path: root/Gas_Dynamics_and_Jet_Propulsion_by_P._Murugaperumal/ch7.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:2b84da90b712d0e24452d78c735ac1dad7be546c737e70f5e892f031f5d70de9"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 7 : Rocket propulsion"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.1 page : 21"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "mp = 12. \t\t\t\t#flow rate in kg/s\n",
      "Ae = 335.*10**-4 \t\t\t\t#exit area in m**2\n",
      "Ce = 2000. \t\t\t\t#exhaust velocity in m/s\n",
      "h = 10. \t\t\t\t#altitude in km\n",
      "Pe = 1.*10**5 \t\t\t\t#exhaust pressure in Pa\n",
      "P0 = 1.*10**5 \t\t\t\t#p0 = atomspheric pressure in Pa at h = 0.\n",
      "P10 = 0.25*10**5 \t\t\t\t#atmospheric pressure in Pa umath.sing gas tables\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculations\n",
      "Fs = mp*Ce*10**-3 \t\t\t\t#thrust of motor at sea level math.since pe = p0 in kN\n",
      "F10 = ((mp*Ce) + Ae*(Pe-P10))*10**-3 \t\t\t\t#thrust of motor at altitude of 10km in kN\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)thrust of motor at sea level is %3i kN upwards  \\\n",
      "\\nB)thrust of motor at an altitude 10km is %3.4f kN'%(Fs,F10)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)thrust of motor at sea level is  24 kN upwards  \n",
        "B)thrust of motor at an altitude 10km is 26.5125 kN\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.2 page : 22"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "P0 = 38*10**5 \t\t\t\t#combustion chamber pressure in Pa\n",
      "T0 = 3500 \t\t\t\t#combustion chamber temperature in K\n",
      "ma = 41.67 \t\t\t\t#oxidizer flow rate in kg/s\n",
      "MR = 5 \t\t\t\t#mixture ratio\n",
      "k = 1.3 \t\t\t\t#adiabatic consmath.tant\n",
      "R = 287 \t\t\t\t#gas consmath.tant in J/kg-K\n",
      "Pamb = 0.0582*10**5 \t\t\t\t#ambient pressure in Pa\n",
      "Pe = Pamb \t\t\t\t#exhaust pressure at sea level in Pa\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation \n",
      "mf = ma/MR \t\t\t\t#mass flow of fuel in kg/s \n",
      "mp = mf+ma \t\t\t\t#propellant mass flow in kg/s\n",
      "Cp = (k*R)/(k-1) \t\t\t\t#specific heat at consmath.tant pressure in J/kg-k\n",
      "p = P0/Pe \t\t\t\t#ratio of pressures at combustion chamber and exhaust \n",
      "Me = ((((p**((k-1)/k))-1)*2)/(k-1))**0.5 \t\t\t\t#Mach number\n",
      "t = 1/(1+(((k-1)/2)*Me**2)) \t\t\t\t#ratio of exhaust temperature to combustion temperature\n",
      "Te = t*T0 \t\t\t\t#exhaust temperature in Kelvin\n",
      "a = (1/Me)*(((2/(k+1))+(((k-1)/(k+1))*Me**2))**((k+1)/(2*(k-1)))) \t\t\t\t#ratio of areas at exit section and throat section of the nozzle\n",
      "Ce = (k*R*Te)**0.5*Me \t\t\t\t#exit velocity in the exhaust in m/s\n",
      "Cj = Ce \t\t\t\t#average effective jet velocity in m/s, math.since Pe = Pamb\n",
      "P1 = P0*(2/(k+1))**(k/(k-1)) \t\t\t\t#pressure at throat section in Pa\n",
      "T1 = T0*(2/(k+1)) \t\t\t\t#temperature at throat section in K\n",
      "d1 = P1/(R*T1) \t\t\t\t#density of fuel at throat section in kg/m**3\n",
      "C1 = (k*R*T1)**0.5 \t\t\t\t#velocity at throat section in m/s\n",
      "A1 = (mp/(d1*C1))*10**4 \t\t\t\t#nozzle throat area in cm**2\n",
      "Ae = a*A1 \t\t\t\t#exit area in cm**2\n",
      "F = (mp*Ce)*10**-3 \t\t\t\t#thrust in kN\n",
      "Cmax1 = (2*Cp*T0)**0.5 \t\t\t\t#maximum possible velocity in m/s\n",
      "Cf = (F*10**3)/(P0*A1*10**-4) \t\t\t\t#thrust coefficient, F in kN and A1 in m**2\n",
      "Cch1 = Cj/Cf \t\t\t\t#characteristic velocity in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)nozzle throat area is %3.2f cm**2  \\\n",
      "\\nB)thrust is %3.1f kN  \\\n",
      "\\nC)thrust coefficient is %3.2f  \\\n",
      "\\nD)characteristic velocity is %3i m/s  \\\n",
      "\\nE)exit velocity in exhaust is %3i m/s \\\n",
      "\\nF)maximum possible exhaust velocity is %3i m/s'%(A1,F,Cf,Cch1,Ce,Cmax1)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)nozzle throat area is 197.65 cm**2  \n",
        "B)thrust is 130.0 kN  \n",
        "C)thrust coefficient is 1.73  \n",
        "D)characteristic velocity is 1502 m/s  \n",
        "E)exit velocity in exhaust is 2599 m/s \n",
        "F)maximum possible exhaust velocity is 2950 m/s\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.3 page : 23"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "a = 3. \t\t\t\t#exit area to throat area ratio\n",
      "T0 = 2973. \t\t\t\t#combustion chamber temperature in K\n",
      "P0 = 20.*10**5 \t\t\t\t#combustion chamber pressure in Pa\n",
      "k = 1.3 \t\t\t\t#adiabatic consmath.tant\n",
      "R = 248. \t\t\t\t#gas consmath.tant in J/kg-K\n",
      "Pamb = 1.*10**5 \t\t\t\t#ambient pressure in Pa\n",
      "Me = 2.52 \t\t\t\t#mach number for k = 1.3 and a = 3 umath.sing gas tables \n",
      "g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "p = 1/((1+(((k-1)/2)*Me**2))**(k/(k-1))) \t\t\t\t#ratio of pressures at exhaust and combustion chamber \n",
      "Pe = p*P0 \t\t\t\t#exhaust pressure in Pa\n",
      "t = 1/(1+(((k-1)/2)*Me**2)) \t\t\t\t#ratio of exhaust temperature to combustion temperature\n",
      "Te = t*T0 \t\t\t\t#exhaust temperature in Kelvin\n",
      "Ce = (k*R*Te)**0.5*Me \t\t\t\t#exit velocity in the exhaust in m/s\n",
      "M = (Pe*Ce)/(R*Te) \t\t\t\t#propellant mass flow per unit area of exit in kg/m**2-s\n",
      "Fa = ((M*Ce)+(Pe-Pamb))*10**-3 \t\t\t\t#thrust per unit area of exit in N/m**2\n",
      "Is = (Fa*10**3)/(M*g) \t\t\t\t#specific impulse in sec\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)thrust per unit area of exit is %3.2f kN/m**2  \\\n",
      "\\nB)specific impulse is %3.2f sec'%(Fa,Is)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)thrust per unit area of exit is 918.93 kN/m**2  \n",
        "B)specific impulse is 181.98 sec\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.4 page : 24"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "mp = 5. \t\t\t\t#propellent flow rate in kg/s (mismath.sing data)\n",
      "de = 0.10 \t\t\t\t#nozzle exit diameter in m\n",
      "Pe = 1.02*10**5 \t\t\t\t#nozzle exit pressure in Pa\n",
      "Pamb = 1.013*10**5 \t\t\t\t#ambient pressure in Pa\n",
      "P0 = 20. \t\t\t\t#thrust chamber pressure in Pa\n",
      "F = 7000. \t\t\t\t#thrust in N\n",
      "u = 1000. \t\t\t\t#rocket speed in m/s\n",
      "g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "Cj = F/mp \t\t\t\t#effective jet velocity in m/s\n",
      "Ca = Cj-u \t\t\t\t#absolute jet velocity in m/s\n",
      "wp = mp*g \t\t\t\t#weight flow rate of propellent in N/s\n",
      "Is = F/(wp) \t\t\t\t#specific impulse in sec\n",
