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    "# Biomechanical analysis of vertical jumps\n",
    "\n",
    "> Marcos Duarte  \n",
    "> [Laboratory of Biomechanics and Motor Control](http://pesquisa.ufabc.edu.br/bmclab)  \n",
    "> Federal University of ABC, Brazil"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Python-setup\" data-toc-modified-id=\"Python-setup-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Python setup</a></span></li><li><span><a href=\"#Introduction\" data-toc-modified-id=\"Introduction-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Introduction</a></span></li><li><span><a href=\"#Center-of-gravity\" data-toc-modified-id=\"Center-of-gravity-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Center of gravity</a></span><ul class=\"toc-item\"><li><span><a href=\"#Measurement-of-the-jump-height-from-flight-time\" data-toc-modified-id=\"Measurement-of-the-jump-height-from-flight-time-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>Measurement of the jump height from flight time</a></span><ul class=\"toc-item\"><li><span><a href=\"#Beware:-the-flight-time-you-measure-not-always-is-the-flight-time-you-want\" data-toc-modified-id=\"Beware:-the-flight-time-you-measure-not-always-is-the-flight-time-you-want-3.1.1\"><span class=\"toc-item-num\">3.1.1&nbsp;&nbsp;</span>Beware: the flight time you measure not always is the flight time you want</a></span></li></ul></li><li><span><a href=\"#Measurement-of-the-jump-height-using-a-force-platform\" data-toc-modified-id=\"Measurement-of-the-jump-height-using-a-force-platform-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>Measurement of the jump height using a force platform</a></span></li><li><span><a href=\"#Force-platform\" data-toc-modified-id=\"Force-platform-3.3\"><span class=\"toc-item-num\">3.3&nbsp;&nbsp;</span>Force platform</a></span><ul class=\"toc-item\"><li><span><a href=\"#Ground-reaction-force-during-vertical-jump\" data-toc-modified-id=\"Ground-reaction-force-during-vertical-jump-3.3.1\"><span class=\"toc-item-num\">3.3.1&nbsp;&nbsp;</span>Ground reaction force during vertical jump</a></span></li></ul></li><li><span><a href=\"#Jump-height-from-the-impulse-measurement\" data-toc-modified-id=\"Jump-height-from-the-impulse-measurement-3.4\"><span class=\"toc-item-num\">3.4&nbsp;&nbsp;</span>Jump height from the impulse measurement</a></span></li><li><span><a href=\"#Kinetic-analysis-of-a-vertical-jump\" data-toc-modified-id=\"Kinetic-analysis-of-a-vertical-jump-3.5\"><span class=\"toc-item-num\">3.5&nbsp;&nbsp;</span>Kinetic analysis of a vertical jump</a></span></li></ul></li><li><span><a href=\"#Further-reading\" data-toc-modified-id=\"Further-reading-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Further reading</a></span></li><li><span><a href=\"#Video-lectures-on-the-internet\" data-toc-modified-id=\"Video-lectures-on-the-internet-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Video lectures on the internet</a></span></li><li><span><a href=\"#Problems\" data-toc-modified-id=\"Problems-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>Problems</a></span></li><li><span><a href=\"#References\" data-toc-modified-id=\"References-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>References</a></span></li></ul></div>"
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   "source": [
    "## Python setup"
   ]
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   "source": [
    "import numpy as np\n",
    "from scipy.integrate import cumtrapz\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import YouTubeVideo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "A vertical jump is the act of raising (in the vertical direction) the body center of gravity using your own muscle forces and jumping into the air ([Wikipedia](https://en.wikipedia.org/wiki/Vertical_jump)).\n",
    "\n",
    "Besides being an important element in several sports, the vertical jump can be used to train and evaluate some physical capacities (e.g., strength and power) of a person.\n",
    "\n",
    "In this notebook we will study some aspects of the biomechanics of vertical jumps."
