diff --git a/Airfoil characteristics - amiya/2412.txt b/Airfoil characteristics - amiya/2412.txt new file mode 100644 index 0000000..97aef5a --- /dev/null +++ b/Airfoil characteristics - amiya/2412.txt @@ -0,0 +1,101 @@ +1.00000000 0.00000000 +0.99910623 0.00020490 +0.99617708 0.00081746 +0.99130721 0.00183029 +0.98451462 0.00323139 +0.97582453 0.00500438 +0.96526923 0.00712879 +0.95288810 0.00958052 +0.93872748 0.01233229 +0.92284056 0.01535412 +0.90528726 0.01861389 +0.88613406 0.02207772 +0.86545377 0.02571051 +0.84332535 0.02947628 +0.81983364 0.03333849 +0.79506903 0.03726034 +0.76912718 0.04120497 +0.74210869 0.04513556 +0.71411868 0.04901549 +0.68526647 0.05280838 +0.65566513 0.05647816 +0.62543106 0.05998915 +0.59468360 0.06330614 +0.56354453 0.06639459 +0.53213763 0.06922076 +0.50058819 0.07175208 +0.46902253 0.07395746 +0.43756749 0.07580769 +0.40634986 0.07727597 +0.37529693 0.07829665 +0.34467975 0.07876445 +0.31467791 0.07866778 +0.28541825 0.07800433 +0.25702472 0.07677852 +0.22961766 0.07500158 +0.20331307 0.07269154 +0.17822186 0.06987304 +0.15444921 0.06657687 +0.13209395 0.06283946 +0.11124803 0.05870205 +0.09199604 0.05420974 +0.07441485 0.04941038 +0.05857330 0.04435333 +0.04453206 0.03908817 +0.03234345 0.03366328 +0.02205147 0.02812454 +0.01369173 0.02251404 +0.00729159 0.01686883 +0.00287020 0.01121992 +0.00043865 0.00559144 +0.00000000 0.00000000 +0.00153463 -0.00539298 +0.00501509 -0.01043258 +0.01042116 -0.01511322 +0.01772511 -0.01942897 +0.02689202 -0.02337383 +0.03788006 -0.02694217 +0.05064089 -0.03012931 +0.06512002 -0.03293202 +0.08125723 -0.03534918 +0.09898696 -0.03738231 +0.11823872 -0.03903610 +0.13893742 -0.04031885 +0.16100369 -0.04124275 +0.18435415 -0.04182406 +0.20890168 -0.04208311 +0.23455554 -0.04204410 +0.26122161 -0.04173481 +0.28880246 -0.04118609 +0.31719754 -0.04043123 +0.34630326 -0.03950521 +0.37601319 -0.03844392 +0.40626883 -0.03728050 +0.43709928 -0.03596314 +0.46818695 -0.03448146 +0.49941181 -0.03286467 +0.53065289 -0.03114093 +0.56178870 -0.02933684 +0.59269771 -0.02747709 +0.62325883 -0.02558417 +0.65335187 -0.02367824 +0.68285808 -0.02177712 +0.71166061 -0.01989635 +0.73964499 -0.01804943 +0.76669961 -0.01624805 +0.79271622 -0.01450235 +0.81759035 -0.01282128 +0.84122175 -0.01121291 +0.86351486 -0.00968469 +0.88437919 -0.00824370 +0.90372973 -0.00689682 +0.92148736 -0.00565085 +0.93757920 -0.00451251 +0.95193895 -0.00348846 +0.96450725 -0.00258516 +0.97523199 -0.00180877 +0.98406854 -0.00116491 +0.99098004 -0.00065856 +0.99593762 -0.00029380 +0.99892050 -0.00007369 +1.00000000 0.00000000 \ No newline at end of file diff --git a/Airfoil characteristics - amiya/Airfoil generator/.ipynb_checkpoints/NACA camber-Copy0-checkpoint.ipynb b/Airfoil characteristics - amiya/Airfoil generator/.ipynb_checkpoints/NACA camber-Copy0-checkpoint.ipynb new file mode 100644 index 0000000..1bf4d1a --- /dev/null +++ b/Airfoil characteristics - amiya/Airfoil generator/.ipynb_checkpoints/NACA camber-Copy0-checkpoint.ipynb @@ -0,0 +1,179 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:08d7474f33be091c07ab73695ad32b733222f333e8c562b3b6af59f3e8923cc3" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "import csv" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "with open (r'C:\\Users\\Amiya\\Documents\\GWU\\AeroHydro\\Project\\Airfoil characteristics/NACA_2412.dat') as file_name:\n", + " x_j, y_j = np.loadtxt(file_name, dtype=float, delimiter='\\t', unpack=True)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "could not convert string to float: NACA 2412", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;32mwith\u001b[0m \u001b[0mopen\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;34mr'C:\\Users\\Amiya\\Documents\\GWU\\AeroHydro\\Project\\Airfoil characteristics/NACA_2412.dat'\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mfile_name\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mx_j\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_j\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloadtxt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfile_name\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfloat\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdelimiter\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'\\t'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0munpack\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;32mC:\\Anaconda\\lib\\site-packages\\numpy\\lib\\npyio.pyc\u001b[0m in \u001b[0;36mloadtxt\u001b[1;34m(fname, dtype, comments, delimiter, converters, skiprows, usecols, unpack, ndmin)\u001b[0m\n\u001b[0;32m 854\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 855\u001b[0m \u001b[1;31m# Convert each value according to its column and store\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 856\u001b[1;33m \u001b[0mitems\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mconv\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mval\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mconv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mval\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mconverters\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvals\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 857\u001b[0m \u001b[1;31m# Then pack it according to the dtype's nesting\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 858\u001b[0m \u001b[0mitems\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpack_items\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mitems\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpacking\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mValueError\u001b[0m: could not convert string to float: NACA 2412" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c = 1.0 #chord\n", + "thickness = 12 #thickness as a percent of chord\n", + "camber = 2.0 #max camber as a percent of chord\n", + "camber_loc = 4.0 #location of max camber as 1/10 percent of a chord\n", + "\n", + "t = thickness/100 #max thickness as a fraction of the chord\n", + "m = camber/100\n", + "p = camber_loc/10 \n", + "\n", + "N = 202 #number of points describing airfoil\n", + "theta_u = np.linspace(0, np.pi, N/2)\n", + "x = np.linspace(0, c, N/2)\n", + "theta_l = np.linspace(np.pi, 2*np.pi, N/2)\n", + "y_t = (t/0.2)*(0.2969*np.sqrt(x) - 0.126*x - 0.3516*x**2 + 0.2843*x**3 - 0.1015*x**4)\n", + "print theta_u.size, theta_l.size\n", + "print x.size\n", + "print y_t.size\n", + "print y_t[0]\n", + "plt.plot(x,y_t)" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = np.zeros(x.size, dtype=float)\n", + "y_u = np.zeros(x.size, dtype=float)\n", + "x_l = np.zeros(x.size, dtype=float)\n", + "y_l = np.zeros(x.size, dtype=float)\n", + "y_c = np.zeros(x.size, dtype=float)\n", + "dyc_dx = np.zeros(x.size, dtype=float)\n", + "\n", + "for i in range(N/2-1):\n", + " if x[i]>p*c:\n", + " y_c[i] = (m/(1-p)**2)*((1-(2*p))+(2*p*x[i])-x[i]**2)\n", + " dyc_dx[i] = (2*m/(1-p)**2)*(p-x[i])\n", + " else:\n", + " y_c[i] = (m/p**2)*((2*p*x[i])-x[i]**2)\n", + " dyc_dx[i] = (2*m/p**2)*(p-x[i])\n", + "\n", + "plt.plot(x[0:N/4],y_c[0:N/4])\n", + "print y_c[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = x - y_t*np.sin(np.arctan(dyc_dx))\n", + "y_u = y_c + y_t*np.cos(np.arctan(dyc_dx))\n", + " #print i, x_u[i]\n", + " \n", + "x_l = x + y_t*np.sin(np.arctan(dyc_dx))\n", + "y_l = y_c - y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + "x_l[0], y_l[0] = x_u[0], y_u[0]\n", + "x_l[N/2 - 1], y_l[N/2 - 1] = x_u[N/2 - 1], y_u[N/2 - 1]\n", + "\n", + "print x_l[0], y_l[0],x_u[0], y_u[0]\n", + "print x_l[N/2 - 1], y_l[N/2 - 1],x_u[N/2 - 1], y_u[N/2 - 1]" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#plt.plot(x_u, y_u, marker='x')\n", + "plt.plot(x_l, y_l, color='#CD2305')\n", + "plt.plot(x_u, y_u)\n", + "#plt.scatter(x_j, y_j, marker='o')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "cb = np.zeros(x.size, dtype=float)" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x_j.size" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x.size" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Airfoil characteristics - amiya/Airfoil generator/NACA 4 cambered/.ipynb_checkpoints/NACA4 camber-checkpoint.ipynb b/Airfoil characteristics - amiya/Airfoil generator/NACA 4 cambered/.ipynb_checkpoints/NACA4 camber-checkpoint.ipynb new file mode 100644 index 0000000..f985ee1 --- /dev/null +++ b/Airfoil characteristics - amiya/Airfoil generator/NACA 4 cambered/.ipynb_checkpoints/NACA4 camber-checkpoint.ipynb @@ -0,0 +1,303 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:7b0bd42ffc992c1c757fc079b99531d6b53c68d96ce19c07cd6b1e6fc4a525a8" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "import csv" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 254 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "with open (r'./2412.txt') as file_name:\n", + " x_j, y_j = numpy.loadtxt(file_name, dtype=float, delimiter='\\t', unpack=True)\n", + " \n", + "plt.plot(x_j,y_j)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 263, + "text": [ + "[]" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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CvXtfbBHYWyK4lF2sU2jTRuHECa0jISJnd/aszBpauVJmDfXpI4lg/Hjb6xpy\n6MVrN9+skJ8PtGmjdTRE5GzOnJEEsHKltAxCQoCJE4H77gM8PLSO7socevGan5+MK4SGah0JETmD\n06dlbGDVKmDDBik+N3GiFJ5r317r6JqWXSSF7t2BAweYFIio6Zw8CaSmSotg0ybgrrskEbz/vnP1\nUthFUujfH9i+HZg8WetIiMiR/PorsGaNtAi2bpWqo9HRwKefAq1bax2dNuwiKdx1l9QBISKyVFER\n8N//SiLIzgYiIoApU6SF0KqV1tFpzy4GmquqFNq2BQ4fBtq10zoiIrI3+fmSBFatAvbvB8aMASZM\nkHLUjlps06EHml1dZaDnu++AceO0joaI7MH+/cDq1ZIICgqAe++VjWnuvhto1kzr6GyXXSQFQLqQ\nNm9mUiCi+ikF/PjjxURw+rSsH1i0CLjjDvlwSddmN5fprruAWbO0joKIbMmFC0BmpiSC1asBFxfp\nFkpKkgkqLhbtQu+c7GJMQSmFigqpM15cDNxyi9ZREZFWqqpkyujq1TJzqG1baRFMmCDF57h1r3Do\nMQUAaN5cdiRat07mDhOR8zh3Tv7fX71aFpX5+Uki2LRJvqfGYzctBUCahKmpMp2MiBzbqVNSaG71\nailFffvtkgjGjQM8PbWOzvY5dO2jmhBPnQK6dJHpZbfeqm1cRNT4SkqAlBT54Ld1KzB0qNQYiori\ndPTr5RRJAZCKhCNGANOmaRgUETWan3+WJLB6NZCTA4wcKS2CkSOBm2/WOjr71dCkYNHYfFlZGcLD\nw9G9e3eMGDEC5VfYTDkjIwMBAQHw8/NDQkKC6eezZ89GYGAggoODMX78eJw6deqa7/nww8Bnn1kS\nNRFpSSlg1y4gLg4IDpY1SAcOAC+8IC2F5GT58MeEoA2LWgpz5sxBu3btMGfOHCQkJODkyZOIj4+v\ndY7RaIS/vz82bNgAvV6P/v37Izk5GYGBgVi/fj2GDx8OFxcXzJs3DwDqPP/ybFdRIRtY/Pgj4OXV\n0MiJyJqMRmDLFpkttGaN/Oy+++QYNAi44QZt43NEmrQUUlNTERMTAwCIiYnBmpr/2pfIysqCr68v\nvL294ebmhujoaKSkpAAAwsPD4fLHROLQ0FAUFhZe8z2bN5epZ8nJlkRORE3t/HmZKRQbKxvQPP00\n4O4uSeHw4YuLypgQbItFSaG0tBQef+wy4eHhgdLS0jrnFBUVweuSj/Senp4oKiqqc95HH32EUaNG\nmfW+U6ZCm8vtAAAQyklEQVQA77wj85WJyHacPCkVRu+/H+jYEXj9dVk7kJUlxef+/nfZtpJrCWzX\nNdcphIeHo6SkpM7PX3nllVqPdToddPX8l67vZ/W9VrNmzfDQQw/V+/u4uDjT92FhYQgLC4OPD/DJ\nJ5IgiEg7R4/KjKE1a4AdO4Bhw6TO0DvvOP6GNLbEYDDAYDBY/DrXTArr16+/4u88PDxQUlKCjh07\n4tixY+jQoUOdc/R6PQoKCkyPCwoK4HnJJOOPP/4YaWlp2Lhx4xXf59KkUOPFF4GpU2WPBdY0IbIe\npYDduyUJpKRIUhg7FnjqKSA8HGjZUusInVPNB+YaCxYsaNDrWNR9FBUVhaVLlwIAli5dinH1VKsL\nCQlBbm4u8vPzUVlZieXLlyMqKgqAzEp67bXXkJKSghtvvPG63nvoUOmn/PxzS/4FRGSOqirgf/+T\n+mPduskA8alTwL/+JTOGkpJkURkTgv2zaPZRWVkZJk2ahKNHj8Lb2xsrVqyAu7s7iouLMW3aNKxd\nuxYAkJ6ejlmzZsFoNCI2Nhbz588HAPj5+aGyshJt/tjrbtCgQXjnnXdqB3iVEfR162Twas8eDlYR\nNbbTp4GMDKkikJ4uySAqSm7+QUEcF7B1TrN47VJKAQMHAs89JwNbRGSZwkJJAikpsqL4jjtkfGDM\nGJaWsDdOmRQA+QQza5YshrnOHigip6eUzAr68ktJBvn5wOjR0iKIiOACMnvmtEkBkKqp3bsDCxda\nKSgiO3b+vIwPfPmlrCO48UZJAmPHcjMaR+LUSaGkROY+r1sH9OljpcCI7EhpqVQc/fJLSQjBwZIE\nxo4F/P05PuCInDopADL7ITER2L6dn3SIaqaNfvWVJIL9+6WQ5NixwKhRsjENOTanTwpKyR99eDgw\nZ44VAiOyMWfPAhs3Sotg7VrZnH7MGDmGDuVm9c7G6ZMCICV4BwyQWRPduzdxYEQ2ID//YhL47jsg\nJEQGikePZreQs2NS+MOSJcDixcC2bUDr1k0YGJEGqqrkQ096uiSC0lIgMlJaAyNG8G+eLmJSuMSM\nGcChQ9KfyvEFsnfFxZIE0tOle8jHRxLB6NFA//5cuEn1Y1K4RHX1xebzm282UWBETaS6Wlq66elA\nWprUFhoxQhJBRIRUHyW6FiaFy5SXA4MHS6vhiSeaIDCiRlRYCHz9tRzr10tJichIOUJD2eKl68ek\nUI/Dh4EhQ4Bly+STFpGtOHsW2LxZksC6dTI2EB4uLYGRI9kaIMsxKVzBd9/JJuBJSdKlRKQFpYCf\nfpIE8PXXQGYm0LevJIGICPmeYwPUmJgUrmL7dinq9dprwJ//3EiBEV1DUZEMDG/cKF1CN90kLdaI\nCNmI5pZbtI6QHBmTwjXk5Eiz/Nlnpdw2UWM7eRIwGC4mgl9+Ae6+Gxg+HLjnHsDXV+sIyZkwKZjh\nyBH5pPbAA8CCBVzYQ5Y5dw7YsuViEti3T8awhg+Xo08fwMWibayIGo5JwUy//iozOnr0AN5+m6WB\nyXxnz8pU0U2b5PjhByksV5MEBg4EmjfXOkoiwaRwHc6ckT0YvvkG+OwzmfJHdLnff5fVwwaDJIFd\nu6Qa79ChcgwZwg8VZLuYFBpg1SpZw/DUU8D8+Zz94exOnJBZQZs3SxLYswfo1+9iEhg0iHsQk/1g\nUmigwkIgJgaorAQ++QTw9m6ytyIbcuECcOCAtARqjqIiaTXecYckgdBQoEULrSMlahgmBQtcuAAs\nWgQkJEi30jPP8BOhozlzBtixQwaGt26VsQF3d1n1XnP06sXWIjkOJoVGcPgw8Le/Ad9+K7OTHnmE\n5QXs0fnzssHM999fPA4dkkHhwYNlLGDQIKBTJ60jJWo6TAqNKCsLmD0bOH5cWg+jR3P6qq2qrAT2\n7pUb/44d8nX/ftlPIyTk4tGrF2cGkXNhUmhkSkm9+rlzgTZtgJkzgXHjADc3q4dCfzh5UmYAXXrs\n3w907Vo7AQQHcyyAyOpJoaysDA888ACOHDkCb29vrFixAu7u7nXOy8jIwKxZs2A0GjF16lTMnTu3\n1u8XLVqE2bNn4/jx42jTpk3dADVKCjWqq2WW0rvvysBkbCzw2GNAly6aheTwjEbp7tm9u3YCKC+X\nT/zBwTI1NDhYHrdqpXXERLbH6klhzpw5aNeuHebMmYOEhAScPHkS8fHxtc4xGo3w9/fHhg0boNfr\n0b9/fyQnJyMwMBAAUFBQgGnTpuHAgQP44YcfbDIpXGrfPuDf/wY+/VT6pf/yF1khzXGHhlFK9grY\ns0e6gPbskePAAaBDB7npX3p07coVwkTmsnpSCAgIwKZNm+Dh4YGSkhKEhYVh//79tc7Ztm0bFixY\ngIyMDAAwJY158+YBAO6//368+OKLuPfee+0iKdQ4cwZYvly2/jx8WAqcjRkjX+v5Jzg9o1FKjBw8\nKIm1Jgns3SvbR/bsCQQFXfwaGMhFYUSWaui9s8GfcUtLS+Hh4QEA8PDwQGlpaZ1zioqK4OXlZXrs\n6emJ7du3AwBSUlLg6emJ3r17NzQEzbRsCUyZIkdhoeyOlZwMTJ8u9W5qNk7v2dO5BqhPnJAb/4ED\nF4+DByVxduggg78BAcCAAXLtevQAbr1V66iJ6FJXTQrh4eEoKSmp8/NXXnml1mOdTgddPXe/+n4G\nAOfOncPChQuxfv1608+ultHi4uJM34eFhSEsLOxqYVuVp6eMMTz2mBRIMxhkgHrsWOkD79cPuP32\ni4ePj/0minPn5BN/Xh6Qny9Hzfc//yybyvv7y83f3x+Ijpavfn5SNpqImo7BYIDBYLD4dSzqPjIY\nDOjYsSOOHTuGYcOG1ek+yszMRFxcnKn76NVXX4WLiwtGjx6N4cOH46Y/7hSFhYXQ6/XIyspChw4d\nagdog91H5iotBXbulMJpNcdvv8mGKr16AbfdJgPWXbrI9x06aJMwjEYpFFhSIsexYxe/LymRfv/8\nfJn906WLrPru2lW+Xvq9h4f9JjwiR6PJQHPbtm0xd+5cxMfHo7y8vM5Ac3V1Nfz9/bFx40Z07twZ\nAwYMqDXQXKNr1652NaZgiV9+kUSRkyM325rjyBFJGF5ekiDat5d+9Vat5OvlR/PmMlB74ULto+Zn\nRqNU9Tx1Cjh9uv7j1ClJXCdOSDdOp06yDWTN0amT3OhrEkGnThzoJbIXmkxJnTRpEo4ePVprSmpx\ncTGmTZuGtWvXAgDS09NNU1JjY2Mxf/78Oq/VrVs3fP/9906RFK7m7FmgoEASxPHjkiR+/12+Xn5U\nVMgN+tJDp6v9uGVL2d3raoeHhyQgrr8gcixcvEZERCYNvXeyM4CIiEyYFIiIyIRJgYiITJgUiIjI\nhEmBiIhMmBSIiMiESYGIiEyYFIiIyIRJgYiITJgUiIjIhEmBiIhMmBSIiMiESYGIiEyYFIiIyIRJ\ngYiITJgUiIjIhEmBiIhMmBSIiMiESYGIiEyYFIiIyIRJgYiITJgUiIjIpMFJoaysDOHh4ejevTtG\njBiB8vLyes/LyMhAQEAA/Pz8kJCQUOt3b731FgIDAxEUFIS5c+c2NBQiImokDU4K8fHxCA8Px8GD\nBzF8+HDEx8fXOcdoNGLGjBn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+ "text": [ + "" + ] + } + ], + "prompt_number": 263 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c = 1.0 #chord\n", + "thickness = 12.0 #thickness as a percent of chord\n", + "camber = 2.0 #max camber as a percent of chord\n", + "camber_loc = 4.0 #location of max camber as 1/10 percent of a chord\n", + "\n", + "t = thickness/100.0 #max thickness as a fraction of the chord\n", + "m = camber/100.0\n", + "p = camber_loc/10.0 \n", + "\n", + "N = 202 #number of points describing airfoil\n", + "theta_u = np.linspace(0., np.pi, N/2)\n", + "x = np.linspace(0., c, N/2)\n", + "#theta_l = np.linspace(np.pi, 2*np.pi, N/2)\n", + "y_t = (t/0.2)*(0.2969*np.sqrt(x) - 0.126*x - 0.3516*x**2 + 0.2843*x**3 - 0.1015*x**4)\n", + "print theta_u.size, theta_l.size\n", + "print x.size\n", + "print y_t.size\n", + "print y_t[0]\n", + "plt.plot(x,y_t)\n", + "print thickness/100\n", + "print camber/100\n", + "print camber_loc/10" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101 101\n", + "101\n", + "101\n", + "0.0\n", + "0.12" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "0.02\n", + "0.4\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 256 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = np.zeros(x.size, dtype=float)\n", + "y_u = np.zeros(x.size, dtype=float)\n", + "x_l = np.zeros(x.size, dtype=float)\n", + "y_l = np.zeros(x.size, dtype=float)\n", + "y_c = np.zeros(x.size, dtype=float)\n", + "dyc_dx = np.zeros(x.size, dtype=float)\n", + "\n", + "for i in range(N/2-1):\n", + " if x[i]>p*c:\n", + " y_c[i] = (m/(1-p)**2)*((1-(2*p))+(2*p*x[i])-x[i]**2)\n", + " dyc_dx[i] = (2*m/(1-p)**2)*(p-x[i])\n", + " else:\n", + " y_c[i] = (m/p**2)*((2*p*x[i])-x[i]**2)\n", + " dyc_dx[i] = (2*m/p**2)*(p-x[i])\n", + "\n", + "plt.plot(x[0:N/4],y_c[0:N/4])\n", + "print y_c[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 257 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = x - y_t*np.sin(np.arctan(dyc_dx))\n", + "y_u = y_c + y_t*np.cos(np.arctan(dyc_dx))\n", + " #print i, x_u[i]\n", + " \n", + "x_l = x + y_t*np.sin(np.arctan(dyc_dx))\n", + "y_l = y_c - y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + "x_l[0], y_l[0] = x_u[0], y_u[0]\n", + "x_l[N/2 - 1], y_l[N/2 - 1] = x_u[N/2 - 1], y_u[N/2 - 1]\n", + "\n", + "print x_l[0], y_l[0],x_u[0], y_u[0]\n", + "print x_l[N/2 - 1], y_l[N/2 - 1],x_u[N/2 - 1], y_u[N/2 - 1]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0 0.0 0.0 0.0\n", + "1.0 0.00126 1.0 0.00126\n" + ] + } + ], + "prompt_number": 258 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#plt.plot(x_u, y_u, marker='x')\n", + "plt.plot(x_l, y_l, color='#CD2305', marker='o')\n", + "plt.plot(x_u, y_u, marker='o')\n", + "plt.plot(x_j,y_j, color='g', marker='x')\n", + "#plt.scatter(x_j, y_j, marker='o')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 264, + "text": [ + "[]" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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wnx+hG0JNC2WEEJbPNMPw3LPwtD8UtYLsTrBmjunozyZN5tGhg2+tnbpa6/c+\nMr1JGreB9jZkrVzN+L1TmT0bwvuFE5caJ/u0C1FDVGQNi4lb3o+8UcuhQQYcfBgONQbWcvZshExd\nvQ41JlMIDp7MunVT4cGn4HQ7+PudsvvfJSrqw5vdTSFENdDqtPhN6E9axO9w7+vguh0SW0D0ZtDX\nqdK2tl0LrjdTsPgN8coP0CkqsgbH4+AVCfseBy8NYDxRTQhR82h1WkI3hDJj4BQ8mnwNq76B5Huh\n6Vl4thc0PFHWchMwmfj4NFnPcBUsfvgosFUgoRtCUderCz0/gz1Pw92fQEw4ICeqCVFTVd5Uz97a\ngTlzPiMvvxl7M1qQZ/sAvNADdg6E+Cag+4zz52VTvatRI4aPtDotD8x/jE2nY+Dg47D2c9A54uEx\nidmz75NxRCFqEVN9sTgEHrkPCjzgh3VQ2AzsNND3fRru8iKgk0eNLkDX6kKzo50jJXltwS6KXoo9\nqoBZZRvfSUAQorapKEKvYcvPg8gdcBbG+MEv70GnbyBmA+d1jrIK+l9YdKZQvhNqbmkxW++cxehG\n4Vj5psj0UyEEUDYBZf0H0P8tCPwUfl8KB0Zc1KZmFqBrXaG5PEVct+l1tjonwpkORC/Q0qt0EKEb\nQtHqtNXdRSFENRs3bgDubd8AmwJYNhSGPAf3TAXKL5ab2L49iaCgMClCl7HY4SPT2cteGlBUsOsl\nkpNfZNGX7/LLn7IuQQhRdVO9hHRbcr6Jh6f7Q8ud8MdLULyZnBzZirsyi80UTGcvZ/qD+2ZTSqjT\nWeFo5ygBQQhh2lRvg2YGP/44Bg+HCPhyH1gXwgtPQTe3ipPdMG6qN3P+KjRHNNXY6+plsZmCrW2p\n8YtOP8DBh6CoASBTUIUQFSp/OKwoQM9Dl34XO07kUtB3MvisgGVLQbcP7Fbyd53VKBMUGOtQKzMG\niyw0a45oyDsIk16L49jAZbBiEZxuR/MeL/LNm6/Uyv9IIcS1CQ6ezLoDQ2H4Q5BvB7/1g7vUxjVO\nOkc8PEKZPTvYYq8ntarQHNgqkE3WkQQ93xAV57jLawVuz/Rn1v9GWux/oBDi1ho3bgAedf+Ahbuh\npBDGL4BdL5o21Kutp7pZZKYAxgVrd4TfiZ/1I3Twz5FpqEKIa6bRbGLm/FVstl1Jif5u4/G9P34E\nGRlAuKmdJWYNtSpTAFAbbNHqM9hEOG8EviEBQQhxzQL7+eEzpoC7dYNh5bcQ/TE8Mx46tKvSzniq\nW+04493Mwx4GAAAgAElEQVRig8JHy//ARmnA8fHHmRE3Q9YlCCGuWfn+Sa+NHYKHRyjsfBl+egwG\njoeHngS7c2UtjesZ7u7/Nl1HDK/Rw0kWFxQ0mk30HfQ6n+4YT8PD3vwTl0p4v3BZsCaEuGYh3iHG\nKewhvZg9O5jg4HdpdL4YvjwAjY/Ai/7g8DuwlpzCBcTZ5pKwYiHjx6+tsYHBomoKpo2urANgyLPw\n9S48mnzN7NnBBPbzkwVrQgizma4zKe/BkOfB63f4JQo6/GqamQS3//YYtaKmYFrFrHOEC61A624a\n65MFa0KIG8GUNfSfSq9zbbDd2xaeC4IT95hmJtXk8xksavGaaRWzz59waKjpfjlIRwhxI4WE9CIk\npFfZyW4a0pb9CA88B/W2wg57INx0PkNN2xrDYjIFzREN6np5gFIWFB40Lk/30sgqZiHEDVflZLeC\ng7BoI/RbCAPPg6rimlPTZiZZTFAIbBVIvfuTce4+0njHeTfoG4q71QZeffXe6u2cEKLGKZ+ZNPyB\nEONwkt9K7JeEQOtN8Pyd0CCVykNJfQe9TthP06u722azqEKzVqel7dS7uJBkR+MG1vhkBvG/MYNr\nTNomhLi9BQdPZl30+zD4BWi7HBYPg+xvjKMWfUNxP2bH3E8fuC2uSdVWaI6KisLHxwcvLy+mT798\nlBw3bhxeXl506tSJhIQEANLS0ujTpw/t27enQ4cOfPHFF//5Wo52jhTr7dC120PcjN/YoJlxW/zy\nhRC1w7hxA/C4I8y431qcP4xaCr7LoG8oxISTcugBRo6cZ9nnMyhmKC0tVTw8PJTjx48rxcXFSqdO\nnZTExMQqbTQajTJw4EBFURQlPj5eCQgIUBRFUU6ePKkkJCQoiqIoubm5ire39yWPLctiTF+naTMU\n3rVWovckKmNWj1FyCnPM6b4QQlyz1as3KsHBk5WGDUcqdFqkEIZC9y8U2KjAJAUU0z8Pj0nK6tUb\nq6Wf13t5NytT2L59O56enri7u2NjY8OIESNYsWJFlTYrV65k5EhjHSAgIACtVkt2djbNmzenc+fO\nANjb2+Pr60tmZua/vpZWp+WpiDHUyelMv06+smBNCFEtQkJ6ERX1IV17NgWXHbBEA/0nQZ9JwNQq\nbS2xCG1WUMjIyMDNzc1029XVlYyMjP9sk56eXqVNSkoKCQkJBAQE/OtrxaXGoT7ji69dH8A4lBTe\nz3jCmhBC3EpanZZ69yfjfswOjg6Cr7eBfwI83Rfqni5rZSxCb01ItqitMcxap6BSqa6qnXJRsaPy\n4/Ly8njkkUeYPXs29vb2l318WFgYAFvXRjC01/Om+2XBmhCiOpSf6BbXeh9z5ryLTmfF3og+aINP\nwktd4LvP4Pw+sHuDC/6hJKwIZ/zOGcDNW88QGxtLbGys2c9jVlBwcXEhLS3NdDstLQ1XV9crtklP\nT8fFxQWAkpISHn74YZ588kmGDh3Kv+nevS8zZ0VR2CeDtJ1n0Wg2SYFZCFFtyj+Mli9yA+P2GOMm\nrOGYz1kY/QwsXQ8dQ01bYxiHkt69adeuoKAggoKCTLenTJlyXc9j1vCRv78/SUlJpKSkUFxcTERE\nBEOGDKnSZsiQIfzwww8AxMfH4+joiLOzM4qiMGrUKNq1a8eECROu+DqvvL6CmMSHQOvN3+s/45XX\nV9SI+cBCiJojJKQXX8waSHCJM3X2ecOoeyBpoMVtjWFWpmBtbc3cuXMJDg5Gr9czatQofH19Wbhw\nIQCjR49m0KBBREZG4unpSf369Vm0aBEAcXFxLFmyBD8/P7p06QLAxx9/zH333XfJ66S00cGFdZB6\nD9hpSWmjY/PPZ+AJc3ovhBA3VkhILwL7+eE3YQ1pq76EYY/CsklwSIelbI1hEYvXsMuBF7vCtvHQ\n5AjEhNM7YBaxsWHV3T0hhDAp3xqjV+kgQl/bQjL3wPDBsH4W7Bhbpe3N3mX1ehevWcaGeDpHsCmA\ngRNg1nHQOcp+R0KI20751hiOdo7YWzswZ856/v59APlDJ0ODdNjwEaACNhG/5x86Pvw4LfPaMG7c\ngNsma7CITMGt4xjShn4Fcw5Dz89wP2bL3E+H3ja/RCGE+DfBwZNZt+speO5uY41h5TNQRwN9daYi\n9M04A7pGn6fgOuoAnG5CQNsf6Es92r96nMB+ftXdLSGE+E/jxg3Aw/EHWJAA7hvhyWehf26VA3tu\np0VuFpEpzI7/gomf7CT/p8XY2RnH7eSUNSGEpdBoNjFnznrOqbTsuHMuZHaGH6OhsAnGmUnraNgw\nnYAA1xs2lHS9mYJFBIWX//gf389zomD9W9XdHSGEuC7lReh9C+HvFluhTh78/TAcKgbdZ6Z27j6v\nMXKyE2FPmHe9q9HDR/uyEmmqtK/ubgghxHUpDwjh/cJ5e/Rw3Df1gXwn6DMHQjKMW29D1Sn31cQi\ngkJSTiJudu3Q6rRojmiquztCCHFNKs9KCgnpxdxPH6Bv9l3USXKHOzYYj/p0TIG+z0JMXXbFna62\nRW4WMXxUZ0o9hiSn4jTsPdMvVgghLF1w8GTWJfeCh0dAvRyYNQa080zfN2dWUo0ePnJU3DnqJgFB\nCFGzjBs3AHebtXC8L+TXhcFHKoaSqJ5ZSRYRFE6RyP2N3pCAIISoUQL7+dH+1WP0zb8D+2X3QvNd\n8PjASoGhYpHbrRpOsoig0DrnGbZZz5ADdYQQNUr5FtwbNDPo6dkRfogFp0TjGdBsBLsVnO/WggOR\n81m3birjx6+96YHBIoICZ70Z115OWhNC1Cwh3iGmEZBx4wbgYR8BX+0A91h44FXoV3jLF7lZRFAo\nOOWMdys5aU0IUXOFhPRi9uxggrv/SLcDj0CX/VD/FBSXHz52a7bftojZR7YdVnN6SwgODtXdGyGE\nuLnK1zTs+VrPFu9lkNENIl4H/V9AuLHe4BaHh2HLFWcm1ejZR6oCZwkIQogar/Iit0kvPI7buoeh\n1VZ46jmwmWQMCH1DIS3wpg0lWURQcLZ3loVrQoga7+JFbl+GP07gP0+ianIGnukN975Rpcag01nd\n8D5YxPBRQN8suv3vA1mnIISole4ZMpa/u82Hc63hh79Amwaso1GjNDrf2YxeTzS7ZK+kGj18dKaD\nBAQhRO2k1WlpeF8mbstfhuIG8GInaPwzMJWcwtn8pSpk8dRTN6zwbBFBoZeVLFwTQtQ+5TWGJc8t\n4suPRtAndQDqXCt4YSm4bjXWF2LCSTn02Q2rL1hEUDjYWBauCSFqn4trDDGaT7nryGhIHgDP94TD\n95fVFzaxfXsSd/d/m64jhpuVNVhEUHjaRRauCSFqn8qL28rVqVMKBU6w+U14/AFw+wJYS07hAuJs\nc0lYsZDx49de92taRFDwdJWFa0IIodVpqXd/Mu7H7GDDdIgJg2cmQLt2pqEkdI4kZ7xx3a9hEbOP\n9u9X6NChunsihBDVS3NEQ2CrQOI27GPOnPXodFZsrb+M4h4HYOlyOPwg2Gmg7/sQuat6Zh9FRUXh\n4+ODl5cX06dPv2ybcePG4eXlRadOnUhISLimxwK0aGFuL4UQwvKVDyeFhPQiKupD/oyagLObLURP\nhWGPQMd3oO97EBN93a9hVlDQ6/W88sorREVFkZiYyNKlSzl48GCVNpGRkRw9epSkpCS++uorXn75\n5at+bLmuPgN5L+xDWbwmhBBlymcmzRg4BY+TBbBxMjw8DfIHmBa3XQ+zgsL27dvx9PTE3d0dGxsb\nRowYwYoVK6q0WblyJSNHjgQgICAArVZLVlbWVT22XGreUqbt/pFtP+82p7tCCFFjlM9MsveFSdP9\naNrlZ9jtAkHToPc71/28ZgWFjIwM3NzcTLddXV3JyMi4qjaZmZn/+ViTvqGUrN/OD/O3mNNdIYSo\ncTo4deDz7KlseGcZ9W2B5N7QZ9p1P59ZQUGlUl1VO7Nr2RtsQDeLc7nHiY2NNe+5hBDCQmmOaExT\n8wNbBRK6IZQNxzYwsF5fBo7pjS41E1I3wl/X/xrW5nTQxcWFtLQ00+20tDRcXV2v2CY9PR1XV1dK\nSkr+87Em/UogZgKNHbYRFBRkTpeFEMJilM82Kl+rENgqkNfXvU7L803J/W0PZ+pkMcb7K+oUGSjy\nNaD3g447rdjvr4eN1/eaZmUK/v7+JCUlkZKSQnFxMREREQwZMqRKmyFDhvDDDz8AEB8fj6OjI87O\nzlf1WJOYcGzu7cHTY3qa010hhLAo5dlA5YW7x08ksXDHLNa4r+VP3720SCklt4EBvzPw1hbY303P\n+5uv/zXNyhSsra2ZO3cuwcHB6PV6Ro0aha+vLwsXLgRg9OjRDBo0iMjISDw9Palfvz6LFi264mMv\np1XdRxnZ9SkCHu9qTneFEOK2dnFm4GjnyJuBbzLst2G0KmpBxPEICpUieuXBX63hx9VqprY2MChZ\nBSh80xmm/QW7XNSA4br6YBGL10798i3Nhj9X3V0RQogb5uIAAHBCe4KxkWNZ8tASNq9bx+d/hrHT\n+RgFVkXobeCdeDWp+wwU91bz0BEVk+/W02IHTD1nzdYWBuJbKkzcZTxjIehQac3dOlt7/J/q7oIQ\nQtxQFw8NaXVaxv40mrwNybi+58SD8cM53PggL+4txuMQrFpuTWIThR09YWyCmuz6MCvGCmsXFV/n\n6BmQasXEXVbscVL4xfaO6+6XRQSFsymJAHL6mhDCIlWeNVRZr9a9eOq7x+j7XDvc3nMmKmMtJVaH\naberBL0tfBZrRaqjirv+VtEyX8WdmSqaWcHXOXruyVDTskBN2H4rjns78oWTHytb380Jx3sZ9tHn\n191Xixg+WjnYg3t+3Wk6u1TOVhBCWJLKZy8nxMSx9JsZrG+1D73OwMkm5ymtA93+hk8yrLFSYIxv\nKdOTrZneQ89b29T8maYwpolxWCjXRmFZQwMFR+BMPUfadOvB4NGv0GdQSJXXvN6T1ywiKMzob8ux\ncc/y0b0fS0AQQty2Llcn0Oq0fLl8Fsd/38jq5jtR5RVw2t1A+zNQ5xA4u6h4cZ8Vb3mUMv2oFT90\nULCNUZhob02ujcK8Lgbu3gp7tTC2ScWZzF/buzPso88vCQblanRQIAwOPRhNW79+1d0dIYT4V5dm\nBJ+yuvlOrC4UcqGVnjrn4EwLWKyxonWuijG+pcw/aI1DiYrP80pJGQxvbVOTdRa2FiiMbWJFro3C\nHieFzelO2Du3pEkDBxRbu8tmB5Vdb1Awa0rqrfLshTbM2PoZn3p3k0xBCFGtrpQNnPolHr0hl3aR\nrbHWFZHVoYhGWfBUjpoeiVa8565n0VZrfmhvoGuWQtctKhzsjTtD9LZSo6wykNwW7ikwTimdpK2D\nS5s2NHR0YexbVw4CN4pFZAoPT2lHuNMIvnDLkpqCEKJaVc4GHO0c0eq0PPXdYxRqErBteorNLgq2\nOXCmOXwfacWWJIXHndXM62L4z2Gh3YUGfi+yMwaCFi7/mQ1cSY0ePuo27Q6W5fSnYdgnxKXGEeJ9\n86OlEEL8G61Oy9vRb1P/jA3fHf6OXFUBnbQq+p9Q0eOkivfc9UxPNmYEtjEK/m3VdD6lIumCYvaw\n0NWq0cNHx/Rn0R0/Qms7RwkIQoib7t+GiGKOx7B/1y6W7viOZIdsSm0UXjqoIm+niol2FRlA1xgV\nLe1VjE1QE9ZLj7LJwD321nStq6K6hoWulkVkCg7h9qxeXY9eW7LR6rSSLQghbqrKQ0Rb1m9g1rIw\ntjc/Sr51Mc3OWDMivYTV9RRmHq7IBibaW7PZxXDZjGBZQwNHjta9IcNCV6tGZwp3NG7DCdsUzmQd\n4/1dnxHeL7y6uySEsHD/lg3EpcahHC7g8PJY3DY6UWhdQtNm8MJ+NZkJCi82NDCvi4qeMVTJBmZu\nKuV/GcZLate6KqLsmvKFk3FYyNrWjrfeu70ygn9jEZmC5xeePLS/hJzAbnwy/FspNAshzHbx9NEf\nv5tOtNt+Skr0nG2YR8ApKDqmsKOXcYuJlvkqFp7T066jis6nVPyYZbjmBWW3Uo3OFIa3H074uXB2\n27wiAUEIcUMkxMSRv2gfbaNcMRQVom1n4M5MsDqgYsp548V+jG8pq5Ybh4jGJqjRK3BPhnF3oDvr\nqZh3Vs/YJlY4lKh45owVX7dyZ/wVFpRZAosICofPHqaNuimzjy1llu55CQxCiP90ueGhVSsjmLt8\nKmfzzpLaOJvCtgYc0yG9Dfy60gqP82oWntODM5cUjMunkJYHgq51L1pL0MKFYdWcHdwIFjF8dDr/\nNG1mtubPzLtZFuIpaxWEEP9Jq9PyzKInabGukBJDPtvsT3DU7RQ2agPOyfBythXtz8D/vCumj45N\nUPNjloGOfqpbPoX0RqvR6xQUReHehYEMjk3n6UV7ZfaREOI/VxYnXThGsv1xsjqWYlCBKg8mHVDT\nO13Nd2cM1bKg7Faq0UFh9eHVbD2xmZRFM/nxhwJU1tYyNVWIWu7iQvGvX39GZLPd2J7Kp/SOUrKt\nYHCGGr9TENrLwGPfqXjdxjhiPv+svkZkA1dSowvNga0C+TbhWxJbqChKP46ueTPTm0EIUfv8Falh\n5YI5KPo8Oq52xy63mJPtClEVwsM5avpstSLuiIEnyrKBVcutebNbKbkHFRxKVNxZT8XWfQr3NFFb\nxIKyW8kiMgVFUVj25088uvtJHtviyYG2RUwNnsHgIcOru3tCiJvg34rE3/76CXUPF5NhOIpz22Ji\n3QwU6+BCY/gi2or9/xh4qbHxs+7neaUU9TUWiR1KVPyt1/NlFwMLynYltdRhoatVo4ePYjSr+W3S\nRLb2TGKPs3HOcKTqDh618KlfQojLKx8auk/fi5hvFpFy5gTxPkfwMxjY2By88lT0TVXRI0vFR65V\n9xmaaG8MCt831XMuReF/9hUDImHWjSnwdqBTsavFDgtdrRodFCYMDmZo0gZe763HyqDQKk/N2AQ1\nK7z7M3PFmuruohDiBikfFlIXF5FUdJqd3kncYSgmvgX4nYEBJ9Sk71d4rU5FYbhyoTisox6XTZgC\nQU3PBq6kRtcUivV5zOti4P0takYM1jN5m4p5XQw0O59b3V0TQlyji4eG/orU8OvXMzlYlIxD4in8\nfIv4q5XCzqYKnc/BFld46CcINdgAMD9XD01gj5PC2AQ1SVaKae1A2H4rlrkbmHS0Yu3AW7UoENwI\nFhEUMhoVMnGXcVzwzpMG4lvA2AQ1n/sXVnfXhBDXKLBVoGn9wIW002QXJHG6j45MPRR1hpJMFQ8c\nVeO+Rk/pPWre26rmzQ5Vi8TzzuoZi3HKqCXvM3Q7MisonDt3juHDh3PixAnc3d359ddfcXS8dFFZ\nVFQUEyZMQK/X8/zzz/PWW28B8MYbb7B69Wrq1KmDh4cHixYtomHDhpc8fvzjHxBxYCJtnY4RlKbi\nT08DZ096MP6xD2RqqhAWZveGv+G3vWxqn06GG+gaQv8T0HK/ivfzrahjUJFro7C4O3xZViR+KUHN\nS11KWXDQmq5cupJ4rGQDN4xZNYU333yTpk2b8uabbzJ9+nRycnKYNm1alTZ6vZ62bdsSHR2Ni4sL\n3bt3Z+nSpfj6+rJ+/Xr69euHWq3m7bffBrjk8eXjYn9Favjtm8/52zmRw44n+brlewx5YWKVE5CE\nENXnSruO2ibpWfjTVI45nOSgfSaNVQb8s1Ss8FL48w8r3PLUzD+rN20wt9nFgCpVqbKI7G+9nsVN\nbOis9q519YHrUS2FZh8fHzZu3IizszNZWVkEBQVx6NChKm22bt3KlClTiIqKAiou+uVBoNwff/zB\nsmXLWLJkSdUOXvSDaXVaenzaln5FLVHf2VMCghC3iYuPqVz25xJe3zgRJbeErCbncddBUKqaM/8o\nvGKlZn4XBVWcghJonDZaeRFZuY+Upha/iKy6VEuhOTs7G2dnZwCcnZ3Jzs6+pE1GRgZubm6m266u\nrmzbtu2Sdt999x2PPfbYf76mo50j4f0/ZtjaUTz9jR0fznkQQx1bhrz0qrxZhKhGjnaOBBZ1wy/U\ng9LCYrKb5tGxCOyOqZi7w7j1NBjXD8zvW1YkLlWIjTEwr69x3yFAhoWq2X8GhXvvvZesrKxL7g8P\nr7qaWKVSoVKpLml3ufsu91x16tTh8ccfv+z3w8LCTF/79/Tnp+TlOGWpSXTexqcbjdvWfjPpGIC8\ngYS4Ca60z9DRZX9x3CGTxAZZnHPIp2uewraWsGS1Fb45xl1HWzauuA40cldxLkbBwV5lXE1cCEtj\nbQnv2owOVr4yW+g6xcbGEhsba/bzmD18FBsbS/PmzTl58iR9+vS5ZPgoPj6esLAw0/DRxx9/jFqt\nNhWbv//+e77++ms2bNiAnZ3dpR2slAKVp6eGbw7R5dRGptyp566TKl5NMAaGJe37yboFIW6CykND\nuzf8zYIlH7DB+QCleh0qe4Ve6SoKDsLrRWq+66hgHadQWjYsVPkwmnK7Cw0sVzfCt30HGRa6Sa53\n+EhtzosOGTKExYsXA7B48WKGDh16SRt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Bp24mwMfH5fsMThjLyUNfM//2JxyTvDt1nfTR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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 264 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "cb = np.zeros(x.size, dtype=float)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 260 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x_j.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101\n" + ] + } + ], + "prompt_number": 261 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101\n" + ] + } + ], + "prompt_number": 262 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 262 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 262 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 262 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Airfoil characteristics - amiya/Airfoil generator/NACA 4 cambered/NACA4 camber.ipynb b/Airfoil characteristics - amiya/Airfoil generator/NACA 4 cambered/NACA4 camber.ipynb new file mode 100644 index 0000000..3a48b33 --- /dev/null +++ b/Airfoil characteristics - amiya/Airfoil generator/NACA 4 cambered/NACA4 camber.ipynb @@ -0,0 +1,271 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:0a5f03f38f100bca0a018824ee2aa0b6a5097208f48e86d9b6031ee53a55fb06" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "import csv" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "with open (r'C:\\Users\\Amiya\\Documents\\GWU\\AeroHydro\\Project\\Airfoil characteristics/2412.txt') as file_name:\n", + " x_j, y_j = np.loadtxt(file_name, dtype=float, delimiter='\\t', unpack=True)\n", + " \n", + "plt.plot(x_j,y_j)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 9, + "text": [ + "[]" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c = 1.0 #chord\n", + "thickness = 12.0 #thickness as a percent of chord\n", + "camber = 2.0 #max camber as a percent of chord\n", + "camber_loc = 4.0 #location of max camber as 1/10 percent of a chord\n", + "\n", + "t = thickness/100.0 #max thickness as a fraction of the chord\n", + "m = camber/100.0\n", + "p = camber_loc/10.0 \n", + "\n", + "N = 202 #number of points describing airfoil\n", + "theta_u = np.linspace(0., np.pi, N/2)\n", + "x = np.linspace(0., c, N/2)\n", + "#theta_l = np.linspace(np.pi, 2*np.pi, N/2)\n", + "y_t = (t/0.2)*(0.2969*np.sqrt(x) - 0.126*x - 0.3516*x**2 + 0.2843*x**3 - 0.1015*x**4)\n", + "\n", + "print x.size\n", + "print y_t.size\n", + "print y_t[0]\n", + "plt.plot(x,y_t)\n", + "print thickness/100\n", + "print camber/100\n", + "print camber_loc/10" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101\n", + "101\n", + "0.0\n", + "0.12\n", + "0.02\n", + "0.4\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = np.zeros(x.size, dtype=float)\n", + "y_u = np.zeros(x.size, dtype=float)\n", + "x_l = np.zeros(x.size, dtype=float)\n", + "y_l = np.zeros(x.size, dtype=float)\n", + "y_c = np.zeros(x.size, dtype=float)\n", + "dyc_dx = np.zeros(x.size, dtype=float)\n", + "\n", + "for i in range(N/2-1):\n", + " if x[i]>p*c:\n", + " y_c[i] = (m/(1-p)**2)*((1-(2*p))+(2*p*x[i])-x[i]**2)\n", + " dyc_dx[i] = (2*m/(1-p)**2)*(p-x[i])\n", + " else:\n", + " y_c[i] = (m/p**2)*((2*p*x[i])-x[i]**2)\n", + " dyc_dx[i] = (2*m/p**2)*(p-x[i])\n", + "\n", + "plt.plot(x[0:N/4],y_c[0:N/4])\n", + "print y_c[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = x - y_t*np.sin(np.arctan(dyc_dx))\n", + "y_u = y_c + y_t*np.cos(np.arctan(dyc_dx))\n", + " #print i, x_u[i]\n", + " \n", + "x_l = x + y_t*np.sin(np.arctan(dyc_dx))\n", + "y_l = y_c - y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + "x_l[0], y_l[0] = x_u[0], y_u[0]\n", + "x_l[N/2 - 1], y_l[N/2 - 1] = x_u[N/2 - 1], y_u[N/2 - 1]\n", + "\n", + "print x_l[0], y_l[0],x_u[0], y_u[0]\n", + "print x_l[N/2 - 1], y_l[N/2 - 1],x_u[N/2 - 1], y_u[N/2 - 1]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0 0.0 0.0 0.0\n", + "1.0 0.00126 1.0 0.00126\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#plt.plot(x_u, y_u, marker='x')\n", + "plt.plot(x_l, y_l, color='#CD2305', marker='o')\n", + "plt.plot(x_u, y_u, marker='o')\n", + "plt.plot(x_j,y_j, color='g', marker='x')\n", + "#plt.scatter(x_j, y_j, marker='o')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 13, + "text": [ + "[]" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "cb = np.zeros(x.size, dtype=float)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x_j.