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1662 lines
63 KiB
HTML
1662 lines
63 KiB
HTML
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|
||
d-byline,
|
||
d-footnote-list,
|
||
d-citation-list,
|
||
distill-footer {
|
||
grid-template-columns: [screen-start] 1fr [page-start kicker-start] 80px [middle-start] 50px [text-start kicker-end] 65px 65px 65px 65px 65px 65px 65px 65px [text-end gutter-start] 65px [middle-end] 65px [page-end gutter-end] 1fr [screen-end];
|
||
grid-column-gap: 16px;
|
||
}
|
||
|
||
.grid {
|
||
grid-column-gap: 16px;
|
||
}
|
||
|
||
d-article {
|
||
font-size: 1.06rem;
|
||
line-height: 1.7em;
|
||
}
|
||
figure .caption, .figure .caption, figure figcaption {
|
||
font-size: 13px;
|
||
}
|
||
}
|
||
|
||
@media(min-width: 1180px) {
|
||
.base-grid,
|
||
distill-header,
|
||
d-title,
|
||
d-abstract,
|
||
d-article,
|
||
d-appendix,
|
||
distill-appendix,
|
||
d-byline,
|
||
d-footnote-list,
|
||
d-citation-list,
|
||
distill-footer {
|
||
grid-template-columns: [screen-start] 1fr [page-start kicker-start] 60px [middle-start] 60px [text-start kicker-end] 60px 60px 60px 60px 60px 60px 60px 60px [text-end gutter-start] 60px [middle-end] 60px [page-end gutter-end] 1fr [screen-end];
|
||
grid-column-gap: 32px;
|
||
}
|
||
|
||
.grid {
|
||
grid-column-gap: 32px;
|
||
}
|
||
}
|
||
|
||
|
||
/* Get the citation styles for the appendix (not auto-injected on render since
|
||
we do our own rendering of the citation appendix) */
|
||
|
||
d-appendix .citation-appendix,
|
||
.d-appendix .citation-appendix {
|
||
font-size: 11px;
|
||
line-height: 15px;
|
||
border-left: 1px solid rgba(0, 0, 0, 0.1);
|
||
padding-left: 18px;
|
||
border: 1px solid rgba(0,0,0,0.1);
|
||
background: rgba(0, 0, 0, 0.02);
|
||
padding: 10px 18px;
|
||
border-radius: 3px;
|
||
color: rgba(150, 150, 150, 1);
|
||
overflow: hidden;
|
||
margin-top: -12px;
|
||
white-space: pre-wrap;
|
||
word-wrap: break-word;
|
||
}
|
||
|
||
/* Include appendix styles here so they can be overridden */
|
||
|
||
d-appendix {
|
||
contain: layout style;
|
||
font-size: 0.8em;
|
||
line-height: 1.7em;
|
||
margin-top: 60px;
|
||
margin-bottom: 0;
|
||
border-top: 1px solid rgba(0, 0, 0, 0.1);
|
||
color: rgba(0,0,0,0.5);
|
||
padding-top: 60px;
|
||
padding-bottom: 48px;
|
||
}
|
||
|
||
d-appendix h3 {
|
||
grid-column: page-start / text-start;
|
||
font-size: 15px;
|
||
font-weight: 500;
|
||
margin-top: 1em;
|
||
margin-bottom: 0;
|
||
color: rgba(0,0,0,0.65);
|
||
}
|
||
|
||
d-appendix h3 + * {
|
||
margin-top: 1em;
|
||
}
|
||
|
||
d-appendix ol {
|
||
padding: 0 0 0 15px;
|
||
}
|
||
|
||
@media (min-width: 768px) {
|
||
d-appendix ol {
|
||
padding: 0 0 0 30px;
|
||
margin-left: -30px;
|
||
}
|
||
}
|
||
|
||
d-appendix li {
|
||
margin-bottom: 1em;
|
||
}
|
||
|
||
d-appendix a {
|
||
color: rgba(0, 0, 0, 0.6);
|
||
}
|
||
|
||
d-appendix > * {
|
||
grid-column: text;
|
||
}
|
||
|
||
d-appendix > d-footnote-list,
|
||
d-appendix > d-citation-list,
|
||
d-appendix > distill-appendix {
|
||
grid-column: screen;
|
||
}
|
||
|
||
/* Include footnote styles here so they can be overridden */
|
||
|
||
d-footnote-list {
|
||
contain: layout style;
|
||
}
|
||
|
||
d-footnote-list > * {
|
||
grid-column: text;
|
||
}
|
||
|
||
d-footnote-list a.footnote-backlink {
|
||
color: rgba(0,0,0,0.3);
|
||
padding-left: 0.5em;
|
||
}
|
||
|
||
|
||
|
||
/* Anchor.js */
|
||
|
||
.anchorjs-link {
|
||
/*transition: all .25s linear; */
|
||
text-decoration: none;
|
||
border-bottom: none;
|
||
}
|
||
*:hover > .anchorjs-link {
|
||
margin-left: -1.125em !important;
|
||
text-decoration: none;
|
||
border-bottom: none;
|
||
}
|
||
|
||
/* Social footer */
