{ "cells": [ { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "from scipy.integrate import solve_ivp\n", "from scipy.optimize import minimize\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The net force for moving with air friction under gravity is\n", "\n", "$$\\vec{F}_{\\text{net}} = \\vec{F}_g + \\vec{F}_f = -mg\\hat{y} - b|\\vec{v}|\\vec{v}$$\n", "\n", "and noting that $\\vec{v} = \\dot{x} \\hat{x} + \\dot{y} \\hat{y}$ we get\n", "\n", "$$\\vec{F}_{\\text{net}} = -mg\\hat{y} - b\\sqrt{\\dot{x}^2 + \\dot{y}^2}(\\dot{x}\\hat{x} + \\dot{y}\\hat{y})$$\n", "\n", "or in vector form\n", "\n", "$$\\vec{F}_{\\text{net}} = \\begin{bmatrix} - b\\sqrt{\\dot{x}^2 + \\dot{y}^2}\\dot{x} \\\\ -mg - b\\sqrt{\\dot{x}^2 + \\dot{y}^2}\\dot{y} \\end{bmatrix} $$\n", "\n", "Using the fact that $$\\vec{F}_{\\text{net}} = m\\vec{a} = m\\left< \\ddot{x}, \\ddot{y} \\right>$$ we get\n", "\n", "$$m \\begin{bmatrix}\\ddot{x} \\\\ \\ddot{y} \\end{bmatrix} = \\begin{bmatrix} - b\\sqrt{\\dot{x}^2 + \\dot{y}^2}\\dot{x} \\\\ -mg - b\\sqrt{\\dot{x}^2 + \\dot{y}^2}\\dot{y} \\end{bmatrix} $$\n", "\n", "and thus have two coupled differential equations\n", "\n", "$$\\ddot{x} = - \\frac{b}{m}\\sqrt{\\dot{x}^2 + \\dot{y}^2}\\dot{x}$$\n", "$$\\ddot{y} = -g - \\frac{b}{m}\\sqrt{\\dot{x}^2 + \\dot{y}^2}\\dot{y}$$\n", "\n", "Defining $x' = x/g$ and $y'=y/g$ we get\n", "\n", "$$\\ddot{x'} = - \\frac{bg}{m}\\sqrt{\\dot{x'}^2 + \\dot{y'}^2}\\dot{x'}$$\n", "$$\\ddot{y'} = -1 - \\frac{bg}{m}\\sqrt{\\dot{x'}^2 + \\dot{y'}^2}\\dot{y'}$$\n", "\n", "We can thus solve this equation for different values of $B \\equiv bg/m$ to get $x'(t)$ and $y'(t)$ which are directly proportional to $x(t)$ and $y(t)$ (we get the same shape). We will drop the primes for now on but recall that there is the divided by $g$ factor.\n", "\n", "In python we can only solve systems of first order ODEs, so defining $v_x=\\dot{x}$ and $v_y=\\dot{y}$ we get a system of 4 coupled first order ODEs.\n", "\n", "* $\\dot{x} = v_x$\n", "* $\\dot{v_x} = - B\\sqrt{\\dot{x}^2 + \\dot{y}^2}\\dot{x}$\n", "* $\\dot{y} = v_y$\n", "* $\\dot{v_y} = - B\\sqrt{\\dot{x}^2 + \\dot{y}^2}\\dot{y}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define $\\vec{S} = \\left$. To solve ODEs in python, need to write a funciton that takes in $\\vec{S}$ and time $t$, and returns $d\\vec{S}/dt$. In other words we want $f$ in \n", "\n", "$$\\frac{d\\vec{S}}{dt} = f(\\vec{S}, t)$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Define function f above\n", "def dSdt(t,S,B):\n", " x, vx, y, vy = S\n", " return [vx,\n", " -B*np.sqrt(vx**2+vy**2)*vx, \n", " vy,\n", " -1-B*np.sqrt(vx**2+vy**2)*vy]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define friction `B`, initial velocity `V`, and a few angles `t1, t2, t3`" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "B = 1\n", "V = 1\n", "t1 = 40 *np.pi / 180\n", "t2 = 45 *np.pi / 180\n", "t3 = 50 *np.pi / 180" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve the ODE using scipy's `solve_ivp` method. Function takes in the $d\\vec{S}/dt$ function, time period to solve over `[0,2]`seconds, initial conditions, `t_eval` to evaluate on, and addition arguments `B` (friction force) for the function. Also we set " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "sol1 = solve_ivp(dSdt, [0, 2], y0=[0,V*np.cos(t1),0,V*np.sin(t1)], t_eval=np.linspace(0,2,1000), args=(B,)) # atol=1e-7, rtol=1e-4)\n", "sol2 = solve_ivp(dSdt, [0, 2], y0=[0,V*np.cos(t2),0,V*np.sin(t2)], t_eval=np.linspace(0,2,1000), args=(B,)) #atol=1e-7, rtol=1e-4)\n", "sol3 = solve_ivp(dSdt, [0, 2], y0=[0,V*np.cos(t3),0,V*np.sin(t3)], t_eval=np.linspace(0,2,1000), args=(B,)) #atol=1e-7, rtol=1e-4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot a few of the solutions" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(sol1.y[0],sol1.y[2], label=r'$\\theta_0=40^{\\circ}$')\n", "plt.plot(sol2.y[0],sol2.y[2], label=r'$\\theta_0=45^{\\circ}$')\n", "plt.plot(sol3.y[0],sol3.y[2], label=r'$\\theta_0=50^{\\circ}$')\n", "plt.ylim(bottom=0)\n", "plt.legend()\n", "plt.xlabel('$x/g$', fontsize=20)\n", "plt.ylabel('$y/g$', fontsize=20)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function gets the distance $x/g$ that the ball traveled before it hits the ground when traveling at an initial velocity $V$." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "def get_distance(angle, B, V=1, t=2):\n", " v0x = V*np.cos(angle*np.pi/180)\n", " v0y = V*np.sin(angle*np.pi/180)\n", " sol = solve_ivp(dSdt, [0, t], y0=[0,v0x,0,v0y], t_eval=np.linspace(0,t,10000), args=(B,), atol=1e-7, rtol=1e-4)\n", " just_above_idx = np.where(np.diff(np.sign(sol.y[2])) < 0)[0][0]\n", " just_below_idx = just_above_idx + 1\n", " x_loc = (sol.y[0][just_above_idx] + sol.y[0][just_below_idx])/2\n", " return x_loc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Look at the two cases above" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Launch angle 45 degrees distance travelled: 0.5890479196032461\n", "Launch angle 40 degrees distance travelled: 0.5933703230246123\n" ] } ], "source": [ "print(f'Launch angle 45 degrees distance travelled: {get_distance(45, B=1, V=1)}')\n", "print(f'Launch angle 40 degrees distance travelled: {get_distance(40, B=1, V=1)}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets find these distances for a bunch of angles:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "angles = np.linspace(30, 60, 200)\n", "x_locs = np.vectorize(get_distance)(angles, B=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the distance travelled before hitting the ground over a bunch of different launch angles (at $V=1$)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(angles, x_locs)\n", "plt.xlabel('Launch Angle [degrees]', fontsize=20)\n", "plt.ylabel('Maximum Distance [distance/gravity]')\n", "plt.axvline(angles[np.argmax(x_locs)], ls='--', color='r')\n", "plt.title('Distance Travelled at $V=1$ and $B=1$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets find the angle that gives the maximum distance as a function of $B$. We will do this for two values of $V$: $V=1$ and $V=2$:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "V1 = 1\n", "V2 = 2\n", "angles = np.linspace(35, 45, 200)\n", "Bs = np.linspace(0, 1, 50)\n", "\n", "results_v1 = [np.vectorize(get_distance)(angles, B=B, V=V1) for B in Bs]\n", "opt_angles_v1 = [angles[np.argmax(result)] for result in results_v1]\n", "results_v2 = [np.vectorize(get_distance)(angles, B=B, V=V2, t=6) for B in Bs]\n", "opt_angles_v2 = [angles[np.argmax(result)] for result in results_v2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the results" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(Bs, opt_angles_v1, 'o--', label='$v_0/g=1$s')\n", "plt.plot(Bs, opt_angles_v2, 'o--', label='$v_0/g=2$s')\n", "plt.legend(fontsize=17)\n", "plt.xlabel('bg/m [1/$s^2$]', fontsize=20)\n", "plt.ylabel('Optimal Angle', fontsize=20)\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How does this correspond to regular objects? Lets look at a golf ball and a soccer ball:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now $b = \\frac{1}{2} \\rho A C_d$ and \n", "\n", "* for a golf ball, $m=0.045~\\text{kg}$ and $r=0.021~\\text{m}$ and $C_d \\approx 0.5$\n", "* for a soccer ball $m=0.45~\\text{kg}$ and $r=0.11~\\text{m}$ and $C_d \\approx 0.2$\n", "* for air, $\\rho = 1.225~\\text{kg/m}$\n", "\n", "The formula for $B$ becomes\n", "\n", "$$B \\equiv \\frac{bg}{m} = \\frac{1}{2}\\frac{\\rho \\pi r^2 C_d g}{m}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Sources\" \n", "\n", "https://www.scirp.org/journal/paperinformation.aspx?paperid=85529\n", "\n", "https://www.brunel.ac.uk/~spstnpl/LearningResources/SoccerKickLab.pdf\n", "\n", "https://athleticlift.com/how-fast-can-you-kick-soccer-ball/#:~:text=From%20research%2C%20it%20shows%20that%20youth%20soccer%20athletes,kick%20a%20soccer%20ball%20through%20your%20phone%20camera." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "rho = 1.225\n", "g = 9.81\n", "\n", "# Golf\n", "r = 0.021\n", "Cd = 0.5\n", "m = 0.045\n", "B_golf = 0.5 * rho * np.pi * r**2 * Cd * g /m\n", "\n", "# Soccer\n", "r = 0.22 / 2\n", "Cd = 0.2\n", "m = 0.45\n", "B_soc = 0.5 * rho * np.pi * r**2 * Cd * g /m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the results next to the values of $B$ for the soccer and golf ball. Note that $V=2$ corresponds to kicking a soccer ball at $v_0/g = 2~\\text{s} \\implies v_0 \\approx 20~\\text{m/s} \\approx 72~\\text{km/h}$ which is representative of a true soccer kick:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(Bs, opt_angles_v1, 'o--', label='$v_0/g=1$s')\n", "plt.plot(Bs, opt_angles_v2, 'o--', label='$v_0/g=2$s')\n", "plt.legend(fontsize=17)\n", "plt.xlabel('bg/m [1/$s^2$]', fontsize=20)\n", "plt.ylabel('Optimal Angle', fontsize=20)\n", "plt.grid()\n", "plt.axvline(B_golf, ls='--', color='r')\n", "plt.axvline(B_soc, ls='--', color='purple')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }