the correct building procedure for a strong and long-lasting end product. Tensioned spokes are usually attached to the rim or sometimes the hub with a <a href="/wiki/Spoke_nipple" title="Spoke nipple">spoke nipple</a>. The other end is commonly peened into a disk or uncommonly bent into a "Z" to keep it from pulling through its hole in the hub. The bent version has the advantage of replacing a broken spoke in a rear bicycle wheel without having to remove the <a href="/wiki/Cogset" title="Cogset">rear gears</a>. </p><p>Wire wheels, with their excellent weight-to-strength ratio, soon became popular for light vehicles. For everyday cars, wire wheels were soon replaced by the less expensive metal disc wheel, but wire wheels remained popular for <a href="/wiki/Sports_car" title="Sports car">sports cars</a> up to the 1960s. Spoked wheels are still popular on <a href="/wiki/Motorcycle" title="Motorcycle">motorcycles</a> and <a href="/wiki/Bicycle" title="Bicycle">bicycles</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Spoke_length">Spoke length</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=8" title="Edit section: Spoke length"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When <a href="/wiki/Wheelbuilding" title="Wheelbuilding">building a bicycle wheel</a>, the spokes must have the correct length, otherwise there may not be enough threads engaged, producing a weaker wheel, or they may protrude through the rim and possibly puncture the inner tube. </p> <div class="mw-heading mw-heading3"><h3 id="Calculation">Calculation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=9" title="Edit section: Calculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For bicycle spokes, the spoke length is defined from the flange seat to the thread tip. For spokes with bent ends, the nominal spoke length does <i>not</i> include the width of the spoke at the bent end. </p><p>For wheels with crossed spokes (which are the norm), the desired spoke length is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l={\sqrt {d^{2}+{r_{1}}^{2}+{r_{2}}^{2}-2\,r_{1}r_{2}\cos(a)}}-r_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mspace width="thinmathspace" /> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l={\sqrt {d^{2}+{r_{1}}^{2}+{r_{2}}^{2}-2\,r_{1}r_{2}\cos(a)}}-r_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0fd10865358cac4d9575019938546f79235d2f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:40.459ex; height:4.843ex;" alt="{\displaystyle l={\sqrt {d^{2}+{r_{1}}^{2}+{r_{2}}^{2}-2\,r_{1}r_{2}\cos(a)}}-r_{3}}"></span></dd></dl> <p>where </p> <ul><li><i><b>d</b></i> = distance from the center of hub (along the axis) to <a href="/wiki/Flange" title="Flange">flange</a>, for example 30 mm,</li> <li><i><b>r</b></i><sub>1</sub> = spoke hole circle radius of the hub, for example 19.5 mm,</li> <li><i><b>r</b></i><sub>2</sub> = half of effective Rim Diameter (ERD), or the diameter the ends of the spokes make in a built wheel (see 'Discussion' attached to this article for explanation) of the rim, for example 301 mm,</li> <li><i><b>r</b></i><sub>3</sub> = radius of spoke holes in the <i>flange</i>, for example 1.1 mm,</li> <li><i><b>m</b></i> = number of spokes to be used for one side of the wheel, for example <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">36</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span>=18,</li> <li><i><b>k</b></i> = number of crossings per spoke, for example 3 and</li> <li><i><b>a</b></i> = 360° <i>k</i>/<i>m</i>, for example <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">360° ⋅ 3</span><span class="sr-only">/</span><span class="den">18</span></span>⁠</span> = 60°.</li></ul> <p>Regarding <i><b>d</b></i>: For a symmetric wheel such as a front wheel with no disc brake, this is half the distance between the flanges. For an asymmetric wheel such as a front wheel with <a href="/wiki/Disc_brake" title="Disc brake">disc brake</a> or a rear wheel with chain <a href="/wiki/Derailleur" title="Derailleur">derailleur</a>, the value of <i><b>d</b></i> is different for the left and right sides. </p><p><i><b>a</b></i> is the angle between (1) the radius to a nipple hole in the rim to which a spoke is attached, and, (2) the radius to the flange hole holding the spoke. The spoke crosses either 1, 2, or 3 oppositely pointing spokes depending on the lacing design. On the flange, the angle between the radii of adjacent holes is 360°/<i>m</i> (for equally spaced holes). For each spoke crossed, the hub is rotated with reference to the rim one "angle between adjacent flange holes". Thus, multiplying the "angle between adjacent flange holes" by <i>k</i> gives the angle <i><b>a</b></i>. For example, a 32 spoke wheel has 16 spokes per side, 360° divided by 16 equals 22.5°. Multiply 22.5° ("angle between