   ]
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   "source": [
    "## Center of gravity\n",
    "\n",
    "Center of gravity or center of mass is a measure of the average location in space of the body considering all body segments, their mass and their position.   \n",
    "From Mechanics, the exact definitions of these quantities are:   \n",
    "\n",
    "- **Center of mass (CM)**: The center of mass (or barycenter) is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. SI unit: $m$ (vector).   \n",
    "- **Center of gravity (CG)**: Center of gravity is the point in an object around which the resultant torque due to gravity forces vanishes. Near the surface of the earth, where the gravity acts downward as a parallel force field, the center of gravity and the center of mass are the same. SI unit: $m$ (vector).\n",
    "\n",
    "The mathematical definition for the center of mass or center of gravity of a system with N objects (or particles), each with mass $m_i$ and position $r_i$ is:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}{l l} \n",
    "\\vec{r}_{cm} = \\dfrac{1}{M}\\sum_{i=1}^N m_{i}\\vec{r}_i \\quad\\quad \\text{where} \\quad M = \\sum_{i=1}^N m_{i} \\\\\n",
    "\\vec{r}_{cg} = \\dfrac{1}{Mg}\\sum_{i=1}^N m_{i}g_{i}\\vec{r}_i \\quad \\text{where} \\quad Mg = \\sum_{i=1}^N m_{i}g_{i}\n",
    "\\end{array}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "If we consider $g$ constant:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}{l l} \n",
    "\\vec{r}_{cg} = \\dfrac{g}{Mg}\\sum_{i=1}^N m_{i} \\: \\vec{r}_i = \\dfrac{1}{M}\\sum_{i=1}^N m_{i}\\:\\vec{r}_i \\\\\n",
    "\\\\\n",
    "\\vec{r}_{cg} = \\vec{r}_{cm}\n",
    "\\end{array}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "This means that how much a person jumps is measured by the displacement of his or her center of gravity, and not by how much the feet was raised in space. For instance, the following Youtube video entitled \"Highest Vertical jump 62 inches\" (157.5 cm!) shows a great vertical jump, but in fact its height is 'just' about half of that:"
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\n",
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    "YouTubeVideo('NUyql5IFTNY')"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the true measurement of the height of a vertical jump is the displacement of the center of gravity in the vertical direction. A problem is that to measure the center of gravity position is usually too complicated because we would have to estimate the position of each body segment.    \n",
    "Instead, there are alternative methods with varying degrees of accuracy for measuring the height of vertical jump ([see here for a list](http://www.topendsports.com/testing/equipment-verticaljump.htm)):   \n",
    "\n",
    " - [**Sargent Jump Test**](http://www.brianmac.co.uk/sgtjump.htm). How high you can reach an object.   \n",
    " - **Flight time measurement**. From Newton's laws of motion, the height of a jump is related to the flight time under controlled conditions. One can measure the flight time using a [contact mat](http://www.probotics.org/JustJump/verticalJump.htm), light sensor, [accelerometer](http://www.jssm.org/vol11/n1/17/v11n1-17pdf.pdf), video (the number of frames the jumper is in the air), attaching a cable to the jumper's waist and measuring the displacement of this cable, etc.      \n",
    " - **Force platform measurements**. A device called [force platform](https://en.wikipedia.org/wiki/Force_platform) which measures the forces applied on the ground as a function of time can also be used to measure the flight time and then the height of vertical jump. But the real utility of the force platform is that it can actually measure the force produced by the jumper to find the displacement of the center of gravity using Newton's laws of motion.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement of the jump height from flight time\n",
    "\n",
    "We can estimate the height of a jump measuring for how long the jumper stayed in the air during the jump (flight time). At the vertical direction and ignoring the air resistance, the only external force that acts on the body in the air is the (constant) gravitational force, with magnitude $P = -mg$, where $g$ is the acceleration of gravity (about $9.8 m/s^2$ on the surface of the Earth). Using the equation of motion for a body with constant acceleration, the height of the center of gravity of a body in the air at a certain time is:   \n",
