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<channel>
	<title>SeanTerrill.com &#187; math</title>
	<atom:link href="http://seanterrill.com/tag/math/feed/" rel="self" type="application/rss+xml" />
	<link>http://seanterrill.com</link>
	<description>Look upon my blog, ye mighty, and despair.</description>
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			<item>
		<title>Steamboat Stagger</title>
		<link>http://seanterrill.com/2010/08/17/steamboat-stagger/</link>
		<comments>http://seanterrill.com/2010/08/17/steamboat-stagger/#comments</comments>
		<pubDate>Tue, 17 Aug 2010 16:07:26 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
				<category><![CDATA[Travel]]></category>
		<category><![CDATA[exercise]]></category>
		<category><![CDATA[family]]></category>
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		<guid isPermaLink="false">http://seanterrill.com/2010/08/17/steamboat-stagger/</guid>
		<description><![CDATA[<p>Yeah, well, let&#8217;s see how you do at 6800 ft.</p>
<p>Name:	 Steamboat
Date:	 Aug 17, 2010 9:08 am
Map:	View on Map
Distance:	 2.05 miles
Elapsed Time:	 19:24.8
Avg Speed:	 6.3 mph
Max Speed:	 7.4 mph
Avg Pace:	 09&#8242; 28&#8243; per mile
Min Altitude:	 6,698 ft
Max Altitude:	 6,798 ft</p>
<p></p>
]]></description>
			<content:encoded><![CDATA[<p>Yeah, well, let&#8217;s see how you do at 6800 ft.</p>
<blockquote><p><strong>Name</strong>:	 Steamboat<br />
<strong>Date</strong>:	 Aug 17, 2010 9:08 am<br />
<strong>Map</strong>:	<a href="http://maps.google.com/?t=p&#038;z=15&#038;ll=40.45880889892578,-106.81851196289062&#038;q=http://api.motionxlive.com/motionx-remote/api/gps/host/098e9bf5-f465-4c7a-9d14-592bf82fd67f" class="bodylink">View on Map</a><br />
<strong>Distance</strong>:	 2.05 miles<br />
<strong>Elapsed Time</strong>:	 19:24.8<br />
<strong>Avg Speed</strong>:	 6.3 mph<br />
<strong>Max Speed</strong>:	 7.4 mph<br />
<strong>Avg Pace</strong>:	 09&#8242; 28&#8243; per mile<br />
<strong>Min Altitude</strong>:	 6,698 ft<br />
<strong>Max Altitude</strong>:	 6,798 ft</p></blockquote>
<p><a href="http://seanterrill.com/wp-content/uploads/2010/08/Steamboat.jpg"><img src="http://seanterrill.com/wp-content/uploads/2010/08/Steamboat.jpg" alt="" title="Steamboat" width="480" height="640" class="alignnone size-full wp-image-1932" /></a></p>
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		<item>
		<title>Same Shift, Different Day</title>
		<link>http://seanterrill.com/2010/07/31/same-shift-different-day/</link>
		<comments>http://seanterrill.com/2010/07/31/same-shift-different-day/#comments</comments>
		<pubDate>Sat, 31 Jul 2010 23:06:01 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
				<category><![CDATA[Updates]]></category>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1917</guid>
		<description><![CDATA[<p>Well, I&#8217;m unemployed again. Today&#8217;s tips, in order, were:</p>

$1.11
$0.09
$0.11
$0.21
$0.00
$2.10
$0.01
$0.00
$0.00
$2.32
$3.21

<p>Not only did I not make minimum wage, I had a flat &#8211; technically, I lost money by going to work today.</p>
<p>The moral of the story is: tip your driver well. You never know how many other people you have to compensate for, to keep him from [...]]]></description>
			<content:encoded><![CDATA[<p>Well, I&#8217;m unemployed again. Today&#8217;s tips, in order, were:</p>
<ul>
<li>$1.11</li>
<li>$0.09</li>
<li>$0.11</li>
<li>$0.21</li>
<li>$0.00</li>
<li>$2.10</li>
<li>$0.01</li>
<li>$0.00</li>
<li>$0.00</li>
<li>$2.32</li>
<li>$3.21</li>
</ul>
<p>Not only did I not make minimum wage, I had a flat &#8211; technically, I <em>lost</em> money by going to work today.</p>
<p>The moral of the story is: tip your driver well. You never know how many other people you have to compensate for, to keep him from quitting.</p>
]]></content:encoded>
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		<title>Toward a Better Refractometer Correlation</title>
		<link>http://seanterrill.com/2010/07/20/toward-a-better-refractometer-correlation/</link>
		<comments>http://seanterrill.com/2010/07/20/toward-a-better-refractometer-correlation/#comments</comments>
		<pubDate>Tue, 20 Jul 2010 04:25:15 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
				<category><![CDATA[Brewing]]></category>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1895</guid>
		<description><![CDATA[<p>Last month I posted a brief summary of the troubles I was having with the de facto standard refractometer correlation for final gravity. Specifically, I found that it under-estimates FGs by, on average, about five &#8220;points&#8221;. More interesting, or at least more useful, I also found that the degree of the discrepancy is fairly well [...]]]></description>
			<content:encoded><![CDATA[<p>Last month I posted a <a href="http://seanterrill.com/2010/06/11/refractometer-estimates-of-final-gravity/" class="bodylink">brief summary</a> of the troubles I was having with the de facto standard refractometer correlation for final gravity. Specifically, I found that it under-estimates FGs by, on average, about five &#8220;points&#8221;. More interesting, or at least more useful, I also found that the degree of the discrepancy is fairly well correlated with the degree of fermentation of the beer. By applying a logarithmic curvefit to the data, I was able to reduce the mean deviation of my (admittedly limited) dataset from 5.1 to 0.1 points, and the standard deviation from 2.2 to 1.2 points. This is comparable to the precision of a consumer-grade hydrometer, and I was pretty satisfied with that, but it wasn&#8217;t a particularly elegant solution.</p>
<p>What was really needed was a real, independent three-dimensional surface fit. Fortunately, I found a truly excellent site that did the heavy lifting for me: <a href="http://zunzun.com/" class="bodylink">ZunZun.com</a>. This is one of those transformative &#8220;cloud apps&#8221; that journalists keep telling us are so revolutionary, and you really ought to check it out. Anyway, equipped with data from twelve FG readings and a little free time today, I decided to see if I could get a reasonable equation together. The data I&#8217;ve collected so far is, I think, pretty representative: OGs range from 1.036 to 1.106, FGs from 1.007 to 1.022, and ADFs from 73% to 91%. It turns out there is actually a <em>very</em> good (R<sup>2</sup> &cong; 0.98) fit, using a full cubic expansion:</p>