      "SPC = 1/Is \t\t\t\t#specific propellent consumption in sec**-1\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)effective jet velocity is %3i m/s  \\\n",
      "\\nB)specific impulse is %3.2f sec  \\\n",
      "\\nC)specific propellent consumption is %3.3f s**-1  \\\n",
      "\\nD)absolute jet velocity is %3i m/s'%(Cj,Is,SPC,Ca)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)effective jet velocity is 1400 m/s  \n",
        "B)specific impulse is 142.71 sec  \n",
        "C)specific propellent consumption is 0.007 s**-1  \n",
        "D)absolute jet velocity is 400 m/s\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.5 page: 24"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data \n",
      "Cj = 2700. \t\t\t\t#average effective jet velocity in m/s\n",
      "u = 1350. \t\t\t\t#forward flight velocity in m/s\n",
      "mp = 78.6 \t\t\t\t#propellant mass flow in kg/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "s = u/Cj \t\t\t\t#effective jet speed ratio\n",
      "np = (2*s)/(1+s**2) \t\t\t\t#propulsive efficiency\n",
      "F = Cj*mp*10**-3 \t\t\t\t#thrust in kN\n",
      "Pt = F*u*10**-3 \t\t\t\t#Thrust power in MW, F in N\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)thrust is %3.2f kN  \\\n",
      "\\nB)Thrust power is %3.3f MW  \\\n",
      "\\nC)propulsive efficiency is %3.1f'%(F,Pt,np)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)thrust is 212.22 kN  \n",
        "B)Thrust power is 286.497 MW  \n",
        "C)propulsive efficiency is 0.8\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.6 page : 24"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from scipy.integrate import quad \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "mi = 15000. \t\t\t\t#mass of the rocket in kg\n",
      "mp = 125. \t\t\t\t#propellant mass flow in kg/s\n",
      "Cj = 2000. \t\t\t\t#velocity of gases coming out in m/s\n",
      "t = 70. \t\t\t\t#time interval in sec\n",
      "t0 = 0. \t\t\t\t#lower limit in integration in sec\n",
      "t1 = 70. \t\t\t\t#upper limit in integration in sec\n",
      "g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "u = (-Cj*(math.log(1-((mp*t)/mi))))-(g*t) \t\t\t\t#velocity attained in 70 sec in m/s\n",
      "\n",
      "def f0(t): \n",
      "\t return ((-2000*(math.log(1-((125*t)/15000))))-(g*t))\n",
      "\n",
      "h1 = ( quad(f0,t0,t1))[0]\n",
      "\n",
      "h2 = (u**2/(2*g))*10**-3 \t\t\t\t#Distance reached after fuel last i.e. after 70 sec due to kinetic energy by umath.sing KE = PE in km\n",
      "h = h1+h2 \t\t\t\t#maximum height the rocket will reach in km\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)velocity attained in %i sec is %3.2f m/s \\\n",
      "\\nB)maximum height the rocket will reach is %3.3f km'%(t,u,h)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)velocity attained in 70 sec is 1064.24 m/s \n",
        "B)maximum height the rocket will reach is 28476.353 km\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.7 page : 25"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "A1 = 18.*10**-4 \t\t\t\t#throat area in m**2\n",
      "P0 = 25.*10**5 \t\t\t\t#combustion chamber pressure in Pa\n",
      "Is = 127.42 \t\t\t\t#specific impulse in sec\n",
      "wp = 44.145 \t\t\t\t#weight flow rate of propellent in N/s\n",
      "g = 9.81 \t\t\t\t#acceleration due to kravity in m/s**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "F = Is*wp \t\t\t\t#thrust in N\n",
      "mp = wp/g \t\t\t\t#propellant mass flow in kg/s\n",
      "Cj = F/mp \t\t\t\t#average effective jet velocity in m/s\n",
      "Cf = F/(P0*A1) \t\t\t\t#thrust coefficient\n",
      "Cw = wp/(P0*A1)/10**-3 \t\t\t\t#propellent weight flow coefficent *10**-3\n",
      "SPC = (wp/F)/10**-3 \t\t\t\t#specific propellent consumption in sec**-1 *10**-3\n",
      "Cch1 = Cj/Cf \t\t\t\t#characteristic velocity in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)thrust coefficient is %3.2f  \\\n",
      "\\nB)propellent weight flow coefficent is %3.2f*10**-3  \\\n",
      "\\nC)specific propellent consumption is %3.2f*10**-3 s**-1  \\\n",
      "\\nD)characteristic velocity is %3.0f m/s'%(Cf,Cw,SPC,Cch1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)thrust coefficient is 1.25  \n",
        "B)propellent weight flow coefficent is 9.81*10**-3  \n",
        "C)specific propellent consumption is 7.85*10**-3 s**-1  \n",
        "D)characteristic velocity is 1000 m/s\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.8 page : 26"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "m1 = 200. \t\t\t\t#internal mass in kg\n",
      "m2 = 130. \t\t\t\t#mass after rocket operation in kg\n",
      "m3 = 110. \t\t\t\t#payload,non-propulsive structure, etc in kg\n",
      "tp = 3. \t\t\t\t#rocket operation duration in sec\n",
      "Is = 240. \t\t\t\t#specific impulse in sec\n",
      "g = 9.81 \t\t\t\t#acceleration due to kravity in m/s**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "MR = m2/m1 \t\t\t\t#mass ratio\n",
      "Mp = m1-m2 \t\t\t\t#mass of propellant in kg\n",
      "mp = Mp/tp \t\t\t\t#propellent flow rate in kg/s\n",
      "wp = mp*g \t\t\t\t#weight flow rate of propellent in N/s\n",
      "IMF = (m2-m3)/(m1-m3) \t\t\t\t#initial mass fraction\n",
      "PMF = 1-IMF \t\t\t\t#propellant mass fraction\n",
      "F = Is*wp \t\t\t\t#thrust in N\n",
      "TWRi = F/(m1*g) \t\t\t\t#initial thrust to weight ratio \n",
      "TWRf = F/(m2*g) \t\t\t\t#final thrust to weight ratio\n",
      "av = F/m2 \t\t\t\t#Maximum accelaration of the vechicle in m/s**2\n",
      "Cj = Is*g \t\t\t\t#effective exhaust velocity in m/s\n",
      "It = Is*Mp*g*10**-3 \t\t\t\t#total impulse in kN-s, units of the answer given in the book is wrong\n",
      "IWR = (It*10**3)/((m1-m3)*g) \t\t\t\t#impulse to weighr ratio, It in N-s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)mass ratio is %3.2f  \\\n",
      "\\nB)propellent mass fraction is %3.3f  \\\n",
      "\\nC)propellent flow rate is %3.1f kg/s \\\n",
      "\\nD)thrust is %3.1f N \\\n",
      "\\nE)thrust to weight ratio is %3.2f intial) and %3.2f final) \\\n",
      "\\nF)accelaration of the vechicle is %3.2f m/s**2 \\\n",
      "\\nG)effective exhaust velocity is %3.1f m/s \\\n",
      "\\nH)total impulse is %3.3f kN-s \\\n",
      "\\nI)impulse to weighr ratio is %3.2f'%(MR,PMF,mp,F,TWRi,TWRf,av,Cj,It,IWR)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)mass ratio is 0.65  \n",
        "B)propellent mass fraction is 0.778  \n",
        "C)propellent flow rate is 23.3 kg/s \n",
        "D)thrust is 54936.0 N \n",
        "E)thrust to weight ratio is 28.00 intial) and 43.08 final) \n",
        "F)accelaration of the vechicle is 422.58 m/s**2 \n",
        "G)effective exhaust velocity is 2354.4 m/s \n",
        "H)total impulse is 164.808 kN-s \n",
        "I)impulse to weighr ratio is 186.67\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.9 page : 27"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "u = 2800. \t\t\t\t#rocket speed in m/s\n",
      "Cj = 1400. \t\t\t\t#effective exhaust velocity in m/s\n",
      "mp = 5. \t\t\t\t#propellent flow rate in kg/s\n",
      "q = 6500. \t\t\t\t#heat of propellent per kg of propellant mixture in kJ/kg\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "s = u/Cj \t\t\t\t#effective jet speed ratio\n",
      "np = (2*s)/(1+s**2) \t\t\t\t#propulsive efficiency\n",
      "F = Cj*mp*10**-3 \t\t\t\t#thrust in kN\n",
      "Pt = F*10**3*u*10**-6 \t\t\t\t#Thrust power in MW, F in N\n",
      "Pe = Pt/np \t\t\t\t#engine outputin MW\n",
      "nth = Pe*10**3/(mp*q) \t\t\t\t#thermal efficiency, Pe in kW\n",
      "no = np*nth \t\t\t\t#overall efficiency\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)propulsive efficiency is %3.1f  \\\n",
      "\\nB)propulsive power is %3.1f MW \\\n",
      "\\nC)engine outut is %3.1f MW \\\n",
      "\\nD)thermal efficiency is %3.4f  \\\n",
      "\\nE)overall efficiency is %3.3f'%(np,Pt,Pe,nth,no)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)propulsive efficiency is 0.8  \n",
        "B)propulsive power is 19.6 MW \n",
        "C)engine outut is 24.5 MW \n",
        "D)thermal efficiency is 0.7538  \n",
        "E)overall efficiency is 0.603\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.10 page : 27"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "Cj = 1250. \t\t\t\t#effective exhaust velocity in m/s\n",
      "s = 0.8 \t\t\t\t#effective jet speed ratio i.e. flight to jet speed ratio\n",
      "ma = 3.5 \t\t\t\t#oxidizer flow rate in kg/s\n",
      "mf = 1. \t\t\t\t#fuel flow rate in kg/s\n",
      "g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
      "q = 2500.*10**3 \t\t\t\t#heat of propellent per kg of propellant mixture in J/kg\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "u = s*Cj \t\t\t\t#flight velocity in m/s\n",
      "mp = ma+mf \t\t\t\t#propellant mass flow in kg/s\n",
      "F = Cj*mp*10**-3 \t\t\t\t#thrust in kN\n",
      "wp = mp*g \t\t\t\t#weight flow rate of propellent in N/s\n",
      "Is = (F*10**3)/(wp) \t\t\t\t#specific impulse in sec,F in N\n",
      "np = (2*s)/(1+s**2) \t\t\t\t#propulsive efficiency\n",
      "nth = 0.5*mp*((Cj**2+u**2)/(mp*q)) \t\t\t\t#thermal efficiency\n",
      "no = np*nth \t\t\t\t#overall efficiency\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)thrust is %3.3f kN \\\n",
      "\\nB)specific impulse is %3.2f sec \\\n",
      "\\nC)propulsive efficiency is %3.4f  \\\n",
      "\\nD)thermal efficiency is %3.4f  \\\n",
      "\\nE)overall efficiency is %3.1f'%(F,Is,np,nth,no)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)thrust is 5.625 kN \n",
        "B)specific impulse is 127.42 sec \n",
        "C)propulsive efficiency is 0.9756  \n",
        "D)thermal efficiency is 0.5125  \n",
        "E)overall efficiency is 0.5\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.11 page : 28"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "mp = 193. \t\t\t\t#propellent flow rate in kg/s\n",
      "P1 = 27.*10**5 \t\t\t\t#pressure at throat section in Pa\n",
      "T1 = 3000. \t\t\t\t#temperature at throat section in K\n",
      "de = 0.6 \t\t\t\t#nozzle exit diameter in m\n",
      "Pe = 1.1*10**5 \t\t\t\t#exhaust pressure in Pa\n",
      "Pamb = 1.013*10**5 \t\t\t\t#ambient pressure in Pa\n",
      "F = 380*10**3 \t\t\t\t#thrust of motor in N\n",
      "u = 694.44 \t\t\t\t#flight velocity in m/s\n",
      "g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
      "q = 6500*10**3 \t\t\t\t#heat of propellent per kg of propellant mixture in J/kg\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "Ae = (math.pi*0.6**2)/4 \t\t\t\t#exit area in m**2\n",
      "Cj = F/mp \t\t\t\t#average effective jet velocity in m/s\n",
      "Ce = (F-((Pe-Pamb)*Ae))/mp \t\t\t\t#exhaust velocity in m/s, wrong answer in textbook\n",
      "wp = mp*g \t\t\t\t#weight flow rate of propellent in N/s\n",
      "Is = (F)/(wp) \t\t\t\t#specific impulse in sec\n",
      "SPC = (wp/F)/10**-3 \t\t\t\t#specific propellent consumption in sec**-1 *10**-3\n",
      "Pt = F*u*10**-6 \t\t\t\t#Thrust power in MW\n",
      "Pl = (0.5*mp*((Cj-u)**2))*10**-6 \t\t\t\t#Power loss in exhaust in MW\n",
      "Pe = Pt+Pl \t\t\t\t#engine output in MW\n",
      "np = Pt/Pe \t\t\t\t#propulsive efficiency\n",
      "nth = Pe*10**3/(mp*q*10**-3) \t\t\t\t#thermal efficiency and Pe,q in kW\n",
      "no = np*nth \t\t\t\t#overall efficiency\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)effective jet velocity is %3.4f m/s \\\n",
      "\\nB)Actual jet velocity is %3.4f m/s \\\n",
      "\\nC)specific impulse is %3.1f sec \\\n",
      "\\nD)specific propellent consumption is %3.4f*10**-3 sec**-1 \\\n",
      "\\nE)propulsive efficiency is %3.5f  \\\n",
      "\\nD)thermal efficiency is %3.3f  \\\n",
      "\\nE)overall efficiency is %3.5f'%(Cj,Ce,Is,SPC,np,nth,no)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)effective jet velocity is 1968.9119 m/s \n",
        "B)Actual jet velocity is 1956.1665 m/s \n",
        "C)specific impulse is 200.7 sec \n",
        "D)specific propellent consumption is 4.9824*10**-3 sec**-1 \n",
        "E)propulsive efficiency is 0.62736  \n",
        "D)thermal efficiency is 0.335  \n",
        "E)overall efficiency is 0.21035\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.12 page : 29"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "m1 = 3600. \t\t\t\t#internal mass in kg\n",
      "Cj = 2070. \t\t\t\t#average effective jet velocity in m/s\n",
      "tp = 80. \t\t\t\t#rocket operation duration in sec\n",
      "g = 9.81 \t\t\t\t#acceleration due to gravity in m/s**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "up = 2*Cj \t\t\t\t#flight velocity in m/s\n",
      "MR = 1/math.exp((up+(g*tp))/Cj) \t\t\t\t#mass ratio\n",
      "m2 = MR*m1 \t\t\t\t#mass after rocket operation in kg\n",
      "PMF = 1-MR \t\t\t\t#propellant mass fraction\n",
      "Mp = m1-m2 \t\t\t\t#mass of propellant in kg\n",
      "mp = Mp/tp \t\t\t\t#propellent flow rate in kg/s\n",
      "F = Cj*mp*10**-3 \t\t\t\t#thrust in kN\n",
      "Zp = (((1+((1-(1/PMF))*math.log(1/MR)))*Cj*tp)-(0.5*g*tp**2))*10**-3 \t\t\t\t#powered altitude gain in km\n",
      "Zc = ((0.5*up**2)/g)*10**-3 \t\t\t\t#coasting altitude gain in km\n",
      "Z = Zp+Zc \t\t\t\t#maximum altitude in km\n",
      "\n",
      "\t\t\t\t\n",
      "#Output\n",
      "print 'A)flow rate of propellent is %3.2f kg/s \\\n",
      "\\nB)thrust developed is %3.3f kN \\\n",
      "\\nC)altitude gains during powered and coasting flights are %3.3f km and %3.3f km respectively'%(mp,F,Zp,Zc)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)flow rate of propellent is 40.83 kg/s \n",
        "B)thrust developed is 84.521 kN \n",
        "C)altitude gains during powered and coasting flights are 93.987 km and 873.578 km respectively\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.13 page : 29"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "s = 0.2105 \t\t\t\t#effective jet speed ratio\n",
      "Is = 203.88 \t\t\t\t#specific impulse in sec\n",
      "tp = 8 \t\t\t\t#rocket operation duration i.e. burn out time in sec\n",
      "g = 9.81 \t\t\t\t#acceleration due to kravity in m/s**2\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "Cj = g*Is \t\t\t\t#average effective jet velocity in m/s\n",
      "up = s*Cj \t\t\t\t#maximum flight speed in m/s\n",
      "MR = 1/math.exp((up+(g*tp))/Cj) \t\t\t\t#mass ratio\n",
      "PMF = 1-MR \t\t\t\t#propellant mass fraction\n",
      "Zp = (((1+((1-(1/PMF))*math.log(1/MR)))*Cj*tp)-(0.5*g*tp**2))*10**-3 \t\t\t\t#powered altitude gain in km\n",
      "Zc = ((0.5*up**2)/g)*10**-3 \t\t\t\t#coasting altitude gain in km\n",
      "Z = Zp+Zc \t\t\t\t#maximum altitude in km\n",
      "\n",
      "\t\t\t\t\n",
      "#Output \n",
      "print 'A)effective jet velocity is %3i m/s \\\n",
      "\\nB)mass ratio and propellent mass fraction are %3.2f and %3.2f respectively \\\n",
      "\\nC)maximum flight speed is %3.2f m/s \\\n",
      "\\nD))altitude gains during powered and coasting flights are %3.3f km and %3.3f km respectively'%(Cj,MR,PMF,up,Zp,Zc)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)effective jet velocity is 2000 m/s \n",
        "B)mass ratio and propellent mass fraction are 0.78 and 0.22 respectively \n",
        "C)maximum flight speed is 421.01 m/s \n",
        "D))altitude gains during powered and coasting flights are 1.601 km and 9.034 km respectively\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.14 page : 30"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "\t\t\t\t\n",
      "#Input data\n",
      "R0 = 6341.6*10**3 \t\t\t\t#radius of earth at mean sea-level in m\n",
      "g = 9.809 \t\t\t\t#acceleration due to gravity in m/s**2\n",
      "Z1 = 0 \t\t\t\t#altitude at sea-level in m\n",
      "Z2 = 300*10**3 \t\t\t\t#altitude above sea-level in m\n",
      "\n",
      "\t\t\t\t\n",
      "#Calculation\n",
      "uorb1 = R0*math.sqrt(g/(R0+Z1)) \t\t\t\t#orbit velocity of a rocket at mean sea level in m/s\n",
      "uesc1 = math.sqrt(2)*uorb1 \t\t\t\t#escape velocity of a rocket at mean sea level in m/s\n",
      "uorb2 = R0*math.sqrt(g/(R0+Z2)) \t\t\t\t#orbit velocity of a rocket at an altitude of 300 km in m/s\n",
      "uesc2 = math.sqrt(2)*uorb2 \t\t\t\t#escape velocity of a rocket at an altitude of 300 km in m/s\n",
      "\n",
      "\t\t\t\t\n",
      "#Output \n",
      "print 'A)orbit and escape velocities of a rocket at mean sea level are %3i m/s and %3i m/s \\\n",
      "\\nB)orbit and escape velocities of a rocket at an altitude of 300 km are %3.1f m/s and %3.2f m/s'%(uorb1,uesc1,uorb2,uesc2 )\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A)orbit and escape velocities of a rocket at mean sea level are 7886 m/s and 11153 m/s \n",
        "B)orbit and escape velocities of a rocket at an altitude of 300 km are 7706.8 m/s and 10899.08 m/s\n"
       ]
      }
     ],
     "prompt_number": 14
    }
   ],
   "metadata": {}
  }
 ]
}