|
||
|
||
.social_footer {
|
||
margin-top: 30px;
|
||
margin-bottom: 0;
|
||
color: rgba(0,0,0,0.67);
|
||
}
|
||
|
||
.disqus-comments {
|
||
margin-right: 30px;
|
||
}
|
||
|
||
.disqus-comment-count {
|
||
border-bottom: 1px solid rgba(0, 0, 0, 0.4);
|
||
cursor: pointer;
|
||
}
|
||
|
||
#disqus_thread {
|
||
margin-top: 30px;
|
||
}
|
||
|
||
.article-sharing a {
|
||
border-bottom: none;
|
||
margin-right: 8px;
|
||
}
|
||
|
||
.article-sharing a:hover {
|
||
border-bottom: none;
|
||
}
|
||
|
||
.sidebar-section.subscribe {
|
||
font-size: 12px;
|
||
line-height: 1.6em;
|
||
}
|
||
|
||
.subscribe p {
|
||
margin-bottom: 0.5em;
|
||
}
|
||
|
||
|
||
.article-footer .subscribe {
|
||
font-size: 15px;
|
||
margin-top: 45px;
|
||
}
|
||
|
||
|
||
.sidebar-section.custom {
|
||
font-size: 12px;
|
||
line-height: 1.6em;
|
||
}
|
||
|
||
.custom p {
|
||
margin-bottom: 0.5em;
|
||
}
|
||
|
||
/* Styles for listing layout (hide title) */
|
||
.layout-listing d-title, .layout-listing .d-title {
|
||
display: none;
|
||
}
|
||
|
||
/* Styles for posts lists (not auto-injected) */
|
||
|
||
|
||
.posts-with-sidebar {
|
||
padding-left: 45px;
|
||
padding-right: 45px;
|
||
}
|
||
|
||
.posts-list .description h2,
|
||
.posts-list .description p {
|
||
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
|
||
}
|
||
|
||
.posts-list .description h2 {
|
||
font-weight: 700;
|
||
border-bottom: none;
|
||
padding-bottom: 0;
|
||
}
|
||
|
||
.posts-list h2.post-tag {
|
||
border-bottom: 1px solid rgba(0, 0, 0, 0.2);
|
||
padding-bottom: 12px;
|
||
}
|
||
.posts-list {
|
||
margin-top: 60px;
|
||
margin-bottom: 24px;
|
||
}
|
||
|
||
.posts-list .post-preview {
|
||
text-decoration: none;
|
||
overflow: hidden;
|
||
display: block;
|
||
border-bottom: 1px solid rgba(0, 0, 0, 0.1);
|
||
padding: 24px 0;
|
||
}
|
||
|
||
.post-preview-last {
|
||
border-bottom: none !important;
|
||
}
|
||
|
||
.posts-list .posts-list-caption {
|
||
grid-column: screen;
|
||
font-weight: 400;
|
||
}
|
||
|
||
.posts-list .post-preview h2 {
|
||
margin: 0 0 6px 0;
|
||
line-height: 1.2em;
|
||
font-style: normal;
|
||
font-size: 24px;
|
||
}
|
||
|
||
.posts-list .post-preview p {
|
||
margin: 0 0 12px 0;
|
||
line-height: 1.4em;
|
||
font-size: 16px;
|
||
}
|
||
|
||
.posts-list .post-preview .thumbnail {
|
||
box-sizing: border-box;
|
||
margin-bottom: 24px;
|
||
position: relative;
|
||
max-width: 500px;
|
||
}
|
||
.posts-list .post-preview img {
|
||
width: 100%;
|
||
display: block;
|
||
}
|
||
|
||
.posts-list .metadata {
|
||
font-size: 12px;
|
||
line-height: 1.4em;
|
||
margin-bottom: 18px;
|
||
}
|
||
|
||
.posts-list .metadata > * {
|
||
display: inline-block;
|
||
}
|
||
|
||
.posts-list .metadata .publishedDate {
|
||
margin-right: 2em;
|
||
}
|
||
|
||
.posts-list .metadata .dt-authors {
|
||
display: block;
|
||
margin-top: 0.3em;
|
||
margin-right: 2em;
|
||
}
|
||
|
||
.posts-list .dt-tags {
|
||
display: block;
|
||
line-height: 1em;
|
||
}
|
||
|
||
.posts-list .dt-tags .dt-tag {
|
||
display: inline-block;
|
||
color: rgba(0,0,0,0.6);
|
||
padding: 0.3em 0.4em;
|
||
margin-right: 0.2em;
|
||
margin-bottom: 0.4em;
|
||
font-size: 60%;
|
||
border: 1px solid rgba(0,0,0,0.2);
|
||
border-radius: 3px;
|
||
text-transform: uppercase;
|
||
font-weight: 500;
|
||
}
|
||
|
||
.posts-list img {
|
||
opacity: 1;
|
||
}
|
||
|
||
.posts-list img[data-src] {
|
||
opacity: 0;
|
||
}
|
||
|
||
.posts-more {
|
||
clear: both;
|
||
}
|
||
|
||
|
||
.posts-sidebar {
|
||
font-size: 16px;
|
||
}
|
||
|
||
.posts-sidebar h3 {
|
||
font-size: 16px;
|
||
margin-top: 0;
|
||
margin-bottom: 0.5em;
|
||
font-weight: 400;
|
||
text-transform: uppercase;
|
||
}
|
||
|
||
.sidebar-section {
|
||
margin-bottom: 30px;
|
||
}
|
||
|
||
.categories ul {
|
||
list-style-type: none;
|
||
margin: 0;
|
||
padding: 0;
|
||
}
|
||
|
||
.categories li {
|
||
color: rgba(0, 0, 0, 0.8);
|
||
margin-bottom: 0;
|
||
}
|
||
|
||
.categories li>a {
|
||
border-bottom: none;
|
||
}
|
||
|
||
.categories li>a:hover {
|
||
border-bottom: 1px solid rgba(0, 0, 0, 0.4);
|
||
}
|
||
|
||
.categories .active {
|
||
font-weight: 600;
|
||
}
|
||
|
||
.categories .category-count {
|
||
color: rgba(0, 0, 0, 0.4);
|
||
}
|
||
|
||
|
||
@media(min-width: 768px) {
|
||
.posts-list .post-preview h2 {
|
||
font-size: 26px;
|
||
}
|
||
.posts-list .post-preview .thumbnail {
|
||
float: right;
|
||
width: 30%;
|
||
margin-bottom: 0;
|
||
}
|
||
.posts-list .post-preview .description {
|
||
float: left;
|
||
width: 45%;
|
||
}
|
||
.posts-list .post-preview .metadata {
|
||
float: left;
|
||
width: 20%;
|
||
margin-top: 8px;
|
||
}
|
||
.posts-list .post-preview p {
|
||
margin: 0 0 12px 0;
|
||
line-height: 1.5em;
|
||
font-size: 16px;
|
||
}
|
||
.posts-with-sidebar .posts-list {
|
||
float: left;
|
||
width: 75%;
|
||
}
|
||
.posts-with-sidebar .posts-sidebar {
|
||
float: right;
|
||
width: 20%;
|
||
margin-top: 60px;
|
||
padding-top: 24px;
|
||
padding-bottom: 24px;
|
||
}
|
||
}
|
||
|
||
|
||
/* Improve display for browsers without grid (IE/Edge <= 15) */
|
||
|
||
.downlevel {
|
||
line-height: 1.6em;
|
||
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
|
||
margin: 0;
|
||
}
|
||
|
||
.downlevel .d-title {
|
||
padding-top: 6rem;
|
||
padding-bottom: 1.5rem;
|
||
}
|
||
|
||
.downlevel .d-title h1 {
|
||
font-size: 50px;
|
||
font-weight: 700;
|
||
line-height: 1.1em;
|
||
margin: 0 0 0.5rem;
|
||
}
|
||
|
||
.downlevel .d-title p {
|
||
font-weight: 300;
|
||
font-size: 1.2rem;
|
||
line-height: 1.55em;
|
||
margin-top: 0;
|
||
}
|
||
|
||
.downlevel .d-byline {
|
||
padding-top: 0.8em;
|
||
padding-bottom: 0.8em;
|
||
font-size: 0.8rem;
|
||
line-height: 1.8em;
|
||
}
|
||
|
||
.downlevel .section-separator {
|
||
border: none;
|
||
border-top: 1px solid rgba(0, 0, 0, 0.1);
|
||
}
|
||
|
||
.downlevel .d-article {
|
||
font-size: 1.06rem;
|
||
line-height: 1.7em;
|
||
padding-top: 1rem;
|
||
padding-bottom: 2rem;
|
||
}
|
||
|
||
|
||
.downlevel .d-appendix {
|
||
padding-left: 0;
|
||
padding-right: 0;
|
||
max-width: none;
|
||
font-size: 0.8em;
|
||
line-height: 1.7em;
|
||
margin-bottom: 0;
|
||
color: rgba(0,0,0,0.5);
|
||
padding-top: 40px;
|
||
padding-bottom: 48px;
|
||
}
|
||
|
||
.downlevel .footnotes ol {
|
||
padding-left: 13px;
|
||
}
|
||
|
||
.downlevel .base-grid,
|
||
.downlevel .distill-header,
|
||
.downlevel .d-title,
|
||
.downlevel .d-abstract,
|
||
.downlevel .d-article,
|
||
.downlevel .d-appendix,
|
||
.downlevel .distill-appendix,
|
||
.downlevel .d-byline,
|
||
.downlevel .d-footnote-list,
|
||
.downlevel .d-citation-list,
|
||
.downlevel .distill-footer,
|
||
.downlevel .appendix-bottom,
|
||
.downlevel .posts-container {
|
||
padding-left: 40px;
|
||
padding-right: 40px;
|
||
}
|
||
|
||
@media(min-width: 768px) {
|
||
.downlevel .base-grid,
|
||
.downlevel .distill-header,
|
||
.downlevel .d-title,
|
||
.downlevel .d-abstract,
|
||
.downlevel .d-article,
|
||
.downlevel .d-appendix,
|
||
.downlevel .distill-appendix,
|
||
.downlevel .d-byline,
|
||
.downlevel .d-footnote-list,
|
||
.downlevel .d-citation-list,
|
||
.downlevel .distill-footer,
|
||
.downlevel .appendix-bottom,
|
||
.downlevel .posts-container {
|
||
padding-left: 150px;
|
||
padding-right: 150px;
|
||
max-width: 900px;
|
||
}
|
||
}
|
||
|
||
.downlevel pre code {
|
||
display: block;
|
||
border-left: 2px solid rgba(0, 0, 0, .1);
