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	<title>Comments on: Sailing into the wind, or faster than the wind</title>
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	<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/</link>
	<description>Updates on my research and expository papers, discussion of open problems, and other maths-related topics.  By Terence Tao</description>
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		<title>By: Sailing</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-142145</link>
		<dc:creator><![CDATA[Sailing]]></dc:creator>
		<pubDate>Tue, 08 May 2012 21:14:16 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-142145</guid>
		<description><![CDATA[Interesting view on how the wind works during Sailing, gonna pass this one through for the newbies!]]></description>
		<content:encoded><![CDATA[<p>Interesting view on how the wind works during Sailing, gonna pass this one through for the newbies!</p>
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		<title>By: Sail of the century &#124; Degree of Freedom</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-108501</link>
		<dc:creator><![CDATA[Sail of the century &#124; Degree of Freedom]]></dc:creator>
		<pubDate>Mon, 21 Nov 2011 15:49:07 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-108501</guid>
		<description><![CDATA[[...] vector addition it&#8217;s possible to attain higher speeds than the wind itself. (There&#8217;s a detailed discussion on Terence Tao&#8217;s [...]]]></description>
		<content:encoded><![CDATA[<p>[...] vector addition it&#8217;s possible to attain higher speeds than the wind itself. (There&#8217;s a detailed discussion on Terence Tao&#8217;s [...]</p>
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		<title>By: Intensive Therapy</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-86700</link>
		<dc:creator><![CDATA[Intensive Therapy]]></dc:creator>
		<pubDate>Thu, 29 Sep 2011 19:53:16 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-86700</guid>
		<description><![CDATA[In the case where the sail is a pure lifting body for which the force on the boat has direction perpendicular to the apparent wind and proportional magnitude, there will be a constant forward resulting force on the boat, because the water speed component of the apparent wind speed is projected to zero.]]></description>
		<content:encoded><![CDATA[<p>In the case where the sail is a pure lifting body for which the force on the boat has direction perpendicular to the apparent wind and proportional magnitude, there will be a constant forward resulting force on the boat, because the water speed component of the apparent wind speed is projected to zero.</p>
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		<title>By: Beating the Breeze &#124; Metaverse Sailing</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-48698</link>
		<dc:creator><![CDATA[Beating the Breeze &#124; Metaverse Sailing]]></dc:creator>
		<pubDate>Tue, 07 Dec 2010 06:15:24 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-48698</guid>
		<description><![CDATA[[...] just to highlight a year-old, nicely written blog post by Terrance Tao on the RL physics of &#8220;Sailing into the wind, or faster than the wind.&#8221; For a pretty inscrutable topic with a numbers-laden discussion, it&#8217;s impressive [...]]]></description>
		<content:encoded><![CDATA[<p>[...] just to highlight a year-old, nicely written blog post by Terrance Tao on the RL physics of &#8220;Sailing into the wind, or faster than the wind.&#8221; For a pretty inscrutable topic with a numbers-laden discussion, it&#8217;s impressive [...]</p>
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		<title>By: Marcin Kostur</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-48074</link>
		<dc:creator><![CDATA[Marcin Kostur]]></dc:creator>
		<pubDate>Tue, 09 Nov 2010 09:21:21 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-48074</guid>
		<description><![CDATA[I put some comments and matlab code simulating the mechanics of sailing:
http://goo.gl/TtEfM

DWFTTW can be explained too. 



Also: In the article you mention that:

