From bd67c9682abcffa24f2bb9bdc2582755c56a3d5c Mon Sep 17 00:00:00 2001 From: Anson Biggs Date: Mon, 3 May 2021 21:37:31 -0700 Subject: [PATCH] Update Air Prop Thumbnail --- .../air-propulsion-simulation.Rmd | 2 +- .../air-propulsion-simulation.html | 2 +- .../figure-html5/unnamed-chunk-6-J1.png | Bin 23076 -> 22805 bytes .../figure-html5/unnamed-chunk-7-J1.png | Bin 48394 -> 49257 bytes docs/index.html | 2 +- docs/index.xml | 122 +++++++++++++++++- .../figure-html5/unnamed-chunk-6-J1.png | Bin 23076 -> 22805 bytes .../figure-html5/unnamed-chunk-7-J1.png | Bin 48394 -> 49257 bytes .../index.html | 6 +- docs/posts/posts.json | 6 +- docs/search.json | 4 +- docs/sitemap.xml | 2 +- 12 files changed, 132 insertions(+), 14 deletions(-) diff --git a/_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.Rmd b/_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.Rmd index 6282d4b..083db74 100644 --- a/_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.Rmd +++ b/_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.Rmd @@ -112,7 +112,7 @@ end 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. -```{julia, code_folding=TRUE, results='show',layout="l-body-outset", fig.cap = "Air Proplsion Simulation", preview=TRUE} +```{julia, code_folding=TRUE, results='show',layout="l-body-outset", fig.cap = "Air Proplsion Simulation", preview=FALSE} thrust_values = df.Thrust .|> ustrip .|> value; thrust_uncertainties = df.Thrust .|> ustrip .|> uncertainty; diff --git a/_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.html b/_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.html index 276f3bb..526223f 100644 --- a/_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.html +++ b/_posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation.html @@ -1580,7 +1580,7 @@ Show code )
-Air Proplsion Simulation +Air Proplsion Simulation

Figure 1: Air Proplsion Simulation

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- +

Air Propulsion Simulation

diff --git a/docs/index.xml b/docs/index.xml index 28431b0..b289d4f 100644 --- a/docs/index.xml +++ b/docs/index.xml @@ -23,12 +23,130 @@ Air Propulsion Simulation Anson Biggs https://projects.ansonbiggs.com/posts/2021-04-01-air-propulsion-simulation - Simulating the performance of an air propulsion system as an alternative to solid rocket motors. + + + +<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> +<pre class="julia"><code>using Plots +theme(:ggplot2); # In true R spirit + +using Unitful +using DataFrames +using Measurements +using Measurements: value, uncertainty +using CSV</code></pre> +<h2 id="the-simulation">The Simulation</h2> +<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> +<pre class="julia"><code># Tank https://www.amazon.com/Empire-Paintball-BASICS-Pressure-Compressed/dp/B07B6M48SR/ +V = (85 ± 5)u&quot;inch^3&quot; +P0 = (4200.0 ± 300)u&quot;psi&quot; +Wtank = (2.3 ± 0.2)u&quot;lb&quot; +Pmax = (250 ± 50)u&quot;psi&quot; # Max