|
||
padding: 0 0 0 20px;
|
||
font-size: 14px;
|
||
}
|
||
|
||
.downlevel code, .downlevel pre {
|
||
color: black;
|
||
background: none;
|
||
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
|
||
text-align: left;
|
||
white-space: pre;
|
||
word-spacing: normal;
|
||
word-break: normal;
|
||
word-wrap: normal;
|
||
line-height: 1.5;
|
||
|
||
-moz-tab-size: 4;
|
||
-o-tab-size: 4;
|
||
tab-size: 4;
|
||
|
||
-webkit-hyphens: none;
|
||
-moz-hyphens: none;
|
||
-ms-hyphens: none;
|
||
hyphens: none;
|
||
}
|
||
|
||
.downlevel .posts-list .post-preview {
|
||
color: inherit;
|
||
}
|
||
|
||
|
||
|
||
</style>
|
||
|
||
<script type="application/javascript">
|
||
|
||
function is_downlevel_browser() {
|
||
if (bowser.isUnsupportedBrowser({ msie: "12", msedge: "16"},
|
||
window.navigator.userAgent)) {
|
||
return true;
|
||
} else {
|
||
return window.load_distill_framework === undefined;
|
||
}
|
||
}
|
||
|
||
// show body when load is complete
|
||
function on_load_complete() {
|
||
|
||
// add anchors
|
||
if (window.anchors) {
|
||
window.anchors.options.placement = 'left';
|
||
window.anchors.add('d-article > h2, d-article > h3, d-article > h4, d-article > h5');
|
||
}
|
||
|
||
|
||
// set body to visible
|
||
document.body.style.visibility = 'visible';
|
||
|
||
// force redraw for leaflet widgets
|
||
if (window.HTMLWidgets) {
|
||
var maps = window.HTMLWidgets.findAll(".leaflet");
|
||
$.each(maps, function(i, el) {
|
||
var map = this.getMap();
|
||
map.invalidateSize();
|
||
map.eachLayer(function(layer) {
|
||
if (layer instanceof L.TileLayer)
|
||
layer.redraw();
|
||
});
|
||
});
|
||
}
|
||
|
||
// trigger 'shown' so htmlwidgets resize
|
||
$('d-article').trigger('shown');
|
||
}
|
||
|
||
function init_distill() {
|
||
|
||
init_common();
|
||
|
||
// create front matter
|
||
var front_matter = $('<d-front-matter></d-front-matter>');
|
||
$('#distill-front-matter').wrap(front_matter);
|
||
|
||
// create d-title
|
||
$('.d-title').changeElementType('d-title');
|
||
|
||
// create d-byline
|
||
var byline = $('<d-byline></d-byline>');
|
||
$('.d-byline').replaceWith(byline);
|
||
|
||
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{"title":"Air Propulsion Simulation","description":"Simulating the performance of an air propulsion system as an alternative to solid rocket motors.","authors":[{"author":"Anson Biggs","authorURL":"https://ansonbiggs.com","affiliation":" ","affiliationURL":"#","orcidID":""}],"publishedDate":"2021-04-01T00:00:00.000-07:00","citationText":"Biggs, 2021"}
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<h1>Air Propulsion Simulation</h1>
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<!--radix_placeholder_categories-->
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<div class="dt-tags">
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<div class="dt=tag">Julia</div>
|
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<div class="dt=tag">Capstone</div>
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<p><p>Simulating the performance of an air propulsion system as an alternative to solid rocket motors.</p></p>
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Anson Biggs <a href="https://ansonbiggs.com" class="uri">https://ansonbiggs.com</a>
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<br/>04-01-2021
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</div>
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<div class="d-article">
|
||
<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>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<details>
|
||
<summary>
|
||
Show code
|
||
</summary>
|
||
