AircraftSizing.ipynb

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   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Work in progress\n",
    "Author: Jonathan Pelham"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction\n",
    "\n",
    "This notebook is a worked example in python 3 of chapter 3 from Aircraft Design: A Conceptual Approach 3rd edition by Daniel P. Raymer. using the ASW(Anti Submarine Warface) aircraft as an example.  Where possible no libraries not in an anaconda distribution basic install will be used.\n",
    "<br/><br/>\n",
    "**Mission:** <br/>Fly 1500nm (2778km) at M=0.6 carrying 10000lb (4535.924kg) of equipment and 4 crew members at 800lb (363.874kg), loiter on station for 3 hrs then return.\n",
    "# Takeoff Gross Weight Estimation\n",
    "\n",
    "\n",
    "$$Takeoff\\; Gross\\; Weight = W_0\\\\ \n",
    "Crew\\; Weight = W_{crew}\\\\ \n",
    "Payload\\; Weight = W_{payload}\\\\ \n",
    "Fuel\\; Weight = W_{fuel}\\\\ \n",
    "Aircraft\\; Empty\\; Weight = W_{empty}\\\\ \n",
    "W_0 = W_{crew} + W_{payload} + W_{fuel} + W_{empty}$$\n",
    "\n",
    "- Simplification of the equation\n",
    "$$Empty\\; Weight\\; Fraction = \\frac{W_{empty}}{W_0}\\\\ \n",
    "Fuel\\; Fraction = \\frac{W_{fuel}}{W_0}\\\\\n",
    "W_0 = W_{crew} + W_{payload} + (\\frac{W_{fuel}}{W_0})W_0 + (\\frac{W_{empty}}{W_0})W_0$$\n",
    "- Solving for $W_0$ as follows\n",
    "$$ W_0 - (\\frac{W_{fuel}}{W_0})W_0 - (\\frac{W_{empty}}{W_0})W_0 = W_{crew} + W_{payload}$$\n",
    "$$W_0 = \\frac{W_{crew} + W_{payload}}{1-(\\frac{W_{fuel}}{W_0})-(\\frac{W_{empty}}{W_0})}$$\n",
    "Since $W_{crew}$ and $W_{payload}$ are normally in the aircraft design requirments this then allows us to estimate the takeoff gross weight $W_0$ of the proposed aircraft by selecting appropriate empty weight fraction $\\frac{W_{empty}}{W_0}$ and fuel fractions $\\frac{W_{fuel}}{W_0}$ based on historical trends and our understanding of the aircraft role based on its design requirments.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
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     "text": [
      "Crew Weight 800.00 lb\n",
      "Payload Weight 10000.00 lb\n",
      "Fuel Fraction 0.3870\n",
      "Empty Weight Fractiont 0.4361\n",
      "Takeoff Gross Weight W_0 61051.44 lb\n"
     ]
    }
   ],
   "source": [
    "def TGW(EmptyW_F, Fuel_F, Crew_W, Payload_W):\n",
    "    return (Crew_W+Payload_W)/(1-Fuel_F-EmptyW_F)\n",
    "#e.g. ASW example\n",
    "Crew_Weight = 800 #lb\n",
    "Payload_Weight = 10000 #lb\n",
    "Fuel_Fraction = 0.387\n",
    "Empty_Weight_Fraction = 0.4361\n",
    "print(\"Crew Weight %.2f lb\" % (Crew_Weight))\n",
    "print(\"Payload Weight %.2f lb\" % (Payload_Weight))\n",
    "print(\"Fuel Fraction %.4f\" % (Fuel_Fraction,))\n",
    "print(\"Empty Weight Fractiont %.4f\" % (Empty_Weight_Fraction,))\n",
    "TGW_tmp_1 = TGW(Empty_Weight_Fraction, Fuel_Fraction, Crew_Weight, Payload_Weight)\n",
    "print(\"Takeoff Gross Weight W_0 %.2f lb\" % (TGW_tmp_1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Empty Weight Estimation\n",
    "Empty weight fractions are estimated based on historical trends for aircraft based on their roles and sized takeoff weight.  Raymer suggests a $5\\%$ reduction should be applied if the proposed aircraft is to be of composite construction.  He suggests that there is not yet enough information to base this reduction in a study of actual aircraft.  Perhaps by now there is such a study and this notebook will perhaps be updated to reflect that in the future.\n",
    "$$Historical\\; metric\\; = A\\\\\n",
