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kinda finished air prop page
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<meta property="description" itemprop="description" content="Simulating the performance of an air propulsion system as an alternative to solid rocket motors."/>
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<link rel="license" href="https://creativecommons.org/licenses/by/4.0/"/>
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<meta property="article:published" itemprop="datePublished" content="2021-04-01"/>
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{"type":"list","attributes":{"names":{"type":"character","attributes":{},"value":["title","description","author","repository_url","date","fig_width","fig_align","output","categories","bibliography"]}},"value":[{"type":"character","attributes":{},"value":["Air Propulsion Simulation"]},{"type":"character","attributes":{},"value":["Simulating the performance of an air propulsion system as an alternative to solid rocket motors. \n"]},{"type":"list","attributes":{},"value":[{"type":"list","attributes":{"names":{"type":"character","attributes":{},"value":["name","url"]}},"value":[{"type":"character","attributes":{},"value":["Anson Biggs"]},{"type":"character","attributes":{},"value":["https://ansonbiggs.com"]}]}]},{"type":"character","attributes":{},"value":["https://gitlab.com/lander-team/air-prop-simulation"]},{"type":"character","attributes":{},"value":["04-01-2021"]},{"type":"integer","attributes":{},"value":[6]},{"type":"character","attributes":{},"value":["center"]},{"type":"list","attributes":{"names":{"type":"character","attributes":{},"value":["distill::distill_article"]}},"value":[{"type":"list","attributes":{"names":{"type":"character","attributes":{},"value":["self_contained"]}},"value":[{"type":"logical","attributes":{},"value":[false]}]}]},{"type":"character","attributes":{},"value":["Julia","Capstone"]},{"type":"character","attributes":{},"value":["../../citations.bib"]}]}
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</div>
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<div class="d-article">
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<p>For my team was tasked with designing a system capable of moving mining equipment and materials around the surface of the Moon using a propolsive landing. The system had to be tested on earth with something that was feasible for our team to build in 2 semesters. One of the first considerations my capstone advisor wanted was to test the feasibility of an air propulsion system instead of the obvious solution that of using solid rocket motors. This document is really just <em>napkin math</em> to determine if the system is even feasibly and is not mean’t to be a rigorous study of an air propulsion system which would easily keep a capstone team busy by itself.</p>
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<p>For Capstone my team was tasked with designing a system capable of moving mining equipment and materials around the surface of the Moon using a propulsive landing. The system had to be tested on Earth with something feasible for our team to build in 2 semesters. One of the first considerations my capstone advisor wanted was to test the feasibility of an air propulsion system instead of the obvious solution that of using solid rocket motors. This document is just <em>napkin math</em> to determine if the system is even feasibly and is not meant to be a rigorous study of an air propulsion system that would easily keep a capstone team busy by itself.</p>
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<div class="layout-chunk" data-layout="l-body">
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<details>
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<summary>
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@@ -1501,7 +1502,7 @@ Show code
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</div>
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<h2 id="the-simulation">The Simulation</h2>
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<p>An off the shelf paintball gun tank was used for the pressure vessel. This was chosen because they are very high pressure for their weight, and are designed to be bumped around.</p>
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<p>I chose an off-the-shelf paintball gun tank for the pressure vessel. The primary consideration was the incredible pressure to weight ratio, and the fact that it is designed to be bumped around would be necessary for proving the safety of the system further into the project.</p>
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<div class="layout-chunk" data-layout="l-body">
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<div class="sourceCode" id="cb2"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Tank https://www.amazon.com/Empire-Paintball-BASICS-Pressure-Compressed/dp/B07B6M48SR/</span></span>
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<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>V <span class="op">=</span> (<span class="fl">85</span> ± <span class="fl">5</span>)u<span class="st">"inch^3"</span></span>
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<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>Wtank <span class="op">=</span> (<span class="fl">2.3</span> ± <span class="fl">0.2</span>)u<span class="st">"lb"</span></span>
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<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>Pmax <span class="op">=</span> (<span class="fl">250</span> ± <span class="fl">50</span>)u<span class="st">"psi"</span> <span class="co"># Max Pressure that can come out the nozzle</span></span></code></pre></div>
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</div>
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<p>The nozzle diameter was changed until the air prop system had a <em>burn time</em> similar to a G18ST rocket motor.</p>
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<p>The nozzle diameter was changed until the air prop system had a <em>burn time</em> similar to a G18ST rocket motor. The propulsion system’s total impulse is not dependant on the nozzle diameter, so this was just done to make it plot nicely with the rest of the rocket motors since, at this time, it is unknown what the optimal thrust profile is.</p>
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<div class="layout-chunk" data-layout="l-body">