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Airfoil characteristics - amiya/Airfoil generator/NACA airfoil gen/Source-vortex panel method-naca foil vary density.ipynb b/Airfoil characteristics - amiya/Airfoil generator/NACA airfoil gen/Source-vortex panel method-naca foil vary density.ipynb new file mode 100644 index 0000000..6ffcbf2 --- /dev/null +++ b/Airfoil characteristics - amiya/Airfoil generator/NACA airfoil gen/Source-vortex panel method-naca foil vary density.ipynb @@ -0,0 +1,853 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:ad7daac29beb4462e64198961c04cbf1dc6de1c296c5669ddfecbbad4a98032c" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as np\n", + "from scipy import integrate\n", + "import matplotlib.pyplot as plt" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 284 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Generate airfoil\n", + "c = 1.0 #chord\n", + "thickness = 12.0 #thickness as a percent of chord\n", + "camber = 2.0 #max camber as a percent of chord\n", + "camber_loc = 4.0 #location of max camber as 1/10 percent of a chord\n", + "\n", + "t = thickness/100.0 #max thickness as a fraction of the chord\n", + "m = camber/100.0\n", + "p = camber_loc/10.0 \n", + "\n", + "r = 1.1019*t**2 #leading edge radius\n", + "\n", + "N = 101 #number of points describing airfoil\n", + "theta_u = np.linspace(0., np.pi, N/2)\n", + "x_for = np.linspace(0,r,N/10)\n", + "x_mid = np.linspace(r+r,(0.75*c)-r,1+N/4)\n", + "x_aft = np.linspace(r + 0.75*c, c, 3*N/20)\n", + "x1 = np.append(x_for,x_mid)\n", + "x_chord = np.append(x1,x_aft)\n", + "\n", + "#theta_l = np.linspace(np.pi, 2*np.pi, N/2)\n", + "y_t = (t/0.2)*(0.2969*np.sqrt(x_chord) - 0.126*x_chord - 0.3516*x_chord**2 + 0.2843*x_chord**3 - 0.1015*x_chord**4)\n", + "\n", + "print x_chord.size\n", + "print x_chord[N/2]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "51\n", + "1.0\n" + ] + } + ], + "prompt_number": 285 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = np.zeros(x_chord.size, dtype=float)\n", + "y_u = np.zeros(x_chord.size, dtype=float)\n", + "x_l = np.zeros(x_chord.size, dtype=float)\n", + "y_l = np.zeros(x_chord.size, dtype=float)\n", + "y_c = np.zeros(x_chord.size, dtype=float)\n", + "dyc_dx = np.zeros(x_chord.size, dtype=float)\n", + "\n", + "for i in range(N/2-1):\n", + " if x_chord[i]>p*c:\n", + " y_c[i] = (m/(1-p)**2)*((1-(2*p))+(2*p*x_chord[i])-x_chord[i]**2)\n", + " dyc_dx[i] = (2*m/(1-p)**2)*(p-x_chord[i])\n", + " else:\n", + " y_c[i] = (m/p**2)*((2*p*x_chord[i])-x_chord[i]**2)\n", + " dyc_dx[i] = (2*m/p**2)*(p-x_chord[i])\n", + "\n", + "plt.plot(x_chord[0:N/4],y_c[0:N/4])\n", + "print y_c[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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Dg7n00ktbbZuUlEROTg4zZ84kJyeHcePGtfj65eXlzuKJiIibOC0O3bp1IzMz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\nkWZUHEREpBkVBxERaeb/AQygXPqwu8KuAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 286 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = x_chord - y_t*np.sin(np.arctan(dyc_dx))\n", + "y_u = y_c + y_t*np.cos(np.arctan(dyc_dx))\n", + " #print i, x_u[i]\n", + " \n", + "x_l = x_chord + y_t*np.sin(np.arctan(dyc_dx))\n", + "y_l = y_c - y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + "#x_l[0], y_l[0] = x_u[0], y_u[0]\n", + "#x_l[N/2 - 1], y_l[N/2 - 1] = x_u[N/2 - 1], y_u[N/2 - 1]\n", + "#x_l[0], y_l[0] = 0.0, 0.0\n", + "#x_u[0], y_u[0] = 0.0, 0.0\n", + "#x_l[N/2 - 1], y_l[N/2 - 1] = 1.0, 0.0\n", + "#x_u[N/2 - 1], y_u[N/2 - 1] = 1.0, 0.0\n", + "\n", + "print x_l[0], y_l[0],x_u[0], y_u[0]\n", + "#print x_l[N/2 - 1], y_l[N/2 - 1],x_u[N/2 - 1], y_u[N/2 - 1]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0 0.0 0.0 0.0\n" + ] + } + ], + "prompt_number": 287 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.scatter(x_l, y_l, color='#CD2305', marker='o')\n", + "#plt.plot(x_u[N/2 - 1], y_u[N/2 - 1],marker='d',markersize=10,color='k')\n", + "plt.scatter(x_u, y_u, marker='o' )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 288, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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UhF7fgrM93Q0wGAIpKSnRMlaN5nNRSEtLIzY2lujoaGbMmHHBNhMmTCA6Opr4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\nxjx4UWCMMebBiwJjjDEPXhQYY4x5/AO36EioF8U76QAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 288 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x = np.concatenate((x_u,list(reversed(x_l))))\n", + "y = np.concatenate((y_u,list(reversed(y_l))))\n", + "#x = np.append(x_u,x_l[1:N/2])\n", + "#y = np.append(y_u,y_l[1:N/2])\n", + "\n", + "# plots the geometry\n", + "%matplotlib inline\n", + "\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = x.min(), x.max()\n", + "y_min, y_max = y.min(), y.max()\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = y_min-val_y*(y_max-y_min), y_max+val_y*(y_max-y_min)\n", + "\n", + "size = 10\n", + "pyplot.figure(figsize=(size, (y_end-y_start)/(x_end-x_start)*size))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('y', fontsize=16)\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "#pyplot.plot(x, y, color='k', linestyle='-', linewidth=2)\n", + "pyplot.scatter(x, y, color='k');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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w7enpifT0dJOPkUgk6NChA4KDg7FixQrzNLoCu3nzpt62KWt5uru74+DBgygoKEBubi4+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\nRE5OTtSmTRuTHj9mZmbSDz/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+ "text": [ + "" + ] + } + ], + "prompt_number": 289 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x_u.size\n", + "print x.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "51\n", + "102\n" + ] + } + ], + "prompt_number": 290 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Panel:\n", + " \"\"\"Contains information related to one panel.\"\"\"\n", + " def __init__(self, xa, ya, xb, yb):\n", + " \"\"\"Creates a panel.\n", + " \n", + " Arguments\n", + " ---------\n", + " xa, ya -- Cartesian coordinates of the first end-point.\n", + " xb, yb -- Cartesian coordinates of the second end-point.\n", + " \"\"\"\n", + " self.xa, self.ya = xa, ya\n", + " self.xb, self.yb = xb, yb\n", + " \n", + " self.xc, self.yc = (xa+xb)/2, (ya+yb)/2 # control-point (center-point)\n", + " self.length = math.sqrt((xb-xa)**2+(yb-ya)**2) # length of the panel\n", + " \n", + " # orientation of the panel (angle between x-axis and panel's normal)\n", + " if xb-xa <= 0.:\n", + " self.beta = math.acos((yb-ya)/self.length)\n", + " elif xb-xa > 0.:\n", + " self.beta = math.pi + math.acos(-(yb-ya)/self.length)\n", + " \n", + " # location of the panel\n", + " if self.beta <= math.pi:\n", + " self.loc = 'extrados'\n", + " else:\n", + " self.loc = 'intrados'\n", + " \n", + " self.sigma = 0. # source strength\n", + " self.vt = 0. # tangential velocity\n", + " self.cp = 0. # pressure coefficient" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 291 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def define_panels(x, y, N=40):\n", + " \"\"\"Discretizes the geometry into panels using 'cosine' method.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y -- Cartesian coordinates of the geometry (1D arrays).\n", + " N - number of panels (default 40).\n", + " \n", + " Returns\n", + " -------\n", + " panels -- Numpy array of panels.\n", + " \"\"\"\n", + " \n", + " panels = np.empty(N, dtype=object)\n", + " for i in xrange(N):\n", + " panels[i] = Panel(x[i], y[i], x[i+1], y[i+1])\n", + " \n", + " return panels" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 292 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#N = 100 # number of panels\n", + "#anelsu = define_panels(x_u[0:N/2], y_u[0:N/2], N/2) # discretizes of the geometry into panels\n", + "#anelsl = define_panels(x_l[0:N/2], y_l[0:N/2], N/2)\n", + "#panels = np.concatenate((panelsu, panelsl))\n", + "panels = define_panels(x,y,(len(x)-1))\n", + "# plots the geometry and the panels\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "y_min, y_max = min( panel.ya for panel in panels ), max( panel.ya for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = y_min-val_y*(y_max-y_min), y_max+val_y*(y_max-y_min)\n", + "\n", + "size = 10\n", + "pyplot.figure(figsize=(size, (y_end-y_start)/(x_end-x_start)*size))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('y', fontsize=16)\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "pyplot.plot(x, y, color='k', linestyle='-', linewidth=2)\n", + "#yplot.plot(x_l, y_l, color='k', linestyle='-', linewidth=2)\n", + "pyplot.plot(np.append([panel.xa for panel in panels], panels[0].xa), \n", + " np.append([panel.ya for panel in panels], panels[0].ya), \n", + " linestyle='-', linewidth=1, marker='o', markersize=6, color='#CD2305');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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KBvpr2W21sjcwkszeN3HtLQP424030u+n/Syb9vgFrY8GdV0wrv5ibokx93QS80vv7L+l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\nPKRF1dfTtvv169e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+ "text": [ + "" + ] + } + ], + "prompt_number": 293 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Freestream:\n", + " \"\"\"Freestream conditions.\"\"\"\n", + " def __init__(self, u_inf=1.0, alpha=0.0):\n", + " \"\"\"Sets the freestream conditions.\n", + " \n", + " Arguments\n", + " ---------\n", + " u_inf -- Farfield speed (default 1.0).\n", + " alpha -- Angle of attack in degrees (default 0.0).\n", + " \"\"\"\n", + " self.u_inf = u_inf\n", + " self.alpha = alpha*math.pi/180 # degrees --> radians" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 294 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "u_inf = 1.0 # freestream spee\n", + "alpha = 0.0 # angle of attack (in degrees)\n", + "freestream = Freestream(u_inf, alpha) # instantiation of the object freestream" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 295 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def integral(x, y, panel, dxdz, dydz):\n", + " \"\"\"Evaluates the contribution of a panel at one point.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y -- Cartesian coordinates of the point.\n", + " panel -- panel which contribution is evaluated.\n", + " dxdz -- derivative of x in the z-direction.\n", + " dydz -- derivative of y in the z-direction.\n", + " \n", + " Returns\n", + " -------\n", + " Integral over the panel of the influence at one point.\n", + " \"\"\"\n", + " def func(s):\n", + " return ( ((x - (panel.xa - math.sin(panel.beta)*s))*dxdz \n", + " + (y - (panel.ya + math.cos(panel.beta)*s))*dydz)\n", + " / ((x - (panel.xa - math.sin(panel.beta)*s))**2 \n", + " + (y - (panel.ya + math.cos(panel.beta)*s))**2) )\n", + " return integrate.quad(lambda s:func(s), 0., panel.length)[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 296 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def source_matrix(panels):\n", + " \"\"\"Builds the source matrix.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " A -- NxN matrix (N is the number of panels).\n", + " \"\"\"\n", + " A = numpy.empty((panels.size, panels.size), dtype=float)\n", + " numpy.fill_diagonal(A, 0.5)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " A[i,j] = 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.cos(p_i.beta), math.sin(p_i.beta))\n", + " \n", + " return A" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 297 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def vortex_array(panels):\n", + " \"\"\"Builds the vortex array.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels - array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " a -- 1D array (Nx1, N is the number of panels).\n", + " \"\"\"\n", + " a = numpy.zeros(panels.size, dtype=float)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " a[i] -= 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.sin(p_i.beta), -math.cos(p_i.beta))\n", + " return a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 298 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def kutta_array(panels):\n", + " \"\"\"Builds the Kutta-condition array.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " a -- 1D array (Nx1, N is the number of panels).\n", + " \"\"\"\n", + " N = panels.size\n", + " a = numpy.zeros(N+1, dtype=float)\n", + " # contribution from the source sheet of the first panel on the last one\n", + " a[0] = 0.5/math.pi*integral(panels[N-1].xc, panels[N-1].yc, panels[0], \n", + " -math.sin(panels[N-1].beta), +math.cos(panels[N-1].beta))\n", + " # contribution from the source sheet of the last panel on the first one\n", + " a[N-1] = 0.5/math.pi*integral(panels[0].xc, panels[0].yc, panels[N-1], \n", + " -math.sin(panels[0].beta), +math.cos(panels[0].beta))\n", + " # contribution from the vortex sheet of the first panel on the last one\n", + " a[N] -= 0.5/math.pi*integral(panels[-1].xc, panels[-1].yc, panels[0], \n", + " +math.cos(panels[-1].beta), math.sin(panels[-1].beta))\n", + " # contribution from the vortex sheet of the last panel on the first one\n", + " a[N] -= 0.5/math.pi*integral(panels[0].xc, panels[0].yc, panels[-1], \n", + " +math.cos(panels[0].beta), math.sin(panels[0].beta))\n", + " # contribution from the vortex sheet of the first panel on itself\n", + " a[N] -= 0.5\n", + " # contribution from the vortex sheet of the last panel on itself\n", + " a[N] -= 0.5\n", + " \n", + " # contribution from the other panels on the first and last ones\n", + " for i, panel in enumerate(panels[1:-1]):\n", + " # contribution from the source sheet\n", + " a[i+1] = 0.5/math.pi*(integral(panels[0].xc, panels[0].yc, panel, \n", + " -math.sin(panels[0].beta), +math.cos(panels[0].beta))\n", + " + integral(panels[N-1].xc, panels[N-1].yc, panel, \n", + " -math.sin(panels[N-1].beta), +math.cos(panels[N-1].beta)) )\n", + "\n", + " # contribution from the vortex sheet\n", + " a[N] -= 0.5/math.pi*(integral(panels[0].xc, panels[0].yc, panel, \n", + " +math.cos(panels[0].beta), math.sin(panels[0].beta))\n", + " + integral(panels[-1].xc, panels[-1].yc, panel, \n", + " +math.cos(panels[-1].beta), math.sin(panels[-1].beta)) )\n", + " \n", + " return a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 299 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_matrix(panels):\n", + " \"\"\"Builds the matrix of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " A -- (N+1)x(N+1) matrix (N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " A = numpy.empty((N+1, N+1), dtype=float)\n", + " \n", + " AS = source_matrix(panels)\n", + " av = vortex_array(panels)\n", + " ak = kutta_array(panels)\n", + " \n", + " A[0:N,0:N], A[0:N,N], A[N,:] = AS[:,:], av[:], ak[:]\n", + " \n", + " return A" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 300 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_rhs(panels, freestream):\n", + " \"\"\"Builds the RHS of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " \n", + " Returns\n", + " -------\n", + " b -- 1D array ((N+1)x1, N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " b = numpy.empty(N+1,dtype=float)\n", + " \n", + " for i, panel in enumerate(panels):\n", + " b[i] = - freestream.u_inf * math.cos(freestream.alpha - panel.beta)\n", + " b[N] = -freestream.u_inf*( math.sin(freestream.alpha-panels[0].beta)\n", + " +math.sin(freestream.alpha-panels[N-1].beta) )\n", + " \n", + " return b" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 301 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "A = build_matrix(panels) # calculates the singularity matrix\n", + "b = build_rhs(panels, freestream) # calculates the freestream RHS" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 302 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# solves the linear system\n", + "variables = numpy.linalg.solve(A, b)\n", + "\n", + "for i, panel in enumerate(panels):\n", + " panel.sigma = variables[i]\n", + "gamma = variables[-1]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 303 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_tangential_velocity(panels, freestream, gamma):\n", + " \"\"\"Computes the tangential velocity on the surface.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " gamma -- circulation density.\n", + " \"\"\"\n", + " N = len(panels)\n", + " A = numpy.empty((N, N+1), dtype=float)\n", + " numpy.fill_diagonal(A, 0.0)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " # contribution from vortex on itself\n", + " A[i, N] = -0.5\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " # contribution from the sources\n", + " A[i,j] = 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " -math.sin(p_i.beta), math.cos(p_i.beta))\n", + " # contribution the vortices\n", + " A[i,N] -= 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.cos(p_i.beta), math.sin(p_i.beta))\n", + "\n", + " b = freestream.u_inf * numpy.sin([freestream.alpha - panel.beta for panel in panels])\n", + " \n", + " var = numpy.append([panel.sigma for panel in panels], gamma)\n", + " \n", + " vt = numpy.dot(A, var) + b\n", + " for i, panel in enumerate(panels):\n", + " panel.vt = vt[i]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 304 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# computes the tangential velocity at each panel center.\n", + "get_tangential_velocity(panels, freestream, gamma)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 305 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_pressure_coefficient(panels, freestream):\n", + " \"\"\"Computes the surface pressure coefficients.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " \"\"\"\n", + " for panel in panels:\n", + " panel.cp = 1.0 - (panel.vt/freestream.u_inf)**2" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 306 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# computes surface pressure coefficient\n", + "get_pressure_coefficient(panels, freestream)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 307 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# plots the surface pressure coefficient\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = cp_min-val_y*(cp_max-cp_min), cp_max+val_y*(cp_max-cp_min)\n", + "\n", + "pyplot.figure(figsize=(10, 6))\n", + "pyplot.grid(True)\n", + "pyplot.xlabel('x', fontsize=16)\n", + "pyplot.ylabel('$C_p$', fontsize=16)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'extrados'], \n", + " [panel.cp for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=2, marker='o', markersize=6)\n", + "pyplot.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cp for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='o', markersize=6)\n", + "pyplot.legend(['lower', 'upper'], loc='best', prop={'size':14})\n", + "pyplot.xlim(x_start, x_end)\n", + "pyplot.ylim(y_start, y_end)\n", + "pyplot.gca().invert_yaxis()\n", + "pyplot.title('Number of panels : %d' % N);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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mq6uryba3t7dV+ywnhuFmEoeZi8fMxWPm4ikxc7W9O2BvMaNHY3JEhMm+SRERiE5IkMX1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\nMyIiIiID+R+oXZYtrHvVpAAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 308 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# calculates the accuracy\n", + "accuracy = sum([panel.sigma*panel.length for panel in panels])\n", + "print '--> sum of source/sink strengths:', accuracy" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "--> sum of source/sink strengths: 0.384916029442\n" + ] + } + ], + "prompt_number": 309 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# calculates of the lift\n", + "cl = gamma*sum(panel.length for panel in panels)/(0.5*freestream.u_inf*(x_max-x_min))\n", + "print '--> Lift coefficient: Cl = %.3f' % cl" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "--> Lift coefficient: Cl = 1.185\n" + ] + } + ], + "prompt_number": 310 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "total_panels = len(panels)\n", + "lift=0.0\n", + "for panel in enumerate(panels):\n", + " lift -= [panel.cp for panel in panels] * [panel.length for panel in panels] * math.sin([panel.beta for panel in panels])\n", + "print lift" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "TypeError", + "evalue": "can't multiply sequence by non-int of type 'list'", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[0mlift\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0.0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mpanel\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpanels\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0mlift\u001b[0m \u001b[1;33m-=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mpanel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcp\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mpanel\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mpanels\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mpanel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlength\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mpanel\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mpanels\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mpanel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbeta\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mpanel\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mpanels\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 5\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[0mlift\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mTypeError\u001b[0m: can't multiply sequence by non-int of type 'list'" + ] + } + ], + "prompt_number": 311 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print math.sin(panel.beta)" + ], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print len(panels)" + ], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Airfoil characteristics - amiya/Airfoil generator/NACA camber-Copy0.ipynb b/Airfoil characteristics - amiya/Airfoil generator/NACA camber-Copy0.ipynb new file mode 100644 index 0000000..b0e0cd2 --- /dev/null +++ b/Airfoil characteristics - amiya/Airfoil generator/NACA camber-Copy0.ipynb @@ -0,0 +1,236 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:1dac7e7a2e4669b403f6d7ada6419065ecc482cb6327127c26da498efd5889e3" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "import csv" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "with open (r'C:\\Users\\Amiya\\Documents\\GWU\\AeroHydro\\Project\\Airfoil characteristics/2412.txt') as file_name:\n", + " x_j, y_j = np.loadtxt(file_name, dtype=float, delimiter='\\t', unpack=True)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c = 1.0 #chord\n", + "thickness = 12 #thickness as a percent of chord\n", + "camber = 2.0 #max camber as a percent of chord\n", + "camber_loc = 4.0 #location of max camber as 1/10 percent of a chord\n", + "\n", + "t = thickness/100 #max thickness as a fraction of the chord\n", + "m = camber/100\n", + "p = camber_loc/10 \n", + "\n", + "N = 202 #number of points describing airfoil\n", + "theta_u = np.linspace(0, np.pi, N/2)\n", + "x = np.linspace(0, c, N/2)\n", + "theta_l = np.linspace(np.pi, 2*np.pi, N/2)\n", + "y_t = (t/0.2)*(0.2969*np.sqrt(x) - 0.126*x - 0.3516*x**2 + 0.2843*x**3 - 0.1015*x**4)\n", + "print theta_u.size, theta_l.size\n", + "print x.size\n", + "print y_t.size\n", + "print y_t[0]\n", + "plt.plot(x,y_t)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101 101\n", + "101\n", + "101\n", + "0.0\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 12, + "text": [ + "[]" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = np.zeros(x.size, dtype=float)\n", + "y_u = np.zeros(x.size, dtype=float)\n", + "x_l = np.zeros(x.size, dtype=float)\n", + "y_l = np.zeros(x.size, dtype=float)\n", + "y_c = np.zeros(x.size, dtype=float)\n", + "dyc_dx = np.zeros(x.size, dtype=float)\n", + "\n", + "for i in range(N/2-1):\n", + " if x[i]>p*c:\n", + " y_c[i] = (m/(1-p)**2)*((1-(2*p))+(2*p*x[i])-x[i]**2)\n", + " dyc_dx[i] = (2*m/(1-p)**2)*(p-x[i])\n", + " else:\n", + " y_c[i] = (m/p**2)*((2*p*x[i])-x[i]**2)\n", + " dyc_dx[i] = (2*m/p**2)*(p-x[i])\n", + "\n", + "plt.plot(x[0:N/4],y_c[0:N/4])\n", + "print y_c[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = x - y_t*np.sin(np.arctan(dyc_dx))\n", + "y_u = y_c + y_t*np.cos(np.arctan(dyc_dx))\n", + " #print i, x_u[i]\n", + " \n", + "x_l = x + y_t*np.sin(np.arctan(dyc_dx))\n", + "y_l = y_c - y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + "x_l[0], y_l[0] = x_u[0], y_u[0]\n", + "x_l[N/2 - 1], y_l[N/2 - 1] = x_u[N/2 - 1], y_u[N/2 - 1]\n", + "\n", + "print x_l[0], y_l[0],x_u[0], y_u[0]\n", + "print x_l[N/2 - 1], y_l[N/2 - 1],x_u[N/2 - 1], y_u[N/2 - 1]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0 0.0 0.0 0.0\n", + "1.0 0.0 1.0 0.0\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#plt.plot(x_u, y_u, marker='x')\n", + "plt.plot(x_l, y_l, color='#CD2305')\n", + "plt.plot(x_u, y_u)\n", + "#plt.scatter(x_j, y_j, marker='o')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 15, + "text": [ + "[]" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "cb = np.zeros(x.size, dtype=float)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x_j.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "101\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 18 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Airfoil characteristics - amiya/NACA_2412.dat b/Airfoil characteristics - amiya/NACA_2412.dat new file mode 100644 index 0000000..fc6af6c --- /dev/null +++ b/Airfoil characteristics - amiya/NACA_2412.dat @@ -0,0 +1,100 @@ +NACA 2412 + 1.00000 0.00126 + 0.99280 0.00274 + 0.97989 0.00537 + 0.96352 0.00862 + 0.94455 0.01231 + 0.92350 0.01629 + 0.90075 0.02045 + 0.87658 0.02474 + 0.85123 0.02907 + 0.82489 0.03340 + 0.79774 0.03769 + 0.76991 0.04190 + 0.74154 0.04600 + 0.71275 0.04995 + 0.68365 0.05374 + 0.65434 0.05734 + 0.62492 0.06073 + 0.59547 0.06388 + 0.56607 0.06679 + 0.53680 0.06944 + 0.50774 0.07180 + 0.47895 0.07387 + 0.45050 0.07564 + 0.42246 0.07709 + 0.39488 0.07821 + 0.36782 0.07893 + 0.34135 0.07922 + 0.31551 0.07907 + 0.29035 0.07849 + 0.26594 0.07750 + 0.24231 0.07609 + 0.21951 0.07429 + 0.19760 0.07211 + 0.17661 0.06957 + 0.15660 0.06670 + 0.13760 0.06350 + 0.11965 0.06001 + 0.10280 0.05625 + 0.08709 0.05226 + 0.07256 0.04805 + 0.05924 0.04366 + 0.04717 0.03911 + 0.03639 0.03443 + 0.02694 0.02965 + 0.01885 0.02480 + 0.01215 0.01988 + 0.00688 0.01493 + 0.00308 0.00996 + 0.00078 0.00498 + 0.00000 0.00000 + 0.00078 -0.00482 + 0.00308 -0.00935 + 0.00688 -0.01357 + 0.01215 -0.01749 + 0.01885 -0.02112 + 0.02694 -0.02445 + 0.03639 -0.02749 + 0.04717 -0.03023 + 0.05924 -0.03269 + 0.07256 -0.03485 + 0.08709 -0.03674 + 0.10280 -0.03833 + 0.11965 -0.03966 + 0.13760 -0.04071 + 0.15660 -0.04151 + 0.17661 -0.04205 + 0.19760 -0.04236 + 0.21951 -0.04244 + 0.24231 -0.04231 + 0.26594 -0.04199 + 0.29035 -0.04150 + 0.31551 -0.04086 + 0.34135 -0.04008 + 0.36782 -0.03919 + 0.39488 -0.03822 + 0.42246 -0.03715 + 0.45050 -0.03592 + 0.47895 -0.03457 + 0.50774 -0.03309 + 0.53680 -0.03151 + 0.56607 -0.02985 + 0.59547 -0.02813 + 0.62492 -0.02635 + 0.65434 -0.02453 + 0.68365 -0.02268 + 0.71275 -0.02082 + 0.74154 -0.01896 + 0.76991 -0.01711 + 0.79774 -0.01527 + 0.82489 -0.01346 + 0.85123 -0.01169 + 0.87658 -0.00997 + 0.90075 -0.00831 + 0.92350 -0.00674 + 0.94455 -0.00526 + 0.96352 -0.00391 + 0.97989 -0.00273 + 0.99280 -0.00179 + 1.00000 -0.00126 diff --git a/Airfoil characteristics - amiya/NACA_2412.txt b/Airfoil characteristics - amiya/NACA_2412.txt new file mode 100644 index 0000000..ed7483a --- /dev/null +++ b/Airfoil characteristics - amiya/NACA_2412.txt @@ -0,0 +1,99 @@ +1.00000 0.00126 +0.99280 0.00274 +0.97989 0.00537 +0.96352 0.00862 +0.94455 0.01231 +0.92350 0.01629 +0.90075 0.02045 +0.87658 0.02474 +0.85123 0.02907 +0.82489 0.03340 +0.79774 0.03769 +0.76991 0.04190 +0.74154 0.04600 +0.71275 0.04995 +0.68365 0.05374 +0.65434 0.05734 +0.62492 0.06073 +0.59547 0.06388 +0.56607 0.06679 +0.53680 0.06944 +0.50774 0.07180 +0.47895 0.07387 +0.45050 0.07564 +0.42246 0.07709 +0.39488 0.07821 +0.36782 0.07893 + 0.34135 0.07922 + 0.31551 0.07907 + 0.29035 0.07849 + 0.26594 0.07750 + 0.24231 0.07609 + 0.21951 0.07429 + 0.19760 0.07211 + 0.17661 0.06957 + 0.15660 0.06670 + 0.13760 0.06350 + 0.11965 0.06001 + 0.10280 0.05625 + 0.08709 0.05226 + 0.07256 0.04805 + 0.05924 0.04366 + 0.04717 0.03911 + 0.03639 0.03443 + 0.02694 0.02965 + 0.01885 0.02480 + 0.01215 0.01988 + 0.00688 0.01493 + 0.00308 0.00996 + 0.00078 0.00498 + 0.00000 0.00000 + 0.00078 -0.00482 + 0.00308 -0.00935 + 0.00688 -0.01357 + 0.01215 -0.01749 + 0.01885 -0.02112 + 0.02694 -0.02445 + 0.03639 -0.02749 + 0.04717 -0.03023 + 0.05924 -0.03269 + 0.07256 -0.03485 + 0.08709 -0.03674 + 0.10280 -0.03833 + 0.11965 -0.03966 + 0.13760 -0.04071 + 0.15660 -0.04151 + 0.17661 -0.04205 + 0.19760 -0.04236 + 0.21951 -0.04244 + 0.24231 -0.04231 + 0.26594 -0.04199 + 0.29035 -0.04150 + 0.31551 -0.04086 + 0.34135 -0.04008 + 0.36782 -0.03919 + 0.39488 -0.03822 + 0.42246 -0.03715 + 0.45050 -0.03592 + 0.47895 -0.03457 + 0.50774 -0.03309 + 0.53680 -0.03151 + 0.56607 -0.02985 + 0.59547 -0.02813 + 0.62492 -0.02635 + 0.65434 -0.02453 + 0.68365 -0.02268 + 0.71275 -0.02082 + 0.74154 -0.01896 + 0.76991 -0.01711 + 0.79774 -0.01527 + 0.82489 -0.01346 + 0.85123 -0.01169 + 0.87658 -0.00997 + 0.90075 -0.00831 + 0.92350 -0.00674 + 0.94455 -0.00526 + 0.96352 -0.00391 + 0.97989 -0.00273 + 0.99280 -0.00179 + 1.00000 -0.00126 diff --git a/Airfoil characteristics - amiya/Report.7z b/Airfoil characteristics - amiya/Report.7z new file mode 100644 index 0000000..eb5536c Binary files /dev/null and b/Airfoil characteristics - amiya/Report.7z differ diff --git a/Airfoil characteristics - amiya/Report/.ipynb_checkpoints/Airfoil Characteristics-checkpoint.ipynb b/Airfoil characteristics - amiya/Report/.ipynb_checkpoints/Airfoil Characteristics-checkpoint.ipynb new file mode 100644 index 0000000..b711772 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/.ipynb_checkpoints/Airfoil Characteristics-checkpoint.ipynb @@ -0,0 +1,1063 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:ed34c8df3966d6997427ecd04c9695924981e3c0ea1d154e0a1402f80a6bca38" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "A study into airfoil geometry using panel methods" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Serious study into the effects of airfoil sections began almost 200 years ago. While it was known that flat plates could generate lift, theorizing that the curved shapes of bird wings may be more efficient in generating lift, researchers began looking at more curved or cambered surfaces. Otto Lilienthal was the first to conduct meticulous and properly documented experiments on airfoil shapes. Lilienthal experimented on varying camber, the nose radii and thickness distribution.\n", + "\n", + "Most airfoils developed during the years after Lilienthal, were designed through trial and error. Some of these designs lay the foundation for the NACA series of airfoils that are predominantly used in modern aircrafts." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Objective" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The effects of changing specific geometric parameters are studied using NACA 4 ***and 5 series airfoils***. The effects on maximum lift, drag, stall characteristics and pitching moment are all taken into account. ***A further analysis is done on airfoil selection***. \n", + "Using these results, the objective is to gain an intuitive understanding of the type of geometry that may meet the design requirements for a specific aircraft.\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the most part, XFLR5 will be used for analysis, in order to study stall characteristics. The geometric parameters used as variables will be;\n", + "\t- camber\n", + "\t- location of max camber\n", + " \t- max thickness\n", + "\t- leading edge radii\n", + "\t- thickness distribution\n", + "\n", + "The thickness distribution is specific to each family of airfoil. The modified series of NACA 4 and 5 digit airfoils change their thickness distribution by changing the leading edge radius and location of maximum thickness.\n", + "\n", + "All of the simulations are carried out at speeds of Mach 0.14 and a Reynold's number of 3 million exactly. These values are typical for light, acrobatic aircrafts which commonly use symmetric airfoils like the NACA0012 and 0015.\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "NACA Airfoils" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Most airfoil sections in use today are either of the NACA series or are heavily influenced by them. They were the first to seperate the effects of camber and thickness distribution. NACA airfoils are the easiest to find and their geometry is easy to reproduce using their numbering system. This study will thus focus on the 4 ***and 5*** digit series of NACA airfoils." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Description of airfoil geometry" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "heading", + "level": 6, + "metadata": {}, + "source": [ + "*Above image courtesy of - https://www.grc.nasa.gov/WWW/k-12/airplane/geom.html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**chord** - a straight line connecting the leading and trailing edges of an airfoil
\n", + "**mean camber line** - a line connecting the leading and trailing edges, which is always equidistant from the top and bottom surfaces of the airfoil.
\n", + "**camber** - the maximum distance between the chord and mean camber line
\n", + "**max thickness** - the maximum distance between the upper and lower surfaces of the airfoil
\n", + "**leading edge radius** - the radius of the curvature of the leading edge. For a sharp leading edge shape, this is zero.
\n", + "**Thickness distribution** - the thickness distribution for the NACA 4 and 5 digit series is defined by the following equation:\n", + "\n", + "\n", + "\n", + "This equation was derived from the thickness distributions of effecient wing sections such as the Gottingen and Clark Y. Changing the leading edge radius ends up changing this distribution. This was studied in the modified NACA 4 and 5 digit series which will be discussed later." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "NACA 4 digit series" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The 4 digit wing profile is defined by the following:\n", + "1) The first digit describes the max camber as a percent of the chord\n", + "2) The second digit describes the distance of the max camber from the leading edge as a percent of the chord\n", + "3) The last two digits describe the maximum thickness of the airfoil as a percent of the chord\n", + "By default, 4 digit series airfoils have a maximum thickness at 30% of the chord.\n", + "For a symmetric airfoil, the airfoil geometry is defined simply by:\n", + "\n", + " \n", + " \n", + "Where the index 'u' and 'l' denotes the upper and lower surfaces respectively. 'yt' is the airfoil thickness as a function of x, shown previously. Theta goes from 0 to 2*pi(*).\n", + "For a cambered airfoil, the mean camber line, yc, must be included. The equation for the mean camber line is;\n", + "Forward of maximum camber;\n", + "\n", + "\n", + "\n", + "Aft of maximum camber;\n", + "\n", + "Where;\n", + "m = maximum ordinate of mean line expressed as a fraction of the chord ( 100*m is the first of the four digits)\n", + "p = position of maximum camber as a fraction of the chord (10*p is the second of the four digits)\n", + "\n", + "Using this equation, the previous equation for the y-coordiantes are modified;\n", + " \n", + "\n", + "$\\theta$ is given by;\n", + "\n", + "Which, after differentiation, gives us;\n", + "" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Results" + ] + }, + { + "cell_type": "heading", + "level": 4, + "metadata": {}, + "source": [ + "Effects of max camber" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following NACA 4 digit airfoils are all of 12 % thickness with the maximum camber located at 40% of the chord, from the leading edge.\n", + "\n", + "**Lift Curve**\n", + "\n", + "The graph above shows that the lift curve is shifted upward with increasing camber. There is no apparent change in the lift slope or the stall angle. In other words, the basic equation for the lift slope changes from;\n", + "\n", + "To;\n", + "\n", + "Where 'a`o`' is the lift slope, and C`lo` is the lift at zero angle of attack.\n", + "\n", + "**Drag**\n", + "\n", + "\n", + "The lift to drag ratio, or the glide-ratio (An important parameter for gliders) also sees a marked improvement with increasing camber. It is interesting to note that the highest lift-drag ratio occurs at an angle of around 5 degrees for most of the airfoils. For the zero camber and the really low cambered airfoil, it is closer to 10 degrees. The performance of the higher cambered airfoils are still greater at that point.\n", + "The range of C`l`, over which drag variation is close to zero is also shown to increase with camber. This gives better cruise performance, as it allows an aircraft to change it's angle of attack over a wider range without experiencing change in drag, and thus, reducing the need for throttle control.\n", + "\n", + "**Pitching moment**\n", + "\n", + "The pitching moment graph clearly shows more negative moments with increasing camber. This would likely lead to better stability, as the aircraft will naturally tend to pitch nose down. Looking at this graph, it is clear why sports aircraft prefer to use symmetric airfoils for their main wing, instead of the higher lift, cambered airfoils.\n", + "While the pitching moment fluctuations remain relatively small, higher camber seems to increase the amplitude of the fluctuations towards the stall angle." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "Effects of camber location" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (, line 1)", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;36m File \u001b[1;32m\"\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m Effects of camber location\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following simulations were ran using NACA 4 digit airfoils with 12% thickness and 3%camber.\n", + "\n", + "**Lift**\n", + "\n", + "\n", + "\n", + "The effects of changing the camber location appear to less straightforward than simply increasing the camber. In the linear part, the Cl seems to increase with increasing distance of the max camber from the leading edge. The zero degree angle lift for camber at 70%, is almost three times higher than the Cl at 10% camber location. Considering this, it makes sense to locate high-lift devices (i.e, flaps, elevators, etc.) at the trailing edge of the wing. \n", + "Towards stall however, the behaviour is a bit more interesting. Zooming in towards that region, we can see the Cl increasing on either side of the mid point mark of the chord. The Cl decreases from from 10% to 40% camber location, but then starts increasing past 50%. This suggests a decrease in the lift slope as the camber moves towards the trailing edge.\n", + "\n", + "**Drag**\n", + "\n", + "\n", + "\n", + "\n", + "The drag chart shows that the drag seems to be higher towards he extremities of the airfoil. The drag is decreasing as the camber moves towards the 50% mark and then starts to increase again, past that.\n", + "\n", + "\n", + "\n", + "The range of minimum drag Cl also appears to increase when moving the camber back. The value of the maximum lift-drag ratio, however, decreases, especially at the 50% mark. The angle at which this maximum occurs also decreases towards the trailing edge location.\n", + "\n", + "**Pitching Moment**\n", + "\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Effect of max Thickness" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Symmetric NACA 4 digit airfoils were used to analyse the effect of maximum thickness.\n", + "\n", + "\n", + "**Lift**\n", + "\n", + "\n", + "Increasing the maximum thickness seems to simultaneously increase the maximum lift cofficient, while decreasing the life-slope.\n", + "\n", + "**Drag**\n", + "\n", + "\n", + "\n", + "The drag is higher for higher thickness up until the stall angle. Since the thinner airfoils stall earlier, their drag increases faster with angle of attack. The lift-drag ratio graph, however, shows more favorable results for relatively thinner airfoils.\n", + "\n", + "\n", + "\n", + "The minimum drag, Cl range appears to increase inversely to thickness with the exception of the NACA 0012. This is likely because it stalls much earlier than the rest, being the thinnest airfoil in this group.\n", + "\n", + "**Pitching Moment**\n", + "\n", + "\n", + "\n", + "The pitching moments is seen to become more positive, i.e., more unstable as the airfoil thickness increases." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Effect of leading edge radius" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following simulations use the NACA 0012 airfoil. The leading edge radius was modified using a multiplier, i.e., 0.25r is a quarter of the original leading edge radius of the NACA 0012.\n", + "\n", + "\n", + "\n", + "The results of this plot show that the airfoils with blunter leading edges have a higher stall angle, and thus, a higher maximum C`l`.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Looking at the drag performance, strangely enough, it seems the blunter airfoils seem to have the better performance again. \n", + "\n", + "However, when it comes to pitching moment, it seems that the pitch gets more unstable with blunter leading edges." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Modifying Panel Method Solver to include a NACA 4 digit airfoil generator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "An attempt was made to modifiy the existing panel codes from class to include a NACA 4 digit airfoil generator. The objective was to set a geometric parameter as a variable and find it's effects on various aerodynamic parameters. While the code gives results, they are very obviously not correct." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as np\n", + "from scipy import integrate\n", + "import matplotlib.pyplot as plt" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Generate airfoil\n", + "c = 1.0 #chord\n", + "thickness = 12.0 #thickness as a percent of chord\n", + "camber = 2.0 #max camber as a percent of chord\n", + "camber_loc = 4.0 #location of max camber as 1/10 percent of a chord\n", + "\n", + "t = thickness/100.0 #max thickness as a fraction of the chord\n", + "m = camber/100.0\n", + "p = camber_loc/10.0 \n", + "\n", + "r = 1.1019*t**2 #leading edge radius\n", + "\n", + "N = 101 #number of points describing airfoil\n", + "\n", + "#The chord line is split into three sections of varying point density\n", + "#This is to allow control over the density distribution of the panels\n", + "x_for = np.linspace(0,r,N/20)\n", + "x_mid = np.linspace(r+r,(0.75*c)-r,1+(3*N/10))\n", + "x_aft = np.linspace(r + 0.75*c, c, 3*N/20)\n", + "x1 = np.append(x_for,x_mid)\n", + "x_chord = np.append(x1,x_aft)\n", + "\n", + "#theta_l = np.linspace(np.pi, 2*np.pi, N/2)\n", + "y_t = (t/0.2)*(0.2969*np.sqrt(x_chord) - 0.126*x_chord - 0.3516*x_chord**2 + 0.2843*x_chord**3 - 0.1015*x_chord**4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = np.zeros(x_chord.size, dtype=float)\n", + "y_u = np.zeros(x_chord.size, dtype=float)\n", + "x_l = np.zeros(x_chord.size, dtype=float)\n", + "y_l = np.zeros(x_chord.size, dtype=float)\n", + "y_c = np.zeros(x_chord.size, dtype=float)\n", + "dyc_dx = np.zeros(x_chord.size, dtype=float)\n", + "\n", + "for i in range(N/2-1):\n", + " if x_chord[i]>p*c:\n", + " y_c[i] = (m/(1-p)**2)*((1-(2*p))+(2*p*x_chord[i])-x_chord[i]**2)\n", + " dyc_dx[i] = (2*m/(1-p)**2)*(p-x_chord[i])\n", + " else:\n", + " y_c[i] = (m/p**2)*((2*p*x_chord[i])-x_chord[i]**2)\n", + " dyc_dx[i] = (2*m/p**2)*(p-x_chord[i])\n", + "\n", + "plt.plot(x_chord,y_c)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 4, + "text": [ + "[]" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Creating the upper and lower surface coordinates\n", + "x_u = x_chord - y_t*np.sin(np.arctan(dyc_dx))\n", + "y_u = y_c + y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + " \n", + "x_l = x_chord + y_t*np.sin(np.arctan(dyc_dx))\n", + "y_l = y_c - y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + "print x_l[0], y_l[0],x_u[0], y_u[0]\n", + "print x_l[N/2], y_l[N/2],x_u[N/2], y_u[N/2]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0 0.0 0.0 0.0\n", + "1.0 -0.00126 1.0 0.00126\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.scatter(x_l, y_l, color='#CD2305', marker='o')\n", + "plt.scatter(x_u, y_u, marker='o' )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 6, + "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x = np.concatenate((x_u,list(reversed(x_l))))\n", + "y = np.concatenate((y_u,list(reversed(y_l))))\n", + "\n", + "\n", + "# plots the geometry\n", + "%matplotlib inline\n", + "\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = x.min(), x.max()\n", + "y_min, y_max = y.min(), y.max()\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = y_min-val_y*(y_max-y_min), y_max+val_y*(y_max-y_min)\n", + "\n", + "size = 10\n", + "plt.figure(figsize=(size, (y_end-y_start)/(x_end-x_start)*size))\n", + "plt.grid(True)\n", + "plt.xlabel('x', fontsize=16)\n", + "plt.ylabel('y', fontsize=16)\n", + "plt.xlim(x_start, x_end)\n", + "plt.ylim(y_start, y_end)\n", + "plt.scatter(x, y, color='k');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ELA+9YdrPw4s55kriCpDEdaObJC4PBziRmPQ74YqpF6zTumklXDpuSZEpiRvQJK6bA2Zs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\nOBEREZEIKYkTERERidD/A4l5v55j+zSsAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x_u.size\n", + "print x.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "51\n", + "102\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Panel:\n", + " \"\"\"Contains information related to one panel.\"\"\"\n", + " def __init__(self, xa, ya, xb, yb):\n", + " \"\"\"Creates a panel.\n", + " \n", + " Arguments\n", + " ---------\n", + " xa, ya -- Cartesian coordinates of the first end-point.\n", + " xb, yb -- Cartesian coordinates of the second end-point.\n", + " \"\"\"\n", + " self.xa, self.ya = xa, ya\n", + " self.xb, self.yb = xb, yb\n", + " \n", + " self.xc, self.yc = (xa+xb)/2, (ya+yb)/2 # control-point (center-point)\n", + " self.length = math.sqrt((xb-xa)**2+(yb-ya)**2) # length of the panel\n", + " \n", + " # orientation of the panel (angle between x-axis and panel's normal)\n", + " if xb-xa <= 0.:\n", + " self.beta = math.acos((yb-ya)/self.length)\n", + " elif xb-xa > 0.:\n", + " self.beta = math.pi + math.acos(-(yb-ya)/self.length)\n", + " \n", + " # location of the panel\n", + " if self.beta <= math.pi:\n", + " self.loc = 'extrados'\n", + " else:\n", + " self.loc = 'intrados'\n", + " \n", + " self.sigma = 0. # source strength\n", + " self.vt = 0. # tangential velocity\n", + " self.cp = 0. # pressure coefficient" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def define_panels(x, y, N=40):\n", + " \"\"\"Discretizes the geometry into panels using 'cosine' method.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y -- Cartesian coordinates of the geometry (1D arrays).\n", + " N - number of panels (default 40).\n", + " \n", + " Returns\n", + " -------\n", + " panels -- Numpy array of panels.\n", + " \"\"\"\n", + " \n", + " panels = np.empty(N, dtype=object)\n", + " for i in xrange(N):\n", + " panels[i] = Panel(x[i], y[i], x[i+1], y[i+1])\n", + " \n", + " return panels" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Creats the panels\n", + "panels = define_panels(x,y,(len(x)-1))\n", + "# plots the geometry and the panels\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "y_min, y_max = min( panel.ya for panel in panels ), max( panel.ya for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = y_min-val_y*(y_max-y_min), y_max+val_y*(y_max-y_min)\n", + "\n", + "size = 10\n", + "plt.figure(figsize=(size, (y_end-y_start)/(x_end-x_start)*size))\n", + "plt.grid(True)\n", + "plt.xlabel('x', fontsize=16)\n", + "plt.ylabel('y', fontsize=16)\n", + "plt.xlim(x_start, x_end)\n", + "plt.ylim(y_start, y_end)\n", + "plt.plot(x, y, color='k', linestyle='-', linewidth=2)\n", + "plt.plot(np.append([panel.xa for panel in panels], panels[0].xa), \n", + " np.append([panel.ya for panel in panels], panels[0].ya), \n", + " linestyle='-', linewidth=1, marker='o', markersize=6, color='#CD2305');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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mae0/vbrmbnXpfS5zF79cfRwXEc6SY+bELY5K4W/jH+Wcc86pdd9r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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Freestream:\n", + " \"\"\"Freestream conditions.\"\"\"\n", + " def __init__(self, u_inf=1.0, alpha=0.0):\n", + " \"\"\"Sets the freestream conditions.\n", + " \n", + " Arguments\n", + " ---------\n", + " u_inf -- Farfield speed (default 1.0).\n", + " alpha -- Angle of attack in degrees (default 0.0).\n", + " \"\"\"\n", + " self.u_inf = u_inf\n", + " self.alpha = alpha*math.pi/180 # degrees --> radians" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 12 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "u_inf = 1.0 # freestream spee\n", + "alpha = 0.0 # angle of attack (in degrees)\n", + "freestream = Freestream(u_inf, alpha) # instantiation of the object freestream" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def integral(x, y, panel, dxdz, dydz):\n", + " \"\"\"Evaluates the contribution of a panel at one point.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y -- Cartesian coordinates of the point.\n", + " panel -- panel which contribution is evaluated.\n", + " dxdz -- derivative of x in the z-direction.\n", + " dydz -- derivative of y in the z-direction.\n", + " \n", + " Returns\n", + " -------\n", + " Integral over the panel of the influence at one point.\n", + " \"\"\"\n", + " def func(s):\n", + " return ( ((x - (panel.xa - math.sin(panel.beta)*s))*dxdz \n", + " + (y - (panel.ya + math.cos(panel.beta)*s))*dydz)\n", + " / ((x - (panel.xa - math.sin(panel.beta)*s))**2 \n", + " + (y - (panel.ya + math.cos(panel.beta)*s))**2) )\n", + " return integrate.quad(lambda s:func(s), 0., panel.length)[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def source_matrix(panels):\n", + " \"\"\"Builds the source matrix.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " A -- NxN matrix (N is the number of panels).\n", + " \"\"\"\n", + " A = np.empty((panels.size, panels.size), dtype=float)\n", + " np.fill_diagonal(A, 0.5)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " A[i,j] = 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.cos(p_i.beta), math.sin(p_i.beta))\n", + " \n", + " return A" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def vortex_array(panels):\n", + " \"\"\"Builds the vortex array.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels - array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " a -- 1D array (Nx1, N is the number of panels).\n", + " \"\"\"\n", + " a = np.zeros(panels.size, dtype=float)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " a[i] -= 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.sin(p_i.beta), -math.cos(p_i.beta))\n", + " return a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def kutta_array(panels):\n", + " \"\"\"Builds the Kutta-condition array.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " a -- 1D array (Nx1, N is the number of panels).\n", + " \"\"\"\n", + " N = panels.size\n", + " a = np.zeros(N+1, dtype=float)\n", + " # contribution from the source sheet of the first panel on the last one\n", + " a[0] = 0.5/math.pi*integral(panels[N-1].xc, panels[N-1].yc, panels[0], \n", + " -math.sin(panels[N-1].beta), +math.cos(panels[N-1].beta))\n", + " # contribution from the source sheet of the last panel on the first one\n", + " a[N-1] = 0.5/math.pi*integral(panels[0].xc, panels[0].yc, panels[N-1], \n", + " -math.sin(panels[0].beta), +math.cos(panels[0].beta))\n", + " # contribution from the vortex sheet of the first panel on the last one\n", + " a[N] -= 0.5/math.pi*integral(panels[-1].xc, panels[-1].yc, panels[0], \n", + " +math.cos(panels[-1].beta), math.sin(panels[-1].beta))\n", + " # contribution from the vortex sheet of the last panel on the first one\n", + " a[N] -= 0.5/math.pi*integral(panels[0].xc, panels[0].yc, panels[-1], \n", + " +math.cos(panels[0].beta), math.sin(panels[0].beta))\n", + " # contribution from the vortex sheet of the first panel on itself\n", + " a[N] -= 0.5\n", + " # contribution from the vortex sheet of the last panel on itself\n", + " a[N] -= 0.5\n", + " \n", + " # contribution from the other panels on the first and last ones\n", + " for i, panel in enumerate(panels[1:-1]):\n", + " # contribution from the source sheet\n", + " a[i+1] = 0.5/math.pi*(integral(panels[0].xc, panels[0].yc, panel, \n", + " -math.sin(panels[0].beta), +math.cos(panels[0].beta))\n", + " + integral(panels[N-1].xc, panels[N-1].yc, panel, \n", + " -math.sin(panels[N-1].beta), +math.cos(panels[N-1].beta)) )\n", + "\n", + " # contribution from the vortex sheet\n", + " a[N] -= 0.5/math.pi*(integral(panels[0].xc, panels[0].yc, panel, \n", + " +math.cos(panels[0].beta), math.sin(panels[0].beta))\n", + " + integral(panels[-1].xc, panels[-1].yc, panel, \n", + " +math.cos(panels[-1].beta), math.sin(panels[-1].beta)) )\n", + " \n", + " return a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_matrix(panels):\n", + " \"\"\"Builds the matrix of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " A -- (N+1)x(N+1) matrix (N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " A = np.empty((N+1, N+1), dtype=float)\n", + " \n", + " AS = source_matrix(panels)\n", + " av = vortex_array(panels)\n", + " ak = kutta_array(panels)\n", + " \n", + " A[0:N,0:N], A[0:N,N], A[N,:] = AS[:,:], av[:], ak[:]\n", + " \n", + " return A" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_rhs(panels, freestream):\n", + " \"\"\"Builds the RHS of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " \n", + " Returns\n", + " -------\n", + " b -- 1D array ((N+1)x1, N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " b = np.empty(N+1,dtype=float)\n", + " \n", + " for i, panel in enumerate(panels):\n", + " b[i] = - freestream.u_inf * math.cos(freestream.alpha - panel.beta)\n", + " b[N] = -freestream.u_inf*( math.sin(freestream.alpha-panels[0].beta)\n", + " +math.sin(freestream.alpha-panels[N-1].beta) )\n", + " \n", + " return b" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 19 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "A = build_matrix(panels) # calculates the singularity matrix\n", + "b = build_rhs(panels, freestream) # calculates the freestream RHS" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 20 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# solves the linear system\n", + "variables = np.linalg.solve(A, b)\n", + "\n", + "for i, panel in enumerate(panels):\n", + " panel.sigma = variables[i]\n", + "gamma = variables[-1]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 21 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_tangential_velocity(panels, freestream, gamma):\n", + " \"\"\"Computes the tangential velocity on the surface.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " gamma -- circulation density.\n", + " \"\"\"\n", + " N = len(panels)\n", + " A = np.empty((N, N+1), dtype=float)\n", + " np.fill_diagonal(A, 0.0)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " # contribution from vortex on itself\n", + " A[i, N] = -0.5\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " # contribution from the sources\n", + " A[i,j] = 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " -math.sin(p_i.beta), math.cos(p_i.beta))\n", + " # contribution the vortices\n", + " A[i,N] -= 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.cos(p_i.beta), math.sin(p_i.beta))\n", + "\n", + " b = freestream.u_inf * np.sin([freestream.alpha - panel.beta for panel in panels])\n", + " \n", + " var = np.append([panel.sigma for panel in panels], gamma)\n", + " \n", + " vt = np.dot(A, var) + b\n", + " for i, panel in enumerate(panels):\n", + " panel.vt = vt[i]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 22 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# computes the tangential velocity at each panel center.\n", + "get_tangential_velocity(panels, freestream, gamma)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 23 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_pressure_coefficient(panels, freestream):\n", + " \"\"\"Computes the surface pressure coefficients.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " \"\"\"\n", + " for panel in panels:\n", + " panel.cp = 1.0 - (panel.vt/freestream.u_inf)**2" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 24 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# computes surface pressure coefficient\n", + "get_pressure_coefficient(panels, freestream)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 25 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# plots the surface pressure coefficient\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = cp_min-val_y*(cp_max-cp_min), cp_max+val_y*(cp_max-cp_min)\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "plt.grid(True)\n", + "plt.xlabel('x', fontsize=16)\n", + "plt.ylabel('$C_p$', fontsize=16)\n", + "plt.plot([panel.xc for panel in panels if panel.loc == 'extrados'], \n", + " [panel.cp for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=2, marker='o', markersize=6)\n", + "plt.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cp for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='o', markersize=6)\n", + "plt.legend(['lower', 'upper'], loc='best', prop={'size':14})\n", + "plt.xlim(x_start, x_end)\n", + "plt.ylim(y_start, y_end)\n", + "plt.gca().invert_yaxis()\n", + "plt.title('Number of panels : %d' % N);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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JJ5/koIMOIj09nRUrVuzy5xEREZHW6fLFWVHREqZPf4ri4uspLZ1LcfH1TJ/+VJsLtI46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\nNusnVjj5J2ZXXml2+eVWc/EldtWeOTa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+ "text": [ + "" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**References**\n", + " - https://www.grc.nasa.gov/WWW/k-12/airplane/geom.html
\n", + " - https://www.flyingfoam.com/content/what-airfoil-should-i-use-0
\n", + " - http://www.pdas.com/naca456thick4m.html
\n", + " - 'Airfoil Design', Tony Kao (Author)
\n", + " - 'Theory of wing sections', Ira H. Abbott(Author), A. E. von Doenhoff(Author), Dover Books on Aeronautical Engineering 1959
\n", + " - 'Using Simple Panel Methods with NACA 4-Series Airfoils', Andrew Cox, 2012\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 26 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Airfoil characteristics - amiya/Report/Airfoil Characteristics.ipynb b/Airfoil characteristics - amiya/Report/Airfoil Characteristics.ipynb new file mode 100644 index 0000000..47e2ee0 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/Airfoil Characteristics.ipynb @@ -0,0 +1,1079 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:186399526e065a50dc75610488e4a1af4fe098ec747660140e040ad08d5efac3" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "A study into airfoil geometry using panel methods" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Serious study into the effects of airfoil sections began almost 200 years ago. While it was known that flat plates could generate lift, theorizing that the curved shapes of bird wings may be more efficient in generating lift, researchers began looking at more curved or cambered surfaces. Otto Lilienthal was the first to conduct meticulous and properly documented experiments on airfoil shapes. Lilienthal experimented on varying camber, the nose radii and thickness distribution.\n", + "\n", + "Most airfoils developed during the years after Lilienthal, were designed through trial and error. Some of these designs lay the foundation for the NACA series of airfoils that are predominantly used in modern aircrafts." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Objective" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The effects of changing specific geometric parameters are studied using NACA 4 ***and 5 series airfoils***. The effects on maximum lift, drag, stall characteristics and pitching moment are all taken into account. ***A further analysis is done on airfoil selection***. \n", + "Using these results, the objective is to gain an intuitive understanding of the type of geometry that may meet the design requirements for a specific aircraft.\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the most part, XFLR5 will be used for analysis, in order to study stall characteristics. The geometric parameters used as variables will be;\n", + "\t- camber\n", + "\t- location of max camber\n", + " \t- max thickness\n", + "\t- leading edge radii\n", + "\t- thickness distribution\n", + "\n", + "The thickness distribution is specific to each family of airfoil. The modified series of NACA 4 and 5 digit airfoils change their thickness distribution by changing the leading edge radius and location of maximum thickness.\n", + "\n", + "All of the simulations are carried out at speeds of Mach 0.14 and a Reynold's number of 3 million exactly. These values are typical for light, acrobatic aircrafts which commonly use symmetric airfoils like the NACA0012 and 0015.\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "NACA Airfoils" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Most airfoil sections in use today are either of the NACA series or are heavily influenced by them. They were the first to seperate the effects of camber and thickness distribution. NACA airfoils are the easiest to find and their geometry is easy to reproduce using their numbering system. This study will thus focus on the 4 ***and 5*** digit series of NACA airfoils." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Description of airfoil geometry" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "heading", + "level": 6, + "metadata": {}, + "source": [ + "*Above image courtesy of - https://www.grc.nasa.gov/WWW/k-12/airplane/geom.html" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**chord** - a straight line connecting the leading and trailing edges of an airfoil
\n", + "**mean camber line** - a line connecting the leading and trailing edges, which is always equidistant from the top and bottom surfaces of the airfoil.
