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@@ -15,7 +15,7 @@ output:
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categories:
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- Julia
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- Capstone
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bibliography: ../../citations.bib
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bibliography: citations.bib
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creative_commons: CC BY
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---
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@@ -29,7 +29,6 @@ library(JuliaCall)
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```{julia, code_folding=TRUE}
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using Plots
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plotly()
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theme(:ggplot2); # In true R spirit
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using Unitful
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@@ -37,7 +36,6 @@ using DataFrames
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using Measurements
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using Measurements: value, uncertainty
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using CSV
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```
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@@ -60,7 +58,6 @@ The nozzle diameter was changed until the air prop system had a _burn time_ simi
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# Params
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d_nozzle = ((1 // 18) ± 0.001)u"inch"
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a_nozzle = (pi / 4) * d_nozzle^2
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```
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These are just universal values for what a typical day would look like during the summer in Northern Arizona. [@cengel_thermodynamics]
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@@ -71,7 +68,6 @@ P_amb = (1 ± 0.2)u"atm"
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γ = 1.4 ± 0.05
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R = 287.05u"J/(kg * K)"
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T = (300 ± 20)u"K"
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```
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The actual simulation is quite simple. The basic idea is that using the current pressure, you can calculate $\dot{m}$, which allows calculating the Thrust, and then you can subtract the current mass of air in the tank by $\dot{m}$ and recalculate pressure using the new mass then repeat the whole process.
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@@ -109,7 +105,6 @@ df = DataFrame(Thrust=(0 ± 0)u"N", Pressure=P0, Time=0.0u"s", Mass=M)
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end
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df
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end
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```
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## Analysis
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@@ -133,7 +128,6 @@ plot(df.Time .|> ustrip, thrust_values,
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ylabel="Thrust (N)",
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size = (1200, 800),
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)
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```
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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.
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@@ -154,7 +148,6 @@ end
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title!("Propulsion Comparison");
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xlabel!("Time (s)");
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ylabel!("Thrust (N)")
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```
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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.
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@@ -162,5 +155,3 @@ In the end, the air propulsion system's performance has a very impressive total
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## Future Work
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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.
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@@ -1491,14 +1491,13 @@ code span.wa { color: #5e5e5e; font-style: italic; } /* Warning */
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Show code
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</summary>
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<div class="sourceCode" id="cb1"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Plots</span>
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>plotly()</span>
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<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>theme(<span class="op">:</span>ggplot2)<span class="op">;</span> <span class="co"># In true R spirit</span></span>
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<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Unitful</span>
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<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> DataFrames</span>
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<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Measurements</span>
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<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Measurements<span class="op">:</span> value<span class="op">,</span> uncertainty</span>
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<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> CSV</span></code></pre></div>
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>theme(<span class="op">:</span>ggplot2)<span class="op">;</span> <span class="co"># In true R spirit</span></span>
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<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Unitful</span>
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<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> DataFrames</span>
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<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Measurements</span>
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<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Measurements<span class="op">:</span> value<span class="op">,</span> uncertainty</span>
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<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> CSV</span></code></pre></div>
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</details>
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</div>
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<h2 id="the-simulation">The Simulation</h2>
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@@ -1579,7 +1578,7 @@ Show code
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<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a> )</span></code></pre></div>
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</details>
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<div class="figure"><span id="fig:unnamed-chunk-6"></span>
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<img src="air-propulsion-simulation_files/figure-html5/unnamed-chunk-6-J1.png" alt="Air Proplsion Simulation" width="350" data-distill-preview=1 />
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<img src="air-propulsion-simulation_files/figure-html5/unnamed-chunk-6-J1.png" alt="Air Proplsion Simulation" width="600" data-distill-preview=1 />
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<p class="caption">
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Figure 1: Air Proplsion Simulation
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</p>
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@@ -1608,7 +1607,7 @@ Show code
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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" data-distill-preview=1 />
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<img src="air-propulsion-simulation_files/figure-html5/unnamed-chunk-7-J1.png" alt="Rocket Motor Data: [@thrustcurve]" width="600" 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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54
_posts/2021-04-01-air-propulsion-simulation/citations.bib
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54
_posts/2021-04-01-air-propulsion-simulation/citations.bib
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@@ -0,0 +1,54 @@
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@book{shackelford_introduction_2015,
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address = {Boston},
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edition = {Eighth edition},
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title = {Introduction to materials science for engineers},
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isbn = {9780133826654},
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publisher = {Pearson},
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author = {Shackelford, James F.},
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year = {2015},
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keywords = {Materials}
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}
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@book{curtis_orbital,
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title = {Orbital mechanics for engineering students},
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isbn = {9780128240250 9780323853453 9780081021330},
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language = {English},
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author = {Curtis, Howard D},
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year = {2020},
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note = {OCLC: 1235349370},
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publisher = {Butterworth-Heinemann Publications},
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edition = {Fourth edition}
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}
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@misc{thrustcurve,
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title = {Rocket {Motor} {Data}},
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url = {https://www.thrustcurve.org/},
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author = {Coker, John}
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}
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@book{cengel_thermodynamics,
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address = {New York},
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edition = {Eighth edition},
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title = {Thermodynamics: an engineering approach},
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isbn = {9780073398174},
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shorttitle = {Thermodynamics},
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publisher = {McGraw-Hill Education},
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author = {Çengel, Yunus A. and Boles, Michael A.},
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year = {2015},
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note = {OCLC: ocn869741544},
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keywords = {Thermodynamics}
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}
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@book{sutton_rocket_2001,
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address = {New York},
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edition = {7th ed},
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title = {Rocket propulsion elements},
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isbn = {9780471326427},
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publisher = {John Wiley \& Sons},
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author = {Sutton, George P. and Biblarz, Oscar},
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year = {2001},
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keywords = {Rocket engines}
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}
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