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<span>Concepts</span> </div> </a> <button aria-controls="toc-Concepts-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Concepts subsection</span> </button> <ul id="toc-Concepts-sublist" class="vector-toc-list"> <li id="toc-Thrust_to_power" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Thrust_to_power"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Thrust to power</span> </div> </a> <ul id="toc-Thrust_to_power-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Thrust_to_propulsive_power" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Thrust_to_propulsive_power"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Thrust to propulsive power</span> </div> </a> <ul id="toc-Thrust_to_propulsive_power-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Excess_thrust" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Excess_thrust"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Excess thrust</span> </div> </a> <ul id="toc-Excess_thrust-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Thrust_axis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Thrust_axis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Thrust axis</span> </div> </a> <ul id="toc-Thrust_axis-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</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">4</span> <span>References</span> </div> </a> <ul id="toc-References-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 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href="https://az.wikipedia.org/wiki/%C4%B0t%C9%99l%C9%99m%C9%99" title="İtələmə – Azerbaijani" lang="az" hreflang="az" data-title="İtələmə" 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%A7%E0%A6%BE%E0%A6%95%E0%A7%8D%E0%A6%95%E0%A6%BE" title="ধাক্কা – Bangla" lang="bn" hreflang="bn" data-title="ধাক্কা" 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%A6%D1%8F%D0%B3%D0%B0" title="Цяга – Belarusian" lang="be" hreflang="be" data-title="Цяга" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Empenyiment" title="Empenyiment – Catalan" lang="ca" hreflang="ca" data-title="Empenyiment" 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/Tah_motoru" title="Tah motoru – Czech" lang="cs" hreflang="cs" data-title="Tah motoru" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Schub" title="Schub – German" lang="de" hreflang="de" data-title="Schub" 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/T%C3%B5mme_(lennundus)" title="Tõmme (lennundus) – Estonian" lang="et" hreflang="et" data-title="Tõmme (lennundus)" 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/Empuje" title="Empuje – Spanish" lang="es" hreflang="es" data-title="Empuje" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%D9%86%D8%B4" title="رانش – Persian" lang="fa" hreflang="fa" data-title="رانش" 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/Pouss%C3%A9e" title="Poussée – French" lang="fr" hreflang="fr" data-title="Poussée" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Impulso_(aerodin%C3%A1mica)" title="Impulso (aerodinámica) – Galician" lang="gl" hreflang="gl" data-title="Impulso (aerodinámica)" 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/%EC%B6%94%EB%A0%A5" title="추력 – Korean" lang="ko" hreflang="ko" data-title="추력" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Gaya_dorong" title="Gaya dorong – Indonesian" lang="id" hreflang="id" data-title="Gaya dorong" 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/Spinta" title="Spinta – Italian" lang="it" hreflang="it" data-title="Spinta" 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%93%D7%97%D7%A3_(%D7%9B%D7%95%D7%97)" title="דחף (כוח) – Hebrew" lang="he" hreflang="he" data-title="דחף (כוח)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Sjtuwkrach" title="Sjtuwkrach – Limburgish" lang="li" hreflang="li" data-title="Sjtuwkrach" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Tol%C3%B3er%C5%91" title="Tolóerő – Hungarian" lang="hu" hreflang="hu" data-title="Tolóerő" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B8%D1%81%D0%BE%D0%BA" title="Потисок – Macedonian" lang="mk" hreflang="mk" data-title="Потисок" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Tujahan" title="Tujahan – Malay" lang="ms" hreflang="ms" data-title="Tujahan" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Stuwkracht" title="Stuwkracht – Dutch" lang="nl" hreflang="nl" data-title="Stuwkracht" 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/%E6%8E%A8%E5%8A%9B" title="推力 – Japanese" lang="ja" hreflang="ja" data-title="推力" 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/Statisk_skyvekraft" title="Statisk skyvekraft – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Statisk skyvekraft" 