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Flywheel - Wikipedia
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id="toc-Applications-sublist" class="vector-toc-list"> </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">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-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">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-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">9</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" > <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">Flywheel</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 60 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-60" 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">60 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Vliegwiel" title="Vliegwiel – Afrikaans" lang="af" hreflang="af" data-title="Vliegwiel" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%B0%D8%A7%D9%81%D8%A9" title="حذافة – Arabic" lang="ar" hreflang="ar" data-title="حذافة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Nazim%C3%A7arx" title="Nazimçarx – Azerbaijani" lang="az" hreflang="az" data-title="Nazimçarx" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AB%E0%A7%8D%E0%A6%B2%E0%A6%BE%E0%A6%87%E0%A6%B9%E0%A7%81%E0%A6%87%E0%A6%B2" title="ফ্লাইহুইল – Bangla" lang="bn" hreflang="bn" data-title="ফ্লাইহুইল" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D1%85%D0%B0%D0%B2%D1%96%D0%BA" title="Махавік – Belarusian" lang="be" hreflang="be" data-title="Махавік" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9C%D0%B0%D1%85%D0%B0%D0%B2%D1%96%D0%BA" title="Махавік – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Махавік" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%85%D0%BE%D0%B2%D0%B8%D0%BA" title="Маховик – Bulgarian" lang="bg" hreflang="bg" data-title="Маховик" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A4%E0%BD%B4%E0%BD%82%E0%BD%A6%E0%BC%8B%E0%BD%A0%E0%BD%81%E0%BD%BC%E0%BD%A2%E0%BC%8D" title="ཤུགས་འཁོར། – Tibetan" lang="bo" hreflang="bo" data-title="ཤུགས་འཁོར།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Zamajac" title="Zamajac – Bosnian" lang="bs" hreflang="bs" data-title="Zamajac" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Volant_d%27in%C3%A8rcia" title="Volant d'inèrcia – Catalan" lang="ca" hreflang="ca" data-title="Volant d'inèrcia" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Setrva%C4%8Dn%C3%ADk" title="Setrvačník – Czech" lang="cs" hreflang="cs" data-title="Setrvačník" 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/Svinghjul" title="Svinghjul – Danish" lang="da" hreflang="da" data-title="Svinghjul" 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/Schwungrad" title="Schwungrad – German" lang="de" hreflang="de" data-title="Schwungrad" 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/Hooratas" title="Hooratas – Estonian" lang="et" hreflang="et" data-title="Hooratas" 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/Volante_de_inercia" title="Volante de inercia – Spanish" lang="es" hreflang="es" data-title="Volante de inercia" 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/Inercirado" title="Inercirado – Esperanto" lang="eo" hreflang="eo" data-title="Inercirado" 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/Inertzia-bolante" title="Inertzia-bolante – Basque" lang="eu" hreflang="eu" data-title="Inertzia-bolante" 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/%DA%86%D8%B1%D8%AE_%D9%84%D9%86%DA%AF%D8%B1" title="چرخ لنگر – Persian" lang="fa" hreflang="fa" data-title="چرخ لنگر" 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/Volant_d%27inertie" title="Volant d'inertie – French" lang="fr" hreflang="fr" data-title="Volant d'inertie" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Roth_l%C3%BAstair" title="Roth lústair – Irish" lang="ga" hreflang="ga" data-title="Roth lústair" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Volante_de_inercia" title="Volante de inercia – Galician" lang="gl" hreflang="gl" data-title="Volante de inercia" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%8C%EB%9D%BC%EC%9D%B4%ED%9C%A0" title="플라이휠 – Korean" lang="ko" hreflang="ko" data-title="플라이휠" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A4%A4%E0%A4%BF%E0%A4%AA%E0%A4%BE%E0%A4%B2%E0%A4%95_%E0%A4%9A%E0%A4%95%E0%A5%8D%E0%A4%B0" title="गतिपालक चक्र – Hindi" lang="hi" hreflang="hi" data-title="गतिपालक चक्र" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Zama%C5%A1njak" title="Zamašnjak – Croatian" lang="hr" hreflang="hr" data-title="Zamašnjak" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Flugroto" title="Flugroto – Ido" lang="io" hreflang="io" data-title="Flugroto" 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/Roda_gila" title="Roda gila – Indonesian" lang="id" hreflang="id" data-title="Roda gila" 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/Volano_(meccanica)" title="Volano (meccanica) – Italian" lang="it" hreflang="it" data-title="Volano (meccanica)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%9C%D7%92%D7%9C_%D7%AA%D7%A0%D7%95%D7%A4%D7%94" title="גלגל תנופה – Hebrew" lang="he" hreflang="he" data-title="גלגל תנופה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%A5%E1%83%9C%E1%83%94%E1%83%95%E1%83%90%E1%83%A0%E1%83%90" title="მქნევარა – Georgian" lang="ka" hreflang="ka" data-title="მქნევარა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%85%D0%BE%D0%B2%D0%B8%D0%BA" title="Маховик – Kazakh" lang="kk" hreflang="kk" data-title="Маховик" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%B0%D1%85%D0%BE%D0%B2%D0%B8%D0%BA" title="Маховик – Kyrgyz" lang="ky" hreflang="ky" data-title="Маховик" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Spararats" title="Spararats – Latvian" lang="lv" hreflang="lv" data-title="Spararats" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Schwongrad" title="Schwongrad – Luxembourgish" lang="lb" hreflang="lb" data-title="Schwongrad" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Lendker%C3%A9k" title="Lendkerék – Hungarian" lang="hu" hreflang="hu" data-title="Lendkerék" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AB%E0%B5%8D%E0%B4%B2%E0%B5%88_%E0%B4%B5%E0%B5%80%E0%B5%BD" title="ഫ്ലൈ വീൽ – Malayalam" lang="ml" hreflang="ml" data-title="ഫ്ലൈ വീൽ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Roda_tenaga" title="Roda tenaga – Malay" lang="ms" hreflang="ms" data-title="Roda tenaga" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%AD%D1%80%D1%87%D0%BB%D2%AF%D2%AF%D1%80_%D0%B4%D1%83%D0%B3%D1%83%D0%B9" title="Эрчлүүр дугуй – Mongolian" lang="mn" hreflang="mn" data-title="Эрчлүүр дугуй" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%96%E1%80%9C%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%B8%E1%80%9D%E1%80%BE%E1%80%AE%E1%80%B8" title="ဖလိုင်းဝှီး – Burmese" lang="my" hreflang="my" data-title="ဖလိုင်းဝှီး" 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/Vliegwiel" title="Vliegwiel – Dutch" lang="nl" hreflang="nl" data-title="Vliegwiel" 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%83%95%E3%83%A9%E3%82%A4%E3%83%9B%E3%82%A4%E3%83%BC%E3%83%AB" title="フライホイール – Japanese" lang="ja" hreflang="ja" data-title="フライホイール" 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/Svinghjul" title="Svinghjul – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Svinghjul" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Svinghjul" title="Svinghjul – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Svinghjul" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%81%D9%84%D8%A7%D8%A6%DB%8C%D9%88%DB%8C%D9%84" title="فلائیویل – Western Punjabi" lang="pnb" hreflang="pnb" data-title="فلائیویل" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ko%C5%82o_zamachowe" title="Koło zamachowe – Polish" lang="pl" hreflang="pl" data-title="Koło zamachowe" 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/Volante_de_in%C3%A9rcia" title="Volante de inércia – Portuguese" lang="pt" hreflang="pt" data-title="Volante de inércia" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Volant" title="Volant – Romanian" lang="ro" hreflang="ro" data-title="Volant" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%85%D0%BE%D0%B2%D0%B8%D0%BA" title="Маховик – Russian" lang="ru" hreflang="ru" data-title="Маховик" 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/Flywheel" title="Flywheel – Simple English" lang="en-simple" hreflang="en-simple" data-title="Flywheel" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Zotrva%C4%8Dn%C3%ADk" title="Zotrvačník – Slovak" lang="sk" hreflang="sk" data-title="Zotrvačník" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Vztrajnik" title="Vztrajnik – Slovenian" lang="sl" hreflang="sl" data-title="Vztrajnik" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a 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</div> </div> <div id="bodyContent" 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">Mechanical device for storing rotational energy</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/Flywheel_(disambiguation)" class="mw-disambig" title="Flywheel (disambiguation)">Flywheel (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Thinktank_Birmingham_-_Trevithick_Locomotive(1).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Thinktank_Birmingham_-_Trevithick_Locomotive%281%29.jpg/220px-Thinktank_Birmingham_-_Trevithick_Locomotive%281%29.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Thinktank_Birmingham_-_Trevithick_Locomotive%281%29.jpg/330px-Thinktank_Birmingham_-_Trevithick_Locomotive%281%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Thinktank_Birmingham_-_Trevithick_Locomotive%281%29.jpg/440px-Thinktank_Birmingham_-_Trevithick_Locomotive%281%29.jpg 2x" data-file-width="1024" data-file-height="768" /></a><figcaption><a href="/wiki/Richard_Trevithick" title="Richard Trevithick">Trevithick</a>'s 1802 steam locomotive, which used a flywheel to evenly distribute the power of its single cylinder</figcaption></figure> <p>A <b>flywheel</b> is a mechanical device that uses the conservation of <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a> to store <a href="/wiki/Rotational_energy" title="Rotational energy">rotational energy</a>, a form of kinetic energy proportional to the product of its <a href="/wiki/Moment_of_inertia" title="Moment of inertia">moment of inertia</a> and the square of its <a href="/wiki/Rotational_speed" class="mw-redirect" title="Rotational speed">rotational speed</a>. In particular, assuming the flywheel's moment of inertia is constant (i.e., a flywheel with fixed mass and <a href="/wiki/Second_moment_of_area" title="Second moment of area">second moment of area</a> revolving about some fixed axis) then the stored (rotational) energy is directly associated with the square of its rotational speed. </p><p>Since a flywheel serves to store mechanical energy for later use, it is natural to consider it as a <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> analogue of an <a href="/wiki/Capacitor" title="Capacitor">electrical capacitor</a>. Once suitably abstracted, this shared principle of energy storage is described in the generalized concept of an <a href="/wiki/Accumulator_(energy)" title="Accumulator (energy)">accumulator</a>. As with other types of accumulators, a flywheel inherently smooths sufficiently small deviations in the power output of a system, thereby effectively playing the role of a <a href="/wiki/Low-pass_filter" title="Low-pass filter">low-pass filter</a> with respect to the mechanical velocity (angular, or otherwise) of the system. More precisely, a flywheel's stored energy will donate a surge in power output upon a drop in power input and will conversely absorb any excess power input (system-generated power) in the form of rotational energy. </p><p>Common uses of a flywheel include smoothing a power output in <a href="/wiki/Reciprocating_engine" title="Reciprocating engine">reciprocating engines</a>, <a href="/wiki/Flywheel_energy_storage" title="Flywheel energy storage">flywheel energy storage</a>, delivering energy at higher rates than the source, and controlling the orientation of a mechanical system using <a href="/wiki/Gyroscope" title="Gyroscope">gyroscope</a> and <a href="/wiki/Reaction_wheel" title="Reaction wheel">reaction wheel</a>. Flywheels are typically made of steel and rotate on conventional bearings; these are generally limited to a maximum revolution rate of a few thousand <a href="/wiki/RPM" class="mw-redirect" title="RPM">RPM</a>.<sup id="cite_ref-BBC_1-0" class="reference"><a href="#cite_note-BBC-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> High energy density flywheels can be made of carbon fiber composites and employ <a href="/wiki/Magnetic_bearing" title="Magnetic bearing">magnetic bearings</a>, enabling them to revolve at speeds up to 60,000 RPM (1 <a href="/wiki/KHz" class="mw-redirect" title="KHz">kHz</a>).<sup id="cite_ref-Kinergy_2-0" class="reference"><a href="#cite_note-Kinergy-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </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=Flywheel&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Leonardo-Flywheel.ogv/220px--Leonardo-Flywheel.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="165" data-durationhint="21" data-mwtitle="Leonardo-Flywheel.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:Leonardo-Flywheel.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Leonardo-Flywheel.ogv/Leonardo-Flywheel.ogv.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="640" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/9/9e/Leonardo-Flywheel.ogv" type="video/ogg; codecs="theora"" data-width="640" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Leonardo-Flywheel.ogv/Leonardo-Flywheel.ogv.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="192" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Leonardo-Flywheel.ogv/Leonardo-Flywheel.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="320" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Leonardo-Flywheel.ogv/Leonardo-Flywheel.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="480" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Leonardo-Flywheel.ogv/Leonardo-Flywheel.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="480" data-height="360" /></video></span><figcaption>A flywheel with variable inertia, conceived by <a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a></figcaption></figure> <p>The principle of the flywheel is found in the <a href="/wiki/Neolithic" title="Neolithic">Neolithic</a> <a href="/wiki/Spindle_(textiles)" title="Spindle (textiles)">spindle</a> and the <a href="/wiki/Potter%27s_wheel" title="Potter's wheel">potter's wheel</a>, as well as circular sharpening stones in antiquity.