Pressure that can come out the nozzle</code></pre> +<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> +<pre class="julia"><code># Params +d_nozzle = ((1 // 18) ± 0.001)u&quot;inch&quot; +a_nozzle = (pi / 4) * d_nozzle^2</code></pre> +<p>These are just universal values for what a typical day would look like during the summer in Northern Arizona. <span class="citation">(Çengel and Boles 2015)</span></p> +<pre class="julia"><code># Universal Stuff +P_amb = (1 ± 0.2)u&quot;atm&quot; +γ = 1.4 ± 0.05 +R = 287.05u&quot;J/(kg * K)&quot; +T = (300 ± 20)u&quot;K&quot;</code></pre> +<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> +<p>The bulk of the equations in the simulation came from <span class="citation">(Çengel and Boles 2015)</span>, while the Thrust and <span class="math inline">\(v_e\)</span> equations came from <span class="citation">(Sutton and Biblarz 2001, eq: 2-14)</span>.</p> +<p><span class="math display">\[ T = \dot{m} \cdot v_\text{Exit} + A_\text{Nozzle} \cdot (P - P_\text{Ambient}) \]</span></p> +<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> +<pre class="julia"><code>df = let +t = 0.0u&quot;s&quot; +P = P0 |&gt; u&quot;Pa&quot; +M = V * (P / (R * T)) |&gt; u&quot;kg&quot; +ts = 1u&quot;ms&quot; +df = DataFrame(Thrust=(0 ± 0)u&quot;N&quot;, Pressure=P0, Time=0.0u&quot;s&quot;, Mass=M) + while M &gt; 0.005u&quot;kg&quot; + # Calculate what is leaving tank + P = minimum([P, Pmax]) + ve = sqrt((2 * γ / (γ - 1)) * R * T * (1 - P_amb / P)^((γ - 1) / γ)) |&gt; u&quot;m/s&quot; + ρ = P / (R * T) |&gt; u&quot;kg/m^3&quot; + ṁ = ρ * a_nozzle * ve |&gt; u&quot;kg/s&quot; + + Thrust = ṁ * ve + a_nozzle * (P - P_amb) |&gt; u&quot;N&quot; + + # Calculate what is still in the tank + M = M - ṁ * ts |&gt; u&quot;kg&quot; + P = (M * R * T) / V |&gt; u&quot;Pa&quot; + t = t + ts + + df_step = DataFrame(Thrust=Thrust, Pressure=P, Time=t, Mass=M) + append!(df, df_step) + end + df +end</code></pre> +<h2 id="analysis">Analysis</h2> +<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> +<pre class="julia"><code> +thrust_values = df.Thrust .|&gt; ustrip .|&gt; value; +thrust_uncertainties = df.Thrust .|&gt; ustrip .|&gt; uncertainty; + +air = DataFrame(Thrust=thrust_values, Uncertainty=thrust_uncertainties, Time=df.Time .|&gt; u&quot;s&quot; .|&gt; ustrip); + + +plot(df.Time .|&gt; ustrip, thrust_values, + title=&quot;Thrust Over Time&quot;, + ribbon=(thrust_uncertainties, thrust_uncertainties), + fillalpha=.2,label=&quot;Thrust&quot;, + xlabel=&quot;Time (s)&quot;, + ylabel=&quot;Thrust (N)&quot;, + size = (1200, 800), + )</code></pre> +<div class="figure"> +<img src="file571aee56c6a_files/figure-html/unnamed-chunk-6-J1.png" alt="Air Proplsion Simulation" width="600" /> +<p class="caption"> +(#fig:unnamed-chunk-6)Air Proplsion Simulation +</p> +</div> +<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> +<pre class="julia"><code> +f10 = CSV.read(&quot;AeroTech_F10.csv&quot;, DataFrame); +f15 = CSV.read(&quot;Estes_F15.csv&quot;, DataFrame); +g8 = CSV.read(&quot;AeroTech_G8ST.csv&quot;, DataFrame); + + +plot(air.Time, air.Thrust, label=&quot;Air Propulsion&quot;, fillalpha=.1, legend=:topleft, size = (1200, 800)); + +for (d, l) in [(f10, &quot;F10&quot;), (f15, &quot;F15&quot;), (g8, &quot;G8ST&quot;)] + plot!