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	<title>TDK Propulsion</title>
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	<link>http://www.tdkpropulsion.com</link>
	<description>Research 2.0</description>
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		<title>Thermite Torch Test</title>
		<link>http://www.tdkpropulsion.com/2010/08/thermite-torch-test/</link>
		<comments>http://www.tdkpropulsion.com/2010/08/thermite-torch-test/#comments</comments>
		<pubDate>Wed, 25 Aug 2010 23:21:45 +0000</pubDate>
		<dc:creator>David Reese</dc:creator>
				<category><![CDATA[Ignition]]></category>

		<guid isPermaLink="false">http://www.tdkpropulsion.com/?p=403</guid>
		<description><![CDATA[More testing on thermite. I knew it wasn&#8217;t going to light, but I needed some photos to prove it. So, bust out the compound, a sample tray, a blowtorch, and a camcorder&#8230; Quite boring, really. But that&#8217;s a good thing. Working in energetics, I&#8217;d much rather have a &#8220;boring&#8221; day than an &#8220;overly exciting&#8221; one.]]></description>
			<content:encoded><![CDATA[<p>More testing on thermite.  I knew it wasn&#8217;t going to light, but I needed some photos to prove it.  So, bust out the compound, a sample tray, a blowtorch, and a camcorder&#8230;<br />
<object width='500' height='281' class='aligncenter' style='margin:10px auto -30px auto;'><param name='allowfullscreen' value='true' /><param name='allowscriptaccess' value='always' /><param name='movie' value='http://vimeo.com/moogaloop.swf?clip_id=14433359&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' /><embed src='http://vimeo.com/moogaloop.swf?clip_id=14433359&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' type='application/x-shockwave-flash' allowfullscreen='true' allowscriptaccess='always' width='500' height='281'></embed></object><br /><div style='font-weight:normal; font-size:10px; margin:10px 0 0 475px;'>(<a href='http://vimeo.com/14433359'>video link</a>)</div><br />
Quite boring, really.  But that&#8217;s a good thing.  Working in energetics, I&#8217;d much rather have a &#8220;boring&#8221; day than an &#8220;overly exciting&#8221; one.</p>
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		<title>Resodyn LabRAM</title>
		<link>http://www.tdkpropulsion.com/2010/08/resodyn-labram/</link>
		<comments>http://www.tdkpropulsion.com/2010/08/resodyn-labram/#comments</comments>
		<pubDate>Sat, 21 Aug 2010 18:47:56 +0000</pubDate>
		<dc:creator>David Reese</dc:creator>
				<category><![CDATA[Motors]]></category>

		<guid isPermaLink="false">http://www.tdkpropulsion.com/?p=400</guid>
		<description><![CDATA[Mixing propellant can be a chore, mostly due to one thing: cleaning the beater and bowl. Resodyn of Butte, MT produces a line of &#8220;resonant acoustic mixers&#8221; (RAMs) that simplify things greatly. The RAM is essentially a glorified paint shaker, with a system of accelerometers and driver masses that automatically tune the mixture to vibrate [...]]]></description>
			<content:encoded><![CDATA[<p>Mixing propellant can be a chore, mostly due to one thing: cleaning the beater and bowl.  <a href="http://www.resodyn.com/">Resodyn</a> of Butte, MT produces a line of &#8220;resonant acoustic mixers&#8221; (RAMs) that simplify things greatly.  The RAM is essentially a glorified paint shaker, with a system of accelerometers and driver masses that automatically tune the mixture to vibrate at its natural frequency, thus imparting as much energy as possible into the mix.  What&#8217;s neat about it is that the mounting table is designed such that you can actually pour all your propellant chemicals into the casting sleeve, put the sleeve right on the mixer table, and mix right there &#8212; no cleanup needed!  (They were demoing this technique at the ARL review meeting.)  It&#8217;s also a tremendously fast way to mix propellant (~10 minute cycle time), and gives tons of data on what is happening during the mix cycle; I just finished working on a Phase I project that used this data to parameterize a model to determine how mixed the propellant is for a given cycle energy input.</p>
<p>Anyways, the RAM mixers were brought up a few months ago on the Tripoli list, to some interest.  I made a quick video of what the mix cycle looks like to hopefully answer some of the questions that were asked.  This mix cycle is of an 83% solids propellant based on AP and HTPB, mixed under vacuum.  I think it&#8217;s really cool how the propellant kneads and folds itself during the mix cycle, going from a system of discrete ingredients to one big well-mixed mass of propellant.  It looks like a superball during the mix, but as soon as the mixer powers down, you see the propellant settle out against the bottom of the mix jar and remember that it is, in fact, a really viscous solid.</p>
