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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Apparent wind</span></span>

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<p><b>Apparent wind</b> is the <a href="Wind" title="Wind">wind</a> experienced by a moving object.

</p>

<div class="mw-heading mw-heading2"><h2 id="Definition_of_apparent_wind">Definition of apparent wind</h2></div>

<p>The <i>apparent wind</i> is the wind experienced by an observer in motion and is the <a href="Relative_velocity" title="Relative velocity">relative velocity</a> of the wind in relation to the observer.

</p><p>The <i><a href="Velocity" title="Velocity">velocity</a> of the apparent wind</i> is the <a href="Vector_sum" class="mw-redirect" title="Vector sum">vector sum</a> of the <i>velocity of the headwind</i> (which is the velocity a moving object would experience in still air) plus the <i>velocity of the true wind</i>. The headwind is the <a href="Additive_inverse" title="Additive inverse">additive inverse</a> of the object's velocity; therefore, the <i>velocity of the apparent wind</i> can also be defined as a vector sum of the <i>velocity of the true wind</i> minus the <i>velocity of the object</i>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Apparent_wind_in_sailing">Apparent wind in sailing</h2></div>

<p>In <a href="Sailing" title="Sailing">sailing</a>, <i>apparent wind</i> is the speed and direction of wind indicated by a wind instrument (<a href="Anemometer" title="Anemometer">anemometer</a>) on a <i>moving</i> craft (on water, land or ice) in undisturbed air. It is composed of the <i>combined</i> speeds and directions of the craft and wind observed by a <i>stationary</i> wind instrument—the <i>true wind</i>. A true wind coming from the bow increases the apparent wind induced by the speed of the craft, coming from the stern it decreases apparent wind, and coming from the side the apparent wind angle and speed change according to the combined speed and direction of each the craft and the true wind. Apparent wind is important to sailors in order to set sail angle with respect to the wind and to anticipate how much power the wind will generate on a <a href="Point_of_sail" title="Point of sail">point of sail</a>. Apparent wind differs in speed and direction from the <b>true wind</b> that is experienced by a stationary observer and composed of the true wind speed (TWS) and true wind direction (TWD) or the TWS and true wind angle (TWA) relative to the boat if it were stationary.<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>

In <a href="Nautical_terminology" class="mw-redirect" title="Nautical terminology">nautical terminology</a>, apparent wind is measured in <a href="Knot_(unit)" title="Knot (unit)">knots</a> and <a href="Degree_(angle)" title="Degree (angle)">degrees</a>.

</p><p>Note that a number of additional factors come into play when converting the measurements from the masthead anemometer into the true wind if a high degree of accuracy is required, including the following:<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><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><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>

</p>

<ul><li><a href="Leeway" title="Leeway">Leeway</a> (or drift on power vessels) - Factors like water currents or slipping sideways due to wind (leeway) mean that the direction a craft is pointing often does not exactly match its actual direction of travel. This must be corrected for when converting apparent wind angle to true wind direction. The same effect is found when the craft is altering course.</li>

<li>Mast twist - the rigging loads often put a significant amount of torsion on the mast, especially if the rig has runners, so it is twisted along its length</li>

<li>Mast rotation - many racing <a href="Multihull" title="Multihull">multihulls</a> have a mast that can be rotated, so the anemometer reading needs to be corrected by the angle of rotation of the mast</li>

<li>Heel angle - this is a simple trigonometric correction</li>

<li>Upwash from the sails - the airflow around the top of the mast is distorted by the presence of the sails. This effect varies with the sails set at the time, the wind speed and the point of sail, but is noticed by the true wind angle changing from port to starboard tack, and the true wind speed changing from when beating to running</li>

<li>Boat motions - as the masthead is so distant from the centre of motion of the craft, inertial effect on both the wind vane and the anemometer cups can be significant when the craft is moving, especially when pitching and rolling</li>

<li>Wind shear - there can be a significant change in both wind speed and direction between the water's surface and the top of the mast, especially in conditions of unstable, light airs. The wind instruments are just measuring conditions at the masthead, and these are not necessarily the same at all heights</li></ul>

<p>In the presence of a current, the true wind is considered to be that measured on the craft drifting with the water over the bottom, and wind with respect to the sea bed as the <i>ground</i> or <i>geographical wind</i>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Instruments">Instruments</h2></div>

<p>The <b>apparent wind</b> on board (a boat) is often quoted as a speed measured by a <a href="Mast_(sailing)" title="Mast (sailing)">masthead</a> <a href="Transducer" title="Transducer">transducer</a> containing an <a href="Anemometer" title="Anemometer">anemometer</a> and <a href="Weather_vane" title="Weather vane">wind vane</a> that measures wind speed in <a href="Knot_(unit)" title="Knot (unit)">knots</a> and wind direction in degrees relative to the <a href="Course_(navigation)" title="Course (navigation)">heading</a> of the boat. Modern instrumentation can calculate the true wind velocity when the apparent wind and boat speed and direction are input.

