{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lumber Drying Time\n",
    "\n",
    "[Source of Red Oak equations](https://en.wikipedia.org/wiki/Wood_drying)\n",
    "\n",
    "8.07131 \t1730.63 \t233.426 \t1 \t99\n",
    "T(°C) = (T(°F) - 32) × 5/9\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Formula](https://upload.wikimedia.org/math/e/9/5/e95d69b400fdbdc5e8af6cc7bb6e7395.png)\n",
    "![Time Constant](https://upload.wikimedia.org/math/a/8/d/a8df91af00c8291dd3b4d399e35f41ae.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "191.8194885201814"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "def p_sat(T):\n",
    "    \"\"\"\n",
    "    Saturation vapor pressure of water - T in degress F\n",
    "    See: https://en.wikipedia.org/wiki/Vapour_pressure_of_water#Approximation_formula\n",
    "    \"\"\"\n",
    "    A = 8.07131\n",
    "    B = 1730.63\n",
    "    C = 233.426\n",
    "    T_C = (T - 32) * 5/9\n",
    "    p = 10**(A - B/(C+T_C))\n",
    "    return p\n",
    "\n",
    "p_sat(150)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def τ(L,T):\n",
    "    \"Time Constant\"\n",
    "    a = 0.0575\n",
    "    b = 0.00142\n",
    "    n = 1.52 \n",
    "    t = L**n / (a+b*p_sat(T))\n",
    "    return t\n",
    "\n",
    "def M_eq(h, T=72):\n",
    "    \"\"\"\n",
    "    Equlibrium Moisture Content \n",
    "    \n",
    "    Temperature (F) \n",
    "    Relative Humidity (h)\n",
    "    See: https://en.wikipedia.org/wiki/Equilibrium_moisture_content\n",
    "    \"\"\"\n",
    "    W = 330+0.452*T+0.00415 * T**2\n",
    "    k = 0.791+4.63*10**-4*T-8.44*10**-7*T**2\n",
    "    k1 = 6.34+7.75*10**-4*T-9.35*10**-5*T**2\n",
    "    k2 = 1.09+2.84*10**-2*T-9.04*10**-5*T**2\n",
    "    a = k1*k2*k**2*h**2\n",
    "    b = k1*k*h\n",
    "    M_e = 1800/W *(k*h/(1-k*h)+(b+2*a)/(1+b+a))\n",
    "    return M_e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Moisture W](https://upload.wikimedia.org/math/4/4/e/44e64c8f85e7b50aeb2c671c3cc7e1c1.png)\n",
    "![Moisture k](https://upload.wikimedia.org/math/2/9/7/297e89503659c6bcb292e67df2b243b7.png)\n",
    "![Moisture k1](https://upload.wikimedia.org/math/e/e/e/eeeafc23f767fd24808b1e9f5cafd6fc.png)\n",
    "![Moisture k2](https://upload.wikimedia.org/math/8/4/6/84664131ca2da179d131756dbfd0da4a.png)\n",
    "\n",
    "![Equilibrium Moisture](https://upload.wikimedia.org/math/4/d/8/4d80598eabc53e943dc7d05d3b417abd.png)\n",
    "\n",
    "![Drying Time](https://upload.wikimedia.org/math/c/b/0/cb0d2622cbbf62e49af6511c4296ea7c.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Drying Time Calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def t(M, M_0, h=0.72, L=1.5, T=72):\n",
    "    \"\"\"\n",
    "    Drying Time in days\n",
    "    \n",
    "    M - Desired Moisture Content\n",
    "    M_0 - Starting Moisture Content\n",
    "    h - relative humidity (72% average annual RH for Gainesville FL)\n",
    "    L - Smallest dimension(inches)\n",
    "    T - Temperature (F)\n",
    "    \"\"\"\n",
    "    M_e = M_eq(h,T)\n",
    "    if M <= M_e:\n",
    "        raise ValueError(\"M must above the Equilibrium Moisture Content of {:.3f}\".format(M_e))\n",
    "    t_ = -τ(L,T)*np.log((M-M_e)/(M_0-M_e))\n",
    "    print(\"\"\"\\tA {} inches thick board of Red Oak with an initial moisture \n",
    "    content of {}% will dry to {}% M.C. in {:.1f} Days if placed in a  \n",
    "    constant {:.0%} Relative Humidity evironment at {} F.\"\"\".format(L,M_0,M,t_,h,T))\n",
    "    return t_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tA 1.5 inches thick board of Red Oak with an initial moisture \n",
      "    content of 100% will dry to 14% M.C. in 113.4 Days if placed in a  \n",
      "    constant 72% Relative Humidity evironment at 72 F.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "113.35498604905855"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t(14,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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