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<div class="sourceCode" id="cb3"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Params</span></span>
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<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>d_nozzle <span class="op">=</span> ((<span class="fl">1</span> <span class="op">//</span> <span class="fl">18</span>) ± <span class="fl">0.001</span>)u<span class="st">"inch"</span></span>
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<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>a_nozzle <span class="op">=</span> (<span class="cn">pi</span> <span class="op">/</span> <span class="fl">4</span>) <span class="op">*</span> d_nozzle<span class="op">^</span><span class="fl">2</span></span></code></pre></div>
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</div>
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<p>These are just universal values for what a normal day would look like in Arizona. <span class="citation" data-cites="cengel_thermodynamics">(<a href="#ref-cengel_thermodynamics" role="doc-biblioref">Çengel and Boles 2015</a>)</span></p>
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<p>These are just universal values for what a typical day would look like during the summer in Northern Arizona. <span class="citation" data-cites="cengel_thermodynamics">(<a href="#ref-cengel_thermodynamics" role="doc-biblioref">Çengel and Boles 2015</a>)</span></p>
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<div class="layout-chunk" data-layout="l-body">
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<div class="sourceCode" id="cb4"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Universal Stuff</span></span>
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<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>P_amb <span class="op">=</span> (<span class="fl">1</span> ± <span class="fl">0.2</span>)u<span class="st">"atm"</span></span>
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<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>R <span class="op">=</span> <span class="fl">287.05</span>u<span class="st">"J/(kg * K)"</span></span>
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<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>T <span class="op">=</span> (<span class="fl">300</span> ± <span class="fl">20</span>)u<span class="st">"K"</span></span></code></pre></div>
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</div>
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<p>The actual simulation is actually quite simple. The basic idea is that using the current pressure you can calculate <span class="math inline">\(\dot{m}\)</span>, which allows calculating the Thrust, and then you can just subtract the current mass of air in the tank by <span class="math inline">\(\dot{m}\)</span> and recalculate pressure using the new mass then repeat the whole process.</p>
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<p>The actual simulation is quite simple. The basic idea is that using the current pressure, you can calculate <span class="math inline">\(\dot{m}\)</span>, which allows calculating the Thrust, and then you can subtract the current mass of air in the tank by <span class="math inline">\(\dot{m}\)</span> and recalculate pressure using the new mass then repeat the whole process.</p>
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<p>The bulk of the equations in the simulation came from <span class="citation" data-cites="cengel_thermodynamics">(<a href="#ref-cengel_thermodynamics" role="doc-biblioref">Çengel and Boles 2015</a>)</span>, while the Thrust and <span class="math inline">\(v_e\)</span> equations came from <span class="citation" data-cites="sutton_rocket_2001">(<a href="#ref-sutton_rocket_2001" role="doc-biblioref">Sutton and Biblarz 2001</a>, eq: 2-14)</span>.</p>
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<p><span class="math display">\[ T = \dot{m} \cdot v_\text{Exit} + A_\text{Nozzle} \cdot (P - P_\text{Ambient}) \]</span></p>
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<p>The initial pressure difference is 4190.0 ± 300.0 psi which is absolutely massive so the area of the nozzle greatly affects the simulation. The paintball tanks do come with pressure regulators, in our case 800 psi which is still a very large number compared to atmospheric pressure. While the total impulse of the system doesn’t really change with different nozzle areas the peak thrust and <em>burn time</em> vary greatly. One of the benefits of doing air propulsion, and the reason it was even considered so seriously, is that it should be possible to vary the nozzle diameter in flight which would make controlled landing much easier.</p>
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<p>The initial pressure difference is 4190.0 ± 300.0 psi, which is massive, so the area of the nozzle significantly alters the thrust profile. The paintball tanks come with pressure regulators, in our case, 800 psi which is still a huge number compared to atmospheric pressure. While the total impulse of the system doesn’t change with different nozzle areas, the peak thrust and <em>burn time</em> vary greatly. One of the benefits of doing air propulsion and the reason it was even considered so seriously is that it should be possible to change the nozzle diameter in flight, allowing thrust to be throttled, making controlled landing easier to control.</p>
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<div class="layout-chunk" data-layout="l-body">
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<div class="sourceCode" id="cb5"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>df <span class="op">=</span> <span class="kw">let</span></span>
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<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>t <span class="op">=</span> <span class="fl">0.0</span>u<span class="st">"s"</span></span>
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<span id="cb5-25"><a href="#cb5-25" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span></code></pre></div>
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</div>
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<h2 id="analysis">Analysis</h2>