<sup id="cite_ref-Lynn_White,_Jr._233_3-0" class="reference"><a href="#cite_note-Lynn_White,_Jr._233-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In the early 11th century, <a href="/wiki/Ibn_Bassal" title="Ibn Bassal">Ibn Bassal</a> pioneered the use of flywheel in <a href="/wiki/Noria" title="Noria">noria</a> and <a href="/wiki/Saqiyah" title="Saqiyah">saqiyah</a>.<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> The use of the flywheel as a general mechanical device to equalize the speed of rotation is, according to the American medievalist <a href="/wiki/Lynn_White" class="mw-redirect" title="Lynn White">Lynn White</a>, recorded in the <i>De diversibus artibus</i> (On various arts) of the German artisan <a href="/wiki/Theophilus_Presbyter" title="Theophilus Presbyter">Theophilus Presbyter</a> (ca. 1070–1125) who records applying the device in several of his machines.<sup id="cite_ref-Lynn_White,_Jr._233_3-1" class="reference"><a href="#cite_note-Lynn_White,_Jr._233-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><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> </p><p>In the <a href="/wiki/Industrial_Revolution" title="Industrial Revolution">Industrial Revolution</a>, <a href="/wiki/James_Watt" title="James Watt">James Watt</a> contributed to the development of the flywheel in the <a href="/wiki/Steam_engine" title="Steam engine">steam engine</a>, and his contemporary <a href="/wiki/James_Pickard" title="James Pickard">James Pickard</a> used a flywheel combined with a <a href="/wiki/Crank_(mechanism)" title="Crank (mechanism)">crank</a> to transform reciprocating motion into rotary motion.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Physics">Physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flywheel&action=edit&section=2" title="Edit section: Physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Volin.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Volin.jpg/220px-Volin.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Volin.jpg/330px-Volin.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Volin.jpg/440px-Volin.jpg 2x" data-file-width="446" data-file-height="595" /></a><figcaption>A mass-produced flywheel</figcaption></figure> <p>The <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> (or more specifically <a href="/wiki/Rotational_energy" title="Rotational energy">rotational energy</a>) stored by the flywheel's <a href="https://en.wiktionary.org/wiki/rotor" class="extiw" title="wikt:rotor">rotor</a> can be calculated by <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="{\textstyle {\frac {1}{2}}I\omega ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>I</mi> <msup> <mi>ω<!-- ω --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {1}{2}}I\omega ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c3d48c95ca114d30774d52d49964f21c3ae3788" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.33ex; height:3.509ex;" alt="{\textstyle {\frac {1}{2}}I\omega ^{2}}"></span>. ω is the <a href="/wiki/Angular_velocity" title="Angular velocity">angular velocity</a>, and <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> is the <a href="/wiki/Moment_of_inertia" title="Moment of inertia">moment of inertia</a> of the flywheel about its axis of symmetry. The moment of inertia is a measure of resistance to <a href="/wiki/Torque" title="Torque">torque</a> applied on a spinning object (i.e. the higher the moment of inertia, the slower it will accelerate when a given torque is applied). The <a href="/wiki/Moment_of_inertia" title="Moment of inertia">moment of inertia</a> can be calculated for cylindrical shapes using mass (<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="{\textstyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3296968aacae7d971a6d649f6b32b5969ed6d4d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\textstyle m}"></span>) and radius (<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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>). For a solid cylinder it is <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="{\textstyle {\frac {1}{2}}mr^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {1}{2}}mr^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93642f3310e8998bf679b98bad947ffe138f344d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:5.801ex; height:3.509ex;" alt="{\textstyle {\frac {1}{2}}mr^{2}}"></span>, for a thin-walled empty cylinder it is approximately <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="{\textstyle mr^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>m</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle mr^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/091a0e9679752d4fb26462e3167fa777aa2e549e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.143ex; height:2.509ex;" alt="{\textstyle mr^{2}}"></span>, and for a thick-walled empty cylinder with constant density it is <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="{\textstyle {\frac {1}{2}}m({r_{\mathrm {external} }}^{2}+{r_{\mathrm {internal} }}^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>m</mi> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </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"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {1}{2}}m({r_{\mathrm {external} }}^{2}+{r_{\mathrm {internal} }}^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d527a28a70a5ed2348b6d70dc14f2b599c7abce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:24.403ex; height:3.509ex;" alt="{\textstyle {\frac {1}{2}}m({r_{\mathrm {external} }}^{2}+{r_{\mathrm {internal} }}^{2})}"></span>.<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><p>For a given flywheel design, the kinetic energy is proportional to the ratio of the <a href="/wiki/Hoop_stress" class="mw-redirect" title="Hoop stress">hoop stress</a> to the material density and to the mass. The <a href="/wiki/Specific_strength" title="Specific strength">specific tensile strength</a> of a flywheel can be defined as <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="{\textstyle {\frac {\sigma _{t}}{\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ<!-- σ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mi>ρ<!-- ρ --></mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {\sigma _{t}}{\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a83480872d035d9fe11328f9ca78a81a9f4752e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.421ex; height:3.676ex;" alt="{\textstyle {\frac {\sigma _{t}}{\rho }}}"></span>. The flywheel material with the highest specific tensile strength will yield the highest energy storage per unit mass. This is one reason why <a href="/wiki/Carbon_fiber" class="mw-redirect" title="Carbon fiber">carbon fiber</a> is a material of interest. For a given design the stored energy is proportional to the hoop stress and the volume.<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. (May 2022)">citation needed</span></a></i>]</sup> </p><p>An electric motor-powered flywheel is common in practice. The output power of the electric motor is approximately equal to the output power of the flywheel. It can be calculated by <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="{\textstyle (V_{i})(V_{t})\left({\frac {\sin(\delta )}{X_{S}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>δ<!