{ "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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", "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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", "text/plain": [ "
" ] }, "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." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we use the [`widget` 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: Install the `ipypmpl` package first. If this does not seem to work, disable adblockers and allow javascript on the page.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%matplotlib widget" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.plot(r[:,1], r[:,3], r[:,2], '.', label=\"no spin\")\n", "ax.plot(rz[:,1], rz[:,3], rz[:,2], '.', label=\"up spin\")\n", "ax.plot(rzy[:,1], rzy[:,3], rzy[:,2], '.', label=\"sideways spin\")\n", "\n", "# hand of the catcher, 0.2m above homeplate\n", "ax.plot([18.4, 18.4], [0, 0], [0, 0.2], color=\"black\", lw=6)\n", "\n", "# drop line for last point\n", "x,y,z = rzy[-1, 1:]\n", "ax.plot([x,x], [z,z], [y,0], color=\"red\")\n", "\n", "ax.set_xlabel(\"$x$ (m)\")\n", "ax.set_ylabel(\"$z$ (m)\")\n", "ax.set_zlabel(\"$y$ (m)\")\n", "ax.legend(loc=\"upper left\", numpoints=1)\n", "ax.figure.tight_layout()\n", "fig.savefig(\"baseball.png\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the plot above we also added the hand of the catcher as a heavy black bar at 0.2 m above the home plate, and a drop-down bar in red to indicate the height of the ball thrown with *sideways spin* to make cleared that it also arrives at almost the same height as the ball with *up spin*." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.8" } }, "nbformat": 4, "nbformat_minor": 4 }