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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>Rotor solidity</b> is a <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless quantity</a> used in design and analysis of <a href="/wiki/Rotorcraft" title="Rotorcraft">rotorcraft</a>, <a href="/wiki/Propeller_(aeronautics)" title="Propeller (aeronautics)">propellers</a> and <a href="/wiki/Wind_turbines" class="mw-redirect" title="Wind turbines">wind turbines</a>. Rotor solidity is a function of the <a href="/wiki/Aspect_ratio" title="Aspect ratio">aspect ratio</a> and number of blades in the rotor and is widely used as a parameter for ensuring <a href="/wiki/Similarity_(geometry)" title="Similarity (geometry)">geometric similarity</a> in rotorcraft experiments. It provides a measure of how close a lifting rotor system is to an ideal actuator disk in <a href="/wiki/Momentum_theory" title="Momentum theory">momentum theory</a>. It also plays an important role in determining the fluid speed across the rotor disk when lift is generated and consequentially the performance of the rotor; amount of <a href="/wiki/Downwash" title="Downwash">downwash</a> around it, and noise levels the rotor generates. It is also used to compare performance characteristics between rotors of different sizes. Typical values of rotor solidity ratio for helicopters fall in the range 0.05 to 0.12.<sup id="cite_ref-Landgrebe_1971_1-0" class="reference"><a href="#cite_note-Landgrebe_1971-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Definitions">Definitions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotor_solidity&action=edit&section=1" title="Edit section: Definitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rotor solidity is the <a href="/wiki/Ratio" title="Ratio">ratio</a> of area of the rotor blades to the area of the rotor disk.<sup id="cite_ref-Leishman_2-0" class="reference"><a href="#cite_note-Leishman-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>For a rotor with <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> blades, each of 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> and chord <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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span>, rotor solidity <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</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> is: </p><p><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 \equiv {\frac {A_{b}}{A_{d}}}={\frac {NcR}{\pi R^{2}}}={\frac {Nc}{\pi R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <mi>c</mi> <mi>R</mi> </mrow> <mrow> <mi>π</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <mi>c</mi> </mrow> <mrow> <mi>π</mi> <mi>R</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma \equiv {\frac {A_{b}}{A_{d}}}={\frac {NcR}{\pi R^{2}}}={\frac {Nc}{\pi R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c06a063001badca6d568fdb8a03cfe938d8d433b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.899ex; height:5.843ex;" alt="{\displaystyle \sigma \equiv {\frac {A_{b}}{A_{d}}}={\frac {NcR}{\pi R^{2}}}={\frac {Nc}{\pi R}}}"></span> </p><p>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 A_{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f872d09ff387e493a18005d4475aade2f7f8e076" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.681ex; height:2.509ex;" alt="{\displaystyle A_{b}}"></span> is the blade area 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 A_{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e4c67aa7c46d8276c9805b1036cd4c2e9887d0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.835ex; height:2.509ex;" alt="{\displaystyle A_{d}}"></span> is the disk area. </p><p>For blades with a non-rectangular planform, solidity is often computed using an equivalent weighted form<sup id="cite_ref-Gessow_3-0" class="reference"><a href="#cite_note-Gessow-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> as </p><p><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 _{e}\equiv {\frac {1}{R}}\int _{0}^{R}w(r)\ \sigma (r)dr}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>≡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>R</mi> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msubsup> <mi>w</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mtext> </mtext> <mi>σ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{e}\equiv {\frac {1}{R}}\int _{0}^{R}w(r)\ \sigma (r)dr}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4515df5eb4f6c66c652008b9a75f94db2ce38ed5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.297ex; height:6.176ex;" alt="{\displaystyle \sigma _{e}\equiv {\frac {1}{R}}\int _{0}^{R}w(r)\ \sigma (r)dr}"></span> </p><p>where: </p> <ul><li><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 w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span> is a