\n", + "**camber** - the maximum distance between the chord and mean camber line
\n", + "**max thickness** - the maximum distance between the upper and lower surfaces of the airfoil
\n", + "**leading edge radius** - the radius of the curvature of the leading edge. For a sharp leading edge shape, this is zero.
\n", + "**Thickness distribution** - the thickness distribution for the NACA 4 and 5 digit series is defined by the following equation:\n", + "\n", + "\n", + "\n", + "This equation was derived from the thickness distributions of effecient wing sections such as the Gottingen and Clark Y. Changing the leading edge radius ends up changing this distribution. This was studied in the modified NACA 4 and 5 digit series which will be discussed later." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "NACA 4 digit series" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The 4 digit wing profile is defined by the following:\n", + "1) The first digit describes the max camber as a percent of the chord\n", + "2) The second digit describes the distance of the max camber from the leading edge as a percent of the chord\n", + "3) The last two digits describe the maximum thickness of the airfoil as a percent of the chord\n", + "By default, 4 digit series airfoils have a maximum thickness at 30% of the chord.\n", + "For a symmetric airfoil, the airfoil geometry is defined simply by:\n", + "\n", + " \n", + " \n", + "Where the index 'u' and 'l' denotes the upper and lower surfaces respectively. 'yt' is the airfoil thickness as a function of x, shown previously. Theta goes from 0 to 2*pi(*).\n", + "For a cambered airfoil, the mean camber line, yc, must be included. The equation for the mean camber line is;\n", + "Forward of maximum camber;\n", + "\n", + "\n", + "\n", + "Aft of maximum camber;\n", + "\n", + "Where;\n", + "m = maximum ordinate of mean line expressed as a fraction of the chord ( 100*m is the first of the four digits)\n", + "p = position of maximum camber as a fraction of the chord (10*p is the second of the four digits)\n", + "\n", + "Using this equation, the previous equation for the y-coordiantes are modified;\n", + " \n", + "\n", + "$\\theta$ is given by;\n", + "\n", + "Which, after differentiation, gives us;\n", + "" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Results" + ] + }, + { + "cell_type": "heading", + "level": 4, + "metadata": {}, + "source": [ + "Effects of max camber" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following NACA 4 digit airfoils are all of 12 % thickness with the maximum camber located at 40% of the chord, from the leading edge.\n", + "\n", + "**Lift Curve**\n", + "\n", + "The graph above shows that the lift curve is shifted upward with increasing camber. There is no apparent change in the lift slope or the stall angle. In other words, the basic equation for the lift slope changes from;\n", + "\n", + "To;\n", + "\n", + "Where 'a`o`' is the lift slope, and C`lo` is the lift at zero angle of attack.\n", + "\n", + "**Drag**\n", + "\n", + "\n", + "The lift to drag ratio, or the glide-ratio (An important parameter for gliders) also sees a marked improvement with increasing camber. It is interesting to note that the highest lift-drag ratio occurs at an angle of around 5 degrees for most of the airfoils. For the zero camber and the really low cambered airfoil, it is closer to 10 degrees. The performance of the higher cambered airfoils are still greater at that point.\n", + "The range of C`l`, over which drag variation is close to zero is also shown to increase with camber. This gives better cruise performance, as it allows an aircraft to change it's angle of attack over a wider range without experiencing change in drag, and thus, reducing the need for throttle control.\n", + "\n", + "**Pitching moment**\n", + "\n", + "The pitching moment graph clearly shows more negative moments with increasing camber. This would likely lead to better stability, as the aircraft will naturally tend to pitch nose down. Looking at this graph, it is clear why sports aircraft prefer to use symmetric airfoils for their main wing, instead of the higher lift, cambered airfoils.\n", + "While the pitching moment fluctuations remain relatively small, higher camber seems to increase the amplitude of the fluctuations towards the stall angle." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "Effects of camber location" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid syntax (, line 1)", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;36m File \u001b[1;32m\"\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m Effects of camber location\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following simulations were ran using NACA 4 digit airfoils with 12% thickness and 3%camber.\n", + "\n", + "**Lift**\n", + "\n", + "\n", + "\n", + "The effects of changing the camber location appear to less straightforward than simply increasing the camber. In the linear part, the Cl seems to increase with increasing distance of the max camber from the leading edge. The zero degree angle lift for camber at 70%, is almost three times higher than the Cl at 10% camber location. Considering this, it makes sense to locate high-lift devices (i.e, flaps, elevators, etc.) at the trailing edge of the wing. \n", + "Towards stall however, the behaviour is a bit more interesting. Zooming in towards that region, we can see the Cl increasing on either side of the mid point mark of the chord. The Cl decreases from from 10% to 40% camber location, but then starts increasing past 50%. This suggests a decrease in the lift slope as the camber moves towards the trailing edge.\n", + "\n", + "**Drag**\n", + "\n", + "\n", + "\n", + "\n", + "The drag chart shows that the drag seems to be higher towards he extremities of the airfoil. The drag is decreasing as the camber moves towards the 50% mark and then starts to increase again, past that.\n", + "\n", + "\n", + "\n", + "The range of minimum drag Cl also appears to increase when moving the camber back. The value of the maximum lift-drag ratio, however, decreases, especially at the 50% mark. The angle at which this maximum occurs also decreases towards the trailing edge location.\n", + "\n", + "**Pitching Moment**\n", + "\n" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Effect of max Thickness" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Symmetric NACA 4 digit airfoils were used to analyse the effect of maximum thickness.\n", + "\n", + "\n", + "**Lift**\n", + "\n", + "\n", + "Increasing the maximum thickness seems to simultaneously increase the maximum lift cofficient, while decreasing the life-slope.\n", + "\n", + "**Drag**\n", + "\n", + "\n", + "\n", + "The drag is higher for higher thickness up until the stall angle. Since the thinner airfoils stall earlier, their drag increases faster with angle of attack. The lift-drag ratio graph, however, shows more favorable results for relatively thinner airfoils.\n", + "\n", + "\n", + "\n", + "The minimum drag, Cl range appears to increase inversely to thickness with the exception of the NACA 0012. This is likely because it stalls much earlier than the rest, being the thinnest airfoil in this group.\n", + "\n", + "**Pitching Moment**\n", + "\n", + "\n", + "\n", + "The pitching moments is seen to become more positive, i.e., more unstable as the airfoil thickness increases." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Effect of leading edge radius" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following simulations use the NACA 0012 airfoil. The leading edge radius was modified using a multiplier, i.e., 0.25r is a quarter of the original leading edge radius of the NACA 0012.\n", + "\n", + "\n", + "\n", + "The results of this plot show that the airfoils with blunter leading edges have a higher stall angle, and thus, a higher maximum C`l`.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Looking at the drag performance, strangely enough, it seems the blunter airfoils seem to have the better performance again. \n", + "\n", + "However, when it comes to pitching moment, it seems that the pitch gets more unstable with blunter leading edges." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Modifying Panel Method Solver to include a NACA 4 digit airfoil generator" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "An attempt was made to modifiy the existing panel codes from class to include a NACA 4 digit airfoil generator. The objective was to set a geometric parameter as a variable and find it's effects on various aerodynamic parameters. While the code gives results, they are very obviously not correct." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as np\n", + "from scipy import integrate\n", + "import matplotlib.pyplot as plt" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 29 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Generate airfoil\n", + "c = 1.0 #chord\n", + "thickness = 12.0 #thickness as a percent of chord\n", + "camber = 0.0 #max camber as a percent of chord\n", + "camber_loc = 1.0 #location of max camber as 1/10 percent of a chord\n", + "\n", + "t = thickness/100.0 #max thickness as a fraction of the chord\n", + "m = camber/100.0\n", + "p = camber_loc/10.0 \n", + "\n", + "r = 1.1019*t**2 #leading edge radius\n", + "\n", + "N = 101 #number of points describing airfoil\n", + "\n", + "#The chord line is split into three sections of varying point density\n", + "#This is to allow control over the density distribution of the panels\n", + "x_for = np.linspace(0,r,N/20)\n", + "x_mid = np.linspace(r+r,(0.75*c)-r,1+(3*N/10))\n", + "x_aft = np.linspace(r + 0.75*c, c, 3*N/20)\n", + "x1 = np.append(x_for,x_mid)\n", + "x_chord = np.append(x1,x_aft)\n", + "\n", + "#theta_l = np.linspace(np.pi, 2*np.pi, N/2)\n", + "y_t = (t/0.2)*(0.2969*np.sqrt(x_chord) - 0.126*x_chord - 0.3516*x_chord**2 + 0.2843*x_chord**3 - 0.1015*x_chord**4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x_u = np.zeros(x_chord.size, dtype=float)\n", + "y_u = np.zeros(x_chord.size, dtype=float)\n", + "x_l = np.zeros(x_chord.size, dtype=float)\n", + "y_l = np.zeros(x_chord.size, dtype=float)\n", + "y_c = np.zeros(x_chord.size, dtype=float)\n", + "dyc_dx = np.zeros(x_chord.size, dtype=float)\n", + "\n", + "for i in range(N/2-1):\n", + " if x_chord[i]>p*c:\n", + " y_c[i] = (m/(1-p)**2)*((1-(2*p))+(2*p*x_chord[i])-x_chord[i]**2)\n", + " dyc_dx[i] = (2*m/(1-p)**2)*(p-x_chord[i])\n", + " else:\n", + " y_c[i] = (m/p**2)*((2*p*x_chord[i])-x_chord[i]**2)\n", + " dyc_dx[i] = (2*m/p**2)*(p-x_chord[i])\n", + "\n", + "plt.plot(x_chord,y_c)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 31, + "text": [ + "[]" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Creating the upper and lower surface coordinates\n", + "x_u = x_chord - y_t*np.sin(np.arctan(dyc_dx))\n", + "y_u = y_c + y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + " \n", + "x_l = x_chord + y_t*np.sin(np.arctan(dyc_dx))\n", + "y_l = y_c - y_t*np.cos(np.arctan(dyc_dx))\n", + "\n", + "print x_l[0], y_l[0],x_u[0], y_u[0]\n", + "print x_l[N/2], y_l[N/2],x_u[N/2], y_u[N/2]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0 0.0 0.0 0.0\n", + "1.0 -0.00126 1.0 0.00126\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.scatter(x_l, y_l, color='#CD2305', marker='o')\n", + "plt.scatter(x_u, y_u, marker='o' )" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 33, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x = np.concatenate((x_u,list(reversed(x_l))))\n", + "y = np.concatenate((y_u,list(reversed(y_l))))\n", + "\n", + "\n", + "# plots the geometry\n", + "%matplotlib inline\n", + "\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = x.min(), x.max()\n", + "y_min, y_max = y.min(), y.max()\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = y_min-val_y*(y_max-y_min), y_max+val_y*(y_max-y_min)\n", + "\n", + "size = 10\n", + "plt.figure(figsize=(size, (y_end-y_start)/(x_end-x_start)*size))\n", + "plt.grid(True)\n", + "plt.xlabel('x', fontsize=16)\n", + "plt.ylabel('y', fontsize=16)\n", + "plt.xlim(x_start, x_end)\n", + "plt.ylim(y_start, y_end)\n", + "plt.scatter(x, y, color='k');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print x_u.size\n", + "print x.size" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "51\n", + "102\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Panel:\n", + " \"\"\"Contains information related to one panel.\"\"\"\n", + " def __init__(self, xa, ya, xb, yb):\n", + " \"\"\"Creates a panel.\n", + " \n", + " Arguments\n", + " ---------\n", + " xa, ya -- Cartesian coordinates of the first end-point.\n", + " xb, yb -- Cartesian coordinates of the second end-point.\n", + " \"\"\"\n", + " self.xa, self.ya = xa, ya\n", + " self.xb, self.yb = xb, yb\n", + " \n", + " self.xc, self.yc = (xa+xb)/2, (ya+yb)/2 # control-point (center-point)\n", + " self.length = math.sqrt((xb-xa)**2+(yb-ya)**2) # length of the panel\n", + " \n", + " # orientation of the panel (angle between x-axis and panel's normal)\n", + " if xb-xa <= 0.:\n", + " self.beta = math.acos((yb-ya)/self.length)\n", + " elif xb-xa > 0.:\n", + " self.beta = math.pi + math.acos(-(yb-ya)/self.length)\n", + " \n", + " # location of the panel\n", + " if self.beta <= math.pi:\n", + " self.loc = 'extrados'\n", + " else:\n", + " self.loc = 'intrados'\n", + " \n", + " self.sigma = 0. # source strength\n", + " self.vt = 0. # tangential velocity\n", + " self.cp = 0. # pressure coefficient" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 36 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def define_panels(x, y, N=40):\n", + " \"\"\"Discretizes the geometry into panels using 'cosine' method.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y -- Cartesian coordinates of the geometry (1D arrays).\n", + " N - number of panels (default 40).\n", + " \n", + " Returns\n", + " -------\n", + " panels -- Numpy array of panels.\n", + " \"\"\"\n", + " \n", + " panels = np.empty(N, dtype=object)\n", + " for i in xrange(N):\n", + " panels[i] = Panel(x[i], y[i], x[i+1], y[i+1])\n", + " \n", + " return panels" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 37 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Creats the panels\n", + "panels = define_panels(x,y,(len(x)-1))\n", + "# plots the geometry and the panels\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "y_min, y_max = min( panel.ya for panel in panels ), max( panel.ya for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = y_min-val_y*(y_max-y_min), y_max+val_y*(y_max-y_min)\n", + "\n", + "size = 10\n", + "plt.figure(figsize=(size, (y_end-y_start)/(x_end-x_start)*size))\n", + "plt.grid(True)\n", + "plt.xlabel('x', fontsize=16)\n", + "plt.ylabel('y', fontsize=16)\n", + "plt.xlim(x_start, x_end)\n", + "plt.ylim(y_start, y_end)\n", + "plt.plot(x, y, color='k', linestyle='-', linewidth=2)\n", + "plt.plot(np.append([panel.xa for panel in panels], panels[0].xa), \n", + " np.append([panel.ya for panel in panels], panels[0].ya), \n", + " linestyle='-', linewidth=1, marker='o', markersize=6, color='#CD2305');" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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SFW2c13SneoIkcUYbN6zn9anjG/w6XpJro2egiWtCFTsqNT/a/LB160VeYSGzq4xjdVyN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\nk3SFEMInnGiStsI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+ "text": [ + "" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "class Freestream:\n", + " \"\"\"Freestream conditions.\"\"\"\n", + " def __init__(self, u_inf=1.0, alpha=0.0):\n", + " \"\"\"Sets the freestream conditions.\n", + " \n", + " Arguments\n", + " ---------\n", + " u_inf -- Farfield speed (default 1.0).\n", + " alpha -- Angle of attack in degrees (default 0.0).\n", + " \"\"\"\n", + " self.u_inf = u_inf\n", + " self.alpha = alpha*math.pi/180 # degrees --> radians" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 39 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# defines and creates the object freestream\n", + "u_inf = 1.0 # freestream spee\n", + "alpha = 5.0 # angle of attack (in degrees)\n", + "freestream = Freestream(u_inf, alpha) # instantiation of the object freestream" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 40 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def integral(x, y, panel, dxdz, dydz):\n", + " \"\"\"Evaluates the contribution of a panel at one point.\n", + " \n", + " Arguments\n", + " ---------\n", + " x, y -- Cartesian coordinates of the point.\n", + " panel -- panel which contribution is evaluated.\n", + " dxdz -- derivative of x in the z-direction.\n", + " dydz -- derivative of y in the z-direction.\n", + " \n", + " Returns\n", + " -------\n", + " Integral over the panel of the influence at one point.\n", + " \"\"\"\n", + " def func(s):\n", + " return ( ((x - (panel.xa - math.sin(panel.beta)*s))*dxdz \n", + " + (y - (panel.ya + math.cos(panel.beta)*s))*dydz)\n", + " / ((x - (panel.xa - math.sin(panel.beta)*s))**2 \n", + " + (y - (panel.ya + math.cos(panel.beta)*s))**2) )\n", + " return integrate.quad(lambda s:func(s), 0., panel.length)[0]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 41 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def source_matrix(panels):\n", + " \"\"\"Builds the source matrix.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " A -- NxN matrix (N is the number of panels).\n", + " \"\"\"\n", + " A = np.empty((panels.size, panels.size), dtype=float)\n", + " np.fill_diagonal(A, 0.5)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " A[i,j] = 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.cos(p_i.beta), math.sin(p_i.beta))\n", + " \n", + " return A" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 42 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def vortex_array(panels):\n", + " \"\"\"Builds the vortex array.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels - array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " a -- 1D array (Nx1, N is the number of panels).\n", + " \"\"\"\n", + " a = np.zeros(panels.size, dtype=float)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " a[i] -= 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.sin(p_i.beta), -math.cos(p_i.beta))\n", + " return a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 43 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def kutta_array(panels):\n", + " \"\"\"Builds the Kutta-condition array.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " a -- 1D array (Nx1, N is the number of panels).\n", + " \"\"\"\n", + " N = panels.size\n", + " a = np.zeros(N+1, dtype=float)\n", + " # contribution from the source sheet of the first panel on the last one\n", + " a[0] = 0.5/math.pi*integral(panels[N-1].xc, panels[N-1].yc, panels[0], \n", + " -math.sin(panels[N-1].beta), +math.cos(panels[N-1].beta))\n", + " # contribution from the source sheet of the last panel on the first one\n", + " a[N-1] = 0.5/math.pi*integral(panels[0].xc, panels[0].yc, panels[N-1], \n", + " -math.sin(panels[0].beta), +math.cos(panels[0].beta))\n", + " # contribution from the vortex sheet of the first panel on the last one\n", + " a[N] -= 0.5/math.pi*integral(panels[-1].xc, panels[-1].yc, panels[0], \n", + " +math.cos(panels[-1].beta), math.sin(panels[-1].beta))\n", + " # contribution from the vortex sheet of the last panel on the first one\n", + " a[N] -= 0.5/math.pi*integral(panels[0].xc, panels[0].yc, panels[-1], \n", + " +math.cos(panels[0].beta), math.sin(panels[0].beta))\n", + " # contribution from the vortex sheet of the first panel on itself\n", + " a[N] -= 0.5\n", + " # contribution from the vortex sheet of the last panel on itself\n", + " a[N] -= 0.5\n", + " \n", + " # contribution from the other panels on the first and last ones\n", + " for i, panel in enumerate(panels[1:-1]):\n", + " # contribution from the source sheet\n", + " a[i+1] = 0.5/math.pi*(integral(panels[0].xc, panels[0].yc, panel, \n", + " -math.sin(panels[0].beta), +math.cos(panels[0].beta))\n", + " + integral(panels[N-1].xc, panels[N-1].yc, panel, \n", + " -math.sin(panels[N-1].beta), +math.cos(panels[N-1].beta)) )\n", + "\n", + " # contribution from the vortex sheet\n", + " a[N] -= 0.5/math.pi*(integral(panels[0].xc, panels[0].yc, panel, \n", + " +math.cos(panels[0].beta), math.sin(panels[0].beta))\n", + " + integral(panels[-1].xc, panels[-1].yc, panel, \n", + " +math.cos(panels[-1].beta), math.sin(panels[-1].beta)) )\n", + " \n", + " return a" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 44 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_matrix(panels):\n", + " \"\"\"Builds the matrix of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " \n", + " Returns\n", + " -------\n", + " A -- (N+1)x(N+1) matrix (N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " A = np.empty((N+1, N+1), dtype=float)\n", + " \n", + " AS = source_matrix(panels)\n", + " av = vortex_array(panels)\n", + " ak = kutta_array(panels)\n", + " \n", + " A[0:N,0:N], A[0:N,N], A[N,:] = AS[:,:], av[:], ak[:]\n", + " \n", + " return A" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 45 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def build_rhs(panels, freestream):\n", + " \"\"\"Builds the RHS of the linear system.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " \n", + " Returns\n", + " -------\n", + " b -- 1D array ((N+1)x1, N is the number of panels).\n", + " \"\"\"\n", + " N = len(panels)\n", + " b = np.empty(N+1,dtype=float)\n", + " \n", + " for i, panel in enumerate(panels):\n", + " b[i] = - freestream.u_inf * math.cos(freestream.alpha - panel.beta)\n", + " b[N] = -freestream.u_inf*( math.sin(freestream.alpha-panels[0].beta)\n", + " +math.sin(freestream.alpha-panels[N-1].beta) )\n", + " \n", + " return b" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 46 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "A = build_matrix(panels) # calculates the singularity matrix\n", + "b = build_rhs(panels, freestream) # calculates the freestream RHS" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 47 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# solves the linear system\n", + "variables = np.linalg.solve(A, b)\n", + "\n", + "for i, panel in enumerate(panels):\n", + " panel.sigma = variables[i]\n", + "gamma = variables[-1]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 48 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_tangential_velocity(panels, freestream, gamma):\n", + " \"\"\"Computes the tangential velocity on the surface.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " gamma -- circulation density.\n", + " \"\"\"\n", + " N = len(panels)\n", + " A = np.empty((N, N+1), dtype=float)\n", + " np.fill_diagonal(A, 0.0)\n", + " \n", + " for i, p_i in enumerate(panels):\n", + " # contribution from vortex on itself\n", + " A[i, N] = -0.5\n", + " for j, p_j in enumerate(panels):\n", + " if i != j:\n", + " # contribution from the sources\n", + " A[i,j] = 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " -math.sin(p_i.beta), math.cos(p_i.beta))\n", + " # contribution the vortices\n", + " A[i,N] -= 0.5/math.pi*integral(p_i.xc, p_i.yc, \n", + " p_j, \n", + " math.cos(p_i.beta), math.sin(p_i.beta))\n", + "\n", + " b = freestream.u_inf * np.sin([freestream.alpha - panel.beta for panel in panels])\n", + " \n", + " var = np.append([panel.sigma for panel in panels], gamma)\n", + " \n", + " vt = np.dot(A, var) + b\n", + " for i, panel in enumerate(panels):\n", + " panel.vt = vt[i]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 49 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# computes the tangential velocity at each panel center.\n", + "get_tangential_velocity(panels, freestream, gamma)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 50 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def get_pressure_coefficient(panels, freestream):\n", + " \"\"\"Computes the surface pressure coefficients.\n", + " \n", + " Arguments\n", + " ---------\n", + " panels -- array of panels.\n", + " freestream -- farfield conditions.\n", + " \"\"\"\n", + " for panel in panels:\n", + " panel.cp = 1.0 - (panel.vt/freestream.u_inf)**2" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 51 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# computes surface pressure coefficient\n", + "get_pressure_coefficient(panels, freestream)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 52 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# plots the surface pressure coefficient\n", + "val_x, val_y = 0.1, 0.2\n", + "x_min, x_max = min( panel.xa for panel in panels ), max( panel.xa for panel in panels )\n", + "cp_min, cp_max = min( panel.cp for panel in panels ), max( panel.cp for panel in panels )\n", + "x_start, x_end = x_min-val_x*(x_max-x_min), x_max+val_x*(x_max-x_min)\n", + "y_start, y_end = cp_min-val_y*(cp_max-cp_min), cp_max+val_y*(cp_max-cp_min)\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "plt.grid(True)\n", + "plt.xlabel('x', fontsize=16)\n", + "plt.ylabel('$C_p$', fontsize=16)\n", + "plt.plot([panel.xc for panel in panels if panel.loc == 'extrados'], \n", + " [panel.cp for panel in panels if panel.loc == 'extrados'], \n", + " color='r', linestyle='-', linewidth=2, marker='o', markersize=6)\n", + "plt.plot([panel.xc for panel in panels if panel.loc == 'intrados'], \n", + " [panel.cp for panel in panels if panel.loc == 'intrados'], \n", + " color='b', linestyle='-', linewidth=1, marker='o', markersize=6)\n", + "plt.legend(['lower', 'upper'], loc='best', prop={'size':14})\n", + "plt.xlim(x_start, x_end)\n", + "plt.ylim(y_start, y_end)\n", + "plt.gca().invert_yaxis()\n", + "plt.title('Number of panels : %d' % N);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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VzJ07g9mzr2TKlCc2uUDrqf2ZGWbW4br77rsPgOeff5477riDO++8k5tuuqnFc2644QZ2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\n0UANVwFXpNnvNLbk++RTTx4N5FNPJXd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+ "text": [ + "" + ] + } + ], + "prompt_number": 53 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**References**\n", + " - https://www.grc.nasa.gov/WWW/k-12/airplane/geom.html
\n", + " - https://www.flyingfoam.com/content/what-airfoil-should-i-use-0
\n", + " - http://www.pdas.com/naca456thick4m.html
\n", + " - 'Airfoil Design', Tony Kao (Author)
\n", + " - 'Theory of wing sections', Ira H. Abbott(Author), A. E. von Doenhoff(Author), Dover Books on Aeronautical Engineering 1959
