obsidian_backup/力学书籍/FASTMotions/auto/FASTMotions_content_list.json

[
    {
        "type": "text",
        "text": "The following are derivations of the output motions available in FAST for a 2-bladed turbine configuration.  The motions for a 3-bladed turbine are very similar.  Note that some of the motions are given multiple names in order to support variation among the user’s preferences. ",
        "page_idx": 0
    },
    {
        "type": "text",
        "text": "Blade 1 Tip Motions:   \nOoPDefl1=TipDxc1=rQS1(BldFlexL)−TipRadj3B1⋅i1B1 Blade 1 OoP tip deflection (relative to rotor) (directed along the xc1-axis), (m)   \nIPDefl1=TipDyc1=rQS1(BldFlexL)−TipRadj3B1⋅i2B1 Blade 1 IP tip deflection (relative to rotor) (directed along the yc1-axis), (m)   \nTipDxb1=rQS1(BldFlexL)−TipRadj3B1⋅j1B1 Blade 1 flapwise tip deflection (relative to rotor) (directed along the xb1-axis), (m)   \nTipDyb1=rQS1(BldFlexL)−TipRadj3B1⋅j2B1 Blade 1 edgewise tip deflection (relative to rotor) (directed along the yb1-axis), (m)   \n$\\begin{array}{r}{T i p D z c I=T i p D z b I=\\Big[r^{\\varrho s I}\\left(B l d F l e x L\\right)-T i p R a d j_{3}^{B I}}\\end{array}$  $\\cdot\\dot{\\pmb{i}}_{3}^{B I}=\\left[r^{Q S I}\\left(B l d F l e x L\\right)\\!-T i p R a d\\pmb{j}_{3}^{B I}\\right.$ ⋅j3B1 Blade  1  axial  tip  deflection  (relative  to  rotor)   \n(directed along the zc1-/zb1-axis), (m)   \n$T i p A L x b I=\\mathbf{\\nabla}^{E}a^{S I}\\left(B l d F l e x L\\right)\\cdot\\mathbf{\\boldsymbol{n}}_{I}^{B I}\\left(B l d F l e x L\\right)$ Blade 1 flapwise tip acceleration (absolute) (directed along the xb1-axis), (m/sec2)   \n$T i p A L y b I=\\mathbf{\\nabla}^{E}a^{S I}\\left(B l d F l e x L\\right)\\cdot\\mathbf{\\mathbf{\\cdot}}\\mathbf{\\mathbf{}}n_{2}^{B I}\\left(B l d F l e x L\\right)$ Blade 1 edgewise tip acceleration (absolute)  (directed along the yb1-axis), (m/sec2)   \n$T i p A L z b I=\\mathbf{\\nabla}^{E}a^{S I}\\left(B l d F l e x L\\right)\\cdot\\mathbf{\\boldsymbol{n}}_{3}^{B I}\\left(B l d F l e x L\\right)$ Blade 1 axial tip acceleration (absolute) (directed along the zc1-/zb1-axis), (m/sec2)   \n$R o l l D e j l I=T i p R D x b I=\\left(\\frac{I\\delta\\theta}{\\pi}\\right)^{H}\\!\\pmb{\\theta}^{M I}\\left(B l d F l e x L\\right)\\cdot\\pmb{j}_{I}^{B I}$ Blade 1 roll tip deflection (relative to the undeflected position), (about the xb1-axis), (deg)   \n$P t c h D e j l-T i p R D y b I=\\left(\\frac{I\\,\\delta\\theta}{\\pi}\\right)^{H}\\!\\theta^{M I}\\left(B l d F l e x L\\right)\\cdot\\dot{J}_{2}^{B I}$ Blade 1 pitch tip deflection (relative to the undeflected position), (about the yb1-axis),   \n(deg) ",
        "page_idx": 0
    },
    {
        "type": "text",
        "text": "where: $^{H}\\!\\theta^{M I}\\left(B l d F l e x L\\right)=^{E}\\!\\omega_{B I F I}^{M I}\\left(B l d F l e x L\\right)q_{B I F I}+^{E}\\!\\omega_{B I E I}^{M I}\\left(B l d F l e x L\\right)q_{B I E I}+^{E}\\!\\omega_{I}^{I}\\,,$ BΜ11F2(BldFlexL) qB1F 2 where: $r^{~o s t}\\left(B l d F l e x L\\right)\\!=\\!r^{~o V}+r^{~V P}+r^{P Q}+r^{Q S I}\\left(B l d F l e x L\\right)$ ",
        "page_idx": 0
    },
    {
        "type": "image",
        "img_path": "images/ff3b6c808f53eed30fb804e400aefda635080690456a987aad15c16d5a0b6883.jpg",
        "img_caption": [],
        "img_footnote": [],
        "page_idx": 0