weighting function corresponding to the blade section</li> <li><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</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> is solidity corresponding to the blade section</li> <li><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 radial length to the blade section</li></ul> <p>The weighing function is determined by the aerodynamic performance parameter that is assumed to be constant in comparison to an equivalent rotor having a rectangular blade planform. For example, when rotor thrust coefficient is assumed to be constant, the weighing function comes out to be: </p><p><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 w(r)=3r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>3</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w(r)=3r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0603af735cc22ef6152acf8595b21496e012d930" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.886ex; height:3.176ex;" alt="{\displaystyle w(r)=3r^{2}}"></span> </p><p>and the corresponding weighted solidity ratio is known as the <b>thrust-weighted solidity ratio</b>.<sup id="cite_ref-Leishman_2-1" class="reference"><a href="#cite_note-Leishman-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>When rotor power or torque coefficient is assumed constant, the weighing function is: </p><p><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 w(r)=4r^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>4</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w(r)=4r^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/953de399d66d4930396f90c63d4392bd1eb5dcf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.886ex; height:3.176ex;" alt="{\displaystyle w(r)=4r^{3}}"></span> </p><p>and the corresponding weighted solidity ratio is known as the <b>power or torque-weighted solidity ratio</b>. This solidity ratio is analogous to the activity factor used in propeller design and is also used in wind turbine analysis. However, it is rarely used in helicopter design.<sup id="cite_ref-Leishman_2-2" class="reference"><a href="#cite_note-Leishman-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Geometric_significance">Geometric significance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotor_solidity&action=edit&section=2" title="Edit section: Geometric significance"><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:SolidityRatio.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/SolidityRatio.svg/220px-SolidityRatio.svg.png" decoding="async" width="220" height="111" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/SolidityRatio.svg/330px-SolidityRatio.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/SolidityRatio.svg/440px-SolidityRatio.svg.png 2x" data-file-width="425" data-file-height="215" /></a><figcaption>Two rotors illustrating the geometric significance of rotor solidity ratio. The rotor on the right has a larger solidity ratio due to the blades covering a larger fraction of the net rotor disk area.</figcaption></figure> <p>A crude idea of what a rotor or propeller geometry looks like can be obtained from the rotor solidity ratio. Rotors with stubbier and/or a larger number of blades have a larger solidity ratio since they cover a larger fraction of the rotor disk. Rotorcraft like helicopters typically use blades with very low solidity ratios compared to fixed-wing and marine propellers. </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rotor_solidity&action=edit&section=3" 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"><ol class="references"> <li id="cite_note-Landgrebe_1971-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Landgrebe_1971_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 id="CITEREFLandgrebe1971" class="citation journal cs1 cs1-prop-long-vol">Landgrebe, Anton J. (1971). <a rel="nofollow" class="external text" href="https://apps.dtic.mil/docs/citations/AD0728835">"An Analytical and Experimental Investigation of Helicopter Rotor Hover Performance and Wake Geometry Characteristics"</a>. <i>USAAMRDL Technical Report</i>. <span class="nowrap">71–</span>24: <span class="nowrap">15–</span>16.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=USAAMRDL+Technical+Report&rft.atitle=An+Analytical+and+Experimental+Investigation+of+Helicopter+Rotor+Hover+Performance+and+Wake+Geometry+Characteristics&rft.volume=71-24&rft.pages=%3Cspan+class%3D%22nowrap%22%3E15-%3C%2Fspan%3E16&rft.date=1971&rft.aulast=Landgrebe&rft.aufirst=Anton+J.&rft_id=https%3A%2F%2Fapps.dtic.mil%2Fdocs%2Fcitations%2FAD0728835&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARotor+solidity" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged June 2022">dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-Leishman-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Leishman_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Leishman_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Leishman_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeishman2006" class="citation book cs1">Leishman, J. Gordon (2006). <i>Principles of Helicopter Aerodynamics</i>. Cambridge aerospace series. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-85860-1" title="Special:BookSources/978-0-521-85860-1"><bdi>978-0-521-85860-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+Helicopter+Aerodynamics&rft.pub=Cambridge+aerospace+series&rft.date=2006&rft.isbn=978-0-521-85860-1&rft.aulast=Leishman&rft.aufirst=J.+Gordon&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARotor+solidity" class="Z3988"></span></span> </li> <li id="cite_note-Gessow-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gessow_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGessowMyers1967" class="citation book cs1">Gessow, A.; Myers, G. C. Jr. (1967). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=OKYXnQEACAAJ"><i>Aerodynamics of the Helicopter</i></a>. New York: Frederick Ungar. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8044-4275-6" title="Special:BookSources/978-0-8044-4275-6"><bdi>978-0-8044-4275-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Aerodynamics+of+the+Helicopter&rft.place=New+York&rft.pub=Frederick+Ungar&rft.date=1967&rft.isbn=978-0-8044-4275-6&rft.aulast=Gessow&rft.aufirst=A.&rft.au=Myers%2C+G.+C.+Jr.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DOKYXnQEACAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARotor+solidity" class="Z3988"></span></span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist 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href="/wiki/Template:Helicopters_and_rotorcraft" title="Template:Helicopters and rotorcraft"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Helicopters_and_rotorcraft" title="Template talk:Helicopters and rotorcraft"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Helicopters_and_rotorcraft" title="Special:EditPage/Template:Helicopters and rotorcraft"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Helicopters_and_other_rotorcraft459" style="font-size:114%;margin:0 4em">Helicopters and other rotorcraft</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Helicopter" title="Helicopter">Helicopters</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Articles</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amphibious_helicopter" title="Amphibious helicopter">Amphibious</a></li> <li><a href="/wiki/Attack_helicopter" title="Attack helicopter">Attack</a></li> <li><a href="/wiki/Autorotation" title="Autorotation">Autorotation</a></li> <li><a href="/wiki/Backpack_helicopter" title="Backpack helicopter">Backpack</a></li> <li><a href="/wiki/Disk_loading" title="Disk loading">Disk loading</a></li> <li><a href="/wiki/Helicopter_dynamics" title="Helicopter dynamics">Dynamics</a></li> <li><a href="/wiki/Helicopter_flight_controls" title="Helicopter flight controls">Flight controls</a></li> <li><a href="/wiki/List_of_countries_by_number_of_heliports" title="List of countries by number of heliports">Number of helicopters and heliports</a></li> <li><a href="/wiki/Helicopter_manufacturer" title="Helicopter manufacturer">Manufacturers</a></li> <li><a href="/wiki/Military_helicopter" title="Military helicopter">Military</a></li> <li><a href="/wiki/Helicopter_rotor" title="Helicopter rotor">Rotor</a></li> <li><a class="mw-selflink selflink">Rotor solidity</a></li> <li><a href="/wiki/Utility_helicopter" title="Utility helicopter">Utility</a></li> <li><a href="/wiki/Wire_strike_protection_system" title="Wire strike protection system">Wire strike protection system</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_accidents_and_incidents_involving_helicopters" title="List of accidents and incidents involving helicopters">Accidents and incidents</a></li> <li><a href="/wiki/List_of_active_Russian_military_aircraft" title="List of active Russian military aircraft">Active Russian military</a></li> <li><a href="/wiki/List_of_helicopter_airlines" title="List of helicopter airlines">Airlines</a> <ul><li><a href="/wiki/List_of_small_airlines_and_helicopter_airlines_of_Russia" title="List of small airlines and helicopter airlines of Russia">Russian helicopter airlines</a></li></ul></li> <li><a href="/wiki/List_of_NATO_reporting_names_for_helicopters" title="List of NATO reporting names for helicopters">NATO reporting names</a></li> <li><a href="/wiki/List_of_helicopter_prison_escapes" title="List of helicopter prison escapes">Prison escapes</a></li> <li><a href="/wiki/List_of_ultralight_helicopters" title="List of ultralight helicopters">Ultralights</a></li> <li><a href="/wiki/List_of_United_States_Air_Force_helicopter_squadrons" title="List of United States Air Force helicopter squadrons">U.S. Air Force squadrons</a></li> <li><a href="/wiki/List_of_United_States_military_helicopters" title="List of United States military helicopters">U.S. military</a></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Pilatus_Agusta_A109_Flug.jpg" class="mw-file-description" title="An Agusta A109K2 rescue helicopter"><img alt="An Agusta A109K2 rescue helicopter" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Pilatus_Agusta_A109_Flug.jpg/146px-Pilatus_Agusta_A109_Flug.jpg" decoding="async" width="146" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Pilatus_Agusta_A109_Flug.jpg/219px-Pilatus_Agusta_A109_Flug.