(d[!,&quot;Time (s)&quot;], d[!, &quot;Thrust (N)&quot;], label=l); +end + +title!(&quot;Propulsion Comparison&quot;); +xlabel!(&quot;Time (s)&quot;); +ylabel!(&quot;Thrust (N)&quot;)</code></pre> +<div class="figure"> +<img src="file571aee56c6a_files/figure-html/unnamed-chunk-7-J1.png" alt="Rocket Motor Data: [@thrustcurve]" width="600" data-distill-preview=1 /> +<p class="caption"> +(#fig:unnamed-chunk-7)Rocket Motor Data: <span class="citation">(Coker, n.d.)</span> +</p> +</div> +<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> +<h2 id="future-work">Future Work</h2> +<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> +<pre class="r distill-force-highlighting-css"><code></code></pre> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-thrustcurve" class="csl-entry"> +Coker, John. n.d. <span>“Rocket <span>Motor</span> <span>Data</span>.”</span> <a href="https://www.thrustcurve.org/">https://www.thrustcurve.org/</a>. +</div> +<div id="ref-cengel_thermodynamics" class="csl-entry"> +Çengel, Yunus A., and Michael A. Boles. 2015. <em>Thermodynamics: An Engineering Approach</em>. Eighth edition. New York: McGraw-Hill Education. +</div> +<div id="ref-sutton_rocket_2001" class="csl-entry"> +Sutton, George P., and Oscar Biblarz. 2001. <em>Rocket Propulsion Elements</em>. 7th ed. New York: John Wiley &amp; Sons. +</div> +</div> + dbf2ace5c1414ee7c72e89cac1535434 Julia Capstone https://projects.ansonbiggs.com/posts/2021-04-01-air-propulsion-simulation Thu, 01 Apr 2021 00:00:00 +0000 - + diff --git a/docs/posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation_files/figure-html5/unnamed-chunk-6-J1.png b/docs/posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation_files/figure-html5/unnamed-chunk-6-J1.png index 250f2d906255b23410337d30c46b6df969943ddd..2030850df301d6088c9d9941a0acc087719ae4a2 100644 GIT binary patch literal 22805 zcmb@ucRW|`8$YghOGXq$G7}jY$rj4Y&WN&JS=p4D%zsIllAMfM5&biNhU-xxi^LbrwA1F!_;!)t?;NTF-+?P|QIcW);Bjmr&m8qdPIJ7u268F@cJ}nHt_@r$V!|`WJO(UmY=o}rs zmzSiN816fQXs$Whrj)!)PujGWH-2PBUj9Kg_i}7bpE)}jWFjGbC5LI`$}iTF+pkW% z=b_EK(DDzi%u7W z6OGq(;Qu&{#JDHORrp4nCPoj2M}?2}*JQ}@4%D-?cmCEAiSGZcW!1=*FAHC^T`cT# zUr(gb$<>$a^u~F2=N0iwD*I8ltwMrt-ekJuVkI-NE>%NOU+KD@Q zF%ihe%g5JOGRYQs+gLI8(L#0Uv#F*!e=?;{{I;75{a2U68x5!1V#@VueFCG;y!2rp z{^x7r=AdC8_F*{Afy{GSH zob$rDK7F{ij43ctW(<8XuQe)YJyH?4teLA{$C^{Y<+i(ij)d{f&SWS;5+$W}Y0=$| z3-nTVR(_DsO9lLPS+3+8@#x8T=&@Z(<1lRB_m<>_RmIBpvox+_-eg>nEkE9pkllR5 z`Fy&CxCW>l&aR`GuI5)ao*?O;Arwr(W0q67>0B!q=dx6qnNwAko{miwJ-{+jS>+qI zSHWb@3$OoziL6f09BnU^FOT%~Z7t-tTj}cI#upcF6$4Qi9m8ak_u#ik<5=d){w@o- z4Hu*-J4QyTRuW^K#^3S>&9p{GG*4MoA8Z;mhcD(fP&ZIH4&jVWwz56WODZpSfjzLa zwCrK?zszQ4X&H0dxNV@&++)Qb^W{;letp1|2FmC1h3&V4CXRMu#wAF z`Do?J&TMGh{$zc*jzhl@o!5L$^&zm&;;8Y;cwJ7_t{LvwA5Wr@$*&qZ_78E#%I34@ zN1tu&9YO2(8$8ney!-fIPTc?M6gFbRmRFf4L(P} z1b_x1|KjziCEC?@&NQsAmme!z>`)a7d`R%T_L%Y?<#;etS#T8R*O2Ql6>i(x_ zZ5hK((4K(fyp-`U(|vz}M)Yud0*<9)eK5^YptbA7=+VI_U;pB2Gl$1)yl>S?p!NQo zM)hu^k~^3C{`LuKkB$V%xV@nnhmjXEz#t9PM+eIhHy=L(F@Ul8e%hcRh>&i70|Y~i z<4AvJXJ>!^i5gsBLyfG*`O`o^x24hBXQAKpJucybpi8=Mti|I&2I0IvoXbv490*_Q%PPMNYn#t~%VE_td?C z^V4RgT(MGjNXkx~@5X=jp5qMZqd51lE5j@s;w^I654(ygV>XB1=a z?12+ipJz@&^w1PDil2U7wC)j7`lsIxqcPr#68ZZXTXt+Xkw$)J{(}a?euQ+?AGY z00C*&%G2k%(~Qa1X~kLK7Y0H12jRk_(-w4Ij+OH|bY370Eb|7_Q)A2Ao`GKmvd+aYN&E+#0ALTS*=v)@)rn^HsX4? zGehJ0_d8JCvU6qo6_M+cp%UBb?K%$L7k>EcB~KbKKQButulKjR7adK{b|fPFL0p3f zy1<+>`}5U@^Iw(a5PswU4gfwFjysbH3;V?6$LnzkCn=Cx4CmtC@Zt)iiD;q40##DU z=$y5xc9A`c(UsA?kuAlKoMS#$txD#z%Yy`_KO+0M?A%vg^lrAu;>Vi{!^6Xsm6g^- z;v3oT>7_TV1r`gs*h~JrrrG~GGZEFYN8NhmC|-&vjF z$s~LEosRgQcQ1p2fdazzr0RrIeekub{tu9^Vdw=(8Sb2v^`y`3L-urOebylk$e zsi`P>u%6?#Xx`I|TijS++6Baq0Ii|pZu7h+_8UmdWRGS!g3gn&EJR{c+wT5asv&%Zd8H=BZ}~=PW0GzK^aj@U&W+(70+8%B+;g zgm<-2ZR6qoG+*`3qP0hPW9{JJAYWYf*_Q>k3`t))t0*w{yuHQO+trod7=GpUQ$)EU z)68+-$n@u^a)NV$9Qk&^`7eu3onSiL^s)inQqh0Dr#z$lp+Xcl_9uO?c9rXn+tx4{ z?^O}WDkBW|#OYXcITR<_1m`s)1$ybx(5sK9FFyuUfH;7^f)o zF7937MnkUh#iBtuV8`_?r7i3I;bnKnX0~FBia{U3tGqA%{LVEH5)@E*|{#71h?6sWj{T@))d!zab2ARU28>mWKf+(^&{dKp8B70^AyU-o98oTD4QT zvC4u&5owNlBJDQK_P4W#4M*EF4KyD65!L%s>8h#hngz3Y&Fs-4Zo6ykqNCOAh^Yi} z8WwJv53}JiYVy0pifEEA+NG=T1Jx~k3H!L6wHXfGifz!JqPw$+(gEbRjG8{o`7K({ zYK`vp;&W8|{UuJ+8Y{e~8n>%vuhJ^%e;LvKV3;($K8;_s(`s$C`fl#ES0BdXK=g1z z)F&{UX2G$RkdM;gw_e=#j~kcSH0@e$HMD%ZHBs27>jDzPx@u<{PEu)#zdS)W`~zE- z+HJi9bkANJXo>2b=;}zIEzI^Zhpuav0$(NQVMP5!*#+WQyoG&=Dg9f6PXq779qrE` z#1O-cl%L*TYmWmFJ_CyW&<*U12y3@_Ekxqf6Wy8qXpqsj`cTKV?h+i^GQ?^E;u6;g zjjRN*ovLYTYXduMW*m4Mq&r91Y{KCpSVl8(9*1>gn2HtB#Dfg{i<_I9Ru%hCs)47s zz;qM^(QggrcwlOHB){!Aqq%ZYKNw)PASPm;w+U$IzL*Nr(Cx2w17o#+pW);?US%Cj z8O~inHcVB;qnnCxB5rFh7%^@eJ-}M>kz7U-_PFA>auMv7R#r=KY5C>l<$}3Q(OH*P zz$g*{OB7~g?J_v{wB=*2!{R`8b~ae3Y7wUh=q8_)!oDEG?%IL*7%T96db)u*q8S{E zmYKE1#l_GYN+WY}^NWj!49B?dOcB>~r>i1Lovr=ou}+rz`fP{R$6FhSAp>S4uf=ap zy&5lUS1OIow-X8q3I|(NKyh12>v`vZ`Q9w8LbINq@9FtGlv&lk{Qjy}Tc4HR7>$9u z8L_dkz>GyjMVrW*k#S zV({g-nL?YuVd7?bMT~><`5xHl;PA=Pp2EQ~dGHS%xKy4OaZljjP<*(Hi-Ys)Gl&eF zmuJ9f_&}PVWy*{U(}ZR5u*2W)XFbMA;&ACm{p%1L4_uce zEOsaOXgk;t0p3wWBDKefR_`92 z#=m?AOiVg2;LW1^{O9m4ofq&FVu34xJLVwD0dIQh!<(ZIG&K4^hh!Yl@L3Jb^<;|U zW@_XtjXoM4>FMG5c9LDYZBsQe3k==T6CD`|~5+buVHu z#!yph>);7~tXR=^T93?T!^5E|@&?T?)A*`MzCD*2MeA!|G|%H{AC#F73+350CnZ<8JIIn7)h7 z&d<*uU?mrOl>bzr(BLajqcw`>VDF1=rStdKr%&Gb<14Zre`2Y>r{`hf&Dhqb(b3Uo zJC$V=B$bmcU5sdbitjBZ5~o!5&IcTCO-;>brP{Ep0w%wK!NCJ`WwM4`R|wyioDw~6 z?yqc;ohp($U}|m-R>agZ0j$_z8dx})dj!vD@BDdrk{Y-PRsD#HpaT1w&g*ghQ#fTD zm?~G`0j)~sjm~5_a6~7sTyLjHwkIrso@W+ zm1<|Ju@D-`XcZp3vKg!K2Jg@rgBexe8|H=pMX<;IL`+P~GB_#iLdzAvMvQ(5(x3&v z*FR5ZXJ_}xb+r)@wTN{EGpgJhULJ9B0~ujrs7zW|SZE27O8R`rlNJ-acr_)1>*glS zS-*OF!_`biUz?QsK4#agaGE$F2g)*I^M1BY`DVN?H69%$L{tpw1F)lG*wi@PB8z^o z%*?p=

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-Air Proplsion Simulation +Air Proplsion Simulation

Figure 1: Air Proplsion Simulation

diff --git a/docs/posts/posts.json b/docs/posts/posts.json index 5b0d490..1b2ba66 100644 --- a/docs/posts/posts.json +++ b/docs/posts/posts.json @@ -37,9 +37,9 @@ "Capstone" ], "contents": "\nFor 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 napkin math 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.\n\n\nShow code\nusing Plots\ntheme(:ggplot2); # In true R spirit\n\nusing Unitful\nusing DataFrames\nusing Measurements\nusing Measurements: value, uncertainty\nusing CSV\n\nThe Simulation\nI 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.\n\n# Tank https://www.amazon.com/Empire-Paintball-BASICS-Pressure-Compressed/dp/B07B6M48SR/\nV = (85 ± 5)u\"inch^3\"\nP0 = (4200.0 ± 300)u\"psi\"\nWtank = (2.3 ± 0.2)u\"lb\"\nPmax = (250 ± 50)u\"psi\" # Max Pressure that can come out the nozzle\n\nThe nozzle diameter was changed until the air prop system had a burn time 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.\n\n# Params\nd_nozzle = ((1 // 18) ± 0.001)u\"inch\"\na_nozzle = (pi / 4) * d_nozzle^2\n\nThese are just universal values for what a typical day would look like during the summer in Northern Arizona. (Çengel and Boles 2015)\n\n# Universal Stuff\nP_amb = (1 ± 0.2)u\"atm\"\nγ = 1.4 ± 0.05\nR = 287.05u\"J/(kg * K)\"\nT = (300 ± 20)u\"K\"\n\nThe 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.\nThe bulk of the equations in the simulation came from (Çengel and Boles 2015), while the Thrust and \\(v_e\\) equations came from (Sutton and Biblarz 2001, eq: 2-14).\n\\[ T = \\dot{m} \\cdot v_\\text{Exit} + A_\\text{Nozzle} \\cdot (P - P_\\text{Ambient}) \\]\nThe 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 burn time 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.\n\ndf = let\nt = 0.0u\"s\"\nP = P0 |> u\"Pa\"\nM = V * (P / (R * T)) |> u\"kg\"\nts = 1u\"ms\"\ndf = DataFrame(Thrust=(0 ± 0)u\"N\", Pressure=P0, Time=0.0u\"s\", Mass=M)\n while M > 0.005u\"kg\"\n # Calculate what is leaving tank\n P = minimum([P, Pmax])\n ve = sqrt((2 * γ / (γ - 1)) * R * T * (1 - P_amb / P)^((γ - 1) / γ)) |> u\"m/s\"\n ρ = P / (R * T) |> u\"kg/m^3\"\n ṁ = ρ * a_nozzle * ve |> u\"kg/s\"\n \n Thrust = ṁ * ve + a_nozzle * (P - P_amb) |> u\"N\"\n \n # Calculate what is still in the tank\n M = M - ṁ * ts |> u\"kg\"\n P = (M * R * T) / V |> u\"Pa\"\n t = t + ts\n \n df_step = DataFrame(Thrust=Thrust, Pressure=P, Time=t, Mass=M)\n append!(df, df_step)\n end\n df\nend\n\nAnalysis\nBelow 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.\n\n\nShow code\n\nthrust_values = df.Thrust .|> ustrip .|> value;\nthrust_uncertainties = df.Thrust .|> ustrip .|> uncertainty;\n\nair = DataFrame(Thrust=thrust_values, Uncertainty=thrust_uncertainties, Time=df.Time .|> u\"s\" .|> ustrip);\n\n\nplot(df.Time .