<object width='500' height='281' class='aligncenter' style='margin:10px auto -30px auto;'><param name='allowfullscreen' value='true' /><param name='allowscriptaccess' value='always' /><param name='movie' value='http://vimeo.com/moogaloop.swf?clip_id=14306348&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' /><embed src='http://vimeo.com/moogaloop.swf?clip_id=14306348&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' type='application/x-shockwave-flash' allowfullscreen='true' allowscriptaccess='always' width='500' height='281'></embed></object><br /><div style='font-weight:normal; font-size:10px; margin:10px 0 0 475px;'>(<a href='http://vimeo.com/14306348'>video link</a>)</div>
]]></content:encoded>
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		<title>C*</title>
		<link>http://www.tdkpropulsion.com/2010/08/c-star/</link>
		<comments>http://www.tdkpropulsion.com/2010/08/c-star/#comments</comments>
		<pubDate>Thu, 19 Aug 2010 20:55:28 +0000</pubDate>
		<dc:creator>David Reese</dc:creator>
				<category><![CDATA[Propulsion Theory]]></category>

		<guid isPermaLink="false">http://www.tdkpropulsion.com/?p=368</guid>
		<description><![CDATA[This post is about the propellant parameter, but I had to put a picture in of the world&#8217;s most awesome N motor, too, since it&#8217;s burning CTI&#8217;s C* propellant. (That&#8217;s in James Dougherty&#8217;s 1/2 scale Patriot &#8212; click through and scroll down for the video.) Continuing in the theme of previous theory posts, this one [...]]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.tdkpropulsion.com/2010/08/c-star/"><img src="http://www.tdkpropulsion.com/wp-content/uploads/2010/08/cstar.jpg" alt="" title="CStar N5800 in James Dougherty&#039;s 1/2 Scale Patriot" width="550" height="215" class="aligncenter size-full wp-image-392" /></a><br />
This post is about the propellant parameter, but I had to put a picture in of the world&#8217;s most awesome N motor, too, since it&#8217;s burning CTI&#8217;s C* propellant.  (That&#8217;s in James Dougherty&#8217;s 1/2 scale Patriot &#8212; click through and scroll down for the video.)  Continuing in the theme of previous theory posts, this one will be about the wonderful, beautiful term called &#8220;characteristic velocity&#8221;, or C*.  C* is one of the terms that is extremely helpful in correlating theoretical and delivered performance, and in discussions I&#8217;ve had with lots of rocketeers over the past year or so, it also seems to be somewhat misunderstood.  So let&#8217;s start at the beginning and see how useful it really is.</p>
<p>C* and <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-f79b76f00b17013f20daffead0a5e0ce.gif" alt="I_{sp}" title="I_{sp}" style="vertical-align: -6px; border: none;"/> are related, and both are found in various forms of the equation for thrust:</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-2bf792e50e2909a916c10f7a2832a320.gif" alt="F_{th} = P_0A^*C_F = \dot m I_{sp} g = \dot m C^* C_F" title="F_{th} = P_0A^*C_F = \dot m I_{sp} g = \dot m C^* C_F" style="vertical-align: -6px; border: none;"/></center></p>
<p>where <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-d3eb61efbbf0dec7e3298c791ee9ac17.gif" alt="F_{th}" title="F_{th}" style="vertical-align: -3px; border: none;"/> is the thrust force, <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-5b7c5aa2a2a15bd892afe579eef0906e.gif" alt="P_0" title="P_0" style="vertical-align: -3px; border: none;"/> is the chamber pressure, <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-1304435c8bc4c0f5b8ecbe7f16727d75.gif" alt="A^*" title="A^*" style="vertical-align: 0px; border: none;"/> is the throat area, <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-fcc5a7d2df8a0d84d5363d88d41fd3c6.gif" alt="C_F" title="C_F" style="vertical-align: -3px; border: none;"/> is the thrust coefficient (provided by the nozzle), <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-1d5875904f4d060f31bef3a06f7b3af7.gif" alt="\dot m" title="\dot m" style="vertical-align: 0px; border: none;"/> is the propellant mass flow rate, and <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-b2f5ff47436671b6e533d8dc3614845d.gif" alt="g" title="g" style="vertical-align: -4px; border: none;"/> is the gravitational constant.  Some quick rearranging shows that</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-6a08a35a1cc83a5e93219ac5b76c8e60.gif" alt="C^* = \frac{I_{sp}g}{C_F} = \frac{P_0A^*}{\dot m}" title="C^* = \frac{I_{sp}g}{C_F} = \frac{P_0A^*}{\dot m}" style="vertical-align: -9px; border: none;"/></center></p>