</p>

<div class="mw-heading mw-heading2"><h2 id="Implications_on_sailing_speeds">Implications on sailing speeds</h2></div>

<p>In <a href="Sailboat_racing" class="mw-redirect" title="Sailboat racing">sailboat racing</a>, and especially in <a href="Speed_sailing" title="Speed sailing">speed sailing</a>, apparent wind is a vital factor, when determining the <a href="Points_of_sail" class="mw-redirect" title="Points of sail">points of sail</a> a sailboat can effectively travel in.

A vessel traveling at increasing speed relative to the <i>prevailing wind</i> will encounter the wind driving the sail at a decreasing angle and increasing velocity. Eventually, the increased drag and diminished degree of efficiency of a sail at extremely low <a href="Angle_of_attack" title="Angle of attack">angles</a> will cause a loss of accelerating force. This constitutes the main limitation to the speed of wind-driven vessels and vehicles.

</p><p><a href="Windsurfing" title="Windsurfing">Windsurfers</a> and certain types of boats are able to sail faster than the true wind. These include fast <a href="Multihull" title="Multihull">multihulls</a> and some <a href="Planing_(sailing)" class="mw-redirect" title="Planing (sailing)">planing</a> monohulls. <a href="Ice_yachting" class="mw-redirect" title="Ice yachting">Ice-sailors</a> and <a href="Land_sailing" title="Land sailing">land-sailors</a> also usually fall into this category, because of their relatively low amount of <a href="Drag_(physics)" title="Drag (physics)">drag</a> or <a href="Friction" title="Friction">friction</a>.

</p><p>The AC72 foiling catamarans used in the America's Cup are an example of this phenomenon, as the boats sail through the water at up to double the environmental wind speed. The effect of this is to radically change the apparent wind direction when sailing "downwind". In these boats the forward speed is so great that the apparent wind is always forward—at an angle that varies between 2 and 4 degrees to the wing sail. This means that AC72's are effectively tacking downwind, although at a greater angle than the normal 45-degree upwind angle, usually between 50 and 70 degrees.<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>

<div class="mw-heading mw-heading2"><h2 id="Other_areas_of_relevance">Other areas of relevance</h2></div>

<p>In <a href="Fixed-wing_aircraft" title="Fixed-wing aircraft">fixed-wing aircraft</a>, apparent wind is what is experienced on board, and it determines the necessary speeds for take-off and landing. <a href="Aircraft_carrier" title="Aircraft carrier">Aircraft carriers</a> generally steam directly upwind at maximum speed, in order to increase apparent wind and reduce the necessary take-off velocity. Land-based <a href="Airport" title="Airport">airport</a> traffic, as well as most mid-sized and large birds generally take off and land facing upwind for the same reason.

</p>

<div class="mw-heading mw-heading2"><h2 id="Calculating_apparent_velocity_and_angle">Calculating apparent velocity and angle</h2></div>

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<annotation encoding="application/x-tex">{\displaystyle A={\sqrt {W^{2}+V^{2}+2WV\cos {\alpha }}}}</annotation>

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</p><p>Where:

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<annotation encoding="application/x-tex">{\displaystyle V}</annotation>

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</math></span><img src="./af0f6064540e84211d0ffe4dac72098adfa52845.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" loading="lazy"></span> = velocity (boat speed over ground, always ≥ 0)</li>

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<annotation encoding="application/x-tex">{\displaystyle W}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>

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</math></span><img src="./b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" loading="lazy"></span> = true pointing angle in degrees (0 = upwind, 180 = downwind)</li>

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" 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}" loading="lazy"></span> = apparent wind velocity (always ≥ 0)</li></ul>

<p>The above formula is derived from the <a href="Law_of_cosines" title="Law of cosines">Law of cosines</a> and using <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 \cos(\alpha ')=\cos(180^{\circ }-\alpha )=-\cos(\alpha )}">

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<annotation encoding="application/x-tex">{\displaystyle \cos(\alpha ')=\cos(180^{\circ }-\alpha )=-\cos(\alpha )}</annotation>

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</math></span><img src="./34cd28917b93a127651de2165c7373ced1893493.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.683ex; height:3.009ex;" alt="{\displaystyle \cos(\alpha ')=\cos(180^{\circ }-\alpha )=-\cos(\alpha )}" loading="lazy"></span>.