-- δ --></mi> <mo stretchy="false">)</mo> </mrow> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle (V_{i})(V_{t})\left({\frac {\sin(\delta )}{X_{S}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93d25cce5880b75a3cfd1effee14cbf937a4d432" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.994ex; height:4.843ex;" alt="{\textstyle (V_{i})(V_{t})\left({\frac {\sin(\delta )}{X_{S}}}\right)}"></span>, where <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 V_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f300b83673e961a9d48f3862216b167f94e5668c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.155ex; height:2.509ex;" alt="{\displaystyle V_{i}}"></span> is the voltage of <a href="/wiki/Rotor_(electric)" title="Rotor (electric)">rotor</a> winding, <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 V_{t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27b61a6ac590c5cd1911b10c484f38de1edb58c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.181ex; height:2.509ex;" alt="{\displaystyle V_{t}}"></span> is <a href="/wiki/Stator" title="Stator">stator</a> voltage, and <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 \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ<!-- δ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }"></span> is the angle between two voltages. Increasing amounts of rotation energy can be stored in the flywheel until the rotor shatters. This happens when the <a href="/wiki/Hoop_stress" class="mw-redirect" title="Hoop stress">hoop stress</a> within the rotor exceeds the <a href="/wiki/Ultimate_tensile_strength" title="Ultimate tensile strength">ultimate tensile strength</a> of the rotor material. <a href="/wiki/Tensile_stress" class="mw-redirect" title="Tensile stress">Tensile stress</a> can be calculated by <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 \rho r^{2}\omega ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ<!-- ρ --></mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>ω<!-- ω --></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho r^{2}\omega ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf873161d2d88fe4ebadd76632d7ebafa6996b94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.805ex; height:3.176ex;" alt="{\displaystyle \rho r^{2}\omega ^{2}}"></span>, where <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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> is the density of the cylinder, <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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> is the radius of the cylinder, and <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 \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω<!-- ω --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span> is the <a href="/wiki/Angular_velocity" title="Angular velocity">angular velocity</a> of the cylinder. </p> <div class="mw-heading mw-heading2"><h2 id="Design">Design</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flywheel&action=edit&section=3" title="Edit section: Design"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/w/index.php?title=Rimmed_flywheel&action=edit&redlink=1" class="new" title="Rimmed flywheel (page does not exist)">rimmed flywheel</a> has a <a href="/wiki/Rim_(wheel)" title="Rim (wheel)">rim</a>, a hub, and <a href="/wiki/Spoke" title="Spoke">spokes</a>.<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> Calculation of the flywheel's moment of inertia can be more easily analysed by applying various simplifications. One method is to assume the spokes, shaft and hub have zero moments of inertia, and the flywheel's moment of inertia is from the rim alone. Another is to <a href="/wiki/Lumped-element_model" title="Lumped-element model">lump</a> moments of inertia of spokes, hub and shaft into the rim. These may be estimated as a percentage of the flywheel's moment of inertia, with the majority from the rim, so that <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 I_{\mathrm {rim} }=KI_{\mathrm {flywheel} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>K</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">y</mi> <mi mathvariant="normal">w</mi> <mi mathvariant="normal">h</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\mathrm {rim} }=KI_{\mathrm {flywheel} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af197ef3e59a9daeee3df734132f25f6fc6a2945" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.101ex; height:2.843ex;" alt="{\displaystyle I_{\mathrm {rim} }=KI_{\mathrm {flywheel} }}"></span>. For example, if the moments of inertia of hub, spokes and shaft are deemed negligible, and the rim's thickness is very small compared to its mean radius (<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 R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span>), the radius of rotation of the rim is equal to its mean radius and thus <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="{\textstyle I_{\mathrm {rim} }=M_{\mathrm {rim} }R^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle I_{\mathrm {rim} }=M_{\mathrm {rim} }R^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26083e55060ce5b62ebcb871b861886d54c3cfc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.6ex; height:2.843ex;" alt="{\textstyle I_{\mathrm {rim} }=M_{\mathrm {rim} }R^{2}}"></span>.<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. (May 2022)">citation needed</span></a></i>]</sup> </p><p>A <a href="/w/index.php?title=Shaftless_flywheel&action=edit&redlink=1" class="new" title="Shaftless flywheel (page does not exist)">shaftless flywheel</a> eliminates the annulus holes, shaft or hub. It has higher energy density than conventional design<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> but requires a specialized magnetic bearing and control system.<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> The specific energy of a flywheel is determined by<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="{\textstyle {\frac {E}{M}}=K{\frac {\sigma }{\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mi>M</mi> </mfrac> </mrow> <mo>=</mo> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>σ<!-- σ --></mi> <mi>ρ<!-- ρ --></mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\frac {E}{M}}=K{\frac {\sigma }{\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be08b2b6d90447c23b4170dee5eee36de3974e98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:9.504ex; height:3.676ex;" alt="{\textstyle {\frac {E}{M}}=K{\frac {\sigma }{\rho }}}"></span>, in which <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 K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.066ex; height:2.176ex;" alt="{\displaystyle K}"></span> is the shape factor, <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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ<!-- σ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span> the material's tensile strength and <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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> the density.<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. (May 2022)">citation needed</span></a></i>]</sup> While a typical flywheel has a shape factor of 0.3, the shaftless flywheel has a shape factor close to 0.6, out of a theoretical limit of about 1.<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> </p><p>A <a href="/w/index.php?title=Superflywheel&action=edit&redlink=1" class="new" title="Superflywheel (page does not exist)">superflywheel</a> consists of a solid core (hub) and multiple thin layers of high-strength flexible materials (such as special steels, carbon fiber composites, glass fiber, or graphene) wound around it.