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Pilatus_Agusta_A109_Flug.jpg/292px-Pilatus_Agusta_A109_Flug.jpg 2x" data-file-width="3322" data-file-height="2215" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br /><a href="/wiki/Rotorcraft" title="Rotorcraft">rotorcraft</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Articles13" scope="row" class="navbox-group" style="width:1%">Articles</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autogyro" title="Autogyro">Autogyro</a> <ul><li><a href="/wiki/CarterCopter" title="CarterCopter">CarterCopter</a></li> <li><a href="/wiki/Juan_de_la_Cierva" title="Juan de la Cierva">Juan de la Cierva</a></li> <li><a href="/wiki/Skyworks_Global" class="mw-redirect" title="Skyworks Global">Skyworks Global</a></li> <li><a href="/wiki/Piasecki_Aircraft" title="Piasecki Aircraft">Piasecki Aircraft</a></li></ul></li> <li><a href="/wiki/Fairey_Rotodyne" title="Fairey Rotodyne">Fairey Rotodyne</a></li> <li><a href="/wiki/Gyrodyne" title="Gyrodyne">Gyrodyne</a></li> <li><a href="/wiki/Monocopter" title="Monocopter">Monocopter</a></li> <li><a href="/wiki/Rotor_kite" title="Rotor kite">Rotor kite</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_rotorcraft" title="List of rotorcraft">Rotorcraft</a> <ul><li><a href="/wiki/List_of_rotorcraft_manufacturers_by_country" title="List of rotorcraft manufacturers by country">Manufacturers by country</a></li> <li><a href="/wiki/List_of_most-produced_rotorcraft" title="List of most-produced rotorcraft">Most-produced</a></li> <li><a href="/wiki/List_of_rotorcraft_used_in_World_War_II" title="List of rotorcraft used in World War II">Used in World War II</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Hazards</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Helicopter_rotor#Limitations_and_hazards" title="Helicopter rotor">Mast bumping and other hazards</a></li> <li><a href="/wiki/Dynamic_rollover" title="Dynamic rollover">Dynamic rollover</a></li> <li><a href="/wiki/Ground_resonance" title="Ground resonance">Ground resonance</a></li> <li><a href="/wiki/Loss_of_tail-rotor_effectiveness" title="Loss of tail-rotor effectiveness">Loss of tail-rotor effectiveness</a></li> <li><a href="/wiki/Low-g_condition" title="Low-g condition">Low-g condition</a></li> <li><a href="/wiki/Retreating_blade_stall" title="Retreating blade stall">Retreating blade stall</a></li> <li><a href="/wiki/Dynamic_stall_on_helicopter_rotors" title="Dynamic stall on helicopter rotors">Dynamic stall</a></li> <li><a href="/wiki/Vortex_ring_state" title="Vortex ring state">Vortex ring state</a></li> <li><a href="/wiki/Servo_transparency" title="Servo transparency">Servo transparency</a></li> <li><a href="/wiki/Tailstrike#Helicopters" title="Tailstrike">Tailstrike</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bamboo-copter" title="Bamboo-copter">Bamboo-copter</a></li> <li><a href="/wiki/Cyclogyro" title="Cyclogyro">Cyclogyro</a></li> <li><a href="/wiki/Helicopter_height%E2%80%93velocity_diagram" title="Helicopter height–velocity diagram">Helicopter height–velocity diagram</a></li> <li><a href="/wiki/Helitack" title="Helitack">Helitack</a></li> <li><a href="/wiki/Human-powered_helicopter" title="Human-powered helicopter">Human-powered helicopter</a></li> <li><a href="/wiki/Ingenuity_(helicopter)" title="Ingenuity (helicopter)"><i>Ingenuity</i> Mars helicopter</a></li> <li><a href="/wiki/Mars_Sample_Retrieval_Helicopter" class="mw-redirect" title="Mars Sample Retrieval Helicopter">Mars Sample Retrieval Helicopters</a></li> <li><a href="/wiki/Jesus_nut" title="Jesus nut">Jesus nut</a></li> <li><a href="/wiki/List_of_aircraft" title="List of aircraft">List of aircraft</a></li> <li><a href="/wiki/Radio-controlled_helicopter" title="Radio-controlled helicopter">Radio-controlled helicopter</a></li> <li><a href="/wiki/Search_and_rescue" title="Search and rescue">Search and rescue</a></li> <li><a href="/wiki/Transverse_flow_effect" title="Transverse flow effect">Transverse flow effect</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3" style="font-weight:bold;"><div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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