<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>
|
||
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>plotly()</span>
|
||
<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>
|
||
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Unitful</span>
|
||
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> DataFrames</span>
|
||
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> Measurements</span>
|
||
<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>
|
||
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="kw">using</span> CSV</span></code></pre></div>
|
||
</details>
|
||
</div>
|
||
<h2 id="the-simulation">The Simulation</h2>
|
||
<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>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<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>
|
||
<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>
|
||
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>P0 <span class="op">=</span> (<span class="fl">4200.0</span> ± <span class="fl">300</span>)u<span class="st">"psi"</span></span>
|
||
<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>
|
||
<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>
|
||
</div>
|
||
<p>The nozzle diameter was changed until the air prop system had a <em>burn time</em> similar to a G18ST rocket motor.</p>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<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>
|
||
<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>
|
||
<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>
|
||
</div>
|
||
<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>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<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>
|
||
<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>
|
||
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>γ <span class="op">=</span> <span class="fl">1.4</span> ± <span class="fl">0.05</span></span>
|
||
<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>
|
||
<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>
|
||
</div>
|
||
<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>
|
||
<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>
|
||
<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 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>
|
||
<div class="layout-chunk" data-layout="l-body">
|
||
<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>
|
||
<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>
|
||
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>P <span class="op">=</span> P0 <span class="op">|></span> u<span class="st">"Pa"</span></span>
|
||
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>M <span class="op">=</span> V <span class="op">*</span> (P <span class="op">/</span> (R <span class="op">*</span> T)) <span class="op">|></span> u<span class="st">"kg"</span></span>
|
||
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>ts <span class="op">=</span> <span class="fl">1</span>u<span class="st">"ms"</span></span>
|
||
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a>df <span class="op">=</span> DataFrame(Thrust<span class="op">=</span>(<span class="fl">0</span> ± <span class="fl">0</span>)u<span class="st">"N"</span><span class="op">,</span> Pressure<span class="op">=</span>P0<span class="op">,</span> <span class="dt">Time</span><span class="op">=</span><span class="fl">0.0</span>u<span class="st">"s"</span><span class="op">,</span> Mass<span class="op">=</span>M)</span>
|
||
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a> <span class="kw">while</span> M <span class="op">></span> <span class="fl">0.005</span>u<span class="st">"kg"</span></span>
