longitudinal_vehicle_dynamics_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Longitudinal Vehicle Dynamics  Model Tutorial\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mike Knerr\n",
    "##### "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "This tutorial notebook explores a general model for automotive vehicle longitudinal physics and dynamics. It includes test scenarios for various 2D terrain and throttle profiles. The dimensional reduction to 2D height and linear position only makes it easier to concentrate on the longitudinal dynamics without being side-tracked by the kinematics of lateral motion. The object oriented vehicle model expresses primary dynamics as an equation of forward, reverse and opposing forces that would be typical for a vehicle in motion. Characteristic parameters of the automobile model are set. A basic terrain geometry and motion profile is defined. When the model is run, Euler time-step integrations\n",
    "yield acceleration, velocity and linear longitudinal position over time. Graphics show different\n",
    "aspects of the motion plan after run is completed. The parameters, 2D terrain geometry can be changed and experimented with to learn about the dynamic behavior of the model.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The primary relations for forces acting on the vehicle moving forward on an incline angle are shown in the diagram and equation below. \n",
    "  \n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div>\n",
    "<img src=\"longitudinal-car-v0.06.png\" alt=\"car\" width=\"80%\"/>\n",
    "<div align=\"right\"><sub>Illustration - Mike Knerr</sub></div>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    "The dynamics model for this project express the overall force equation shown above with more\n",
    "specific equations and parameters that can be set to model a particular vehicle design. The main longitudinal components from head to tail basically are: engine, torque converter, tranmission, and finally the wheels where the frictional forces from the tires on the road surface move the vehicle. \n",
    "\n",
    "The main input to the system is the throttle level and the output will be a one-dimensional linear position. Vehicle specific values that can be set are: overall engine inertia value, vehicle mass, gear ratio, effective radius, tire force, acceleration due to gravity, aerodynamic and frictional cooeficients, and a tire force coeeficient on the slip ratio. The runtime parameters that can be set are: sample increment for discrete time, and total seconds to run the simulation.\n",
    "\n",
    "The model consists of the main vehicle equations for torque (rotational force) and force (longitudinal force). \n",
    "\n",
    "\\begin{align}\n",
    "    J_e \\dot{\\omega}_e &= T_e - (GR)(r_{eff} F_{load}) \\\\ m\\ddot{x} &= F_x - F_{load}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "$J_e$ is the engine moment of inertia value, $\\dot{\\omega}_e$ is the engine angular acceleration , $T_e$ is the engine torque, $GR$ is the combined gear ratio, $r_{eff}$ is the effective tire radius, $F_{load}$ is the total load force, $m$ is the vehicle mass, $x$ is the vehicle position, and $F_x$ is the tire force. The forces are condensed into $F_x$ = $F_{xf}$ + $F_{xr}$ and $F_{load}$ = $F_{aero}$ - $R_{xf}$ - $R_{xr}$ - $mg\\sin{\\alpha}$\n",
    "\n",
    "The engine torque is calculated from the throttle input and the engine angular velocity $\\omega_e$ using a simplified quadratic model. \n",
    "\n",
    "\\begin{align}\n",
    "    T_e = x_{\\theta}(a_0 + a_1 \\omega_e + a_2 \\omega_e^2)\n",
    "\\end{align}\n",
    "\n",
    "The load forces consist of aerodynamic drag $F_{aero}$, rolling friction $R_x$, and gravitational force $F_g$ produced from the incline angle $\\alpha$. The aerodynamic drag is a quadratic model and the friction is a linear one.\n",
    "\n",
    "\\begin{align}\n",
    "    F_{load} &= F_{aero} + R_x + F_g \\\\\n",
    "    F_{aero} &= \\frac{1}{2} C_a \\rho A \\dot{x}^2 = c_a \\dot{x}^2\\\\\n",
    "    R_x &= N(\\hat{c}_{r,0} + \\hat{c}_{r,1}|\\dot{x}| + \\hat{c}_{r,2}\\dot{x}^2) \\approx c_{r,1} \\dot{x}\\\\\n",
    "    F_g &= mg\\sin{\\alpha}\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "Since the model is basically designed for forward motion only, where ($\\dot{x} \\ge 0$}, the absolute value in the friction equation is not essential, but may have an impact if the vehicle would not have enough forward force to overcome an incline that is too steep and slip backwards.\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tire force is calculated from the engine rotational rate and wheel slip equations\n",
    "\n",
    "\\begin{align}\n",
    "    \\omega_w &= (GR)\\omega_e \\\\\n",
    "    s &= \\frac{\\omega_w r_e - \\dot{x}}{\\dot{x}}\\\\\n",
    "    F_x &= \\left\\{\\begin{array}{lr}\n",
    "        cs, &  |s| < 1\\\\\n",
    "        F_{max}, & \\text{otherwise}\n",
    "        \\end{array}\\right\\} \n",
    "\\end{align}\n",
    "\n",
    "where $\\omega_w$ is the wheel angular velocity and $s$ is the slip ratio. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The overall longitudinal force relation for the vehicle and its motion is\n",
    "\n",
    "\\begin{align}\n",
    "    m\\ddot{x} &= F_x - F_{load}\\\\\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "and then expressed in terms of acceleration to begin the time step\n",
    "integrations to obtain velocity and linear position \n",
    "\n",
    "\\begin{align}\n",
    "    \\ddot{x} &= \\frac{F_x - F_{load}}{m}\\\\ \n",
    "\\end{align}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Implementation\n",
    "\n",
    "The primary input to the system is a throttle signal. This is used to directly calculate engine torque that is then transformed through the powertrain and vehicle model equations to accelerate the vehicle into forward motion. \n",
    "\n",
    "The model runs by incrementing through discrete time for a specified period while calculating the longitudinal dynamic equations and updating the state space components of acceleration, velocity and position.\n",
    "\n",
    "In this implementation, throttle signal is in the range $x_\\theta \\in [0,1]$. The vehicle has an initial velocity of 5 m/s and engine speed of 100 rad/s and also when the reset() function is used. A discrete sampling time of 10ms is used for numerical integration. All other model parameters are defined in the Vehicle class.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "#mk v0.14\n",
    "\n",
    "#import sys\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "class Vehicle():\n",
    "    def __init__(self):\n",
    "\n",
    "        # ==================================\n",
    "        #  longitudinal vehicle model \n",
    "        #  system equation parameters & variables\n",
    "        # ==================================\n",
    "        \n",
    "        # set parameters\n",
    "        \n",
    "        # Te engine torque from throttle percentage in range [0,1]\n",
    "        # coefficients for engine torque quadratic Te <- (throttle input * quadratic)\n",
    "        self.a_0 = 400 \n",
    "        self.a_1 = 0.1\n",
    "        self.a_2 = -0.0002\n",
    "\n",
    "        # gear ratio, effective radius, mass, inertia\n",
    "        self.GR = 0.35  # gear ratio\n",
    "        self.r_e = 0.3  # effective radius [meters]\n",
    "        self.J_e = 10   # overall engine inertia for vehicle model \n",
    "        self.m = 2000   # mass of vehicle [kg]\n",
    "        self.g = 9.81   # acceleration due to gravity on earth [m/s^2]\n",
    "\n",
    "        # aerodynamic & friction coefficients\n",
    "        self.c_a = 1.36     # aerodynamic \n",
    "        self.c_r1 = 0.01    # frictional \n",
    "\n",
    "        # tire force\n",
    "        self.c = 10000  # coef on slip ratio when abs(c*s) < 1\n",
    "        self.F_max = 10000 # otherwise is Fmax\n",
    "\n",
    "        # vehicle system state variables\n",
    "        self.x = 0  # x linear position\n",
    "        self.v = 5  # x-dot velocity (of vehicle)\n",
    "        self.a = 0  # x-double-dot acceleration of vehicle\n",
    "        self.w_e = 100  # engine angular velocity (or speed) omega-sub-e\n",
    "        self.w_e_dot = 0   # engine angular acceleration omega-sub-e-dot\n",
    "\n",
    "        # time increment for discrete time space\n",
    "        self.sample_time = 0.01\n",
    "\n",
    "    def reset(self):\n",
    "        # reset state variables\n",
    "        self.x = 0\n",
    "        self.v = 5\n",
    "        self.a = 0\n",
    "        self.w_e = 100 # [r/s] ~955 RPM idle probably something\n",
    "        self.w_e_dot = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The engine dynamic and force equations are implemented in the cell below. The function $\\textit{time_step}$ takes the inputs throttle $x_\\theta$ and incline angle $\\alpha$ and performs numerical integrations over a single timestep to update the state variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Vehicle(Vehicle):\n",
    "    def time_step(self, throttle, alpha):\n",
    "        \n",
    "        # euler forward time step integration\n",
    "        \n",
    "        assert(self.g == 9.81) # make sure on planet earth\n",
    "        \n",
    "        #  vehicle model equations\n",
    "        \n",
    "        ### engine torque from throttle & engine angular velocity\n",
    "        Te = throttle*(self.a_0 + self.a_1*self.w_e + self.a_2*(self.w_e*self.w_e))\n",
    "                \n",
    "        ### calculate tire force Fx ###\n",
    "        \n",
    "        # wheel angular velocity\n",
    "        w_w = self.GR * self.w_e\n",
    "        \n",
    "        # slip ratio\n",
    "        s = (w_w * self.r_e - self.v)/self.v \n",
    "        \n",
    "        ## tire force ##\n",
    "        if ( np.abs(s) < 1):\n",
    "            Fx=self.c * s\n",
    "        else:\n",
    "            Fx = self.F_max\n",
    "            \n",
    "        ### calculate total load force  F_load ###\n",
    "    \n",
    "        # gravitational force due to road inclination\n",
    "        Fg = self.m* self.g * np.sin(alpha)\n",
    "        \n",
    "        # rolling friction (rolling road resistance)\n",
    "        Rx = self.c_r1 * self.v #approximation from front only\n",
    "        \n",
    "        # aerodynamic forces (drag)\n",
    "        F_aero = self.c_a * (self.v*self.v) #x-dot squared\n",
    "        \n",
    "        ## total load force ##\n",
    "        F_load = F_aero + Rx + Fg\n",
    "        \n",
    "        # now have:\n",
    "        # engine torque (from throttle) Te, Load force F_load, Tire force Fx\n",
    "        # so can get acceleration and time step integrate the state variables\n",
    "        \n",
    "        #vehicle acceleration       \n",
    "        self.a = (Fx - F_load)/self.m \n",
    "        \n",
    "        # step integration using time_step as delta-t\n",
    "        # set the current position, velocity, and engine speed\n",
    "\n",
    "        self.v = self.v + self.a*self.sample_time # \n",
    "        self.x = self.x + self.v*self.sample_time # \n",
    "            \n",
    "        #engine angular (rotational) acceleration \n",
    "        self.w_e_dot = (Te - (self.GR * self.r_e * F_load)) / self.J_e \n",
    "        \n",
    "        # engine rotational velocity          \n",
    "        self.w_e = self.w_e + self.w_e_dot*self.sample_time \n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing the model over a flat surface\n",
    "\n",
    "First test the equations by moving the vehicle over a flat surface with a constant throttle.\n",
    "If the model is working properly, the velocity will gradually reach a limiting\n",
    "value as the vehicle gains over opposing forces, aerodynamic drag, and tire force limit and attains a steady state. At the same time, the acceleraion will decline and level out as the rate of change of velocity decreases.\n",
    "\n",
    "Experiment by changing the inclination angle while keeping the throttle constant to see how the model responds.\n",
    "\n",
    "Also try negative angles (for a downward slope). In this case, downward directed forces due to gravity also accelerate the vehicle to a terminal velocity where it is eventually balanced by opposing forces.\n",
    "\n",
    "Observe the relative changes of velocity, acceleration and position displayed in the plots to get an idea\n",
    "of how the dynamics of system respond and change over time.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Using: throttle = 0.3      Angle =  0 (degrees)\n",
      "\n",
      "\n",
      "Position over time\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Velocity over position\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEGCAYAAABiq/5QAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAfVElEQVR4nO3deZhU9Z3v8fe3V+huoIFukNVmE9wAFZeIicYlUbO4jDHjdRKSMZrVaG6SJ3qTiTrJZGJinMkkd0yMOiEJ0bjl0XhdorhEjFuzCoKCLNJs3Q003dB71ff+UQdsmm7shq4+Ved8Xs9TT9U5darO90fJxx+/c87vmLsjIiLxkRN2ASIi0r8U/CIiMaPgFxGJGQW/iEjMKPhFRGImL+wCeqKsrMwrKirCLkNEJKssXLiw1t3LO6/PiuCvqKigsrIy7DJERLKKmW3oan3ahnrMbICZvWZmS81shZndEqwfZmZPm9nq4HloumoQEZEDpXOMvwU4291nADOB883sNOAGYL67TwHmB8siItJP0hb8nrI7WMwPHg5cBMwN1s8FLk5XDSIicqC0ntVjZrlmtgSoBp5291eBke6+BSB4HtHNZ68xs0ozq6ypqUlnmSIisZLW4Hf3hLvPBMYCp5jZcb347J3uPsvdZ5WXH3BQWkREDlG/nMfv7nXA88D5wDYzGwUQPFf3Rw0iIpKSzrN6ys2sNHg9EDgXWAU8CswJNpsDPJKuGkRE5EDpPI9/FDDXzHJJ/Q/mfnd/zMxeBu43s6uAd4FPpbEGkazm7iQd2pNJEkmnPem0J/y95YS/tz6Z3G85EaxLJiHpTtIdd/Z7TnpqH06n5Q7vJ92h07LvrS0ZfCZYPrD+4Bk/YF1q/YHbdty+u1njO+6rq+/r6rsOtu9MdskJY5hQVtyn35m24Hf3ZcAJXazfDpyTrv2KpFtLe4I9LQkaW9tpbE2wpyX1nHq073tvT0uCxrZ2mlsTtLQnaW1P0rLvkdi33Lp3OZGkpS2577ktkaQ9mS3xJOly4vjS7Al+kUzX2p5k+54Wahtaqd3dQu3uFnY1tVHf1MauDo/65vb9llvbkz3eR0FeDgPzcynMy6EgLyd4fm950IA8CvNyKMzL7fB+6jkvN4f8HCMvN4fcHCMvx957Dt7LzTHyco3cnBzygvc6LufmGDlm5OaAmWFAjqXWmbHfc44F23RYzjEDICfnvWUjtV1Oh88bhnUYOLYOfwYWfMf+6zpua12u7822vdpfVzuJGQW/RE4i6VQ3NLO5rpktu5rYXNfE5rpmahpaqAkCfvvuVnY1tXX5eTMYVJjHkKJ8hgxMPUYOLmHIwHwGD8hn8MB8igtyKSrMo7ggj6KCXIoKciku3Ps6j6LCXIryc8nL1TyIknkU/JKV6pvbWF+7h/XbG1PPtXvYuLORzXXNbK1vJtFpiKS4IJeRQwZQVlLItCMGUVZSuO8xvKQgeF1AaVEBgwrzyMlRr1CiS8EvGW3HnlZWbaln1dYG3trawJqa3ayv3cP2Pa37bTdqyADGDSvi1AnDGFU6gFFDBjKmdCCjSgcwunQggwfkh9QCkcyj4JeM4O5U7WxiycY6llXVsWprA6u2NlDT0LJvm2HFBUwZUcJ5x4ykoqyYiuHFTCgrZvywIgYW5IZYvUh2UfBLKPa0tLNww06WbKxjycY6lm6s29eLL8jL4aiRJZx5VDnTjhjE1OBRXlKoA3MifUDBL/1iT0s7lRt28sra7byydjvLqnaRSDpmMLm8hA9PG8HMcaXMHFfK1CMGka+DoiJpo+CXtHB3Vm5p4Lm3qnluVTWLN9aRSDp5OcbMcaV8+cxJnDpxGDPHlTJI4+8i/UrBL32muS3BgtW1zF+1jedW1bC1vhmA48cM4YsfmsgHJg3npCOHUlSg/+xEwqS/gXJYWtuTLFhTw2NLt/D0m9toaGmnuCCXD04p5+xpIzhrajkjBg8Iu0wR6UDBL73m7lRu2MkDlRt5cvlW6pvbGTwgj/OPO4KPTR/F6ZPKKMjTGL1IplLwS49VNzTz0MJNPFC5kbW1eyguyOX840bx8emjmD1ZYS+SLRT8clDuzmvrdnDPS+t4ZmU1iaRzcsVQvnzWJD42fZTG60WykP7WSpda2hM8tnQL97y0jhWb6yktyucLH5zAp2eNY2J5SdjlichhUPDLfhpb25n3yrvc+eJaahpamDKihH+/9HgunjlGV8eKRISCXwDY3dLO71/ewG9eXMuOPa2cMbmM2y+fwRmTy3S1rEjEKPhjrrktwdy/r+eOF96hrrGNM48q5+vnTOGkI4eGXZqIpImCP6aSSecvyzbzkyffYlNdE2dNLef6c49i5rjSsEsTkTRT8MfQ6+t38K9/eZM3Nu3i2NGD+ell0zl9clnYZYlIP1Hwx8iOPa38++MreWBhFaOHDOD2y2dw8cwxuumISMwo+GMgmXQeXFjFj55Yye7mdr505iS+fs5knYMvElP6mx9xG3c08u0Hl/LK2h2cXDGUf7vkeI4aOSjsskQkRAr+iHJ37q/cyA8eWwnAjy89nstnjdOwjogo+KOopqGFGx5axvxV1Zw2cRg/vWwG44YVhV2WiGQIBX/EvPzOdr5+32Lqm9r4/seP4XOnV6iXLyL7UfBHRDLp3PHCO/zsr29RUVbM7686hWlHDA67LBHJQAr+CNjV2MZ1f1rM82/V8MkZo/nRpcdTUqifVkS6pnTIcu/U7OYLcyup2tnIDy8+jitPHa+5dUTkoBT8WezF1TV8dd4i8nJz+OPVp3FyxbCwSxKRLKDgz1J/eGUDNz26gsnlJdw1Z5bO2hGRHlPwZxl35z+fWc3P56/m7Gkj+K8rTtB4voj0ihIjiySTzs1/WcHvXt7AZSeN5ceXHk9eru5zKyK9k7bUMLNxZvacma00sxVmdl2w/mYz22RmS4LHhemqIUpa25Nc96cl/O7lDVzzoYn89LLpCn0ROSTp7PG3A99090VmNghYaGZPB+/9h7vflsZ9R0pbIsm19y7iqRXb+M750/jyWZPCLklEsljagt/dtwBbgtcNZrYSGJOu/UVVWyLJ1+9dzFMrtnHTJ47h87MnhF2SiGS5fhkrMLMK4ATg1WDV18xsmZndY2Zd3uPPzK4xs0ozq6ypqemPMjNOWyLJdfct5onlW/mXjyv0RaRvpD34zawEeAi43t3rgTuAScBMUv8i+FlXn3P3O919lrvPKi8vT3eZGSeZdL71wFIef2Mr3/vY0Vx1hkJfRPpGWoPfzPJJhf48d38YwN23uXvC3ZPAb4BT0llDNnJ3fvD/3uSRJZv59ken8oUPTgy7JBGJkHSe1WPA3cBKd7+9w/pRHTa7BFierhqy1a9eWMv/vLSef549ga/oQK6I9LF0ntUzG/gM8IaZLQnW/R/gCjObCTiwHvhiGmvIOg8urOLWJ1fxyRmj+d7Hjta8OyLS59J5Vs8CoKvUejxd+8x2f3+nlhseWsYHp5Rx26dmaB59EUkLXQGUITZs38NX5i1iQlkx/33liRTk6acRkfRQumSAhuY2rppbCcBdc2YxaEB+yBWJSJQp+EOWSDpfv3cx62v38N9XnsiRw4vDLklEIk7BH7JfPLua596q4aZPHsvpk8rCLkdEYkDBH6IFq2v5+fzVXHriGP7p1PFhlyMiMaHgD8m2+mau/9NiJpeX8MOLj9NpmyLSbzQffwjaE0muvXcxe1oS3Hv1iRQV6GcQkf6jxAnBL59bw2vrdnD75TOYMnJQ2OWISMxoqKefLd1Yxy+eXcPFM0dz6Yljwy5HRGJIwd+PmloTfOP+JYwYVMgtFx0XdjkiElMa6ulHtz65irU1e5j3hVMZMlAXaYlIONTj7ycvranlt39fz+dOr2D2ZJ2vLyLhUfD3g6bWBDc+/AYTyoq54YJpYZcjIjGnoZ5+8PP5q3l3RyP3Xn0aA/Jzwy5HRGJOPf40e3NzPb95cS2fnjWOD0waHnY5IiIK/nRKJJ0bH17G0KJ8brxQQzwikhkU/Gk079UNLK3axfc/cSylRQVhlyMiAij402bnnlZ+9te3mT15OJ+YPur9PyAi0k8U/Gly+9Nvs7ulne9//FhNwCYiGUXBnwarttYz79UN/NOp45l6hObiEZHMouDvY+7OLY++yeCB+XzjvKPCLkdE5AAK/j721ze38fLa7XzzvKN0QFdEMpKCvw8lks5Pn3qLieXFXHGK7qglIplJwd+HHl5UxZrq3Xz7I1PJy9UfrYhkJqVTH2lpT/Cfz6xm+tghnH/cEWGXIyLSLQV/H5n3yrtsqmviO+dP0+mbIpLRFPx9YHdLO798bg2zJw/XlMsikvEU/H3gD69sYMeeVr71kalhlyIi8r4U/IepqTXBXS+u5UNHlXPC+KFhlyMi8r4U/IfpvtffpXZ3K9eePTnsUkREekTBfxha2hP8+oW1nDphGCdXDAu7HBGRHklb8JvZODN7zsxWmtkKM7suWD/MzJ42s9XBc9aOjzy4sIqt9c1ce/aUsEsREemxdPb424FvuvvRwGnAV83sGOAGYL67TwHmB8tZpz2R5I7n32HmuFJmT9adtUQke6Qt+N19i7svCl43ACuBMcBFwNxgs7nAxemqIZ2eWrGNqp1NfOnMSTpvX0SySr+M8ZtZBXAC8Cow0t23QOp/DsCIbj5zjZlVmlllTU1Nf5TZK3cvWMv4YUWcd8zIsEsREemV9w1+M7vNzI491B2YWQnwEHC9u9f39HPufqe7z3L3WeXl5Ye6+7RY/O5OFr1bx+dnV5Cbo96+iGSXnvT4VwF3mtmrZvYlMxvS0y83s3xSoT/P3R8OVm8zs1HB+6OA6t4WHba7F6xjUGEen5o1LuxSRER67X2D393vcvfZwGeBCmCZmf3RzD58sM9ZauD7bmClu9/e4a1HgTnB6znAI4dSeFg21TXxxPKtXHHqeEoK88IuR0Sk13o0xm9mucC04FELLAX+t5ndd5CPzQY+A5xtZkuCx4XAj4HzzGw1cF6wnDV+9/J6AOacXhFqHSIih+p9u6xmdjvwCeBZ4Efu/lrw1q1m9lZ3n3P3BUB3A+Dn9LbQTNDcluD+1zdy3tEjGVM6MOxyREQOSU/GKpYD33P3xi7eO6WP68loT63Yys7GNq48TXfXEpHs1ZOhnis7h76ZzQdw911pqSpDzXv1XcYPK2L2JE29LCLZq9sev5kNAIqAsmBahb3DNoOB0f1QW0ZZU93Aa+t2cMMF08jRKZwiksUONtTzReB6UiG/qMP6euD/prGmjPTHVzeSn2tcdtLYsEsRETks3Qa/u/8c+LmZXevuv+jHmjJOc1uChxZV8dFjj6CspDDsckREDsvBhnrOdvdngU1mdmnn9ztckBV5T63Yyq6mNv7XKTqoKyLZ72BDPWeSOoXzE12850Bsgv/hRZsYUzqQ0yZqFk4RyX4HG+q5KXj+fP+Vk3mq65t5cXUNXzlrsg7qikgk9GSSth+ZWWmH5aFm9sO0VpVBHlmymaTDJSeOCbsUEZE+0ZPz+C9w97q9C+6+E7gwbRVlmIcWVTFjXCmTykvCLkVEpE/0JPhzzWzfqSxmNhCIxaktb26uZ9XWBv5BvX0RiZCeTNnwB2C+mf0PqYO6/8x7d9CKtD8vriI/1/j49NhdryYiEfa+we/uPzGzZcC5waofuPtT6S0rfMmk85elWzjzqHKGFReEXY6ISJ/p6YTyi4F8Uj3+xekrJ3Ms3ljH1vpmvnPB1LBLERHpUz05q+dy4DXgMuBy4FUzuyzdhYXt8Te2UJCbwzlH6566IhItPenxfxc42d2rAcysHHgGeDCdhYUpmXSeeGMLHzqqjMED8sMuR0SkT/XkrJ6cvaEf2N7Dz2WtJVV1bN7VzIXHjwq7FBGRPteTHv+TZvYUcG+w/Gng8fSVFL7Hl6WGec49RsM8IhI9PTmr59tm9g+k7qFrwJ3u/ue0VxYSd+eJ5Vv54BQN84hINPXorB53fwh4KM21ZIQVm+vZVNfE9edOCbsUEZG0ONi0zA2kTt884C3A3X1w2qoK0TMrt2EGZ08bEXYpIiJpcbDZOQf1ZyGZYv7Kak4YV8pw3XBFRCKqR2fnmNkZZvb54HWZmU1Ib1nh2FbfzBubduncfRGJtJ5cwHUT8B3gxmBVAan5eyLn2VWps1bPVfCLSIT1pMd/CfBJYA+Au28GIjkMNH9lNWNKB3LUSE3BLCLR1ZPgb3V3JzjQa2bF6S0pHM1tCRasqeHco0dgpjttiUh09ST47zezXwOlZnY1qekafpPesvrfy2u309yW5GwN84hIxPXkAq7bzOw8oB6YCnzf3Z9Oe2X97MW3aynMy+HUCcPCLkVEJK3eN/jN7BvAA1EM+44WrKnhlAnDGJCfG3YpIiJp1ZOhnsHAU2b2opl91cwiNxayrb6Zt7ftZvbksrBLERFJu/cNfne/xd2PBb4KjAZeMLNn0l5ZP3ppTS0AZyj4RSQGejO9cjWwldS0zJGaz2DB6lqGFxdwzKhIzkIhIrKfnlzA9WUzex6YD5QBV7v79B587h4zqzaz5R3W3Wxmm8xsSfC48HCK7wvuzoI1tZw+uYycHJ3GKSLR15PZOY8Ernf3Jb387t8CvwR+12n9f7j7bb38rrR5e9tuqhtaOGPy8LBLERHpFz05nfOGQ/lid/+bmVUcymf708vvpMb3dWBXROIijFsofs3MlgVDQUO728jMrjGzSjOrrKmpSVsxr63fwZjSgYwdWpS2fYiIZJL+Dv47gEnATGAL8LPuNnT3O919lrvPKi8vT0sx7s5r63ZyckW3//8REYmcnhzc/YaZje2Lnbn7NndPuHuS1LQPp/TF9x6q9dsbqd3dwsm6WldEYqRfL+Ays1EdFi8Blne3bX94fd0OAE3TICKx0pODu7cAt5jZdODTpC7gqnL3cw/2OTO7FzgLKDOzKuAm4Cwzm0lqps/1wBcPq/rD9Nr6HQwrLmBSuaZhFpH46NHN1gO9uoDL3a/oYvXdvdhf2r22bgezjhyqaZhFJFbSdgFXpttW38y7Oxo5RcM8IhIz6byAK6MtfncnACcdqTN6RCRe0nYBV6ZbsnEX+bnGMaM1P4+IxEsYF3BlhKUb6zh61GAK8zT/vojESyyDP5l03ti0ixljS8MuRUSk38Uy+NfW7mZ3SzvTxw4JuxQRkX4Xy+BfsnEXADPHlYZbiIhICGIZ/Muq6igpzGOiLtwSkRiKZfAv3VjHcWMGk6sbr4hIDMUu+NsTSVZubeC40RrfF5F4il3wr9++h9b2JEfr/roiElOxC/43tzQAKPhFJLZiF/yrttSTl2NMGlEcdikiIqGIXfCv3FLP5BElumJXRGIrdsG/amsD044YFHYZIiKhiVXw1zW2smVXs8b3RSTWYhX8K4MDu9MU/CISY7EK/jU1uwGYMkJX7IpIfMUq+NfW7GZgfi5HDB4QdikiIqGJWfDvYUJZMTmaqkFEYixewV+7m4nlOn9fROItNsHf3JagameTZuQUkdiLTfBv2N6IO0xSj19EYi42wb82OKNnYpl6/CISb7EJ/nXb9wAwQT1+EYm52AT/xh1NDC8uoKQwL+xSRERCFZvg31TXxJihA8MuQ0QkdLEJ/qqdjYxV8IuIxCP43Z1NO5sYU6rgFxGJRfDX7m6lpT3J2KFFYZciIhK6WAR/1c5GAPX4RURIY/Cb2T1mVm1myzusG2ZmT5vZ6uB5aLr239GmuiYAxg5T8IuIpLPH/1vg/E7rbgDmu/sUYH6wnHabg+AfrR6/iEj6gt/d/wbs6LT6ImBu8HoucHG69t9RdX0LA/JzGKRz+EVE+n2Mf6S7bwEInkd0t6GZXWNmlWZWWVNTc1g7rdndwohBAzDTdMwiIhl7cNfd73T3We4+q7y8/LC+q6ahhfJBhX1UmYhIduvv4N9mZqMAgufq/thpTUML5SUKfhER6P/gfxSYE7yeAzzSHzutVo9fRGSfdJ7OeS/wMjDVzKrM7Crgx8B5ZrYaOC9YTquW9gS7mtoYoeAXEQEgbae5uPsV3bx1Trr22ZXa3a0A6vGLiAQy9uBuX6lpaAGgTGP8IiJADIK/rjHV4x9anB9yJSIimSHywb+rqQ2AIQMV/CIiEIPgrw+Cf7CCX0QEiEHw1zWqxy8i0lHkg39XUxsD83MpzMsNuxQRkYwQi+BXb19E5D2RD/66pjZKixT8IiJ7RT74dzW16cCuiEgHkQ/++qY2Bg9Q8IuI7BX54G9qS1BUoAO7IiJ7RT74G1sV/CIiHUU++JtaExQV6JaLIiJ7RTr43Z3G1nb1+EVEOoh08Le0J0k6DFTwi4jsE+ngb2pNAKjHLyLSQaSDv7FNwS8i0lmkg7+ptR2AgTq4KyKyT6SDv3HvUE++evwiIntFOvg1xi8icqBIB39rIglAQV6kmyki0iuRTsS2IPjzcyPdTBGRXol0IrYlHIC8XAu5EhGRzBHx4A+GetTjFxHZJ9KJ2L6vxx/pZoqI9EqkE7F13xi/hnpERPaKdPDr4K6IyIEinYh7h3oU/CIi74l0IrZpqEdE5AARD371+EVEOot0ImqMX0TkQJFOxLZEEjPIzdFQj4jIXqHMV2xm64EGIAG0u/usdOynLeHq7YuIdBLmRPUfdvfadO6gLZEkX719EZH9RLo73J5Ikq+ZOUVE9hNWj9+Bv5qZA7929zs7b2Bm1wDXAIwfP/6QdnL0qME0BbdfFBGRFHP3/t+p2Wh332xmI4CngWvd/W/dbT9r1iyvrKzsvwJFRCLAzBZ2dQw1lHEQd98cPFcDfwZOCaMOEZE46vfgN7NiMxu09zXwEWB5f9chIhJXYYzxjwT+bGZ79/9Hd38yhDpERGKp34Pf3dcCM/p7vyIikqJzHUVEYkbBLyISMwp+EZGYUfCLiMRMKBdw9ZaZ1QAbDvHjZUBa5wTKEGpntKid0RJWO4909/LOK7Mi+A+HmVWma/bPTKJ2RovaGS2Z1k4N9YiIxIyCX0QkZuIQ/AfM/BlRame0qJ3RklHtjPwYv4iI7C8OPX4REelAwS8iEjORDn4zO9/M3jKzNWZ2Q9j1HA4zW29mb5jZEjOrDNYNM7OnzWx18Dy0w/Y3Bu1+y8w+Gl7l78/M7jGzajNb3mFdr9tmZicFf0ZrzOy/LJgCNlN0086bzWxT8LsuMbMLO7yXde00s3Fm9pyZrTSzFWZ2XbA+Ur/nQdqZHb+nu0fyAeQC7wATgQJgKXBM2HUdRnvWA2Wd1v0EuCF4fQNwa/D6mKC9hcCE4M8hN+w2HKRtHwJOBJYfTtuA14APAAY8AVwQdtt60M6bgW91sW1WthMYBZwYvB4EvB20JVK/50HamRW/Z5R7/KcAa9x9rbu3AvcBF4VcU1+7CJgbvJ4LXNxh/X3u3uLu64A1ZPBdzjx1280dnVb3qm1mNgoY7O4ve+pv0+86fCYjdNPO7mRlO919i7svCl43ACuBMUTs9zxIO7uTUe2McvCPATZ2WK7i4D9Mptt7g/qFwY3oAUa6+xZI/YcIjAjWR6HtvW3bmOB15/XZ4GtmtiwYCto7BJL17TSzCuAE4FUi/Ht2aidkwe8Z5eDvapwsm89dne3uJwIXAF81sw8dZNuotb2j7tqWrW2+A5gEzAS2AD8L1md1O82sBHgIuN7d6w+2aRfrsrmdWfF7Rjn4q4BxHZbHAptDquWwedc3qN8W/FOR4Lk62DwKbe9t26qC153XZzR33+buCXdPAr/hvSG5rG2nmeWTCsN57v5wsDpyv2dX7cyW3zPKwf86MMXMJphZAfCPwKMh13RIrPsb1D8KzAk2mwM8Erx+FPhHMys0swnAFFIHkLJJr9oWDB80mNlpwVkRn+3wmYy1NwwDl5D6XSFL2xnUdDew0t1v7/BWpH7P7tqZNb9n2EfH0/kALiR1tP0d4Lth13MY7ZhI6oyApcCKvW0BhgPzgdXB87AOn/lu0O63yKCzIbpp372k/lncRqoHdNWhtA2YReov2jvALwmuTM+URzft/D3wBrCMVDiMyuZ2AmeQGqpYBiwJHhdG7fc8SDuz4vfUlA0iIjET5aEeERHpgoJfRCRmFPwiIjGj4BcRiRkFv4hIzCj4RfqImX3JzD4bvP6cmY3u8N5dZnZMeNWJvEenc4qkgZk9T2qWxsqwaxHpTD1+iTQzOzmYMGtAcAX0CjM7rtM2FWa2yszmBts+aGZFwXvnmNniYL70e8ysMFj/YzN7M9j+tmDdzWb2LTO7jNRFOfOCOdkHmtnzZjYr2O6K4PuWm9mtHerYbWb/ZmZLzewVMxvZX39OEi8Kfok0d3+d1BWUPyQ1J/wf3H15F5tOBe509+lAPfAVMxsA/Bb4tLsfD+QBXzazYaQuxz822P6Hnfb5IFAJXOnuM929ae97wfDPrcDZpCbyOtnMLg7eLgZecfcZwN+Aqw//T0DkQAp+iYN/Bc4j1Qv/STfbbHT3l4LXfyB1Sf5UYJ27vx2sn0vqZir1QDNwl5ldCjT2opaTgefdvcbd24F5wXcCtAKPBa8XAhW9+F6RHlPwSxwMA0pI3SlpQDfbdD7Y1d2UuQSBfQqpmRkvBp7sRS0Hu61em7930C1B6l8YIn1OwS9xcCfwL6R617d2s814M/tA8PoKYAGwCqgws8nB+s8ALwRzsA9x98eB60kN2XTWQOp/NJ29CpxpZmVmlhvs64Vet0jkMKhHIZEWnF7Z7u5/DIL272Z2trs/22nTlcAcM/s1qRkk73D3ZjP7PPCAmeWRmur7V6T+BfFIcAzAgG90sevfAr8ysyZS91MFUnefMrMbgeeCzz7u7hkz3bDEg07nlNgLbp33mLsf937bikSBhnpERGJGPX4RkZhRj19EJGYU/CIiMaPgFxGJGQW/iEjMKPhFRGLm/wP6yciBdZ41AQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Velocity over time\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEGCAYAAABiq/5QAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAfr0lEQVR4nO3deXxV9Z3/8dcnGyFACJCAYY0ssqhsAm5drErrMtZqbUdtrba2dkadqbXT1k77m7azdPzZbfqbaTulasVf1Y51qdZWraKtG2IDIoKAYEC2QBYI2XOTez/zxz1gigQukJuTe8/7+Xjcxz3LPfd8vizvnHzPOd9j7o6IiERHTtgFiIhI31Lwi4hEjIJfRCRiFPwiIhGj4BcRiZi8sAtIRWlpqVdUVIRdhohIRlm+fHmdu5cduDwjgr+iooLKysqwyxARyShm9vbBlqetq8fMCs3sFTN7zczWmNm3g+XDzewpM9sQvA9LVw0iIvJu6ezj7wDOdvdZwGzgPDM7DbgFWOLuU4AlwbyIiPSRtAW/JzUHs/nBy4GLgcXB8sXAR9JVg4iIvFtar+oxs1wzWwnUAE+5+zJglLtXAwTvI3vY9jozqzSzytra2nSWKSISKWkNfnePu/tsYCywwMxOOoJtF7n7PHefV1b2rpPSIiJylPrkOn53bwD+CJwH7DKzcoDgvaYvahARkaR0XtVTZmYlwfRA4FxgHfAocHXwsauBR9JVg4iIvFs6r+MvBxabWS7JHzD3u/tjZrYUuN/MrgW2AB9LYw0ikRVPOJ3xBB1dCTrjCWJdCeIJpyvhxBNOwpPv+1/d5hP7PufJ6QM/k3DHHdxJTgM4OMFyCN73fc7fWdZ9muQ88M53HrAtwWdSHUE+1YHmj2REek/xW3u7RoBL5ozh+NJBR7DF4aUt+N19FTDnIMvrgXPStV+RTNDRFaexrYvG9k4a2zppbO+itaOL1lic1s44bbEu2mIJWju7aIvFaY3FaYvFaeuM0xrroqMrGeT7Aj3WlSAWd2JdcTrjTiyeDHnJfHPHl2RO8ItERXtnnPqWGPXNHdQ3x6gN3uubO6hvibGnNcbetncCvrGtk46uRErfXZCXQ1FBLgPzcxlYkEtRQS5F+XkMHpBHQVEO+bk5FOQlX/m5OQzYP20U5OaSn2cUBMvzc3PIy80hNwdyzMjNMfJybP/0/pcZOfvWBfN/sT7Yxkh+j1myVjOwYLkZGBYs6zbNuz+DQU4P29JtPsdS/zsxS+3DR/CVpPiVKe87TAp+kUPojCfY0dDG9oY2qhvaqd7bxvbgvbqhnR1722hq7zrotgPzcykdUsCwogKGDsxn9NCBFA/Mo7gwn+KB+RQX5gXv+QwpzKOoIC8Z7AXJkB+Yn0tersZRlN6n4JfISySc7Q1tVNW1sLmuhU11LWyuT05v3dP2ri6T4YMKGF1SyPgRRZw2cTgjiwsZMaiA0sEDGDH4nfeiAv33kv5J/zIlUhrbO1m/s4l11Y2s3dnE+uDV3PHOUXtRQS4VIwZx4uih/NXM0YwfUcTYkoGUlwykfGghhfm5IbZA5Ngp+CVrdcYTrKtu4tWte1i5pYGVWxuoqmvZv764MI9p5cV8dO4Yph5XzKSyQRxfOoiyIQMyop9W5Ggp+CVrtHfGWfH2HpZW1fNyVT2rtu3dfxK1dPAA5owv4dK5Y5gxuphpxxVTPrRQAS+RpOCXjJVIOKu27+W5N2t56a06VmxpINaVIDfHOHnMUK46bQKzx5cwe1wJY0oGKuRFAgp+ySitsS5e2FDHkrU1PLO+htqmDsxgRnkxV58+gdMnjWB+xXCGFOaHXapIv6Xgl36vNdbF02treHTlDp7bUEusK8GQAXm8b2oZ504fyftPGMnwQQVhlymSMRT80i/FuhL8cX0Nv11VzdNv7KKtM86o4gFcuWA8C2eMYn7FcArydI27yNFQ8Eu/UlXbzK/+vJUHl2+jviXGsKJ8Lp07hotmjWZBxXByjuT2TRE5KAW/hC7WleDx1dXcu2wLyzbtJi/HOGf6SC6fP573TCklX3evivQqBb+EpqE1xj3LtrD4pc3UNHUwYUQRXzlvKpedMpaRQwrDLk8kayn4pc9t3d3K7c9XcX/lNto647x3Sim3XTaT900pU1eOSB9Q8Euf2bq7lf96ZiMPrtiGGXx41hg++97jmV5eHHZpIpGi4Je0297Qxn89s5FfV24lJ8f45GkT+Jv3T+K4oerOEQmDgl/SZm9bJz95diO/eHEzAFeeOp7rz5qswBcJmYJfel1XPMF9r2zhh09vYE9rjI/OHcvNC09gdMnAsEsTERT80steequOf3pkDRtrmjlt4nC+ceEMThozNOyyRKQbBb/0ivrmDv7t92t5aMV2xg8vYtFVp7BwxigNjCbSDyn45Zi4O79evo3v/H4tLR1d3PiBydx49mQ9rESkH1Pwy1HbubedLz/wGs9vqGN+xTC+c8nJTBk1JOyyROQwFPxyVB5ZuZ3/85vVdMadf/3ISVy5YLxuvhLJEAp+OSINrTG+8ZvVPLaqmrnjS/jBx2dTUToo7LJE5Ago+CVlK7c2cMM9K9jV2M6XPzSVz79vInkaQE0k4yj45bDcnbte2sx3fr+WkUMKefBvz2DWuJKwyxKRo6Tgl0Nqau/kKw+s4vHVOzl3+ki+/7HZDC3SYw1FMpmCX3r0dn0L1y6uZFNdC1+/YDqffe/xui5fJAso+OWgXnqrjuvvWQHAL689ldMnjQi5IhHpLQp+eZd7lr3NNx9ZQ0XpIO64eh4TRuiqHZFsouCX/RIJ598fX8vPn9/EB6aW8aMr5lBcqP58kWyj4BcAOuMJvvLAKh5+dTufOn0C37zoRHJ1Q5ZIVkrbRdhmNs7MnjWztWa2xsy+ECz/lpltN7OVweuCdNUgqWnp6OLaxZU8/Op2vvyhqXz7wwp9kWyWziP+LuBL7r7CzIYAy83sqWDdD939e2nct6RoT0uMa+76M69va+DWS0/m8gXjwy5JRNIsbcHv7tVAdTDdZGZrgTHp2p8cufrmDj5x+zKq6lr42VXzWDhjVNgliUgf6JP77c2sApgDLAsW3Whmq8zsTjMb1sM215lZpZlV1tbW9kWZkVLb1MEVP3+ZTXUt3Hn1fIW+SISkPfjNbDDwIHCTuzcCPwUmAbNJ/kbw/YNt5+6L3H2eu88rKytLd5mRUtPYzuWLlrJ1dxu/+PR83jOlNOySRKQPpTX4zSyfZOjf4+4PAbj7LnePu3sC+DmwIJ01yF9Khv7LVO9t565Pz+eMSQp9kahJ51U9BtwBrHX3H3RbXt7tY5cAq9NVg/ylPS0xPnnHMnY2trP4Mws4daLuxhWJonRe1XMmcBXwupmtDJb9I3CFmc0GHNgMfD6NNUiguaOLa+76M5vrW7nrmvnMrxgedkkiEpJ0XtXzAnCwi8F/n659ysG1d8b53OJKVm/fy08/MZczJqt7RyTK9BSNLNcVT/B3973K0qp6vvexmXzwxOPCLklEQqbgz2LuzjcfXcNTb+ziny8+kUvmjA27JBHpBxT8Wexnz1Vxz7ItXH/WJD51ekXY5YhIP6Hgz1KPrdrBrY+v46JZo/mHD04NuxwR6UcU/FmocvNubr7/NeZXDOO7l80kRwOuiUg3Cv4ss3V3K5+7u5KxJQNZdNU8CvNzwy5JRPoZBX8WaY118bm7K4knnDuvmc+wQQVhlyQi/ZAexJIl3J0vP7CKN3c18YtPL6CiVI9LFJGD0xF/lvjvP1Xxu1XVfPW8abz/BA1qJyI9U/BngT+ur+G2J5NX8Fz3volhlyMi/ZyCP8Nt3d3K39/3KtOPK+a2j84kOTaeiEjPFPwZLNaV4MZ7V+DAz646hYEFuoJHRA5PJ3cz2K2Pr+O1bXv570+ewrjhRWGXIyIZQkf8GerJNTu588VNXHNGBeedpIHXRCR1Cv4MtHV3K1/+9WucPGYoX7tgWtjliEiGUfBnmM5gmGV3+PGVcxmQp359ETky6uPPMP/5zEZWbm3gx1fOZfwI9euLyJHTEX8GWbFlDz9+diOXzh3DhTPLD7+BiMhBKPgzREtHFzf/z0qOKy7kWx8+MexyRCSDqasnQ/zr79by9u5WfvW50yguzA+7HBHJYDrizwBL1u7ivle2cN37JnLqxBFhlyMiGU7B38/taYnx1QdfZ3p5MTcvPCHsckQkC6irp5/758feoKE1xt2fWaBLN0WkV+iIvx97dl0ND7+6nevPmsSM0cVhlyMiWULB3081tXfyjw+/zpSRg7nh7MlhlyMiWUTB30/9++Pr2NXYzm2XzVQXj4j0KgV/P7T0rXruXbaFz5x5PHPGDwu7HBHJMgr+fqa9M84tD61iwogivvTBqWGXIyJZSFf19DM/eXYjb9e3cu9nT9WDVUQkLXTE349U1Tbz33+q4iOzR3PG5NKwyxGRLKXg7yfcnX96ZA0D8nL4xwunh12OiGSxtAW/mY0zs2fNbK2ZrTGzLwTLh5vZU2a2IXjX2Uvgd69X88LGOv7hQ1MZOaQw7HJEJIul84i/C/iSu08HTgNuMLMZwC3AEnefAiwJ5iOtqb2Tf/7tG5w4uphPnjYh7HJEJMulLfjdvdrdVwTTTcBaYAxwMbA4+Nhi4CPpqiFT/PCpDdQ2d/Bvl5xMbo6FXY6IZLk+6eM3swpgDrAMGOXu1ZD84QCM7GGb68ys0swqa2tr+6LMUKzb2chdL23iygXjmT2uJOxyRCQCDhv8ZvY9MzvqJ3+Y2WDgQeAmd29MdTt3X+Tu89x9XllZ2dHuvl9zd/7lsTcYUpjPP+iafRHpI6kc8a8DFpnZMjP7GzMbmuqXm1k+ydC/x90fChbvMrPyYH05UHOkRWeLp9fW8OLGer547hSGDSoIuxwRiYjDBr+73+7uZwKfAiqAVWZ2r5l94FDbmZkBdwBr3f0H3VY9ClwdTF8NPHI0hWe6jq44//a7N5g8cjCf0AldEelDKfXxm1kuMC141QGvATeb2a8OsdmZwFXA2Wa2MnhdANwKLDSzDcDCYD5y7n7pbTbXt/KNC6eTn6vbKUSk7xx2yAYz+wFwEfAM8B13fyVY9X/NbH1P27n7C0BPl6icc6SFZpO65g7+35INnDW1jLOmHvTctohI2qQyVs9q4Bvu3nqQdQt6uZ5I+P4f3qStM843LpwRdikiEkGp9DF84sDQN7MlAO6+Ny1VZbG11Y38z5+3cNXpE5g8cnDY5YhIBPV4xG9mhUARUBoMq7Cv26YYGN0HtWWl255Yx+ABeXzhnClhlyIiEXWorp7PAzeRDPkV3ZY3Aj9OY01Za+lb9Ty7vpZbzp9GSZEu3xSRcPQY/O7+I+BHZvZ37v6ffVhTVnJ3bn1iHccVF3LNGRVhlyMiEXaorp6z3f0ZYLuZXXrg+m43ZEkKnli9k9e2NnDbR2dSmK8HrIhIeA7V1fN+kpdwXnSQdQ4o+FPUFU/w3SfXM3nkYC6dOybsckQk4g7V1fPN4P3TfVdOdrq/chtVdS0suuoU8nSzloiELJVB2r5jZiXd5oeZ2b+mtaos0hrr4j+efpNTJgxj4YxRYZcjIpLSdfznu3vDvhl33wNckLaKsswvXtxMTVMHt5w/jeTwRSIi4Uol+HPNbMC+GTMbCAw4xOcl0NTeyaLnqjhrahnzK4aHXY6ICJDakA2/BJaY2S9IntT9DO88QUsO4a4XN7O3rZObF54QdikiIvsdNvjd/TYzWwWcGyz6F3d/Mr1lZb69bZ38/Pkqzp0+ipljS8IuR0Rkv1SO+AFeBfJJHvG/mr5yssedL2yisb2Lm87V0Awi0r+kclXPx4FXgMuAjwPLzOyydBeWyfa2dnLnC5v40ImjOGlMyg8sExHpE6kc8X8dmO/uNQBmVgY8DTyQzsIy2e0vVNHU0cVN56pvX0T6n1Su6snZF/qB+hS3i6Q9LTHufGETF55czvTy4rDLERF5l1SO+J8wsyeB+4L5vwZ+n76SMtui56to7YzzBfXti0g/lcpVPV82s4+SfIauAYvc/eG0V5aB9rZ2cvdLm7ng5HJOGDUk7HJERA4qpat63P1B4ME015LxFi/dTEsszo0fmBx2KSIiPTrUsMxNJC/ffNcqwN1dHdjdtHR0ceeLmzhn2kj17YtIv3ao0TnVV3EE7ntlCw2tnVyvo30R6edSujrHzN5jZp8OpkvN7Pj0lpVZOrri/Pz5Kk6fOIJTJgwLuxwRkUNK5QaubwJfBb4WLCogOX6PBB5asZ1djR3coKN9EckAqRzxXwJ8GGgBcPcdgLqBAl3xBD/941vMGjuUMyePCLscEZHDSiX4Y+7uBCd6zWxQekvKLL97vZotu1u5/gOTNd6+iGSEVIL/fjP7GVBiZp8jOVzDz9NbVmZwd37y7FucMGowC6fr6VoikhlSuYHre2a2EGgEpgL/5O5Ppb2yDPCnN2tZv6uJ739sFjk5OtoXkcxw2OA3sy8Cv1bYv9vtz29iVPEALpo1OuxSRERSlkpXTzHwpJk9b2Y3mJn6NIA3djTywsY6rjnjeAryNGadiGSOwyaWu3/b3U8EbgBGA38ys6fTXlk/d/vzVRQV5HLlgvFhlyIickSO5FC1BthJcljmkekpJzPs3NvOo6/t4OPzxjG0KD/sckREjkgqN3D9rZn9EVgClAKfc/eZKWx3p5nVmNnqbsu+ZWbbzWxl8LrgWIoPy10vbSbhzrXv0Q3MIpJ5UhmdcwJwk7uvPMLvvgv4L+DuA5b/0N2/d4Tf1W+0dHRx77K3Of+kcsYNLwq7HBGRI5bK5Zy3HM0Xu/tzZlZxNNv2Z/dXbqWxvYvPvldH+yKSmcK4HOVGM1sVdAX1OKKZmV1nZpVmVllbW9uX9fUonnDufHET8yYMY854DcYmIpmpr4P/p8AkYDZQDXy/pw+6+yJ3n+fu88rKyvqovEN7dl0NW3e38Rn17YtIBkvl5O4XzWxsb+zM3Xe5e9zdEySHfVjQG9/bVxYv3Uz50EI+OEO3MohI5urTG7jMrLzb7CXA6p4+299srGnm+Q11fOLU8eTl6oYtEclcqZzc/TbwbTObCfw1yRu4trn7uYfazszuA84CSs1sG/BN4Cwzm01ypM/NwOePqfo+9MuX36YgN4fLdcOWiGS4lB62HjiiG7jc/YqDLL7jCPbXbzR3dPHA8m1cOLOc0sEDwi5HROSYpO0Grmzy8IptNHd0cfUZFWGXIiJyzNJ5A1dWcHcWL32bWWOHMntcSdjliIgcs1QGabslqqEPsPStejbWNPOp0yvCLkVEpFfo8pTDuHvp2wwfVMCFM8sP/2ERkQyg4D+E2qYOnl67i8tOGUthfm7Y5YiI9AoF/yE8sHwbXQnnr+ePC7sUEZFeo+DvgbvzP3/ewoLjhzOpbHDY5YiI9BoFfw+WVtWzub6VKxboaF9EsouCvwe/emUrxYV5nH+STuqKSHZR8B/EnpYYT6zeyaVzdVJXRLKPgv8gHlyxjVg8weXq5hGRLKTgP4C7c3/lVmaPK2HaccVhlyMi0usU/AdYs6ORN3c187F5vfIIAhGRfkfBf4CHVmynIDeHvzp5dNiliIikhYK/m854gkdf284500cytCg/7HJERNJCwd/N8xtqqWuOccmcMWGXIiKSNgr+bh5asZ1hRfmcNfWwz5kREclYCv5AY3snf3hjFxfNGk1Bnv5YRCR7KeECj79eTawrwaVzdTWPiGQ3BX/gt69VUzGiiFljh4ZdiohIWin4gfrmDpZW1XPhzHLMLOxyRETSSsEPPLlmF/GEc8HJGpBNRLKfgh/4/evJbp4Z5RqiQUSyX+SDf3dLjKVV9Vxwsrp5RCQaIh/8T67ZSTzhepi6iERG5INf3TwiEjWRDv6m9k5erqrngycep24eEYmMSAf/Cxvq6Iw750zTEA0iEh2RDv6n19YwdGA+p0wYFnYpIiJ9JrLBH084f1xfw1lTy8jLjewfg4hEUGQTb+XWBupbYpytbh4RiZi0Bb+Z3WlmNWa2utuy4Wb2lJltCN5D62N5Zt0ucnOMs05Q8ItItKTziP8u4LwDlt0CLHH3KcCSYD4Uz71Zx9zxJXrSlohETtqC392fA3YfsPhiYHEwvRj4SLr2fygNrTFW79jLmZNLw9i9iEio+rqPf5S7VwME7z32s5jZdWZWaWaVtbW1vVrEy1X1uKPgF5FI6rcnd919kbvPc/d5ZWVlvfrdL26sp6ggl1ljS3r1e0VEMkFfB/8uMysHCN5r+nj/ALz4Vh0Ljh+uRyyKSCT1dfI9ClwdTF8NPNLH+6d6bxtVtS2cOUndPCISTem8nPM+YCkw1cy2mdm1wK3AQjPbACwM5vvUsqrk+ebTJ43o612LiPQLeen6Yne/oodV56Rrn6lYsWUPgwpymXbckDDLEBEJTeQ6uZe/vYdZ40o0TIOIRFak0q811sW6nU0alE1EIi1Swf/a1r3EE87c8Qp+EYmuSAX/ii17AJgzviTcQkREQhSp4F+5tYGJZYMoKSoIuxQRkdBEKvjf2NHISaOHhl2GiEioIhP8e1s72d7QxnQ9VF1EIi4ywf9GdSMAM0Yr+EUk2qIX/DriF5GIi07w72ikbMgAyoYMCLsUEZFQRSb411Y3qn9fRISIBH8i4VTVNTNl5OCwSxERCV0kgr+6sZ32zgQTywaFXYqISOgiEfxVtc0ATCzVEb+ISESCvwVAR/wiIkQm+JsZVJDLSF3RIyISkeCva2Fi2WDMLOxSRERCF4ng31zfQkWpunlERCACwR9PODv3tjN22MCwSxER6ReyPvhrmzrojDujSxT8IiIQgeDf3tAGwFgFv4gIEIHg3xEEv474RUSSsj74t+8P/sKQKxER6R+yPvh3NLRRXJjHkML8sEsREekXIhD87ermERHpJuuDv665Q2Pwi4h0k/XBX9/SQelgBb+IyD7ZH/zNMYYPKgi7DBGRfiOrg7811kVrLM6IwQp+EZF9sjr465tjAJQOUlePiMg+2R38Lcng1xG/iMg7sjv4mzsAGKGTuyIi++WFsVMz2ww0AXGgy93npWM/+7p6RujkrojIfqEEf+AD7l6Xzh2oq0dE5N2yvqunqCCXooIwf76JiPQvYQW/A38ws+Vmdt3BPmBm15lZpZlV1tbWHtVOJo8czEUzRx9LnSIiWcfcve93ajba3XeY2UjgKeDv3P25nj4/b948r6ys7LsCRUSygJktP9g51FCO+N19R/BeAzwMLAijDhGRKOrz4DezQWY2ZN808EFgdV/XISISVWGc9RwFPGxm+/Z/r7s/EUIdIiKR1OfB7+5VwKy+3q+IiCRl9eWcIiLybgp+EZGIUfCLiESMgl9EJGJCuYHrSJlZLfD2UW5eCqR1TKB+SG2OBrU5Go6lzRPcvezAhRkR/MfCzCrTNfpnf6U2R4PaHA3paLO6ekREIkbBLyISMVEI/kVhFxACtTka1OZo6PU2Z30fv4iI/KUoHPGLiEg3Cn4RkYjJ6uA3s/PMbL2ZbTSzW8Kup7eZ2Tgze9bM1prZGjP7QrB8uJk9ZWYbgvdhYdfa28ws18xeNbPHgvmsbrOZlZjZA2a2Lvj7Pj0Cbf5i8O96tZndZ2aF2dZmM7vTzGrMbHW3ZT220cy+FuTZejP70NHuN2uD38xygR8D5wMzgCvMbEa4VfW6LuBL7j4dOA24IWjjLcASd58CLAnms80XgLXd5rO9zT8CnnD3aSRHt11LFrfZzMYAfw/Mc/eTgFzgcrKvzXcB5x2w7KBtDP5vXw6cGGzzkyDnjljWBj/Jp3ptdPcqd48BvwIuDrmmXuXu1e6+IphuIhkGY0i2c3HwscXAR0IpME3MbCxwIXB7t8VZ22YzKwbeB9wB4O4xd28gi9scyAMGmlkeUATsIMvaHDxydvcBi3tq48XAr9y9w903ARs5yqcXZnPwjwG2dpvfFizLSmZWAcwBlgGj3L0akj8cgJEhlpYO/wF8BUh0W5bNbZ4I1AK/CLq3bg+eXpe1bXb37cD3gC1ANbDX3f9AFre5m57a2GuZls3BbwdZlpXXrprZYOBB4CZ3bwy7nnQys78Catx9edi19KE8YC7wU3efA7SQ+V0chxT0a18MHA+MBgaZ2SfDrSp0vZZp2Rz824Bx3ebHkvxVMauYWT7J0L/H3R8KFu8ys/JgfTlQE1Z9aXAm8GEz20yy++5sM/sl2d3mbcA2d18WzD9A8gdBNrf5XGCTu9e6eyfwEHAG2d3mfXpqY69lWjYH/5+BKWZ2vJkVkDwp8mjINfUqSz64+A5grbv/oNuqR4Grg+mrgUf6urZ0cfevuftYd68g+Xf6jLt/kuxu805gq5lNDRadA7xBFreZZBfPaWZWFPw7P4fkOaxsbvM+PbXxUeByMxtgZscDU4BXjmoP7p61L+AC4E3gLeDrYdeThva9h+SvequAlcHrAmAEyasBNgTvw8OuNU3tPwt4LJjO6jYDs4HK4O/6N8CwCLT528A6YDXw/4EB2dZm4D6S5zA6SR7RX3uoNgJfD/JsPXD+0e5XQzaIiERMNnf1iIjIQSj4RUQiRsEvIhIxCn4RkYhR8IuIRIyCX4T9o19en8o6MxttZg/0XXUivUuXc4qwf6yjxzw5EmTK60QykY74RZJuBSaZ2Uoz++6h1plZxb7x083sGjP7jZn91sw2mdmNZnZzMJjay2Y2PPjcJDN7wsyWm9nzZjatj9snsl9e2AWI9BO3ACe5++zDrQt+A+juJJIjoxaSHCr3q+4+x8x+CHyK5Giii4C/cfcNZnYq8BPg7N5vhsjhKfhFjt2znnweQpOZ7QV+Gyx/HZgZjJ56BvDr5LAzQHL4AZFQKPhFjl1Ht+lEt/kEyf9jOUBDD79NiPQ59fGLJDUBQ45i3WF58hkJm8zsY5AcVdXMZh3t94kcKwW/CODu9cCLwYO9v5vquiPwCeBaM3sNWEOWPQZUMosu5xQRiRgd8YuIRIyCX0QkYhT8IiIRo+AXEYkYBb+ISMQo+EVEIkbBLyISMf8LavZDEYHb/4kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Relative velocity and acceleration\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# FIRST linear flat surface test (alpha = 0)\n",
    "# with constant throttle\n",
    "\n",
    "\n",
    "sample_time = 0.01 # 10 ms\n",
    "# can test with different total time to run\n",
    "time_end = 100\n",
    "\n",
    "model = Vehicle()\n",
    "model.reset()\n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time)\n",
    "v_data = np.zeros_like(t_data)\n",
    "\n",
    "# position\n",
    "x_data = np.zeros_like(t_data)\n",
    "# acceleration\n",
    "a_data = np.zeros_like(t_data)\n",
    "\n",
    "\n",
    "# CAN CHANGE THIS #################\n",
    "\n",
    "# throttle value in [0,1]\n",
    "\n",
    "throttle = 0.3 #2#.2\n",
    "\n",
    "###################################\n",
    "\n",
    "# try some incline angles (in radians)\n",
    "alpha = np.arctan(0.5/1)#np.pi/# np.pi/8 #flat surface\n",
    "alpha_1 = np.arctan(3/60)\n",
    "alpha_2 = np.arctan(9/90)\n",
    "alpha_3 = 0\n",
    "\n",
    "# select an incline angle to test\n",
    "#alpha=alpha_1\n",
    "\n",
    "## CAN CHANGE INCLINE ANGLE HERE #\n",
    "\n",
    "alpha=0 # flat surface all the way if =0\n",
    "#alpha=np.pi/8\n",
    "\n",
    "##################################\n",
    "\n",
    "for i in range(t_data.shape[0]):\n",
    "    v_data[i] = model.v\n",
    "    x_data[i] = model.x\n",
    "    a_data[i] = model.a\n",
    "    model.time_step(throttle, alpha)\n",
    "#\n",
    "print();print();print(\"Using: throttle =\",throttle,\"     Angle = \",int(np.rad2deg(alpha)),\"(degrees)\");print()\n",
    "\n",
    "# position over time\n",
    "print();print(\"Position over time\")\n",
    "plt.plot(t_data, x_data)\n",
    "plt.xlabel(\"t time\")\n",
    "plt.ylabel(\"x position\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "# velocity over position\n",
    "print();print(\"Velocity over position\")\n",
    "plt.plot(x_data, v_data)\n",
    "plt.xlabel(\"x position\")\n",
    "plt.ylabel(\"v velocity\")\n",
    "plt.show()\n",
    "\n",
    "# velocity over time\n",
    "print();print(\"Velocity over time\")\n",
    "plt.plot(t_data, v_data)\n",
    "plt.xlabel(\"t time\")\n",
    "plt.ylabel(\"v velocity\")\n",
    "plt.show()\n",
    "\n",
    "# velocity acceleration\n",
    "print();print(\"Relative velocity and acceleration\")\n",
    "plt.plot(t_data, v_data, label='v')\n",
    "plt.plot(t_data, a_data, label='a')\n",
    "plt.xlabel(\"t time\")\n",
    "plt.legend()\n",
    "#plt.ylabel(\"a acceleration\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model dynamics with terrain and velocity profiles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple two dimensional terrain model is used that has the linear horizontal distance and vertical height changes represented in Figure 1. The geometric throttle input profile is calculated from the diagram specifications in Figure 2.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![ramp](terraindiagram_v3.png)\n",
    "<center>Figure 1 - Terrain</center>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![throttle](throttle-v0.05.png)\n",
    "\n",
    "<center>Figure 2 - Velocity</center>\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Implementation\n",
    "\n",
    "Using the Figure 2 profile, the throttle is applied for a total runtime of 20 seconds The vehicle begins at 20% throttle and gradually increases to 50% throttle. This is maintained for 10 seconds. Then the throttle decreases until it reaches 0 at 20 seconds. \n",
    "\n",
    "The implementation iteratively timesteps through the terrain geometry and throttle profile while calculating the vehicle dynamics. A 10ms time increment is specified. The time, position, velocity, acceleration and incline angle are saved for analysis.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "sample_time = 0.01 # 10 ms\n",
    "time_end = 20 #total run time in seconds  480#120#20 #  120# \n",
    "\n",
    "t_data = np.arange(0,time_end,sample_time) # discrete time\n",
    "x_data = np.zeros_like(t_data) # position\n",
    "v_data = np.zeros_like(t_data) # velocity\n",
    "a_data = np.zeros_like(t_data) # acceleration\n",
    "y_data = np.zeros_like(t_data) # height (y )\n",
    "angle_data = np.zeros_like(t_data) # save alpha also for analysis\n",
    "\n",
    "# keep throttle data for analysis\n",
    "throttle_data = np.zeros_like(t_data) \n",
    "\n",
    "# initialization\n",
    "\n",
    "#throttle is expressed as a percent in [0,1]\n",
    "\n",
    "# throttle starting position is 0.2\n",
    "throttle = 0.2\n",
    "# alpha the incline angle (in radians)\n",
    "alpha = 0\n",
    "\n",
    "# following the diagram\n",
    "\n",
    "incline_angle_1 = np.arctan(4/50)\n",
    "incline_angle_2 = 0\n",
    "incline_angle_3 = np.arctan(8/60)\n",
    "incline_angle_4 = 0\n",
    "\n",
    "\n",
    "#incline_angle_1 = np.arctan(3/60)\n",
    "#incline_angle_2 = np.arctan(9/90)\n",
    "#incline_angle_3 = 0\n",
    "#incline_angle_4 = 0\n",
    "\n",
    "# make it easy\n",
    "seconds = int(t_data.shape[0]/time_end)\n",
    "\n",
    "# assume throttle changes are linear\n",
    "# dx/dt is slope\n",
    "throttle_rate_1 = (0.50-0.20)/(5*seconds) #slope 1 starts at 20%\n",
    "throttle_rate_2 = 0 # keep throttle at position\n",
    "throttle_rate_3 = -(0.50/(5*seconds))#slope 3\n",
    "\n",
    "# create car model instance\n",
    "model = Vehicle()\n",
    "model.reset() # just to make sure\n",
    "#model.v = 0 # don't use reset defaults?\n",
    "\n",
    "for i in range(t_data.shape[0]): # i index into time increments \n",
    "\n",
    "    x_data[i] = model.x \n",
    "    v_data[i] = model.v\n",
    "    a_data[i] = model.a\n",
    "    \n",
    "    # terrain\n",
    "    # set incline angle depending on x position\n",
    "    # ie how far along the path the auto is at\n",
    "    \n",
    "    if (model.x >=0 and model.x <= 50):\n",
    "        alpha = incline_angle_1\n",
    "       \n",
    "    if (model.x > 50 and model.x <= 90):\n",
    "        alpha = incline_angle_2\n",
    "            \n",
    "    if (model.x > 90 and model.x <= 150):\n",
    "        alpha = incline_angle_3\n",
    "       \n",
    "    if (model.x > 150):\n",
    "        alpha = incline_angle_4\n",
    "\n",
    "    \n",
    "    # throttle profile\n",
    "    # set throttle depending on time traveled\n",
    "        \n",
    "    if (i <= 5*seconds):\n",
    "        throttle = 0.20 + throttle_rate_1*i\n",
    "        \n",
    "    if (i > 5*seconds and i <= 15*seconds):       \n",
    "        throttle = 0.50 + throttle_rate_2*i   \n",
    "     \n",
    "    if (i > 15*seconds): #\n",
    "        throttle = 2 + (throttle_rate_3*i)\n",
    "        if (throttle <=0):\n",
    "            throttle =0 # dont reverse throttle\n",
    "        \n",
    "    model.time_step(throttle, alpha)        \n",
    "        \n",
    "    throttle_data[i]=throttle\n",
    "    angle_data[i]=alpha\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Various plots runtime data for analysis\n",
    "\n",
    "First, check the inputs over time to see if they correspond to the specified profiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# angle over position\n",
    "plt.plot(x_data, angle_data)\n",
    "plt.xlabel(\"x position\")\n",
    "plt.ylabel(\"angle\")\n",
    "plt.show()\n",
    "print()\n",
    "\n",
    " # throttle over time\n",
    "plt.plot(t_data, throttle_data)\n",
    "plt.xlabel(\"t time\")\n",
    "plt.ylabel(\"throttle\")\n",
    "plt.show()  \n",
    "print()\n",
    "\n",
    "\n",
    "#print();print(\"Check the inputs...\");print()\n",
    "\n",
    "# throttle angle\n",
    "plt.plot(t_data, throttle_data, label='throttle')\n",
    "plt.plot(t_data, angle_data, label='angle')\n",
    "plt.xlabel(\"t time\")\n",
    "plt.legend()\n",
    "#plt.ylabel(\"a acceleration\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check positon over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# horizontal position over time\n",
    "plt.plot(t_data, x_data)\n",
    "plt.xlabel(\"t time\")\n",
    "plt.ylabel(\"x position\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check velocity over time and position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# velocity over time\n",
    "plt.plot(t_data, v_data)\n",
    "plt.xlabel(\"t time\")\n",
    "plt.ylabel(\"v velocity\")\n",
    "plt.show()\n",
    "\n",
    "# velocity over position\n",
    "plt.plot(x_data, v_data)\n",
    "plt.xlabel(\"x position\")\n",
    "plt.ylabel(\"v velocity\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare relative changes in velocity and acceleration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# velocity acceleration\n",
    "plt.plot(x_data, v_data, label='v')\n",
    "plt.plot(x_data, a_data, label='a')\n",
    "plt.xlabel(\"x position\")\n",
    "plt.legend()\n",
    "#plt.ylabel(\"a acceleration\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "# velocity acceleration\n",
    "plt.plot(t_data, v_data, label='v')\n",
    "plt.plot(t_data, a_data, label='a')\n",
    "plt.xlabel(\"t time\")\n",
    "plt.legend()\n",
    "#plt.ylabel(\"a acceleration\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The velocity and acceleration comparison shows a jump in acceleration at the begining of each level surface\n",
    "and some noticeable decreasing velocity when driving up the steeper slope\n",
    "\n",
    "Where there is a flat surface the velocity may increase.\n",
    "After 150 meters, there would eventually be enough aerodynamic resistance or other forces to eventually slow the vehicle down (if the throttle remains at zero and the model runs for enough time)\n",
    "and the velocity would level off.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further model observations and analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Experiment by going back and changing the total runtime to 120s, 240s, 480s or more. \n",
    "Without any opposing forces generated from an incline or aerodynamic conditions\n",
    "it can take some time and *distance* before the velocity finally starts to level off after the throttle input reaches zero.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "# save data for analysis\n",
    "\n",
    "#data = np.vstack([t_data, x_data, v_data, a_data, angle_data]).T\n",
    "#np.savetxt('test_data.txt', data, delimiter=', ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### \n",
    "\n",
    "\n",
    "Copyright (c) 2021-2023 Mike Knerr\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}