{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "#%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#LLT inviscid implementation for rectangular and trapezoidal wings with and without twist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Aerodynamics for engineers. J. Bertin, R. Cummings. 6ed. Example 7.2\n",
    "\n",
    "rho = 1.225\n",
    "v_inf = 100\n",
    "\n",
    "target_weight = 4000\n",
    "\n",
    "#Number of setions\n",
    "n = 40       #D(4)\n",
    "\n",
    "#Manual input of AR and TR\n",
    "AR = 9     #D(9)\n",
    "TR = 0.4   #D(0.4)\n",
    "\n",
    "c_root = 0.726  #D(0.726)\n",
    "c_tip = 0.290   #D(0.290)\n",
    "\n",
    "b      = 2*2.286  #semi-span - one wing\n",
    "b_half = 2.286   #semi-span - one wing - D(2.286)\n",
    "\n",
    "#Area when using wing-span b\n",
    "#area = ((b)**2)/AR\n",
    "\n",
    "#Area when using wing semi-span b/2\n",
    "#This is the area for one wing.\n",
    "#area = ((2*b_half)**2)/AR\n",
    "area = (0.5*(c_root + c_tip))*b_half\n",
    "\n",
    "#Computed AR using compute area\n",
    "#Attention is area computed using one b/2 you must multiply area by 2\n",
    "AR_computed = b**2/(2*area)\n",
    "\n",
    "#Cmputed TR\n",
    "TR_computed = c_tip/c_root\n",
    "\n",
    "#Airfoil cl slope\n",
    "a0 = 2*np.pi\n",
    "\n",
    "#Alpha zero-lift\n",
    "alpha_0 = -1.2  #D(-1.2)\n",
    "\n",
    "#i_w = 2            # wing setting angle (deg)\n",
    "#alpha_twist = -1;  # Twist angle (deg)\n",
    "\n",
    "AOA = 2;            # Wing angle of attack (deg) - D(2)\n",
    "i_w = 2;             # wing setting angle (deg) - This is the angle at the root - D(2)\n",
    "alpha_twist = 0;    # Twist angle (deg), for washout the value is negative - D(0)\n",
    "\n",
    "alpha_effective = AOA + i_w    #Actual AOA at root (deg)\n",
    "\n",
    "#alpha = i_w+alpha_twist:-alpha_twist/(N-1):i_w;\n",
    "#alpha = np.linspace(i_w+alpha_twist,i_w,n)  \n",
    "alpha = np.linspace(alpha_effective+alpha_twist,alpha_effective,n)   #(deg)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed area for semi wingspan =  1.161288\n",
      "Computed area for wingspan =  2.322576\n",
      "Computed AR =  8.999999999999998\n",
      "Computed TR =  0.39944903581267216\n"
     ]
    }
   ],
   "source": [
    "print(\"Computed area for semi wingspan = \", 1*area)\n",
    "print(\"Computed area for wingspan = \", 2*area)\n",
    "print(\"Computed AR = \", AR_computed)\n",
    "print(\"Computed TR = \", TR_computed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Angle of attack AOA (deg) =  2\n",
      "Wing setting angle (deg) =  2\n",
      "Effective angle of attack at the root (AOA + wing setting angle) =  4\n",
      "Geometrical twist in deg (negative means washout) =  0\n",
      "Twist distribution tip-to-root (deg) =  [4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4.\n",
      " 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4.]\n"
     ]
    }
   ],
   "source": [
    "print(\"Angle of attack AOA (deg) = \", AOA)\n",
    "print(\"Wing setting angle (deg) = \", i_w )\n",
    "print(\"Effective angle of attack at the root (AOA + wing setting angle) = \", alpha_effective)\n",
    "print(\"Geometrical twist in deg (negative means washout) = \", alpha_twist)\n",
    "#print(\"Twist distribution (in degrees) = \", alpha)\n",
    "print(\"Twist distribution tip-to-root (deg) = \", alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#theta = np.linspace(np.pi/(2*n),np.pi/2,n)\n",