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Empencha" title="Empencha – Occitan" lang="oc" hreflang="oc" data-title="Empencha" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Si%C5%82a_ci%C4%85gu" title="Siła ciągu – Polish" lang="pl" hreflang="pl" data-title="Siła ciągu" 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/Empuxo" title="Empuxo – Portuguese" lang="pt" hreflang="pt" data-title="Empuxo" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%8F%D0%B3%D0%B0_(%D0%B0%D0%B2%D0%B8%D0%B0%D1%86%D0%B8%D1%8F)" title="Тяга (авиация) – Russian" lang="ru" hreflang="ru" data-title="Тяга (авиация)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Ammuttata" title="Ammuttata – Sicilian" lang="scn" hreflang="scn" data-title="Ammuttata" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Thrust" title="Thrust – Simple English" lang="en-simple" hreflang="en-simple" data-title="Thrust" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Potisk" title="Potisk – Slovenian" lang="sl" hreflang="sl" data-title="Potisk" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%BE%D8%A7%DA%B5_%D9%BE%DB%8E%D9%88%DB%95%D9%86%D8%A7%D9%86" title="پاڵ پێوەنان – Central Kurdish" lang="ckb" hreflang="ckb" data-title="پاڵ پێوەنان" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D1%82%D0%B8%D1%81%D0%B0%D0%BA" title="Потисак – Serbian" lang="sr" hreflang="sr" data-title="Потисак" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Potisak" title="Potisak – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Potisak" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Ty%C3%B6nt%C3%B6voima" title="Työntövoima – Finnish" lang="fi" hreflang="fi" data-title="Työntövoima" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dragkraft" title="Dragkraft – Swedish" lang="sv" hreflang="sv" data-title="Dragkraft" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%89%E0%AE%A8%E0%AF%8D%E0%AE%A4%E0%AF%81%E0%AE%B5%E0%AE%BF%E0%AE%9A%E0%AF%88" title="உந்துவிசை – Tamil" lang="ta" hreflang="ta" data-title="உந்துவிசை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0tme_(ak%C4%B1%C5%9Fkanlar_mekani%C4%9Fi)" title="İtme (akışkanlar mekaniği) – Turkish" lang="tr" hreflang="tr" data-title="İtme (akışkanlar mekaniği)" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%8F%D0%B3%D0%B0_%D0%BB%D1%96%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B3%D0%BE_%D0%B0%D0%BF%D0%B0%D1%80%D0%B0%D1%82%D0%B0" title="Тяга літального апарата – Ukrainian" lang="uk" hreflang="uk" data-title="Тяга літального апарата" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%8E%A8%E5%8A%9B" title="推力 – Chinese" lang="zh" hreflang="zh" data-title="推力" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit 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class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Thrust" title="Special:EditPage/Thrust">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Thrust%22">"Thrust"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Thrust%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Thrust%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Thrust%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Thrust%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Thrust%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">December 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:F-35_Heritage_Flight_Team_performs_in_Bell_Fort_Worth_Alliance_AirShow.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/F-35_Heritage_Flight_Team_performs_in_Bell_Fort_Worth_Alliance_AirShow.jpg/330px-F-35_Heritage_Flight_Team_performs_in_Bell_Fort_Worth_Alliance_AirShow.jpg" decoding="async" width="330" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/F-35_Heritage_Flight_Team_performs_in_Bell_Fort_Worth_Alliance_AirShow.jpg/495px-F-35_Heritage_Flight_Team_performs_in_Bell_Fort_Worth_Alliance_AirShow.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/F-35_Heritage_Flight_Team_performs_in_Bell_Fort_Worth_Alliance_AirShow.jpg/660px-F-35_Heritage_Flight_Team_performs_in_Bell_Fort_Worth_Alliance_AirShow.jpg 2x" data-file-width="3384" data-file-height="2615" /></a><figcaption>A <a href="/wiki/Lockheed_Martin_F-35_Lightning_II" title="Lockheed Martin F-35 Lightning II">Lockheed Martin F-35 Lightning II</a> aircraft performing a vertical climb using its <a href="/wiki/Pratt_%26_Whitney_F135" title="Pratt & Whitney F135">Pratt & Whitney F135</a> jet engine, which produces 43,000 lbf (190,000 N) of thrust.