\n", + " - 'Using Simple Panel Methods with NACA 4-Series Airfoils', Andrew Cox, 2012\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 53 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-0.25r_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-0.25r_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..733b7ff --- /dev/null +++ b/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-0.25r_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,73 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012-0.25r + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.9691 0.03192 0.02942 -0.0175 1.0000 0.0012 -10.3157 0.0000 0.2223 + -9.500 -0.9257 0.03281 0.03031 -0.0169 1.0000 0.0013 -8.6411 0.0000 0.2229 + -8.500 -0.9234 0.01573 0.01181 0.0004 0.9998 0.0022 -9.7888 0.0000 0.2424 + -8.000 -0.8590 0.01566 0.01174 -0.0021 0.9978 0.0026 -8.2287 0.0000 0.2401 + -7.500 -0.7943 0.01555 0.01163 -0.0046 0.9953 0.0029 -6.7965 0.0000 0.2372 + -7.000 -0.7371 0.01335 0.00922 -0.0059 0.9923 0.0035 -5.7971 0.0000 0.2354 + -6.500 -0.6867 0.01144 0.00715 -0.0054 0.9820 0.0039 -4.9602 0.0000 0.2360 + -6.000 -0.6387 0.01016 0.00574 -0.0040 0.9657 0.0041 -4.2727 0.0000 0.2380 + -5.500 -0.5921 0.00902 0.00441 -0.0021 0.9440 0.0042 -3.7884 0.0000 0.2411 + -5.000 -0.5419 0.00819 0.00339 -0.0009 0.9195 0.0042 -3.2921 0.0000 0.2434 + -4.500 -0.4891 0.00768 0.00272 -0.0003 0.8899 0.0047 -2.7496 0.0000 0.2448 + -4.000 -0.4355 0.00729 0.00213 0.0002 0.8542 0.0062 -2.3202 0.0000 0.2463 + -3.500 -0.3806 0.00702 0.00181 0.0003 0.8191 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0.26016 -0.0707 0.0016 1.0000 -1.9597 0.0000 0.3173 + 20.500 0.8204 0.26783 0.26684 -0.0751 0.0014 1.0000 -1.9958 0.0000 0.3200 + 21.000 0.8374 0.27423 0.27324 -0.0796 0.0013 1.0000 -2.0411 0.0000 0.3226 + 21.500 0.8542 0.28060 0.27962 -0.0841 0.0012 1.0000 -2.0980 0.0000 0.3252 + 22.000 0.8707 0.28706 0.28608 -0.0886 0.0011 1.0000 -2.1653 0.0000 0.3276 + 22.500 0.8868 0.29348 0.29251 -0.0931 0.0010 1.0000 -2.2548 0.0000 0.3299 + 23.000 0.9026 0.29979 0.29882 -0.0976 0.0010 1.0000 -2.3852 0.0000 0.3320 + 23.500 0.9179 0.30605 0.30508 -0.1021 0.0009 1.0000 -2.5391 0.0000 0.3341 + + diff --git a/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-0.5r_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-0.5r_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..e796db9 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-0.5r_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,71 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012-0.5r + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.0965 0.01386 0.00938 -0.0021 1.0000 0.0038 -8.5395 0.0000 0.2377 + -9.500 -1.0603 0.01265 0.00802 0.0016 1.0000 0.0040 -7.9527 0.0000 0.2418 + -8.500 -0.9589 0.01065 0.00581 0.0032 0.9977 0.0056 -6.6888 0.0000 0.2448 + -8.000 -0.8941 0.01021 0.00540 0.0011 0.9955 0.0067 -5.8793 0.0000 0.2432 + -7.000 -0.7685 0.00910 0.00422 -0.0023 0.9881 0.0079 -4.4614 0.0000 0.2400 + -6.500 -0.7088 0.00852 0.00361 -0.0032 0.9797 0.0102 -3.8571 0.0000 0.2390 + -6.000 -0.6552 0.00816 0.00324 -0.0026 0.9646 0.0121 -3.2892 0.0000 0.2399 + -5.500 -0.6027 0.00774 0.00282 -0.0018 0.9451 0.0183 -2.7692 0.0000 0.2414 + -5.000 -0.5491 0.00740 0.00245 -0.0012 0.9220 0.0283 -2.2963 0.0000 0.2425 + 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amiya/Report/LE curvature/NACA 0012-1.5r_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,79 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012-1.5r + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1441 0.01108 0.00614 -0.0025 1.0000 0.0278 -5.2623 0.0000 0.2360 + -9.500 -1.1006 0.01049 0.00555 0.0004 1.0000 0.0317 -4.9214 0.0000 0.2392 + -8.500 -0.9804 0.00956 0.00465 -0.0009 0.9974 0.0362 -4.1465 0.0000 0.2392 + -8.000 -0.9150 0.00910 0.00421 -0.0026 0.9954 0.0403 -3.7658 0.0000 0.2378 + -7.500 -0.8486 0.00861 0.00379 -0.0045 0.9936 0.0456 -3.3960 0.0000 0.2358 + -7.000 -0.7850 0.00827 0.00345 -0.0058 0.9895 0.0487 -3.0889 0.0000 0.2342 + -6.500 -0.7240 0.00784 0.00309 -0.0065 0.9820 0.0568 -2.8021 0.0000 0.2331 + -6.000 -0.6673 0.00756 0.00283 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0.0058 0.0127 1.0000 -10.7249 0.0000 0.2128 + 21.000 1.3119 0.13339 0.13128 -0.0105 0.0130 1.0000 -9.6456 0.0000 0.2239 + 21.500 1.2243 0.15728 0.15542 -0.0251 0.0131 1.0000 -8.8021 0.0000 0.2356 + 22.000 1.1567 0.17883 0.17720 -0.0387 0.0129 1.0000 -8.0473 0.0000 0.2479 + 23.000 1.0591 0.22067 0.21943 -0.0655 0.0121 1.0000 -6.5547 0.0000 0.2757 + 23.500 1.0424 0.23550 0.23433 -0.0748 0.0119 1.0000 -6.1506 0.0000 0.2852 + + diff --git a/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-2.0r_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-2.0r_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..9652982 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012-2.0r_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,80 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012-2.0r + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1521 0.01089 0.00599 -0.0044 1.0000 0.0363 -5.0605 0.0000 0.2338 + -9.500 -1.1069 0.01043 0.00551 -0.0017 1.0000 0.0380 -4.7642 0.0000 0.2368 + -8.500 -0.9870 0.00941 0.00455 -0.0025 0.9975 0.0452 -4.1101 0.0000 0.2369 + -8.000 -0.9208 0.00904 0.00420 -0.0041 0.9955 0.0468 -3.7774 0.0000 0.2355 + -7.500 -0.8536 0.00868 0.00384 -0.0060 0.9938 0.0488 -3.4539 0.0000 0.2334 + -7.000 -0.7895 0.00822 0.00345 -0.0073 0.9904 0.0550 -3.1512 0.0000 0.2318 + -6.500 -0.7278 0.00790 0.00316 -0.0079 0.9832 0.0586 -2.8879 0.0000 0.2305 + -6.000 -0.6696 0.00762 0.00290 -0.0077 0.9724 0.0619 -2.6485 0.0000 0.2303 + -5.500 -0.6145 0.00729 0.00261 -0.0068 0.9568 0.0693 -2.4229 0.0000 0.2311 + -5.000 -0.5592 0.00708 0.00239 -0.0059 0.9361 0.0724 -2.2026 0.0000 0.2320 + -4.500 -0.5040 0.00685 0.00215 -0.0050 0.9080 0.0812 -1.9910 0.0000 0.2330 + 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0.2801 0.00658 0.00144 0.0022 0.1210 0.6819 -1.2822 0.0000 0.2358 + 3.000 0.3368 0.00660 0.00158 0.0027 0.1094 0.7441 -1.4483 0.0000 0.2356 + 3.500 0.3930 0.00661 0.00174 0.0033 0.0993 0.8083 -1.6192 0.0000 0.2350 + 4.000 0.4483 0.00672 0.00195 0.0041 0.0870 0.8684 -1.7938 0.0000 0.2339 + 4.500 0.5041 0.00685 0.00215 0.0049 0.0812 0.9080 -1.9911 0.0000 0.2330 + 5.000 0.5592 0.00708 0.00239 0.0059 0.0724 0.9361 -2.2027 0.0000 0.2320 + 5.500 0.6145 0.00729 0.00261 0.0068 0.0693 0.9568 -2.4230 0.0000 0.2311 + 6.000 0.6697 0.00762 0.00290 0.0077 0.0619 0.9724 -2.6486 0.0000 0.2304 + 6.500 0.7278 0.00790 0.00316 0.0079 0.0586 0.9832 -2.8880 0.0000 0.2306 + 7.000 0.7896 0.00822 0.00345 0.0072 0.0550 0.9904 -3.1513 0.0000 0.2318 + 7.500 0.8537 0.00868 0.00383 0.0060 0.0488 0.9938 -3.4541 0.0000 0.2335 + 8.000 0.9209 0.00904 0.00420 0.0041 0.0468 0.9955 -3.7777 0.0000 0.2355 + 8.500 0.9871 0.00941 0.00455 0.0025 0.0452 0.9975 -4.1104 0.0000 0.2369 + 9.000 1.0518 0.00988 0.00498 0.0011 0.0421 0.9993 -4.4486 0.0000 0.2379 + 9.500 1.1067 0.01043 0.00551 0.0017 0.0380 1.0000 -4.7636 0.0000 0.2367 + 10.500 1.2002 0.01126 0.00636 0.0065 0.0358 1.0000 -5.3796 0.0000 0.2315 + 11.000 1.2491 0.01170 0.00681 0.0084 0.0348 1.0000 -5.7153 0.0000 0.2294 + 11.500 1.2986 0.01226 0.00737 0.0101 0.0330 1.0000 -6.0927 0.0000 0.2277 + 12.000 1.3477 0.01295 0.00805 0.0118 0.0308 1.0000 -6.4763 0.0000 0.2259 + 12.500 1.3958 0.01374 0.00886 0.0135 0.0284 1.0000 -6.8615 0.0000 0.2242 + 13.000 1.4427 0.01461 0.00982 0.0154 0.0269 1.0000 -7.2490 0.0000 0.2224 + 13.500 1.4917 0.01523 0.01047 0.0170 0.0268 1.0000 -7.6666 0.0000 0.2208 + 14.000 1.5397 0.01588 0.01117 0.0186 0.0266 1.0000 -8.0892 0.0000 0.2192 + 14.500 1.5859 0.01661 0.01194 0.0205 0.0262 1.0000 -8.5132 0.0000 0.2175 + 15.000 1.6296 0.01745 0.01282 0.0227 0.0255 1.0000 -8.9333 0.0000 0.2156 + 15.500 1.6691 0.01845 0.01387 0.0253 0.0245 1.0000 -9.3405 0.0000 0.2133 + 16.000 1.6990 0.01963 0.01511 0.0294 0.0234 1.0000 -9.7083 0.0000 0.2102 + 16.500 1.7238 0.02115 0.01669 0.0335 0.0223 1.0000 -10.0521 0.0000 0.2071 + 17.000 1.7436 0.02312 0.01875 0.0374 0.0209 1.0000 -10.3681 0.0000 0.2040 + 17.500 1.7577 0.02570 0.02148 0.0408 0.0200 1.0000 -10.6503 0.0000 0.2012 + 18.000 1.7648 0.02921 0.02518 0.0432 0.0194 1.0000 -10.8892 0.0000 0.1988 + 18.500 1.7624 0.03422 0.03041 0.0440 0.0190 1.0000 -11.0636 0.0000 0.1970 + 19.000 1.7587 0.04008 0.03645 0.0431 0.0188 1.0000 -11.2320 0.0000 0.1962 + 19.500 1.7489 0.04737 0.04393 0.0405 0.0188 1.0000 -11.3776 0.0000 0.1962 + 20.000 1.7167 0.05811 0.05489 0.0353 0.0188 1.0000 -11.3526 0.0000 0.1973 + 20.500 1.6401 0.07595 0.07306 0.0255 0.0188 1.0000 -10.9634 0.0000 0.2009 + 21.000 1.3906 0.12158 0.11935 -0.0015 0.0188 1.0000 -9.0902 0.0000 0.2163 + 21.500 1.2801 0.14813 0.14619 -0.0179 0.0188 1.0000 -8.2099 0.0000 0.2283 + 22.000 1.2117 0.16879 0.16705 -0.0311 0.0188 1.0000 -7.6124 0.0000 0.2391 + 22.500 1.1740 0.18458 0.18298 -0.0413 0.0187 1.0000 -7.2560 0.0000 0.2479 + 23.000 1.1625 0.19543 0.19390 -0.0485 0.0186 1.0000 -7.1503 0.0000 0.2534 + 23.500 1.1365 0.21024 0.20883 -0.0585 0.0182 1.0000 -6.8258 0.0000 0.2623 + 24.000 1.0930 0.23094 0.22966 -0.0723 0.0168 1.0000 -6.1630 0.0000 0.2768 + + diff --git a/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..48ca10d --- /dev/null +++ b/Airfoil characteristics - amiya/Report/LE curvature/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,79 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1329 0.01145 0.00651 -0.0006 1.0000 0.0164 -6.0202 0.0000 0.2383 + -9.500 -1.0892 0.01091 0.00597 0.0021 1.0000 0.0180 -5.5706 0.0000 0.2414 + -8.500 -0.9718 0.00987 0.00490 0.0011 0.9975 0.0223 -4.5968 0.0000 0.2418 + -8.000 -0.9072 0.00932 0.00440 -0.0008 0.9953 0.0260 -4.1143 0.0000 0.2404 + -7.500 -0.8408 0.00887 0.00397 -0.0029 0.9935 0.0294 -3.6464 0.0000 0.2383 + -7.000 -0.7793 0.00839 0.00353 -0.0040 0.9886 0.0357 -3.2165 0.0000 0.2371 + -6.500 -0.7185 0.00794 0.00314 -0.0049 0.9808 0.0448 -2.8614 0.0000 0.2359 + -6.000 -0.6640 0.00757 0.00281 -0.0043 0.9670 0.0544 -2.5473 0.0000 0.2367 + -5.500 -0.6102 0.00721 0.00250 -0.0035 0.9493 0.0672 -2.2476 0.0000 0.2378 + -5.000 -0.5564 0.00687 0.00219 -0.0027 0.9268 0.0843 -1.9599 0.0000 0.2390 + -4.500 -0.5022 0.00653 0.00191 -0.0021 0.8996 0.1105 -1.7042 0.0000 0.2401 + -4.000 -0.4471 0.00625 0.00166 -0.0016 0.8685 0.1374 -1.4791 0.0000 0.2409 + -3.500 -0.3924 0.00596 0.00142 -0.0011 0.8297 0.1778 -1.2633 0.0000 0.2419 + -2.500 -0.2815 0.00553 0.00107 -0.0005 0.7429 0.2651 -0.9210 0.0000 0.2433 + -2.000 -0.2255 0.00535 0.00095 -0.0003 0.6995 0.3140 -0.7816 0.0000 0.2438 + -1.500 -0.1695 0.00523 0.00085 -0.0002 0.6514 0.3643 -0.6647 0.0000 0.2443 + -1.000 -0.1132 0.00513 0.00078 -0.0001 0.6043 0.4145 -0.5667 0.0000 0.2447 + -0.500 -0.0565 0.00508 0.00075 -0.0001 0.5581 0.4619 -0.4865 0.0000 0.2446 + 0.000 -0.0000 0.00509 0.00074 -0.0000 0.5072 0.5072 -0.4190 0.0000 0.0211 + 0.500 0.0565 0.00508 0.00075 0.0001 0.4619 0.5581 -0.4865 0.0000 0.2446 + 1.000 0.1132 0.00513 0.00078 0.0001 0.4145 0.6043 -0.5667 0.0000 0.2447 + 1.500 0.1695 0.00523 0.00085 0.0002 0.3643 0.6514 -0.6647 0.0000 0.2443 + 2.000 0.2255 0.00535 0.00095 0.0003 0.3140 0.6995 -0.7816 0.0000 0.2438 + 2.500 0.2815 0.00553 0.00107 0.0005 0.2651 0.7429 -0.9210 0.0000 0.2433 + 3.000 0.3370 0.00572 0.00123 0.0008 0.2198 0.7898 -1.0844 0.0000 0.2426 + 3.500 0.3924 0.00596 0.00142 0.0011 0.1778 0.8297 -1.2634 0.0000 0.2419 + 4.000 0.4471 0.00625 0.00166 0.0016 0.1374 0.8685 -1.4791 0.0000 0.2409 + 4.500 0.5022 0.00653 0.00191 0.0020 0.1105 0.8996 -1.7042 0.0000 0.2401 + 5.000 0.5565 0.00687 0.00219 0.0027 0.0843 0.9268 -1.9601 0.0000 0.2390 + 5.500 0.6103 0.00721 0.00250 0.0035 0.0671 0.9493 -2.2477 0.0000 0.2378 + 6.000 0.6640 0.00757 0.00281 0.0043 0.0544 0.9670 -2.5474 0.0000 0.2367 + 6.500 0.7185 0.00794 0.00314 0.0049 0.0448 0.9808 -2.8615 0.0000 0.2359 + 7.000 0.7793 0.00839 0.00353 0.0040 0.0357 0.9886 -3.2167 0.0000 0.2371 + 7.500 0.8408 0.00887 0.00397 0.0029 0.0294 0.9936 -3.6468 0.0000 0.2383 + 8.000 0.9073 0.00932 0.00440 0.0008 0.0260 0.9953 -4.1147 0.0000 0.2404 + 8.500 0.9719 0.00987 0.00490 -0.0011 0.0222 0.9975 -4.5972 0.0000 0.2418 + 9.500 1.0890 0.01091 0.00597 -0.0021 0.0181 1.0000 -5.5698 0.0000 0.2414 + 10.000 1.1328 0.01145 0.00650 0.0006 0.0164 1.0000 -6.0198 0.0000 0.2383 + 10.500 1.1769 0.01214 0.00720 0.0031 0.0142 1.0000 -6.4778 0.0000 0.2355 + 11.000 1.2215 0.01300 0.00816 0.0054 0.0124 1.0000 -6.9362 0.0000 0.2331 + 11.500 1.2696 0.01367 0.00888 0.0069 0.0121 1.0000 -7.4543 0.0000 0.2313 + 12.000 1.3186 0.01427 0.00950 0.0082 0.0119 1.0000 -8.0060 0.0000 0.2297 + 12.500 1.3668 0.01494 0.01020 0.0096 0.0116 1.0000 -8.6247 0.0000 0.2281 + 13.000 1.4128 0.01576 0.01105 0.0113 0.0107 1.0000 -9.2650 0.0000 0.2263 + 13.500 1.4549 0.01682 0.01214 0.0135 0.0095 1.0000 -9.8918 0.0000 0.2241 + 14.000 1.4922 0.01815 0.01355 0.0163 0.0085 1.0000 -10.4893 0.0000 0.2216 + 14.500 1.5222 0.01968 0.01524 0.0200 0.0079 1.0000 -11.0441 0.0000 0.2185 + 15.000 1.5405 0.02151 0.01724 0.0251 0.0076 1.0000 -11.5269 0.0000 0.2144 + 15.500 1.5530 0.02395 0.01988 0.0296 0.0074 1.0000 -11.9673 0.0000 0.2106 + 16.000 1.5574 0.02738 0.02354 0.0332 0.0073 1.0000 -12.3391 0.0000 0.2074 + 16.500 1.5523 0.03237 0.02879 0.0349 0.0071 1.0000 -12.6181 0.0000 0.2050 + 17.000 1.5357 0.03974 0.03644 0.0337 0.0070 1.0000 -12.7714 0.0000 0.2043 + 17.500 1.5056 0.05008 0.04707 0.0294 0.0070 1.0000 -12.7656 0.0000 0.2054 + 18.000 1.4616 0.06331 0.06057 0.0228 0.0069 1.0000 -12.5863 0.0000 0.2080 + 18.500 1.4054 0.07922 0.07675 0.0145 0.0070 1.0000 -12.2382 0.0000 0.2120 + 19.000 1.3413 0.09677 0.09453 0.0055 0.0070 1.0000 -11.7541 0.0000 0.2170 + 19.500 1.2725 0.11606 0.11403 -0.0046 0.0071 1.0000 -11.1427 0.0000 0.2238 + 20.000 1.2064 0.13545 0.13362 -0.0151 0.0072 1.0000 -10.4790 0.0000 0.2317 + 20.500 1.1462 0.15525 0.15361 -0.0264 0.0072 1.0000 -9.7735 0.0000 0.2414 + 21.000 1.0903 0.17533 0.17387 -0.0382 0.0073 1.0000 -8.9953 0.0000 0.2529 + 21.500 1.0299 0.19913 0.19787 -0.0523 0.0073 1.0000 -7.9219 0.0000 0.2685 + 22.000 0.9138 0.24928 0.24825 -0.0783 0.0063 1.0000 -4.7212 0.0000 0.3066 + 22.500 0.9282 0.25560 0.25457 -0.0827 0.0057 1.0000 -4.8331 0.0000 0.3089 + 24.000 0.9396 0.29898 0.29797 -0.1049 0.0048 1.0000 -2.5370 0.0000 0.3313 + 24.500 0.9555 0.30433 0.30332 -0.1092 0.0042 1.0000 -2.7097 0.0000 0.3328 + 25.000 0.9713 0.30941 0.30841 -0.1136 0.0038 1.0000 -2.9101 0.0000 0.3341 + + diff --git a/Airfoil characteristics - amiya/Report/LE 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curvature/NACA3612 cp-10.bmp new file mode 100644 index 0000000..2ed7888 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE curvature/NACA3612 cp-10.bmp differ diff --git a/Airfoil characteristics - amiya/Report/LE curvature/T1_A1 0.00_M0.14_N9.0 polars.bmp b/Airfoil characteristics - amiya/Report/LE curvature/T1_A1 0.00_M0.14_N9.0 polars.bmp new file mode 100644 index 0000000..5655f6c Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE curvature/T1_A1 0.00_M0.14_N9.0 polars.bmp differ diff --git a/Airfoil characteristics - amiya/Report/LE curvature/Thumbs.db b/Airfoil characteristics - amiya/Report/LE curvature/Thumbs.db new file mode 100644 index 0000000..0108b05 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE curvature/Thumbs.db differ diff --git a/Airfoil characteristics - amiya/Report/LE radii/Thumbs.db b/Airfoil characteristics - amiya/Report/LE radii/Thumbs.db new file mode 100644 index 0000000..8002270 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE radii/Thumbs.db differ diff --git a/Airfoil characteristics - amiya/Report/LE radii/cd-a.GIF b/Airfoil characteristics - amiya/Report/LE radii/cd-a.GIF new file mode 100644 index 0000000..027443c Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE radii/cd-a.GIF differ diff --git a/Airfoil characteristics - amiya/Report/LE radii/cd-cl.GIF b/Airfoil characteristics - amiya/Report/LE radii/cd-cl.GIF new file mode 100644 index 0000000..7f7a1b6 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE radii/cd-cl.GIF differ diff --git a/Airfoil characteristics - amiya/Report/LE radii/cl-a.GIF b/Airfoil characteristics - amiya/Report/LE radii/cl-a.GIF new file mode 100644 index 0000000..fdbc484 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE radii/cl-a.GIF differ diff --git a/Airfoil characteristics - amiya/Report/LE radii/cl-cd-a.GIF b/Airfoil characteristics - amiya/Report/LE radii/cl-cd-a.GIF new file mode 100644 index 0000000..b1822e0 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE radii/cl-cd-a.GIF differ diff --git a/Airfoil characteristics - amiya/Report/LE radii/cm-a.GIF b/Airfoil characteristics - amiya/Report/LE radii/cm-a.GIF new file mode 100644 index 0000000..aebadcc Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE radii/cm-a.GIF differ diff --git a/Airfoil characteristics - amiya/Report/LE radii/legend.GIF b/Airfoil characteristics - amiya/Report/LE radii/legend.GIF new file mode 100644 index 0000000..4fed75c Binary files /dev/null and b/Airfoil characteristics - amiya/Report/LE radii/legend.GIF differ diff --git a/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..48ca10d --- /dev/null +++ b/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,79 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1329 0.01145 0.00651 -0.0006 1.0000 0.0164 -6.0202 0.0000 0.2383 + -9.500 -1.0892 0.01091 0.00597 0.0021 1.0000 0.0180 -5.5706 0.0000 0.2414 + -8.500 -0.9718 0.00987 0.00490 0.0011 0.9975 0.0223 -4.5968 0.0000 0.2418 + -8.000 -0.9072 0.00932 0.00440 -0.0008 0.9953 0.0260 -4.1143 0.0000 0.2404 + -7.500 -0.8408 0.00887 0.00397 -0.0029 0.9935 0.0294 -3.6464 0.0000 0.2383 + -7.000 -0.7793 0.00839 0.00353 -0.0040 0.9886 0.0357 -3.2165 0.0000 0.2371 + -6.500 -0.7185 0.00794 0.00314 -0.0049 0.9808 0.0448 -2.8614 0.0000 0.2359 + -6.000 -0.6640 0.00757 0.00281 -0.0043 0.9670 0.0544 -2.5473 0.0000 0.2367 + -5.500 -0.6102 0.00721 0.00250 -0.0035 0.9493 0.0672 -2.2476 0.0000 0.2378 + -5.000 -0.5564 0.00687 0.00219 -0.0027 0.9268 0.0843 -1.9599 0.0000 0.2390 + -4.500 -0.5022 0.00653 0.00191 -0.0021 0.8996 0.1105 -1.7042 0.0000 0.2401 + -4.000 -0.4471 0.00625 0.00166 -0.0016 0.8685 0.1374 -1.4791 0.0000 0.2409 + -3.500 -0.3924 0.00596 0.00142 -0.0011 0.8297 0.1778 -1.2633 0.0000 0.2419 + -2.500 -0.2815 0.00553 0.00107 -0.0005 0.7429 0.2651 -0.9210 0.0000 0.2433 + -2.000 -0.2255 0.00535 0.00095 -0.0003 0.6995 0.3140 -0.7816 0.0000 0.2438 + -1.500 -0.1695 0.00523 0.00085 -0.0002 0.6514 0.3643 -0.6647 0.0000 0.2443 + -1.000 -0.1132 0.00513 0.00078 -0.0001 0.6043 0.4145 -0.5667 0.0000 0.2447 + -0.500 -0.0565 0.00508 0.00075 -0.0001 0.5581 0.4619 -0.4865 0.0000 0.2446 + 0.000 -0.0000 0.00509 0.00074 -0.0000 0.5072 0.5072 -0.4190 0.0000 0.0211 + 0.500 0.0565 0.00508 0.00075 0.0001 0.4619 0.5581 -0.4865 0.0000 0.2446 + 1.000 0.1132 0.00513 0.00078 0.0001 0.4145 0.6043 -0.5667 0.0000 0.2447 + 1.500 0.1695 0.00523 0.00085 0.0002 0.3643 0.6514 -0.6647 0.0000 0.2443 + 2.000 0.2255 0.00535 0.00095 0.0003 0.3140 0.6995 -0.7816 0.0000 0.2438 + 2.500 0.2815 0.00553 0.00107 0.0005 0.2651 0.7429 -0.9210 0.0000 0.2433 + 3.000 0.3370 0.00572 0.00123 0.0008 0.2198 0.7898 -1.0844 0.0000 0.2426 + 3.500 0.3924 0.00596 0.00142 0.0011 0.1778 0.8297 -1.2634 0.0000 0.2419 + 4.000 0.4471 0.00625 0.00166 0.0016 0.1374 0.8685 -1.4791 0.0000 0.2409 + 4.500 0.5022 0.00653 0.00191 0.0020 0.1105 0.8996 -1.7042 0.0000 0.2401 + 5.000 0.5565 0.00687 0.00219 0.0027 0.0843 0.9268 -1.9601 0.0000 0.2390 + 5.500 0.6103 0.00721 0.00250 0.0035 0.0671 0.9493 -2.2477 0.0000 0.2378 + 6.000 0.6640 0.00757 0.00281 0.0043 0.0544 0.9670 -2.5474 0.0000 0.2367 + 6.500 0.7185 0.00794 0.00314 0.0049 0.0448 0.9808 -2.8615 0.0000 0.2359 + 7.000 0.7793 0.00839 0.00353 0.0040 0.0357 0.9886 -3.2167 0.0000 0.2371 + 7.500 0.8408 0.00887 0.00397 0.0029 0.0294 0.9936 -3.6468 0.0000 0.2383 + 8.000 0.9073 0.00932 0.00440 0.0008 0.0260 0.9953 -4.1147 0.0000 0.2404 + 8.500 0.9719 0.00987 0.00490 -0.0011 0.0222 0.9975 -4.5972 0.0000 0.2418 + 9.500 1.0890 0.01091 0.00597 -0.0021 0.0181 1.0000 -5.5698 0.0000 0.2414 + 10.000 1.1328 0.01145 0.00650 0.0006 0.0164 1.0000 -6.0198 0.0000 0.2383 + 10.500 1.1769 0.01214 0.00720 0.0031 0.0142 1.0000 -6.4778 0.0000 0.2355 + 11.000 1.2215 0.01300 0.00816 0.0054 0.0124 1.0000 -6.9362 0.0000 0.2331 + 11.500 1.2696 0.01367 0.00888 0.0069 0.0121 1.0000 -7.4543 0.0000 0.2313 + 12.000 1.3186 0.01427 0.00950 0.0082 0.0119 1.0000 -8.0060 0.0000 0.2297 + 12.500 1.3668 0.01494 0.01020 0.0096 0.0116 1.0000 -8.6247 0.0000 0.2281 + 13.000 1.4128 0.01576 0.01105 0.0113 0.0107 1.0000 -9.2650 0.0000 0.2263 + 13.500 1.4549 0.01682 0.01214 0.0135 0.0095 1.0000 -9.8918 0.0000 0.2241 + 14.000 1.4922 0.01815 0.01355 0.0163 0.0085 1.0000 -10.4893 0.0000 0.2216 + 14.500 1.5222 0.01968 0.01524 0.0200 0.0079 1.0000 -11.0441 0.0000 0.2185 + 15.000 1.5405 0.02151 0.01724 0.0251 0.0076 1.0000 -11.5269 0.0000 0.2144 + 15.500 1.5530 0.02395 0.01988 0.0296 0.0074 1.0000 -11.9673 0.0000 0.2106 + 16.000 1.5574 0.02738 0.02354 0.0332 0.0073 1.0000 -12.3391 0.0000 0.2074 + 16.500 1.5523 0.03237 0.02879 0.0349 0.0071 1.0000 -12.6181 0.0000 0.2050 + 17.000 1.5357 0.03974 0.03644 0.0337 0.0070 1.0000 -12.7714 0.0000 0.2043 + 17.500 1.5056 0.05008 0.04707 0.0294 0.0070 1.0000 -12.7656 0.0000 0.2054 + 18.000 1.4616 0.06331 0.06057 0.0228 0.0069 1.0000 -12.5863 0.0000 0.2080 + 18.500 1.4054 0.07922 0.07675 0.0145 0.0070 1.0000 -12.2382 0.0000 0.2120 + 19.000 1.3413 0.09677 0.09453 0.0055 0.0070 1.0000 -11.7541 0.0000 0.2170 + 19.500 1.2725 0.11606 0.11403 -0.0046 0.0071 1.0000 -11.1427 0.0000 0.2238 + 20.000 1.2064 0.13545 0.13362 -0.0151 0.0072 1.0000 -10.4790 0.0000 0.2317 + 20.500 1.1462 0.15525 0.15361 -0.0264 0.0072 1.0000 -9.7735 0.0000 0.2414 + 21.000 1.0903 0.17533 0.17387 -0.0382 0.0073 1.0000 -8.9953 0.0000 0.2529 + 21.500 1.0299 0.19913 0.19787 -0.0523 0.0073 1.0000 -7.9219 0.0000 0.2685 + 22.000 0.9138 0.24928 0.24825 -0.0783 0.0063 1.0000 -4.7212 0.0000 0.3066 + 22.500 0.9282 0.25560 0.25457 -0.0827 0.0057 1.0000 -4.8331 0.0000 0.3089 + 24.000 0.9396 0.29898 0.29797 -0.1049 0.0048 1.0000 -2.5370 0.0000 0.3313 + 24.500 0.9555 0.30433 0.30332 -0.1092 0.0042 1.0000 -2.7097 0.0000 0.3328 + 25.000 0.9713 0.30941 0.30841 -0.1136 0.0038 1.0000 -2.9101 0.0000 0.3341 + + diff --git a/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 13012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 13012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..c517e80 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 13012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,67 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 13012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.0921 0.01565 0.01172 -0.0064 1.0000 0.0012 -9.8383 0.0000 0.2350 + -9.500 -1.0593 0.01394 0.00977 -0.0019 1.0000 0.0011 -9.0657 0.0000 0.2396 + -9.000 -1.0249 0.01231 0.00788 0.0024 1.0000 0.0011 -8.3103 0.0000 0.2444 + -8.500 -0.9887 0.01094 0.00623 0.0066 1.0000 0.0012 -7.5837 0.0000 0.2493 + -8.000 -0.9311 0.00999 0.00508 0.0064 0.9990 0.0024 -6.7666 0.0000 0.2501 + -7.500 -0.8679 0.00935 0.00445 0.0048 0.9974 0.0035 -5.7815 0.0000 0.2493 + -7.000 -0.8034 0.00874 0.00387 0.0030 0.9959 0.0075 -4.8521 0.0000 0.2479 + -6.500 -0.7444 0.00811 0.00330 0.0023 0.9936 0.0158 -4.1746 0.0000 0.2478 + -6.000 -0.6823 0.00763 0.00289 0.0010 0.9905 0.0235 -3.5359 0.0000 0.2467 + -5.500 -0.6178 0.00728 0.00255 -0.0007 0.9876 0.0265 -2.9319 0.0000 0.2444 + -5.000 -0.5521 0.00690 0.00223 -0.0028 0.9850 0.0351 -2.3723 0.0000 0.2409 + -4.500 -0.4873 0.00657 0.00195 -0.0046 0.9821 0.0436 -1.9280 0.0000 0.2368 + -4.000 -0.4295 0.00625 0.00167 -0.0048 0.9719 0.0512 -1.6512 0.0000 0.2354 + -3.500 -0.3575 0.00579 0.00137 -0.0084 0.9620 0.0861 -1.3614 0.0000 0.2233 + -3.000 -0.2980 0.00533 0.00110 -0.0091 0.9346 0.1407 -1.1560 0.0000 0.2164 + -2.500 -0.2449 0.00504 0.00090 -0.0083 0.8885 0.1956 -0.9698 0.0000 0.2132 + -2.000 -0.1958 0.00480 0.00072 -0.0066 0.8301 0.2660 -0.8016 0.0000 0.2136 + -1.500 -0.1477 0.00463 0.00060 -0.0047 0.7663 0.3362 -0.6526 0.0000 0.2153 + -1.000 -0.0986 0.00452 0.00051 -0.0031 0.6958 0.4008 -0.5222 0.0000 0.2161 + -0.500 -0.0485 0.00441 0.00047 -0.0017 0.6369 0.4722 -0.4046 0.0000 0.2125 + 0.000 -0.0000 0.00425 0.00045 -0.0000 0.5744 0.5744 -0.3156 0.0000 -0.0831 + 0.500 0.0485 0.00441 0.00047 0.0017 0.4722 0.6371 -0.4046 0.0000 0.2125 + 1.000 0.0986 0.00452 0.00052 0.0031 0.4008 0.6959 -0.5222 0.0000 0.2161 + 1.500 0.1477 0.00463 0.00060 0.0047 0.3362 0.7663 -0.6526 0.0000 0.2153 + 2.000 0.1958 0.00480 0.00072 0.0066 0.2660 0.8301 -0.8016 0.0000 0.2136 + 2.500 0.2449 0.00504 0.00090 0.0083 0.1956 0.8885 -0.9698 0.0000 0.2132 + 3.000 0.2980 0.00533 0.00110 0.0091 0.1407 0.9346 -1.1560 0.0000 0.2164 + 3.500 0.3575 0.00579 0.00137 0.0084 0.0861 0.9620 -1.3614 0.0000 0.2233 + 4.000 0.4295 0.00625 0.00167 0.0048 0.0512 0.9719 -1.6512 0.0000 0.2354 + 4.500 0.4873 0.00657 0.00195 0.0046 0.0436 0.9821 -1.9280 0.0000 0.2368 + 5.000 0.5521 0.00690 0.00223 0.0028 0.0351 0.9850 -2.3724 0.0000 0.2409 + 5.500 0.6178 0.00728 0.00255 0.0007 0.0265 0.9876 -2.9320 0.0000 0.2444 + 6.000 0.6823 0.00763 0.00289 -0.0010 0.0235 0.9905 -3.5360 0.0000 0.2467 + 6.500 0.7444 0.00811 0.00330 -0.0023 0.0158 0.9936 -4.1748 0.0000 0.2478 + 7.000 0.8035 0.00874 0.00386 -0.0030 0.0075 0.9959 -4.8525 0.0000 0.2480 + 7.500 0.8680 0.00935 0.00445 -0.0048 0.0035 0.9974 -5.7820 0.0000 0.2493 + 8.000 0.9312 0.00999 0.00508 -0.0064 0.0024 0.9990 -6.7672 0.0000 0.2501 + 8.500 0.9887 0.01094 0.00623 -0.0066 0.0012 1.0000 -7.5834 0.0000 0.2493 + 9.000 1.0249 0.01231 0.00787 -0.0024 0.0011 1.0000 -8.3100 0.0000 0.2444 + 9.500 1.0593 0.01394 0.00976 0.0019 0.0011 1.0000 -9.0655 0.0000 0.2396 + 10.000 1.0921 0.01565 0.01172 0.0064 0.0012 1.0000 -9.8381 0.0000 0.2350 + 10.500 1.1238 0.01745 0.01374 0.0108 0.0012 1.0000 -10.6383 0.0000 0.2305 + 11.000 1.1536 0.01940 0.01594 0.0152 0.0013 1.0000 -11.4570 0.0000 0.2262 + 11.500 1.1791 0.02163 0.01842 0.0200 0.0014 1.0000 -12.2397 0.0000 0.2218 + 12.000 1.1965 0.02447 0.02155 0.0253 0.0016 1.0000 -12.9136 0.0000 0.2169 + 12.500 1.1898 0.02843 0.02590 0.0331 0.0017 1.0000 -13.2303 0.0000 0.2096 + 13.000 1.1378 0.03563 0.03360 0.0404 0.0019 1.0000 -12.8129 0.0000 0.2011 + 13.500 1.0903 0.04780 0.04615 0.0337 0.0020 1.0000 -12.3938 0.0000 0.2045 + 14.000 1.0667 0.06243 0.06097 0.0216 0.0019 1.0000 -12.2928 0.0000 0.2143 + 14.500 1.0299 0.07928 0.07793 0.0116 0.0017 1.0000 -11.8924 0.0000 0.2226 + 15.000 0.9579 0.10122 0.09995 0.0005 0.0016 1.0000 -10.6672 0.0000 0.2330 + 15.500 0.8813 0.12410 0.12291 -0.0110 0.0015 1.0000 -9.1276 0.0000 0.2460 + 16.000 0.8233 0.14652 0.14540 -0.0218 0.0014 1.0000 -7.6530 0.0000 0.2602 + 16.500 0.7851 0.16639 0.16533 -0.0306 0.0015 1.0000 -6.3598 0.0000 0.2731 + + diff --git a/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 23012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 23012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..104d72a --- /dev/null +++ b/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 23012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,83 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 23012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -9.500 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0.2562 + 23.500 1.2315 0.20420 0.20231 -0.0675 0.0068 1.0000 -8.2698 0.0000 0.2625 + 24.000 1.2289 0.21343 0.21163 -0.0743 0.0067 1.0000 -8.3205 0.0000 0.2669 + 24.500 1.2277 0.22246 0.22074 -0.0811 0.0065 1.0000 -8.3736 0.0000 0.2712 + 25.000 1.2270 0.23151 0.22986 -0.0881 0.0063 1.0000 -8.4149 0.0000 0.2757 + + diff --git a/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 33012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 33012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..723f118 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/NACA 5 series/camber/NACA 33012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,67 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 33012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- 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diff --git a/Airfoil characteristics - amiya/Report/airfoil section2.gif b/Airfoil characteristics - amiya/Report/airfoil section2.gif new file mode 100644 index 0000000..1e3e93a Binary files /dev/null and b/Airfoil characteristics - amiya/Report/airfoil section2.gif differ diff --git a/Airfoil characteristics - amiya/Report/airfoil study.rtf b/Airfoil characteristics - amiya/Report/airfoil study.rtf new file mode 100644 index 0000000..3043254 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/airfoil study.rtf @@ -0,0 +1,83315 @@ +{\rtf1\ansi\ansicpg1252\deff0\nouicompat\deflang1033{\fonttbl{\f0\fnil\fcharset0 Calibri;}} +{\colortbl ;\red0\green0\blue255;} +{\*\generator Riched20 6.3.9600}\viewkind4\uc1 +\pard\sa200\sl276\slmult1\ul\b\f0\fs22\lang9 A study into airfoil geometry using panel methods\par +\ulnone\b0 Serious study into the effects of airfoil sections began almost 200 years ago. While it was known that flat plates could generate lift, theorizing that the curved shapes of bird wings may be more efficient in generating lift, researchers began looking at more curved or cambered surfaces. Otto Lilienthal was the first to conduct a meticulous, well-documented on airfoil shapes. Asides from camber, he experimented on varying the nose radii and thickness distribution*.