    "\n",
    "if n == 4:\n",
    "    #theta_force = 22.5    #Force theta so we have same setup as in bertin\n",
    "    #theta = np.linspace(0,90,n-1) + theta_force\n",
    "    theta = np.array([22.5,45,67.5,90])\n",
    "else:\n",
    "    eps = 1e-8     #Do not start from zero in will divide by zero\n",
    "    theta = np.linspace(eps,90,n)\n",
    "    \n",
    "\n",
    "theta_r = theta*np.pi/180\n",
    "theta_deg = theta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta angle (rad) =  [1.74532925e-10 4.02768291e-02 8.05536579e-02 1.20830487e-01\n",
      " 1.61107316e-01 2.01384145e-01 2.41660974e-01 2.81937802e-01\n",
      " 3.22214631e-01 3.62491460e-01 4.02768289e-01 4.43045118e-01\n",
      " 4.83321947e-01 5.23598776e-01 5.63875605e-01 6.04152433e-01\n",
      " 6.44429262e-01 6.84706091e-01 7.24982920e-01 7.65259749e-01\n",
      " 8.05536578e-01 8.45813407e-01 8.86090236e-01 9.26367065e-01\n",
      " 9.66643893e-01 1.00692072e+00 1.04719755e+00 1.08747438e+00\n",
      " 1.12775121e+00 1.16802804e+00 1.20830487e+00 1.24858170e+00\n",
      " 1.28885852e+00 1.32913535e+00 1.36941218e+00 1.40968901e+00\n",
      " 1.44996584e+00 1.49024267e+00 1.53051950e+00 1.57079633e+00]\n"
     ]
    }
   ],
   "source": [
    "print(\"Theta angle (rad) = \", theta_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta angle (deg) =  [1.00000000e-08 2.30769232e+00 4.61538462e+00 6.92307693e+00\n",
      " 9.23076924e+00 1.15384615e+01 1.38461539e+01 1.61538462e+01\n",
      " 1.84615385e+01 2.07692308e+01 2.30769231e+01 2.53846154e+01\n",
      " 2.76923077e+01 3.00000000e+01 3.23076923e+01 3.46153846e+01\n",
      " 3.69230769e+01 3.92307692e+01 4.15384615e+01 4.38461539e+01\n",
      " 4.61538462e+01 4.84615385e+01 5.07692308e+01 5.30769231e+01\n",
      " 5.53846154e+01 5.76923077e+01 6.00000000e+01 6.23076923e+01\n",
      " 6.46153846e+01 6.69230769e+01 6.92307692e+01 7.15384615e+01\n",
      " 7.38461538e+01 7.61538462e+01 7.84615385e+01 8.07692308e+01\n",
      " 8.30769231e+01 8.53846154e+01 8.76923077e+01 9.00000000e+01]\n"
     ]
    }
   ],
   "source": [
    "print(\"Theta angle (deg) = \", theta_deg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Compute spanwise stations using angular values\n",
    "\n",
    "#When using wing-span b\n",
    "z = (b/2)*np.cos(theta_r)\n",
    "\n",
    "#When using wing semi-span b/2\n",
    "#z = 0.5*(2*b_half)*np.cos(theta_r)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Span location (+s - center line) =  [2.28600000e+00 2.28414605e+00 2.27858721e+00 2.26933249e+00\n",
      " 2.25639690e+00 2.23980143e+00 2.21957299e+00 2.19574440e+00\n",
      " 2.16835431e+00 2.13744713e+00 2.10307301e+00 2.06528769e+00\n",
      " 2.02415247e+00 1.97973407e+00 1.93210454e+00 1.88134112e+00\n",
      " 1.82752616e+00 1.77074694e+00 1.71109557e+00 1.64866879e+00\n",
      " 1.58356787e+00 1.51589840e+00 1.44577013e+00 1.37329682e+00\n",
      " 1.29859601e+00 1.22178888e+00 1.14300000e+00 1.06235717e+00\n",
      " 9.79991195e-01 8.96035670e-01 8.10626772e-01 7.23903034e-01\n",
      " 6.36005122e-01 5.47075609e-01 4.57258736e-01 3.66700188e-01\n",
      " 2.75546851e-01 1.83946576e-01 9.20479391e-02 1.39977129e-16]\n"
     ]
    }
   ],
   "source": [
    "print(\"Span location (+s - center line) = \", z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Twist distribution (in degrees) =  [4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4.\n",