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p><b>Thrust</b> is a <a href="/wiki/Reaction_(physics)" title="Reaction (physics)">reaction</a> <a href="/wiki/Force_(physics)" class="mw-redirect" title="Force (physics)">force</a> described quantitatively by <a href="/wiki/Newton%27s_third_law" class="mw-redirect" title="Newton's third law">Newton's third law</a>. When a system expels or <a href="/wiki/Acceleration" title="Acceleration">accelerates</a> <a href="/wiki/Mass" title="Mass">mass</a> in one direction, the accelerated mass will cause a force of equal <a href="/wiki/Magnitude_(vector)" class="mw-redirect" title="Magnitude (vector)">magnitude</a> but opposite direction to be applied to that system.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The force applied on a surface in a direction perpendicular or <a href="/wiki/Normal_vector" class="mw-redirect" title="Normal vector">normal</a> to the surface is also called thrust. Force, and thus thrust, is measured using the <a href="/wiki/International_System_of_Units" title="International System of Units">International System of Units</a> (SI) in <a href="/wiki/Newton_(unit)" title="Newton (unit)">newtons</a> (symbol: N), and represents the amount needed to accelerate 1 kilogram of mass at the rate of 1 <a href="/wiki/Metre_per_second_squared" title="Metre per second squared">meter per second per second</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Mechanical_engineering" title="Mechanical engineering">mechanical engineering</a>, force <a href="/wiki/Orthogonal" class="mw-redirect" title="Orthogonal">orthogonal</a> to the main load (such as in parallel <a href="/wiki/Helical_gear" class="mw-redirect" title="Helical gear">helical gears</a>) is referred to as <a href="/wiki/Statics" title="Statics">static thrust</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thrust&action=edit&section=1" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Fixed-wing_aircraft" title="Fixed-wing aircraft">fixed-wing aircraft</a> propulsion system generates forward thrust when air is pushed in the direction opposite to flight. This can be done by different means such as the spinning blades of a <a href="/wiki/Propeller_(aircraft)" class="mw-redirect" title="Propeller (aircraft)">propeller</a>, the propelling jet of a <a href="/wiki/Jet_engine" title="Jet engine">jet engine</a>, or by ejecting hot gases from a <a href="/wiki/Rocket_engine" title="Rocket engine">rocket engine</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> Reverse thrust can be generated to aid braking after landing by reversing the pitch of variable-pitch propeller blades, or using a <a href="/wiki/Thrust_reversal" title="Thrust reversal">thrust reverser</a> on a jet engine. <a href="/wiki/Rotary_wing_aircraft" class="mw-redirect" title="Rotary wing aircraft">Rotary wing aircraft</a> use rotors and <a href="/wiki/Thrust_vectoring" title="Thrust vectoring">thrust vectoring</a> <a href="/wiki/V/STOL" title="V/STOL">V/STOL</a> aircraft use propellers or engine thrust to support the weight of the aircraft and to provide forward propulsion. </p><p>A <a href="/wiki/Motorboat" title="Motorboat">motorboat</a> propeller generates thrust when it rotates and forces water backwards. </p><p>A <a href="/wiki/Rocket" title="Rocket">rocket</a> is propelled forward by a thrust equal in magnitude, but opposite in direction, to the time-rate of momentum change of the <a href="/wiki/Exhaust_gas" title="Exhaust gas">exhaust gas</a> accelerated from the combustion chamber through the rocket engine nozzle. This is the <a href="/wiki/Exhaust_velocity" class="mw-redirect" title="Exhaust velocity">exhaust velocity</a> with respect to the rocket, times the time-rate at which the mass is expelled, or in mathematical terms: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {T} =\mathbf {v} {\frac {\mathrm {d} m}{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {T} =\mathbf {v} {\frac {\mathrm {d} m}{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a76ba4f9089bff8a0c4db8a1f6f6a0ea41e546c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.538ex; height:5.509ex;" alt="{\displaystyle \mathbf {T} =\mathbf {v} {\frac {\mathrm {d} m}{\mathrm {d} t}}}"></span></dd></dl> <p>Where <b>T</b> is the thrust generated (force), <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 {\frac {\mathrm {d} m}{\mathrm {d} t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a3707093243f5e61026b3985286633f994d0f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:4.169ex; height:5.509ex;" alt="{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}}"></span> is the rate of change of mass with respect to time (mass flow rate of exhaust), and <b>v</b> is the velocity of the exhaust gases measured relative to the rocket. </p><p>For vertical launch of a rocket the initial thrust at <a href="https://en.wiktionary.org/wiki/liftoff" class="extiw" title="wikt:liftoff">liftoff</a> must be more than the weight. </p><p>Each of the three <a href="/wiki/Space_Shuttle" title="Space Shuttle">Space Shuttle</a> <a href="/wiki/Space_Shuttle_Main_Engine" class="mw-redirect" title="Space Shuttle Main Engine">Main Engines</a> could produce a thrust of 1.8 <a href="/wiki/Meganewton" class="mw-redirect" title="Meganewton">meganewton</a>, and each of the Space Shuttle's two <a href="/wiki/Space_Shuttle_Solid_Rocket_Booster" title="Space Shuttle Solid Rocket Booster">Solid Rocket Boosters</a> 14.7 <a href="/wiki/Newton_(unit)" title="Newton (unit)">MN</a> (3,300,000 <a href="/wiki/Pound_(force)" title="Pound (force)">lbf</a>), together 29.4 MN.