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<p>Heres the results plotted. Notice the massive error once the tank starts running low. This is because the calculation for pressure has a lot of variables that are very uncertain. This is mostly due to air being a compressible fluid which is what makes this simulation so difficult to do accurately. The thrust being below 0 N might not make intuitive sense, but its technically possible for the pressure to compress which would leave the inside of the rocket nozzle with a pressure thats actually below atmospheric pressure. The effect would likely last a fraction of a second but the point stands that this simulation is very inaccurate and only meant to get an idea of what an air propulsion system is capable of.</p>
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<p>Below in figure 1, the result of the simulation is plotted. Notice the massive error once the tank starts running low. This is because the calculation for pressure has a lot of very uncertain variables. This is primarily due to air being a compressible fluid, making this simulation challenging to do accurately. The thrust being below 0 N might not make intuitive sense, but it’s technically possible for the pressure to compress, leaving the inside of the rocket nozzle with a pressure that’s actually below atmospheric pressure. The effect would likely last a fraction of a second, but the point stands that this simulation is wildly inaccurate and only meant to get an idea of what an air propulsion system is capable of.</p>
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<details>
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<summary>
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@@ -1584,7 +1585,7 @@ Figure 1: Air Proplsion Simulation
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</p>
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<p>In Figure 2, the air propulsion simulation is compared to commercially available rocket motors. This early in the project we have no idea whether short burns or longer burns are ideal for a propulsive landing so the air propulsion system was compared to a variety of different motors.</p>
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<p>In Figure 2, the air propulsion simulation is compared to commercially available rocket motors. This early in the project, we have no idea whether short burns or longer burns are ideal for a propulsive landing, so the air propulsion system was compared to a variety of different motors with unique profiles.</p>
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<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a>ylabel<span class="op">!</span>(<span class="st">"Thrust (N)"</span>)</span></code></pre></div>
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</details>
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<div class="figure"><span id="fig:unnamed-chunk-7"></span>
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<img src="air-propulsion-simulation_files/figure-html5/unnamed-chunk-7-J1.png" alt="Rocket Motor Data: [@thrustcurve]" width="350" />
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<img src="air-propulsion-simulation_files/figure-html5/unnamed-chunk-7-J1.png" alt="Rocket Motor Data: [@thrustcurve]" width="350" data-distill-preview=1 />
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<p class="caption">
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Figure 2: Rocket Motor Data: <span class="citation" data-cites="thrustcurve">(<a href="#ref-thrustcurve" role="doc-biblioref">Coker, n.d.</a>)</span>
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</p>
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</div>
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</div>
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<p>Big conclusion about things.</p>
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<p>In the end, the air propulsion system’s performance has a very impressive total impulse and, with more time and resources, could be a serious option for a propulsive landing on Earth. One of the largest abstractions from the Moon mission that the mission here on Earth will have to deal with is the lack of Throttling engines since any propulsion system outside of model rocket motors is well beyond the scope of this Capstone.</p>
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<h2 id="future-work">Future Work</h2>
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<p>After determining that solid model rocket motors are the best option for the current mission scope, the next step is determining what motor to use. There are many great options, and deciding what thrust profile is ideal may have to wait until a Simulink simulation of the landing can be built so that the metrics of each motor can be constrained more. Instead of throttling motors, the current working idea is that thrust vector control may be a way to squeeze a little more control out of a solid rocket motor. Thrust Vector Control will undoubtedly be challenging to control, so another essential piece that needs exploring is whether an LQR controller is feasible or if a PID controller is accurate enough to control our system.</p>
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<div class="sourceCode" id="cb8"><pre class="sourceCode r distill-force-highlighting-css"><code class="sourceCode r"></code></pre></div>
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<div id="refs" class="references csl-bib-body hanging-indent" role="doc-bibliography">
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<div id="ref-thrustcurve" class="csl-entry" role="doc-biblioentry">
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@@ -1651,6 +1654,8 @@ Sutton, George P., and Oscar Biblarz. 2001. <em>Rocket Propulsion Elements</em>.
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<div id="references-listing"></div>
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<h3 id="updates-and-corrections">Corrections</h3>
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<p>If you see mistakes or want to suggest changes, please <a href="https://gitlab.com/lander-team/air-prop-simulation">create an issue</a> on the source repository.</p>
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<h3 id="reuse">Reuse</h3>
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<p>Text and figures are licensed under Creative Commons Attribution <a rel="license" href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a>. Source code is available at <a href="https://gitlab.com/lander-team/air-prop-simulation">https://gitlab.com/lander-team/air-prop-simulation</a>, unless otherwise noted. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".</p>
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