    },
    {
        "type": "text",
        "text": "",
        "page_idx": 0
    },
    {
        "type": "equation",
        "text": "$$\n{\\begin{array}{l}{S p n i A L x b{I}{\\,=\\,}^{E}a^{S t}\\left(R^{S p a n i}\\right)\\cdot{n}_{I}^{B I}\\left(R^{S p a n i}\\right)}\\\\ {1,2,...{\\,,5)},\\,(\\mathrm{m/sec}^{2})}\\\\ {S p n i A L y b{I}{\\,=\\,}^{E}a^{S t}\\left(R^{S p a n i}\\right)\\cdot{n}_{2}^{B I}\\left(R^{S p a n i}\\right)}\\\\ {1,2,...{\\,,5)},\\,(\\mathrm{m/sec}^{2})}\\\\ {S p n i A L z b{I}{\\,=\\,}^{E}a^{S t}\\left(R^{S p a n i}\\right)\\cdot{n}_{3}^{B I}\\left(R^{S p a n i}\\right)}\\\\ {1,2,...{\\,,5)},\\,(\\mathrm{m/sec}^{2})}\\end{array}}\n$$",
        "text_format": "latex",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Blade 1 local flapwise acceleration (absolute) of span station $i$ (directed along the local xb1-axis) ${\\bf\\nabla}^{i}={\\bf\\nabla}$ Blade 1 local edgewise acceleration (absolute) of span station $i$ (directed along the local yb1-axis) ${\\boldsymbol{\\mathbf{\\mathit{i}}}}=$ ",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Blade 1 axial acceleration (absolute) of span station $i$ (directed along the zc1-/zb1-/local zb1-axis) $(i=$ ",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Blade 2 Tip Motions: The output motions of blade 2 are similar to those of blade 1. ",
        "page_idx": 1
    },
    {
        "type": "image",
        "img_path": "images/2057057aaac1479c30036b6175385a20823e1b62a204561d7dd450dc0ac8fb7a.jpg",
        "img_caption": [],
        "img_footnote": [],
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Blade 1 pitch angle (position) (positive towards feather / about the minus zc1- ",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "/minus zb2-axis), (deg) ",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Blade 2 pitch angle (position) (positive towards feather / about the minus zc2- ",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Teeter Motions: ",
        "page_idx": 1
    },
    {
        "type": "equation",
        "text": "$$\nT e e t D e f l=R o t T e e t P=T e e t P y a=\\left(\\frac{I\\,\\delta\\theta}{\\pi}\\right)q_{T e e t}\n$$",
        "text_format": "latex",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Rotor teeter angle (position) (about the ya-axis), (deg) ",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Rotor teeter angular velocity (about the ya-axis), (deg/sec) ",
        "page_idx": 1
    },
    {
        "type": "text",
        "text": "Rotor teeter angular acceleration (about the ya-axis), (deg/sec) ",
        "page_idx": 1
    },
    {
        "type": "image",
        "img_path": "images/5ae9ae923e89b7ee52899a62a43cb9af6327bdd5839b12f492c4132f898ce7f4.jpg",
        "img_caption": [],
        "img_footnote": [],
        "page_idx": 2
    },
    {
        "type": "image",
        "img_path": "images/e1db52774350e87a4ba12810c360d943d26c454ca95528c4ecf6eee0cda1fa87.jpg",
        "img_caption": [],
        "img_footnote": [],
        "page_idx": 3
    },
    {
        "type": "text",
        "text": "Rotor-Furl Motions: ",
        "page_idx": 3
    },
    {
        "type": "text",
        "text": "180 RotFurl=RotFurlP RF ",
        "page_idx": 3
    },
    {
        "type": "text",