adjacent flange holes") by the number of crossings to get the angle <i><b>a</b></i>—if 3-crosses, the 32 spoke wheel has an angle <i><b>a</b></i> of 67.5°. Regarding <i><b>r</b></i><sub>3</sub>: The size of the spoke holes in the flange does not matter for the needed spoke length. This term removes the effect of the hole size. Since the holes are usually small (just over 2 mm in diameter), the effect is small and in practice matters little. </p><p>For <a href="/wiki/Wheelbuilding" title="Wheelbuilding">radially</a> spoked wheels (zero crossings), the formula simplifies to the <a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a>, with spoke length <i><b>l</b></i> plus <i><b>r</b></i><sub>3</sub> being the slope, <i><b>r</b></i><sub>2</sub> minus <i><b>r</b></i><sub>1</sub> being the base, and <i><b>d</b></i> being the rise: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (l+r_{3})^{2}=(r_{2}-r_{1})^{2}+d^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>l</mi> <mo>+</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (l+r_{3})^{2}=(r_{2}-r_{1})^{2}+d^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a31b55533a1eaf44a4120dc42553c6bebb08d19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.621ex; height:3.176ex;" alt="{\displaystyle (l+r_{3})^{2}=(r_{2}-r_{1})^{2}+d^{2}}"></span>; or solving for the length</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l={\sqrt {d^{2}+(r_{2}-r_{1})^{2}}}-r_{3}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l={\sqrt {d^{2}+(r_{2}-r_{1})^{2}}}-r_{3}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5a07c63a2c1ced490c8d0dd060eb06f824b81e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:26.728ex; height:4.843ex;" alt="{\displaystyle l={\sqrt {d^{2}+(r_{2}-r_{1})^{2}}}-r_{3}.}"></span></dd></dl> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Spoke-length.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Spoke-length.png/300px-Spoke-length.png" decoding="async" width="300" height="301" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Spoke-length.png/450px-Spoke-length.png 1.5x, //upload.wikimedia.org/wikipedia/commons/1/1a/Spoke-length.png 2x" data-file-width="598" data-file-height="600" /></a><figcaption>A flat view of a crossed wheel with one spoke visible</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Derivation">Derivation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=10" title="Edit section: Derivation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The spoke length formula computes the length of the <a href="/wiki/Space_diagonal" title="Space diagonal">space diagonal</a> of an imaginary <a href="/wiki/Cuboid" title="Cuboid">rectangular box</a>. Imagine holding a wheel in front of you such that a nipple is at the top. Look at the wheel from along the axis. The spoke through the top hole is now a diagonal of the imaginary box. The box has a depth of <i>d</i>, a height of <i>r</i><sub>2</sub>-<i>r</i><sub>1</sub>cos(<i>α</i>) and a width of <i>r</i><sub>1</sub>sin(<i>a</i>). </p><p>Equivalently, the <a href="/wiki/Law_of_cosines" title="Law of cosines">law of cosines</a> may be used to first compute the length of the spoke as projected on the wheel's plane (as illustrated in the diagram), followed by an application of the <a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a>. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=11" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Bicycle_wheel" title="Bicycle wheel">Bicycle wheel</a></li> <li><a href="/wiki/Spoke_nipple" title="Spoke nipple">Spoke nipple</a></li> <li><a href="/wiki/Spoke_wrench" title="Spoke wrench">Spoke wrench</a></li> <li><a href="/wiki/Spokeshave" title="Spokeshave">Spokeshave</a></li> <li><a href="/wiki/Wheelbuilding" title="Wheelbuilding">Wheelbuilding</a></li> <li><a href="/wiki/Wire_wheel" title="Wire wheel">Wire wheel</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spoke&action=edit&section=12" title="Edit section: Notes"><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"><ol class="references"> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Neumayer 1800-1200 BCE;<sup id="cite_ref-Neumayer_Chariots_slideshow_2-0" class="reference"><a href="#cite_note-Neumayer_Chariots_slideshow-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Harappan_Neumayer_3-0" class="reference"><a href="#cite_note-Harappan_Neumayer-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Celeste Paxton 2300-1000 BCE).<sup id="cite_ref-Paxton_4-0" class="reference"><a href="#cite_note-Paxton-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> See Bradshaw Foundation, <a rel="nofollow" class="external text" href="http://www.bradshawfoundation.com/india/pachmarhi/index.php">The Prehistoric Paintings of the Pachmarhi Hills</a>, for proto-historic/chalocolithic.