    "Variable\\; Wing\\; Sweep\\; penalty\\; = K_{vs}\\\\\n",
    "K_{vs} = 1.04\\; if\\; variable\\; sweep\\; K_{vs} = 1\\; otherwise\\\\\n \\\\\n",
    "Weight\\; Sensitivity\\; Exponent\\; = C\\\\\n",
    "\\frac{W_{empty}}{W_0} = A {W_0}^C K_{vs}$$\n"
   ]
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     "text": [
      "0.436068833653\n"
     ]
    }
   ],
   "source": [
    "def EWF(TakeoffG_W,HS_metric,WeightS_E,VWS=False,VWS_penalty=1.04):\n",
    "    if VWS:\n",
    "        VWS_p_factor = VWS_penalty\n",
    "    else:\n",
    "        VWS_p_factor = 1\n",
    "        \n",
    "    return HS_metric*pow(TakeoffG_W, WeightS_E)*VWS_p_factor\n",
    "\n",
    "bomber_HS_metric = 0.93\n",
    "bomber_weight_sensitivty_e = -0.07\n",
    "estimated_TGW = 50000\n",
    "print(EWF(estimated_TGW,bomber_HS_metric,bomber_weight_sensitivty_e))"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fuel Fraction Estimation\n",
    "To estimate the fuel fraction of the aircraft we need to understand more about how it will be used to inform us regarding the rate of fuel consumption at different points during the mission and the aerodynamics.<br/>\n",
    "An aircraft mission can be broken down into multiple segments.  The weight at the start of the mission is taken as the Takeoff Gross Weight $W_0$ and for each mission segment $i$ the weight of the aircraft at the end of that segment will be $W_i$.  The weight fraction of each segment is expressed as $(\\frac{W_i}{W_{i-1}})$.  In a mission with a total number of segments $x$ the weight of the aircraft at the end of the mission will be $W_x$.  The ratio $\\frac{W_x}{W_0}$ can then be used to calculate the fuel fraction.  In our simple sizing study we presume no other weight change apart from fuel burn occurs during the mission.  Raymer suggests a $6\\%$ allowance should be made for reserve and trapped fuel.\n",
    "$$\\frac{W_{fuel}}{W_0} = 1.06(1 - \\frac{W_x}{W_0})$$"
   ]
  },
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   "execution_count": 54,
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   "source": [
    "def FF(mission_ratio,RT_Allowance=1.06):\n",
    "    return RT_Allowance*(1-mission_ratio)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cruise fuel burn\n",
    "Cruise weight fractions can be found by using the breguet range equation\n",
    "$$Range = R\\; in\\; ft\\\\\n",
    "Specific\\; Fuel\\; Consumption = C \\\\\n",
    "Velocity = V\\; in\\; \\frac{ft}{s}\\\\\n",
    "Lift\\; to\\; Drag\\; ratio\\; = \\frac{L}{D} \\\\\n",
    "R = \\frac{V}{C} \\frac{L}{D} \\ln(\\frac{W_{i-1}}{W_i})$$\n",
    "\n",
    "Which can be rearranged to give the weight fraction for that segment.\n",
    "$$\\frac{W_i}{W_{i-1}} = exp(\\frac{-R C}{V (\\frac{L}{D})})$$"
   ]
  },
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   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
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   "source": [
    "def cruise_WF(Range, Specific_FC, velocity, LD_ratio):\n",
    "    return numpy.exp((-1*Range*Specific_FC)/(velocity*LD_ratio))\n",
    "\n",
    "high_bypass_turbofan_cruise_SFC = 0.0001389"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loiter fuel burn\n",
    "Loiter weight fractions can be found using the endurance equation.\n",
    "$$ Endurance = E\\; in\\; s\\\\\n",
    "E = \\frac{\\frac{L}{D}}{C}\\ln(\\frac{W_{i-1}}{W_i})$$\n",
    "Rearranged again to put it in terms of the weight fraction we get\n",
    "$$\\frac{W_i}{W_{i-1}} = exp(\\frac{-E C}{(\\frac{L}{D})})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