        "text": "Nacelle IMU translational velocity (directed along the xs-axis), (m/sec) Nacelle IMU translational velocity (directed along the ys-axis), (m/sec) Nacelle IMU translational velocity (directed along the zs-axis), (m/sec) Nacelle IMU translational acceleration (directed along the xs-axis), $(\\mathrm{m/sec}^{2})$ Nacelle IMU translational acceleration (directed along the ys-axis), $(\\mathrm{m/sec}^{2})$ Nacelle IMU translational acceleration (directed along the zs-axis), $(\\mathrm{m/sec}^{2})$ ",
        "page_idx": 3
    },
    {
        "type": "text",
        "text": "Nacelle IMU angular (rotational) velocity (about the xs-axis), (deg/sec) ",
        "page_idx": 3
    },
    {
        "type": "text",
        "text": "Nacelle IMU angular (rotational) velocity (about the zs-axis), (deg/sec) Nacelle IMU angular (rotational) acceleration (about the xs-axis), (deg/sec2) Nacelle IMU angular (rotational) acceleration (about the ys-axis), (deg/sec2) Nacelle IMU angular (rotational) acceleration (about the zs-axis), (deg/sec2) ",
        "page_idx": 3
    },
    {
        "type": "text",
        "text": "Rotor-furl angle (position) (about the rotor-furl axis), (deg) ",
        "page_idx": 3
    },
    {
        "type": "text",
        "text": "Rotor-furl angular velocity (about the rotor-furl axis), (deg/sec) ",
        "page_idx": 3
    },
    {
        "type": "text",
        "text": "Rotor-furl angular acceleration (about the rotor-furl axis), (deg/sec2) ",
        "page_idx": 3
    },
    {
        "type": "image",
        "img_path": "images/c80ac1f42a7cf2cd3aa056fddb53af0ebc8b8cdb5e5d6fbd15630e314107e179.jpg",
        "img_caption": [],
        "img_footnote": [],
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "Nacelle yaw angle (position) (about the zn-/zp-axis), (deg) Nacelle yaw angular velocity (about the zn-/zp-axis), (deg/sec) Nacelle yaw angular acceleration (about the zn-/zp-axis), (deg/sec2) ",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "Tower-Top Motions: ",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "Nacelle yaw error (about the zt-axis), (deg) ",
        "page_idx": 4
    },
    {
        "type": "equation",
        "text": "$$\n\\ Y a w B r T D x p=\\Big[\\pmb{r}^{z o}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)\\pmb{a}_{2}\\Big]\\cdot\\pmb{b}_{I}\n$$",
        "text_format": "latex",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "Tower-top / yaw bearing translational deflection (relative to undeflected position) ",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "(directed along the xp-axis), (m)   \n$\\ Y a w B r T D y p=-\\Big[{r}^{Z O}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)\\,{a}_{2}\\Big]\\cdot{b}_{3}$   \n(directed along the yp-axis), (m)   \n$\\ Y a w B r T D z p=\\Big[\\pmb{r}^{z o}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)\\pmb{a}_{2}\\Big]\\cdot\\pmb{b}_{2}$   \n(directed along the zp-axis), (m)   \n$\\begin{array}{r}{T T D s p F A=Y a w B r T D x t=\\Big[\\underline{{r}}^{Z O}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)a_{2}\\Big]\\cdot a_{I}}\\end{array}$   \nposition) (directed along the xt-axis), (m)   \n$T T D s p S S=Y a w B r T D y t=-\\Big[r^{Z O}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)a_{2}\\Big]\\cdot a_{3}$   \nundeflected position) (directed along the yt-axis), (m)   \n$T T D s p A x=Y a w B r T D z