<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>By contrast, the <a href="/wiki/Simplified_Aid_for_EVA_Rescue" class="mw-redirect" title="Simplified Aid for EVA Rescue">Simplified Aid for EVA Rescue</a> (SAFER) has 24 thrusters of 3.56 N (0.80 lbf) each.<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><p>In the air-breathing category, the AMT-USA AT-180 jet engine developed for <a href="/wiki/Radio-controlled_aircraft" title="Radio-controlled aircraft">radio-controlled aircraft</a> produce 90 N (20 <a href="/wiki/Pound-force" class="mw-redirect" title="Pound-force">lbf</a>) of thrust.<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> The <a href="/wiki/GE90" class="mw-redirect" title="GE90">GE90</a>-115B engine fitted on the <a href="/wiki/Boeing_777" title="Boeing 777">Boeing 777</a>-300ER, recognized by the <a href="/wiki/Guinness_Book_of_World_Records" class="mw-redirect" title="Guinness Book of World Records">Guinness Book of World Records</a> as the "World's Most Powerful Commercial Jet Engine," has a thrust of 569 kN (127,900 lbf) until it was surpassed by the <a href="/wiki/General_Electric_GE9X" title="General Electric GE9X">GE9X</a>, fitted on the upcoming <a href="/wiki/Boeing_777X" title="Boeing 777X">Boeing 777X</a>, at 609 kN (134,300 lbf). </p> <div class="mw-heading mw-heading2"><h2 id="Concepts">Concepts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thrust&action=edit&section=2" title="Edit section: Concepts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Thrust_to_power">Thrust to power</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thrust&action=edit&section=3" title="Edit section: Thrust to power"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The power needed to generate thrust and the force of the thrust can be related in a <a href="/wiki/Non-linear" class="mw-redirect" title="Non-linear">non-linear</a> way. In general, <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 \mathbf {P} ^{2}\propto \mathbf {T} ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>∝</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} ^{2}\propto \mathbf {T} ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83d5b65bd195863a6a58ad081af0d79081155332" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.893ex; height:2.676ex;" alt="{\displaystyle \mathbf {P} ^{2}\propto \mathbf {T} ^{3}}"></span>. The proportionality constant varies, and can be solved for a uniform flow, 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_{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26145027656115364f96e031bca0c0c11022986e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.003ex; height:2.009ex;" alt="{\displaystyle v_{\infty }}"></span> is the incoming air velocity, <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_{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eac4aa20f05fda74ee30f9f9842229d087f33133" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.22ex; height:2.009ex;" alt="{\displaystyle v_{d}}"></span> is the velocity at the actuator disc, 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 v_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99259350b2b7a4c8d47eb2dc6bafd373da5bbb8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.264ex; height:2.343ex;" alt="{\displaystyle v_{f}}"></span> is the final exit velocity: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho A{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>ρ</mi> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho A{v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dacd4604bc0bb34b38f6145620fa8888a1a6ef5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.34ex; height:5.509ex;" alt="{\displaystyle {\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho A{v}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {T} ={\frac {\mathrm {d} m}{\mathrm {d} t}}\left(v_{f}-v_{\infty }\right),{\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho Av_{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>ρ</mi> <mi>A</mi> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {T} ={\frac {\mathrm {d} m}{\mathrm {d} t}}\left(v_{f}-v_{\infty }\right),{\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho Av_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/763764d74e4309311b5eea31b2076d1b56ac7571" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:33.284ex; height:5.509ex;" alt="{\displaystyle \mathbf {T} ={\frac {\mathrm {d} m}{\mathrm {d} t}}\left(v_{f}-v_{\infty }\right),{\frac {\mathrm {d} m}{\mathrm {d} t}}=\rho Av_{d}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} ={\frac {1}{2}}{\frac {\mathrm {d} m}{\mathrm {d} t}}(v_{f}^{2}-v_{\infty }^{2}),\mathbf {P} =\mathbf {T} v_{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>m</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>t</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} ={\frac {1}{2}}{\frac {\mathrm {d} m}{\mathrm {d} t}}(v_{f}^{2}-v_{\infty }^{2}),\mathbf {P} =\mathbf {T} v_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a906499019709bd19ad70fea95d467d84a82cc48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:31.047ex; height:5.509ex;" alt="{\displaystyle \mathbf {P} ={\frac {1}{2}}{\frac {\mathrm {d} m}{\mathrm {d} t}}(v_{f}^{2}-v_{\infty }^{2}),\mathbf {P} =\mathbf {T} v_{d}}"></span></dd></dl> <p>Solving for the velocity at the disc, <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_{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eac4aa20f05fda74ee30f9f9842229d087f33133" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.22ex; height:2.009ex;" alt="{\displaystyle v_{d}}"></span>, we then have: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{d}={\frac {1}{2}}(v_{f}-v_{\infty })}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{d}={\frac {1}{2}}(v_{f}-v_{\infty })}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d371c1a761f7487455c1e36082d3507ce64f928" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.233ex; height:5.176ex;" alt="{\displaystyle v_{d}={\frac {1}{2}}(v_{f}-v_{\infty })}"></span></dd></dl> <p>When incoming air is accelerated from a standstill – for example when hovering – then <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_{\infty }=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\infty }=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55af15751b6e3b821d67ecc88e3db075aa2353ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.264ex; height:2.509ex;" alt="{\displaystyle v_{\infty }=0}"></span>, and we can find: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {T} ={\frac {1}{2}}\rho A{v_{f}}^{2},\mathbf {P} ={\frac {1}{4}}\rho A{v_{f}}^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ρ</mi> <mi>A</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mi>ρ</mi> <mi>A</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {T} ={\frac {1}{2}}\rho A{v_{f}}^{2},\mathbf {P} ={\frac {1}{4}}\rho A{v_{f}}^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/749dd7bf3a2f771d2c23fa83a7ffe0553c480618" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:27.44ex; height:5.176ex;" alt="{\displaystyle \mathbf {T} ={\frac {1}{2}}\rho A{v_{f}}^{2},\mathbf {P} ={\frac {1}{4}}\rho A{v_{f}}^{3}}"></span></dd></dl> <p>From here we can see the <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 \mathbf {P} ^{2}\propto \mathbf {T} ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>∝</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} ^{2}\propto \mathbf {T} ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83d5b65bd195863a6a58ad081af0d79081155332" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.893ex; height:2.676ex;" alt="{\displaystyle \mathbf {P} ^{2}\propto \mathbf {T} ^{3}}"></span> relationship, finding: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} ^{2}={\frac {\mathbf {T} ^{3}}{2\rho A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>ρ</mi> <mi>A</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} ^{2}={\frac {\mathbf {T} ^{3}}{2\rho A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf5e4c1b637a176c64c1868e1967fa701dd4f002" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:10.923ex; height:6.343ex;" alt="{\displaystyle \mathbf {P} ^{2}={\frac {\mathbf {T} ^{3}}{2\rho A}}}"></span></dd></dl> <p>The inverse of the proportionality constant, the "efficiency" of an otherwise-perfect thruster, is proportional to the area of the cross section of the propelled volume of fluid (<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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>) and the density of the fluid (<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</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>). This helps to explain why moving through water is easier and why aircraft have much larger propellers than watercraft. </p> <div class="mw-heading mw-heading3"><h3 id="Thrust_to_propulsive_power">Thrust to propulsive