      " 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4. 4.]\n"
     ]
    }
   ],
   "source": [
    "print(\"Twist distribution (in degrees) = \", alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Compute local chord\n",
    "\n",
    "#c1 = 1 + (TR - 1) * np.cos(theta_r) * c_root\n",
    "c = c_root *(1-(1-TR)*np.cos(theta_r))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Local chord =  [0.2904     0.29075327 0.29181252 0.29357601 0.29604091 0.29920319\n",
      " 0.30305774 0.30759831 0.31281753 0.31870692 0.32525695 0.33245699\n",
      " 0.34029536 0.34875933 0.3578352  0.36750823 0.37776273 0.38858208\n",
      " 0.39994872 0.41184421 0.42424927 0.43714377 0.45050679 0.46431667\n",
      " 0.478551   0.49318669 0.5082     0.52356659 0.53926152 0.55525934\n",
      " 0.57153411 0.58805942 0.60480847 0.6217541  0.63886881 0.65612485\n",
      " 0.67349422 0.69094876 0.70846016 0.726     ]\n"
     ]
    }
   ],
   "source": [
    "print(\"Local chord = \", c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#mu = ( a0/(2*(1 + TR)*AR) ) * ( 1+(TR-1)*np.cos(theta_r) );\n",
    "mu = (c*a0)/(2*AR*c_root*(1+TR))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Local mu =  [0.0997331  0.09985443 0.10021821 0.10082385 0.10167038 0.10275641\n",
      " 0.10408019 0.10563958 0.10743203 0.10945465 0.11170415 0.11417688\n",
      " 0.11686884 0.11977565 0.12289261 0.12621465 0.12973639 0.13345212\n",
      " 0.1373558  0.14144112 0.14570143 0.15012983 0.15471914 0.15946192\n",
      " 0.16435046 0.16937685 0.17453293 0.17981033 0.18520049 0.19069468\n",
      " 0.19628398 0.20195933 0.20771152 0.21353121 0.21940898 0.22533528\n",
      " 0.23130051 0.23729498 0.24330898 0.24933275]\n"
     ]
    }
   ],
   "source": [
    "print(\"Local mu = \", mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Assemble matrices\n",
    "\n",
    "#Ax=b\n",
    "#x=A^-1*b\n",
    "#In our case the matrices are Bx=LHS\n",
    "\n",
    "#Angles alpha and alpha_0 must be in RAD\n",
    "LHS = mu * (alpha - alpha_0)/57.3\n",
    "\n",
    "#Coefficients of monoplane equation\n",
    "B = np.zeros((n,n))\n",
    "\n",
    "for i in range(0,n):\n",
    "    for j in range(0,n):\n",
    "        B[i,j] = np.sin((2*(j+1)-1) * theta_r[i]) * ( 1 + ((mu[i] * (2*(j+1)-1)) / np.sin(theta_r[i])) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Solve linear system for x - Assign x to A for consistency in notation\n",
    "\n",
    "x = np.linalg.solve(B,LHS)\n",
    "A = x\n",
    "\n",
    "\n",
    "#Compute lift coefficient of the wing\n",
    "CL_wing = np.pi * AR * A[0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "An coefficients =  [ 1.63477218e-02  2.26233730e-04  8.39388834e-04  1.21613097e-04\n",
      "  1.55821148e-04  1.82441946e-05  4.51675580e-05  1.46264299e-06\n",
      "  1.79124671e-05 -1.26373079e-06  8.77647747e-06 -1.50103784e-06\n",
      "  4.95877851e-06 -1.30003583e-06  3.09672472e-06 -1.06318164e-06\n",
      "  2.08216040e-06 -8.65656128e-07  1.48206059e-06 -7.12900578e-07\n",
      "  1.10408596e-06 -5.96857070e-07  8.53976505e-07 -5.08707692e-07\n",
      "  6.81822896e-07 -4.41387759e-07  5.59501836e-07 -3.89679769e-07\n",
      "  4.70337268e-07 -3.49828977e-07  4.04013912e-07 -3.19154366e-07\n",
      "  3.53922746e-07 -2.95748423e-07  3.15707029e-07 -2.78263152e-07\n",
      "  2.86452193e-07 -2.65796761e-07  6.21512083e-07  3.48901815e-07]\n"
     ]
    }
   ],
   "source": [