<p>FG = 1.0929176 &#8211; 0.0956887RI<sub>i</sub> + 0.160699RI<sub>f</sub> + 0.0103753RI<sub>i</sub>&sup2; &#8211; 0.00449931RI<sub>f</sub>&sup2; + 0.000585957RI<sub>i</sub>&sup3; &#8211; 0.00911434RI<sub>f</sub>&sup3; &#8211; 0.0165360RI<sub>i</sub>RI<sub>f</sub> &#8211; 0.00538394RI<sub>i</sub>&sup2;RI<sub>f</sub> + 0.0128988RI<sub>i</sub>RI<sub>f</sub>&sup2;</p>
<p>Where RI<sub>i</sub> and RI<sub>f</sub> are the initial and final refractive indices, respectively, in wort-corrected degrees Brix. The concern, of course, is that mapping 12 data points to 10 coefficients will result in substantial over-fitting. For the time being, I&#8217;m sticking with a simplified cubic form:</p>
<p>FG = 1.0111958 &#8211; 0.00813003RI<sub>i</sub> + 0.0144032RI<sub>f</sub> + 0.000523555RI<sub>i</sub>&sup2; &#8211; 0.00166862RI<sub>f</sub>&sup2; &#8211; 0.0000125754RI<sub>i</sub>&sup3; + 0.0000812663RI<sub>f</sub>&sup3;</p>
<p>The mean deviation is, essentially, zero (10<sup>-15</sup>), with a maximum of 2.1 points, and the standard deviation is reduced to 0.98 points &#8211; still not as good as a quality hydrometer, but quite possibly acceptable to most brewers. In fact, you can reduce the polynomial quite a bit and retain accuracy; I&#8217;m reporting the simplified cubic because it can be quickly inserted into existing software by changing the coefficients. A basic linear fit has an SD of 1.1 points, with a maximum deviation of 2.0, and the added advantage of being able to be (quickly) worked out on paper:</p>
<p>FG = 1.00358522 &#8211; 0.00123861*RI<sub>i</sub> + 0.00380186*RI<sub>f</sub></p>
<p>It&#8217;s worth noting that even this highly simplified equation is superior to the default correlation, although again, this is based on a set of only twelve points. Caveat calculator.</p>
<p><a href="http://seanterrill.com/wp-content/uploads/2010/08/correlations.png"><img src="http://seanterrill.com/wp-content/uploads/2010/08/correlations.png" alt="" title="correlations" width="600" height="400" class="alignnone size-full wp-image-1921" /></a></p>
<p>Finally, we come to what I thought was a pretty neat visualization of all this razzmatazz. I plotted the old-school (red), logarithmically corrected (yellow), new cubic fit (green), and simplified linear (blue) correlations against the expected FG values. A perfect fit would result in all the data points lying on the dotted line. As you can see, anything other than the stock correlation provides reasonably good results.</p>
<p>My FG/Attenuation/ABV spreadsheet has been updated to utilize the new correlation, and add the new visuals. If you find it useful and/or accurate, please drop me a line. I&#8217;d love to hear more brewers&#8217; experiences with using refractometers to estimate FGs.<br />
&nbsp;<br />
&nbsp;<br />
<strong>Update: 06 Aug 2010</strong></p>
<p>I made a minor adjustment to the spreadsheet, changing the default wort correction factor to 1.02, which is what my own refractometer data support. The current version is now 2.1.<br />
&nbsp;<br />
&nbsp;<br />
<strong>Spreadsheet download:<br />
<a href='http://seanterrill.com/wp-content/uploads/2010/07/fg_calculator_v2.1.ods' class="bodylink">fg_calculator_v2.1.ods</a> | <a href='http://seanterrill.com/wp-content/uploads/2010/07/fg_calculator_v2.1.xls' class="bodylink">fg_calculator_v2.1.xls</a></strong></p>
]]></content:encoded>
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		<title>Forty-Two</title>
		<link>http://seanterrill.com/2010/06/16/forty-two/</link>
		<comments>http://seanterrill.com/2010/06/16/forty-two/#comments</comments>
		<pubDate>Wed, 16 Jun 2010 19:07:40 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
				<category><![CDATA[Brewing]]></category>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1850</guid>
		<description><![CDATA[<p>That&#8217;s how many batches I&#8217;ve brewed (since I started keeping notes). A question about preferred OG ranges came up in an NB forum topic, and I couldn&#8217;t decide if I liked 1.050-1.059, or 1.060-1.069. Turns out the answer is a little of both: the mean is 1.065 (with a standard deviation of 0.029 &#8211; outliers [...]]]></description>
			<content:encoded><![CDATA[<p>That&#8217;s how many batches I&#8217;ve brewed (since I started keeping notes). A question about preferred OG ranges came up in an <a href="http://forum.northernbrewer.com/viewtopic.php?f=4&#038;t=90098" class="bodylink">NB forum topic</a>, and I couldn&#8217;t decide if I liked 1.050-1.059, or 1.060-1.069. Turns out the answer is a little of both: the mean is 1.065 (with a standard deviation of 0.029 &#8211; outliers ftw), but 43% of the OGs fall in the 1.050-1.059 range.</p>
<p><a href="http://seanterrill.com/wp-content/uploads/2010/06/histogram.png"><img src="http://seanterrill.com/wp-content/uploads/2010/06/histogram.png" alt="" title="histogram" width="640" height="400" class="size-full wp-image-1852" /></a>&nbsp;</p>
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		<title>Ten Deliveries</title>
		<link>http://seanterrill.com/2010/06/14/ten-deliveries/</link>
		<comments>http://seanterrill.com/2010/06/14/ten-deliveries/#comments</comments>
		<pubDate>Mon, 14 Jun 2010 04:24:12 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
				<category><![CDATA[Updates]]></category>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1842</guid>
		<description><![CDATA[<p>What&#8217;s the point of having GPS on your iPhone if you aren&#8217;t going to geek out about stuff?</p>
<p>Name:&#160;&#160;&#160;&#160;13 June 2010
Date:&#160;&#160;&#160;&#160;Jun 13, 2010 6:17 pm
Map:&#160;&#160;&#160;&#160;Google Maps
Distance:&#160;&#160;&#160;&#160;48.3 miles
Elapsed Time:&#160;&#160;&#160;&#160;1:50:30
Avg Speed:&#160;&#160;&#160;&#160;26.2 mph
Max Speed:&#160;&#160;&#160;&#160;55.1 mph
Avg Pace:&#160;&#160;&#160;&#160;02&#8242; 17&#8243; per mile
Min Altitude:&#160;&#160;&#160;&#160;656 ft
Max Altitude:&#160;&#160;&#160;&#160;819 ft
Start Time:&#160;&#160;&#160;&#160;2010-06-13T22:17:01Z</p>
<p>View Larger Map
&#160;</p>
]]></description>
			<content:encoded><![CDATA[<p>What&#8217;s the point of having <a href="http://gps.motionx.com/iphone/overview/" class="bodylink">GPS</a> on your iPhone if you aren&#8217;t going to geek out about stuff?</p>
