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+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Frames of Reference · OWENS.jl</title><meta name="title" content="Frames of Reference · OWENS.jl"/><meta property="og:title" content="Frames of Reference · OWENS.jl"/><meta property="twitter:title" content="Frames of Reference · OWENS.jl"/><meta name="description" content="Documentation for OWENS.jl."/><meta property="og:description" content="Documentation for OWENS.jl."/><meta property="twitter:description" content="Documentation for OWENS.jl."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">OWENS.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../setup/">Installation</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../examples/A_simplyRunningOWENS/">Simply Running OWENS</a></li><li><a class="tocitem" href="../examples/B_detailedInputs/">Detailed Inputs</a></li><li><a class="tocitem" href="../examples/C_customizablePreprocessing/">Customizable Preprocessing</a></li></ul></li><li><a class="tocitem" href="../OWENS_Dev_Guide/">Developer Guide</a></li><li class="is-active"><a class="tocitem" href>Frames of Reference</a></li><li><a class="tocitem" href="../reference/reference/">API Reference</a></li><li><a class="tocitem" href="../legacyUserGuide/">Legacy User Guide</a></li><li><a class="tocitem" href="../VAWTGenUserGuide/">Legacy VAWTGen Guide</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Frames of Reference</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Frames of Reference</a></li></ul></nav><div class="docs-right"><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><p>OWENS X is outwards on blade, y is trailing edge always</p><p>Struts, CCW, z is inwards, y trailing, and CW z is outwards</p><p>Aerodyn </p><p>if CW z is up, y is trailing (root at bottom) blades, z is outwards and y is towards trailing edge.  If struts have asymmetric, then you need to align your desired suction side with the x-vector, which means you might have to invert your airfoil lookup tables for struts that the suction side isn’t where you want it.</p><p>Aerodyn if CCW, root is at top and z is down, y is trailing edge, for struts, z is outwards, and y is trailing edge. </p><p>Hub is rotated such that the axis of rotation is x. So for a VAWT hub-x points up, and hawt hub-x point in x.</p><p><img src="../figs/image1.png" alt/>{width=&quot;4.917280183727034in&quot; height=&quot;4.585993000874891in&quot;}<img src="../figs/image2.png" alt/>{width=&quot;5.469136045494313in&quot; height=&quot;5.071805555555556in&quot;}Meet porcupine the OWENS element orientation helper. It is comprised of a tower, horizonal struts, and blades that have both curved and vertical sections. Let&#39;s start with all of the orientations set to 0. We can see that the 1,0,0 norm is in the positive x direction, and likewise for the y and z norms.</p><p>Now, let&#39;s turn on just the yaw orientation, (psi in OWENS). The top blade gets a -90 degree yaw shift (like the other blades), and the other blades&#39; yaw is additionally rotated to match the global blade orientation around the turbine axis of rotation. Yes the initial 90 degree shift is confusing, but it is the convention in the structural solver – is seems that the z-norm of the blade is intended to be eventually pointing away from the axis of rotation.</p><p><img src="../figs/image3.png" alt/>{width=&quot;5.595138888888889in&quot; height=&quot;4.875694444444444in&quot;}<img src="../figs/image4.png" alt/>{width=&quot;5.737141294838145in&quot; height=&quot;5.283430664916885in&quot;}</p><p>If we add 30 degrees of rotation to the yaw, this is what it looks like.</p><p><img src="../figs/image5.png" alt/>{width=&quot;4.91704615048119in&quot; height=&quot;4.992732939632546in&quot;}</p><p>Ok, let&#39;s now turn on roll (in addition to yaw), which is the blade slope, or theta in OWENS. Now, the z norm is no longer always vertical, but now aligned with the blade slope.</p><p><img src="../figs/image6.png" alt/>{width=&quot;4.382957130358705in&quot; height=&quot;4.783430664916885in&quot;}<img src="../figs/image7.png" alt/>{width=&quot;5.226388888888889in&quot; height=&quot;4.833333333333333in&quot;}</p><p><img src="../figs/image8.png" alt/>{width=&quot;4.406944444444444in&quot; height=&quot;3.9298611111111112in&quot;}If we add 30 degrees of roll, this is what it looks like:</p><p><img src="../figs/image9.png" alt/>{width=&quot;5.124857830271216in&quot; height=&quot;4.771802274715661in&quot;}</p><p><img src="../figs/image10.png" alt/>{width=&quot;4.45625in&quot; height=&quot;4.469444444444444in&quot;}Now, the blade pitch, also angle of attack, is generally 0, but can be offset similarly to the yaw, but the rotation is truly in a blade angle of attack frame of reference. Here it is with 30 degrees offset.</p><p><img src="../figs/image11.png" alt/>{width=&quot;4.095165135608049in&quot; height=&quot;4.388081802274716in&quot;}</p><p>In all, these are the rotation matrices were used to create the plots: Twist/aoa about the x-axis, slope/theta about the y-axis, and psi/yaw about the z axis.</p><p><em># apply the twist rotation, which is about the x (1) axis</em></p><p>myvec = myvec*[1.0 0.0 0.0</p><p>0.0 cosd(Twist<em>d</em>el) sind(Twist<em>d</em>el)</p><p>0.0 -sind(Twist<em>d</em>el) cosd(Twist<em>d</em>el)]</p><p><em># apply theta rotation, which is the tilt angle, or about the y (2) axis in global</em></p><p>myvec = myvec*[cosd(Theta<em>d</em>el) 0.0 -sind(Theta<em>d</em>el)</p><p>0.0 1.0 0.0</p><p>sind(Theta<em>d</em>el) 0.0 cosd(Theta<em>d</em>el)]</p><p><em># apply Psi rotation, which is about Z (3) axis in global</em></p><p>myvec = myvec*[cosd(Psi<em>d</em>el) sind(Psi<em>d</em>el) 0.0</p><p>-sind(Psi<em>d</em>el) cosd(Psi<em>d</em>el) 0.0</p><p>0.0 0.0 1.0]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../OWENS_Dev_Guide/">« Developer Guide</a><a class="docs-footer-nextpage" href="../reference/reference/">API Reference »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 10 April 2024 22:48">Wednesday 10 April 2024</span>. 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