    "print(\"An coefficients = \", A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Compute delta or induced drag factor\n",
    "\n",
    "delta=0\n",
    "for i in range(1,n):\n",
    "    delta = delta + (2*(i+1)-1)*A[i]**2/A[0]**2\n",
    "\n",
    "#Attention in the previous equation i=1 is A[3] in the equation of llt\n",
    "\n",
    "    \n",
    "#Compute oswald span efficiency\n",
    "oswald = 1/(1+delta)\n",
    "\n",
    "#Compute induced drag\n",
    "CD_ind = (CL_wing**2/(np.pi*AR)) * (1+delta)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Induced drag factor (delta) =  0.015107157179578385\n",
      "Oswald span efficiency (e) =  0.9851176724814423\n",
      "Induced drag coefficient CD_i =  0.007670413012592394\n"
     ]
    }
   ],
   "source": [
    "print(\"Induced drag factor (delta) = \", delta)\n",
    "print(\"Oswald span efficiency (e) = \", oswald)\n",
    "print(\"Induced drag coefficient CD_i = \", CD_ind)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#For lift coefficient distribution\n",
    "\n",
    "sum1=np.zeros((n))\n",
    "\n",
    "for i in range(0,n):\n",
    "    for j in range(0,n):\n",
    "    \n",
    "#For lift coefficient distribution\n",
    "        sum1[i] = sum1[i] + A[j]*np.sin((2*(j+1)-1)*theta_r[i])\n",
    "\n",
    "    \n",
    "#Atention b is +s \n",
    "#C_L distribution is equal to 2*gamma/u.c\n",
    "#gamma is equal to 4*s*u*(sum)\n",
    "gamma = 4*b*sum1\n",
    "#gamma = 4*b*v_inf*sum1\n",
    "#gamma0=gamma[n-1]\n",
    "\n",
    "C_L = 2*4*b*sum1 / c;\n",
    "\n",
    "#lift distribution per unit span\n",
    "Ls = C_L * 0.5 * rho * v_inf * v_inf * c\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lift coefficient CL distribution =  [5.51185982e-10 1.25538998e-01 2.44448712e-01 3.53593220e-01\n",
      " 4.51617790e-01 5.38183172e-01 6.13612400e-01 6.78623491e-01\n",
      " 7.34147005e-01 7.81202094e-01 8.20806614e-01 8.53931243e-01\n",
      " 8.81461574e-01 9.04193284e-01 9.22819214e-01 9.37942962e-01\n",
      " 9.50075346e-01 9.59654180e-01 9.67042602e-01 9.72549296e-01\n",
      " 9.76425869e-01 9.78885187e-01 9.80097344e-01 9.80205274e-01\n",
      " 9.79319845e-01 9.77532364e-01 9.74909724e-01 9.71503326e-01\n",
      " 9.67345413e-01 9.62453401e-01 9.56828841e-01 9.50454991e-01\n",
      " 9.43300495e-01 9.35305228e-01 9.26392236e-01 9.16428330e-01\n",
      " 9.05251068e-01 8.92552058e-01 8.77927031e-01 8.60206497e-01]\n"
     ]
    }
   ],
   "source": [
    "print(\"Lift coefficient CL distribution = \", C_L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lift distribution =  [9.80394506e-07 2.23567857e+02 4.36915811e+02 6.35814740e+02\n",
      " 8.18896205e+02 9.86285003e+02 1.13900494e+03 1.27855357e+03\n",
      " 1.40663106e+03 1.52496892e+03 1.63520999e+03 1.73885939e+03\n",
      " 1.83723834e+03 1.93149332e+03 2.02258033e+03 2.11129826e+03\n",
      " 2.19828123e+03 2.28403955e+03 2.36895063e+03 2.45330015e+03\n",
      " 2.53726878e+03 2.62097056e+03 2.70443564e+03 2.78764460e+03\n",
      " 2.87050874e+03 2.95289893e+03 3.03462587e+03 3.11546091e+03\n",
      " 3.19511947e+03 3.27326887e+03 3.34951947e+03 3.42340958e+03\n",
      " 3.49441131e+03 3.56187038e+03 3.62503901e+03 3.68290981e+03\n",
      " 3.73429835e+03 3.77733491e+03 3.80960497e+03 3.82512324e+03]\n"
     ]
    }
   ],
   "source": [
    "print(\"Lift distribution = \", Ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CL =  0.4622209445394826\n",