<blockquote><p><strong>Name:</strong>&nbsp;&nbsp;&nbsp;&nbsp;13 June 2010<br />
<strong>Date:</strong>&nbsp;&nbsp;&nbsp;&nbsp;Jun 13, 2010 6:17 pm<br />
<strong>Map:</strong>&nbsp;&nbsp;&nbsp;&nbsp;<a href="http://maps.google.com/?t=p&#038;z=15&#038;ll=39.86140823364258,-85.97515869140625&#038;q=http://api.motionxlive.com/motionx-remote/api/gps/host/bd30ade9-5e74-4717-a549-bbcdbb30ea9d" class="bodylink">Google Maps</a><br />
<strong>Distance:</strong>&nbsp;&nbsp;&nbsp;&nbsp;48.3 miles<br />
<strong>Elapsed Time:</strong>&nbsp;&nbsp;&nbsp;&nbsp;1:50:30<br />
<strong>Avg Speed:</strong>&nbsp;&nbsp;&nbsp;&nbsp;26.2 mph<br />
<strong>Max Speed:</strong>&nbsp;&nbsp;&nbsp;&nbsp;55.1 mph<br />
<strong>Avg Pace:</strong>&nbsp;&nbsp;&nbsp;&nbsp;02&#8242; 17&#8243; per mile<br />
<strong>Min Altitude:</strong>&nbsp;&nbsp;&nbsp;&nbsp;656 ft<br />
<strong>Max Altitude:</strong>&nbsp;&nbsp;&nbsp;&nbsp;819 ft<br />
<strong>Start Time:</strong>&nbsp;&nbsp;&nbsp;&nbsp;2010-06-13T22:17:01Z</p></blockquote>
<p><iframe width="640" height="480" frameborder="0" scrolling="no" marginheight="0" marginwidth="0" src="http://maps.google.com/?q=http:%2F%2Fapi.motionxlive.com%2Fmotionx-remote%2Fapi%2Fgps%2Fhost%2Fbd30ade9-5e74-4717-a549-bbcdbb30ea9d&amp;ie=UTF8&amp;ll=39.861263,-85.974884&amp;spn=0.063248,0.109863&amp;t=h&amp;z=13&amp;output=embed"></iframe><br /><small><a href="http://maps.google.com/?q=http:%2F%2Fapi.motionxlive.com%2Fmotionx-remote%2Fapi%2Fgps%2Fhost%2Fbd30ade9-5e74-4717-a549-bbcdbb30ea9d&amp;ie=UTF8&amp;ll=39.861263,-85.974884&amp;spn=0.063248,0.109863&amp;t=h&amp;z=13&amp;source=embed" style="color:#0000FF;text-align:left">View Larger Map</a></small><br />
&nbsp;</p>
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		<title>Refractometer Estimates of Final Gravity</title>
		<link>http://seanterrill.com/2010/06/11/refractometer-estimates-of-final-gravity/</link>
		<comments>http://seanterrill.com/2010/06/11/refractometer-estimates-of-final-gravity/#comments</comments>
		<pubDate>Sat, 12 Jun 2010 01:05:27 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
				<category><![CDATA[Brewing]]></category>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1828</guid>
		<description><![CDATA[<p>A refractometer is one of the most useful tools a brewer can have. It allows for near-instantaneous measurements of specific gravity, without having to compensate for or adjust sample temperature or withdraw a large volume of wort/beer (a significant concern at homebrew scales). There are a few issues associated with accurately using a refractometer for [...]]]></description>
			<content:encoded><![CDATA[<p>A refractometer is one of the most useful tools a brewer can have. It allows for near-instantaneous measurements of specific gravity, without having to compensate for or adjust sample temperature or withdraw a large volume of wort/beer (a significant concern at homebrew scales). There are a few issues associated with accurately using a refractometer for brewing, though. First, a refractometer does not actually measure specific gravity, or sugar content. Instead it simply projects a line through a reticle, and relies on the fact that the <a href="http://en.wikipedia.org/wiki/Refractive_index" class="bodylink">refractive index</a> of the fluid will move a line up and down the reticle. For a simple sucrose solution (the refractometers common to homebrewers are &#8220;borrowed&#8221; from the wine industry) the refractive index depends only on the sugar content and the temperature. Automatic temperature correcting (ATC) refractometers use a bimetal strip to cancel out the temperature variable (within a given range), meaning that the reticle can be marked directly in units of sugar content. Brewers&#8217; wort, however, is not a sucrose solution, and so a &#8220;wort correction factor&#8221; must be applied. Generally this is done by dividing the refractometer reading by 1.04.</p>
<p>The second, more intractable problem with using a refractometer to determine specific gravity is that once fermentation begins, the beer becomes a three-part solution: sugars, water, and alcohol. There is no longer fidelity of measurement &#8211; that is to say, there can be more than one specific gravity that will correlate to the same refractive index. Generally speaking, however, only one of the potential data points will be sensible for a real beer. Making that assumption, it should be possible to develop a correlation between the measured refractive index and the actual gravity of the beer, as long as the alcohol content can be estimated. This means that if both pre- and post-fermentation readings are taken, the FG can be predicted. Various software packages and websites incorporate tools to do just that, all of which seem to use the same correlation:</p>
<p>FG = 1.001843 &#8211; 0.002318474*RI<sub>i</sub> &#8211; 0.000007775*RI<sub>i</sub>&sup2; &#8211; 0.000000034*RI<sub>i</sub>&sup3; + 0.00574*RI<sub>f</sub> + 0.00003344*RI<sub>f</sub>&sup2; + 0.000000086*RI<sub>f</sub>&sup3;</p>
<p>Where RI<sub>i</sub> and RI<sub>f</sub> are the initial and final refractive indices, respectively, in wort-corrected degrees Brix.</p>
<p>I took pre- and post-fermentation readings of ten beers, with OGs ranging from 1.036 to 1.103, using both a refractometer and hydrometer. In every case the refractometer correlation provided an FG that was lower than the hydrometer reading, by anywhere from 0.5 to 8.5 &#8220;gravity points&#8221; (1000*(SG-1)). The mean discrepancy is 5.1 points. The main variable of concern seems to be the attenuation of the beer; the greater the attenuation, the larger the discrepancy. The results are plotted below.</p>
<p><img src="http://seanterrill.com/wp-content/uploads/2010/06/fg_discrepancies.png" alt="" title="fg_discrepancies" width="500" height="400" class="alignnone size-full wp-image-1836" /></p>
<p>Note that the discrepancy is zero at about 58% attenuation (71% apparent attenuation). I have no information on who originally developed the correlation, but my supposition is that they only tested worts with about this degree of fermentability. A logarithmic curvefit provides a reasonably good (R&sup2; &cong; 0.7) approximation for the offset that is needed; by adding this correction factor to the standard correlation, the maximum discrepancy for this dataset is reduced to only 2.1 points, and the average to 0.1 points. Unfortunately, the resulting equation is a bit unwieldy:</p>