<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> Compared to conventional flywheels, superflywheels can store more energy and are safer to operate.<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> In case of failure, a superflywheel does not explode or burst into large shards like a regular flywheel, but instead splits into layers. The separated layers then slow a superflywheel down by sliding against the inner walls of the enclosure, thus preventing any further destruction. Although the exact value of energy density of a superflywheel would depend on the material used, it could theoretically be as high as 1200 Wh (4.4 MJ) per kg of mass for graphene superflywheels.<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. (May 2022)">citation needed</span></a></i>]</sup> The first superflywheel was patented in 1964 by the Soviet-Russian scientist <a href="/w/index.php?title=Nurbei_Guilia&action=edit&redlink=1" class="new" title="Nurbei Guilia (page does not exist)">Nurbei Guilia</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><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> </p> <div class="mw-heading mw-heading2"><h2 id="Materials">Materials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flywheel&action=edit&section=4" title="Edit section: Materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Flywheels are made from many different materials; the application determines the choice of material. Small flywheels made of lead are found in children's toys.<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. (August 2020)">citation needed</span></a></i>]</sup> Cast iron flywheels are used in old steam engines. Flywheels used in car engines are made of cast or nodular iron, steel or aluminum.<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> Flywheels made from high-strength steel or composites have been proposed for use in vehicle energy storage and braking systems. </p><p>The efficiency of a flywheel is determined by the maximum amount of energy it can store per unit weight. As the flywheel's rotational speed or angular velocity is increased, the stored energy increases; however, the stresses also increase. If the hoop stress surpass the tensile strength of the material, the flywheel will break apart. Thus, the tensile strength limits the amount of energy that a flywheel can store. </p><p>In this context, using lead for a flywheel in a child's toy is not efficient; however, the flywheel velocity never approaches its burst velocity because the limit in this case is the pulling-power of the child. In other applications, such as an automobile, the flywheel operates at a specified angular velocity and is constrained by the space it must fit in, so the goal is to maximize the stored energy per unit volume. The material selection therefore depends on the application.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flywheel&action=edit&section=5" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Landini_VL30(Italien)2.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Landini_VL30%28Italien%292.JPG/220px-Landini_VL30%28Italien%292.JPG" decoding="async" width="220" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Landini_VL30%28Italien%292.JPG/330px-Landini_VL30%28Italien%292.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Landini_VL30%28Italien%292.JPG/440px-Landini_VL30%28Italien%292.JPG 2x" data-file-width="1041" data-file-height="959" /></a><figcaption>A <a href="/wiki/Landini_(tractor)" title="Landini (tractor)">Landini</a> tractor with exposed flywheel</figcaption></figure> <p>Flywheels are often used to provide continuous power output in systems where the energy source is not continuous. For example, a flywheel is used to smooth the fast angular velocity fluctuations of the <a href="/wiki/Crankshaft" title="Crankshaft">crankshaft</a> in a reciprocating engine. In this case, a crankshaft flywheel stores energy when torque is exerted on it by a firing <a href="/wiki/Piston" title="Piston">piston</a> and then returns that energy to the piston to compress a fresh charge of air and fuel. Another example is the <a href="/wiki/Friction_motor" title="Friction motor">friction motor</a> which powers devices such as <a href="/wiki/Toy_car" class="mw-redirect" title="Toy car">toy cars</a>. In unstressed and inexpensive cases, to save on cost, the bulk of the mass of the flywheel is toward the rim of the wheel. Pushing the mass away from the axis of rotation heightens <a href="/wiki/Rotational_inertia" class="mw-redirect" title="Rotational inertia">rotational inertia</a> for a given total mass. </p><p>A flywheel may also be used to supply intermittent pulses of energy at power levels that exceed the abilities of its energy source. This is achieved by accumulating energy in the flywheel over a period of time, at a rate that is compatible with the energy source, and then releasing energy at a much higher rate over a relatively short time when it is needed. For example, flywheels are used in <a href="/wiki/Power_hammer" title="Power hammer">power hammers</a> and <a href="/wiki/Riveting_machines" class="mw-redirect" title="Riveting machines">riveting machines</a>. </p><p>Flywheels can be used to control direction and oppose unwanted motions. Flywheels in this context have a wide range of applications: <a href="/wiki/Gyroscope" title="Gyroscope">gyroscopes</a> for instrumentation, <a href="/wiki/Ship_stability" title="Ship stability">ship stability</a>, satellite stabilization (<a href="/wiki/Reaction_wheel" title="Reaction wheel">reaction wheel</a>), keeping a toy spin spinning (<a href="/wiki/Friction_motor" title="Friction motor">friction motor</a>), stabilizing magnetically-levitated objects (<a href="/wiki/Spin-stabilized_magnetic_levitation" title="Spin-stabilized magnetic levitation">spin-stabilized magnetic levitation</a>). </p><p>Flywheels may also be used as an electric compensator, like a <a href="/wiki/Synchronous_compensator" class="mw-redirect" title="Synchronous compensator">synchronous compensator</a>, that can either produce or sink reactive power but would not affect the real power. The purposes for that application are to improve the power factor of the system or adjust the grid voltage. Typically, the flywheels used in this field are similar in structure and installation as the synchronous motor (but it is called synchronous compensator or synchronous condenser in this context). There are also some other kinds of compensator using flywheels, like the single phase induction machine. But the basic ideas here are the same, the flywheels are controlled to spin exactly at the frequency which you want to compensate. For a synchronous compensator, the voltage of rotor and stator also must be kept in phase, which is the same as keeping the magnetic field of rotor and the total magnetic field in phase (in the <a href="/wiki/Rotating_reference_frame" title="Rotating reference frame">rotating frame reference</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=Flywheel&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Accumulator_(energy)" title="Accumulator (energy)">Accumulator (energy)</a></li> <li><a href="/wiki/Clutch" title="Clutch">Clutch</a></li> <li><a href="/wiki/Diesel_rotary_uninterruptible_power_supply" title="Diesel rotary uninterruptible power supply">Diesel rotary uninterruptible power supply</a></li> <li><a href="/wiki/Dual-mass_flywheel" title="Dual-mass flywheel">Dual-mass flywheel</a></li> <li><a href="/wiki/Fidget_spinner" title="Fidget spinner">Fidget spinner</a></li> <li><a href="/wiki/Flywheel_training" title="Flywheel training">Flywheel training</a></li> <li><a href="/wiki/List_of_moments_of_inertia" title="List of moments of inertia">List of moments of inertia</a></li></ul> <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=Flywheel&action=edit&section=7" 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-BBC-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-BBC_1-0">^</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.bbc.com/future/story/20120629-reinventing-the-wheel">"Flywheels move from steam age technology to Formula 1"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120703101332/http://www.bbc.com/future/story/20120629-reinventing-the-wheel">Archived</a> from the original on 2012-07-03<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-07-03</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Flywheels+move+from+steam+age+technology+to+Formula+1&rft_id=http%3A%2F%2Fwww.bbc.com%2Ffuture%2Fstory%2F20120629-reinventing-the-wheel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" class="Z3988"></span>; "Flywheels move from steam age technology to Formula 1"; Jon Stewart | 1 July 2012, retrieved 2012-07-03</span> </li> <li id="cite_note-Kinergy-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kinergy_2-0">^</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="http://www.ricardo.com/en-GB/News--Media/Press-releases/News-releases1/2011/Breakthrough-in-Ricardo-Kinergy-second-generation-high-speed-flywheel-technology/">"Breakthrough in Ricardo Kinergy 'second generation' high-speed flywheel technology"</a>. 2011-08-21. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120705032651/http://www.ricardo.com/en-GB/News--Media/Press-releases/News-releases1/2011/Breakthrough-in-Ricardo-Kinergy-second-generation-high-speed-flywheel-technology/">Archived</a> from the original on 2012-07-05<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-07-03</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Breakthrough+in+Ricardo+Kinergy+%27second+generation%27+high-speed+flywheel+technology&rft.date=2011-08-21&rft_id=http%3A%2F%2Fwww.ricardo.com%2Fen-GB%2FNews--Media%2FPress-releases%2FNews-releases1%2F2011%2FBreakthrough-in-Ricardo-Kinergy-second-generation-high-speed-flywheel-technology%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" class="Z3988"></span>, "Breakthrough in Ricardo Kinergy ‘second generation’ high-speed flywheel technology"; Press release date: 22 August 2011. retrieved 2012-07-03</span> </li> <li id="cite_note-Lynn_White,_Jr._233-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Lynn_White,_Jr._233_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Lynn_White,_Jr._233_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Lynn White, Jr., "Theophilus Redivivus", <i>Technology and Culture</i>, Vol. 5, No. 2. (Spring, 1964), Review, pp. 224–233 (233)</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="CITEREFLetcher2017" class="citation book cs1">Letcher, Trevor M. (2017). <i>Wind energy engineering: a handbook for onshore and offshore wind turbines</i>. <a href="/wiki/Academic_Press" title="Academic Press">Academic Press</a>. pp. 127–143. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0128094518" title="Special:BookSources/978-0128094518"><bdi>978-0128094518</bdi></a>. <q>Ibn Bassal (AD 1038–75) of Al Andalus (Andalusia) pioneered the use of a flywheel mechanism in the noria and saqiya to smooth out the delivery of power from the driving device to the driven machine</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Wind+energy+engineering%3A+a+handbook+for+onshore+and+offshore+wind+turbines&rft.pages=127-143&rft.pub=Academic+Press&rft.date=2017&rft.isbn=978-0128094518&rft.aulast=Letcher&rft.aufirst=Trevor+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" 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">Lynn White, Jr., "Medieval Engineering and the Sociology of Knowledge", <i>The Pacific Historical Review</i>, Vol. 44, No. 1. (Feb., 1975), pp. 1–21 (6)</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="CITEREFOsbourne2013" class="citation book cs1">Osbourne, Roger (2013). <i>Iron, Steam & Money: The Making of the Industrial Revolution</i>. Random House. p. 131. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781446483282" title="Special:BookSources/9781446483282"><bdi>9781446483282</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Iron%2C+Steam+%26+Money%3A+The+Making+of+the+Industrial+Revolution&rft.pages=131&rft.pub=Random+House&rft.date=2013&rft.isbn=9781446483282&rft.aulast=Osbourne&rft.aufirst=Roger&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" 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="CITEREFDunn" class="citation web cs1">Dunn, D.J. <a rel="nofollow" class="external text" href="http://www.freestudy.co.uk/dynamics/moment%20of%20inertia.pdf">"Tutorial – Moment of Inertia"</a> <span class="cs1-format">(PDF)</span>. <i>FreeStudy.co.uk</i>. p. 10. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120105181252/http://www.freestudy.co.uk/dynamics/moment%20of%20inertia.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2012-01-05<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-12-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=FreeStudy.co.uk&rft.atitle=Tutorial+%E2%80%93+Moment+of+Inertia&rft.pages=10&rft.aulast=Dunn&rft.aufirst=D.J.&rft_id=http%3A%2F%2Fwww.freestudy.co.uk%2Fdynamics%2Fmoment%2520of%2520inertia.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Flywheel Rotor And Containment Technology Development, FY83. Livermore, Calif: Lawrence Livermore National Laboratory, 1983. pp. 1–2</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiAnvariPalazzoloWang2018" class="citation journal cs1">Li, Xiaojun; Anvari, Bahar; Palazzolo, Alan; Wang, Zhiyang; Toliyat, Hamid (2018-08-14). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/321059437">"A Utility Scale Flywheel Energy Storage System with a Shaftless, Hubless, High Strength Steel Rotor"</a>. <i>IEEE Transactions on Industrial Electronics</i>. <b>65</b> (8): 6667–6675. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTIE.2017.2772205">10.1109/TIE.2017.2772205</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:4557504">4557504</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Industrial+Electronics&rft.atitle=A+Utility+Scale+Flywheel+Energy+Storage+System+with+a+Shaftless%2C+Hubless%2C+High+Strength+Steel+Rotor&rft.volume=65&rft.issue=8&rft.pages=6667-6675&rft.date=2018-08-14&rft_id=info%3Adoi%2F10.1109%2FTIE.2017.2772205&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4557504%23id-name%3DS2CID&rft.aulast=Li&rft.aufirst=Xiaojun&rft.au=Anvari%2C+Bahar&rft.au=Palazzolo%2C+Alan&rft.au=Wang%2C+Zhiyang&rft.au=Toliyat%2C+Hamid&rft_id=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F321059437&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" 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 id="CITEREFLiPalazzolo2018" class="citation journal cs1">Li, Xiaojun; Palazzolo, Alan (2018-05-07). "Multi-Input–Multi-Output Control of a Utility-Scale, Shaftless Energy Storage Flywheel With a Five-Degrees-of-Freedom Combination Magnetic Bearing". <i>Journal of Dynamic Systems, Measurement, and Control</i>. <b>140</b> (10): 101008. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1115%2F1.4039857">10.1115/1.4039857</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0022-0434">0022-0434</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Dynamic+Systems%2C+Measurement%2C+and+Control&rft.atitle=Multi-Input%E2%80%93Multi-Output+Control+of+a+Utility-Scale%2C+Shaftless+Energy+Storage+Flywheel+With+a+Five-Degrees-of-Freedom+Combination+Magnetic+Bearing&rft.volume=140&rft.issue=10&rft.pages=101008&rft.date=2018-05-07&rft_id=info%3Adoi%2F10.1115%2F1.4039857&rft.issn=0022-0434&rft.aulast=Li&rft.aufirst=Xiaojun&rft.au=Palazzolo%2C+Alan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" 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 id="CITEREFGenta1985" class="citation cs2">Genta, G. 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(2014-04-24). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=LKXpAgAAQBAJ"><i>Kinetic Energy Storage: Theory and Practice of Advanced Flywheel Systems</i></a>. Butterworth-Heinemann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4831-0159-0" title="Special:BookSources/978-1-4831-0159-0"><bdi>978-1-4831-0159-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Kinetic+Energy+Storage%3A+Theory+and+Practice+of+Advanced+Flywheel+Systems&rft.pub=Butterworth-Heinemann&rft.date=2014-04-24&rft.isbn=978-1-4831-0159-0&rft.aulast=Genta&rft.aufirst=G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DLKXpAgAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEgorovaBarbashov2020" class="citation book cs1">Egorova, Olga; Barbashov, Nikolay (2020-04-20). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=tpreDwAAQBAJ&q=gulia+patent+superflywheel&pg=PA117"><i>Proceedings of the 2020 USCToMM Symposium on Mechanical Systems and Robotics</i></a>. Springer Nature. pp. 117–118. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-030-43929-3" title="Special:BookSources/978-3-030-43929-3"><bdi>978-3-030-43929-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Proceedings+of+the+2020+USCToMM+Symposium+on+Mechanical+Systems+and+Robotics&rft.pages=117-118&rft.pub=Springer+Nature&rft.date=2020-04-20&rft.isbn=978-3-030-43929-3&rft.aulast=Egorova&rft.aufirst=Olga&rft.au=Barbashov%2C+Nikolay&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DtpreDwAAQBAJ%26q%3Dgulia%2Bpatent%2Bsuperflywheel%26pg%3DPA117&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" 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"><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation patent"><a rel="nofollow" class="external autonumber" href="https://patents.google.com/patent/SU1048196A1/ru">[1]</a>, "Маховик", issued 1964-05-15</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=&rft.cc=&rft.title=%D0%9C%D0%B0%D1%85%D0%BE%D0%B2%D0%B8%D0%BA&rft.date=1964-05-15"><span style="display: none;"> </span></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 web cs1"><a rel="nofollow" class="external text" href="https://fidanza.com/aluminum-vs-steel/">"Flywheels: Iron vs. Steel vs. Aluminum"</a>. <i>Fidanza Performance</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161010183339/https://fidanza.com/aluminum-vs-steel/">Archived</a> from the original on 10 October 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">6 October</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Fidanza+Performance&rft.atitle=Flywheels%3A+Iron+vs.+Steel+vs.+Aluminum&rft_id=https%3A%2F%2Ffidanza.com%2Faluminum-vs-steel%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" 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="CITEREFAshby2011" class="citation book cs1">Ashby, Michael (2011). <i>Materials Selection in Mechanical Design</i> (4th ed.). Burlington, MA: Butterworth-Heinemann. pp. 142–146. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-095223-9" title="Special:BookSources/978-0-08-095223-9"><bdi>978-0-08-095223-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Materials+Selection+in+Mechanical+Design&rft.place=Burlington%2C+MA&rft.pages=142-146&rft.edition=4th&rft.pub=Butterworth-Heinemann&rft.date=2011&rft.isbn=978-0-08-095223-9&rft.aulast=Ashby&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flywheel&action=edit&section=8" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeissbachKaradyFarmer2001" class="citation journal cs1">Weissbach, R. S.; Karady, G.G.; Farmer, R. G. (April 2001). "A combined uninterruptible power supply and dynamic voltage compensator using a flywheel energy storage system". <i>IEEE Transactions on Power Delivery</i>. <b>16</b> (2): 265–270. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F61.915493">10.1109/61.915493</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0885-8977">0885-8977</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Power+Delivery&rft.atitle=A+combined+uninterruptible+power+supply+and+dynamic+voltage+compensator+using+a+flywheel+energy+storage+system&rft.volume=16&rft.issue=2&rft.pages=265-270&rft.date=2001-04&rft_id=info%3Adoi%2F10.1109%2F61.915493&rft.issn=0885-8977&rft.aulast=Weissbach&rft.aufirst=R.+S.&rft.au=Karady%2C+G.G.&rft.au=Farmer%2C+R.+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" class="Z3988"></span></li> <li><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.egr.unlv.edu/~eebag/Synchronous%20Generator%20I.pdf">"Synchronous Generators I"</a> <span class="cs1-format">(PDF)</span>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://www.egr.unlv.edu/~eebag/Synchronous%20Generator%20I.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2022-10-09.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Synchronous+Generators+I&rft_id=http%3A%2F%2Fwww.egr.unlv.edu%2F~eebag%2FSynchronous%2520Generator%2520I.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlywheel" class="Z3988"></span></li> <li><a rel="nofollow" class="external free" href="https://pserc.wisc.edu/documents/general_information/presentations/presentations_by_pserc_university_members/heydt_synchronous_mach_sep03.pdf">https://pserc.wisc.edu/documents/general_information/presentations/presentations_by_pserc_university_members/heydt_synchronous_mach_sep03.pdf</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170830043655/https://pserc.wisc.edu/documents/general_information/presentations/presentations_by_pserc_university_members/heydt_synchronous_mach_sep03.pdf">Archived</a> 2017-08-30 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul> </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=Flywheel&action=edit&section=9" 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"><span><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" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/flywheel" class="extiw" title="wiktionary:Special:Search/flywheel">flywheel</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Flywheels" class="extiw" title="commons:Category:Flywheels">Flywheels</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://itotd.com/articles/332/flywheel-batteries/">Flywheel batteries</a> on <i>Interesting Thing of the Day</i></li> <li><a rel="nofollow" class="external text" href="http://reneweconomy.com.au/2015/darwin-made-outback-tested-energy-storage-system-to-be-used-in-remote-africa-88338">"Darwin-made, outback-tested energy storage system to be used in remote Africa"</a>, Renew Economy—Flywheel-based microgrid stabilization technology</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist 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<li><a href="/wiki/Core_plug" title="Core plug">Core plug (freeze plug)</a></li> <li><a href="/wiki/Cylinder_(engine)" title="Cylinder (engine)">Cylinder</a> (<a href="/wiki/Cylinder_bank" class="mw-redirect" title="Cylinder bank">bank</a>, <a href="/wiki/Engine_configuration" title="Engine configuration">layout</a>)</li> <li><a href="/wiki/Engine_displacement" title="Engine displacement">Displacement</a></li> <li><a class="mw-selflink selflink">Flywheel</a></li> <li><a href="/wiki/Firing_order" title="Firing order">Firing order</a></li> <li><a href="/wiki/Stroke_(engine)" title="Stroke (engine)">Stroke</a></li> <li><a href="/wiki/Main_bearing" title="Main bearing">Main bearing</a></li> <li><a href="/wiki/Piston" title="Piston">Piston</a></li> <li><a href="/wiki/Piston_ring" title="Piston ring">Piston ring</a></li> <li><a href="/wiki/Starter_ring_gear" title="Starter ring gear">Starter ring gear</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Valvetrain" title="Valvetrain">Valvetrain</a> and<br /> <a href="/wiki/Cylinder_head" title="Cylinder head">Cylinder head</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/Flathead_engine" title="Flathead engine">Flathead layout</a></li> <li><a href="/wiki/Overhead_camshaft_engine" title="Overhead camshaft engine">Overhead camshaft layout</a></li> <li><a href="/wiki/Overhead_valve_engine" title="Overhead valve engine">Overhead valve (pushrod) layout</a></li></ul> <ul><li><a href="/wiki/Tappet" title="Tappet">Tappet / lifter</a></li> <li><a href="/wiki/Camshaft" title="Camshaft">Camshaft</a></li> <li><a href="/wiki/Chest_(mechanical_engineering)" title="Chest (mechanical engineering)">Chest</a></li> <li><a href="/wiki/Combustion_chamber" title="Combustion chamber">Combustion chamber</a></li> <li><a href="/wiki/Compression_ratio" title="Compression ratio">Compression ratio</a></li> <li><a href="/wiki/Head_gasket" title="Head gasket">Head gasket</a></li> <li><a href="/wiki/Rocker_arm" title="Rocker arm">Rocker arm</a></li> <li><a href="/wiki/Timing_belt_(camshaft)" title="Timing belt (camshaft)">Timing belt</a></li> <li><a href="/wiki/Poppet_valve" title="Poppet valve">Valve</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Forced_induction" title="Forced induction">Forced induction</a></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/Blowoff_valve" title="Blowoff valve">Blowoff valve</a></li> <li><a href="/wiki/Boost_controller" title="Boost controller">Boost controller</a></li> <li><a href="/wiki/Intercooler" title="Intercooler">Intercooler</a></li> <li><a href="/wiki/Supercharger" title="Supercharger">Supercharger</a></li> <li><a href="/wiki/Turbocharger" title="Turbocharger">Turbocharger</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fuel system</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/Diesel_engine" title="Diesel engine">Diesel engine</a></li> <li><a href="/wiki/Petrol_engine" title="Petrol engine">Petrol engine</a></li> <li><a href="/wiki/Carburetor" title="Carburetor">Carburetor</a></li> <li><a href="/wiki/Fuel_filter" title="Fuel filter">Fuel filter</a></li> <li><a href="/wiki/Fuel_injection" title="Fuel injection">Fuel injection</a></li> <li><a href="/wiki/Fuel_pump" title="Fuel pump">Fuel pump</a></li> <li><a href="/wiki/Fuel_tank" title="Fuel tank">Fuel tank</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ignition_system" title="Ignition system">Ignition</a></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/Ignition_magneto" title="Ignition magneto">Magneto</a></li> <li><a href="/wiki/Compression_ignition" class="mw-redirect" title="Compression ignition">Compression ignition</a></li> <li><a href="/wiki/Coil-on-plug_ignition" class="mw-redirect" title="Coil-on-plug ignition">Coil-on-plug</a></li> <li><a href="/wiki/Distributor" title="Distributor">Distributor</a></li> <li><a href="/wiki/Glow_plug_(diesel_engine)" class="mw-redirect" title="Glow plug (diesel engine)">Glow plug</a></li> <li><a href="/wiki/Ignition_coil" title="Ignition coil">Ignition coil</a></li> <li><a href="/wiki/Spark_plug" title="Spark plug">Spark plug</a></li> <li><a href="/wiki/Spark_plug_wires" title="Spark plug wires">Spark plug wires</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Engine management</div></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/Engine_control_unit" title="Engine control unit">Engine control unit (ECU)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Electrical system</div></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/Alternator_(automotive)" title="Alternator (automotive)">Alternator</a></li> <li><a href="/wiki/Automotive_battery" title="Automotive battery">Battery</a></li> <li><a href="/wiki/Dynamo" title="Dynamo">Dynamo</a></li> <li><a href="/wiki/Starter_(engine)" title="Starter (engine)">Starter motor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Intake system</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/Airbox" title="Airbox">Airbox</a></li> <li><a href="/wiki/Air_filter#Internal_combustion_engine_air_filters" title="Air filter">Air filter</a></li> <li><a href="/wiki/Idle_air_control_actuator" title="Idle air control actuator">Idle air control actuator</a></li> <li><a href="/wiki/Inlet_manifold" title="Inlet manifold">Inlet manifold</a></li> <li><a href="/wiki/MAP_sensor" title="MAP sensor">MAP sensor</a></li> <li><a href="/wiki/Mass_flow_sensor" title="Mass flow sensor">MAF sensor</a></li> <li><a href="/wiki/Throttle" title="Throttle">Throttle</a></li> <li><a href="/wiki/Throttle_position_sensor" title="Throttle position sensor">Throttle position sensor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Exhaust_system" title="Exhaust system">Exhaust system</a></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/Catalytic_converter" title="Catalytic converter">Catalytic converter</a></li> <li><a href="/wiki/Diesel_particulate_filter" title="Diesel particulate filter">Diesel particulate filter</a></li> <li><a href="/wiki/Exhaust_gas_temperature_gauge" title="Exhaust gas temperature gauge">EGT sensor</a></li> <li><a href="/wiki/Exhaust_manifold" title="Exhaust manifold">Exhaust manifold</a></li> <li><a href="/wiki/Muffler" title="Muffler">Muffler</a></li> <li><a href="/wiki/Oxygen_sensor#Automotive_applications" title="Oxygen sensor">Oxygen sensor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Internal_combustion_engine_cooling" title="Internal combustion engine cooling">Cooling system</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/Air_cooling" title="Air cooling">Air cooling</a></li> <li><a href="/wiki/Water_cooling" title="Water cooling">Water cooling</a></li></ul> <ul><li><a href="/wiki/Fan_(machine)" title="Fan (machine)">Electric fan</a></li> <li><a href="/wiki/Radiator_(engine_cooling)" title="Radiator (engine cooling)">Radiator</a></li> <li><a href="/wiki/Thermostat" title="Thermostat">Thermostat</a></li> <li><a href="/wiki/Fan_clutch" title="Fan clutch">Viscous fan (fan clutch)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lubrication</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/Motor_oil" title="Motor oil">Oil</a></li> <li><a href="/wiki/Oil_filter" title="Oil filter">Oil filter</a></li> <li><a href="/wiki/Oil_pump_(internal_combustion_engine)" title="Oil pump (internal combustion engine)">Oil pump</a></li> <li><a href="/wiki/Sump" title="Sump">Sump</a> (<a 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