power</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thrust&action=edit&section=4" title="Edit section: Thrust to propulsive power"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A very common question is how to compare the thrust rating of a jet engine with the power rating of a piston engine. Such comparison is difficult, as these quantities are not equivalent. A piston engine does not move the aircraft by itself (the propeller does that), so piston engines are usually rated by how much power they deliver to the propeller. Except for changes in temperature and air pressure, this quantity depends basically on the throttle setting. </p><p>A jet engine has no propeller, so the propulsive power of a jet engine is determined from its thrust as follows. Power is the force (F) it takes to move something over some distance (d) divided by the time (t) it takes to move that distance:<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> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} =\mathbf {F} {\frac {d}{t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mi>t</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} =\mathbf {F} {\frac {d}{t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b172cdbdf965fa2da08b745ea43d7e0666408c74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.66ex; height:5.343ex;" alt="{\displaystyle \mathbf {P} =\mathbf {F} {\frac {d}{t}}}"></span></dd></dl> <p>In case of a rocket or a jet aircraft, the force is exactly the thrust (T) produced by the engine. If the rocket or aircraft is moving at about a constant speed, then distance divided by time is just speed, so power is thrust times speed:<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> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {P} =\mathbf {T} {v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">P</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">T</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {P} =\mathbf {T} {v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a90beef91973eb53fe33b87f8a539754a98e238" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.912ex; height:2.176ex;" alt="{\displaystyle \mathbf {P} =\mathbf {T} {v}}"></span></dd></dl> <p>This formula looks very surprising, but it is correct: the <i>propulsive power</i> (or <i>power available</i> <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>) of a jet engine increases with its speed. If the speed is zero, then the propulsive power is zero. If a jet aircraft is at full throttle but attached to a static test stand, then the jet engine produces no propulsive power, however thrust is still produced. The combination <a href="/wiki/Piston_engine" class="mw-redirect" title="Piston engine">piston engine</a>–propeller also has a propulsive power with exactly the same formula, and it will also be zero at zero speed – but that is for the engine–propeller set. The engine alone will continue to produce its rated power at a constant rate, whether the aircraft is moving or not. </p><p>Now, imagine the strong chain is broken, and the jet and the piston aircraft start to move. At low speeds: </p> <blockquote> <p>The piston engine will have constant 100% power, and the propeller's thrust will vary with speed<br /> The jet engine will have constant 100% thrust, and the engine's power will vary with speed </p> </blockquote> <div class="mw-heading mw-heading3"><h3 id="Excess_thrust">Excess thrust</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thrust&action=edit&section=5" title="Edit section: Excess thrust"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If a powered aircraft is generating thrust T and experiencing <a href="/wiki/Aerodynamic_drag" class="mw-redirect" title="Aerodynamic drag">drag</a> D, the difference between the two, T − D, is termed the excess thrust. The instantaneous performance of the aircraft is mostly dependent on the excess thrust. </p><p>Excess thrust is a <a href="/wiki/Euclidean_vector" title="Euclidean vector">vector</a> and is determined as the vector difference between the thrust vector and the drag vector. </p> <div class="mw-heading mw-heading3"><h3 id="Thrust_axis">Thrust axis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Thrust&action=edit&section=6" title="Edit section: Thrust axis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The thrust axis for an airplane is the <a href="/wiki/Line_of_action" title="Line of action">line of action</a> of the total thrust at any instant. It depends on the location, number, and characteristics of the jet engines or propellers. It usually differs from the drag axis. If so, the distance between the thrust axis and the drag axis will cause a <a href="/wiki/Moment_(physics)" title="Moment (physics)">moment</a> that must be resisted by a change in the aerodynamic force on the horizontal stabiliser.