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{
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"name": "",
"signature": "sha256:d72d7a460d9b71cf807c7b5c8c2c9f862a173662c7054f2ccff6208191319c71"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER05:INCOMPRESSIBLE FLOW OVER FINITE WINGS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E01 : Pg 182"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import pi,sqrt\n",
"AR = 8.; # Aspect ratio of the wing\n",
"alpha = 5.*pi/180.; # Angle of attack experienced by the wing\n",
"a0 = 2.*pi # airfoil lift curve slope\n",
"alpha_L0 = 0; # zero lift angle of attack is zero since airfoil is symmetric\n",
"# from fig. 5.20, for AR = 8 and taper ratio of 0.8\n",
"delta = 0.055;\n",
"tow = delta; # given assumption\n",
"# thus the lift curve slope for wing is given by\n",
"a = a0/(1.+(a0/pi/AR/(1.+tow)));\n",
"# thus C_l can be calculated as\n",
"C_l = a*alpha;\n",
"# from eq.(5.61)\n",
"C_Di = C_l**2./pi/AR*(1.+delta);\n",
"print\"Cl =\",round(C_l,2)\n",
"print\"CDi =\",round(C_Di,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Cl = 0.44\n",
"CDi = 0.01\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E02 : Pg 185"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import sqrt,pi\n",
"CDi1 = 0.01; # induced drag coefficient for first wing\n",
"delta = 0.055; # induced drag factor for both wings\n",
"tow = delta;\n",
"alpha_L0 = -2.*pi/180.; # zero lift angle of attack\n",
"alpha = 3.4*pi/180.; # angle of attack\n",
"AR1 = 6.; # Aspect ratio of the first wing\n",
"AR2 = 10.; # Aspect ratio of the second wing\n",
"\n",
"# from eq.(5.61), lift coefficient can be calculated as\n",
"C_l1 = sqrt(pi*AR1*CDi1/(1.+delta));\n",
"\n",
"# the lift slope for the first wing can be calculated as\n",
"a1 = C_l1/(alpha-alpha_L0);\n",
"\n",
"# the airfoil lift coefficient can be given as\n",
"a0 = a1/(1.-(a1/pi/AR1*(1.+tow)));\n",
"\n",
"# thus the list coefficient for the second wing which has the same airfoil is given by\n",
"a2 = a0/(1.+(a0/pi/AR2*(1.+tow)));\n",
"C_l2 = a2*(alpha-alpha_L0);\n",
"CDi2 = C_l2**2./pi/AR2*(1.+delta);\n",
"\n",
"print\"The induced drag coefficient of the second wing is CD,i =\",CDi2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The induced drag coefficient of the second wing is CD,i = 0.00741411360464\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E03 : Pg 189"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# all the quantities are expressed in SI units\n",
"import math \n",
"from math import pi\n",
"a0 = 0.1*180./pi; # airfoil lift curve slope\n",
"AR = 7.96; # Wing aspect ratio\n",
"alpha_L0 = -2.*pi/180.; # zero lift angle of attack\n",
"tow = 0.04; # lift efficiency factor\n",
"C_l = 0.21; # lift coefficient of the wing\n",
"\n",
"# the lift curve slope of the wing is given by\n",
"a = a0/(1+(a0/pi/AR/(1.+tow)));\n",
"\n",
"# thus angle of attack can be calculated as\n",
"alpha = C_l/a + alpha_L0;\n",
"\n",
"print\"alpha =\",alpha*180./pi,\"degrees\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"alpha = 0.562642629213 degrees\n",
"\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E04 : Pg 191"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the qunatities are expressed in SI units\n",
"import math \n",
"from math import pi,sqrt\n",
"alpha_L0 = -1.*pi/180.; # zero lift angle of attack\n",
"alpha1 = 7.*pi/180.; # reference angle of attack\n",
"C_l1 = 0.9; # wing lift coefficient at alpha1\n",
"alpha2 = 4.*pi/180.;\n",
"AR = 7.61; # aspect ratio of the wing\n",
"taper = 0.45; # taper ratio of the wing\n",
"delta = 0.01; # delta as calculated from fig. 5.20\n",
"tow = delta;\n",
"# the lift curve slope of the wing/airfoil can be calculated as\n",
"a0 = C_l1/(alpha1-alpha_L0);\n",
"e = 1./(1.+delta);\n",
"# from eq. (5.70)\n",
"a = a0/(1.+(a0/pi/AR/(1.+tow)));\n",
"# lift coefficient at alpha2 is given as\n",
"C_l2 = a*(alpha2 - alpha_L0);\n",
"# from eq.(5.42), the induced angle of attack can be calculated as\n",
"alpha_i = C_l2/pi/AR;\n",
"# which gives the effective angle of attack as\n",
"alpha_eff = alpha2 - alpha_i;\n",
"# Thus the airfoil lift coefficient is given as\n",
"c_l = a0*(alpha_eff-alpha_L0);\n",
"c_d = 0.0065; # section drag coefficient for calculated c_l as seen from fig. 5.2b\n",
"# Thus the wing drag coefficient can be calculated as\n",
"C_D = c_d + ((C_l2**2.)/pi/e/AR);\n",
"print\"The drag coefficient of the wing is C_D =\",C_D"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The drag coefficient of the wing is C_D = 0.014827553741\n"
]
}
],
"prompt_number": 4
}
],
"metadata": {}
}
]
}
|