</span> </li> </ol></div></div> <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=Spoke&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap"><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">Lindner, Stephan, (2020). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C4FDF8C5E7D1D20A28BEB7F6C50A9AF4/S0003598X2000037Xa.pdf/chariots_in_the_eurasian_steppe_a_bayesian_approach_to_the_emergence_of_horsedrawn_transport_in_the_early_second_millennium_bc.pdf">"Chariots in the Eurasian Steppe: a Bayesian approach to the emergence of horse-drawn transport in the earlysecond millennium BC"</a>, in Antiquity, Vol 94, Issue 374, April 2020, p. 367: "...The 12 calibrated radiocarbon dates belonging to the Sintashta horizon range between 2050 and 1760 cal BC (at 95.4% confidence; Epimakhov & Krause 2013: 137). These dates correlate well with the seven AMS-sampled Sintashta graves in the associated KA-5cemetery, which date to 2040–1730 cal BC (95.4% confidence...)".</span> </li> <li id="cite_note-Neumayer_Chariots_slideshow-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Neumayer_Chariots_slideshow_2-0">^</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 id="CITEREFNeumayer" class="citation web cs1">Neumayer, Erwin. <a rel="nofollow" class="external text" href="https://www.harappa.com/sites/default/files/pdf/WHEELS%20in%20Indian%20Rock%20Art%20Erwin%20Neumayer.pdf">"Chariots in the Chalcolithic Rock Art of Indian"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Chariots+in+the+Chalcolithic+Rock+Art+of+Indian&rft.aulast=Neumayer&rft.aufirst=Erwin&rft_id=https%3A%2F%2Fwww.harappa.com%2Fsites%2Fdefault%2Ffiles%2Fpdf%2FWHEELS%2520in%2520Indian%2520Rock%2520Art%2520Erwin%2520Neumayer.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASpoke" class="Z3988"></span></span> </li> <li id="cite_note-Harappan_Neumayer-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Harappan_Neumayer_3-0">^</a></b></span> <span class="reference-text">harappa.com, <a rel="nofollow" class="external text" href="https://www.harappa.com/content/chariots-chalcolithic-rock-art-india">Chariots in the Chalcolithic Rock Art of India</a></span> </li> <li id="cite_note-Paxton-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Paxton_4-0">^</a></b></span> <span class="reference-text">Celeste Paxton (2016), in <a rel="nofollow" class="external text" href="https://www.horsetalk.co.nz/2016/07/22/voices-past-researcher-mystery-40-centuries/">Voices from the past: Researcher explores a mystery across 40 centuries </a>.</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="CITEREFNeumayer2013" class="citation book cs1">Neumayer, Erwin (28 March 2013). <i>Prehistoric Rock Art of India</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0198060987" title="Special:BookSources/978-0198060987"><bdi>978-0198060987</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Prehistoric+Rock+Art+of+India&rft.date=2013-03-28&rft.isbn=978-0198060987&rft.aulast=Neumayer&rft.aufirst=Erwin&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASpoke" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeumayer" class="citation web cs1">Neumayer, Erwin. <a rel="nofollow" class="external text" href="https://www.harappa.com/sites/default/files/pdf/WHEELS%20in%20Indian%20Rock%20Art%20Erwin%20Neumayer.pdf">"The Chariot in Indian Rock Art"</a> <span class="cs1-format">(PDF)</span>. <i>Harrapa.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Harrapa.com&rft.atitle=The+Chariot+in+Indian+Rock+Art&rft.aulast=Neumayer&rft.aufirst=Erwin&rft_id=https%3A%2F%2Fwww.harappa.com%2Fsites%2Fdefault%2Ffiles%2Fpdf%2FWHEELS%2520in%2520Indian%2520Rock%2520Art%2520Erwin%2520Neumayer.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASpoke" class="Z3988"></span></span> </li> <li id="cite_note-Herlihy-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Herlihy_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHerlihy2004" class="citation book cs1">Herlihy, David (2004). <a rel="nofollow" class="external text" href="https://archive.org/details/bicyclehistory0000herl/page/141"><i>Bicycle: the History</i></a>. Yale University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bicyclehistory0000herl/page/141">141</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-300-10418-9" title="Special:BookSources/0-300-10418-9"><bdi>0-300-10418-9</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2009-09-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Bicycle%3A+the+History&rft.pages=141&rft.pub=Yale+University+Press&rft.date=2004&rft.isbn=0-300-10418-9&rft.aulast=Herlihy&rft.aufirst=David&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbicyclehistory0000herl%2Fpage%2F141&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASpoke" class="Z3988"></span></span> </li> <li id="cite_note-Hansen-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hansen_9-0">^</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/20060814231954/http://www.hansenwheel.com/Wagon%20Wheels.htm">"Hansen Wheel and Wagon Shop"</a>. 2006. Archived from <a rel="nofollow" class="external text" href="http://www.hansenwheel.com/Wagon%20Wheels.htm">the original</a> on 2006-08-14<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-08-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Hansen+Wheel+and+Wagon+Shop&rft.date=2006&rft_id=http%3A%2F%2Fwww.hansenwheel.com%2FWagon%2520Wheels.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASpoke" class="Z3988"></span></span> </li> <li id="cite_note-spinergy-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-spinergy_10-0">^</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/20111030122350/http://www.spinergy.com/catalog/tech_special_feature_v2.php">"PBO Spoke Technology"</a>. 2006. Archived from <a rel="nofollow" class="external text" href="http://www.spinergy.com/catalog/tech_special_feature_v2.php">the original</a> on 2011-10-30<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-10-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=PBO+Spoke+Technology&rft.date=2006&rft_id=http%3A%2F%2Fwww.spinergy.com%2Fcatalog%2Ftech_special_feature_v2.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASpoke" 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="https://www.sapim.be/spokes/basic/leader">"Basic spokes"</a>. Sapim N.V.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Basic+spokes&rft.pub=Sapim+N.V.&rft_id=https%3A%2F%2Fwww.sapim.be%2Fspokes%2Fbasic%2Fleader&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASpoke" 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=Spoke&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wiktionary-logo-en-v2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/spoke" class="extiw" title="wiktionary:Special:Search/spoke">spoke</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.rst.mp-all.de/splaenge.htm">Online spoke length calculator (German), uses slightly different measures than the above formula</a> <span class="languageicon">(in German)</span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl 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title="Seatpost">Seatpost</a></li> <li><a href="/wiki/Bicycle_saddle" title="Bicycle saddle">Saddle</a></li> <li><a href="/wiki/Bottom_bracket" title="Bottom bracket">Bottom bracket</a></li> <li><a href="/wiki/Fork_end" title="Fork end">Fork end</a></li> <li><a href="/wiki/Bicycle_suspension" title="Bicycle suspension">Suspension</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Bicycle_diagram.svg" class="mw-file-description" title="Diagram"><img alt="Diagram" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Bicycle_diagram.svg/450px-Bicycle_diagram.svg.png" decoding="async" width="450" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Bicycle_diagram.svg/675px-Bicycle_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Bicycle_diagram.svg/900px-Bicycle_diagram.svg.png 2x" data-file-width="1000" data-file-height="500" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bicycle_wheel" title="Bicycle wheel">Wheels</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bicycle_tire" title="Bicycle tire">Tire</a></li> <li><a class="mw-selflink selflink">Spoke</a></li> <li><a href="/wiki/Spoke_nipple" title="Spoke nipple">Spoke nipple</a></li> <li><a href="/wiki/Valve_stem" title="Valve stem">Valve stem</a></li> <li><a href="/wiki/Dustcap" title="Dustcap">Dustcap</a></li> <li><a href="/wiki/Quick_release_skewer" title="Quick release skewer">Quick release skewer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bicycle_drivetrain_systems" title="Bicycle drivetrain systems">Drivetrain</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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title="Shifter (bicycle part)">Shifter</a></li> <li><a href="/wiki/Bowden_cable" title="Bowden cable">Bowden cable</a></li> <li><a href="/wiki/Cable_guide" title="Cable guide">Cable guide</a></li> <li><a href="/wiki/Bicycle_brake" title="Bicycle brake">Brake</a></li> <li><a href="/wiki/Ferrule" title="Ferrule">Ferrule</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Peripherals</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bicycle_basket" title="Bicycle basket">Basket</a></li> <li><a href="/wiki/Bicycle_bell" title="Bicycle bell">Bell</a></li> <li><a href="/wiki/Bottle_cage" title="Bottle cage">Bottle cage</a></li> <li><a href="/wiki/Bicycle_fairing" title="Bicycle fairing">Fairing</a></li> <li><a href="/wiki/Cyclocomputer" title="Cyclocomputer">Cyclocomputer</a></li> <li><a href="/wiki/Kickstand" title="Kickstand">Kickstand</a></li> <li><a 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