</p><p>The angle of apparent wind (<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 \beta }">

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<annotation encoding="application/x-tex">{\displaystyle \arccos }</annotation>

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</math></span><img src="./b2f10121c1f582201ae32a56303e36bee4191336.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.218ex; height:1.676ex;" alt="{\displaystyle \arccos }" loading="lazy"></span>)

</p><p><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =\arccos \left({\frac {W\cos \alpha +V}{A}}\right)=\arccos \left({\frac {W\cos \alpha +V}{\sqrt {W^{2}+V^{2}+2WV\cos {\alpha }}}}\right)}">

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<annotation encoding="application/x-tex">{\displaystyle \beta =\arccos \left({\frac {W\cos \alpha +V}{A}}\right)=\arccos \left({\frac {W\cos \alpha +V}{\sqrt {W^{2}+V^{2}+2WV\cos {\alpha }}}}\right)}</annotation>

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</p><p>If the velocity of the boat and the velocity and the angle of the apparent wind are known, for instance from a <a class="mw-selflink-fragment" href="#Instruments">measurement</a>, the true wind velocity and direction can be calculated with:

</p><p><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W={\sqrt {A^{2}+V^{2}-2AV\cos {\beta }}}}">

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<annotation encoding="application/x-tex">{\displaystyle W={\sqrt {A^{2}+V^{2}-2AV\cos {\beta }}}}</annotation>

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</p><p>and

</p><p><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =\arccos \left({\frac {A\cos \beta -V}{W}}\right)=\arccos \left({\frac {A\cos \beta -V}{\sqrt {A^{2}+V^{2}-2AV\cos {\beta }}}}\right)}">

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<annotation encoding="application/x-tex">{\displaystyle \alpha =\arccos \left({\frac {A\cos \beta -V}{W}}\right)=\arccos \left({\frac {A\cos \beta -V}{\sqrt {A^{2}+V^{2}-2AV\cos {\beta }}}}\right)}</annotation>

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</p><p><i>Note:</i> Due to quadrant ambiguity, this equation for <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 \alpha }">

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<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>

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</math></span><img src="./b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" loading="lazy"></span> is only valid when the apparent winds are coming from the <a href="Starboard" class="mw-redirect" title="Starboard">starboard</a> direction (0° < <i>β</i> < 180°). For <a href="Port" title="Port">port</a> apparent winds (180° < <i>β</i> < 360° or 0° > <i>β</i> > -180°), the true pointing angle (<i>α</i>) has the opposite sign:

</p><p><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =-\arccos \left({\frac {A\cos \beta -V}{W}}\right)=-\arccos \left({\frac {A\cos \beta -V}{\sqrt {A^{2}+V^{2}-2AV\cos {\beta }}}}\right)}">

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<annotation encoding="application/x-tex">{\displaystyle \alpha =-\arccos \left({\frac {A\cos \beta -V}{W}}\right)=-\arccos \left({\frac {A\cos \beta -V}{\sqrt {A^{2}+V^{2}-2AV\cos {\beta }}}}\right)}</annotation>

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sailingworld.com/what-are-my-electronics-telling-me-about-boatspeed-and-heading">"What are My Electronics Telling Me About Boatspeed and Heading?"</a>. <i>Sailing World</i>. 21 May 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">22 October</span> 2017</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="CITEREFThornton" class="citation book cs1">Thornton, Tim. <i>The Offshore Yacht</i>. Adlard Coles.</cite></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFMarchaj" class="citation book cs1">Marchaj, C.A. <i>The AeroHydrodynamics of Sailing</i>. Adlard Coles.</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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.ockam.com/category/sailing-instruments-calibration/">"Sailing Instruments Calibration"</a>. <i>Ockam Instruments</i><span class="reference-accessdate">. Retrieved <span class="nowrap">10 June</span> 2015</span>.</cite></span>

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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">TVNZ Live America's cup Broadcast. Interview with Tom Schnackenburg. 22/9/2013</span>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external free" href="http://www.csgnetwork.com/twscorcalc.html">http://www.csgnetwork.com/twscorcalc.html</a></li>

<li><a rel="nofollow" class="external free" href="https://www.tecepe.com.br/nav/inav_c11.htm">https://www.tecepe.com.br/nav/inav_c11.htm</a>.</li></ul></div><div><div class="zim-footer">

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