    "\n",
    "\\begin{equation}\n",
    "h(t) = h_0 + v_0 t - \\frac{gt^2}{2}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "At the maximum height ($h$, the jump height), the vertical velocity of the body is zero. We can take use this property to calculate the jump height from the time of falling:\n",
    "\n",
    "\\begin{equation}\n",
    "h = \\frac{gt_{fall}^2}{2}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Because the time of falling is equal to the time of rising, $t_{flight} = t_{rise} + t_{fall} = 2 t_{fall}$, the jump height as a function of the flight time is:\n",
    "\n",
    "\\begin{equation}\n",
    "h = \\frac{gt_{\\text{flight}}^2}{8}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "This simple equation is the principle of measurement of the jump height any an instrument that measures the time the feet is not in contact with ground (using a pressure mat or a photocell sensor).  \n",
    "There are (were) even shoes using this principle of measurement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:02.740049Z",
     "start_time": "2021-02-09T21:13:02.652681Z"
    }
   },
   "outputs": [
    {
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/QXnQ4ENjTuY\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fc77515fac0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('QXnQ4ENjTuY')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Beware: the flight time you measure not always is the flight time you want\n",
    "\n",
    "However, the flight time, measured as the time without contact with the ground, during a jump is not necessarily equal to the flight time of the body center of gravity (which is the measure we need to estimate the actual height jump).  \n",
    "\n",
    "For example, if the jumper flexes knees and hips at the landing phase, the measured flight time will be larger but not the flight time of the body center of gravity. Because that, a more accurate method is to use a force platform as we will see now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement of the jump height using a force platform\n",
    "\n",
    "Let's draw the [free body diagram](https://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/FreeBodyDiagram.ipynb) for a person performing a jump:\n",
    "\n",
    "<div class='center-align'><figure><img src=\"./../images/FBDjump.png\" alt=\"Vertical jump FBD\"/><figcaption><center><i>A person during the propulsion phase of jumping and the corresponding free body diagram drawn for the center of mass. GRF(t) is the time-varying ground reaction force.</i></center></figcaption></figure></div>\n",
    "\n",
    "So, according to the Euler's version of the Newton's second law (for the motion of the body center of mass), the dynamics (as a function of time) for the body center of mass during a jump is given by:\n",
    "\n",
    "\\begin{equation}\n",
    "GRF(t) - mg = ma(t)\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Where $GRF(t)$ is the ground reaction force applied by the ground on the jumper, $m$ is the subject mass, and $a(t)$ the center of mass acceleration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Force platform  \n",
    "\n",
    "Force platform or force plate is an instrument for measuring the forces generated by a body acting on the platform. A force plate is an electromechanical transducer that measures force typically by measuring the deformation (strain) on its sensors and converting that to electrical signals. These electrical signals are converted back to force and moment of force using calibration factors. \n",
    "\n",
    "<div class='center-align'><figure><img src=\"./../images/KistlerForcePlate.png\" alt=\"A force plate and its coordinate system convention\"/><figcaption><center><i>Figure. A force plate and its coordinate system convention (from <a href=\"http://isbweb.org/software/movanal/vaughan/kistler.pdf\">Kistler Force Plate Formulae</a>).</i></center></figcaption></figure></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usually the force platform is placed on the floor and we are interested not in the force applied on the force platform, but in its reaction, the force that the force platform applied on the jumper, which, according to Newton's third law of motion, has the same magnitude and line of action but opposite direction. Because of that, usually the forces measured by the force platform are referred as ground reaction forces. \n",
