path: root/Fundamentals_Of_Aerodynamics_by_J._D._Anderson_Jr./CHAPTER04.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "CHAPTER04:INCOMPRESSIBLE FLOW OVER AIRFOILS"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E01 : Pg 126"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "import math\n",
      "c = 0.64;                                # chord length of the airfoil\n",
      "V_inf = 70.;                              # freestream velocity\n",
      "L_dash = 1254.;                           # lift per unit span L'\n",
      "rho_inf = 1.23;                          # density of air\n",
      "mu_inf = 1.789*10.**-5.;                       # freestream coefficient of viscosity\n",
      "q_inf = 1./2.*rho_inf*V_inf*V_inf;         # freestream dynamic pressure\n",
      "\n",
      "# thus the lift coefficient can be calculated as\n",
      "c_l = L_dash/q_inf/c;\n",
      "\n",
      "# for this value of C_l, from fig. 4.10\n",
      "alpha = 4.;\n",
      "\n",
      "# the Reynold's number is given as\n",
      "Re = rho_inf*V_inf*c/mu_inf;\n",
      "\n",
      "# for the above Re and alpha values, from fig. 4.11\n",
      "c_d = 0.0068;\n",
      "\n",
      "# thus the drag per unit span can be calculated as\n",
      "D_dash = q_inf*c*c_d;\n",
      "\n",
      "print\"c_l =\",c_l\n",
      "print\"\\nfor this c_l value, from fig. 4.10we get alpha =\",alpha\n",
      "print\"\\nRe =\",Re/1000000. \n",
      "print\"\\nfor this value of Re, from fig. 4.11 we get c_d =\",c_d\n",
      "print\"\\nD=\",D_dash,\"N/m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "c_l = 0.650199104032\n",
        "\n",
        "for this c_l value, from fig. 4.10we get alpha = 4.0\n",
        "\n",
        "Re = 3.08015651202\n",
        "\n",
        "for this value of Re, from fig. 4.11 we get c_d = 0.0068\n",
        "\n",
        "D= 13.114752 N/m\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E02 : Pg 126"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "\n",
      "c = 0.64;                                # chord length of the airfoil\n",
      "V_inf = 70.;                              # freestream velocity\n",
      "rho_inf = 1.23;                          # density of air\n",
      "q_inf = 1./2.*rho_inf*V_inf*V_inf;         # freestream dynamic pressure\n",
      "c_m_ac = -0.05                           # moment coefficient about the aerodynamic center as seen from fig. 4.11\n",
      "\n",
      "# thus moment per unit span about the aerodynamic center is given as\n",
      "M_dash = q_inf*c*c*c_m_ac;\n",
      "\n",
      "print\"The Moment per unit span about the aerodynamic center is is M=\",M_dash,\"Nm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Moment per unit span about the aerodynamic center is is M= -61.71648 Nm\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E04 : Pg 127"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "import math\n",
      "from math import pi\n",
      "alpha = 5.*pi/180.;            # angle of attack in radians\n",
      "\n",
      "# from eq.(4.33)according to the thin plate theory, the lift coefficient is given by\n",
      "c_l = 2.*pi*alpha;\n",
      "\n",
      "# from eq.(4.39) the coefficient of moment about the leading edge is given by\n",
      "c_m_le = -c_l/4.;\n",
      "\n",
      "# from eq.(4.41)\n",
      "c_m_qc = 0;\n",
      "\n",
      "# thus the coefficient of moment about the trailing can be calculated as\n",
      "c_m_te = 3./4.*c_l;\n",
      "\n",
      "print\"(a)Cl =\", c_l\n",
      "print\"(b)Cm_le =\",c_m_le\n",
      "print\"(c)m_c/4 =\",c_m_qc\n",
      "print\"(d)Cm_te =\",c_m_te"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Cl = 0.548311355616\n",
        "(b)Cm_le = -0.137077838904\n",
        "(c)m_c/4 = 0\n",