      "CD_ind =  0.007670413012592394\n",
      "CL_alpha (slope lift curve wing per rad) =  8.27603416395714\n"
     ]
    }
   ],
   "source": [
    "#Print lift and drag coefficients\n",
    "\n",
    "print(\"CL = \",CL_wing)\n",
    "print(\"CD_ind = \",CD_ind)\n",
    "\n",
    "#CLalpha = CL_wing/( (i_w*np.pi/180) - (alpha_0*np.pi/180))\n",
    "CLalpha = CL_wing/( (AOA*np.pi/180) - (alpha_0*np.pi/180))\n",
    "\n",
    "print(\"CL_alpha (slope lift curve wing per rad) = \",CLalpha)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reference velocity (m/s) =  100\n",
      "Reference density (kg/m^3) =  1.225\n",
      "Reference area (m^2) =  1.161288\n"
     ]
    }
   ],
   "source": [
    "#Compute lift and darg forces\n",
    "\n",
    "Lift = CL_wing * 0.5 * rho * v_inf * v_inf * area\n",
    "Drag_ind = CD_ind * 0.5 * rho * v_inf * v_inf * area\n",
    "\n",
    "\n",
    "print(\"Reference velocity (m/s) = \", v_inf)\n",
    "print(\"Reference density (kg/m^3) = \", rho)\n",
    "print(\"Reference area (m^2) = \", area)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lift (N) =  3287.7262719844966\n",
      "Induced drag (N) =  54.55879634272531\n"
     ]
    }
   ],
   "source": [
    "print(\"Lift (N) = \", Lift)\n",
    "print(\"Induced drag (N) = \", Drag_ind)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Required lift =  4000\n",
      "Target velocity to generate required lift =  110.30169077197355\n"
     ]
    }
   ],
   "source": [
    "v_target = np.sqrt(target_weight/(0.5*rho*area*CL_wing))\n",
    "print(\"Required lift = \", target_weight)\n",
    "print(\"Target velocity to generate required lift = \", v_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Induced angle and downwash computation\n",
    "\n",
    "sum2=np.zeros((n))\n",
    "\n",
    "for i in range(0,n):\n",
    "    for j in range(0,n):\n",
    "        sum2[i] = sum2[i] + ( (2*(j+1)-1) * A[j] * np.sin((2*(j+1)-1) * theta_r[i]) ) / np.sin(theta_r[i])\n",
    "\n",
    "#for i in range(0,n):\n",
    "#    sum2[i] = sum2[i] + ( (2*(i+1)-1) * A[i] * np.sin((2*(i+1)-1) * theta_r[i]) ) / np.sin(theta_r[i])\n",
    "\n",
    "#Downwash\n",
    "dw = -1*v_inf * sum2\n",
    "\n",
    "#Induced angle\n",
    "ind_a = -1*sum2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downwash (m/s) =  [-9.07504363 -8.07564271 -7.12901674 -6.26013039 -5.47976854 -4.79063191\n",
      " -4.19014887 -3.67260337 -3.23058733 -2.8559874  -2.54070057 -2.27699937\n",
      " -2.0578337  -1.87686929 -1.72859049 -1.60819214 -1.51160769 -1.43535174\n",
      " -1.37653339 -1.33269526 -1.30183433 -1.282256   -1.27260616 -1.27174694\n",
      " -1.27879574 -1.29302566 -1.31390419 -1.34102211 -1.37412276 -1.41306748\n",
      " -1.45784393 -1.50858538 -1.56554147 -1.62919083 -1.70014609 -1.77946755\n",
      " -1.86844839 -1.96954369 -2.08597177 -2.22704282]\n"
     ]
    }
   ],
   "source": [
    "print(\"Downwash (m/s) = \", dw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Induced angle (rad) =  [-0.09075044 -0.08075643 -0.07129017 -0.0626013  -0.05479769 -0.04790632\n",
      " -0.04190149 -0.03672603 -0.03230587 -0.02855987 -0.02540701 -0.02276999\n",
      " -0.02057834 -0.01876869 -0.0172859  -0.01608192 -0.01511608 -0.01435352\n",
      " -0.01376533 -0.01332695 -0.01301834 -0.01282256 -0.01272606 -0.01271747\n",
      " -0.01278796 -0.01293026 -0.01313904 -0.01341022 -0.01374123 -0.01413067\n",