<p>FG = (1.001843 &#8211; 0.002318474*RI<sub>i</sub> &#8211; 0.000007775*RI<sub>i</sub>&sup2; &#8211; 0.000000034*RI<sub>i</sub>&sup3; + 0.00574*RI<sub>f</sub> + 0.00003344*RI<sub>f</sub>&sup2; + 0.000000086*RI<sub>f</sub>&sup3;) + 0.0216*LN(1 &#8211; (0.1808*(668.72*(1.000898 + 0.003859118*RI<sub>i</sub> + 0.00001370735*RI<sub>i</sub>&sup2; + 0.00000003742517*RI<sub>i</sub>&sup3;) &#8211; 463.37 &#8211; 205.347*(1.000898 + 0.003859118*RI<sub>i</sub> + 0.00001370735*RI<sub>i</sub>&sup2; + 0.00000003742517*RI<sub>i</sub>&sup3;)&sup2;) + 0.8192*(668.72*(1.001843 &#8211; 0.002318474*RI<sub>i</sub> &#8211; 0.000007775*RI<sub>i</sub>&sup2; &#8211; 0.000000034*RI<sub>i</sub>&sup3; + 0.00574*RI<sub>f</sub> + 0.00003344*RI<sub>f</sub>&sup2; + 0.000000086*RI<sub>f</sub>&sup3;) &#8211; 463.37 &#8211; 205.347*(1.001843 &#8211; 0.002318474*RI<sub>i</sub> &#8211; 0.000007775*RI<sub>i</sub>&sup2; &#8211; 0.000000034*RI<sub>i</sub>&sup3; + 0.00574*RI<sub>f</sub> + 0.00003344*RI<sub>f</sub>&sup2; + 0.000000086*RI<sub>f</sub>&sup3;)&sup2;))/(668.72*(1.000898 + 0.003859118*RI<sub>i</sub> + 0.00001370735*RI<sub>i</sub>&sup2; + 0.00000003742517*RI<sub>i</sub>&sup3;) &#8211; 463.37 &#8211; 205.347*(1.000898 + 0.003859118*RI<sub>i</sub> + 0.00001370735*RI<sub>i</sub>&sup2; + 0.00000003742517*RI<sub>i</sub>&sup3;)&sup2;)) + 0.0116</p>
<p>In order to spare anyone who might be interested some trouble, I&#8217;ve put together a simple spreadsheet that will calculate FG using both the old and new correlations, in addition to attenuation and ABV. If you end up using it for a significant number of batches, please share your results.<br />
&nbsp;<br />
&nbsp;<br />
<strong>Update: 20 July 2010</strong></p>
<p>I&#8217;ve since refined the FG correlation, using a more mathematically rigorous method. I leave the original post up for transparency&#8217;s sake, but if you&#8217;re looking for an FG calculator, please check out the <a href="http://seanterrill.com/2010/07/20/toward-a-better-refractometer-correlation/" class="bodylink">new post</a>.<br />
&nbsp;<br />
&nbsp;<br />
<strong>Spreadsheet download:<br />
<a href='http://seanterrill.com/wp-content/uploads/2010/06/fg_calculator.ods' class="bodylink">fg_calculator.ods</a> | <a href='http://seanterrill.com/wp-content/uploads/2010/06/fg_calculator.xls' class="bodylink">fg_calculator.xls</a></strong></p>
]]></content:encoded>
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		<title>Thermometer Calibration</title>
		<link>http://seanterrill.com/2010/05/24/thermometer-calibration/</link>
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		<pubDate>Mon, 24 May 2010 20:22:41 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1819</guid>
		<description><![CDATA[<p>It&#8217;s spring cleaning time in the brewery. I&#8217;ve given the kegerator a good once-over, scrubbed the kettles shiny, replaced all the vinyl tubing, and so now it must be time for instrument calibrations. I check the hydrometer and refractometer every few batches because it&#8217;s so easy (use water and a 10% sucrose solution), but it [...]]]></description>
			<content:encoded><![CDATA[<p>It&#8217;s spring cleaning time in the brewery. I&#8217;ve given the kegerator a good once-over, scrubbed the kettles shiny, replaced all the vinyl tubing, and so now it must be time for instrument calibrations. I check the hydrometer and refractometer every few batches because it&#8217;s so easy (use water and a 10% sucrose solution), but it occurred to me that I&#8217;ve <strong>never</strong> checked my thermometers. There are seven types that get regular use in my brewery:</p>
<ul>
<li>My newest toy &#8211; a <a href="http://www.arborsci.com/prod-Digital_Thermometer-61.aspx" class="bodylink">NIST-traceable waterproof digital probe model</a></li>
<li>A TruTemp-branded compact digital that set me back about $9</li>
<li>An AcuRite-branded digital &#8220;meat&#8221; thermometer</li>
<li>A no-brand kitchen probe thermometer from Walmart</li>
<li>An ordinary <a href="http://www.greatfermentations.com/Thermometer-floating/productinfo/5424/" class="bodylink">floating alcohol thermometer</a></li>
<li>Several <a href="http://www.northernbrewer.com/brewing/brewing-equipment/testing-measuring/thermometers/fermometer.html" class="bodylink">LCD strip thermometers</a></li>
<li>The bulkhead thermometer in my boil kettle</li>
</ul>
<p>Since the kettle thermometer requires about three gallons, and the strips five gallons, of liquid in order to be submerged, it didn&#8217;t really seem practical to check them against the others. All the others read to 0.1&deg;C, except for the AcuRite (1&deg;C) and the Walmart thermometer, which only does Fahrenheit and which I <em>know</em> not to be accurate anyway.</p>
<p>The other five thermometers were checked at four temperatures: 0.0&deg;C (ice water), ~23&deg;C (room temperature), ~59&deg;C (mixture of ice-cold and boiling water), and 99.2&deg;C (boiling water). That gives me, roughly speaking, fermentation and mash temperature calibrations for each, plus a couple of outliers for pretty curve fits. For the two middle values, the traceable thermometer&#8217;s readings were assumed to be correct, which given the readings at freezing and boiling seems justifiable.</p>
<p>Generally speaking, all the thermometers did well. Throwing out the no-name Walmart model and the surprisingly inaccurate alcohol thermometer, the maximum variation was 1.3&deg;C, which isn&#8217;t great for lab equipment but is probably fine for brewing. Surprisingly, the AcuRite kitchen thermometer is every bit as accurate as the ISO 17025-calibrated lab thermometer, landing all four readings within its (admittedly larger) resolution. The TruTemp model turned out to be less accurate, albeit with a highly linear discrepancy. This is interesting because it could point to a design problem &#8211; assuming a linear voltage response for the thermocouple rather than doing a multi-point calibration. More to the point, it means that it can still be useful for brewing once the proper offset is applied.</p>
<p><a href="http://seanterrill.com/wp-content/uploads/2010/05/thermo_cal.png"><img src="http://seanterrill.com/wp-content/uploads/2010/05/thermo_cal.png" alt="thermo_cal" title="thermo_cal" width="675" height="575" class="alignnone size-full wp-image-1820" /></a>&nbsp;</p>
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		<title>One Year Later</title>
		<link>http://seanterrill.com/2010/05/15/one-year-later/</link>
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		<pubDate>Sat, 15 May 2010 15:50:14 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1800</guid>
		<description><![CDATA[<p>One year ago today, I decided I didn&#8217;t really want to be fat anymore, and was going to lose 35 pounds in the next year. I didn&#8217;t quite make it, but I can say that I&#8217;m probably in better shape now than at any time since that last high school water polo game. I seriously [...]]]></description>
			<content:encoded><![CDATA[<p>One year ago today, I decided I didn&#8217;t really want to be fat anymore, and was going to lose 35 pounds in the next year. I didn&#8217;t <em>quite</em> make it, but I can say that I&#8217;m probably in better shape now than at any time since that last high school water polo game. I seriously recommend that anyone with similar goals move within walking distance of a gym.</p>
<p><div class="wp-caption alignnone" style="width: 460px"><img alt="Note the precipitous change in slope once it got warm enough to run outside." src="http://caloriecount.about.com/images/dynamic/weight-large/2/24/245/range_197536.png?count=1273935758" title="range_197536" width="450" height="400" /><p class="wp-caption-text">Note the precipitous change in slope once it got warm enough to run outside.</p></div>&nbsp;</p>
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		<title>Yeast Pitching Rate Results</title>
		<link>http://seanterrill.com/2010/05/09/yeast-pitching-rate-results/</link>
		<comments>http://seanterrill.com/2010/05/09/yeast-pitching-rate-results/#comments</comments>
		<pubDate>Sun, 09 May 2010 19:34:31 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1739</guid>
		<description><![CDATA[<p>Background</p>
<p>The ale yeast pitching rate generally recommended by commercial brewers is one billion cells, per liter of wort, per degree Plato. Assuming a 25% loss in viability prior to re-pitching results in the rule of thumb of 0.75 billion/L-°P. Since yeast products designed to inoculate at this level are not available on the homebrew scale, [...]]]></description>
			<content:encoded><![CDATA[<p><strong>Background</strong></p>
<p>The ale yeast pitching rate generally recommended by commercial brewers is one billion cells, per liter of wort, per degree Plato. Assuming a 25% loss in viability prior to re-pitching results in the rule of thumb of 0.75 billion/L-°P. Since yeast products designed to inoculate at this level are not available on the homebrew scale, many home brewers will make a  Directly pitching a vial or pack of commercial yeast without a starter results in about half of the recommended pitching rate. The effects of under-pitching are varied, but generally held to be undesirable. Wyeast Laboratories, for example, <a href="http://www.wyeastlab.com/com-pitch-rates.cfm" class="bodylink">states</a> that under-pitching can cause &#8220;excess levels of diacetyl, [an] increase in higher/fusel alcohol formation, [an] increase in ester formation, [an] increase in volatile sulfur compounds, high terminal gravities, stuck fermentations, [and an] increased risk of infection&#8221;.</p>
<p>Among home brewers, however, the effects of under-pitching are less universally agreed upon, with some brewers maintaining that under-pitching has no impact, or at least no negative impact, on the final product. Many others pitch multiple yeast products, or make <a href="http://www.mrmalty.com/starter_faq.htm" class="bodylink">starters</a> prior to brewing, in the belief that it will result in better beer. To test these assertions, a controlled experiment needed to be conducted.</p>
<p><strong>Experimental Setup</strong></p>
<p>In order to provide a reasonable baseline for comparison, I brewed six gallons of an <a href="http://www.bjcp.org/2008styles/style10.php#1b" class="bodylink">American Amber Ale</a>, targeting a BU:GU ratio of about 0.5. The idea was to come up with a middle-of-the-road representation of a style that would be accessible to most craft beer drinkers. After chilling, the wort was split into two plastic bucket fermenters, with one pitched at 0.73 billion cells/L-&deg;P (&#8220;control&#8221;), and the other at 0.29 B/L-&deg;P (&#8220;under-pitched&#8221;), which is roughly the pitching rate that would result from using a month-old smack pack in a five gallon batch. Since the cell counts used to calculate the pitching rates are based on slurry volume rather a true count, the associated error is high &#8211; I would suggest &plusmn;10%. More complete information on the beer brewed and the yeast propagation procedures can be found in the <a href="http://seanterrill.com/2010/02/18/yeast-pitching-rate-experiment/" class="bodylink">experiment proposal</a> and <a href="http://seanterrill.com/2010/03/23/yeast-ranching-and-you/" class="bodylink">yeast ranching</a> posts, respectively.</p>
<p>Seventeen sample sets of three bottles each were distributed to home brewers from Oregon to Florida. One (presumably) broke in transit and was not delivered, and there was one non-respondent. The 15 effective sets resulted in feedback from 37 individual tasters. Twenty-three received &#8220;Set 1&#8243;, which contained two controls and one under-pitched sample, with the remaining fourteen having &#8220;Set 2&#8243;, with two under-pitched beers and one control. All sets were labeled only as &#8220;A&#8221;, &#8220;B&#8221;, and &#8220;C&#8221;, resulting in a <a href="http://www.astm.org/Standards/E1885.htm" class="bodylink">blind triangle test</a>. Aside from being recruited via a <a href="http://forum.northernbrewer.com/viewtopic.php?f=1&#038;t=85604" class="bodylink">topic</a> on a brewing forum, no effort was made to establish the participants&#8217; credentials with regard to brewing or judging beer. I&#8217;d like to think they can therefore be considered a representative sample of the (online) home brewing community.</p>