        "(d)Cm_te = 0.411233516712\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E06 : Pg 131"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "\n",
      "alpha1 = 4.;\n",
      "alpha2 = -1.1;\n",
      "alpha3 = -4.;\n",
      "cl_1 = 0.55;                # cl at alpha1\n",
      "cl_2 = 0;                   # cl at alpha2\n",
      "c_m_qc1 = -0.005;           # c_m_qc at alpha1\n",
      "c_m_qc3 = -0.0125;          # c_m_qc at alpha3\n",
      "\n",
      "# the lift slope is given by\n",
      "a0 = (cl_1 - cl_2)/(alpha1-alpha2);\n",
      "\n",
      "# the slope of moment coefficient curve is given by\n",
      "m0 = (c_m_qc1 - c_m_qc3)/(alpha1-alpha3);\n",
      "\n",
      "# from eq.4.71\n",
      "x_ac = -m0/a0 + 0.25;\n",
      "\n",
      "print\"The location of the aerodynamic center is x_ac =\",x_ac"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The location of the aerodynamic center is x_ac = 0.241306818182\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E07 : Pg 139"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "import math \n",
      "c = 1.5;            # airfoil chord\n",
      "Re_c = 3.1e6;       # Reynolds number at trailing edge\n",
      "\n",
      "# from eq.(4.84), the laminar boundary layer thickness at trailing edge is given by\n",
      "delta = 5*c/math.sqrt(Re_c);\n",
      "\n",
      "# from eq(4.86)\n",
      "Cf = 1.328/math.sqrt(Re_c);\n",
      "\n",
      "# the net Cf for both surfaces is given by\n",
      "Net_Cf = 2*Cf;\n",
      "\n",
      "print\"(a)delta =\",delta,\"m\"\n",
      "print\"(b)Cf =\",Cf*10000  \n",
      "print\"Net Cf =\",Net_Cf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)delta = 0.00425971375685 m\n",
        "(b)Cf = 7.5425331588\n",
        "Net Cf = 0.00150850663176\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E08 : Pg 150"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "import math \n",
      "c = 1.5;            # airfoil chord\n",
      "Re_c = 3.1e6;       # Reynolds number at trailing edge\n",
      "\n",
      "# from eq.(4.87), the turbulent boundary layer thickness at trailing edge is given by\n",
      "delta = 0.37*c/(Re_c**0.2);\n",
      "\n",
      "# from eq(4.86)\n",
      "Cf = 0.074/(Re_c**0.2);\n",
      "\n",
      "# the net Cf for both surfaces is given by\n",
      "Net_Cf = 2*Cf;\n",
      "\n",
      "print\"(a)delta =\",delta,\"m\"\n",
      "print\"(b)Cf =\",Cf\n",
      "print\"Net Cf =\",Net_Cf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)delta = 0.0279267658904 m\n",
        "(b)Cf = 0.00372356878539\n",
        "Net Cf = 0.00744713757078\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example E09 : Pg 162"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# All the quantities are expressed in SI units\n",
      "import math \n",
      "from math import sqrt\n",
      "c = 1.5;                # airfoil chord length\n",
      "Rex_cr = 5e5;           # critical Reynold's number\n",
      "Re_c = 3.1e6;           # Reynold's number at the trailing edge\n",
      "\n",
      "# the point of transition is given by\n",
      "x1 = Rex_cr/Re_c*c;\n",
      "\n",
      "# the various skin friction coefficients are given as\n",
      "Cf1_laminar = 1.328/sqrt(Rex_cr);\n",
      "Cfc_turbulent = 0.074/(Re_c**0.2);\n",
      "Cf1_turbulent = 0.074/(Rex_cr**0.2);\n",
      "\n",
      "# thus the total skin friction coefficient is given by\n",
      "Cf = x1/c*Cf1_laminar + Cfc_turbulent - x1/c*Cf1_turbulent;\n",
      "\n",
      "# taking both sides of plate into account\n",
      "Net_Cf = 2*Cf;\n",
      "\n",
      "print\"The net skin friction coefficient is Net Cf=\",round(Net_Cf,5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The net skin friction coefficient is Net Cf= 0.00632\n"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}