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<h1 id="firstHeading" class="firstHeading mw-first-heading">
<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Ragone plot</span></span>
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<p>A <b>Ragone plot</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa">/<span style="border-bottom:1px dotted"><span title="'r' in 'rye'">r</span><span title="/ə/: 'a' in 'about'">ə</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="/ɡ/: 'g' in 'guy'">ɡ</span><span title="/oʊ/: 'o' in 'code'">oʊ</span><span title="'n' in 'nigh'">n</span><span title="/iː/: 'ee' in 'fleece'">iː</span></span>/</span></span> <i title="English pronunciation respelling">rə-<span style="font-size:90%">GOH</span>-nee</i>)<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> is a plot used for comparing the energy density of various energy-storing devices. On such a chart the values of <a href="Specific_energy" title="Specific energy">specific energy</a> (in <a href="Watt-hour" class="mw-redirect" title="Watt-hour">W·h</a>/<a href="Kg" class="mw-redirect" title="Kg">kg</a>) are plotted versus <a href="Power-to-weight_ratio" title="Power-to-weight ratio">specific power</a> (in W/kg). Both axes are <a href="Logarithmic_scale" title="Logarithmic scale">logarithmic</a>, which allows comparing performance of very different devices. Ragone plots can reveal information about gravimetric energy density, but do not convey details about <a href="Volumetric_energy_density" class="mw-redirect" title="Volumetric energy density">volumetric energy density</a>.
</p><p>The Ragone plot was first used to compare performance of <a href="Electric_battery" title="Electric battery">batteries</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> However, it is suitable for comparing any energy-storage devices,<sup id="cite_ref-Theory_3-0" class="reference"><a href="#cite_note-Theory-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> as well as energy devices such as engines, gas turbines, and fuel cells.<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 plot is named after <a href="David_V._Ragone" title="David V. Ragone">David V. Ragone</a>.<sup id="cite_ref-Theory_3-1" class="reference"><a href="#cite_note-Theory-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>
</p><p>Conceptually, the vertical axis describes how much <a href="Energy" title="Energy">energy</a> is available per unit mass, while the horizontal axis shows how quickly that energy can be delivered, otherwise known as <a href="Power_(physics)" title="Power (physics)">power</a> per unit mass. A point in a Ragone plot represents a particular energy device or technology.
</p><p>The amount of time (in hours) during which a device can be operated at its rated power is given as the ratio between the specific energy (Y-axis) and the specific power (X-axis). This is true regardless of the overall scale of the device, since a larger device would have proportional increases in both power and energy. Consequently, the <a href="Contour_line" title="Contour line">iso curves</a> (constant operating time) in a Ragone plot are straight lines.
</p><p>For electrical systems, the following equations are relevant:
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<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{specific energy}}={\frac {V\times I\times t}{m}},}">
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<mtext>specific energy</mtext>
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<mo>=</mo>
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<mfrac>
<mrow>
<mi>V</mi>
<mo>×<!-- × --></mo>
<mi>I</mi>
<mo>×<!-- × --></mo>
<mi>t</mi>
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<mi>m</mi>
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<mo>,</mo>
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<annotation encoding="application/x-tex">{\displaystyle {\text{specific energy}}={\frac {V\times I\times t}{m}},}</annotation>
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</math></span><img src="./327d2970c28cb3e52a33ac04aa898c1da9dd1901.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.612ex; height:5.176ex;" alt="{\displaystyle {\text{specific energy}}={\frac {V\times I\times t}{m}},}" loading="lazy"></span></dd></dl>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{specific power}}={\frac {V\times I}{m}},}">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mtext>specific power</mtext>
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<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>V</mi>
<mo>×<!-- × --></mo>
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<mi>m</mi>
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<annotation encoding="application/x-tex">{\displaystyle {\text{specific power}}={\frac {V\times I}{m}},}</annotation>
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</math></span><img src="./7710461359523e4ef3af924312b6b74927acd4a3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:24.35ex; height:5.176ex;" alt="{\displaystyle {\text{specific power}}={\frac {V\times I}{m}},}" loading="lazy"></span></dd></dl>
<p>where <i>V</i> is <a href="Voltage" title="Voltage">voltage</a> (V), <i>I</i> <a href="Electric_current" title="Electric current">electric current</a> (A), <i>t</i> <a href="Time" title="Time">time</a> (s) and <i>m</i> <a href="Mass" title="Mass">mass</a> (kg).
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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.case.edu/its/archives/presidents/ragsummary.htm">"President David V. Ragone"</a>. <i><a href="Case_Western_Reserve_University" title="Case Western Reserve University">Case Western Reserve University</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">21 April</span> 2015</span>.</cite></span>
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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFRagone1968" class="citation journal cs1">Ragone, D. V. (1968). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://saemobilus.sae.org/papers/review-battery-systems-electrically-powered-vehicles-680453">"Review of Battery Systems for Electrically Powered Vehicles"</a></span>. <i>SAE Technical Paper</i>. SAE Technical Paper Series. <b>1</b>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4271%2F680453">10.4271/680453</a>. 680453.</cite></span>
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<li id="cite_note-Theory-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Theory_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Theory_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFChristenCarlen2000" class="citation journal cs1">Christen, Thomas; Carlen, Martin W. (2000). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/229122460">"Theory of Ragone plots"</a>. <i><a href="Journal_of_Power_Sources" title="Journal of Power Sources">Journal of Power Sources</a></i>. <b>91</b> (2): <span class="nowrap">210–</span>216. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000JPS....91..210C">2000JPS....91..210C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0378-7753%2800%2900474-2">10.1016/S0378-7753(00)00474-2</a>.</cite></span>
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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFLeeWoo_Young_Jung2016" class="citation journal cs1">Lee, Sang C.; Woo Young Jung (June 2016). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.egypro.2016.06.073">"Analogical understanding of the Ragone plot and a new categorization of energy device"</a>. <i>Energy Procedia</i>. <b>88</b>: <span class="nowrap">526–</span>530. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.egypro.2016.06.073">10.1016/j.egypro.2016.06.073</a></span>.</cite></span>
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