    "\n",
    "Most of the commercial force platforms are able to measure the vectors force, $[F_X,\\, F_Y,\\, F_Z]$, and moment of force, $[M_X,\\, M_Y,\\, M_Z]$, from which the [center of pressure](https://en.wikipedia.org/wiki/Center_of_pressure_(terrestrial_locomotion) (COP, the point of application of the resultant force on the force plate) can be calculated $[COP_X,\\, COP_Y]$. Because of that, these force platforms are known as six-components. Force platforms that can measure only the vertical force component and two moments of force (or the two COPs) are known as three-components.\n",
    "\n",
    "Read more about force platforms in chapter 5 or Winter's book and in Cross (1999). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ground reaction force during vertical jump\n",
    "\n",
    "Here is a video from Youtube of a person jumping and a plot of the ground reaction force measured with a force platform:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:02.824992Z",
     "start_time": "2021-02-09T21:13:02.741306Z"
    }
   },
   "outputs": [
    {
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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/qN3apht8zRs\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fc77518b370>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('qN3apht8zRs')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a plot of the vertical component of the ground reaction force measured with a force platform during a vertical jump with countermovement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:02.946896Z",
     "start_time": "2021-02-09T21:13:02.825938Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load data file\n",
    "GRFv = np.loadtxt('https://raw.githubusercontent.com/BMClab/BMC/master/data/GRFZjump.txt',\n",
    "                  skiprows=0, unpack=False)\n",
    "#GRFv = np.loadtxt('./../data/GRFZjump.txt', skiprows=0, unpack=False)\n",
    "\n",
    "# sampling frequency (Hz)\n",
    "freq = 600\n",
    "time = np.arange(0, len(GRFv)/freq, 1/freq)\n",
    "# gravitational acceleration, m/s2\n",
    "g = 9.8\n",
    "# subject's mass\n",
    "m = np.mean(GRFv[0:int(freq/10)])/g\n",
    "# plot GRF data\n",
    "fig, ax = plt.subplots(1, 1, figsize=(10, 4))\n",
    "ax.plot(time, GRFv, 'b', linewidth='3')\n",
    "# plot subject's weight\n",
    "ax.plot([time[0], time[-1]], [m*g, m*g], 'k', linewidth='2')\n",
    "ax.set_xlabel('Time [s]', fontsize=16)\n",
    "ax.set_ylabel('Vertical GRF [N]', fontsize=16)\n",
    "ax.set_xticks(np.arange(time[0], time[-1], .2))\n",
    "ax.grid()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This graph of the vertical component of the ground reaction force shown above has very interesting things: \n",
    "\n",
    " 1. At the beginning the jumper was standing still and the GRF is equal to the jumper's body weight;  \n",
    " 2. After the jumper started the movement to jump there is a phase where GRF is lower than the body weight even with the jumper completely on the ground;   \n",
    " 3. The GRF increases to about two times the body weight while the jumper is still on the ground;   \n",
    " 4. When the jumper is in the air is clearly indicated by the zero values of GRF;   \n",
    " 5. After landing the GRF reaches a peak of about six times the jumper's body weight.  \n",
    " \n",
    "These are all interesting things but we will discuss only some of them next.  \n",
    "We can detect the takeoff and landing instants by detecting the first and last time GRF is under a certain threshold (close to zero):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:02.950674Z",
     "start_time": "2021-02-09T21:13:02.947801Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Takeoff instant 0.907 s\n",
      "Landing instant 1.323 s\n"
     ]
    }
   ],
   "source": [
    "# make sure GRFv has no offset\n",
    "GRFv -= np.min(GRFv)\n",
    "\n",
    "limiar = 10\n",
    "\n",
    "inds = np.where(GRFv < limiar)\n",
    "i1 = inds[0][0]\n",
    "i2 = inds[0][-1]\n",
    "print('Takeoff instant {:.3f} s'.format(time[i1]))\n",
    "print('Landing instant {:.3f} s'.format(time[i2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The jump height can be calculated from these instants using the kinematic expression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:02.954099Z",
