{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Terminal Velocity\n",
    "\n",
    "---\n",
    "\n",
    "This notebook discusses the [drag forces](https://en.wikipedia.org/wiki/Drag_%28physics%29) exerted on a body when traveling through air. It's also done in [Julia](julialang.org) so that I can better understand the potencial of the language.\n",
    "\n",
    "![Drag Forces](http://upload.wikimedia.org/wikipedia/en/8/89/Parachuters_in_hybrid_formation.jpg)  \n",
    "\n",
    "Image courtesy of [WikiMedia](http://upload.wikimedia.org/wikipedia/en/8/89/Parachuters_in_hybrid_formation.jpg).\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A falling body is subject to two forces: a downward force, $\\vec{F_g}$, due to gravity, and an upward force $\\vec{F_a}$, due to air resistance. Let's consider a body with mass $m$. Assuming an upward oriented Y axis, the following applies:\n",
    "\n",
    "$$ F_g = - g \\cdot m $$\n",
    "\n",
    "$$ F_a = - sgn(v) \\cdot {1 \\over 2} \\rho C_D A v^2 $$\n",
    "\n",
    "In these formulas, $m$ is the mass of the body, $\\rho$ is the density of air ($\\approx 1.2 Kg/m^3$), $g$ is the accelaration of gravity ($\\approx 9.8 m/s^2$), $v$ is the velocity of the body, $C_D$ is the drag coeficient of the body and $A$ is its cross-section area. $sgn(x)$ is the sign function that given a number returns +1 for positives and -1 for negatives. In the formula it makes the force always contrary to the movement of the body.\n",
    "\n",
    "Thus, the resulting force $\\vec{F}$ experienced by the body is:\n",
    "\n",
    "$$ F = - g \\cdot m - sgn(v) \\cdot {1 \\over 2} \\rho C_D A v^2 $$\n",
    "\n",
    "Given that force is directly related to accelaration, and accelaration to velocity:\n",
    "\n",
    "$$ v = \\frac{dy}{dt} $$\n",
    "\n",
    "$$ F = m \\cdot \\frac{dv}{dt} $$\n",
    "\n",
    "substituting, we get this differencial equation:\n",
    "\n",
    "$$ m \\cdot \\frac{dv}{dt} = - g \\cdot m - sgn(v) \\cdot {1 \\over 2} \\rho C_D A v^2 $$\n",
    "\n",
    "In fact, this can be expressed as a system of differential equations in the form ${\\bf f}' = {\\bf g}({\\bf f}, t)$:\n",
    "\n",
    "$$ \\begin{cases} \\frac{dy}{dt} = v \\\\\\\\ \\frac{dv}{dt} = -g - sgn(v) \\cdot {1 \\over 2} {\\rho \\over m} C_D A v^2 \\end{cases} $$\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "using ODE;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now define the initial conditions and constants of the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Constants \n",
    "const g  = 9.8                # Accelaration of gravity\n",
    "const p  = 1.2                # Density of air\n",
    "\n",
    "# Caracteristics of the problem\n",
    "const m  = 0.100              # A 100 g ball\n",
    "const r  = 0.10               # 10 cm radius\n",
    "const Cd = 0.5                # Drag coeficient for a small spherical object\n",
    "const y0 = 1000.0             # Initial height of the body (1000 m)\n",
    "const v0 = 10.0               # Initial velocity of the body (10 m/s^2, going up)\n",
    "const A  = pi*r^2;            # Cross-section area of the body;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As said, let's define a system of ordinary differential equations in its normal form ${\\bf f}' = {\\bf g}({\\bf f}, t)$. (In the code bellow we substitute $g()$ for $gm()$ so that it doesn't clash with the acceleration of gravity constant - $g$). Note that $f$ is an $R^2$ function containing $y$ and $y'$ (and $v = y'$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "function gm(t, f)\n",
    "    (y, v) = f                                          # Extract y and v (i.e., dy/dt) from the f mapping\n",
    "    \n",
    "    dy_dt = v                                           # The differential equations\n",
    "    dv_dt = -1.0*g - sign(v)*(1./2.)*(p/m)*Cd*A*v^2.0\n",
    "    \n",
    "    [dy_dt; dv_dt]                                      # Return the derivatives\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define the conditions to numerically solve the problem, including a time vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Initial conditions (position and velocity)\n",
    "const start = [y0; v0]\n",
    "\n",
    "# Time span (from 0 to 5 secs)\n",
    "ts = [0.0; 5.0];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's solve the equations numericaly and extract the corresponding $y(t)$ and $v(t)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "t, res = ode45(gm, start, ts)\n",
    "y = map(x -> x[1], res)\n",
    "v = map(x -> x[2], res);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can plot the solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x313de9b50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using PyPlot\n",
    "fig, ax = subplots(1, 2, sharex=true, figsize=(10,4))\n",
    "\n",
    "ax[1][:plot](t, v)\n",
    "ax[1][:set_title](\"Velocity over time\");\n",
    "ax[1][:set_xlabel](\"Time (sec)\")\n",
    "ax[1][:set_ylabel](\"Velocity (m/sec)\")\n",
    "\n",
    "ax[2][:plot](t, y)\n",
    "ax[2][:set_title](\"Height over time\");\n",
    "ax[2][:set_xlabel](\"Time (sec)\")\n",
    "ax[2][:set_ylabel](\"Height (m)\");\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the velocity starts at 10 $m/s^2$, with the ball going up. Its velocity starts decreasing, goes to zero at max height, and then becomes negative as the ball starts coming down. After a while it reaches its maximum speed: terminal velocity. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The theorerically [terminal velocity](http://en.wikipedia.org/wiki/Terminal_velocity), $V_t$, is:\n",
    "\n",
    "$$ V_t = \\sqrt{\\frac{2 m g}{\\rho A C_D}} $$\n",
    "\n",
    "Calculating it is easy enough:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.197118685526071"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vt = sqrt( (2.0*m*g) / (p*A*Cd) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, with our numerical simulation, the terminal velocity is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.190666752444804"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The terminal velocity\n",
    "vt_numeric = abs(minimum(v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two agree."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.4.3",
   "language": "julia",
   "name": "julia-0.4"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}