|
||
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a> <span class="co"># Calculate what is leaving tank</span></span>
|
||
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a> P <span class="op">=</span> minimum([P<span class="op">,</span> Pmax])</span>
|
||
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a> ve <span class="op">=</span> sqrt((<span class="fl">2</span> <span class="op">*</span> γ <span class="op">/</span> (γ <span class="op">-</span> <span class="fl">1</span>)) <span class="op">*</span> R <span class="op">*</span> T <span class="op">*</span> (<span class="fl">1</span> <span class="op">-</span> P_amb <span class="op">/</span> P)<span class="op">^</span>((γ <span class="op">-</span> <span class="fl">1</span>) <span class="op">/</span> γ)) <span class="op">|></span> u<span class="st">"m/s"</span></span>
|
||
<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a> ρ <span class="op">=</span> P <span class="op">/</span> (R <span class="op">*</span> T) <span class="op">|></span> u<span class="st">"kg/m^3"</span></span>
|
||
<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a> ṁ <span class="op">=</span> ρ <span class="op">*</span> a_nozzle <span class="op">*</span> ve <span class="op">|></span> u<span class="st">"kg/s"</span></span>
|
||
<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a> </span>
|
||
<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a> Thrust <span class="op">=</span> ṁ <span class="op">*</span> ve <span class="op">+</span> a_nozzle <span class="op">*</span> (P <span class="op">-</span> P_amb) <span class="op">|></span> u<span class="st">"N"</span></span>
|
||
<span id="cb5-15"><a href="#cb5-15" aria-hidden="true" tabindex="-1"></a> </span>
|
||
<span id="cb5-16"><a href="#cb5-16" aria-hidden="true" tabindex="-1"></a> <span class="co"># Calculate what is still in the tank</span></span>
|
||
<span id="cb5-17"><a href="#cb5-17" aria-hidden="true" tabindex="-1"></a> M <span class="op">=</span> M <span class="op">-</span> ṁ <span class="op">*</span> ts <span class="op">|></span> u<span class="st">"kg"</span></span>
|
||
<span id="cb5-18"><a href="#cb5-18" aria-hidden="true" tabindex="-1"></a> P <span class="op">=</span> (M <span class="op">*</span> R <span class="op">*</span> T) <span class="op">/</span> V <span class="op">|></span> u<span class="st">"Pa"</span></span>
|
||
<span id="cb5-19"><a href="#cb5-19" aria-hidden="true" tabindex="-1"></a> t <span class="op">=</span> t <span class="op">+</span> ts</span>
|
||
<span id="cb5-20"><a href="#cb5-20" aria-hidden="true" tabindex="-1"></a> </span>
|
||
<span id="cb5-21"><a href="#cb5-21" aria-hidden="true" tabindex="-1"></a> df_step <span class="op">=</span> DataFrame(Thrust<span class="op">=</span>Thrust<span class="op">,</span> Pressure<span class="op">=</span>P<span class="op">,</span> <span class="dt">Time</span><span class="op">=</span>t<span class="op">,</span> Mass<span class="op">=</span>M)</span>
|
||
<span id="cb5-22"><a href="#cb5-22" aria-hidden="true" tabindex="-1"></a> <span class="cn">append</span><span class="op">!</span>(df<span class="op">,</span> df_step)</span>
|
||
<span id="cb5-23"><a href="#cb5-23" aria-hidden="true" tabindex="-1"></a> <span class="kw">end</span></span>
|
||
<span id="cb5-24"><a href="#cb5-24" aria-hidden="true" tabindex="-1"></a> df</span>
|
||
<span id="cb5-25"><a href="#cb5-25" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span></code></pre></div>
|
||
</div>
|
||
<h2 id="analysis">Analysis</h2>
|
||
<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>
|
||
<div class="layout-chunk" data-layout="l-body-outset">
|
||
<details>
|
||
<summary>
|
||
Show code
|
||
</summary>
|