     "start_time": "2021-02-09T21:13:02.951775Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jump height 0.213 m\n"
     ]
    }
   ],
   "source": [
    "h = g*(time[i2]-time[i1])**2/8\n",
    "print('Jump height {:.3f} m'.format(h))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can detect the beginning of movement by detecting when GRFv starts to go below the body weight:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:02.958053Z",
     "start_time": "2021-02-09T21:13:02.955615Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jump start 0.188 s\n"
     ]
    }
   ],
   "source": [
    "inds = np.where(GRFv < 0.95*m*g)\n",
    "i0 = inds[0][0]\n",
    "print('Jump start {:.3f} s'.format(time[i0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Jump height from the impulse measurement\n",
    "\n",
    "We know that the [mechanical impulse](http://nbviewer.ipython.org/github/BMClab/bmc/blob/master/notebooks/KineticsFundamentalConcepts.ipynb#Impulse) is equal to the change in linear momentum of a body, which for a body with constant mass is simply the body mass times the change in velocity. For a time-varying force, the impulse is:\n",
    "\n",
    "\\begin{equation}\n",
    "\\vec{Imp} = \\int_{t_0}^{t_f} \\vec{F}(t) \\mathrm{d}t = m [\\vec{v}_{t_f} - \\vec{v}_{t_0}]\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "For the analysis of a vertical jump, in the vertical direction $F(t) = GRF(t) - mg$ and $F(t)$ is discrete in time (sampled at intervals $\\Delta t$):\n",
    "\n",
    "\\begin{equation}\n",
    "Imp = \\sum_{t_0}^{t_f} F(t)\\Delta t = m [v_{t_f} - v_{t_0}]\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "For a jump starting from a rest position, the initial velocity is zero. This means that the change in velocity is equal to the final velocity (at the moment of takeoff). Therefore, we can calculate the final velocity of the propulsion phase as:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}{l l}\n",
    "\\sum_{t_0}^{t_f} F(t)\\Delta t = m[v_f-0] \\implies \\\\\n",
    "v_f = \\dfrac{\\sum_{t_0}^{t_f} F(t)\\Delta t}{m}\n",
    "\\end{array}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "This final velocity is the initial velocity of the aerial phase of the jump.  \n",
    "If we know the initial velocity of the jump, it's straightforward to calculate the jump height, for example, using the [Torricelli's equation](http://en.wikipedia.org/wiki/Torricelli's_equation): \n",
    "\n",
    "\\begin{equation}\n",
    "v_f^2 = v_0^2 - 2gh\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Where $v_i$ and $v_f$ are the initial and final velocities and $h$ is the change in the position of the body center of gravity (the height of the vertical jump) and we considered just the first part of the jump, the upward phase.\n",
    "\n",
    "From Mechanics we know that the velocities at takeoff and at landing are equal in magnitude and that the time of the upward phase is equal to the time of the downward phase of this ballistic flight.\n",
    "\n",
    "For the upward phase of the vertical jump:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}{l l} \n",
    "0 = v_0^2 - 2gh \\implies \\\\\n",
    "h = \\dfrac{v_0^2}{2g}\n",
    "\\end{array}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "We could also have calculated the jump height from the velocity using the [principle of conservation of the mechanical energy](https://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/KineticsFundamentalConcepts.ipynb#Principles-of-conservation). The sum of the potential and kinetic energies at the instants beginning of the jump ($t_0$) and highest point of the jump trajectory ($t_{hmax}$) are equal:\n",
    "\n",
    "\\begin{equation}\n",
    "mgh(t_0) + \\frac{mv^2(t_0)}{2} = mgh(t_{hmax}) + \\frac{mv^2(t_{hmax})}{2}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "0 + \\frac{mv^2(t_0)}{2} =  mgh(t_{hmax}) + 0\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "h(t_{hmax}) = \\frac{v^2(t_0)}{2g}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Same expression as before.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kinetic analysis of a vertical jump\n",
    "\n",
    "The force plate can also be used to calculate other mechanical variables to characterize the subject's performance (see Dowling and Vamos 1993) for a list of such variables). For example, \n",
    "\n",
    "Resultant vertical force on the subject:\n",
    "\n",
    "\\begin{equation}\n",
    "F(t) = GRF(t) - mg\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Vertical acceleration of the center of mass:\n",
    "\n",
    "\\begin{equation}\n",
    "a(t) = \\frac{F(t)}{m}\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Vertical velocity of the center of mass (initial velocity equals zero):\n",
    "\n",
    "\\begin{equation}\n",
    "v(t) = \\sum_{t_0}^{t_f} a(t) \\Delta t\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Vertical displacement of the center of mass (initial displacement equals zero):\n",
    "\n",
    "\\begin{equation}\n",
    "h(t) = \\sum_{t_0}^{t_f} v(t) \\Delta t\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Power due to the resultant vertical force:\n",
    "\n",
    "\\begin{equation}\n",
    "P(t) = GRF(t)v(t)\n",
    "\\label{}\n",
    "\\end{equation}\n",
    "\n",
    "Note that we used the vertical ground reaction force for the calculation of mechanical power, not the resultant force on the body, to represent the total power the jumper is producing. One could argue that during standing the jumper is not actually 'generating' any force (so we should not use GRF), but in this phase, the jumper's speed is zero, and the power is zero.\n",
    "\n",
    "Let's work with the ground reaction force data from a vertical jump and calculate such quantities.  \n",
    "For now, let's ignore the landing and focus on the propulsion phase of the jump."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:02.962356Z",
     "start_time": "2021-02-09T21:13:02.959414Z"
    }
   },
   "outputs": [],
   "source": [
    "time = time[i0:i1+1] - time[i0]\n",
    "# resultant vertical force\n",
    "F = GRFv[i0:i1+1] - m*g\n",
    "# vertical acceleration of the center of mass\n",
    "a = F/m\n",
    "# vertical velocity of the center of mass\n",
    "v = cumtrapz(a, dx=1/freq, initial=0)\n",
    "# vertical displacement of the center of mass\n",
    "h = cumtrapz(v, dx=1/freq, initial=0)\n",
    "# power due to the resultant vertical force\n",
    "P = (F+m*g)*v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here are the plots for these quantities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:03.416195Z",
     "start_time": "2021-02-09T21:13:02.963611Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(5, 1, sharex=True, squeeze=True, figsize=(8, 8))\n",
    "axs[0].plot(time, F, 'b', lw='4', label='Force')\n",
    "axs[1].plot(time, a, 'b', lw='4', label='Acceleration')\n",
    "axs[2].plot(time, v, 'b', lw='4', label='Velocity')\n",
    "axs[3].plot(time, h, 'b', lw='4', label='Displacement')\n",
    "axs[4].plot(time, P, 'b', lw='4', label='Power')\n",
    "axs[4].set_xlabel('Time [$s$]', fontsize=14)\n",
    "axs[4].set_xticks(np.arange(time[0], time[-1], .1))\n",
    "axs[4].set_xlim([time[0], time[-1]])\n",
    "ylabel = ['F [$N$]', 'a [$m/s^2$]', 'v [$m/s$]', 'h [$m$]', 'P [$W$]']\n",
    "for (axi, ylabeli) in zip(axs, ylabel):\n",
    "    axi.axhline(0, c='r', linewidth='2', alpha=.6)\n",
    "    axi.set_ylabel(ylabeli, fontsize=14)\n",
    "    axi.text(.03, .75, axi.get_legend_handles_labels()[1][0],\n",
    "             transform=axi.transAxes, fontsize=14, c='r')\n",
    "    axi.yaxis.set_major_locator(plt.MaxNLocator(4))\n",
    "    axi.yaxis.set_label_coords(-.1, 0.5)\n",
    "    axi.grid(True)\n",
    "plt.tight_layout(h_pad=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at these graphs, we can see that the instant where the jumper has the lowest position is approximately at 0.44 s, where the velocity is also zero. Up to this instant the jumper was moving down (countermovement phase) and from this instant on the jumper starts to rise until loses contact with the ground. This instant also indicates when the power starts to be positive. Looking at the graph of the force, the total area under the curve (the impulse) up to this instant should be zero because if the jumper started at rest and came to zero velocity again, the impulse is zero.  \n",
    "\n",
    "This turning point is used to indicate the change from eccentric (negative power) to concentric (positive power) phase of the jump. Although this instant was detected based on the movement of the center of mass, this roughly indicates the change in the net muscle activation in the body to perform the jump.\n",
    "\n",
    "Let's visualize these phases in the plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:03.419285Z",
     "start_time": "2021-02-09T21:13:03.417118Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Instant of the lowest position 0.438 s\n"
     ]
    }
   ],
   "source": [
    "inds = np.where(v > 0)\n",
    "iec = inds[0][0]\n",
    "print('Instant of the lowest position {:.3f} s'.format(time[iec]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-09T21:13:03.606781Z",
     "start_time": "2021-02-09T21:13:03.420151Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, sharex=True, squeeze=True, figsize=(12, 4))\n",
    "axs[0].plot(time, F+m*g, 'b', linewidth='2')\n",
    "axs[0].plot([time[0], time[-1]], [m*g, m*g], 'k', linewidth='1')\n",
    "axs[0].fill_between(time[0:iec], F[0:iec]+m*g, m*g, color=[1, 0, 0, .2])\n",
    "axs[0].fill_between(time[iec:-1], F[iec:-1]+m*g, m*g, color=[0, 1, 0, .2])\n",
    "axs[0].plot([], [], linewidth=10, color=[1, 0, 0, .2], label='Eccentric')\n",
    "axs[0].plot([], [], linewidth=10, color=[0, 1, 0, .2], label='Concentric')\n",
    "axs[0].legend(frameon=False, loc='upper left', fontsize=12)\n",
    "axs[0].set_ylabel('Vertical GRF [$N$]', fontsize=14)\n",
    "axs[0].set_xlabel('Time [$s$]', fontsize=14)\n",
    "axs[0].yaxis.set_major_locator(plt.MaxNLocator(5))\n",
    "axs[1].plot(time, P, 'b', linewidth='2')\n",
    "axs[1].plot([time[0], time[-1]], [0, 0], 'k', linewidth='1')\n",
    "axs[1].fill_between(time[0:iec], P[0:iec], color=[1, 0, 0, .2])\n",
    "axs[1].fill_between(time[iec:-1], P[iec:-1], color=[0, 1, 0, .2])\n",
    "axs[1].set_ylabel('Power [$W$]', fontsize=14)\n",
    "axs[1].set_xlabel('Time [$s$]', fontsize=14)\n",
    "axs[1].set_xticks(np.arange(time[0], time[-1], .1))\n",
    "axs[1].yaxis.set_major_locator(plt.MaxNLocator(5))\n",
    "axs[1].set_xlim([time[0], time[-1]])\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further reading\n",
    "\n",
    "- [The Physics of Nike+ Hyperdunk](https://www.wired.com/2012/09/the-physics-of-nike-hyperdunk-2/)  \n",
    "- Linthorne NP (2001) <a href=\"http://www.brunel.ac.uk/~spstnpl/Publications/VerticalJump(Linthorne).pdf\" target=\"_blank\">Analysis of standing vertical jumps using a force platform</a>. American Journal of Physics, 69, 1198-1204. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Video lectures on the internet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Physics breakdown of a jump](https://youtu.be/ZaGreqCFOJM)  \n",
    "- [Recap of the force plate analysis](https://youtu.be/u05pLtC-T1s)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problems\n",
    "\n",
    "1. The mechanical work ($W$) by the vertical force is defined as:  \n",
    "$$ W = \\int_{h_0}^{h_f} F(h) \\mathrm{d}h $$  \n",
    "Which can also be calculated as the variation in the kinetic energy or the integral of mechanical power:  \n",
    "$$ W = \\Delta E_K = \\int_{t_0}^{t_f} P(t) \\mathrm{d}t $$  \n",
    " a) Use the data of the vertical jump in this text to plot the graph for the ground reaction force versus displacement.  \n",
    " b) Calculate the mechanical work produced in the entire jump and in the eccentric and concentric phases using the two methods described above.  \n",
    "  \n",
    "2. For the dataset in this text, calculate all the variables described in Dowling, Vamos (1993)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "- Cross R (1999) [Standing, walking, running, and jumping on a force plate](https://pdfs.semanticscholar.org/1ad0/3557c2bc1ac8e02d89946a17eeadfb7d8a78.pdf). American Journal of Physics, 67, 4, 304-309.  \n",
    "- Dowling JJ, Vamos L (1993) [Identification of Kinetic and Temporal Factors Related to Vertical Jump Performance](./../refs/Dowling93JABvert_jump.pdf). Journal of Applied Biomechanics, 9, 95-110.   \n",
    "- Linthorne NP (2001) <a href=\"http://www.brunel.ac.uk/~spstnpl/Publications/VerticalJump(Linthorne).pdf\" target=\"_blank\">Analysis of standing vertical jumps using a force platform</a>. American Journal of Physics, 69, 1198-1204.  \n",
    "- Winter DA (2009) [Kinetics: Forces and Moments of Force](https://elearning2.uniroma1.it/pluginfile.php/92521/mod_folder/content/0/Biomechanics%20and%20Motor%20Control%20of%20Human%20Movement%20-%20ch5.pdf). Chapter 5 of [Biomechanics and motor control of human movement](http://books.google.com.br/books?id=_bFHL08IWfwC). 4 ed. Hoboken, EUA: Wiley."
   ]
  }
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