<p>The chief difficulty associated with collecting impressions from such a widely divergent group of respondents is converting them into unambiguous numerical data. My first thought was to have each taster complete a standard <a href="http://www.bjcp.org/docs/SCP_BeerScoreSheet.pdf" class="bodylink">BJCP Scoresheet</a>, but there were several obvious problems with that method. First, filling out the scoresheet can be a daunting, time-consuming task, especially considering that most respondents were not BJCP judges and would probably be completing it for the first time. Second, since by design it addresses only a single beer, a minimum of three sheets per &#8220;judge&#8221; would be required. Finally, since it lacks room for additional, comparative questions, at least one additional sheet, for a total of four, would be required. In order to minimize the amount of paper and the time commitment required, I laid out a simple <a href="http://seanterrill.com/wp-content/uploads/2010/02/Sensory-Evaluation-Form.pdf" class="bodylink">feedback form</a>, loosely based on the BJCP scoresheet, which was distributed to all participants.</p>
<p>In order to obtain objective, internally consistent data, two different methods were used. First, the volunteers were asked to perform two simple, quantifiable tasks: identify the control and under-pitched beers; and express a preference for one or the other. In addition to providing these definitive, binary answers, each respondent was also able to share more detailed impressions about appearance, aroma, flavor, and mouthfeel. The descriptive adjectives used were then compiled by means of a simple frequency count. In order to simplify the dataset as much as possible, some descriptors were combined &#8211; first, variations on the same root word (&#8220;malt&#8221; and &#8220;malty&#8221;, e.g.), then words with substantially similar meanings (&#8220;hot&#8221; and &#8220;solventy&#8221;, e.g.).</p>
<p><strong>Personal Observations</strong></p>
<p><a href="http://seanterrill.com/wp-content/uploads/2010/05/IMG_2318.JPG"><img src="http://seanterrill.com/wp-content/uploads/2010/05/IMG_2318-384x288.jpg" alt="IMG_2318" title="IMG_2318" width="384" height="288" class="alignright size-medium wp-image-1741" /></a><a href="http://seanterrill.com/wp-content/uploads/2010/05/IMG_2316.JPG"><img src="http://seanterrill.com/wp-content/uploads/2010/05/IMG_2316-384x288.jpg" alt="IMG_2316" title="IMG_2316" width="384" height="288" class="alignright size-medium wp-image-1740" /></a>My personal tasting notes for the two beers should be taken with a grain of salt, since they don&#8217;t represent a blind tasting, but the photographs are so dramatic that I thought they should be included. The photos show, left and right, the under-pitched and control beers. The first photo was taken two minutes after the beers were poured; the second after they had been drunk over the course of about 35 minutes.</p>
<p>The under-pitched beer is slightly lighter in color (10.5-11 SRM instead of 12), and has minimal head retention or lacing when compared to the control beer. The aroma is malty with a slight hot alcohol character, whereas the control has a perfumy, floral hop aroma, with the malt more subdued. The under-pitched beer has a vaguely spicy or vegetal off-flavor, particularly in the aftertaste, and a slightly solventy finish. The control also has a peppery or spicy taste (which I would attribute to the use of Munich malt), but a lingering citrus flavor predominates. The mouthfeel of the under-pitched beer is thin and astringent compared to relative fullness of the control, although it&#8217;s difficult to make a fair comparison due to the difference in head retention. The control may have a very slightly more compact, &#8220;stickier&#8221; yeast sediment.</p>
<p><strong>Results</strong></p>
<p>As a means of gauging fermentation performance, a refractometer reading was taken every twenty-four hours after pitching. The difference in the time required to start and finish fermentation is striking.</p>
<p>The control beer not only exhibited faster fermentation to begin with, but reached terminal gravity approximately twice as fast as the under-pitched fermenter. This provides a clear rationale for the use of higher pitching rates in commercial breweries, where fermenter time is extremely valuable. It could also point to a potential advantage for the higher pitching rate in allowing the yeast to out-compete any contaminating microbes.</p>
<p><a href="http://seanterrill.com/wp-content/uploads/2010/05/fermentation_progress.png"><img src="http://seanterrill.com/wp-content/uploads/2010/05/fermentation_progress.png" alt="The gravity of the two beers over time, as indicated by (uncorrected) refractometer readings." title="fermentation_progress" width="470" height="330" class="size-full wp-image-1748" /></a></p>
<p>Of the 30 tasters who attempted to differentiate the beers, thirteen were able to do so, with nine tasters correctly identifying the beers. This seems to support a hypothesis that there is a difference between the beers &#8211; if the three samples were truly indistinguishable, ten respondents could be expected to differentiate the beers, and five identify them.</p>
<p>Since the results follow a <a href="http://en.wikipedia.org/wiki/Binomial_distribution" class="bodylink">binomial distribution</a> (a given sample is either identified or not, with no middle ground), the probability that these results are purely due to chance can be assessed. Given a random distribution, 13 of 30 respondents (or more) would be expected to differentiate the samples about 16.6% of the time. Based on these results, one can conclude, with 83% confidence, that the two beers do in fact taste different.</p>
<p>But what, specifically, are the differences between the beers? In addition to the more subjective descriptors I&#8217;ll get to in a bit, we can make a reasonable inference from the 13 tasters who correctly differentiated the samples. If the beers tasted different, but those differences revealed nothing about their identities, we would expect half of the 13 to guess correctly; in fact, the probability that nine or more would guess correctly is only 13.3%. This leads me to believe that at least some of the flavors generally associated with under-pitching &#8211; increased esters, fusel alcohols, diacetyl, acetaldehyde, etc. &#8211; are in fact present.</p>