||
<div class="sourceCode" id="cb6"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>thrust_values <span class="op">=</span> df.Thrust .<span class="op">|></span> ustrip .<span class="op">|></span> value<span class="op">;</span></span>
|
||
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>thrust_uncertainties <span class="op">=</span> df.Thrust .<span class="op">|></span> ustrip .<span class="op">|></span> uncertainty<span class="op">;</span></span>
|
||
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>air <span class="op">=</span> DataFrame(Thrust<span class="op">=</span>thrust_values<span class="op">,</span> Uncertainty<span class="op">=</span>thrust_uncertainties<span class="op">,</span> <span class="dt">Time</span><span class="op">=</span>df.<span class="dt">Time</span> .<span class="op">|></span> u<span class="st">"s"</span> .<span class="op">|></span> ustrip)<span class="op">;</span></span>
|
||
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a>plot(df.<span class="dt">Time</span> .<span class="op">|></span> ustrip<span class="op">,</span> thrust_values<span class="op">,</span> </span>
|
||
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a> title<span class="op">=</span><span class="st">"Thrust Over Time"</span><span class="op">,</span> </span>
|
||
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a> ribbon<span class="op">=</span>(thrust_uncertainties<span class="op">,</span> thrust_uncertainties)<span class="op">,</span> </span>
|
||
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a> fillalpha<span class="op">=</span><span class="fl">.2</span><span class="op">,</span>label<span class="op">=</span><span class="st">"Thrust"</span><span class="op">,</span></span>
|
||
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a> xlabel<span class="op">=</span><span class="st">"Time (s)"</span><span class="op">,</span> </span>
|
||
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a> ylabel<span class="op">=</span><span class="st">"Thrust (N)"</span><span class="op">,</span></span>
|
||
<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a> size <span class="op">=</span> (<span class="fl">1200</span><span class="op">,</span> <span class="fl">800</span>)<span class="op">,</span></span>
|
||
<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a> )</span></code></pre></div>
|
||
</details>
|
||
<div class="figure"><span id="fig:unnamed-chunk-6"></span>
|
||
<img src="air-propulsion-simulation_files/figure-html5/unnamed-chunk-6-J1.png" alt="Air Proplsion Simulation" width="350" />
|
||
<p class="caption">
|
||
Figure 1: Air Proplsion Simulation
|
||
</p>
|
||
</div>
|
||
</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.</p>
|
||
<div class="layout-chunk" data-layout="l-body-outset">
|
||
<details>
|
||
<summary>
|
||
Show code
|
||
</summary>
|
||
<div class="sourceCode" id="cb7"><pre class="sourceCode julia"><code class="sourceCode julia"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>f10 <span class="op">=</span> CSV.<span class="cn">read</span>(<span class="st">"AeroTech_F10.csv"</span><span class="op">,</span> DataFrame)<span class="op">;</span></span>
|
||
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>f15 <span class="op">=</span> CSV.<span class="cn">read</span>(<span class="st">"Estes_F15.csv"</span><span class="op">,</span> DataFrame)<span class="op">;</span></span>
|
||
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>g8 <span class="op">=</span> CSV.<span class="cn">read</span>(<span class="st">"AeroTech_G8ST.csv"</span><span class="op">,</span> DataFrame)<span class="op">;</span></span>
|
||
