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@kastnerp
Created May 7, 2021 15:02
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area-projection-factor
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "area-projection-factor",
"provenance": [],
"authorship_tag": "ABX9TyNGLPwYDqUPQHnuz7yvspQw",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/kastnerp/2b7d0fa0b38c7e435674266c959d75cf/area-projection-factor.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 283
},
"id": "TcKeVKtSQ4mQ",
"outputId": "90e52faa-208b-470a-f751-c1d720dbe7cb"
},
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import math\n",
"\n",
"def projected_angle_fac_park_tuller(theta, mode= \"both\"):\n",
" # mode: standing, walking, both\n",
"\n",
" # Park, S., & Tuller, S. E. (2011). Human body area factors for radiation exchange analysis: standing and walking postures. International journal of biometeorology, 55(5), 695-709.\n",
"\n",
" # Mean of Standing posture:\n",
" # y = 3.01E-07x3 - 6.46E-05x2 + 8.34E-04x + 0.298\n",
" # R² = 0.9998\n",
" # Mean of Walking posture:\n",
" # y = 3.67E-07x3 - 6.74E-05x2 + 8.49E-04x + 0.297\n",
" # R² = 0.9996\n",
" # Mean of Standing and Walking postures:\n",
" # y = 3.34E-07x3 - 6.60E-05x2 + 8.42E-04x + 0.297\n",
" # R² = 0.9997\n",
"\n",
" x = theta\n",
" y = 0\n",
"\n",
" if mode == \"both\":\n",
" y = 3.34E-07*x**3 - 6.60E-05*x**2 + 8.42E-04*x + 0.297\n",
" elif mode == \"standing\":\n",
" y = 3.01E-07*x**3 - 6.46E-05*x**2 + 8.34E-04*x + 0.298\n",
" elif mode == \"walking\": \n",
" y = 3.67E-07*x**3 - 6.74E-05*x**2 + 8.49E-04*x + 0.297 \n",
"\n",
" return y\n",
"\n",
"\n",
"\n",
"def projected_angle_fac_matzarakis(theta):\n",
" # Staiger, H., & Matzarakis, A. (2020). Accuracy of Mean Radiant Temperature Derived from Active and Passive Radiometry. Atmosphere, 11(8), 805.\n",
" # https://www.mdpi.com/2073-4433/11/8/805/htm#B11-atmosphere-11-00805\n",
" return 0.308*math.cos(theta*(0.998-(theta**2/50000)))\n",
"\n",
"def projected_cylinder_area(theta, r, h):\n",
" # From scratch:\n",
" # Consider a cylinder of radius r and height h rotated with respect to the flow direction of a fluid by about an axis parallel to the base. The frontal area of the cylinder is the area perpendicular to the flow direction. If this shape is projected onto the 2D plane, the resulting 2D area is pi r^2 sin theta + 2 r h cos theta\n",
" # Test: For a cylinder with r = 1 and h = 2 this should be\n",
" # A = 2*1 = 2 m^2 for theta = 90°\n",
" # A = r^2 * PI = 3.14 m^2 for theta = 0°\n",
" # PI*r*2*cos(B) + 2*r*h*sin*(B)\n",
" diameter = 2*r\n",
" return math.pi * r**2 * math.sin(theta) + diameter* h* math.cos(theta)\n",
"\n",
"h = 2\n",
"r = 0.3\n",
"\n",
"cyl_surf_area = 2*r**2*math.pi+2*r*math.pi*h\n",
"\n",
"fig =plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"size = 5\n",
"\n",
"for theta in range(0,90,1):\n",
" deg = np.deg2rad(theta)\n",
" sa = projected_cylinder_area(deg, r,h)\n",
" am = projected_angle_fac_matzarakis(deg)\n",
" \n",
"\n",
" # Normalize this one by cylinder surface area\n",
"\n",
" plt.scatter(theta, sa/cyl_surf_area, color = \"black\", s=size, )\n",
" # Mazarakis equation\n",
" plt.scatter(theta,am, color = \"red\", s= size, )\n",
"\n",
"\n",
"\n",
" # Park, S., & Tuller\n",
" mode = [\"both\", \"standing\", \"walking\"]\n",
" colors = [\"darkgreen\", \"lightgreen\", \"green\"]\n",
"\n",
"\n",
" for i in zip(mode, colors):\n",
" apt = projected_angle_fac_park_tuller(theta, i[0])\n",
" plt.scatter(theta,apt, color = i[1], s= size, )\n",
"\n",
"\n",
"ax.legend([\"Simple Cylinder Approach\", \n",
" \"Matzarakis (2020)\",\n",
" \"Park & Tuller (2011) - Both\",\n",
" \"Park & Tuller (2011) - Standing\",\n",
" \"Park & Tuller (2011) - Walking\"])\n",
"ax.set(xlim=(0,90), ylim=(0, 0.35))\n",
"ax.set_ylabel(\"Area Projection Factor\")\n",
"ax.set_xlabel(\"Azimuth [°]\")\n",
"plt.show()\n",
"\n"
],
"execution_count": 10,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
}
]
}
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