&quot;It is reasonable (in light of results such as the Kutta-Joukowski theorem) to assume that the amount of lift provided by an aerofoil or hydrofoil is linearly proportional to the apparent wind speed or water speed&quot;

which is not precise as in the Kuttta formula there is circulation which depends on velocity too ;-), thus lift and drag can be approximated rather by v^2, see e.g. http://en.wikipedia.org/wiki/Lift_(force)]]></description>
		<content:encoded><![CDATA[<p>I put some comments and matlab code simulating the mechanics of sailing:<br />
<a href="http://goo.gl/TtEfM" rel="nofollow">http://goo.gl/TtEfM</a></p>
<p>DWFTTW can be explained too. </p>
<p>Also: In the article you mention that:</p>
<p>&#8220;It is reasonable (in light of results such as the Kutta-Joukowski theorem) to assume that the amount of lift provided by an aerofoil or hydrofoil is linearly proportional to the apparent wind speed or water speed&#8221;</p>
<p>which is not precise as in the Kuttta formula there is circulation which depends on velocity too ;-), thus lift and drag can be approximated rather by v^2, see e.g. <a href="http://en.wikipedia.org/wiki/Lift_(force)" rel="nofollow">http://en.wikipedia.org/wiki/Lift_(force)</a></p>
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		<title>By: andy ruina</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-44229</link>
		<dc:creator><![CDATA[andy ruina]]></dc:creator>
		<pubDate>Fri, 16 Apr 2010 03:36:20 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-44229</guid>
		<description><![CDATA[A few things:
  
1) I didn&#039;t see reference to Lanchester&#039;s course theorem. It seems relevant and is pretty.
    It relates the set of all achievable speeds and directions to the wind speed and
    the lift to drag ratios of the keel and sail.   The locus is mating circles each 
    with a cord cut off.

2) A nice paper about sailing theory in general terms, mentioning Lanchester&#039;s thm, is  this:

  V. Radhakrishnan: &quot;From square sails to wing sails: The physics of sailing craft.&quot;
  Current Science, Vol. 73, No. 6, 25 September 1997.   

  http://dspace.rri.res.in/bitstream/2289/1002/1/1997%20CS%20V73%20p503.pdf

3) I wrote a paper about sailing downwind faster than the wind (DWFTTW) in 1978.
    Actually my first paper.   Its still in revision for Am. J. Physics.  It has a few
    explanations of things that I think were there before other places. Its on my
    www page.  Its all tangled up in this parameter called &quot;a&quot;.  That&#039;s because I
    wrote it in reaction to a paper I didn&#039;t like that used that parameter.  Ignore that
    and just read the analogies and such like.  That paper
    is on my www site:

    http://ruina.tam.cornell.edu/research/topics/miscellaneous/index.php]]></description>
		<content:encoded><![CDATA[<p>A few things:</p>
<p>1) I didn&#8217;t see reference to Lanchester&#8217;s course theorem. It seems relevant and is pretty.<br />
    It relates the set of all achievable speeds and directions to the wind speed and<br />
    the lift to drag ratios of the keel and sail.   The locus is mating circles each<br />
    with a cord cut off.</p>
<p>2) A nice paper about sailing theory in general terms, mentioning Lanchester&#8217;s thm, is  this:</p>
<p>  V. Radhakrishnan: &#8220;From square sails to wing sails: The physics of sailing craft.&#8221;<br />
  Current Science, Vol. 73, No. 6, 25 September 1997.   </p>
<p>  <a href="http://dspace.rri.res.in/bitstream/2289/1002/1/1997%20CS%20V73%20p503.pdf" rel="nofollow">http://dspace.rri.res.in/bitstream/2289/1002/1/1997%20CS%20V73%20p503.pdf</a></p>
<p>3) I wrote a paper about sailing downwind faster than the wind (DWFTTW) in 1978.<br />
    Actually my first paper.   Its still in revision for Am. J. Physics.  It has a few<br />
    explanations of things that I think were there before other places. Its on my<br />
    www page.  Its all tangled up in this parameter called &#8220;a&#8221;.  That&#8217;s because I<br />
    wrote it in reaction to a paper I didn&#8217;t like that used that parameter.  Ignore that<br />
    and just read the analogies and such like.  That paper<br />
    is on my www site:</p>
<p>    <a href="http://ruina.tam.cornell.edu/research/topics/miscellaneous/index.php" rel="nofollow">http://ruina.tam.cornell.edu/research/topics/miscellaneous/index.php</a></p>
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		<title>By: seacliffsailor</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-44218</link>
		<dc:creator><![CDATA[seacliffsailor]]></dc:creator>
		<pubDate>Wed, 14 Apr 2010 17:30:27 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-44218</guid>
		<description><![CDATA[I just posted a video to youtube with a tinny &quot;sail boat&quot; that can sail directly into the wind - http://www.youtube.com/watch?v=ZlFIxmJwlcU. as far as i know, this has never been done before???]]></description>
		<content:encoded><![CDATA[<p>I just posted a video to youtube with a tinny &#8220;sail boat&#8221; that can sail directly into the wind &#8211; <a href="http://www.youtube.com/watch?v=ZlFIxmJwlcU" rel="nofollow">http://www.youtube.com/watch?v=ZlFIxmJwlcU</a>. as far as i know, this has never been done before???</p>
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		<title>By: themotorman</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-43474</link>
		<dc:creator><![CDATA[themotorman]]></dc:creator>
		<pubDate>Thu, 04 Feb 2010 05:54:38 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-43474</guid>
		<description><![CDATA[It seems that since a sail boat can move directly against the direction of the wind by &quot;tacking&quot; it should be possible to move directly against the wind by a high speed version of tacking where the tacking was made in very small increments. If the increments are made smaller and smaller to ultimately reach zero we should still be going against the wind ..Where&#039;s the problem  with this?
Also an airplane can fly with flat wings i.e no airfoil is needed.. check out model planes with flat wings to see how well they do.. it is simply that the momentum of air pushed down is high enough to provide &quot;lift&quot; This is true for planes with an airfoil wing , you still have to push air down for the plane to stay up. No free lunch even with airfoils!]]></description>
		<content:encoded><![CDATA[<p>It seems that since a sail boat can move directly against the direction of the wind by &#8220;tacking&#8221; it should be possible to move directly against the wind by a high speed version of tacking where the tacking was made in very small increments. If the increments are made smaller and smaller to ultimately reach zero we should still be going against the wind ..Where&#8217;s the problem  with this?<br />
Also an airplane can fly with flat wings i.e no airfoil is needed.. check out model planes with flat wings to see how well they do.. it is simply that the momentum of air pushed down is high enough to provide &#8220;lift&#8221; This is true for planes with an airfoil wing , you still have to push air down for the plane to stay up. No free lunch even with airfoils!</p>
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		<title>By: Jane @ marine supplies</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-43246</link>
		<dc:creator><![CDATA[Jane @ marine supplies]]></dc:creator>
		<pubDate>Fri, 15 Jan 2010 17:53:17 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-43246</guid>
		<description><![CDATA[I agree with you Tino&#039;s, had a similar misconception about the max speed. +rep Argon.]]></description>
		<content:encoded><![CDATA[<p>I agree with you Tino&#8217;s, had a similar misconception about the max speed. +rep Argon.</p>
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		<title>By: Tinos</title>
		<link>http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/#comment-43189</link>
		<dc:creator><![CDATA[Tinos]]></dc:creator>
		<pubDate>Sun, 10 Jan 2010 23:43:41 +0000</pubDate>
		<guid isPermaLink="false">http://terrytao.wordpress.com/?p=1165#comment-43189</guid>
		<description><![CDATA[Ah, unfortunately &lt;a href=&quot;http://en.wikipedia.org/wiki/Thin_airfoil_theory#Derivation_of_thin_airfoil_theory&quot; rel=&quot;nofollow&quot;&gt;thin aerofoil theory&lt;/a&gt; is a bit over my head at this point. I&#039;ll have to do some more maths courses (@ UQ). It seems that velocity fields are more convenient to work with than pressure fields, though.]]></description>
		<content:encoded><![CDATA[<p>Ah, unfortunately <a href="http://en.wikipedia.org/wiki/Thin_airfoil_theory#Derivation_of_thin_airfoil_theory" rel="nofollow">thin aerofoil theory</a> is a bit over my head at this point. I&#8217;ll have to do some more maths courses (@ UQ). It seems that velocity fields are more convenient to work with than pressure fields, though.</p>
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