<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> Notably, the <a href="/wiki/Boeing_737_MAX" title="Boeing 737 MAX">Boeing 737 MAX</a>, with larger, lower-slung engines than previous 737 models, had a greater distance between the thrust axis and the drag axis, causing the nose to rise up in some flight regimes, necessitating a pitch-control system, <a href="/wiki/Maneuvering_Characteristics_Augmentation_System" title="Maneuvering Characteristics Augmentation System">MCAS</a>. Early versions of MCAS malfunctioned in flight with catastrophic consequences, leading to the <a href="/wiki/Boeing_737_MAX_groundings" title="Boeing 737 MAX groundings">deaths of over 300 people</a> in 2018 and 2019.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </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=Thrust&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Aerodynamic_force" title="Aerodynamic force">Aerodynamic force</a> – Force exerted on a body as it moves through air or gas</li> <li><a href="/wiki/Astern_propulsion" title="Astern propulsion">Astern propulsion</a> – Use of a ship's propelling mechanism to develop thrust in a retrograde direction</li> <li><a href="/wiki/Gas_turbine_engine_thrust" title="Gas turbine engine thrust">Gas turbine engine thrust</a></li> <li><a href="/wiki/Gimballed_thrust" class="mw-redirect" title="Gimballed thrust">Gimballed thrust</a> – System of thrust vectoring used in rockets<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span> (most common in modern rockets)</li> <li><a href="/wiki/Pound_(force)" title="Pound (force)">Pound (force)</a> – Earth's gravitational pull on a one-pound mass <ul><li>"Pound of thrust": thrust (force) required to accelerate one pound at one <a href="/wiki/Standard_gravity" title="Standard gravity">g</a></li></ul></li> <li><a href="/wiki/Stream_thrust_averaging" title="Stream thrust averaging">Stream thrust averaging</a> – Process to convert 3D flow into 1D</li> <li><a href="/wiki/Thrust-to-weight_ratio" title="Thrust-to-weight ratio">Thrust-to-weight ratio</a> – Dimensionless ratio of thrust to weight of a jet or propeller engine</li> <li><a href="/wiki/Thrust_vectoring" title="Thrust vectoring">Thrust vectoring</a> – Facet of ballistics and aeronautics</li> <li><a href="/wiki/Thrust_reversal" title="Thrust reversal">Thrust reversal</a> – Temporary diversion of an aircraft engine's thrust</li> <li><a href="/wiki/Tractive_effort" title="Tractive effort">Tractive effort</a> – Mechanical engineering term that refers to the amount of traction.</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=Thrust&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style 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Archived from <a rel="nofollow" class="external text" href="http://usamt.com/Mel/comm/comm_products.html">the original</a> on 10 November 2006<span class="reference-accessdate">. Retrieved <span class="nowrap">13 December</span> 2006</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=AMT-USA+jet+engine+product+information&rft_id=http%3A%2F%2Fusamt.com%2FMel%2Fcomm%2Fcomm_products.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThrust" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYoon" class="citation web cs1">Yoon, Joe. <a rel="nofollow" class="external text" href="http://www.aerospaceweb.org/question/propulsion/q0195.shtml">"Convert Thrust to Horsepower"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100613154846/http://www.aerospaceweb.org/question/propulsion/q0195.shtml">Archived</a> from the original on 13 June 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">1 May</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Convert+Thrust+to+Horsepower&rft.aulast=Yoon&rft.aufirst=Joe&rft_id=http%3A%2F%2Fwww.aerospaceweb.org%2Fquestion%2Fpropulsion%2Fq0195.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThrust" class="Z3988"></span></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="CITEREFYechoutMorris" class="citation book cs1">Yechout, Thomas; Morris, Steven. <i>Introduction to Aircraft Flight Mechanics</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-56347-577-4" title="Special:BookSources/1-56347-577-4"><bdi>1-56347-577-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Aircraft+Flight+Mechanics&rft.isbn=1-56347-577-4&rft.aulast=Yechout&rft.aufirst=Thomas&rft.au=Morris%2C+Steven&rfr_id=info%3Asid%2Fen.wikipedia.org%3AThrust" 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="CITEREFAndersonEberhardt2001" class="citation book cs1">Anderson, David; Eberhardt, Scott (2001). <i>Understanding Flight</i>. 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