<p>Twenty-four of the participants expressed a preference for one beer over the others, with the control being preferred sixteen to eight. When weighted appropriately for the number of samples, the control beer was preferred by 54.9% of tasters. Interestingly enough, this would seem to suggest that while the beers almost certainly are different, there is no consensus about which is <em>better</em>. Simply put, nearly half of people prefer under-pitched beers. An argument could be made, though, that only the opinions of the participants who actually differentiated the samples should be considered. And the data would seem to bear that out. Five of the differentiating tasters preferred the under-pitched beer; however, fully eight of the thirteen tasted Set 2, and when weighted accordingly they overwhelmingly prefer the control, 65.8% to 34.2%.</p>
<p>It is also worth noting that the first half of the respondents (those who tasted the beers after four weeks in the bottle or less) also preferred the control about two to one. So it&#8217;s entirely possible that additional conditioning time can reduce the off-flavors that result from under-pitching, but another controlled experiment, with the date of the tasting as a variable, would be needed to satisfactorily answer that question.</p>
<p><a href="http://seanterrill.com/wp-content/uploads/2010/05/descriptors1.png"><img src="http://seanterrill.com/wp-content/uploads/2010/05/descriptors1.png" alt="descriptors" title="descriptors" width="615" height="365" class="alignnone size-full wp-image-1779" /></a></p>
<p>Finally, we come to the subjective tasting results. I think the above image largely speaks for itself, so I won&#8217;t elaborate too much further. The ten most common descriptors for the control beer are:</p>
<p>&nbsp;&nbsp;&nbsp;&nbsp;1: Malty<br />
&nbsp;&nbsp;&nbsp;&nbsp;2: Hoppy<br />
&nbsp;&nbsp;&nbsp;&nbsp;3: Bitter<br />
&nbsp;&nbsp;&nbsp;&nbsp;4: Fruity<br />
&nbsp;&nbsp;&nbsp;&nbsp;4: Sweet<br />
&nbsp;&nbsp;&nbsp;&nbsp;6: Estery<br />
&nbsp;&nbsp;&nbsp;&nbsp;6: Smooth<br />
&nbsp;&nbsp;&nbsp;&nbsp;8: Thin<br />
&nbsp;&nbsp;&nbsp;&nbsp;9: Solventy<br />
&nbsp;&nbsp;&nbsp;&nbsp;9: Clean<br />
&nbsp;&nbsp;&nbsp;&nbsp;9: Dry<br />
&nbsp;&nbsp;&nbsp;&nbsp;9: Cidery</p>
<p>For the under-pitched beer, they are:</p>
<p>&nbsp;&nbsp;&nbsp;&nbsp;1: Bitter<br />
&nbsp;&nbsp;&nbsp;&nbsp;2: Malty<br />
&nbsp;&nbsp;&nbsp;&nbsp;3: Hoppy<br />
&nbsp;&nbsp;&nbsp;&nbsp;4: Astringent<br />
&nbsp;&nbsp;&nbsp;&nbsp;5: Fruity<br />
&nbsp;&nbsp;&nbsp;&nbsp;5: Estery<br />
&nbsp;&nbsp;&nbsp;&nbsp;5: Solventy<br />
&nbsp;&nbsp;&nbsp;&nbsp;8: Clean<br />
&nbsp;&nbsp;&nbsp;&nbsp;9: Smooth<br />
&nbsp;&nbsp;&nbsp;&nbsp;9: Thin</p>
<p>Based on the relative frequencies of some words, I think one can reasonably conclude that the under-pitched beer was perceived to be more bitter, more astringent, more solventy, less sweet, and &#8211; bizarrely &#8211; cleaner than the beer using the standard rate. Obviously, the increased perception of negative characteristics makes a persuasive case for the use of higher pitching rates.</p>
<p><strong>Summary</strong></p>
<ul>
<li>No difference in attenuation was observed, but fermentation in the control finished twice as quickly.</li>
<li>Under-pitching negatively impacts head retention and lacing.</li>
<li>There is a 43% chance that an &#8220;average&#8221; home brewer will be able to distinguish between under-pitched and standard-pitched ales.</li>
<li>There is a 30% chance that he will be able to identify which beer is which.</li>
<li>Overall, home brewers exhibit no strong preference for either beer.</li>
<li>Among tasters who <em>can</em> differentiate the two beers, the standard pitching rate is preferred nearly two to one.</li>
<li>The control beer was described as malty, hoppy, bitter, fruity, and sweet.</li>
<li>The under-pitched beer was described as being more bitter, more astringent, more solventy, less sweet, and cleaner than the control.</li>
</ul>
<p><strong>Summary of the Summary</strong></p>
<p>Using a starter makes better beer.<br />
&nbsp;<br />
&nbsp;<br />
&nbsp;<br />
<strong>Download the full dataset:<br />
<a href='http://seanterrill.com/wp-content/uploads/2010/05/pitchrate_experiment.ods'>pitchrate_experiment.ods</a> | <a href='http://seanterrill.com/wp-content/uploads/2010/05/pitchrate_experiment.xls'>pitchrate_experiment.xls</a></strong></p>
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		<title>Build a Better Stirplate</title>
		<link>http://seanterrill.com/2010/04/26/build-a-better-stirplate/</link>
		<comments>http://seanterrill.com/2010/04/26/build-a-better-stirplate/#comments</comments>
		<pubDate>Mon, 26 Apr 2010 05:35:24 +0000</pubDate>
		<dc:creator>webmaster</dc:creator>
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		<guid isPermaLink="false">http://seanterrill.com/?p=1712</guid>
		<description><![CDATA[<p><p class="wp-caption-text">It probably isn't necessary to stir Iodophor.</p>OK, so the world probably won&#8217;t be beating a path to my door. But there&#8217;s a right way to do it, and a wrong way &#8211; and a lot of home brewers are doing it the wrong way.</p>
<p>The basic idea behind these homebrew stirplates is to control the [...]]]></description>
			<content:encoded><![CDATA[<p><div id="attachment_1718" class="wp-caption alignright" style="width: 298px"><a href="http://seanterrill.com/wp-content/uploads/2010/04/IMG_2325.jpg"><img src="http://seanterrill.com/wp-content/uploads/2010/04/IMG_2325-288x384.jpg" alt="It probably isn&#039;t necessary to stir Iodophor." title="IMG_2325" width="288" height="384" class="size-medium wp-image-1718" /></a><p class="wp-caption-text">It probably isn't necessary to stir Iodophor.</p></div>OK, so the world probably won&#8217;t be beating a path to my door. But there&#8217;s a right way to do it, and a wrong way &#8211; and a lot of home brewers are doing it the wrong way.</p>
