{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# How fast should you drive at night?\n", "The first question we're talking about in class involves the fastest speed it might be safe to drive at at night. \n", "\n", "Situation: you're driving at a speed $v0$ and you see something ahead of you that makes you panic stop. The relevant coefficient of friction is $\\mu_s=[0.4,0.7]$ and the object is $d=106m$ (350ft) ahead of you.\n", "\n", "Human reaction time (visual) is about $t_v=0.25$ seconds. While reacting, the car travels \n", "\n", "$x1=v0~t_v$.\n", "\n", "Then, while braking, the car travels $x2$, where we've shown algebraically that $2~a~x2={v_2}^2-{v_1}^2$. In this specific example we have, \n", "\n", "$2~\\mu_s~g~x2=v0^2$.\n", "\n", "So now, remember that the total travel distance is $x1+x2=106$ meters. This gives the equation:\n", "\n", "$v0~t_v+\\frac{v0^2}{2~\\mu_s~g}=106$ meters\n", "\n", "So, what velocity makes this equation true? In the context of the problem, what is the fastest velocity that will still allow us to stop in time? \n", "\n", "Mathematically, this is a root-finding problem. One approach is to make a plot - when does the function on the left equal 106meters on the right?" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# define parameters\n", "g=9.8\n", "mu_1=0.4\n", "mu_2=0.7\n", "tv=0.25\n", "# make two lists - one of velocities, v0 and \n", "# another list of the left hand side of the equation\n", "list_of_v0=[]\n", "list_of_eq_lhs_1=[]\n", "list_of_eq_lhs_2=[]\n", "# iterate over possible v0's\n", "for i in range(50):\n", " # generate v0 from 0 to 49\n", " v0 = 1+i \n", " # for each v0, compute the other side of the equation\n", " lhs_mu_1 = v0*tv+v0*v0/(2*mu_1*g)\n", " lhs_mu_2 = v0*tv+v0*v0/(2*mu_2*g)\n", " # store the data in lists to plot\n", " list_of_v0.append(v0)\n", " list_of_eq_lhs_1.append(lhs_mu_1)\n", " list_of_eq_lhs_2.append(lhs_mu_2)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEKCAYAAAAIO8L1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "# plot the two lhs data, note that this is stoppnig distance\n", "plt.plot(list_of_v0,list_of_eq_lhs_1,label=\"$mu_s=0.4$\")\n", "plt.plot(list_of_v0,list_of_eq_lhs_2,label=\"$mu_s=0.7$\")\n", "# plot the problem's stopping distance\n", "plt.plot([0,50],[106,106],label=\"106m=350ft\")\n", "plt.ylabel(\"stopping distance (meters)\")\n", "plt.xlabel(\"intial speed (m/s)\")\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the graph, you can visually estimate where the lines intersect and solve the problem approximately. If you need more precision than looking at graph provides, you can use a \"root-finding\" library. This is the approach that most TI calculators take when you use them to solve an equation." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# root-finding takes an additional library\n", "# using the function \"fsolve\" frim scipy.optimize\n", "from scipy.optimize import fsolve" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the root-finding function takes an equation (as a function) as input. It finds the input variable (v0) that makes the function zero. This means we need to re-write the equation we're trying to solve as\n", "\n", "$v0~t_v+\\frac{v0^2}{2~\\mu_s~g} - 106~meters = 0$\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# then, we need to specify the equation we want to solve\n", "# rewite so that it equals zero, eg\n", "# v0*tv+v0*v0/(2*mu_1*g) - distance =0\n", "def func(v0,tv,mu,g,distance):\n", " return v0*tv + v0*v0/(2*mu*g) - distance" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 27.86441714]\n" ] } ], "source": [ "# then, specif parameters for the function,\n", "tv,mu,g,distance = 0.25,0.4,9.8,106.\n", "\n", "# and specify an initial guess for v0\n", "guess_v0 = [30,] \n", "\n", "# and then run the solver\n", "first_v=fsolve(func,guess_v0,args=(tv,mu,g,distance)) \n", "print(first_v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So one intersection is 27.8 m/s. Run the solver again for the other $\\mu$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 36.45909102]\n" ] } ], "source": [ "# then, specif parameters for the function,\n", "tv,mu,g,distance = 0.25,0.7,9.8,106.\n", "\n", "# and specify an initial guess for v0\n", "guess_v0 = [30,] \n", "\n", "# and then run the solver\n", "second_v=fsolve(func,guess_v0,args=(tv,mu,g,distance)) \n", "print(second_v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, put these roots in a plot." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEWCAYAAAB8LwAVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the two roots\n", "plt.plot([first_v[0],second_v[0]],[106,106],\"ro\",\n", " label=\"roots from fsolve\")\n", "plt.title(\"critical velocities are 36.4 m/s and 27.8 m/s \")\n", "# everything following is from above\n", "# plot the two lhs data, note that this is stoppnig distance\n", "plt.plot(list_of_v0,list_of_eq_lhs_1,label=\"$mu_s=0.4$\")\n", "plt.plot(list_of_v0,list_of_eq_lhs_2,label=\"$mu_s=0.7$\")\n", "# plot the problem's stopping distance\n", "plt.plot([0,50],[106,106],label=\"106m=350ft\")\n", "plt.ylabel(\"stopping distance (meters)\")\n", "plt.xlabel(\"intial speed (m/s)\")\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Coasting down hwy 43\n", "\n", "Also discussed in class is coasting down highway 43 from the I-90 interchange south of Winona. Recall that the speed you achieve is limited by air resistance (drag). The specific force balance could be modeled as:\n", "\n", "$m~g~\\sin[1.7 degrees] = \\frac{1}{2}~C_D~A~\\rho_{air}~v^2$\n", "\n", "Below, I solve this equation for $v$ and estimate a value based on numbers for a modern VW Golf. " ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "29.793978576556203 m/s\n", "66.50016018287344 mph\n" ] } ], "source": [ "import math\n", "m=1360 # kg\n", "g=9.8 # N/kg\n", "A=2.3 # m^2, 71\" x 51\"\n", "Cd=0.32\n", "rho_air=1.2 # kg/m^3\n", "sin_theta=150/5100 # from the geography of Winona\n", "\n", "v_terminal = math.sqrt(m*g*sin_theta/(0.5*Cd*A*rho_air))\n", "\n", "print(v_terminal,\"m/s\")\n", "print(v_terminal*(6.2/10000)*(3600/1),\"mph\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Another version of this calculation is asking how much power it takes to drive a given speed. $Power=\\frac{Energy~Transfer}{Time}=\\frac{F_{ext}~x}{t}=F_{ext}~v$. \n", "\n", "So, if air resistance is the only force we care about, engine power to travel at a constant speed is, $P=\\frac{1}{2}~C_D~A~\\rho_{air}~v^3$. For a VW Golf, this is, " ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAb0AAAEWCAYAAADy9UlpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhaFJT0RECkOTnoiIFIYmPRERKYxf/yRvecPxgCQAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m=1360 # kg\n", "g=9.8 # N/kg\n", "A=2.3 # m^2, 71\" x 51\"\n", "Cd=0.32\n", "rho_air=1.2 # kg/m^3\n", "\n", "v_mps_list=[]\n", "v_mph_list=[]\n", "p_W_list=[]\n", "p_hp_list=[]\n", "for i in range(50):\n", " v_mps=i+1\n", " v_mph=v_mps*2.23693629\n", " p_W=0.5*Cd*A*rho_air*v_mps**3\n", " p_hp=p_W*(1.0/746.0)\n", " v_mps_list.append(v_mps)\n", " v_mph_list.append(v_mph)\n", " p_hp_list.append(p_hp)\n", " p_W_list.append(p_W)\n", "# Now that data is generated, plot\n", "plt.plot(v_mps_list,p_W_list,label=\"2006 VW Golf\")\n", "plt.ylabel(\"required engine power (W)\")\n", "plt.xlabel(\"car speed (m/s)\")\n", "plt.title(\"Engine power necessary to maintain a constant speed on a level road\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbQAAAEWCAYAAAAO4GKjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBUEDoIKgAVBB0ACo8ACxfxHvU7jn9gAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# here's the same plot, using \"American\" units of horsepower\n", "# and miles per hour.\n", "plt.plot(v_mph_list,p_hp_list,label=\"2006 VW Golf\")\n", "plt.ylabel(\"required engine power (hp)\")\n", "plt.xlabel(\"car speed (mph)\")\n", "plt.title(\"Engine power necessary to maintain a constant speed on a level road\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gas mileage of a car based on air resistance losses\n", "\n", "Of course, this graph leads to another interesting calculation. What's the upper bound on gas mileage for a car travelling at a constant speed. I'll ignore frictional losses in the drivetrain, and use the following ideas:\n", "1. One gallon of gas contains 121MJ of energy (note this is the EPA's [mpg-e](https://en.wikipedia.org/wiki/Miles_per_gallon_gasoline_equivalent) )\n", "2. $Power=\\frac{Energy~Transfer}{time}=\\frac{Force \\cdot distance}{time}$ so $Power=F\\cdot v$.\n", "3. As I've already used, if air resistance is the only relevant interaction, $P=\\frac{1}{2}~C_D~A~\\rho_{air}~v^3$\n", "4. Automotive engine efficiency varies! Standard gas engines that use the \"Otto\" cycle have a thermal efficiency of about $20-25\\%$. Some Hybrids have \"Atkinson\" cycle engines which have efficiency [as high as](http://newatlas.com/toyota-atkinson-engines-improved-thermal-fuel-efficiency/31615/) $38\\%$. Mathematically, the efficiency tells you how much of the fuel (gasoline) energy the engine is able to turn into usable energy transfer to push the car forward. $P_{out}=eff\\cdot P_{in}$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZsAAAEWCAYAAACwtjr+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n27GzMcYY03bsbIwxxrQdOxtjjDFt5x+8t+/uJSxPogAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# scale the list of engine power by efficiency to \n", "# make a list of fuel power (the fuel/sec the engine requires)\n", "eff=0.25\n", "fuel_power_in = [p_out/eff for p_out in p_W_list]\n", " \n", "plt.plot(v_mps_list,fuel_power_in,label=\"fuel power in (W)\")\n", "plt.plot(v_mps_list,p_W_list,label=\"engine power out (W)\")\n", "plt.ylabel(\"power (W)\")\n", "plt.xlabel(\"car speed (m/s)\")\n", "plt.title(\"Data for 2006 VW Golf\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that 1 mpg-e assumes a gallon of gasoline has an energy of 121MJ, and that 1 Watt = 1 Joule/sec." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdkAAAEWCAYAAAAq+e1jAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrJmZWUmcZM3MzEriJGtmZlaS/wGF/I4789RkqQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# rescale the fuel_power_in list from units of Watts to units\n", "# of mpg-e, ie, gallons of gasoline per second\n", "#conversion Watts = J/s = (J/s)*(1 gal-e/121e6 J)\n", "gallons_eps = [x*(1.0/121.0e6) for x in fuel_power_in]\n", "\n", "plt.plot(v_mph_list,gallons_eps,label=\"gasoline per second\")\n", "plt.ylabel(\"Gallons-electric of gasoline per second\")\n", "plt.xlabel(\"car speed (mph)\")\n", "plt.title(\"Data for 2006 VW Golf, using 121MJ as the gallons-eletric value for gasoline\")\n", "#plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The vertical scale on the graph above, gallons/second, tells me how many gallons of gasoline the car requires each second at various speeds. The inverse of this number, seconds/gallon, will tell me how many seconds a gallon of gas will last at a given speed. \n", "\n", "$t_G=seconds/gallon$\n", "\n", "If I know how many seconds a gallon will last, I can multiply by the speed and figure out how many miles I'll be able to drive for a gallon of gas, at that speed.\n", "\n", "$distance = t_G\\cdot speed$ = miles per gallon of gas" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEWCAYAAABliCz2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIGxCb3UjAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# the time a gallon-e of gas will last, in seconds \n", "tG_s = [1.0/x for x in gallons_eps]\n", "\n", "plt.plot(v_mph_list,tG_s,label=\"seconds per gallon of gasoline\")\n", "plt.ylabel(\"seconds per gallon of gasoline\")\n", "plt.xlabel(\"car speed (mph)\")\n", "plt.title(\"Data for 2006 VW Golf, using 121MJ as gal-e\")\n", "#plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEWCAYAAABxMXBSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzjnnGsQTh3POuQbxxOGcc65B/j85ZjPqfUAUsgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tG_hr = [(1.0/x)*(1.0/3600.0) for x in gallons_eps]\n", "\n", "plt.semilogy(v_mph_list,tG_hr,label=\"seconds per gallon of gasoline\")\n", "plt.ylabel(\"hours per gallon of gasoline\")\n", "plt.xlabel(\"car speed (mph)\")\n", "plt.title(\"Data for 2006 VW Golf, using 121MJ as gal-e\")\n", "#plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the trick is just to multiply the \"time for a gallon\" list by the \"miles in an hour\" list.\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEWCAYAAAB8LwAVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUkp59P98eIuU60AOTwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mpg=[]\n", "\n", "# in this for loop, we're indexing over list index (subscript) i, rather \n", "# than iteracting over list value x[i]\n", "for i in range(len(tG_hr)):\n", " \n", " miles_in_a_gallon=v_mph_list[i]*tG_hr[i]\n", " mpg.append(miles_in_a_gallon)\n", "\n", "plt.plot(v_mph_list,mpg,label=\"2006 VW Golf\")\n", "plt.plot([20,100],[27.5,27.5],label=\"before 2010, CAFE 27.5mpg\")\n", "plt.plot([20,100],[54.5,54.5],label=\"post 2025, CAFE 54.5mpg\")\n", "plt.ylabel(\"mpg-e\")\n", "plt.xlabel(\"car speed (mph)\")\n", "plt.title(\"Data for 2006 VW Golf, using 121MJ as gal-e\")\n", "plt.ylim([0,100])\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mpg-e numbers from above are the federal standards for auto manufacturers, the \"Corporate Average Fuel Economy\" or CAFE standards. This number is the average fuel economy of all cars sold by a manufacturer. See https://en.wikipedia.org/wiki/Corporate_Average_Fuel_Economy\n", "\n", "The average speed during city driving is about 20mph, during the highway cycle, average speed is 48mph. See https://www.fueleconomy.gov/feg/fe_test_schedules.shtml\n" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnkAAAEWCAYAAAAaQ4GzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(v_mph_list,mpg,label=\"2006 VW Golf\")\n", "plt.plot([80,100],[27.5,27.5],label=\"CAFE 27.5mpg, before 2010\")\n", "plt.plot([55,75],[54.5,54.5],label=\"CAFE 54.5mpg, post 2025\")\n", "plt.plot([21,21],[10,100],label=\"Average speed for 'city' EPA driving\")\n", "plt.plot([48,48],[10,100],label=\"Average speed for 'highway' EPA driving\")\n", "plt.ylabel(\"mpg-e\")\n", "plt.xlabel(\"car speed (mph)\")\n", "plt.title(\"Data for 2006 VW Golf, using 121MJ as gal-e\")\n", "plt.ylim([0,100])\n", "#plt.legend()\n", "plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [conda root]", "language": "python", "name": "conda-root-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }