{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 3.141592653589793)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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"
    },
    {
     "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": [
    "# coding: utf-8\n",
    "from pylab import *\n",
    "%matplotlib inline\n",
    "psi=linspace(pi*.0,pi*.95,100) #lever angle range (rad)\n",
    "l=6#linkage arm length\n",
    "r_0=4.#linkage arm attachment point on the lever - sets travel on piston\n",
    "r_1=16. #total length of lever arm\n",
    "M=r_0/r_1*(-sin(psi)+sin(psi)*cos(psi)/sqrt(sin(psi)**2+(l/r_0)**2))\n",
    "\n",
    "q=sqrt(r_0**2*sin(psi)**2+l**2) #distance front to aft of the piston from the lever arm attachment point\n",
    "w=r_0*cos(psi) # location of the lever arm attachment point front to aft during the stroke\n",
    "x=q+w #location of the piston relative to the base of the lever arm\n",
    "d=max(x)-x #displacement of the piston from bottom of the stroke\n",
    "\n",
    "plot(psi,d)\n",
    "xlabel('angle (rad)')\n",
    "ylabel('Displacement [inch]')\n",
    "ylim(ymin=0)\n",
    "xlim(0,pi)\n",
    "figure()\n",
    "plot(psi,-M)\n",
    "xlabel('angle (rad)')\n",
    "ylabel('Mechanical disadvantage')\n",
    "ylim(ymin=0)\n",
    "xlim(0,pi)\n",
    "figure()\n",
    "plot(psi[1:-1],1.0/-M[1:-1])\n",
    "xlabel('angle (rad)')\n",
    "ylabel('Mechanical advantage')\n",
    "ylim(ymin=0)\n",
    "xlim(0,pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 3.141592653589793)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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"
    },
    {
     "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": [
    "V_c = 1.1 #Chamber volume [inches^3]\n",
    "P_0 = 14.7 #pressure of atmosphere (lbs/inch^2)\n",
    "diam = 1.25 #piston diameter (inches)\n",
    "A = (0.5*diam)**2*pi #area of the piston face [inch^2]\n",
    "V=V_c+d*A #volume as a function of the stroke [inches^3]\n",
    "Vmax = max(V) #volume at maximum extent. [inch^3]\n",
    "rV = V/Vmax #volume ratio [dimensionless]\n",
    "gamma= 1#7./5 #for adiabatic, 1 for isothermal\n",
    "rP=1/rV**gamma #isothermal assumption... fix later with addition of gamma\n",
    "T_0 = 300 #kelvin\n",
    "T = T_0*rV**(1-gamma)\n",
    "\n",
    "dP=rP-1 #Gauge pressure in atmospheres\n",
    "\n",
    "plot(psi,1/rV)\n",
    "xlabel('angle (rad)')\n",
    "ylabel('Compression ratio')\n",
    "axhline(1,color='k',linestyle='--')\n",
    "ylim(ymin=0)\n",
    "xlim(0,pi)\n",
    "\n",
    "figure()\n",
    "plot(psi,rP)\n",
    "xlabel('angle (rad)')\n",
    "ylabel('absolute pressure (atm)')\n",
    "axhline(1,color='k',linestyle='--')\n",
    "ylim(ymin=0)\n",
    "xlim(0,pi)\n",
    "\n",
    "figure()\n",
    "plot(psi,dP)\n",
    "xlabel('angle (rad)')\n",
    "ylabel('Gauge pressure (atm)')\n",
    "title('Peak pressure: %.1f atm'%dP.max())\n",
    "ylim(ymin=0)\n",
    "xlim(0,pi)\n",
    "\n",
    "figure()\n",
    "plot(psi,dP)\n",
    "xlabel('angle (rad)')\n",
    "ylabel('Temperature (Kelvin)')\n",
    "title('Peak temperature: %.1f K'%T.max())\n",
    "ylim(ymin=0)\n",
    "xlim(0,pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Packing fraction: 0.466742\\nPeak force 9.79935 (lb)\\n Advantage: 10.7983')"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "Fs=M*dP*A*P_0 #Force on handle [lb]\n",
    "plot(psi,-Fs)\n",
    "xlabel('angle (rad)')\n",
    "ylabel('Force on handle (lb)')\n",
    "ylim(ymin=0)\n",
    "xlim(0,pi)\n",
    "\n",
    "Fmax=max(-Fs)\n",
    "Favg=mean(-Fs)\n",
    "packing = Favg/Fmax\n",
    "peak_force = max(dP)*P_0/A\n",
    "advantage = peak_force/Fmax\n",
    "title(\"Packing fraction: %g\\nPeak force %g (lb)\\n Advantage: %g\"%(packing,Fmax,advantage))"
   ]
  },
  {
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