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a>plot(air.<span class="dt">Time</span><span class="op">,</span> air.Thrust<span class="op">,</span> label<span class="op">=</span><span class="st">"Air Propulsion"</span><span class="op">,</span> fillalpha<span class="op">=</span><span class="fl">.1</span><span class="op">,</span> legend<span class="op">=:</span>topleft<span class="op">,</span> size <span class="op">=</span> (<span class="fl">1200</span><span class="op">,</span> <span class="fl">800</span>))<span class="op">;</span></span>
|
||
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a><span class="kw">for</span> (d<span class="op">,</span> l) <span class="kw">in</span> [(f10<span class="op">,</span> <span class="st">"F10"</span>)<span class="op">,</span> (f15<span class="op">,</span> <span class="st">"F15"</span>)<span class="op">,</span> (g8<span class="op">,</span> <span class="st">"G8ST"</span>)]</span>
|
||
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a> plot<span class="op">!</span>(d[<span class="op">!,</span><span class="st">"Time (s)"</span>]<span class="op">,</span> d[<span class="op">!,</span> <span class="st">"Thrust (N)"</span>]<span class="op">,</span> label<span class="op">=</span>l)<span class="op">;</span></span>
|
||
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span>
|
||
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a>title<span class="op">!</span>(<span class="st">"Propulsion Comparison"</span>)<span class="op">;</span></span>
|
||
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a>xlabel<span class="op">!</span>(<span class="st">"Time (s)"</span>)<span class="op">;</span></span>
|
||
<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>
|
||
</details>
|
||
<div class="figure"><span id="fig:unnamed-chunk-7"></span>
|
||
<img src="air-propulsion-simulation_files/figure-html5/unnamed-chunk-7-J1.png" alt="Rocket Motor Data: [@thrustcurve]" width="350" />
|
||
<p class="caption">
|
||
Figure 2: Rocket Motor Data: <span class="citation" data-cites="thrustcurve">(<a href="#ref-thrustcurve" role="doc-biblioref">Coker, n.d.</a>)</span>
|
||
</p>
|
||
</div>
|
||
</div>
|
||
<p>Big conclusion about things.</p>
|
||
<div class="sourceCode" id="cb8"><pre class="sourceCode r distill-force-highlighting-css"><code class="sourceCode r"></code></pre></div>
|
||
<div id="refs" class="references csl-bib-body hanging-indent" role="doc-bibliography">
|
||
<div id="ref-thrustcurve" class="csl-entry" role="doc-biblioentry">
|
||
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" role="doc-biblioentry">
|
||
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" role="doc-biblioentry">
|
||
Sutton, George P., and Oscar Biblarz. 2001. <em>Rocket Propulsion Elements</em>. 7th ed. New York: John Wiley & Sons.
|
||
</div>
|
||
</div>
|
||
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|
||
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|
||
</div>
|
||
|
||
<div class="d-appendix">
|
||
</div>
|
||
|
||
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<script>
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(function () {
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var script = document.createElement("script");
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script.type = "text/javascript";
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script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
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<div class="appendix-bottom">
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<h3 id="references">References</h3>
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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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