|> ustrip, thrust_values, \n title=\"Thrust Over Time\", \n ribbon=(thrust_uncertainties, thrust_uncertainties), \n fillalpha=.2,label=\"Thrust\",\n xlabel=\"Time (s)\", \n ylabel=\"Thrust (N)\",\n size = (1200, 800),\n )\n\n\nFigure 1: Air Proplsion Simulation\n\n\n\nIn 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.\n\n\nShow code\n\nf10 = CSV.read(\"AeroTech_F10.csv\", DataFrame);\nf15 = CSV.read(\"Estes_F15.csv\", DataFrame);\ng8 = CSV.read(\"AeroTech_G8ST.csv\", DataFrame);\n\n\nplot(air.Time, air.Thrust, label=\"Air Propulsion\", fillalpha=.1, legend=:topleft, size = (1200, 800));\n\nfor (d, l) in [(f10, \"F10\"), (f15, \"F15\"), (g8, \"G8ST\")]\n plot!(d[!,\"Time (s)\"], d[!, \"Thrust (N)\"], label=l);\nend\n\ntitle!(\"Propulsion Comparison\");\nxlabel!(\"Time (s)\");\nylabel!(\"Thrust (N)\")\n\n\nFigure 2: Rocket Motor Data: (Coker, n.d.)\n\n\n\nIn 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.\nFuture Work\nAfter 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.\n\n\n\nCoker, John. n.d. “Rocket Motor Data.” https://www.thrustcurve.org/.\n\n\nÇengel, Yunus A., and Michael A. Boles. 2015. Thermodynamics: An Engineering Approach. Eighth edition. New York: McGraw-Hill Education.\n\n\nSutton, George P., and Oscar Biblarz. 2001. Rocket Propulsion Elements. 7th ed. New York: John Wiley & Sons.\n\n\n\n\n", - "preview": "posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation_files/figure-html5/unnamed-chunk-6-J1.png", - "last_modified": "2021-05-03T19:31:26-07:00", - "input_file": {}, + "preview": "posts/2021-04-01-air-propulsion-simulation/air-propulsion-simulation_files/figure-html5/unnamed-chunk-7-J1.png", + "last_modified": "2021-05-03T21:36:23-07:00", + "input_file": "air-propulsion-simulation.utf8.md", "preview_width": 1200, "preview_height": 800 } diff --git a/docs/search.json b/docs/search.json index 942bb99..a9cc35d 100644 --- a/docs/search.json +++ b/docs/search.json @@ -6,14 +6,14 @@ "description": "I'm an Astronautical Engineer studying at Embry-Riddle Prescott.", "author": [], "contents": "\nI mostly write code, but sometimes I make 3D Models. This website is where I plan on breaking down some of my more interesting findings and sharing them with the World Wide Web. If you think I could be a could fit at your company then take a look at my Resume, otherwise you can reach me on Telegram or by Email.\n\n\n\n", - "last_modified": "2021-05-03T21:24:36-07:00" + "last_modified": "2021-05-03T21:28:01-07:00" }, { "path": "index.html", "title": "Anson's Projects", "author": [], "contents": "\n\n\n\n", - "last_modified": "2021-05-03T21:24:37-07:00" + "last_modified": "2021-05-03T21:28:01-07:00" } ], "collections": ["posts/posts.json"] diff --git a/docs/sitemap.xml b/docs/sitemap.xml index 9ef6d72..899b56f 100644 --- a/docs/sitemap.xml +++ b/docs/sitemap.xml @@ -14,6 +14,6 @@ https://projects.ansonbiggs.com/posts/2021-04-01-air-propulsion-simulation/ - 2021-05-03T19:31:26-07:00 + 2021-05-03T21:36:23-07:00