<p>which is also pretty handy, since we know all the terms in the rightmost equation, or at least can measure them directly.  This means that we can calculate C* from test data -- hey, another reason to build a test stand!</p>
<p>The true beauty of C* comes out, though, when we look at it from the other direction, ahead of time.  As motor designers, we get to pick <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-5b7c5aa2a2a15bd892afe579eef0906e.gif" alt="P_0" title="P_0" style="vertical-align: -3px; border: none;"/> and <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-1304435c8bc4c0f5b8ecbe7f16727d75.gif" alt="A^*" title="A^*" style="vertical-align: 0px; border: none;"/>, so all we need to calculate is <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-1d5875904f4d060f31bef3a06f7b3af7.gif" alt="\dot m" title="\dot m" style="vertical-align: 0px; border: none;"/>, and we can calculate C*.  And <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-1d5875904f4d060f31bef3a06f7b3af7.gif" alt="\dot m" title="\dot m" style="vertical-align: 0px; border: none;"/> isn&#8217;t that bad to derive, either.  So let&#8217;s give it a go, yes?<span id="more-368"></span></p>
<p>Everything in gas dynamics has something to do with the continuity equation:</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-794290f7cf47c9fba9f3ea6923971743.gif" alt="\dot m = \rho UA" title="\dot m = \rho UA" style="vertical-align: -4px; border: none;"/></center></p>
<p>where <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-d2606be4e0cd2c9a6179c8f2e3547a85.gif" alt="\rho" title="\rho" style="vertical-align: -4px; border: none;"/> is the gas density, <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-4c614360da93c0a041b22e537de151eb.gif" alt="U" title="U" style="vertical-align: 0px; border: none;"/> is the gas velocity, and <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-7fc56270e7a70fa81a5935b72eacbe29.gif" alt="A" title="A" style="vertical-align: 0px; border: none;"/> is the flow area in question.  Since we don&#8217;t have a density meter to measure <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-d2606be4e0cd2c9a6179c8f2e3547a85.gif" alt="\rho" title="\rho" style="vertical-align: -4px; border: none;"/> directly, it&#8217;s easiest to rewrite <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-d2606be4e0cd2c9a6179c8f2e3547a85.gif" alt="\rho" title="\rho" style="vertical-align: -4px; border: none;"/> in terms of things we know, using the perfect gas law:</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-a8c52db15fd41df7f1cd68c13ddc519d.gif" alt="P = \rho R_g T \rightarrow \rho =\frac{P}{R_gT}" title="P = \rho R_g T \rightarrow \rho =\frac{P}{R_gT}" style="vertical-align: -10px; border: none;"/></center></p>
<p>where <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-b9ece18c950afbfa6b0fdbfa4ff731d3.gif" alt="T" title="T" style="vertical-align: 0px; border: none;"/> is the temperature at the given location, and <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-4b3817e7a262df256ae373f84c03f008.gif" alt="R_g" title="R_g" style="vertical-align: -6px; border: none;"/> is the real gas constant (just the ideal gas constant divided by the molecular weight &#8212; <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-e758473b14cb87296a8cd67ea272e461.gif" alt="\frac{R}{\mathfrak{M}}" title="\frac{R}{\mathfrak{M}}" style="vertical-align: -6px; border: none;"/>) for the gas in question.  The only place that we know the flow velocity <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-4c614360da93c0a041b22e537de151eb.gif" alt="U" title="U" style="vertical-align: 0px; border: none;"/> with certainty is at the throat, where we know it&#8217;s going exactly sonic speed.  (All throat conditions are denoted by superscript *, by the way.)  Leaning on one more important gasdynamic relation, we know that <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-4c614360da93c0a041b22e537de151eb.gif" alt="U" title="U" style="vertical-align: 0px; border: none;"/> at the throat is simply</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-5617aba92b8281a44ebe19a9a12aebdf.gif" alt="U^* = \sqrt{\gamma R_g T^*}" title="U^* = \sqrt{\gamma R_g T^*}" style="vertical-align: -6px; border: none;"/></center></p>
<p>where <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-ae539dfcc999c28e25a0f3ae65c1de79.gif" alt="\gamma" title="\gamma" style="vertical-align: -4px; border: none;"/> is the ratio of specific heats for the gas and <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-89cdaade8ab2be96ff644dad9846ffe7.gif" alt="T^*" title="T^*" style="vertical-align: 0px; border: none;"/> is the temperature of the gas at the throat.  Rewriting the continuity equation with our newly defined parameters, using conditions at the throat *:</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-34dba5f3d6280157f8445ff14e0ed5a2.gif" alt="\dot m = \frac{P^*A^*}{R_gT^*}\sqrt{\gamma R_g T^*}" title="\dot m = \frac{P^*A^*}{R_gT^*}\sqrt{\gamma R_g T^*}" style="vertical-align: -10px; border: none;"/></center></p>