      " -0.01457844 -0.01508585 -0.01565541 -0.01629191 -0.01700146 -0.01779468\n",
      " -0.01868448 -0.01969544 -0.02085972 -0.02227043]\n"
     ]
    }
   ],
   "source": [
    "print(\"Induced angle (rad) = \", ind_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Induced angle (deg) =  [-5.19961699 -4.62700244 -4.08462571 -3.58679051 -3.1396761  -2.7448299\n",
      " -2.40077846 -2.10424673 -1.85099019 -1.63636025 -1.4557142  -1.30462454\n",
      " -1.17905186 -1.07536689 -0.9904094  -0.92142622 -0.86608741 -0.82239597\n",
      " -0.78869554 -0.76357814 -0.74589613 -0.73467857 -0.72914962 -0.72865732\n",
      " -0.73269599 -0.74084913 -0.75281165 -0.76834907 -0.78731435 -0.80962803\n",
      " -0.83528304 -0.86435575 -0.89698919 -0.93345758 -0.97411195 -1.0195598\n",
      " -1.07054207 -1.12846541 -1.19517379 -1.27600155]\n"
     ]
    }
   ],
   "source": [
    "print(\"Induced angle (deg) = \", ind_a*180/np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x268b6dd14c8>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "\n",
    "#plt.plot(z,C_L)\n",
    "#plt.plot(z,C_L/CL_wing)\n",
    "#plt.plot(z,C_L/(2*CL_wing))\n",
    "#plt.plot(z,C_L/np.max(C_L))\n",
    "\n",
    "#Normalized +s\n",
    "#plt.plot(z/np.max(z),C_L)\n",
    "#plt.plot(z/np.max(z),C_L/(CL_wing))\n",
    "plt.plot(z/np.max(z),C_L/(2*CL_wing))\n",
    "#plt.plot(z/np.max(z),C_L/np.max(C_L))\n",
    "\n",
    "\n",
    "#plt.hlines(y=np.max(C_L), xmin=0.0, xmax=b/1, color='b', label=\"cl_max\")\n",
    "#plt.hlines(y=C_L[n-1], xmin=0.0, xmax=b/1, color='r', label=\"cl_root\")\n",
    "\n",
    "plt.hlines(y=np.max(C_L/(2*CL_wing)), xmin=0.0, xmax=z/np.max(z),linestyles='dashdot',color='b',label=\"$C_{l_{max}}$\")\n",
    "plt.hlines(y=C_L[n-1]/(2*CL_wing), xmin=0.0, xmax=z/np.max(z), linestyles='dashdot',color='r', label=\"$C_{l_{root}}$\")\n",
    "\n",
    "\n",
    "#plt.xlabel('+s (m)')\n",
    "plt.xlabel('$\\dfrac{+s}{+s_{max}}$',fontsize=14)\n",
    "#plt.ylabel(r'$c_l$',fontsize=14)\n",
    "plt.ylabel(r'$\\dfrac{C_l}{2*C_L}$',fontsize=14)\n",
    "plt.title('Lift coefficient distribution',fontsize=20)\n",
    "plt.grid()\n",
    "\n",
    "plt.plot(0,np.max(C_L), 1,0.4)\n",
    "\n",
    "plt.legend(loc=0,fontsize=18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "\n",
    "#plt.plot(z,ind_a*180/np.pi)\n",
    "plt.plot(z/np.max(z),ind_a*180/np.pi)\n",
    "\n",
    "#For downwash\n",
    "#plt.plot(z,dw)\n",
    "\n",
    "#plt.xlabel('+s (m)')\n",
    "plt.xlabel('$\\dfrac{+s}{+s_{max}}$',fontsize=14)\n",
    "plt.ylabel('Induced angle $(^{\\circ})$',fontsize=14)\n",
    "plt.title('Induced angle distribution',fontsize=20)\n",
    "plt.grid()\n",
    "\n",
    "#plt.legend(loc=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x268b80e3ac8>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "\n",
    "#plt.plot(z/np.max(z),Ls)\n",
    "#plt.plot(z/np.max(z),Ls/np.max(Ls))\n",
    "plt.plot(z,Ls,label=\"Computed lift distribution\")\n",
    "#plt.plot(z/np.max(z),Ls)\n",
    "\n",
    "#elliptical lift distribution\n",
    "el=np.sqrt( (1 - (z/(b/2))**2)*np.max(Ls)**2)\n",
    "plt.plot(z,el,'-.',label=\"Ideal elliptical lift distribution\")\n",
    "\n",
    "plt.xlabel('$+s$ (m)',fontsize=14)\n",
    "#plt.xlabel('$\\dfrac{+s}{+s_{max}}$',fontsize=14)\n",
    "plt.ylabel('Lift (N)',fontsize=14)\n",
    "plt.title('Lift distribution',fontsize=20)\n",
    "plt.grid()\n",
    "\n",
    "plt.legend(loc=0,fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}