t=\\left[r^{z o}-\\left(T o w e r H t+P t f m\\,R e\\,f\\right)a_{2}\\right]$ ⋅a2   \nposition) (directed along the zt-axis), (m) ",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "Tower-top / yaw bearing translational deflection (relative to undeflected position) Tower-top / yaw bearing translational deflection (relative to undeflected position) Tower-top / yaw bearing fore-aft (translational) deflection (relative to undeflected Tower-top  /  yaw  bearing  side-to-side  (translational)  deflection  (relative  to Tower-top / yaw bearing axial (translational) deflection (relative to undeflected ",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "$Y a w B r T A x p={}^{E}a^{o}\\cdot b_{_{I}}$ $Y a w B r T A y p=-\\,^{E}a^{o}\\cdot b_{s}$ $Y a w B r T A z p={}^{E}a^{o}\\cdot b_{2}$ ",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "Tower-top / yaw bearing translational acceleration (directed along the xp-axis), (m/sec) Tower-top / yaw bearing translational acceleration (directed along the yp-axis), (m/sec) Tower-top / yaw bearing translational acceleration (directed along the zp-axis), (m/sec2) ",
        "page_idx": 4
    },
    {
        "type": "equation",
        "text": "$$\nT T D s p R o l l=Y a w B r R D x t=\\left(\\frac{l\\,\\delta\\boldsymbol{\\theta}}{\\pi}\\right)^{\\,x}\\!\\!\\!\\boldsymbol{\\theta}^{B}\\cdot\\!\\boldsymbol{a}_{l}\n$$",
        "text_format": "latex",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "Tower-top / yaw bearing roll deflection (relative to the undeflected position) (about the xt-axis), ",
        "page_idx": 4
    },
    {
        "type": "text",
        "text": "(deg) ",
        "page_idx": 4
    },
    {
        "type": "image",
        "img_path": "images/b38c4988ac1e5719ff698fcbf8f729662bca9a2a8b26838cf362115222c35539.jpg",
        "img_caption": [],
        "img_footnote": [],
        "page_idx": 5
    },
    {
        "type": "image",
        "img_path": "images/0c218afa5aa05229840608cb8327fe4452c4006430a61cd378e0c48bb48f3d00.jpg",
        "img_caption": [],
        "img_footnote": [
            "Tower Local Gage Motions: "
        ],
        "page_idx": 5
    },
    {
        "type": "text",
        "text": "Tower local fore-aft translational acceleration (absolute) of node $i$ (directed along the local xt-axis) $(i=$ ",
        "page_idx": 5
    },
    {
        "type": "text",
        "text": "Tower local side-to-side translational acceleration (absolute) of node $i$ (directed along the local yt-axis) ",
        "page_idx": 5
    },
    {
        "type": "text",
        "text": "Tail-Furl Motions: ",
        "text_level": 1,
        "page_idx": 6
    },
    {
        "type": "text",
        "text": "TailFurl=TailFurlP ",
        "page_idx": 6
    },
    {
        "type": "image",
        "img_path": "",
        "img_caption": [],
        "img_footnote": [],
        "page_idx": 6
    },
    {
        "type": "text",
        "text": "Tail-furl angle (position) (about the tail-furl axis), (deg) ",
        "page_idx": 6
    },
    {
        "type": "text",
        "text": "$T a i l F u r l V=\\left(\\frac{I\\,\\!\\delta O}{\\pi}\\right)\\dot{q}_{\\scriptscriptstyle T F r l}$ $T a i l F u r l A=\\left(\\frac{I\\,\\delta0}{\\pi}\\right)\\ddot{q}_{\\scriptscriptstyle T F r l}$ ",
        "page_idx": 6
    },
    {
        "type": "text",