<p>The only problem with this equation (let&#8217;s call it Eq. (1)) is that everything is in terms of throat conditions &#8212; and just imagine how much of a pain it would be to measure stuff at the throat, where the heat flux has peaked and all your thermocouples and pressure tubes just melted.  Yeah.  Not fun.  To make things easier, we can use the magic of the isentropic flow relations to move everything upstream into the chamber, where we can measure it (and consider it) with a bit more ease.  Pause a minute to reflect and remember these old friends from the <a href="http://www.grc.nasa.gov/WWW/K-12/airplane/isentrop.html">NASA Education page</a> (or your favorite gas dynamics textbook):</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-39cc2de22a2be6ae34935a3197ddd231.gif" alt="\frac{P_0}{P} = \left(1+\frac{\gamma-1}{2}M^2\right)^\frac{\gamma}{\gamma-1}\;\;\;\;\;\frac{T_0}{T} = \left(1+\frac{\gamma-1}{2}M^2\right)" title="\frac{P_0}{P} = \left(1+\frac{\gamma-1}{2}M^2\right)^\frac{\gamma}{\gamma-1}\;\;\;\;\;\frac{T_0}{T} = \left(1+\frac{\gamma-1}{2}M^2\right)" style="vertical-align: -12px; border: none;"/></center></p>
<p>They give stagnation (chamber) pressure and temperature as a function of <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-ae539dfcc999c28e25a0f3ae65c1de79.gif" alt="\gamma" title="\gamma" style="vertical-align: -4px; border: none;"/> and downstream Mach number <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-69691c7bdcc3ce6d5d8a1361f22d04ac.gif" alt="M" title="M" style="vertical-align: 0px; border: none;"/>.  And since we&#8217;re dealing with throat conditions here, <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-b539f6c980fd73458742075683f13723.gif" alt="M^*=1" title="M^*=1" style="vertical-align: -1px; border: none;"/> (oh, life is sweet), so these equations collapse into something even simpler.  Rewrite and solve for <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-dc0b195945be991e74020d59fee4192e.gif" alt="P = P^*" title="P = P^*" style="vertical-align: 0px; border: none;"/> and <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-f829a42cdbdce58ef08da9221ceedf46.gif" alt="T = T^*" title="T = T^*" style="vertical-align: 0px; border: none;"/>:</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-a1a596c69e446549be854c2a664e7895.gif" alt="P^* = P_0\left(\frac{2}{\gamma+1}\right)^\frac{\gamma}{\gamma-1}\;\;\;\;\;T^* = T_0\left(\frac{2}{\gamma+1}\right)" title="P^* = P_0\left(\frac{2}{\gamma+1}\right)^\frac{\gamma}{\gamma-1}\;\;\;\;\;T^* = T_0\left(\frac{2}{\gamma+1}\right)" style="vertical-align: -12px; border: none;"/></center></p>
<p>and then substituting these into Eq. (1) gives us the lovely mess of</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-a0c36a25966785d6dede373e56148e26.gif" alt="\dot m = \frac{P_0\left(\frac{2}{\gamma+1}\right)^\frac{\gamma}{\gamma-1}A^*}{R_gT_0\left(\frac{2}{\gamma+1}\right)}\sqrt{\gamma R_g T_0 \left(\frac{2}{\gamma+1}\right)}" title="\dot m = \frac{P_0\left(\frac{2}{\gamma+1}\right)^\frac{\gamma}{\gamma-1}A^*}{R_gT_0\left(\frac{2}{\gamma+1}\right)}\sqrt{\gamma R_g T_0 \left(\frac{2}{\gamma+1}\right)}" style="vertical-align: -23px; border: none;"/></center></p>
<p>Since I haven&#8217;t thrown up my hands in frustration and walked away from this post, you know it has to get simpler.  So we massage all the <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-2a7938c842d4f500845f6ae006a0479d.gif" alt="\frac{2}{\gamma+1}" title="\frac{2}{\gamma+1}" style="vertical-align: -9px; border: none;"/> terms around</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-a35f03ee21c718d3aa48279f8b5f70fd.gif" alt="\dot m = \frac{P_0\left(\frac{2}{\gamma+1}\right)^\frac{(\gamma+1)}{2(\gamma-1)}A^*}{R_gT_0}\sqrt{\gamma R_g T_0}" title="\dot m = \frac{P_0\left(\frac{2}{\gamma+1}\right)^\frac{(\gamma+1)}{2(\gamma-1)}A^*}{R_gT_0}\sqrt{\gamma R_g T_0}" style="vertical-align: -10px; border: none;"/></center></p>
<p>and then push around <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-4b3817e7a262df256ae373f84c03f008.gif" alt="R_g" title="R_g" style="vertical-align: -6px; border: none;"/> and <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-ab4ffa55f688360e0c12aef543c18351.gif" alt="T_0" title="T_0" style="vertical-align: -3px; border: none;"/>:</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-911d6a5a928b1066cda150efa874724e.gif" alt="\dot m = P_0A^*\left(\frac{2}{\gamma+1}\right)^\frac{(\gamma+1)}{2(\gamma-1)}\sqrt{\frac{\gamma}{R_gT_0}}" title="\dot m = P_0A^*\left(\frac{2}{\gamma+1}\right)^\frac{(\gamma+1)}{2(\gamma-1)}\sqrt{\frac{\gamma}{R_gT_0}}" style="vertical-align: -14px; border: none;"/></center></p>