\par +\ul\b Objective\par +\ulnone\b0 The effects of changing specific geometric parameters are studied using NACA 4 and 5 series airfoils. The effects on maximum lift, drag, stall characteristics and pitching moment are all taken into account. A further analysis is done on airfoil selection. \par +Using these results, the objective is to gain an intuitive understanding of the type of geometry that may meet the design requirements for an aircraft*.\par +\par +\ul\b Analysis\par +\ulnone\b0 For the most part, XFLR5 will be used for analysis, in order to study stall characteristics. The NACA 4 and 5 series are studied individually. An attempt at cross analysis is made at the end*.\par +The geometric parameters used as variables will be;\par +\tab - camber\par +\tab - location of max camber\par + \tab - max thickness\par +\tab - location of max thickness\par +\tab - leading edge radii\par +\tab - normal and reflex camber\par +\tab - thickness distribution*\par +All of the simulations are carried out at speeds of Mach 0.14 and a Reynold's number of 3 million exactly. These values are typical for light, acrobatic aircrafts which commonly use symmetric airfoils like the NACA0012 and 0015.\par +\ul\b NACA series\ulnone\b0\par +Most airfoil sections in use today are either of the NACA series or are heavily influenced by them. They were the first to seperate the effects of camber and thickness distribution. NACA airfoils are the easiest to find and their geometry is easy to reproduce using their numbering system. This study will thus focus on the 4 and 5 digit series of NACA airfoils. The geometry of the other types are generated by working backwards from certain aerodynamic parameters. This makes a progressive, comparative* analysis difficult and so they will not be cosidered.\par +\par +\ul\b Description of airfoil geometry\par + +\pard\sa200\sl240\slmult1{\pict{\*\picprop}\wmetafile8\picw12700\pich8096\picwgoal5100\pichgoal3255 +0100090000032a21010000000121010000000400000003010800050000000b0200000000050000 +000c023201e001030000001e000400000007010400040000000701040001210100410b2000cc00 +3201e001000000003201e0010000000028000000e0010000320100000100080000000000000000 +000000000000000000000000000000000000000000ffffff00c0c0c000cccccc00996666006666 +66006633660099999900cc666600cc000000cc333300ffcccc0099336600ff000000cc99990099 +6699006633330080808000cc00330033333300ccffff0099cc9900999966003366000033663300 +66993300666600006699660066663300669999009933330099993300cc990000cccc9900cc9966 +00cc9933003366660099cccc009966000066000000990000009999cc006699cc000066cc003366 +cc000066990033669900ccccff00333300003399cc003300000099663300800000000033990066 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always equidistant from the top and bottom surfaces of the airfoil.\par +\b camber\b0 - the maximum distance between the chord and mean camber line\par +\b max thickness \b0 - the maximum distance between the upper and lower surfaces of the airfoil\par +\b leading edge radius \b0 - the radius of the curvature of the leading edge. 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+111111111111111111111111111111111111111111111111111111111111111111111111111111 +111111111111111111111111111111111111111111111111111111111111111111111111111111 +111111111111111111111111111111111111111111111111111111111111111111111111111111 +1111111111111111111111111111111111111111111111111111111110040000002701ffff0300 +00000000 +}\par + +\pard\sa200\sl276\slmult1 This equation was derived from the thickness distributions of effecient wing sections such as the Gottingen and Clark Y. Changing the leading edge radius ends up changing this distribution. This was studied in the modified NACA 4 and 5 digit series which will be discussed later.\par +\par +\ul\b NACA 4 digit series\par +\ulnone\b0 The 4 digit wing profile is defined by the following:\par +1) The first digit describes the max camber as a percent of the chord\par +2) The second digit describes the distance of the max camber from the leading edge as a percent of the chord\par +3) The last two digits describe the maximum thickness of the airfoil as a percent of the chord\par +By default, 4 digit series airfoils have a maximum thickness at 30% of the chord.\par +For a symmetric airfoil, the airfoil geometry is defined simply by:\par + +\pard\sa200\sl240\slmult1\qc{\pict{\*\picprop}\wmetafile8\picw3175\pich450\picwgoal1800\pichgoal255 +0100090000036802000000003f02000000000400000003010800050000000b0200000000050000 +000c0211007800030000001e00040000000701040004000000070104003f020000410b2000cc00 +110078000000000011007800000000002800000078000000110000000100040000000000000000 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'yt' is the airfoil thickness as a function of x, shown previously. Theta goes from 0 to 2*pi(*).\par +For a cambered airfoil, the mean camber line, yc, must be included. The equation for the mean camber line is;\par +Forward of maximum camber - \par +{\pict{\*\picprop}\wmetafile8\picw3678\pich979\picwgoal2085\pichgoal555 +0100090000039e05000000007505000000000400000003010800050000000b0200000000050000 +000c0225008b00030000001e000400000007010400040000000701040075050000410b2000cc00 +25008b000000000025008b0000000000280000008b000000250000000100040000000000000000 +000000000000000000000000000000000000000000ffffff00999999008080800066666600c0c0 +c000cccccc00333333000000000000000000000000000000000000000000000000000000000000 +000000111111111111111111111111111111111111111111157041111111111111111111111111 +111111111111111111111111111111111111111111111111111111111111111111100101111111 +111111111111111111111111111111111111116011111111111111111111111111111111111111 +111111111111111111111111111111111111111111111111111111100101111111111111111111 +111111111111111111111111111061111111111111111111111111111111111111111111111111 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with increasing camber. There is no apparent change in the lift slope or the stall angle. In other words, the basic equation for the lift slope changes from;\par + +\pard\sa200\sl240\slmult1\qc{\pict{\*\picprop}\wmetafile8\picw1826\pich397\picwgoal1035\pichgoal225 +0100090000037801000000004f01000000000400000003010800050000000b0200000000050000 +000c020f004500030000001e00040000000701040004000000070104004f010000410b2000cc00 +0f004500000000000f0045000000000028000000450000000f0000000100040000000000000000 +000000000000000000000000000000000000000000ffffff008080800066666600cccccc003333 +3300c0c0c000999999000000000000000000000000000000000000000000000000000000000000 +000000111111111111143711111111111111111111111111111111111122241111111111111001 +111111111111172711111111111111111111111111111111111631154111111111111000111111 +111111145111111111111111111111111111111111111731165111111111111001111232224111 +110111111111111111111111111111162774321451110114277714321000115211114211115411 +111111111111111111111111101115217137115115411165211001135111111121112211111111 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It is interesting to note that the highest lift-drag ratio occurs at an angle of around 5 degrees for most of the airfoils. For the zero camber and the really low cambered airfoil, it is closer to 10 degrees. The performance of the higher cambered airfoils are still greater at that point. (Important parameter for gliders)*\par +The range of CL, over which drag variation is close to zero is also shown to increase with camber. This gives better cruise performance, as it allows an aircraft to change it's angle of attack over a wider range without experiencing change in drag, and thus, reducing the need for throttle control.\par +\b Pitching moment\b0\par +{\pict{\*\picprop}\wmetafile8\picw16589\pich8149\picwgoal8640\pichgoal4245 +010009000003127c01000000e97b010000000400000003010800050000000b0200000000050000 +000c0234017302030000001e0004000000070104000400000007010400e97b0100410b2000cc00 +340173020000000034017302000000002800000073020000340100000100080000000000000000 +000000000000000000000000000000000000000000ffffff000a050000c8c8c800140a0000dc9d +5800dcdcdc00367dbd00be7d32007ebddc005c040000dcdc9d000a5a9d005c9ddc00dcbd7c00be +9d58009ebdbd000a0458007e3400007ebdbd000a347c009e5a00009e7d7c005c9dbd009ebd7c00 +7ebd9d00dcdcbd007e7d9d00bedcdc00367d9d00b96900006eb8ff00dc913a00b9ffff00140a66 +00b9b86600bebd7c00450a0000dcdb8f00143e8f00943e0000b9dbdb00ffdbb6004569b600ffdb 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+040404040404040404040404040404040404040404040404040404040404040404040404040404 +0404040404040404040400040000002701ffff030000000000 +}\par +The pitching moment graph clearly shows more negative moments with increasing camber. This would likely lead to better stability, as the aircraft will naturally tend to pitch nose down. Looking at this graph, it is clear why sports aircraft prefer to use symmetric airfoils for their main wing, instead of the higher lift, cambered airfoils.\par +While the pitching moment fluctuations remain relatively small, higher camber seems to increase the amplitude of the fluctuations towards the stall angle.\par +\par +\b Effects of camber location\par +\b0 The following simulations were ran using NACA 4 digit airfoils with 12% thickness and 3%camber.\par +\b Lift\par +\b0{\pict{\*\picprop}\wmetafile8\picw18045\pich16589\picwgoal8640\pichgoal7950 +010009000003ec4703000000c347030000000400000003010800050000000b0200000000050000 +000c027302aa02030000001e0004000000070104000400000007010400c3470300410b2000cc00 +7302aa02000000007302aa020000000028000000aa020000730200000100080000000000000000 +000000000000000000000000000000000000000000ffffff00c8c8c80090dbff00903a3a00ffff +db0066b6ff00b66600003a90db0066000000ffffb6006666b60090dbb600dbffff003a3a9000ff 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In the linear part, the Cl seems to increase with increasing distance of the max camber from the leading edge. The zero degree angle lift for camber at 70%, is almost three times higher than the Cl at 10% camber location. Considering this, it makes sense to locate high-lift devices (i.e, flaps, elevators, etc.) at the trailing edge of the wing. \par +Towards stall however, the behaviour is a bit more interesting. Zooming in towards that region, we can see the Cl increasing on either side of the mid point mark of the chord. The Cl decreases from from 10% to 40% camber location, but then starts increasing past 50%. 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The value of the maximum lift-drag ratio, however, decreases, especially at the 50% mark. 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This is likely because it stalls much earlier than the rest, being the thinnest airfoil in this group.\par +\par +\par +\par +\par +\par + +\pard\sa200\sl276\slmult1\ul\b\par +\ulnone\b0\par +\par +} + \ No newline at end of file diff --git a/Airfoil characteristics - amiya/Report/camber loc/5-series camber.wpa b/Airfoil characteristics - amiya/Report/camber loc/5-series camber.wpa new file mode 100644 index 0000000..4cc6bbd Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/5-series camber.wpa differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber loc/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..48ca10d --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,79 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1329 0.01145 0.00651 -0.0006 1.0000 0.0164 -6.0202 0.0000 0.2383 + -9.500 -1.0892 0.01091 0.00597 0.0021 1.0000 0.0180 -5.5706 0.0000 0.2414 + -8.500 -0.9718 0.00987 0.00490 0.0011 0.9975 0.0223 -4.5968 0.0000 0.2418 + -8.000 -0.9072 0.00932 0.00440 -0.0008 0.9953 0.0260 -4.1143 0.0000 0.2404 + -7.500 -0.8408 0.00887 0.00397 -0.0029 0.9935 0.0294 -3.6464 0.0000 0.2383 + -7.000 -0.7793 0.00839 0.00353 -0.0040 0.9886 0.0357 -3.2165 0.0000 0.2371 + -6.500 -0.7185 0.00794 0.00314 -0.0049 0.9808 0.0448 -2.8614 0.0000 0.2359 + -6.000 -0.6640 0.00757 0.00281 -0.0043 0.9670 0.0544 -2.5473 0.0000 0.2367 + -5.500 -0.6102 0.00721 0.00250 -0.0035 0.9493 0.0672 -2.2476 0.0000 0.2378 + -5.000 -0.5564 0.00687 0.00219 -0.0027 0.9268 0.0843 -1.9599 0.0000 0.2390 + 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24.000 0.9396 0.29898 0.29797 -0.1049 0.0048 1.0000 -2.5370 0.0000 0.3313 + 24.500 0.9555 0.30433 0.30332 -0.1092 0.0042 1.0000 -2.7097 0.0000 0.3328 + 25.000 0.9713 0.30941 0.30841 -0.1136 0.0038 1.0000 -2.9101 0.0000 0.3341 + + diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA 13012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber loc/NACA 13012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..c517e80 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 13012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,67 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 13012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.0921 0.01565 0.01172 -0.0064 1.0000 0.0012 -9.8383 0.0000 0.2350 + -9.500 -1.0593 0.01394 0.00977 -0.0019 1.0000 0.0011 -9.0657 0.0000 0.2396 + -9.000 -1.0249 0.01231 0.00788 0.0024 1.0000 0.0011 -8.3103 0.0000 0.2444 + -8.500 -0.9887 0.01094 0.00623 0.0066 1.0000 0.0012 -7.5837 0.0000 0.2493 + -8.000 -0.9311 0.00999 0.00508 0.0064 0.9990 0.0024 -6.7666 0.0000 0.2501 + -7.500 -0.8679 0.00935 0.00445 0.0048 0.9974 0.0035 -5.7815 0.0000 0.2493 + -7.000 -0.8034 0.00874 0.00387 0.0030 0.9959 0.0075 -4.8521 0.0000 0.2479 + -6.500 -0.7444 0.00811 0.00330 0.0023 0.9936 0.0158 -4.1746 0.0000 0.2478 + -6.000 -0.6823 0.00763 0.00289 0.0010 0.9905 0.0235 -3.5359 0.0000 0.2467 + -5.500 -0.6178 0.00728 0.00255 -0.0007 0.9876 0.0265 -2.9319 0.0000 0.2444 + -5.000 -0.5521 0.00690 0.00223 -0.0028 0.9850 0.0351 -2.3723 0.0000 0.2409 + -4.500 -0.4873 0.00657 0.00195 -0.0046 0.9821 0.0436 -1.9280 0.0000 0.2368 + -4.000 -0.4295 0.00625 0.00167 -0.0048 0.9719 0.0512 -1.6512 0.0000 0.2354 + -3.500 -0.3575 0.00579 0.00137 -0.0084 0.9620 0.0861 -1.3614 0.0000 0.2233 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-6.3598 0.0000 0.2731 + + diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA 23012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber loc/NACA 23012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..104d72a --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 23012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,83 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 23012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -9.500 -0.9402 0.01201 0.00762 -0.0149 0.9978 0.0108 -8.4561 0.0000 0.2246 + -9.000 -0.8762 0.01129 0.00686 -0.0163 0.9954 0.0113 -7.7632 0.0000 0.2223 + -8.500 -0.8105 0.01066 0.00619 -0.0181 0.9932 0.0117 -7.0840 0.0000 0.2191 + -8.000 -0.7492 0.01001 0.00550 -0.0189 0.9872 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-0.0881 0.0063 1.0000 -8.4149 0.0000 0.2757 + + diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA 3112_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber loc/NACA 3112_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..ef8aaa4 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 3112_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,80 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 3112 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -9.000 -0.4037 0.08269 0.08176 -0.0280 1.0000 0.0075 -3.1071 0.0000 0.1715 + -8.500 -0.3904 0.07528 0.07436 -0.0352 0.9926 0.0078 -2.9832 0.0000 0.1513 + -8.000 -0.3894 0.06479 0.06373 -0.0483 0.9441 0.0080 -3.0491 0.0000 0.1185 + -7.500 -0.3757 0.05835 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loc/NACA 3212_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..d56379d --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 3212_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,81 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 3212 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.7959 0.01152 0.00745 -0.0617 0.9801 0.0101 -9.2935 0.0000 0.1615 + -9.500 -0.7432 0.01108 0.00701 -0.0604 0.9670 0.0112 -8.6145 0.0000 0.1582 + -9.000 -0.6888 0.01078 0.00670 -0.0594 0.9520 0.0117 -7.9278 0.0000 0.1536 + -8.500 -0.6333 0.01055 0.00647 -0.0587 0.9368 0.0120 -7.2542 0.0000 0.1475 + -8.000 -0.5774 0.01036 0.00624 -0.0581 0.9183 0.0121 -6.6078 0.0000 0.1399 + -7.500 -0.5221 0.01002 0.00583 -0.0574 0.8962 0.0122 -6.0044 0.0000 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0.04780 0.04615 0.0337 0.0020 1.0000 -12.3938 0.0000 0.2045 + 14.000 1.0667 0.06243 0.06097 0.0216 0.0019 1.0000 -12.2928 0.0000 0.2143 + 14.500 1.0299 0.07928 0.07793 0.0116 0.0017 1.0000 -11.8924 0.0000 0.2226 + 15.000 0.9579 0.10122 0.09995 0.0005 0.0016 1.0000 -10.6672 0.0000 0.2330 + 15.500 0.8813 0.12410 0.12291 -0.0110 0.0015 1.0000 -9.1276 0.0000 0.2460 + 16.000 0.8233 0.14652 0.14540 -0.0218 0.0014 1.0000 -7.6530 0.0000 0.2602 + 16.500 0.7851 0.16639 0.16533 -0.0306 0.0015 1.0000 -6.3598 0.0000 0.2731 + + diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA 3312_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber loc/NACA 3312_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..aa1b3ea --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 3312_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,81 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 3312 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.7829 0.01151 0.00747 -0.0719 0.9685 0.0120 -7.8053 0.0000 0.1467 + -9.500 -0.7289 0.01112 0.00705 -0.0710 0.9552 0.0121 -7.1828 0.0000 0.1416 + -9.000 -0.6772 0.01021 0.00596 -0.0698 0.9405 0.0127 -6.6437 0.0000 0.1363 + -8.500 -0.6245 0.00941 0.00498 -0.0687 0.9203 0.0135 -6.1233 0.0000 0.1296 + -8.000 -0.5702 0.00884 0.00425 -0.0679 0.8973 0.0147 -5.6035 0.0000 0.1208 + -7.500 -0.5148 0.00838 0.00372 -0.0674 0.8764 0.0166 -5.0866 0.0000 0.1093 + -7.000 -0.4581 0.00806 0.00336 -0.0671 0.8569 0.0183 -4.5748 0.0000 0.0938 + -6.500 -0.4010 0.00786 0.00309 -0.0669 0.8353 0.0188 -4.0749 0.0000 0.0734 + -6.000 -0.3447 0.00752 0.00263 -0.0665 0.8081 0.0214 -3.6199 0.0000 0.0471 + -5.500 -0.2884 0.00727 0.00231 -0.0662 0.7767 0.0251 -3.2156 0.0000 0.0100 + -4.500 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Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.7653 0.01099 0.00682 -0.0826 0.9582 0.0125 -7.0454 0.0000 0.1302 + -9.500 -0.7140 0.01008 0.00572 -0.0815 0.9434 0.0134 -6.5306 0.0000 0.1245 + -9.000 -0.6602 0.00942 0.00493 -0.0807 0.9276 0.0147 -6.0095 0.0000 0.1168 + -8.500 -0.6046 0.00886 0.00434 -0.0803 0.9161 0.0166 -5.4884 0.0000 0.1065 + -8.000 -0.5487 0.00849 0.00391 -0.0799 0.9005 0.0183 -4.9741 0.0000 0.0938 + -7.500 -0.4915 0.00822 0.00360 -0.0798 0.8864 0.0188 -4.4693 0.0000 0.0772 + -7.000 -0.4350 0.00780 0.00309 -0.0795 0.8695 0.0214 -4.0037 0.0000 0.0568 + -6.500 -0.3785 0.00746 0.00271 -0.0793 0.8503 0.0252 -3.5523 0.0000 0.0300 + -6.000 -0.3210 0.00724 0.00244 -0.0792 0.8325 0.0269 -3.1635 0.0000 -0.0077 + -5.500 -0.2640 0.00695 0.00212 -0.0791 0.8111 0.0333 -2.8157 0.0000 -0.0613 + -5.000 -0.2065 0.00678 0.00188 -0.0791 0.7885 0.0364 -2.4739 0.0000 -0.1458 + -4.500 -0.1494 0.00657 0.00164 -0.0790 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22.500 1.5593 0.14301 0.14044 -0.0525 0.0062 1.0000 -12.2862 0.0000 0.2424 + 23.000 1.5296 0.15505 0.15264 -0.0590 0.0061 1.0000 -12.1864 0.0000 0.2459 + 23.500 1.4920 0.16935 0.16712 -0.0675 0.0059 1.0000 -11.9364 0.0000 0.2513 + 24.000 1.4620 0.18279 0.18072 -0.0759 0.0058 1.0000 -11.7287 0.0000 0.2566 + 24.500 1.4248 0.19854 0.19665 -0.0864 0.0056 1.0000 -11.3473 0.0000 0.2641 + 25.000 1.3950 0.21345 0.21171 -0.0966 0.0054 1.0000 -10.9995 0.0000 0.2716 + + diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA 3512_T1_Al 0.00_M0.14_N9.0 (2).txt b/Airfoil characteristics - amiya/Report/camber loc/NACA 3512_T1_Al 0.00_M0.14_N9.0 (2).txt new file mode 100644 index 0000000..1dc225b --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 3512_T1_Al 0.00_M0.14_N9.0 (2).txt @@ -0,0 +1,83 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 3512 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.7408 0.01030 0.00594 -0.0946 0.9475 0.0136 -6.5557 0.0000 0.1100 + -9.500 -0.6860 0.00961 0.00518 -0.0942 0.9395 0.0152 -6.0334 0.0000 0.1008 + -9.000 -0.6309 0.00907 0.00459 -0.0938 0.9287 0.0172 -5.5170 0.0000 0.0898 + -8.500 -0.5742 0.00868 0.00417 -0.0937 0.9194 0.0185 -5.0030 0.0000 0.0755 + -8.000 -0.5173 0.00839 0.00384 -0.0936 0.9079 0.0188 -4.5045 0.0000 0.0579 + -7.500 -0.4609 0.00788 0.00327 -0.0934 0.8968 0.0229 -4.0477 0.0000 0.0362 + -7.000 -0.4039 0.00753 0.00289 -0.0933 0.8837 0.0260 -3.5951 0.0000 0.0077 + -6.500 -0.3462 0.00726 0.00258 -0.0934 0.8714 0.0282 -3.2014 0.0000 -0.0314 + -6.000 -0.2892 0.00694 0.00225 -0.0934 0.8555 0.0351 -2.8539 0.0000 -0.0850 + -5.500 -0.2311 0.00670 0.00198 -0.0935 0.8428 0.0405 -2.5141 0.0000 -0.1678 + -5.000 -0.1738 0.00649 0.00174 -0.0935 0.8242 0.0471 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0.03014 0.02537 -0.0378 0.0075 1.0000 -10.2194 0.0000 0.2489 + 16.000 1.7549 0.03404 0.02946 -0.0344 0.0072 1.0000 -10.5744 0.0000 0.2458 + 16.500 1.7528 0.03896 0.03460 -0.0315 0.0069 1.0000 -10.8722 0.0000 0.2430 + 17.000 1.7562 0.04369 0.03948 -0.0297 0.0069 1.0000 -11.2352 0.0000 0.2408 + 17.500 1.7611 0.04862 0.04453 -0.0287 0.0068 1.0000 -11.6176 0.0000 0.2389 + 18.000 1.7638 0.05409 0.05013 -0.0282 0.0068 1.0000 -11.9843 0.0000 0.2373 + 18.500 1.7634 0.06016 0.05635 -0.0282 0.0068 1.0000 -12.3249 0.0000 0.2361 + 19.000 1.7548 0.06745 0.06378 -0.0290 0.0068 1.0000 -12.5910 0.0000 0.2353 + 19.500 1.7439 0.07531 0.07180 -0.0304 0.0067 1.0000 -12.8305 0.0000 0.2348 + 20.000 1.7287 0.08404 0.08069 -0.0324 0.0067 1.0000 -13.0203 0.0000 0.2348 + 20.500 1.7042 0.09440 0.09123 -0.0356 0.0066 1.0000 -13.1042 0.0000 0.2356 + 21.000 1.6749 0.10548 0.10249 -0.0395 0.0066 1.0000 -13.1206 0.0000 0.2369 + 21.500 1.6407 0.11779 0.11499 -0.0445 0.0065 1.0000 -13.0583 0.0000 0.2391 + 22.000 1.5996 0.13167 0.12908 -0.0511 0.0065 1.0000 -12.8800 0.0000 0.2425 + 22.500 1.5564 0.14622 0.14383 -0.0587 0.0064 1.0000 -12.6288 0.0000 0.2470 + 23.000 1.5166 0.16064 0.15844 -0.0669 0.0064 1.0000 -12.3644 0.0000 0.2521 + 23.500 1.4713 0.17710 0.17511 -0.0772 0.0063 1.0000 -11.9532 0.0000 0.2592 + 24.000 1.4281 0.19417 0.19238 -0.0884 0.0062 1.0000 -11.4799 0.0000 0.2675 + 24.500 1.3978 0.20931 0.20766 -0.0988 0.0061 1.0000 -11.1193 0.0000 0.2751 + 25.000 1.3611 0.22706 0.22558 -0.1112 0.0059 1.0000 -10.5444 0.0000 0.2851 + + diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA 3512_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber loc/NACA 3512_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..1dc225b --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 3512_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,83 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 3512 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.7408 0.01030 0.00594 -0.0946 0.9475 0.0136 -6.5557 0.0000 0.1100 + -9.500 -0.6860 0.00961 0.00518 -0.0942 0.9395 0.0152 -6.0334 0.0000 0.1008 + -9.000 -0.6309 0.00907 0.00459 -0.0938 0.9287 0.0172 -5.5170 0.0000 0.0898 + -8.500 -0.5742 0.00868 0.00417 -0.0937 0.9194 0.0185 -5.0030 0.0000 0.0755 + -8.000 -0.5173 0.00839 0.00384 -0.0936 0.9079 0.0188 -4.5045 0.0000 0.0579 + -7.500 -0.4609 0.00788 0.00327 -0.0934 0.8968 0.0229 -4.0477 0.0000 0.0362 + -7.000 -0.4039 0.00753 0.00289 -0.0933 0.8837 0.0260 -3.5951 0.0000 0.0077 + -6.500 -0.3462 0.00726 0.00258 -0.0934 0.8714 0.0282 -3.2014 0.0000 -0.0314 + -6.000 -0.2892 0.00694 0.00225 -0.0934 0.8555 0.0351 -2.8539 0.0000 -0.0850 + -5.500 -0.2311 0.00670 0.00198 -0.0935 0.8428 0.0405 -2.5141 0.0000 -0.1678 + 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1.0000 -9.8241 0.0000 0.2522 + 15.500 1.7498 0.03014 0.02537 -0.0378 0.0075 1.0000 -10.2194 0.0000 0.2489 + 16.000 1.7549 0.03404 0.02946 -0.0344 0.0072 1.0000 -10.5744 0.0000 0.2458 + 16.500 1.7528 0.03896 0.03460 -0.0315 0.0069 1.0000 -10.8722 0.0000 0.2430 + 17.000 1.7562 0.04369 0.03948 -0.0297 0.0069 1.0000 -11.2352 0.0000 0.2408 + 17.500 1.7611 0.04862 0.04453 -0.0287 0.0068 1.0000 -11.6176 0.0000 0.2389 + 18.000 1.7638 0.05409 0.05013 -0.0282 0.0068 1.0000 -11.9843 0.0000 0.2373 + 18.500 1.7634 0.06016 0.05635 -0.0282 0.0068 1.0000 -12.3249 0.0000 0.2361 + 19.000 1.7548 0.06745 0.06378 -0.0290 0.0068 1.0000 -12.5910 0.0000 0.2353 + 19.500 1.7439 0.07531 0.07180 -0.0304 0.0067 1.0000 -12.8305 0.0000 0.2348 + 20.000 1.7287 0.08404 0.08069 -0.0324 0.0067 1.0000 -13.0203 0.0000 0.2348 + 20.500 1.7042 0.09440 0.09123 -0.0356 0.0066 1.0000 -13.1042 0.0000 0.2356 + 21.000 1.6749 0.10548 0.10249 -0.0395 0.0066 1.0000 -13.1206 0.0000 0.2369 + 21.500 1.6407 0.11779 0.11499 -0.0445 0.0065 1.0000 -13.0583 0.0000 0.2391 + 22.000 1.5996 0.13167 0.12908 -0.0511 0.0065 