<p>The basic idea behind these homebrew stirplates is to control the speed of a motor (computer case fans being a cheap and accessible source) by varying the supply voltage. The <em>best</em> way to do it would actually be using pulse width modulation via a microcontroller, but I didn&#8217;t have one on hand, and energy efficiency probably isn&#8217;t a major concern for most people interested in powering a motor drawing around a couple watts. The simplest way to provide voltage adjustment (though not regulation, which I&#8217;ll get to in a second) is simply to put a resistor in series with the motor, which is what <a href="http://www.homebrewtalk.com/f51/my-stirplate-cheap-easy-build-86252/" class="bodylink">a</a> <a href="http://www.donosborn.com/homebrew/stir_plate.htm" class="bodylink">lot</a> <a href="http://davidtrumbell.com/Beer/Setup/StirPlate/StirPlate.html" class="bodylink">of</a> <a href="http://onebeer.net/sp_howto.shtml" class="bodylink">home</a> <a href="http://forum.northernbrewer.com/viewtopic.php?t=54575" class="bodylink">brewers</a> do. The problem with that (aside from the engineer in me hating the kludginess) is that electronic components are sold on profit margins more frequently associated with Wal-Mart stores, and are therefore made of plastic. If you have one lying around, or pick one up at Radio Shack, it will typically be rated 0.5 W, sometimes less. We&#8217;re going to be sinking around 12 V &bull; 150 mA = 1.8 W into it. It <strong>will</strong> melt.</p>
<p>So, the bare minimum takeaway here is to use a potentiometer rated for <em>at least</em> 2 W continuous power. A better, or at least more elegant, solution is to incorporate some actual voltage regulation. Which brings us to one of the most useful components ever invented, the <a href="http://www.national.com/mpf/LM/LM317.html" class="bodylink">LM317 adjustable voltage regulator</a>. The LM317 is capable of providing anything from 1.25 to (V<sub>in</sub> &#8211; 1.7) V with good regulation (&plusmn;1%), using only two resistors to set the output voltage:</p>
<p>V<sub>out</sub> = 1.25(1 + R<sub>2</sub>/R<sub>1</sub>)</p>
<p><div class="wp-caption alignleft" style="width: 310px"><a href="http://www.national.com/profile/snip.cgi/openDS=LM317"><img alt="The basic schematic for the LM317. Note the potential error in the value of R1." src="http://www.national.com/images/pf/LM317/00906301.jpg" title="317_schematic" width="300" height="200" /></a><p class="wp-caption-text">The basic schematic for the LM317. Note the potential problem with the value of R1.</p></div>Replace R2 with a potentiometer and you have a nifty little 1.5 A adjustable power supply using only three components. A couple filter capacitors probably aren&#8217;t necessary for our purposes, but they&#8217;re cheap insurance. The only downside to the LM317 as a regulator is that it&#8217;s inefficient; any excess current is dissipated in the regulator as heat. Again, that could be up to 1.8 W in this application. The most common regulator package is a TO-220, which can only safely dissipate around 1.5 W. So a heat sink is definitely a good idea. The LM317 has a built-in thermal shutdown, though, so you might be able to get away without a heat sink if you&#8217;re careful not to run the fan at very low speeds. If you do sink it, be aware that the tab on the TO-220 package is tied to V<sub>out</sub> &#8211; so be careful to avoid shorts. In the photo of the internals, you can see that I sealed the heat sink bolt with heat shrink tubing just to be safe.</p>
<p>Technically, an LM317 can have a minimum load current as high as 10 mA, although most will be much lower. That puts the maximum value of R1 at about 120 &Omega; (10.4 mA). Note that the <a href="http://www.national.com/profile/snip.cgi/openDS=LM317" class="bodylink">datasheet</a> specifies 240 &Omega; because it&#8217;s lifted from the specs for the LM117, which tops out at 5 mA. It&#8217;s also worth noting that I&#8217;m using a 220 &Omega; resistor simply because I had a 2.5 k&Omega; pot and didn&#8217;t feel like buying another. Do as I say, not as I do.</p>
<p>Circuitry aside, the rest of the build is pretty easy. I had a plastic kitchen container that happens to be the perfect size for my 1 gallon starter jugs. I bought a pair of neodymium rare earth magnets, which are simply adhered magnetically to the hub of the case fan. At 4 pounds of lift each, they aren&#8217;t going anywhere. If the fan was attached directly to the container, the magnets would make contact with its surface, so you&#8217;ll need some sort of spacer. I used roughly 5 mm lengths cut from a plastic drinking straw. The magnets and the power supply both came from <a href="http://www.sciplus.com/" class="bodylink">American Science and Surplus</a>, and the only other thing I needed to buy was a stir bar: $6 on eBay. If you&#8217;re going to use your stirplate with a convex-bottomed vessel, it might be worth noting the type of stir bar that works for me. It&#8217;s <a href="http://www.coleparmer.com/catalog/product_view.asp?sku=0855000" class="bodylink">1&#8243; x 3/8&#8243; with a ring</a>.</p>
<p><div id="attachment_1720" class="wp-caption alignright" style="width: 394px"><a href="http://seanterrill.com/wp-content/uploads/2010/04/IMG_2327.JPG"><img src="http://seanterrill.com/wp-content/uploads/2010/04/IMG_2327-384x288.jpg" alt="The stirplate internals. Blue LEDs optional but awesome." title="IMG_2327" width="384" height="288" class="size-medium wp-image-1720" /></a><p class="wp-caption-text">The stirplate internals. Blue LEDs optional but awesome.</p></div>The complete parts list would be:</p>
<ul>
<li>Project box or other plastic container</li>
<li>12 VDC power supply (at least 300 mA to allow for power spikes on startup)</li>
<li>PC case fan</li>
<li>Mounting hardware for fan</li>
<li>LM317T</li>
<li>TO-220 heat sink</li>
<li>120 &Omega; resistor</li>
<li>1 k&Omega; potentiometer</li>
<li>Knob for potentiometer</li>
<li>0.1 &mu;F ceramic disc capacitor</li>
<li>1 &mu;F electrolytic capacitor</li>
<li>2 rare earth magnets</li>
<li>Magnetic stir bar</li>
</ul>
<p>Plus wire, solder, perf board, etc. If you&#8217;re a tinkerer you probably already have some of this stuff on hand. Even if you had to buy everything online and pay shipping, it would only cost about $30. <a href="http://www.taydaelectronics.com/servlet/StoreFront" class="bodylink">Tayda Electronics</a> is a great source for components. Avoid Radio Shack like the plague.</p>
<p>Now that I&#8217;ve gotten off my lazy ass and put this thing together, I&#8217;ll be updating my <a href="http://seanterrill.com/2010/01/14/aeration-and-yeast-starters/" class="bodylink">aeration experiments</a> with one last trial, to test my assertion that frequent shaking and a stirplate are equivalent.</p>
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