<p>and we&#8217;re done.  It&#8217;s not that bad, when you look at it for a while, and we know everything in that equation from doing propellant combustion calculations (<img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-ae539dfcc999c28e25a0f3ae65c1de79.gif" alt="\gamma" title="\gamma" style="vertical-align: -4px; border: none;"/>, <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-ab4ffa55f688360e0c12aef543c18351.gif" alt="T_0" title="T_0" style="vertical-align: -3px; border: none;"/>, <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-4b3817e7a262df256ae373f84c03f008.gif" alt="R_g" title="R_g" style="vertical-align: -6px; border: none;"/>) or motor design (<img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-5b7c5aa2a2a15bd892afe579eef0906e.gif" alt="P_0" title="P_0" style="vertical-align: -3px; border: none;"/>, <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-1304435c8bc4c0f5b8ecbe7f16727d75.gif" alt="A^*" title="A^*" style="vertical-align: 0px; border: none;"/>).  But wait&#8230; we were starting on our quest to solve <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-0f1a0bf001f82a76496bc5b40d6efaf7.gif" alt="C^*" title="C^*" style="vertical-align: 0px; border: none;"/>, so things get even simpler:</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-d41d8cd98f00b204e9800998ecf8427e.gif" alt="" title="" style="vertical-align: -2147483647px; border: none;"/></center></p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-a6c87e142dded5ec42fde43e19c21b06.gif" alt="C^* = \frac{P_0A^*}{\dot m} = \frac{P_0A^*}{P_0A^*\left(\frac{2}{\gamma+1}\right)^\frac{(\gamma+1)}{2(\gamma-1)}\sqrt{\frac{\gamma}{R_gT_0}}} = \sqrt{\frac{R_g T_0}{\gamma}}\left(\frac{\gamma+1}{2}\right)^\frac{(\gamma+1)}{2(\gamma-1)}" title="C^* = \frac{P_0A^*}{\dot m} = \frac{P_0A^*}{P_0A^*\left(\frac{2}{\gamma+1}\right)^\frac{(\gamma+1)}{2(\gamma-1)}\sqrt{\frac{\gamma}{R_gT_0}}} = \sqrt{\frac{R_g T_0}{\gamma}}\left(\frac{\gamma+1}{2}\right)^\frac{(\gamma+1)}{2(\gamma-1)}" style="vertical-align: -35px; border: none;"/></center></p>
<p>or, massaging a little more,</p>
<p><center><img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-3104bfed49bd38620aaf991e5f0314ba.gif" alt="C^* = \sqrt{\frac{R_gT_0}{\gamma}\left(\frac{\gamma+1}{2}\right)^\frac{\gamma+1}{\gamma-1}}\;\;." title="C^* = \sqrt{\frac{R_gT_0}{\gamma}\left(\frac{\gamma+1}{2}\right)^\frac{\gamma+1}{\gamma-1}}\;\;." style="vertical-align: -13px; border: none;"/></center></p>
<p>At this point it should become apparent why C* is such a valuable term &#8212; in this form, it depends solely on the propellant&#8217;s combustion characteristics, so we can calculate it ahead of time with excellent accuracy.  And because its other definition relies on things that we can measure with some simple instrumentation, we can measure it with decent accuracy as well.  So C* is one of the most useful parameters to keep track of, because it quickly and easily tells us exactly how well our rocket motor combustion device is performing.  If <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-c81086e94cc11392bc08344156ee454b.gif" alt="P_c" title="P_c" style="vertical-align: -3px; border: none;"/> is lower than expected for a given throat area, C* must be lower than expected, indicating inefficiencies in the design.</p>
<p>Also, hopefully this exercise has taken some of the magic out of equilibrium programs like PEP or CEA that spit out a C* value from simple chemical formulation inputs.  It&#8217;s not really any magic &#8212; just some math.  And it&#8217;s only a short hop from there to <img src="http://www.tdkpropulsion.com/wp-content/ql-cache/quicklatex-f79b76f00b17013f20daffead0a5e0ce.gif" alt="I_{sp}" title="I_{sp}" style="vertical-align: -6px; border: none;"/> and performance calculation.</p>
<p>So learn C*.  Calculate it.  Measure it.  Love it.  It&#8217;s one more way to have fun with data from your test stand, and a good way to measure how well you&#8217;re doing as a research rocketeer.</p>
<p>Oh yeah, and the video from <a href="http://www.youtube.com/user/jamesfdougherty">James Dougherty</a>:<br />
<div style="margin: 0px auto;"><span class="youtube">
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</span><p><a href="http://www.youtube.com/watch?v=adS8blxbaFE&fmt=18">www.youtube.com/watch?v=adS8blxbaFE</a></p></div><br />
That&#8217;s his 7.5&#8243; 1/2 scale Patriot on an N5800 C-Star.  Wow.  Can&#8217;t wait to see one of these in person.</p>