1.0000 -12.8800 0.0000 0.2425 + 22.500 1.5564 0.14622 0.14383 -0.0587 0.0064 1.0000 -12.6288 0.0000 0.2470 + 23.000 1.5166 0.16064 0.15844 -0.0669 0.0064 1.0000 -12.3644 0.0000 0.2521 + 23.500 1.4713 0.17710 0.17511 -0.0772 0.0063 1.0000 -11.9532 0.0000 0.2592 + 24.000 1.4281 0.19417 0.19238 -0.0884 0.0062 1.0000 -11.4799 0.0000 0.2675 + 24.500 1.3978 0.20931 0.20766 -0.0988 0.0061 1.0000 -11.1193 0.0000 0.2751 + 25.000 1.3611 0.22706 0.22558 -0.1112 0.0059 1.0000 -10.5444 0.0000 0.2851 + + diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA 3612_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber loc/NACA 3612_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..f862f9b --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber loc/NACA 3612_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,84 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 3612 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.7011 0.00991 0.00550 -0.1096 0.9428 0.0152 -6.1100 0.0000 0.0808 + -9.500 -0.6455 0.00931 0.00490 -0.1095 0.9376 0.0173 -5.5915 0.0000 0.0678 + -9.000 -0.5890 0.00890 0.00444 -0.1095 0.9302 0.0185 -5.0819 0.0000 0.0519 + -8.500 -0.5315 0.00858 0.00409 -0.1096 0.9227 0.0189 -4.5831 0.0000 0.0316 + -8.000 -0.4746 0.00802 0.00350 -0.1097 0.9183 0.0232 -4.1253 0.0000 0.0068 + -7.500 -0.4172 0.00764 0.00311 -0.1098 0.9114 0.0262 -3.6711 0.0000 -0.0255 + -7.000 -0.3596 0.00736 0.00278 -0.1100 0.9007 0.0287 -3.2626 0.0000 -0.0684 + -6.500 -0.3018 0.00697 0.00244 -0.1102 0.8948 0.0354 -2.9120 0.0000 -0.1284 + -6.000 -0.2441 0.00670 0.00214 -0.1103 0.8837 0.0418 -2.5756 0.0000 -0.2162 + -5.500 -0.1859 0.00644 0.00188 -0.1106 0.8741 0.0481 -2.2500 0.0000 -0.3613 + -5.000 -0.1275 0.00617 0.00164 -0.1109 0.8653 0.0591 -1.9416 0.0000 -0.6402 + -4.500 -0.0698 0.00593 0.00143 -0.1110 0.8518 0.0762 -1.6600 0.0000 -1.3730 + -4.000 -0.0110 0.00566 0.00124 -0.1114 0.8451 0.0959 -1.4216 0.0000 -10.0228 + -3.500 0.0470 0.00545 0.00108 -0.1117 0.8325 0.1191 -1.1966 0.0000 2.6596 + -3.000 0.1054 0.00523 0.00095 -0.1120 0.8212 0.1508 -0.9961 0.0000 1.3256 + -2.500 0.1636 0.00504 0.00084 -0.1123 0.8076 0.1872 -0.8218 0.0000 0.9429 + -2.000 0.2219 0.00489 0.00076 -0.1126 0.7932 0.2212 -0.6692 0.0000 0.7610 + -1.500 0.2794 0.00478 0.00070 -0.1127 0.7731 0.2630 -0.5376 0.0000 0.6552 + -1.000 0.3374 0.00466 0.00068 -0.1130 0.7542 0.3063 -0.5419 0.0000 0.5853 + -0.500 0.3945 0.00464 0.00068 -0.1130 0.7263 0.3477 -0.5842 0.0000 0.5361 + 0.000 0.4500 0.00472 0.00072 -0.1127 0.6829 0.3917 -0.6300 0.0000 0.4994 + 0.500 0.5039 0.00493 0.00081 -0.1121 0.6190 0.4359 -0.6802 0.0000 0.4708 + 1.000 0.5578 0.00519 0.00095 -0.1116 0.5597 0.4775 -0.7375 0.0000 0.4478 + 1.500 0.6119 0.00544 0.00111 -0.1111 0.5051 0.5231 -0.8059 0.0000 0.4288 + 2.000 0.6656 0.00573 0.00129 -0.1105 0.4499 0.5637 -0.8937 0.0000 0.4128 + 2.500 0.7190 0.00608 0.00150 -0.1099 0.3948 0.6013 -1.0085 0.0000 0.3991 + 3.000 0.7719 0.00646 0.00174 -0.1091 0.3401 0.6339 -1.1495 0.0000 0.3872 + 3.500 0.8241 0.00689 0.00203 -0.1083 0.2855 0.6666 -1.3178 0.0000 0.3768 + 4.000 0.8759 0.00733 0.00234 -0.1074 0.2348 0.7072 -1.5120 0.0000 0.3675 + 4.500 0.9258 0.00784 0.00275 -0.1061 0.1784 0.7764 -1.7206 0.0000 0.3590 + 5.000 0.9724 0.00800 0.00316 -0.1040 0.1357 1.0000 -1.9468 0.0000 0.3508 + 5.500 1.0230 0.00861 0.00358 -0.1028 0.1006 1.0000 -2.2154 0.0000 0.3438 + 6.000 1.0737 0.00920 0.00401 -0.1017 0.0760 1.0000 -2.4937 0.0000 0.3375 + 6.500 1.1246 0.00973 0.00444 -0.1006 0.0584 1.0000 -2.7843 0.0000 0.3316 + 7.000 1.1749 0.01028 0.00492 -0.0994 0.0458 1.0000 -3.1272 0.0000 0.3261 + 7.500 1.2246 0.01085 0.00541 -0.0980 0.0362 1.0000 -3.4945 0.0000 0.3210 + 8.000 1.2739 0.01140 0.00592 -0.0966 0.0312 1.0000 -3.8767 0.0000 0.3161 + 8.500 1.3224 0.01196 0.00646 -0.0951 0.0264 1.0000 -4.2704 0.0000 0.3115 + 9.000 1.3694 0.01257 0.00705 -0.0932 0.0231 1.0000 -4.6729 0.0000 0.3070 + 9.500 1.4138 0.01329 0.00776 -0.0909 0.0188 1.0000 -5.0740 0.0000 0.3025 + 10.000 1.4576 0.01385 0.00833 -0.0885 0.0180 1.0000 -5.4986 0.0000 0.2981 + 10.500 1.4967 0.01459 0.00907 -0.0853 0.0161 1.0000 -5.9120 0.0000 0.2936 + 11.000 1.5330 0.01550 0.01001 -0.0817 0.0136 1.0000 -6.3453 0.0000 0.2891 + 11.500 1.5680 0.01652 0.01111 -0.0779 0.0121 1.0000 -6.8208 0.0000 0.2847 + 12.000 1.6051 0.01735 0.01197 -0.0747 0.0120 1.0000 -7.3400 0.0000 0.2808 + 12.500 1.6413 0.01829 0.01295 -0.0716 0.0117 1.0000 -7.8697 0.0000 0.2769 + 13.000 1.6742 0.01941 0.01412 -0.0680 0.0110 1.0000 -8.3940 0.0000 0.2730 + 13.500 1.7026 0.02085 0.01560 -0.0640 0.0099 1.0000 -8.8997 0.0000 0.2691 + 14.000 1.7266 0.02259 0.01741 -0.0597 0.0088 1.0000 -9.3813 0.0000 0.2651 + 14.500 1.7474 0.02465 0.01959 -0.0553 0.0080 1.0000 -9.8446 0.0000 0.2612 + 15.000 1.7644 0.02710 0.02220 -0.0510 0.0076 1.0000 -10.2887 0.0000 0.2574 + 15.500 1.7750 0.03008 0.02536 -0.0465 0.0073 1.0000 -10.6936 0.0000 0.2537 + 16.000 1.7788 0.03388 0.02936 -0.0421 0.0071 1.0000 -11.0501 0.0000 0.2501 + 16.500 1.7782 0.03835 0.03405 -0.0384 0.0069 1.0000 -11.3778 0.0000 0.2469 + 17.000 1.7868 0.04231 0.03814 -0.0360 0.0069 1.0000 -11.8029 0.0000 0.2443 + 17.500 1.7935 0.04682 0.04277 -0.0342 0.0068 1.0000 -12.2166 0.0000 0.2420 + 18.000 1.7958 0.05217 0.04827 -0.0331 0.0068 1.0000 -12.5955 0.0000 0.2401 + 18.500 1.7948 0.05823 0.05447 -0.0328 0.0068 1.0000 -12.9452 0.0000 0.2387 + 19.000 1.7889 0.06512 0.06150 -0.0332 0.0068 1.0000 -13.2474 0.0000 0.2376 + 19.500 1.7762 0.07336 0.06991 -0.0346 0.0067 1.0000 -13.4776 0.0000 0.2372 + 20.000 1.7558 0.08302 0.07975 -0.0372 0.0067 1.0000 -13.6196 0.0000 0.2375 + 20.500 1.7276 0.09405 0.09098 -0.0407 0.0066 1.0000 -13.6650 0.0000 0.2386 + 21.000 1.6892 0.10681 0.10395 -0.0456 0.0066 1.0000 -13.5764 0.0000 0.2406 + 21.500 1.6429 0.12143 0.11880 -0.0522 0.0066 1.0000 -13.3607 0.0000 0.2440 + 22.000 1.5911 0.13754 0.13514 -0.0604 0.0066 1.0000 -13.0238 0.0000 0.2489 + 22.500 1.5353 0.15475 0.15258 -0.0701 0.0065 1.0000 -12.5693 0.0000 0.2554 + 23.000 1.4815 0.17287 0.17092 -0.0813 0.0065 1.0000 -12.0444 0.0000 0.2634 + 23.500 1.4324 0.19129 0.18955 -0.0934 0.0065 1.0000 -11.4781 0.0000 0.2727 + 24.000 1.3984 0.20742 0.20584 -0.1044 0.0064 1.0000 -11.0474 0.0000 0.2810 + 24.500 1.3610 0.22558 0.22418 -0.1172 0.0063 1.0000 -10.4437 0.0000 0.2915 + 25.000 1.3402 0.23969 0.23840 -0.1285 0.0061 1.0000 -10.0146 0.0000 0.3002 + + diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA0012 cp-10.bmp b/Airfoil characteristics - amiya/Report/camber loc/NACA0012 cp-10.bmp new file mode 100644 index 0000000..67bdddb Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/NACA0012 cp-10.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA3112 cp-10.bmp b/Airfoil characteristics - amiya/Report/camber loc/NACA3112 cp-10.bmp new file mode 100644 index 0000000..5a0b83b Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/NACA3112 cp-10.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA3212 cp-10.bmp b/Airfoil characteristics - amiya/Report/camber loc/NACA3212 cp-10.bmp new file mode 100644 index 0000000..a88503d Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/NACA3212 cp-10.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA3312 cp-10.bmp b/Airfoil characteristics - amiya/Report/camber loc/NACA3312 cp-10.bmp new file mode 100644 index 0000000..faf96c2 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/NACA3312 cp-10.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA3412 cp-10.bmp b/Airfoil characteristics - amiya/Report/camber loc/NACA3412 cp-10.bmp new file mode 100644 index 0000000..05b8a16 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/NACA3412 cp-10.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA3512 cp-10.bmp b/Airfoil characteristics - amiya/Report/camber loc/NACA3512 cp-10.bmp new file mode 100644 index 0000000..e24f31a Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/NACA3512 cp-10.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/NACA3612 cp-10.bmp b/Airfoil characteristics - amiya/Report/camber loc/NACA3612 cp-10.bmp new file mode 100644 index 0000000..7834ee4 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/NACA3612 cp-10.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars.bmp b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars.bmp new file mode 100644 index 0000000..3066327 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars2.bmp b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars2.bmp new file mode 100644 index 0000000..82b6b35 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars2.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars3.bmp b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars3.bmp new file mode 100644 index 0000000..4955c42 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars3.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars4.bmp b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars4.bmp new file mode 100644 index 0000000..67b8d79 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars4.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars5.bmp b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars5.bmp new file mode 100644 index 0000000..f662e93 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars5.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars6.bmp b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars6.bmp new file mode 100644 index 0000000..9ad8558 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/T1_Al 0.00_M0.14_N9.0 polars6.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/Thumbs.db b/Airfoil characteristics - amiya/Report/camber loc/Thumbs.db new file mode 100644 index 0000000..f3cab1e Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/Thumbs.db differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/camber loc 4-12 series.wpa b/Airfoil characteristics - amiya/Report/camber loc/camber loc 4-12 series.wpa new file mode 100644 index 0000000..a27f26d Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/camber loc 4-12 series.wpa differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/cd-a zoom.GIF b/Airfoil characteristics - amiya/Report/camber loc/cd-a zoom.GIF new file mode 100644 index 0000000..f17e449 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/cd-a zoom.GIF differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/cd-cl.bmp b/Airfoil characteristics - amiya/Report/camber loc/cd-cl.bmp new file mode 100644 index 0000000..a84a949 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/cd-cl.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/cl-a zoom.GIF b/Airfoil characteristics - amiya/Report/camber loc/cl-a zoom.GIF new file mode 100644 index 0000000..bc870ad Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/cl-a zoom.GIF differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/cl-a.bmp b/Airfoil characteristics - amiya/Report/camber loc/cl-a.bmp new file mode 100644 index 0000000..365e856 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/cl-a.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/cl-a2.bmp b/Airfoil characteristics - amiya/Report/camber loc/cl-a2.bmp new file mode 100644 index 0000000..0cae575 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/cl-a2.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/cm-a.GIF b/Airfoil characteristics - amiya/Report/camber loc/cm-a.GIF new file mode 100644 index 0000000..3788571 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/cm-a.GIF differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/drag.bmp b/Airfoil characteristics - amiya/Report/camber loc/drag.bmp new file mode 100644 index 0000000..7af4341 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/drag.bmp differ diff --git a/Airfoil characteristics - amiya/Report/camber loc/legend.GIF b/Airfoil characteristics - amiya/Report/camber loc/legend.GIF new file mode 100644 index 0000000..83687c9 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/camber loc/legend.GIF differ diff --git a/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..48ca10d --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,79 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1329 0.01145 0.00651 -0.0006 1.0000 0.0164 -6.0202 0.0000 0.2383 + -9.500 -1.0892 0.01091 0.00597 0.0021 1.0000 0.0180 -5.5706 0.0000 0.2414 + -8.500 -0.9718 0.00987 0.00490 0.0011 0.9975 0.0223 -4.5968 0.0000 0.2418 + -8.000 -0.9072 0.00932 0.00440 -0.0008 0.9953 0.0260 -4.1143 0.0000 0.2404 + -7.500 -0.8408 0.00887 0.00397 -0.0029 0.9935 0.0294 -3.6464 0.0000 0.2383 + -7.000 -0.7793 0.00839 0.00353 -0.0040 0.9886 0.0357 -3.2165 0.0000 0.2371 + -6.500 -0.7185 0.00794 0.00314 -0.0049 0.9808 0.0448 -2.8614 0.0000 0.2359 + -6.000 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Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.0180 0.01113 0.00639 -0.0268 0.9959 0.0145 -6.3853 0.0000 0.2128 + -9.500 -0.9541 0.01041 0.00568 -0.0285 0.9942 0.0167 -5.8313 0.0000 0.2098 + -9.000 -0.8881 0.00987 0.00514 -0.0305 0.9928 0.0184 -5.2807 0.0000 0.2058 + -8.500 -0.8289 0.00948 0.00473 -0.0310 0.9868 0.0188 -4.7770 0.0000 0.2033 + -8.000 -0.7693 0.00888 0.00412 -0.0315 0.9795 0.0232 -4.3072 0.0000 0.2002 + -7.500 -0.7163 0.00846 0.00371 -0.0306 0.9665 0.0262 -3.8716 0.0000 0.1989 + -7.000 -0.6616 0.00812 0.00334 -0.0299 0.9533 0.0286 -3.4468 0.0000 0.1968 + -6.500 -0.6073 0.00772 0.00296 -0.0293 0.9383 0.0353 -3.0782 0.0000 0.1942 + -6.000 -0.5522 0.00740 0.00263 -0.0287 0.9201 0.0422 -2.7482 0.0000 0.1907 + -5.500 -0.4965 0.00713 0.00234 -0.0283 0.8990 0.0493 -2.4291 0.0000 0.1860 + -5.000 -0.4407 0.00686 0.00206 -0.0280 0.8749 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0.16932 -0.0468 0.0069 1.0000 -9.6867 0.0000 0.2539 + 22.000 1.1740 0.18759 0.18612 -0.0570 0.0069 1.0000 -9.2059 0.0000 0.2630 + 23.000 1.0943 0.22768 0.22654 -0.0818 0.0068 1.0000 -7.6818 0.0000 0.2884 + 23.500 1.0431 0.25628 0.25527 -0.0989 0.0066 1.0000 -6.1139 0.0000 0.3096 + 25.000 1.0268 0.31206 0.31108 -0.1275 0.0041 1.0000 -3.0222 0.0000 0.3397 + + diff --git a/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 2412_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 2412_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..1f36af9 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 2412_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,82 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 2412 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- 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-0.0057 0.0070 1.0000 -11.1424 0.0000 0.2291 + 17.000 1.6789 0.04202 0.03805 -0.0048 0.0069 1.0000 -11.3743 0.0000 0.2274 + 17.500 1.6789 0.04776 0.04394 -0.0050 0.0069 1.0000 -11.7023 0.0000 0.2263 + 18.000 1.6723 0.05462 0.05095 -0.0059 0.0069 1.0000 -11.9708 0.0000 0.2256 + 18.500 1.6614 0.06243 0.05892 -0.0077 0.0068 1.0000 -12.1938 0.0000 0.2253 + 19.000 1.6452 0.07116 0.06783 -0.0101 0.0068 1.0000 -12.3609 0.0000 0.2256 + 19.500 1.6183 0.08161 0.07846 -0.0135 0.0068 1.0000 -12.4110 0.0000 0.2265 + 20.000 1.5867 0.09319 0.09024 -0.0178 0.0068 1.0000 -12.3934 0.0000 0.2280 + 20.500 1.5531 0.10530 0.10253 -0.0228 0.0068 1.0000 -12.3312 0.0000 0.2301 + 21.000 1.5081 0.11952 0.11696 -0.0292 0.0068 1.0000 -12.1137 0.0000 0.2336 + 21.500 1.4613 0.13478 0.13243 -0.0368 0.0068 1.0000 -11.8233 0.0000 0.2382 + 22.000 1.4151 0.15048 0.14834 -0.0454 0.0067 1.0000 -11.4799 0.0000 0.2439 + 22.500 1.3766 0.16514 0.16317 -0.0539 0.0067 1.0000 -11.1754 0.0000 0.2498 + 23.000 1.3348 0.18160 0.17981 -0.0642 0.0067 1.0000 -10.7439 0.0000 0.2577 + 23.500 1.3076 0.19581 0.19415 -0.0733 0.0067 1.0000 -10.4530 0.0000 0.2646 + 24.000 1.2844 0.20982 0.20829 -0.0827 0.0066 1.0000 -10.1562 0.0000 0.2718 + 24.500 1.2641 0.22381 0.22240 -0.0922 0.0065 1.0000 -9.8394 0.0000 0.2793 + 25.000 1.2463 0.23773 0.23643 -0.1020 0.0063 1.0000 -9.4835 0.0000 0.2873 + + diff --git a/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 3412_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 3412_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..4f816db --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 3412_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,83 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 3412 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.7653 0.01099 0.00682 -0.0826 0.9582 0.0125 -7.0454 0.0000 0.1302 + -9.500 -0.7140 0.01008 0.00572 -0.0815 0.9434 0.0134 -6.5306 0.0000 0.1245 + -9.000 -0.6602 0.00942 0.00493 -0.0807 0.9276 0.0147 -6.0095 0.0000 0.1168 + -8.500 -0.6046 0.00886 0.00434 -0.0803 0.9161 0.0166 -5.4884 0.0000 0.1065 + -8.000 -0.5487 0.00849 0.00391 -0.0799 0.9005 0.0183 -4.9741 0.0000 0.0938 + -7.500 -0.4915 0.00822 0.00360 -0.0798 0.8864 0.0188 -4.4693 0.0000 0.0772 + -7.000 -0.4350 0.00780 0.00309 -0.0795 0.8695 0.0214 -4.0037 0.0000 0.0568 + -6.500 -0.3785 0.00746 0.00271 -0.0793 0.8503 0.0252 -3.5523 0.0000 0.0300 + -6.000 -0.3210 0.00724 0.00244 -0.0792 0.8325 0.0269 -3.1635 0.0000 -0.0077 + -5.500 -0.2640 0.00695 0.00212 -0.0791 0.8111 0.0333 -2.8157 0.0000 -0.0613 + -5.000 -0.2065 0.00678 0.00188 -0.0791 0.7885 0.0364 -2.4739 0.0000 -0.1458 + -4.500 -0.1494 0.00657 0.00164 -0.0790 0.7641 0.0456 -2.1532 0.0000 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0.00640 -0.0696 0.0318 1.0000 -4.0536 0.0000 0.2911 + 9.500 1.3725 0.01248 0.00703 -0.0681 0.0264 1.0000 -4.4414 0.0000 0.2874 + 10.000 1.4180 0.01319 0.00772 -0.0663 0.0224 1.0000 -4.8383 0.0000 0.2838 + 10.500 1.4622 0.01392 0.00845 -0.0643 0.0187 1.0000 -5.2406 0.0000 0.2802 + 11.000 1.5052 0.01462 0.00917 -0.0621 0.0174 1.0000 -5.6879 0.0000 0.2767 + 11.500 1.5395 0.01552 0.01007 -0.0583 0.0151 1.0000 -6.1391 0.0000 0.2725 + 12.000 1.5703 0.01662 0.01123 -0.0542 0.0125 1.0000 -6.5791 0.0000 0.2683 + 13.000 1.6364 0.01872 0.01344 -0.0476 0.0118 1.0000 -7.5496 0.0000 0.2611 + 13.500 1.6660 0.02006 0.01484 -0.0443 0.0112 1.0000 -8.0363 0.0000 0.2576 + 14.000 1.6908 0.02179 0.01663 -0.0407 0.0101 1.0000 -8.5020 0.0000 0.2541 + 14.500 1.7100 0.02403 0.01893 -0.0370 0.0090 1.0000 -8.9358 0.0000 0.2507 + 15.000 1.7250 0.02678 0.02180 -0.0336 0.0081 1.0000 -9.3414 0.0000 0.2474 + 15.500 1.7368 0.03008 0.02525 -0.0305 0.0076 1.0000 -9.7278 0.0000 0.2445 + 16.000 1.7406 0.03427 0.02963 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-0.0525 0.0062 1.0000 -12.2862 0.0000 0.2424 + 23.000 1.5296 0.15505 0.15264 -0.0590 0.0061 1.0000 -12.1864 0.0000 0.2459 + 23.500 1.4920 0.16935 0.16712 -0.0675 0.0059 1.0000 -11.9364 0.0000 0.2513 + 24.000 1.4620 0.18279 0.18072 -0.0759 0.0058 1.0000 -11.7287 0.0000 0.2566 + 24.500 1.4248 0.19854 0.19665 -0.0864 0.0056 1.0000 -11.3473 0.0000 0.2641 + 25.000 1.3950 0.21345 0.21171 -0.0966 0.0054 1.0000 -10.9995 0.0000 0.2716 + + diff --git a/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 4412_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 4412_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..c9b4ea6 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/camber/NACA 4 series/NACA 4412_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,84 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 4412 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.6552 0.01129 0.00735 -0.1063 0.9208 0.0121 -7.5057 0.0000 0.0745 + -9.500 -0.6010 0.01052 0.00643 -0.1058 0.9059 0.0124 -6.9261 0.0000 0.0610 + -9.000 -0.5465 0.00956 0.00526 -0.1054 0.8947 0.0133 -6.3938 0.0000 0.0443 + -8.500 -0.4909 0.00892 0.00445 -0.1050 0.8790 0.0144 -5.8616 0.0000 0.0233 + -8.000 -0.4341 0.00839 0.00386 -0.1048 0.8655 0.0162 -5.3317 0.0000 -0.0045 + -7.500 -0.3772 0.00804 0.00346 -0.1046 0.8481 0.0181 -4.8105 0.0000 -0.0408 + -7.000 -0.3195 0.00782 0.00318 -0.1046 0.8311 0.0187 -4.2998 0.0000 -0.0914 + -6.500 -0.2619 0.00747 0.00273 -0.1046 0.8154 0.0206 -3.8240 0.0000 -0.1645 + -6.000 -0.2048 0.00715 0.00236 -0.1045 0.7951 0.0244 -3.3931 0.0000 -0.2775 + -5.500 -0.1474 0.00699 0.00213 -0.1044 0.7708 0.0267 -3.0202 0.0000 -0.4798 + -5.000 -0.0896 0.00676 0.00184 -0.1045 0.7511 0.0318 -2.6681 0.0000 -0.9463 + -4.500 -0.0318 0.00660 0.00164 -0.1046 0.7298 0.0360 -2.3285 0.0000 -3.1122 + -4.000 0.0257 0.00646 0.00145 -0.1046 0.7039 0.0439 -2.0076 0.0000 4.4040 + -3.500 0.0832 0.00637 0.00130 -0.1046 0.6784 0.0518 -1.7019 0.0000 1.5272 + -3.000 0.1406 0.00628 0.00117 -0.1047 0.6516 0.0644 -1.4286 0.0000 1.0041 + -2.500 0.1979 0.00622 0.00107 -0.1047 0.6232 0.0791 -1.1986 0.0000 0.7844 + -2.000 0.2552 0.00617 0.00100 -0.1048 0.5968 0.0988 -0.9798 0.0000 0.6635 + -1.500 0.3126 0.00615 0.00096 -0.1049 0.5721 0.1215 -0.7827 0.0000 0.5869 + -1.000 0.3702 0.00608 0.00093 -0.1051 0.5515 0.1538 -0.7028 0.0000 0.5340 + -0.500 0.4275 0.00606 0.00094 -0.1052 0.5293 0.1886 -0.7445 0.0000 0.4954 + 0.000 0.4846 0.00606 0.00097 -0.1054 0.5070 0.2323 -0.7890 0.0000 0.4659 + 0.500 0.5421 0.00602 0.00101 -0.1056 0.4926 0.2847 -0.8346 0.0000 0.4426 + 1.000 0.5994 0.00597 0.00108 -0.1058 0.4763 0.3525 -0.8831 0.0000 0.4238 + 1.500 0.6560 0.00573 0.00117 -0.1060 0.4637 0.5118 -0.9332 0.0000 0.4083 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characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 0012_T1_Al 0.00_M0.14_N9.0 (2).txt @@ -0,0 +1,13 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..48ca10d --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,79 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1329 0.01145 0.00651 -0.0006 1.0000 0.0164 -6.0202 0.0000 0.2383 + -9.500 -1.0892 0.01091 0.00597 0.0021 1.0000 0.0180 -5.5706 0.0000 0.2414 + -8.500 -0.9718 0.00987 0.00490 0.0011 0.9975 0.0223 -4.5968 0.0000 0.2418 + -8.000 -0.9072 0.00932 0.00440 -0.0008 0.9953 0.0260 -4.1143 0.0000 0.2404 + -7.500 -0.8408 0.00887 0.00397 -0.0029 0.9935 0.0294 -3.6464 0.0000 0.2383 + -7.000 -0.7793 0.00839 0.00353 -0.0040 0.9886 0.0357 -3.2165 0.0000 0.2371 + -6.500 -0.7185 0.00794 0.00314 -0.0049 0.9808 0.0448 -2.8614 0.0000 0.2359 + -6.000 -0.6640 0.00757 0.00281 -0.0043 0.9670 0.0544 -2.5473 0.0000 0.2367 + -5.500 -0.6102 0.00721 0.00250 -0.0035 0.9493 0.0672 -2.2476 0.0000 0.2378 + -5.000 -0.5564 0.00687 0.00219 -0.0027 0.9268 0.0843 -1.9599 0.0000 0.2390 + 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0.00553 0.00107 0.0005 0.2651 0.7429 -0.9210 0.0000 0.2433 + 3.000 0.3370 0.00572 0.00123 0.0008 0.2198 0.7898 -1.0844 0.0000 0.2426 + 3.500 0.3924 0.00596 0.00142 0.0011 0.1778 0.8297 -1.2634 0.0000 0.2419 + 4.000 0.4471 0.00625 0.00166 0.0016 0.1374 0.8685 -1.4791 0.0000 0.2409 + 4.500 0.5022 0.00653 0.00191 0.0020 0.1105 0.8996 -1.7042 0.0000 0.2401 + 5.000 0.5565 0.00687 0.00219 0.0027 0.0843 0.9268 -1.9601 0.0000 0.2390 + 5.500 0.6103 0.00721 0.00250 0.0035 0.0671 0.9493 -2.2477 0.0000 0.2378 + 6.000 0.6640 0.00757 0.00281 0.0043 0.0544 0.9670 -2.5474 0.0000 0.2367 + 6.500 0.7185 0.00794 0.00314 0.0049 0.0448 0.9808 -2.8615 0.0000 0.2359 + 7.000 0.7793 0.00839 0.00353 0.0040 0.0357 0.9886 -3.2167 0.0000 0.2371 + 7.500 0.8408 0.00887 0.00397 0.0029 0.0294 0.9936 -3.6468 0.0000 0.2383 + 8.000 0.9073 0.00932 0.00440 0.0008 0.0260 0.9953 -4.1147 0.0000 0.2404 + 8.500 0.9719 0.00987 0.00490 -0.0011 0.0222 0.9975 -4.5972 0.0000 0.2418 + 9.500 1.0890 0.01091 0.00597 -0.0021 0.0181 1.0000 -5.5698 0.0000 0.2414 + 10.000 1.1328 0.01145 0.00650 0.0006 0.0164 1.0000 -6.0198 0.0000 0.2383 + 10.500 1.1769 0.01214 0.00720 0.0031 0.0142 1.0000 -6.4778 0.0000 0.2355 + 11.000 1.2215 0.01300 0.00816 0.0054 0.0124 1.0000 -6.9362 0.0000 0.2331 + 11.500 1.2696 0.01367 0.00888 0.0069 0.0121 1.0000 -7.4543 0.0000 0.2313 + 12.000 1.3186 0.01427 0.00950 0.0082 0.0119 1.0000 -8.0060 0.0000 0.2297 + 12.500 1.3668 0.01494 0.01020 0.0096 0.0116 1.0000 -8.6247 0.0000 0.2281 + 13.000 1.4128 0.01576 0.01105 0.0113 0.0107 1.0000 -9.2650 0.0000 0.2263 + 13.500 1.4549 0.01682 0.01214 0.0135 0.0095 1.0000 -9.8918 0.0000 0.2241 + 14.000 1.4922 0.01815 0.01355 0.0163 0.0085 1.0000 -10.4893 0.0000 0.2216 + 14.500 1.5222 0.01968 0.01524 0.0200 0.0079 1.0000 -11.0441 0.0000 0.2185 + 15.000 1.5405 0.02151 0.01724 0.0251 0.0076 1.0000 -11.5269 0.0000 0.2144 + 15.500 1.5530 0.02395 0.01988 0.0296 0.0074 1.0000 -11.9673 0.0000 0.2106 + 16.000 1.5574 0.02738 0.02354 0.0332 0.0073 1.0000 -12.3391 0.0000 0.2074 + 16.500 1.5523 0.03237 0.02879 0.0349 0.0071 1.0000 -12.6181 0.0000 0.2050 + 17.000 1.5357 0.03974 0.03644 0.0337 0.0070 1.0000 -12.7714 0.0000 0.2043 + 17.500 1.5056 0.05008 0.04707 0.0294 0.0070 1.0000 -12.7656 0.0000 0.2054 + 18.000 1.4616 0.06331 0.06057 0.0228 0.0069 1.0000 -12.5863 0.0000 0.2080 + 18.500 1.4054 0.07922 0.07675 0.0145 0.0070 1.0000 -12.2382 0.0000 0.2120 + 19.000 1.3413 0.09677 0.09453 0.0055 0.0070 1.0000 -11.7541 0.0000 0.2170 + 19.500 1.2725 0.11606 0.11403 -0.0046 0.0071 1.0000 -11.1427 0.0000 0.2238 + 20.000 1.2064 0.13545 0.13362 -0.0151 0.0072 1.0000 -10.4790 0.0000 0.2317 + 20.500 1.1462 0.15525 0.15361 -0.0264 0.0072 1.0000 -9.7735 0.0000 0.2414 + 21.000 1.0903 0.17533 0.17387 -0.0382 0.0073 1.0000 -8.9953 0.0000 0.2529 + 21.500 1.0299 0.19913 0.19787 -0.0523 0.0073 1.0000 -7.9219 0.0000 0.2685 + 22.000 0.9138 0.24928 0.24825 -0.0783 0.0063 1.0000 -4.7212 0.0000 0.3066 + 22.500 0.9282 0.25560 0.25457 -0.0827 0.0057 1.0000 -4.8331 0.0000 0.3089 + 24.000 0.9396 0.29898 0.29797 -0.1049 0.0048 1.0000 -2.5370 0.0000 0.3313 + 24.500 0.9555 0.30433 0.30332 -0.1092 0.0042 1.0000 -2.7097 0.0000 0.3328 + 25.000 0.9713 0.30941 0.30841 -0.1136 0.0038 1.0000 -2.9101 0.0000 0.3341 + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2412_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2412_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..1f36af9 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2412_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,82 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 2412 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + 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1.0000 -11.3743 0.0000 0.2274 + 17.500 1.6789 0.04776 0.04394 -0.0050 0.0069 1.0000 -11.7023 0.0000 0.2263 + 18.000 1.6723 0.05462 0.05095 -0.0059 0.0069 1.0000 -11.9708 0.0000 0.2256 + 18.500 1.6614 0.06243 0.05892 -0.0077 0.0068 1.0000 -12.1938 0.0000 0.2253 + 19.000 1.6452 0.07116 0.06783 -0.0101 0.0068 1.0000 -12.3609 0.0000 0.2256 + 19.500 1.6183 0.08161 0.07846 -0.0135 0.0068 1.0000 -12.4110 0.0000 0.2265 + 20.000 1.5867 0.09319 0.09024 -0.0178 0.0068 1.0000 -12.3934 0.0000 0.2280 + 20.500 1.5531 0.10530 0.10253 -0.0228 0.0068 1.0000 -12.3312 0.0000 0.2301 + 21.000 1.5081 0.11952 0.11696 -0.0292 0.0068 1.0000 -12.1137 0.0000 0.2336 + 21.500 1.4613 0.13478 0.13243 -0.0368 0.0068 1.0000 -11.8233 0.0000 0.2382 + 22.000 1.4151 0.15048 0.14834 -0.0454 0.0067 1.0000 -11.4799 0.0000 0.2439 + 22.500 1.3766 0.16514 0.16317 -0.0539 0.0067 1.0000 -11.1754 0.0000 0.2498 + 23.000 1.3348 0.18160 0.17981 -0.0642 0.0067 1.0000 -10.7439 0.0000 0.2577 + 23.500 1.3076 0.19581 0.19415 -0.0733 0.0067 1.0000 -10.4530 0.0000 0.2646 + 24.000 1.2844 0.20982 0.20829 -0.0827 0.0066 1.0000 -10.1562 0.0000 0.2718 + 24.500 1.2641 0.22381 0.22240 -0.0922 0.0065 1.0000 -9.8394 0.0000 0.2793 + 25.000 1.2463 0.23773 0.23643 -0.1020 0.0063 1.0000 -9.4835 0.0000 0.2873 + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2415_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2415_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..d19c0c1 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2415_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,84 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 2415 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.8827 0.01037 0.00561 -0.0568 0.9430 0.0269 -4.9411 0.0000 0.1719 + -9.500 -0.8303 0.00983 0.00501 -0.0558 0.9267 0.0306 -4.5877 0.0000 0.1696 + -9.000 -0.7761 0.00935 0.00453 -0.0551 0.9124 0.0342 -4.2329 0.0000 0.1661 + -8.500 -0.7205 0.00902 0.00415 -0.0547 0.8977 0.0361 -3.8832 0.0000 0.1616 + -8.000 -0.6649 0.00868 0.00376 -0.0542 0.8794 0.0397 -3.5478 0.0000 0.1563 + -7.500 -0.6092 0.00830 0.00338 -0.0539 0.8618 0.0454 -3.2232 0.0000 0.1497 + -7.000 -0.5524 0.00805 0.00307 -0.0537 0.8439 0.0489 -2.9107 0.0000 0.1411 + -6.500 -0.4965 0.00773 0.00275 -0.0534 0.8217 0.0577 -2.6472 0.0000 0.1310 + -6.000 -0.4398 0.00752 0.00249 -0.0531 0.7967 0.0651 -2.3906 0.0000 0.1176 + -5.500 -0.3830 0.00731 0.00225 -0.0530 0.7726 0.0725 -2.1424 0.0000 0.1000 + -5.000 -0.3263 0.00708 0.00201 -0.0528 0.7464 0.0857 -1.9046 0.0000 0.0761 + -4.500 -0.2693 0.00688 0.00181 -0.0527 0.7216 0.1010 -1.6861 0.0000 0.0416 + -4.000 -0.2122 0.00673 0.00164 -0.0526 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1.5426 0.12647 0.12342 -0.0233 0.0121 1.0000 -9.3524 0.0000 0.2225 + 23.000 1.5169 0.13724 0.13435 -0.0285 0.0120 1.0000 -9.3487 0.0000 0.2248 + 23.500 1.4910 0.14810 0.14536 -0.0342 0.0120 1.0000 -9.3255 0.0000 0.2275 + 24.000 1.4661 0.15909 0.15650 -0.0404 0.0119 1.0000 -9.2894 0.0000 0.2306 + 24.500 1.4427 0.17027 0.16783 -0.0473 0.0118 1.0000 -9.2418 0.0000 0.2343 + 25.000 1.4204 0.18163 0.17932 -0.0546 0.0117 1.0000 -9.1791 0.0000 0.2385 + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2421_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2421_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..c73348e --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2421_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,84 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 2421 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.8691 0.01036 0.00526 -0.0578 0.8344 0.0724 -3.5079 0.0000 0.1625 + -9.500 -0.8176 0.00997 0.00485 -0.0568 0.8150 0.0792 -3.2933 0.0000 0.1600 + -9.000 -0.7656 0.00961 0.00446 -0.0558 0.7949 0.0850 -3.0821 0.0000 0.1568 + -8.500 -0.7111 0.00937 0.00416 -0.0552 0.7742 0.0882 -2.8709 0.0000 0.1523 + -8.000 -0.6582 0.00900 0.00381 -0.0544 0.7542 0.0987 -2.6777 0.0000 0.1475 + -7.500 -0.6029 0.00879 0.00354 -0.0540 0.7332 0.1036 -2.4950 0.0000 0.1407 + -7.000 -0.5491 0.00850 0.00325 -0.0533 0.7102 0.1151 -2.3196 0.0000 0.1331 + -6.500 -0.4936 0.00836 0.00304 -0.0529 0.6843 0.1209 -2.1451 0.0000 0.1229 + -6.000 -0.4385 0.00809 0.00280 -0.0525 0.6665 0.1347 -1.9772 0.0000 0.1102 + -5.500 -0.3827 0.00791 0.00261 -0.0521 0.6444 0.1468 -1.8277 0.0000 0.0931 + -5.000 -0.3266 0.00778 0.00244 -0.0518 0.6213 0.1563 -1.6813 0.0000 0.0698 + -4.500 -0.2713 0.00762 0.00229 -0.0514 0.5972 0.1727 -1.5397 0.0000 0.0378 + -4.000 -0.2149 0.00748 0.00215 -0.0512 0.5786 0.1890 -1.4117 0.0000 -0.0129 + -3.500 -0.1577 0.00739 0.00204 -0.0511 0.5599 0.2017 -1.2877 0.0000 -0.1027 + -3.000 -0.1018 0.00730 0.00195 -0.0508 0.5361 0.2193 -1.1719 0.0000 -0.2854 + -2.500 -0.0449 0.00718 0.00187 -0.0506 0.5221 0.2398 -1.0653 0.0000 -0.9445 + -2.000 0.0118 0.00710 0.00181 -0.0505 0.5039 0.2610 -0.9634 0.0000 4.7126 + -1.500 0.0685 0.00705 0.00177 -0.0503 0.4876 0.2821 -0.8711 0.0000 1.0062 + -1.000 0.1259 0.00697 0.00173 -0.0503 0.4739 0.3054 -0.8130 0.0000 0.6551 + -0.500 0.1827 0.00696 0.00173 -0.0502 0.4589 0.3284 -0.8641 0.0000 0.5243 + 0.000 0.2400 0.00689 0.00173 -0.0501 0.4468 0.3564 -0.9171 0.0000 0.4555 + 0.500 0.2968 0.00687 0.00174 -0.0500 0.4348 0.3839 -0.9731 0.0000 0.4131 + 1.000 0.3533 0.00683 0.00177 -0.0499 0.4210 0.4193 -1.0309 0.0000 0.3843 + 1.500 0.4100 0.00676 0.00181 -0.0498 0.4116 0.4614 -1.0923 0.0000 0.3634 + 2.000 0.4654 0.00679 0.00189 -0.0494 0.3943 0.5009 -1.1558 0.0000 0.3473 + 2.500 0.5224 0.00679 0.00197 -0.0493 0.3853 0.5365 -1.2235 0.0000 0.3348 + 3.000 0.5773 0.00690 0.00209 -0.0489 0.3672 0.5719 -1.2947 0.0000 0.3243 + 3.500 0.6331 0.00695 0.00221 -0.0486 0.3562 0.6078 -1.3696 0.0000 0.3158 + 4.000 0.6875 0.00707 0.00237 -0.0481 0.3398 0.6439 -1.4489 0.0000 0.3083 + 4.500 0.7413 0.00723 0.00255 -0.0474 0.3249 0.6778 -1.5331 0.0000 0.3018 + 5.000 0.7957 0.00737 0.00274 -0.0469 0.3114 0.7117 -1.6223 0.0000 0.2961 + 5.500 0.8466 0.00762 0.00299 -0.0458 0.2915 0.7510 -1.7160 0.0000 0.2906 + 6.000 0.8993 0.00778 0.00323 -0.0449 0.2808 0.7898 -1.8181 0.0000 0.2859 + 6.500 0.9492 0.00806 0.00352 -0.0436 0.2640 0.8254 -1.9223 0.0000 0.2812 + 7.000 0.9929 0.00835 0.00385 -0.0410 0.2486 0.8659 -2.0306 0.0000 0.2759 + 7.500 1.0397 0.00865 0.00419 -0.0390 0.2358 0.9004 -2.1467 0.0000 0.2715 + 8.000 1.0815 0.00909 0.00467 -0.0362 0.2189 0.9390 -2.2665 0.0000 0.2667 + 8.500 1.1212 0.00960 0.00516 -0.0329 0.2056 0.9685 -2.3869 0.0000 0.2618 + 9.000 1.1685 0.01010 0.00563 -0.0314 0.1937 0.9874 -2.5306 0.0000 0.2586 + 9.500 1.2220 0.01086 0.00629 -0.0316 0.1759 0.9961 -2.6852 0.0000 0.2569 + 10.000 1.2762 0.01164 0.00699 -0.0321 0.1632 1.0000 -2.8540 0.0000 0.2555 + 10.500 1.3081 0.01224 0.00756 -0.0280 0.1537 1.0000 -2.9960 0.0000 0.2509 + 11.000 1.3403 0.01321 0.00846 -0.0245 0.1407 1.0000 -3.1399 0.0000 0.2469 + 11.500 1.3772 0.01413 0.00935 -0.0220 0.1315 1.0000 -3.2945 0.0000 0.2437 + 12.000 1.4093 0.01532 0.01049 -0.0190 0.1195 1.0000 -3.4579 0.0000 0.2404 + 12.500 1.4452 0.01644 0.01161 -0.0168 0.1141 1.0000 -3.6317 0.0000 0.2376 + 13.000 1.4729 0.01806 0.01318 -0.0139 0.1036 1.0000 -3.7907 0.0000 0.2344 + 13.500 1.5051 0.01951 0.01464 -0.0117 0.0990 1.0000 -3.9614 0.0000 0.2318 + 14.000 1.5261 0.02170 0.01679 -0.0088 0.0894 1.0000 -4.1097 0.0000 0.2287 + 14.500 1.5557 0.02352 0.01866 -0.0069 0.0854 1.0000 -4.2903 0.0000 0.2263 + 15.000 1.5781 0.02593 0.02108 -0.0048 0.0805 1.0000 -4.4624 0.0000 0.2238 + 15.500 1.5942 0.02891 0.02406 -0.0026 0.0735 1.0000 -4.6195 0.0000 0.2213 + 16.000 1.6163 0.03161 0.02682 -0.0011 0.0713 1.0000 -4.7936 0.0000 0.2192 + 16.500 1.6318 0.03498 0.03024 0.0003 0.0682 1.0000 -4.9518 0.0000 0.2171 + 17.000 1.6384 0.03925 0.03455 0.0018 0.0638 1.0000 -5.0856 0.0000 0.2149 + 17.500 1.6454 0.04363 0.03899 0.0029 0.0591 1.0000 -5.2199 0.0000 0.2130 + 18.000 1.6543 0.04793 0.04338 0.0036 0.0579 1.0000 -5.3604 0.0000 0.2113 + 18.500 1.6558 0.05311 0.04864 0.0041 0.0556 1.0000 -5.4786 0.0000 0.2096 + 19.000 1.6490 0.05925 0.05485 0.0043 0.0528 1.0000 -5.5736 0.0000 0.2081 + 19.500 1.6394 0.06582 0.06150 0.0042 0.0491 1.0000 -5.6686 0.0000 0.2067 + 20.000 1.6313 0.07228 0.06807 0.0038 0.0471 1.0000 -5.7666 0.0000 0.2055 + 20.500 1.6253 0.07873 0.07465 0.0031 0.0466 1.0000 -5.8706 0.0000 0.2045 + 21.000 1.6152 0.08577 0.08181 0.0019 0.0457 1.0000 -5.9574 0.0000 0.2038 + 21.500 1.6010 0.09335 0.08950 0.0004 0.0444 1.0000 -6.0266 0.0000 0.2032 + 22.000 1.5851 0.10100 0.09725 -0.0013 0.0426 1.0000 -6.0863 0.0000 0.2028 + 22.500 1.5663 0.10926 0.10559 -0.0036 0.0403 1.0000 -6.1293 0.0000 0.2028 + 23.000 1.5442 0.11819 0.11463 -0.0066 0.0378 1.0000 -6.1523 0.0000 0.2031 + 23.500 1.5245 0.12697 0.12353 -0.0099 0.0363 1.0000 -6.1781 0.0000 0.2038 + 24.000 1.5118 0.13488 0.13158 -0.0134 0.0361 1.0000 -6.2289 0.0000 0.2046 + 24.500 1.5111 0.14098 0.13776 -0.0162 0.0357 1.0000 -6.3283 0.0000 0.2049 + 25.000 1.4952 0.14936 0.14628 -0.0205 0.0350 1.0000 -6.3548 0.0000 0.2062 + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2424_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2424_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..cc51745 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA 2424_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,83 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 2424 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.8349 0.01051 0.00534 -0.0630 0.7774 0.1018 -3.1633 0.0000 0.1485 + -9.500 -0.7901 0.01023 0.00501 -0.0607 0.7597 0.1055 -2.9946 0.0000 0.1475 + -9.000 -0.7443 0.00987 0.00463 -0.0587 0.7378 0.1141 -2.8279 0.0000 0.1459 + -8.500 -0.6939 0.00963 0.00432 -0.0574 0.7132 0.1191 -2.6672 0.0000 0.1421 + -8.000 -0.6427 0.00932 0.00402 -0.0563 0.6975 0.1288 -2.5136 0.0000 0.1373 + -7.500 -0.5909 0.00907 0.00375 -0.0553 0.6766 0.1359 -2.3615 0.0000 0.1314 + -7.000 -0.5378 0.00891 0.00352 -0.0545 0.6530 0.1434 -2.2108 0.0000 0.1235 + -6.500 -0.4854 0.00866 0.00329 -0.0536 0.6353 0.1539 -2.0671 0.0000 0.1142 + -6.000 -0.4313 0.00849 0.00309 -0.0530 0.6156 0.1644 -1.9343 0.0000 0.1014 + -5.500 -0.3780 0.00833 0.00291 -0.0522 0.5939 0.1746 -1.8050 0.0000 0.0854 + -5.000 -0.3232 0.00820 0.00276 -0.0516 0.5766 0.1856 -1.6767 0.0000 0.0625 + -4.500 -0.2685 0.00805 0.00262 -0.0511 0.5585 0.1971 -1.5597 0.0000 0.0302 + -4.000 -0.2148 0.00794 0.00250 -0.0504 0.5374 0.2128 -1.4487 0.0000 -0.0166 + -3.500 -0.1582 0.00785 0.00240 -0.0502 0.5249 0.2227 -1.3367 0.0000 -0.1043 + -3.000 -0.1040 0.00774 0.00231 -0.0496 0.5064 0.2406 -1.2387 0.0000 -0.2736 + -2.500 -0.0481 0.00764 0.00224 -0.0493 0.4951 0.2566 -1.1412 0.0000 -0.8555 + -2.000 0.0074 0.00762 0.00219 -0.0489 0.4778 0.2711 -1.0504 0.0000 7.2023 + -1.500 0.0636 0.00752 0.00214 -0.0486 0.4689 0.2890 -0.9643 0.0000 1.0448 + -1.000 0.1180 0.00750 0.00213 -0.0480 0.4514 0.3089 -0.9246 0.0000 0.6653 + -0.500 0.1750 0.00741 0.00210 -0.0479 0.4452 0.3292 -0.9778 0.0000 0.5239 + 0.000 0.2304 0.00743 0.00211 -0.0475 0.4336 0.3469 -1.0307 0.0000 0.4520 + 0.500 0.2858 0.00740 0.00213 -0.0471 0.4213 0.3692 -1.0877 0.0000 0.4080 + 1.000 0.3419 0.00735 0.00215 -0.0469 0.4146 0.3942 -1.1458 0.0000 0.3784 + 1.500 0.3949 0.00738 0.00221 -0.0461 0.3988 0.4254 -1.2055 0.0000 0.3565 + 2.000 0.4501 0.00732 0.00226 -0.0457 0.3917 0.4602 -1.2685 0.0000 0.3402 + 2.500 0.5032 0.00736 0.00234 -0.0449 0.3798 0.4942 -1.3328 0.0000 0.3269 + 3.000 0.5564 0.00742 0.00245 -0.0441 0.3666 0.5243 -1.4004 0.0000 0.3161 + 3.500 0.6099 0.00748 0.00257 -0.0434 0.3575 0.5533 -1.4706 0.0000 0.3072 + 4.000 0.6591 0.00764 0.00273 -0.0419 0.3411 0.5820 -1.5417 0.0000 0.2988 + 4.500 0.7079 0.00770 0.00286 -0.0402 0.3346 0.6093 -1.6143 0.0000 0.2913 + 5.000 0.7540 0.00794 0.00310 -0.0381 0.3178 0.6393 -1.6900 0.0000 0.2844 + 5.500 0.8068 0.00809 0.00332 -0.0374 0.3108 0.6686 -1.7729 0.0000 0.2795 + 6.000 0.8542 0.00841 0.00365 -0.0357 0.2952 0.7010 -1.8579 0.0000 0.2743 + 6.500 0.9061 0.00862 0.00394 -0.0349 0.2869 0.7338 -1.9481 0.0000 0.2704 + 7.000 0.9523 0.00901 0.00434 -0.0332 0.2727 0.7669 -2.0412 0.0000 0.2660 + 7.500 1.0017 0.00930 0.00470 -0.0320 0.2631 0.8027 -2.1386 0.0000 0.2624 + 8.000 1.0467 0.00974 0.00519 -0.0302 0.2506 0.8411 -2.2400 0.0000 0.2585 + 8.500 1.0927 0.01017 0.00569 -0.0286 0.2397 0.8763 -2.3446 0.0000 0.2551 + 9.000 1.1344 0.01069 0.00628 -0.0262 0.2294 0.9177 -2.4516 0.0000 0.2512 + 9.500 1.1724 0.01131 0.00694 -0.0232 0.2175 0.9530 -2.5584 0.0000 0.2471 + 10.000 1.2088 0.01203 0.00767 -0.0200 0.2081 0.9792 -2.6653 0.0000 0.2430 + 11.000 1.3088 0.01394 0.00948 -0.0204 0.1856 0.9997 -2.9367 0.0000 0.2405 + 11.500 1.3407 0.01490 0.01040 -0.0173 0.1756 1.0000 -3.0527 0.0000 0.2369 + 12.000 1.3748 0.01601 0.01151 -0.0149 0.1691 1.0000 -3.1820 0.0000 0.2339 + 12.500 1.4032 0.01755 0.01299 -0.0121 0.1566 1.0000 -3.3027 0.0000 0.2307 + 13.000 1.4376 0.01885 0.01430 -0.0102 0.1510 1.0000 -3.4349 0.0000 0.2282 + 13.500 1.4614 0.02088 0.01628 -0.0075 0.1409 1.0000 -3.5543 0.0000 0.2252 + 14.000 1.4921 0.02265 0.01807 -0.0059 0.1357 1.0000 -3.6950 0.0000 0.2229 + 14.500 1.5170 0.02486 0.02029 -0.0039 0.1296 1.0000 -3.8262 0.0000 0.2205 + 15.000 1.5350 0.02762 0.02303 -0.0017 0.1196 1.0000 -3.9444 0.0000 0.2178 + 15.500 1.5591 0.03008 0.02553 -0.0002 0.1161 1.0000 -4.0756 0.0000 0.2157 + 16.000 1.5707 0.03362 0.02907 0.0017 0.1097 1.0000 -4.1816 0.0000 0.2133 + 16.500 1.5825 0.03731 0.03279 0.0031 0.1027 1.0000 -4.3004 0.0000 0.2111 + 17.000 1.5986 0.04078 0.03634 0.0041 0.1006 1.0000 -4.4292 0.0000 0.2092 + 17.500 1.6039 0.04516 0.04076 0.0053 0.0964 1.0000 -4.5334 0.0000 0.2071 + 18.000 1.6007 0.05047 0.04611 0.0064 0.0906 1.0000 -4.6162 0.0000 0.2050 + 18.500 1.6046 0.05532 0.05104 0.0070 0.0867 1.0000 -4.7148 0.0000 0.2033 + 19.000 1.6126 0.05979 0.05558 0.0073 0.0845 1.0000 -4.8236 0.0000 0.2018 + 19.500 1.6023 0.06612 0.06197 0.0075 0.0806 1.0000 -4.8848 0.0000 0.2001 + 20.000 1.5865 0.07311 0.06903 0.0075 0.0757 1.0000 -4.9289 0.0000 0.1986 + 20.500 1.5769 0.07974 0.07576 0.0069 0.0724 1.0000 -4.9909 0.0000 0.1974 + 21.000 1.5699 0.08620 0.08233 0.0061 0.0715 1.0000 -5.0662 0.0000 0.1964 + 21.500 1.5701 0.09181 0.08802 0.0052 0.0694 1.0000 -5.1609 0.0000 0.1956 + 22.000 1.5511 0.09955 0.09584 0.0038 0.0667 1.0000 -5.1965 0.0000 0.1949 + 22.500 1.5278 0.10805 0.10442 0.0018 0.0631 1.0000 -5.2140 0.0000 0.1945 + 23.000 1.5071 0.11647 0.11294 -0.0007 0.0592 1.0000 -5.2335 0.0000 0.1945 + 23.500 1.5130 0.12160 0.11816 -0.0025 0.0587 1.0000 -5.3372 0.0000 0.1943 + 24.000 1.5002 0.12917 0.12584 -0.0054 0.0578 1.0000 -5.3762 0.0000 0.1946 + 24.500 1.4988 0.13520 0.13193 -0.0080 0.0559 1.0000 -5.4516 0.0000 0.1948 + 25.000 1.4777 0.14376 0.14056 -0.0119 0.0532 1.0000 -5.4538 0.0000 0.1957 + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA0012 cp-5.bmp b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series camber/NACA0012 cp-5.bmp new file mode 100644 index 0000000..2e40fb1 Binary files /dev/null and b/Airfoil characteristics - 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thickness/NACA 4 series/Cl-a.GIF differ diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/Cm-a.GIF b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/Cm-a.GIF new file mode 100644 index 0000000..db684b9 Binary files /dev/null and b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/Cm-a.GIF differ diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..48ca10d --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0012_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,79 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0012 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1329 0.01145 0.00651 -0.0006 1.0000 0.0164 -6.0202 0.0000 0.2383 + -9.500 -1.0892 0.01091 0.00597 0.0021 1.0000 0.0180 -5.5706 0.0000 0.2414 + -8.500 -0.9718 0.00987 0.00490 0.0011 0.9975 0.0223 -4.5968 0.0000 0.2418 + -8.000 -0.9072 0.00932 0.00440 -0.0008 0.9953 0.0260 -4.1143 0.0000 0.2404 + -7.500 -0.8408 0.00887 0.00397 -0.0029 0.9935 0.0294 -3.6464 0.0000 0.2383 + -7.000 -0.7793 0.00839 0.00353 -0.0040 0.9886 0.0357 -3.2165 0.0000 0.2371 + -6.500 -0.7185 0.00794 0.00314 -0.0049 0.9808 0.0448 -2.8614 0.0000 0.2359 + -6.000 -0.6640 0.00757 0.00281 -0.0043 0.9670 0.0544 -2.5473 0.0000 0.2367 + -5.500 -0.6102 0.00721 0.00250 -0.0035 0.9493 0.0672 -2.2476 0.0000 0.2378 + -5.000 -0.5564 0.00687 0.00219 -0.0027 0.9268 0.0843 -1.9599 0.0000 0.2390 + -4.500 -0.5022 0.00653 0.00191 -0.0021 0.8996 0.1105 -1.7042 0.0000 0.2401 + -4.000 -0.4471 0.00625 0.00166 -0.0016 0.8685 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0.0000 0.2426 + 3.500 0.3924 0.00596 0.00142 0.0011 0.1778 0.8297 -1.2634 0.0000 0.2419 + 4.000 0.4471 0.00625 0.00166 0.0016 0.1374 0.8685 -1.4791 0.0000 0.2409 + 4.500 0.5022 0.00653 0.00191 0.0020 0.1105 0.8996 -1.7042 0.0000 0.2401 + 5.000 0.5565 0.00687 0.00219 0.0027 0.0843 0.9268 -1.9601 0.0000 0.2390 + 5.500 0.6103 0.00721 0.00250 0.0035 0.0671 0.9493 -2.2477 0.0000 0.2378 + 6.000 0.6640 0.00757 0.00281 0.0043 0.0544 0.9670 -2.5474 0.0000 0.2367 + 6.500 0.7185 0.00794 0.00314 0.0049 0.0448 0.9808 -2.8615 0.0000 0.2359 + 7.000 0.7793 0.00839 0.00353 0.0040 0.0357 0.9886 -3.2167 0.0000 0.2371 + 7.500 0.8408 0.00887 0.00397 0.0029 0.0294 0.9936 -3.6468 0.0000 0.2383 + 8.000 0.9073 0.00932 0.00440 0.0008 0.0260 0.9953 -4.1147 0.0000 0.2404 + 8.500 0.9719 0.00987 0.00490 -0.0011 0.0222 0.9975 -4.5972 0.0000 0.2418 + 9.500 1.0890 0.01091 0.00597 -0.0021 0.0181 1.0000 -5.5698 0.0000 0.2414 + 10.000 1.1328 0.01145 0.00650 0.0006 0.0164 1.0000 -6.0198 0.0000 0.2383 + 10.500 1.1769 0.01214 0.00720 0.0031 0.0142 1.0000 -6.4778 0.0000 0.2355 + 11.000 1.2215 0.01300 0.00816 0.0054 0.0124 1.0000 -6.9362 0.0000 0.2331 + 11.500 1.2696 0.01367 0.00888 0.0069 0.0121 1.0000 -7.4543 0.0000 0.2313 + 12.000 1.3186 0.01427 0.00950 0.0082 0.0119 1.0000 -8.0060 0.0000 0.2297 + 12.500 1.3668 0.01494 0.01020 0.0096 0.0116 1.0000 -8.6247 0.0000 0.2281 + 13.000 1.4128 0.01576 0.01105 0.0113 0.0107 1.0000 -9.2650 0.0000 0.2263 + 13.500 1.4549 0.01682 0.01214 0.0135 0.0095 1.0000 -9.8918 0.0000 0.2241 + 14.000 1.4922 0.01815 0.01355 0.0163 0.0085 1.0000 -10.4893 0.0000 0.2216 + 14.500 1.5222 0.01968 0.01524 0.0200 0.0079 1.0000 -11.0441 0.0000 0.2185 + 15.000 1.5405 0.02151 0.01724 0.0251 0.0076 1.0000 -11.5269 0.0000 0.2144 + 15.500 1.5530 0.02395 0.01988 0.0296 0.0074 1.0000 -11.9673 0.0000 0.2106 + 16.000 1.5574 0.02738 0.02354 0.0332 0.0073 1.0000 -12.3391 0.0000 0.2074 + 16.500 1.5523 0.03237 0.02879 0.0349 0.0071 1.0000 -12.6181 0.0000 0.2050 + 17.000 1.5357 0.03974 0.03644 0.0337 0.0070 1.0000 -12.7714 0.0000 0.2043 + 17.500 1.5056 0.05008 0.04707 0.0294 0.0070 1.0000 -12.7656 0.0000 0.2054 + 18.000 1.4616 0.06331 0.06057 0.0228 0.0069 1.0000 -12.5863 0.0000 0.2080 + 18.500 1.4054 0.07922 0.07675 0.0145 0.0070 1.0000 -12.2382 0.0000 0.2120 + 19.000 1.3413 0.09677 0.09453 0.0055 0.0070 1.0000 -11.7541 0.0000 0.2170 + 19.500 1.2725 0.11606 0.11403 -0.0046 0.0071 1.0000 -11.1427 0.0000 0.2238 + 20.000 1.2064 0.13545 0.13362 -0.0151 0.0072 1.0000 -10.4790 0.0000 0.2317 + 20.500 1.1462 0.15525 0.15361 -0.0264 0.0072 1.0000 -9.7735 0.0000 0.2414 + 21.000 1.0903 0.17533 0.17387 -0.0382 0.0073 1.0000 -8.9953 0.0000 0.2529 + 21.500 1.0299 0.19913 0.19787 -0.0523 0.0073 1.0000 -7.9219 0.0000 0.2685 + 22.000 0.9138 0.24928 0.24825 -0.0783 0.0063 1.0000 -4.7212 0.0000 0.3066 + 22.500 0.9282 0.25560 0.25457 -0.0827 0.0057 1.0000 -4.8331 0.0000 0.3089 + 24.000 0.9396 0.29898 0.29797 -0.1049 0.0048 1.0000 -2.5370 0.0000 0.3313 + 24.500 0.9555 0.30433 0.30332 -0.1092 0.0042 1.0000 -2.7097 0.0000 0.3328 + 25.000 0.9713 0.30941 0.30841 -0.1136 0.0038 1.0000 -2.9101 0.0000 0.3341 + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0015_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0015_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..8ca93d9 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0015_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,84 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0015 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.1183 0.01114 0.00613 -0.0047 0.9948 0.0360 -4.4190 0.0000 0.2325 + -9.500 -1.0532 0.01057 0.00558 -0.0067 0.9932 0.0407 -4.0509 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0.0000 0.2414 + -2.500 -0.2845 0.00596 0.00128 -0.0003 0.6500 0.2964 -0.9464 0.0000 0.2417 + -2.000 -0.2280 0.00581 0.00117 -0.0002 0.6143 0.3327 -0.8398 0.0000 0.2422 + -1.500 -0.1712 0.00574 0.00109 -0.0001 0.5773 0.3657 -0.7458 0.0000 0.2425 + -1.000 -0.1142 0.00570 0.00104 -0.0000 0.5388 0.3992 -0.6630 0.0000 0.2428 + -0.500 -0.0572 0.00563 0.00101 -0.0000 0.5052 0.4364 -0.5898 0.0000 0.2431 + 0.000 -0.0000 0.00561 0.00100 -0.0000 0.4716 0.4716 -0.5248 0.0000 0.0521 + 0.500 0.0572 0.00563 0.00101 0.0000 0.4364 0.5052 -0.5898 0.0000 0.2431 + 1.000 0.1142 0.00570 0.00104 0.0000 0.3992 0.5388 -0.6630 0.0000 0.2428 + 1.500 0.1712 0.00574 0.00109 0.0001 0.3657 0.5773 -0.7458 0.0000 0.2426 + 2.000 0.2280 0.00581 0.00117 0.0002 0.3327 0.6143 -0.8398 0.0000 0.2422 + 2.500 0.2845 0.00596 0.00128 0.0003 0.2964 0.6500 -0.9465 0.0000 0.2417 + 3.000 0.3411 0.00610 0.00140 0.0004 0.2641 0.6846 -1.0673 0.0000 0.2414 + 3.500 0.3973 0.00624 0.00155 0.0006 0.2351 0.7243 -1.2002 0.0000 0.2408 + 4.000 0.4526 0.00648 0.00175 0.0010 0.1997 0.7615 -1.3531 0.0000 0.2400 + 4.500 0.5086 0.00669 0.00195 0.0012 0.1748 0.7954 -1.5157 0.0000 0.2394 + 5.000 0.5638 0.00697 0.00219 0.0017 0.1487 0.8279 -1.7013 0.0000 0.2386 + 5.500 0.6186 0.00724 0.00246 0.0022 0.1275 0.8598 -1.8927 0.0000 0.2377 + 6.000 0.6727 0.00759 0.00278 0.0028 0.1050 0.8878 -2.1052 0.0000 0.2366 + 6.500 0.7269 0.00793 0.00310 0.0035 0.0899 0.9122 -2.3377 0.0000 0.2356 + 7.000 0.7807 0.00828 0.00343 0.0042 0.0787 0.9330 -2.5779 0.0000 0.2345 + 7.500 0.8339 0.00864 0.00379 0.0051 0.0688 0.9507 -2.8252 0.0000 0.2334 + 8.000 0.8857 0.00909 0.00419 0.0062 0.0583 0.9660 -3.0927 0.0000 0.2319 + 8.500 0.9366 0.00955 0.00462 0.0075 0.0514 0.9794 -3.3876 0.0000 0.2304 + 9.000 0.9955 0.01000 0.00505 0.0070 0.0460 0.9871 -3.7150 0.0000 0.2308 + 9.500 1.0534 0.01057 0.00558 0.0066 0.0406 0.9932 -4.0515 0.0000 0.2310 + 10.000 1.1185 0.01114 0.00613 0.0046 0.0360 0.9949 -4.4197 0.0000 0.2325 + 10.500 1.1823 0.01171 0.00668 0.0029 0.0335 0.9969 -4.7986 0.0000 0.2335 + 11.000 1.2429 0.01250 0.00743 0.0017 0.0281 0.9991 -5.1750 0.0000 0.2339 + 11.500 1.2937 0.01307 0.00802 0.0026 0.0267 1.0000 -5.5515 0.0000 0.2325 + 12.000 1.3283 0.01356 0.00854 0.0069 0.0260 1.0000 -5.9080 0.0000 0.2286 + 12.500 1.3654 0.01420 0.00919 0.0105 0.0244 1.0000 -6.2826 0.0000 0.2254 + 13.000 1.4030 0.01504 0.01003 0.0136 0.0223 1.0000 -6.6658 0.0000 0.2225 + 13.500 1.4346 0.01599 0.01101 0.0178 0.0199 1.0000 -7.0281 0.0000 0.2190 + 14.000 1.4658 0.01703 0.01213 0.0216 0.0188 1.0000 -7.3962 0.0000 0.2157 + 14.500 1.5006 0.01799 0.01315 0.0245 0.0187 1.0000 -7.7975 0.0000 0.2132 + 15.000 1.5333 0.01914 0.01436 0.0274 0.0184 1.0000 -8.1968 0.0000 0.2108 + 15.500 1.5636 0.02054 0.01582 0.0301 0.0179 1.0000 -8.5897 0.0000 0.2084 + 16.000 1.5896 0.02232 0.01767 0.0327 0.0172 1.0000 -8.9654 0.0000 0.2060 + 16.500 1.6103 0.02467 0.02009 0.0351 0.0163 1.0000 -9.3153 0.0000 0.2037 + 17.000 1.6253 0.02768 0.02318 0.0371 0.0154 1.0000 -9.6339 0.0000 0.2016 + 17.500 1.6353 0.03149 0.02710 0.0383 0.0144 1.0000 -9.9193 0.0000 0.1998 + 18.000 1.6380 0.03629 0.03206 0.0387 0.0137 1.0000 -10.1560 0.0000 0.1983 + 18.500 1.6322 0.04243 0.03838 0.0380 0.0132 1.0000 -10.3346 0.0000 0.1973 + 19.000 1.6152 0.05037 0.04652 0.0360 0.0127 1.0000 -10.4315 0.0000 0.1969 + 19.500 1.5859 0.06019 0.05657 0.0327 0.0124 1.0000 -10.4335 0.0000 0.1971 + 20.000 1.5455 0.07203 0.06865 0.0280 0.0122 1.0000 -10.3412 0.0000 0.1981 + 20.500 1.4926 0.08595 0.08283 0.0220 0.0121 1.0000 -10.1399 0.0000 0.2001 + 21.000 1.4384 0.10072 0.09783 0.0151 0.0121 1.0000 -9.8997 0.0000 0.2029 + 21.500 1.3773 0.11682 0.11416 0.0070 0.0121 1.0000 -9.5698 0.0000 0.2068 + 22.000 1.3176 0.13355 0.13112 -0.0019 0.0121 1.0000 -9.2026 0.0000 0.2120 + 22.500 1.2752 0.14806 0.14580 -0.0103 0.0121 1.0000 -8.9408 0.0000 0.2173 + 23.000 1.2391 0.16176 0.15966 -0.0185 0.0121 1.0000 -8.6978 0.0000 0.2229 + 23.500 1.2013 0.17660 0.17466 -0.0279 0.0121 1.0000 -8.3871 0.0000 0.2299 + 24.000 1.1899 0.18676 0.18491 -0.0346 0.0120 1.0000 -8.3244 0.0000 0.2345 + 24.500 1.1723 0.19860 0.19686 -0.0426 0.0120 1.0000 -8.1595 0.0000 0.2405 + 25.000 1.1547 0.21091 0.20927 -0.0511 0.0118 1.0000 -7.9608 0.0000 0.2472 + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0021_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0021_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..6387550 --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0021_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,84 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0021 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.0590 0.01083 0.00593 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--------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -1.0212 0.01119 0.00632 -0.0220 0.8595 0.1450 -2.8722 0.0000 0.2046 + -9.500 -0.9786 0.01062 0.00573 -0.0198 0.8333 0.1537 -2.7309 0.0000 0.2065 + -9.000 -0.9309 0.01025 0.00529 -0.0184 0.8076 0.1598 -2.5841 0.0000 0.2076 + -8.500 -0.8872 0.00974 0.00478 -0.0163 0.7815 0.1728 -2.4568 0.0000 0.2096 + -8.000 -0.8385 0.00943 0.00441 -0.0149 0.7553 0.1811 -2.3257 0.0000 0.2108 + -7.500 -0.7927 0.00903 0.00401 -0.0129 0.7300 0.1934 -2.2007 0.0000 0.2127 + -7.000 -0.7457 0.00883 0.00375 -0.0110 0.7041 0.2018 -2.0820 0.0000 0.2148 + -6.500 -0.7018 0.00855 0.00348 -0.0085 0.6791 0.2165 -1.9734 0.0000 0.2180 + -6.000 -0.6502 0.00839 0.00326 -0.0074 0.6527 0.2268 -1.8577 0.0000 0.2191 + -5.500 -0.5996 0.00817 0.00304 -0.0062 0.6289 0.2402 -1.7527 0.0000 0.2206 + -5.000 -0.5473 0.00797 0.00284 -0.0053 0.6078 0.2549 -1.6494 0.0000 0.2217 + -4.500 -0.4934 0.00784 0.00269 -0.0046 0.5867 0.2651 -1.5497 0.0000 0.2222 + 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0.10599 0.0325 0.0477 1.0000 -5.8511 0.0000 0.1715 + 23.500 1.3744 0.11790 0.11464 0.0289 0.0470 1.0000 -5.8589 0.0000 0.1720 + 24.000 1.3735 0.12414 0.12097 0.0260 0.0468 1.0000 -5.9313 0.0000 0.1726 + 24.500 1.3575 0.13247 0.12942 0.0219 0.0462 1.0000 -5.9397 0.0000 0.1736 + 25.000 1.3383 0.14123 0.13830 0.0173 0.0453 1.0000 -5.9285 0.0000 0.1751 + + diff --git a/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0028_T1_Al 0.00_M0.14_N9.0.txt b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0028_T1_Al 0.00_M0.14_N9.0.txt new file mode 100644 index 0000000..b4a896a --- /dev/null +++ b/Airfoil characteristics - amiya/Report/max thickness/NACA 4 series/NACA 0028_T1_Al 0.00_M0.14_N9.0.txt @@ -0,0 +1,84 @@ +XFLR5 v6.09.01 beta + + Calculated polar for: NACA 0028 + + 1 1 Reynolds number fixed Mach number fixed + + xtrf = 1.000 (top) 1.000 (bottom) + Mach = 0.139 Re = 3.000 e 6 Ncrit = 9.000 + + alpha CL CD CDp Cm Top Xtr Bot Xtr Cpmin Chinge XCp + ------- -------- --------- --------- -------- ------- ------- -------- --------- --------- + -10.000 -0.9539 0.01249 0.00756 -0.0306 0.7664 0.1864 -2.7092 0.0000 0.1867 + -9.500 -0.9112 0.01184 0.00687 -0.0290 0.7406 0.1944 -2.5964 0.0000 0.1875 + -9.000 -0.8642 0.01140 0.00634 -0.0279 0.7144 0.1978 -2.4795 0.0000 0.1876 + -8.500 -0.8207 0.01083 0.00577 -0.0263 0.6942 0.2101 -2.3776 0.0000 0.1885 + -8.000 -0.7754 0.01038 0.00528 -0.0247 0.6718 0.2181 -2.2743 0.0000 0.1891 + -7.500 -0.7265 0.01005 0.00490 -0.0237 0.6492 0.2266 -2.1684 0.0000 0.1888 + -7.000 -0.6819 0.00965 0.00448 -0.0218 0.6248 0.2371 -2.0729 0.0000 0.1899 + -6.500 -0.6311 0.00942 0.00420 -0.0209 0.6063 0.2427 -1.9755 0.0000 0.1890 + -6.000 -0.5853 0.00906 0.00386 -0.0192 0.5889 0.2572 -1.8844 0.0000 0.1899 + -5.500 -0.5357 0.00887 0.00362 -0.0179 0.5653 0.2646 -1.7938 0.0000 0.1894 + -5.000 -0.4867 0.00864 0.00338 -0.0166 0.5506 0.2764 -1.7088 0.0000 0.1891 + -4.500 -0.4399 0.00843 0.00317 -0.0147 0.5327 0.2875 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