{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Baseball problem: Solution\n", "Copyright © 2022 Oliver Beckstein.\n", "\n", "This notebook is based on `11-ODE-applications.ipynb`. The whole problem was live-coded from scratch during class and this notebook is a cleaned-up and commented solution. The lesson showed how\n", "1. to define the physical problem (obtain trajectory of a baseball with spin and air resistance)\n", "2. to derive the underlying equations (Newton's equations of motions and the forces acting on the ball)\n", "3. to adapt an algorithm to solve the equations (use RK4 for integrating the ODEs and express the problem in ODE standard form so that one can use `ode.rk4()`)\n", "4. to visualize and discuss the results (plot trajectories and assess the influence of spin) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Packages\n", "We use numpy and our ODE solvers (`ode.py`):" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import ode" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For 3D graphs, install `ipympl` with `conda install ipympl` and then you can use \n", "```\n", "%matplotlib notebook\n", "```\n", "but you have to do this as the very first thing (before loading `matplotlib`). You will also have to \"close\" active figures before you can plot into a new one." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "#%matplotlib notebook\n", "import matplotlib.pyplot as plt\n", "plt.style.use('ggplot')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple Baseball physics\n", "\n", "- quadratic air resistance (with velocity-independent drag coefficient)\n", "- Magnus force due to spin\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Quadratic air resistance\n", "Occurs at high Reynolds numbers, i.e., turbulent flow. Only approximate:\n", "\n", "$$\n", "\\mathbf{F}_2 = -b_2 v \\mathbf{v}\n", "$$\n", "\n", "with \n", "$$\n", "b_2 = \\frac{1}{2} C_D \\rho A\n", "$$\n", "where $C_D$ is the drag coefficient, $\\rho$ the density of air, and $A = r^2 \\pi$ the cross sectional area of the baseball." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Magnus effect " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Magnus effect**: airflow is changed around a spinning object. The Magnus force is\n", "\n", "$$\n", "\\mathbf{F}_M = \\alpha \\boldsymbol{\\omega} \\times \\mathbf{v}\n", "$$\n", "\n", "where $\\boldsymbol{\\omega}$ is the ball's angular velocity in rad/s (e.g., 200/s for a baseball).\n", "\n", "For a sphere the proportionality constant $\\alpha$ can be written\n", "\n", "$$\n", "\\mathbf{F}_M = \\frac{1}{2} C_L \\rho A \\frac{v}{\\omega} \\boldsymbol{\\omega} \\times \\mathbf{v}\n", "$$\n", "\n", "where $C_L$ is the lift coefficient, $\\rho$ the air density, $A$ the ball's cross section. (Advantage of defining $C_L$ this way: when spin and velocity are perpendicular, the Magnus force is simply $F_M = \\frac{1}{2} C_L \\rho A v^2$.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$C_L$ is mainly a function of the *spin parameter*\n", "\n", "$$\n", "S = \\frac{r\\omega}{v}\n", "$$\n", "\n", "with the radius $r$ of the ball. In general we write\n", "\n", "$$\n", "\\mathbf{F}_M = \\frac{1}{2} C_L(S) \\frac{\\rho A r}{S} \\boldsymbol{\\omega} \\times \\mathbf{v}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a baseball, experimental data show approximately a power law dependence of $C_L$ on $S$\n", "\n", "$$\n", "C_L(S) = 0.62 \\times S^{0.7}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All together:\n", "\n", "\\begin{align}\n", "\\mathbf{F}_M &= \\alpha\\ \\boldsymbol{\\omega} \\times \\mathbf{v}\\\\\n", "v &= \\sqrt{\\mathbf{v}\\cdot\\mathbf{v}}\\\\\n", "S &= \\frac{r\\omega}{v}\\\\\n", "C_L &= 0.62 \\times S^{0.7}\\\\\n", "\\alpha &= \\frac{1}{2} C_L \\frac{\\rho A r}{S}\n", "\\end{align}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Equations of motion\n", "\n", "\\begin{align}\n", "\\frac{d\\mathbf{r}}{dt} &= \\mathbf{v}\\\\\n", "\\frac{d\\mathbf{v}}{dt} &= -g \\hat{\\mathbf{e}}_y -\\frac{b_2}{m} v \\mathbf{v} + \\frac{\\alpha}{m}\\ \\boldsymbol{\\omega} \\times \\mathbf{v}\n", "\\end{align}\n", "\n", "(quadratic drag $-\\frac{b_2}{m} v \\mathbf{v}$ included and dividing through by $m$ to get accelerations in the second equation.)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Baseball simulation \n", "\n", "Implement the full baseball equations of motions:\n", "- gravity $a_\\text{gravity}$\n", "- quadratic drag $a_\\text{drag}$\n", "- Magnus effect $a_\\text{Magnus}$\n", "\n", "For the cross product you can look at [numpy.cross()](https://docs.scipy.org/doc/numpy/reference/generated/numpy.cross.html)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def C_L(S):\n", " return 0.62 * S**0.7\n", "\n", "def simulate_baseball(v0, omega, r0=None,\n", " h=0.01, C_D=0.40, g=9.81, rho=1.225,\n", " r=0.07468/2, m=0.14883,\n", " R_homeplate=18.4):\n", " \"\"\"simulate baseball pitch\n", " \n", " Parameters\n", " ----------\n", " v0 : array\n", " initial velocity (vx, vy, vz) in m/s\n", " omega : array\n", " angular velocity vector of the ball (\"spin\"), in rad/s\n", " r0 : array, optional\n", " initial position of the ball (in m) when it leaves the pitcher's hand\n", " as (x, y, z); the default is (0, 2, 0)\n", " h : float, optional\n", " integration time step in s, default is 0.01 s\n", " C_D : float, optional\n", " drag coefficient, default is 0.40\n", " g : float, optional\n", " acceleration due to gravity, default 9.81 kg/(m*s^2)\n", " rho : float, optional\n", " density of air, default 1.225 kg/m^3\n", " r : float, optional\n", " radius of the baseball\n", " m : float, optional\n", " mass of the baseball\n", " R_homeplate : float, optional\n", " distance of the catcher from the pitcher\n", " \n", " Returns\n", " -------\n", " \n", " positions : array\n", " The array contains an entry (time, x, y, z) for each time step.\n", " \"\"\"\n", " # all SI units (kg, m)\n", " if r0 is None:\n", " r0 = np.array([0, 2.0, 0]) # pitching at 2m height\n", " \n", " omega = np.asarray(omega)\n", " \n", " domega = np.linalg.norm(omega)\n", " A = np.pi*r**2\n", " rhoArm = rho * A * r / m\n", " b2 = 0.5 * C_D * rho * A\n", " \n", " a_gravity = np.array([0, -g, 0])\n", "\n", " def f(t, y):\n", " # y = [x, y, z, vx, vy, vz]\n", " v = y[3:]\n", " dv = np.linalg.norm(v)\n", " S = r*domega/dv\n", " a_magnus = 0.5 * C_L(S) * rhoArm / S * np.cross(omega, v)\n", " a_drag = -b2/m * dv * v\n", " a = a_gravity + a_drag + a_magnus\n", " return np.array([y[3], y[4], y[5],\n", " a[0], a[1], a[2]])\n", "\n", " t = 0\n", " # initialize 3D!\n", " y = np.array([r0[0], r0[1], r0[2], v0[0], v0[1], v0[2]], dtype=np.float64)\n", " positions = [[t, y[0], y[1], y[2]]] # record t, x and y, z\n", " \n", " while y[0] < R_homeplate and y[1] >= 0.2:\n", " t += h\n", " y[:] = ode.rk4(y, f, t, h)\n", " positions.append([t, y[0], y[1], y[2]]) # record t, x and y, z\n", " \n", " return np.array(positions)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Simulate throws " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulate baseball throw for initial velocity $\\mathbf{v} = (30\\,\\text{m/s}, 0)$.\n", "\n", "Plot x vs y and x vs z (to see curving).\n", "\n", "Try out different spins; a good value is $\\boldsymbol{\\omega} = 200\\,\\text{rad/s} \\times (0, 1, 1)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "200 rad/s is 32 revolutions per second or almost 2000 rpm." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "31.830988618379067 revolutions per second\n", "1909.859317102744 rpm\n" ] } ], "source": [ "print(200/(2*np.pi), \"revolutions per second\")\n", "print(200/(2*np.pi) * 60, \"rpm\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulate the baseball throw with\n", "- almost no spin: $\\omega = 0.001 \\times (0, 0, 1)$ (our code does not handle $\\omega = 0$ gracefully...)\n", "- full upward spin: $\\omega = 200 \\times (0, 0, 1)$\n", "- sideways spin: $\\omega = 200 \\times (0, 1, 1)$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "r = simulate_baseball([30, 0, 0], omega=0.001 * np.array([0,0,1]))\n", "rz = simulate_baseball([30, 0, 0], omega=200. * np.array([0,0,1]))\n", "rzy = simulate_baseball([30, 0, 0], omega=200. * 2**(-0.5) * np.array([0,1,1]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plotting\n", "\n", "Plot the three scenarios in 2D planes: x-y (side view) and x-z (top view)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "idx = 2 # y\n", "plt.plot(r[:,1], r[:,idx], label=\"no spin\")\n", "plt.plot(rz[:,1], rz[:,idx], label=\"upward spin\")\n", "plt.plot(rzy[:,1], rzy[:,idx], label=\"sideways spin\")\n", "plt.xlabel(\"$x$ (m)\")\n", "plt.ylabel(\"$y$ (m)\")\n", "plt.legend(loc=\"best\")\n", "plt.title(\"Side view\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note how the balls with spin fly higher: the Magnus force lifts them up (due to the component of the spin along $z$)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "idx = 3 # z\n", "plt.plot(r[:,1], r[:,idx], label=\"no spin\")\n", "plt.plot(rz[:,1], rz[:,idx], label=\"upward spin\")\n", "plt.plot(rzy[:,1], rzy[:,idx], label=\"sideways spin\")\n", "plt.xlabel(\"$x$ (m)\")\n", "plt.ylabel(\"$z$ (m)\")\n", "plt.legend(loc=\"best\")\n", "plt.title(\"Top-down view\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ball with a component of the spin along the $y$ direction ($\\boldsymbol{\\omega} = \\omega_0 \\, \\left(\\begin{array}{c} 0\\\\1\\\\1\\end{array}\\right)$) has a 0.6 m deflection in the $-z$ direction." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3D plot\n", "Use simple `matplotlib` 3D plot. (BONUS: Make it work with vpython)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we use the [`notebook` backend for matplotlib](http://ipython.readthedocs.io/en/stable/interactive/plotting.html) then we will be able to interactively rotate our [matplotlib 3D graphics](http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html). (Note: If this does not seem to work, disable adblockers and allow javascript on the page.)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "%matplotlib widget" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "42beb109eaf142388defe8d3471000d6", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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