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		<title>JPC 2010</title>
		<link>http://www.tdkpropulsion.com/2010/08/jpc-2010/</link>
		<comments>http://www.tdkpropulsion.com/2010/08/jpc-2010/#comments</comments>
		<pubDate>Thu, 05 Aug 2010 04:19:55 +0000</pubDate>
		<dc:creator>David Reese</dc:creator>
				<category><![CDATA[Propulsion Theory]]></category>

		<guid isPermaLink="false">http://www.tdkpropulsion.com/?p=342</guid>
		<description><![CDATA[The 46th AIAA Joint Propulsion Conference happened a few weeks back down in Nashville, and things have finally stabilized around here long enough for me to write about it! I had a great time attending all sorts of presentations on cool state-of-the-art chemical rocket propulsion technologies of all flavors (solid, liquid, and hybrid) &#8212; the [...]]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.tdkpropulsion.com/2010/08/jpc-2010/"><img src="http://www.tdkpropulsion.com/wp-content/uploads/2010/08/IMG_3710-300x224.jpg" alt="" title="Me, Dr. Son, Luigi DeLuca, Ken Kuo, and my labmate Andrew at JPC 2010." width="300" height="224" class="aligncenter size-medium wp-image-343" /></a><br />
The 46th AIAA Joint Propulsion Conference happened a few weeks back down in Nashville, and things have finally stabilized around here long enough for me to write about it!  I had a great time attending all sorts of presentations on cool state-of-the-art chemical rocket propulsion technologies of all flavors (solid, liquid, and hybrid) &#8212; the problem was that there just wasn&#8217;t enough time to head to all of the presentations I wanted to see.  Some of the highlights of the event included meeting Dr. Ken Kuo and Dr. Luigi DeLuca (above), both of whom are titans of the field, the Moog party on Tuesday night and running into Luke Colby from Scaled (it&#8217;s a small world!), giving my presentation, seeing my old compressible flow professor as session chair of TWO sessions (go Dr. Marcu!), seeing two of Martin Summerfield&#8217;s students battle it out during a presentation (Herman Krier and Luigi DeLuca, like watching lions fighting on the savanna &#8212; you step back and watch in awe), and being herded into the hotel basement with all the other attendees for a tornado warning.  More details on the sessions I attended and more photos after the jump.<span id="more-342"></span></p>
<p>I started out at <a href="http://pdf.aiaa.org/preview/2010/CDReadyMJPC10_2347/PV2010_6586.pdf">Niklas Wingborg&#8217;s presentation on GAP/ADN propellants</a>, in which he discussed the development and processing of test motors containing just under 7 lbs of propellant, and had some beautiful static firing videos and results.  Their spray prilling process is really nice, and seems to avoid many of the hazards of mechanical (emulsion) prilling that we&#8217;ve been working around lately.  The presentation was really quite inspirational.</p>
<p>The first of my labmates to go was Stephen Bluestone, talking about his development of propellants using dicyclopentadiene (DCPD) binder.  DCPD shows a lot of promise for future propellants; it has a viscosity like that of water when being processed, but maintains tremendous strength, and so can be loaded up with tremendous amounts of solids.  It also produces some incredibly quick-burning propellant.  However, there are still issues with post-cure rheology; the polymer&#8217;s typical use is for things like snowmobile windshields, so it&#8217;s very hard.  Bluestone&#8217;s work before he graduated focused mainly on finding a plasticizer for the polymer; we&#8217;ll see what comes of it in the future.</p>
<p>At this point on Monday, I made my presentation on numerical modeling (and experimental correlation) of nanoparticle dispersion in composite and double base propellants.  It went quite well.  Here I am with Dr. Son just after the presentation:<br />
<a href="http://www.tdkpropulsion.com/wp-content/uploads/2010/08/IMG_3709.jpeg"><img src="http://www.tdkpropulsion.com/wp-content/uploads/2010/08/IMG_3709-300x225.jpg" alt="" title="Me and Dr. Son after my presentation.  Yay!" width="300" height="225" class="aligncenter size-medium wp-image-344" /></a></p>
<p>There was a lot of ADN work presented (it even got mentioned, albeit horribly mispronounced, at the opening speech on Monday morning).  Another paper I found really cool was about the development of an ADN/water monopropellant for the replacement of hydrazine in spacecraft, presented by Georg Schulte (who also took the pic of me and Dr. Son &#8211; thanks!).  The stuff not only was delivering a higher Isp than hydrazine, but also gave a higher density specific impulse &#8211; impressive!  The main drawback was the need for significantly greater preheating of the cat bed before use, but this didn&#8217;t seem to be too much of an issue, as the speaker detailed a system that was currently in use on a spacecraft.</p>
<p>After a quick Starbucks run with Chris and Andrew, I headed up to the session on aluminum agglomeration, to see the new work coming out of SPLab.  Dr. Filippo Maggi presented an excellent paper on prediction of agglomerate size, and Dr. DeLuca summarized the past ten years of the lab&#8217;s work in an awesome presentation on agglomeration across a variety of metals and intermetallics.  The high speed videos of agglomerate formation which they showed were breathtaking.  I would LOVE to go work with these guys for a semester or two&#8230; the quality of their work is awesome, and I&#8217;d love to get back to Italy, too&#8230;</p>
<p>Several papers were presented on work taking place under the umbrella of the Constellation program, each of which had a light patina of angst dusted on the surface (sigh).  Andrew and I checked out a presentation on deep throttling for exploration engines (deeeeeeeeep throttling in the words of Steve&#8230;), which essentially rehashed most of the issues covered in a deep throttling project that we worked on for a kerosene biprop earlier this year.  Good to know we got the bases covered, at least.</p>
<p>Monday night was the Young Professionals reception, and also the night we got hit with the tornado warning.  With all the Purdue peeps there, we were bound to win something in the door prize raffle; two people took home copies of <a href="http://www.amazon.com/gp/product/156347655X/">a book written by Purdue professor Jim Longuski</a> (HAHA) and one got a blue and green AIAA tie.  We all had an awesome time, even though we kind of looked like a cult in our Purdue Propulsion polos&#8230;<br />
<a href="http://www.tdkpropulsion.com/wp-content/uploads/2010/08/IMG_3715.jpeg"><img src="http://www.tdkpropulsion.com/wp-content/uploads/2010/08/IMG_3715-300x225.jpg" alt="" title="Group photo at the Young Professionals reception" width="300" height="225" class="aligncenter size-medium wp-image-357" /></a></p>
<p>Tuesday morning was taken up by a set of presentations on erosive burning; the first was a numerical treatment by one of <a href="http://www.csar.illinois.edu/">Tom Jackson&#8217;s</a> students, and the second was a, um, philosophical (?) treatment by Dr. Bob Glick.  I was kind of stoked to see Glick&#8217;s presentation, since I relied heavily on work that he and Lynn Caveny had performed a long time ago for my <a href="http://www.tdkpropulsion.com/2010/06/silver-wire/">wire-enhanced burning rate</a> paper.  He delivered a hilarious, long-winded, roundabout talk about burning surface irregularities and how they require us all to throw out the QSHOD assumptions for computations.  Yeah, saw that one coming.  Very entertaining, though.</p>
<p>I also caught up with Dr. Marcu on Tuesday, in a session on large-scale LRE development.  He was in great spirits, and we talked briefly about possibly collaborating on some turbine research.  (Dr. Key, our resident turbine expert, seemed receptive to the idea when I told her.)</p>
<p>Tuesday night was the Moog party at the Wildhorse saloon.  It was a really nice party with a live band on the big stage and an expansive dance floor; Moog was handing out cowboy hats, handkerchiefs, and boot-shaped coozies (which are AWESOME).  I ran into a lot of people I didn&#8217;t know were there, which was really awesome; aerospace is a small world, and it&#8217;s great to see people around, we&#8217;re all like family.  Jacob Dennis also somehow ended up with at least ten cowboy hats stacked on his head by the end of the night.</p>
<p>Wednesday was a packed day, with a GAP hybrid presentation to kick things off, followed by a presentation on CARS in LOX/methane engines (look for the hydrogen!), one on Boeing&#8217;s suggested replacement for Ares (surprise surprise, take a Delta IV and a couple of GEMs to boost cargo&#8230; didn&#8217;t see that one coming&#8230;), one from ESA on the development of large solids for the Vega vehicle (their test site is on Sardinia, SO JEALOUS), and ended with a nice series on combustion stability in solids and biprops, where I got to meet Fred Blomshield (anybody who&#8217;s been through my motor seminar has seen some of Dr. Blomshield&#8217;s static test videos) and cheer on our last Purdue presentation of the meeting, presented by Mark Pfeil.</p>
<p>The drive back was long in the dark, through several awesome thunderstorms.  Chris somehow got the bright idea to use the cologne machine in the bathroom at a truck stop, which made the car ride a bit unbearable at times for the last few hours, but he was driving, so nobody else in the car could complain, really.</p>
<p>Overall, it was a great conference.  Nashville was a neat place to have the conference; there was all sorts of cool nightlife to keep us from sleeping, so by the end of Wednesday I was totally zonked.  But gathering loads of cool information, meeting tons of great people, and bonding with the lab was a really worthwhile experience.  I can&#8217;t wait for JANNAF, ASM, and of course JPC next year&#8230; it&#8217;s gonna be in SAN DIEGO!  See you there?</p>
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		<title>Thermite High Speed Videos</title>
		<link>http://www.tdkpropulsion.com/2010/07/thermite-high-speed-videos/</link>
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		<pubDate>Fri, 16 Jul 2010 12:17:44 +0000</pubDate>
		<dc:creator>David Reese</dc:creator>
				<category><![CDATA[Ignition]]></category>
		<category><![CDATA[Media]]></category>

		<guid isPermaLink="false">http://www.tdkpropulsion.com/?p=309</guid>
		<description><![CDATA[One of my friends here has been having some issues getting a clean, reliable start on a motor, so I suggested using a thermite igniter to get things moving quickly. Seeking some evidence to use for convincing the higher-ups, we did some high speed videos of a couple thermite igniters to see what goes on. [...]]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.tdkpropulsion.com/2010/07/thermite-high-speed-videos/#more-309"><img src="http://www.tdkpropulsion.com/wp-content/uploads/2010/07/Screen-shot-2010-07-15-at-11.46.10-PM-300x225.png" alt="CuO and MnO2 thermite firings" title="Thermite igniter comparison" width="300" height="225" class="aligncenter size-medium wp-image-310" /></a><br />
One of my friends here has been having some issues getting a clean, reliable start on a motor, so I suggested using a thermite igniter to get things moving quickly.  Seeking some evidence to use for convincing the higher-ups, we did some high speed videos of a couple thermite igniters to see what goes on.  We fired a standard copper thermite compound, as well as one based on manganese dioxide and aluminum.  Each shot was 5 grams of material.  The CuO igniter was filmed at 2000 frames per second, and the MnO<sub>2</sub> at 10,000 frames per second.  I also sped up the MnO<sub>2</sub> video and stuck the shots next to each other, to allow easier comparison between the two types.<br />
<span id="more-309"></span><br />
CuO/Al (2k fps):<br />
<object width='500' height='281' class='aligncenter' style='margin:10px auto -30px auto;'><param name='allowfullscreen' value='true' /><param name='allowscriptaccess' value='always' /><param name='movie' value='http://vimeo.com/moogaloop.swf?clip_id=13350190&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' /><embed src='http://vimeo.com/moogaloop.swf?clip_id=13350190&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' type='application/x-shockwave-flash' allowfullscreen='true' allowscriptaccess='always' width='500' height='281'></embed></object><br /><div style='font-weight:normal; font-size:10px; margin:10px 0 0 475px;'>(<a href='http://vimeo.com/13350190'>video link</a>)</div></p>
<p>MnO<sub>2</sub>/Al (10k fps):<br />
<object width='500' height='281' class='aligncenter' style='margin:10px auto -30px auto;'><param name='allowfullscreen' value='true' /><param name='allowscriptaccess' value='always' /><param name='movie' value='http://vimeo.com/moogaloop.swf?clip_id=13374639&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' /><embed src='http://vimeo.com/moogaloop.swf?clip_id=13374639&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' type='application/x-shockwave-flash' allowfullscreen='true' allowscriptaccess='always' width='500' height='281'></embed></object><br /><div style='font-weight:normal; font-size:10px; margin:10px 0 0 475px;'>(<a href='http://vimeo.com/13374639'>video link</a>)</div></p>
<p>Comparison of both types (2k fps):<br />
<object width='500' height='281' class='aligncenter' style='margin:10px auto -30px auto;'><param name='allowfullscreen' value='true' /><param name='allowscriptaccess' value='always' /><param name='movie' value='http://vimeo.com/moogaloop.swf?clip_id=13374599&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' /><embed src='http://vimeo.com/moogaloop.swf?clip_id=13374599&amp;server=vimeo.com&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=&amp;fullscreen=1' type='application/x-shockwave-flash' allowfullscreen='true' allowscriptaccess='always' width='500' height='281'></embed></object><br /><div style='font-weight:normal; font-size:10px; margin:10px 0 0 475px;'>(<a href='http://vimeo.com/13374599'>video link</a>)</div></p>
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