Atmosphere.ipynb

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  "name": ""
 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Introduction to Aeronotical Engineering, Atmosphere#"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this Notebook we show how to compute temperature, density and pressure at any height in the atmosphere. These calculations are based on the edX course https://www.edx.org/course/delftx/delftx-ae1110x-introduction-aeronautical-1201. First, we define a number of constants and utility methods."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g = 9.80665 # m / s^2\n",
      "R = 287.00  # J / kg * K\n",
      "\n",
      "def celcius_to_kelvin(c):\n",
      "    return c + 273.15\n",
      "\n",
      "ISA_T_0 = celcius_to_kelvin(15.0)\n",
      "ISA_p_0 = 101325\n",
      "ISA_rho_0 = ISA_p_0 / (R * ISA_T_0)\n",
      "\n",
      "# Layers represents the thicknes and lapse rate for every segment of the atmosphere.\n",
      "layers = [\n",
      "    (11.0e3, -0.0065),\n",
      "    (9.0e3, 0.0),\n",
      "    (12.0e3, 0.001),\n",
      "    (15.0e3, 0.0028),\n",
      "    (np.infty, 0.0)\n",
      "]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def T(h, T_0=ISA_T_0, layers=layers):\n",
      "    \"\"\"Computes the temperature at height h (in meters).\"\"\"\n",
      "    lh, a = layers[0]\n",
      "    if h < lh:\n",
      "        return T_0 + a * h\n",
      "    return T(h - lh, T_0 + a * lh, layers[1:])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def rho(h, T_0=ISA_T_0, rho_0=ISA_rho_0, layers=layers):\n",
      "    \"\"\"Computes the density at height h (in meters).\"\"\"\n",
      "    lh, a = layers[0]\n",
      "    \n",
      "    if a == 0.0:\n",
      "        if h < lh:\n",
      "            return rho_0 * np.exp(-g * h / (T_0 * R))\n",
      "        return rho(h - lh, T_0, rho_0 * np.exp(-g * lh / (T_0 * R)), layers[1:])\n",
      "    else:\n",
      "        if h < lh:\n",
      "            T_1 = T_0 + a * h\n",
      "            return rho_0 * np.power(T_1 / T_0, -g / (a * R) - 1.0)\n",
      "        T_1 = T_0 + a * lh\n",
      "        return rho(h - lh, T_1, rho_0 * np.power(T_1 / T_0, -g / (a * R) - 1.0), layers[1:])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def p(h, T_0=ISA_T_0, p_0=ISA_p_0, layers=layers):\n",
      "    \"\"\"Computes the pressure at height h (in meters).\"\"\"\n",
      "    lh, a = layers[0]\n",
      "    \n",
      "    if a == 0.0:\n",
      "        if h < lh:\n",
      "            return p_0 * np.exp(-g * h / (T_0 * R))\n",
      "        return p(h - lh, T_0, p_0 * np.exp(-g * lh / (T_0 * R)), layers[1:])\n",
      "    else:\n",
      "        if h < lh:\n",
      "            T_1 = T_0 + a * h\n",
      "            return p_0 * np.power(T_1 / T_0, -g / (a * R))\n",
      "        T_1 = T_0 + a * lh\n",
      "        return p(h - lh, T_1, p_0 * np.power(T_1 / T_0, -g / (a * R)), layers[1:])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now compute the temperature, density and pressure up to 60km."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hs = np.arange(start=0.0, stop=60000.0, step=1000.0)\n",
      "Ts = np.zeros_like(hs)\n",
      "rhos = np.zeros_like(hs)\n",
      "ps = np.zeros_like(hs)\n",
      "for i in xrange(len(hs)):\n",
      "    Ts[i] = T(hs[i])\n",
      "    rhos[i] = rho(hs[i])\n",
      "    ps[i] = p(hs[i])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_layers(width):\n",
      "    cs = 0.0\n",
      "    for h, _ in layers:\n",
      "        cs += h\n",
      "        plt.plot([0.0, width], [cs, cs], 'k-.')\n",
      "        \n",
      "plt.figure(figsize=(16,4))\n",
      "plt.subplot(131)\n",
      "plt.plot(Ts, hs)\n",
      "plot_layers(np.max(Ts))\n",
      "plt.title(\"Temperature (Kelvin)\")\n",
      "plt.subplot(132)\n",
      "plt.semilogx(rhos, hs)\n",
      "plot_layers(np.max(rhos))\n",
      "plt.title(\"Density (Kg/m3)\")\n",
      "plt.subplot(133)\n",
      "plt.semilogx(ps, hs)\n",
      "plot_layers(np.max(ps))\n",
      "plt.title(\"Pressure (Pascal)\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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8dcXOba1atbjpppto3LgxTZs2BSA1NZXo6GhuuOEG2rZty5EjR9zvnzRpEhER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\nAigsBBISgH79gKVLuZCBJ7DXEXnfc88BTz4JPP8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       "text": [
        "<matplotlib.figure.Figure at 0x112141790>"
       ]
      }
     ],
     "prompt_number": 54
    }
   ],
   "metadata": {}
  }
 ]
}