        "text": "Tail-furl angular velocity (about the tail-furl axis), (deg/sec) ",
        "page_idx": 6
    },
    {
        "type": "text",
        "text": "Tail-furl angular acceleration (about the tail-furl axis), (deg/sec2) ",
        "page_idx": 6
    },
    {
        "type": "text",
        "text": "Platform Motions:   \n$P t f m T D x t=r^{Z}\\cdot{\\pmb a}_{I}$   \n$P t f m T D y t=-r^{Z}\\cdot{\\bf{\\boldsymbol{a}}}_{3}$   \n$P t f m T D z t=r^{Z}\\cdot{\\bf{a}}_{2}$   \nPtfmSurge=PtfmTDxi=qS g   \n$P t f m S w a y=P t f m T D y i=q_{S w}$   \n$P t f m H e a\\nu e=P t f m T D z i=q_{H\\nu}$   \n$P t f m T V x t={}^{E}\\nu^{Z}\\cdot{\\bf{a}}_{I}$   \n$P t f m T V y t=-\\,^{E}\\nu^{Z}\\cdot{\\bf{a}}_{3}$   \n$P t f m T V z t={}^{E}\\nu^{Z}\\cdot{\\bf{a}}_{2}$   \nPtfmTVxi= qSg   \n$P t\\/m T\\o V\\!y i=\\dot{q}_{S w}$   \nPtfmTVzi= qHv   \n$P t f m T A x t={}^{E}{\\pmb{a}}^{Z}\\cdot{\\pmb{a}}_{I}$   \nPtfmTAyt= −EaZ   \nPtfmTAzt= a a   \nPtfmTAxi= qSg   \nPtfmTAyi= qSw   \nPtfmTAzi= qHv ",
        "page_idx": 6
    },
    {
        "type": "text",
        "text": "Platform horizontal surge displacement (directed along the xt-axis), (m) Platform horizontal sway displacement (directed along the yt-axis), (m) Platform vertical heave displacement (directed along the zt-axis), (m) Platform horizontal surge displacement (directed along the xi-axis), (m) Platform horizontal sway displacement (directed along the yi-axis), (m) Platform vertical heave displacement (directed along the zi-axis), (m) Platform horizontal surge velocity (directed along the xt-axis), (m/sec) Platform horizontal sway velocity (directed along the yt-axis), (m/sec) Platform vertical heave velocity (directed along the zt-axis), (m/sec) Platform horizontal surge velocity (directed along the xi-axis), (m/sec) Platform horizontal sway velocity (directed along the yi-axis), (m/sec) Platform vertical heave velocity (directed along the zi-axis), (m/sec) Platform horizontal surge acceleration (directed along the xt-axis), $(\\mathrm{m/sec}^{2})$ Platform horizontal sway acceleration (directed along the yt-axis), $(\\mathrm{m/sec}^{2})$ Platform vertical heave acceleration (directed along the zt-axis), $(\\mathrm{m/sec}^{2})$ Platform horizontal surge acceleration (directed along the xi-axis), $(\\mathrm{m/sec}^{2})$ Platform horizontal sway acceleration (directed along the yi-axis), $(\\mathrm{m/sec}^{2})$ Platform vertical heave acceleration (directed along the zi-axis), $(\\mathrm{m/sec}^{2})$ ",
        "page_idx": 6
    },
    {
        "type": "table",
        "img_path": "images/b59ad39bbceeabad86b89deae4877fa31e3dd12c070fc6930f2087c9303b729e.jpg",
        "table_caption": [],
        "table_footnote": [],
        "table_body": "\n\n<html><body><table><tr><td>180 PtfmRoll=PtfmRDxi= 4R π 180 PtfmPitch = PtfmRDyi qp π</td><td>Platform roll tilt displacement (about the xi-axis), (deg) Platform pitch tilt displacement (about the yi-axis), (deg)</td></tr><tr><td>180 PtfmYaw = PtfmRDzi = π</td><td>Platform yaw displacement (about the zi-axis), (deg) qy</td></tr><tr><td>180 E a</td><td></td></tr><tr><td>PtfmRVxt = π 180</td><td>Platform roll tilt velocity (about the xt-axis), (deg/sec)</td></tr><tr><td>PtfmRVyt = π 180 E</td><td>Platform pitch tilt velocity (about the yt-axis), (deg/sec)</td></tr><tr><td>PtfmRVzt = π 180</td><td>Platform yaw velocity (about the zt-axis), (deg/sec)</td></tr><tr><td>PtfmRVxi = π</td><td>Platform roll tilt velocity (about the xi-axis), (deg/sec)</td></tr><tr><td>180 PtfmRVyi = qp π</td><td>Platform pitch tilt velocity (about the yi-axis), (deg/sec)</td></tr><tr><td>180 PtfmRVzi = qy π</td><td>Platform yaw velocity (about the zi-axis), (deg/sec)</td></tr><tr><td>180 PtfmRAxt = π</td><td>Platform roll tilt acceleration (about the xt-axis), (deg/sec2)</td></tr><tr><td>180 PtfmRAyt = π</td><td>Platform pitch tilt acceleration (about the yt-axis), (deg/sec?)</td></tr><tr><td>180 PtfmRAzt = π</td><td>Platform yaw acceleration (about the zt-axis), (deg/sec²)</td></tr><tr><td>180 PtfmRAxi = YR π</td><td>Platform roll tilt acceleration (about the xi-axis), (deg/sec²)</td></tr><tr><td>180 PtfmRAyi = dip π</td><td>Platform pitch tilt acceleration (about the yi-axis), (deg/sec2)</td></tr></table></body></html>\n\n",
        "page_idx": 7
    },
    {
        "type": "equation",
        "text": "$P t j m R A z i=\\left(\\frac{l\\,{\\delta}O}{\\pi}\\right)\\ddot{q}_{_Y}$ ",
        "text_format": "latex",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "Platform yaw acceleration (about the zi-axis), (deg/sec) ",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "Tail-Furl Motions: ",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "$T F i n A l p h a=\\Bigg(\\frac{I\\,\\!\\!\\delta\\boldsymbol{\\theta}}{\\pi}\\Bigg)T F i n A O A$ $T F i n C L i f t=T F i n C L$ $T F i n C D r a g=T F i n C D$ $T F i n D n\\,P r\\,s=T F i n Q$ $T F i n C P F x=T F i n K F x\\,/\\,l,000$ $T F i n C P F y=T F i n K F y\\ /\\ l,O O O$ ",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "Tail fin lift coefficient, (-) Tail fin drag coefficient, (-) Tail fin dynamic pressure, (Pa) Tail fin tangential force, (kN) Tail fin normal force, (kN) ",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "Wind Motions: ",
        "text_level": 1,
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "Wind $V x i=u$ Wind $W i n d V y i=\\nu W i n d$ Wind $V z i=w$ Wind ",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "Nominal hub-height wind velocity (directed along the xi-axis), $(\\mathrm{m/s})$ Cross-wind hub-height velocity (directed along the yi-axis), $(\\mathrm{m/s})$ Vertical hub-height wind velocity (directed along the zi-axis), $(\\mathrm{m/s})$ ",
        "page_idx": 8
    },
    {
        "type": "equation",
        "text": "$$\nT o t W i n d V=\\sqrt{W i n d V x i^{2}+W i n d V y i^{2}+W i n d V z i^{2}}\n$$",
        "text_format": "latex",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "Total hub-height wind velocity magnitude, $(\\mathrm{m/s})$ ) ",
        "page_idx": 8
    },
    {
        "type": "equation",
        "text": "$$\nH o r W i n d V=\\sqrt{W i n d V\\!x i^{2}+W i n d V\\!y i^{2}}\n$$",
        "text_format": "latex",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "Horizontal hub-height wind velocity magnitude (in the xi-/yi-plane), (m/s) ",
        "page_idx": 8
    },
    {
        "type": "text",
        "text": "HorWndDir Horizontal hub-height wind direction (about the zi-axis), (deg) VerWndDir Vertical hub-height wind direction (about an axis orthogonal to the zi-axis and the horizontal wind vector), (deg) ",
        "page_idx": 8
    }
]