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   "outputs": [],
   "source": [
    "def loiter_WF(Endurance, Specific_FC, LD_ratio):\n",
    "    return numpy.exp((-1*Endurance*Specific_FC)/(LD_ratio))\n",
    "\n",
    "high_bypass_turbofan_loiter_SFC = 0.0001111"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# L/D Ratio esimation\n",
    "\n",
    "Raymer suggests that during initial sizing for a jet aircraft the cruise L/D should be taken as 86.6% of the maximum L/D of the aircraft.  The loiter L/D ratio will of course be the maxium L/D as loiter is done in the most efficent configuration to ensure as much time on station as possible.\n",
    "\n",
    "This then leavs us with the problem of estimating L/D.\n",
    "Raymer suggests estimating it based on the wetted aspect ratio of the aircraft.  This then leaves us to use the conceptual sketch which has been done of the ASW aircraft concept Raymer use as an example and he gives the wetted area ratio $\\frac{S_{wet}}{S_{ref}}$ as 5.5 and the wetted aspect ratio is 1.27.  Looking up these values on the figure he provides on page 26 gives us our design L/D max of 16."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
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   "source": [
    "class AircraftMission:\n",
    "    variable_stan_disp = {'name':{'description':'Name:','format':'%s'},\n",
    "                         'weight_fraction':{'description':'WF:','format':'%.4f'},\n",
    "                         'description':{'description':'Description:','format':'%s'},\n",
    "                         'segment':{'description':'Segment:','format':'%i'}}\n",
    "    def __init__(self):\n",
    "        self.segments=[]\n",
    "    \n",
    "    def append_segment(self, seg_name, seg_WF, seg_description='None Provided'):\n",
    "        no_of_segments = len(self.segments)\n",
    "        self.segments.append({'segment':no_of_segments+1,'name':seg_name,'weight_fraction':seg_WF,'description':seg_description})\n",
    "    \n",
    "    def mission_weight_ratio(self):\n",
    "        no_of_segments = len(self.segments)\n",
    "        if no_of_segments <= 0:\n",
    "            raise ValueError('No mission segments have been added to the mission!')\n",
    "        \n",
    "        mwr = 1\n",
    "        for a in range(0,no_of_segments):\n",
    "            mwr = mwr*self.segments[a]['weight_fraction']\n",
    "        return mwr\n",
    "    \n",
    "    def landing_weight(self, TakeoffG_W):\n",
    "        return TakeoffG_W * self.mission_weight_ratio()\n",
    "    \n",
    "    def display_mission(self,itp=['segment','name','weight_fraction','description'],p_dict=variable_stan_disp):\n",
    "        no_of_segments = len(self.segments)\n",
    "        if no_of_segments <= 0:\n",
    "            raise ValueError('No mission segments have been added to the mission!')\n",
    "        \n",
    "        for a in range(0,no_of_segments):\n",
    "            disp_list = [p_dict[item_a]['description']+p_dict[item_a]['format']+' ' for item_a in itp]\n",
    "            variable_list = [self.segments[a][item_b] for item_b in itp]\n",
    "            disp_string = ''.join(disp_list) % tuple(variable_list)\n",
    "            print(disp_string)\n",
    "            \n",
    "        \n",
    "        \n",
    "    \n",
    "    \n",
    "    "
   ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Segment:1 Name:Warmup and Takeoff WF:0.9700 Description:None Provided \n",
      "Segment:2 Name:Climb WF:0.9850 Description:None Provided \n",
      "Segment:3 Name:Cruise WF:0.8581 Description:1500 nm range \n",
      "Segment:4 Name:Loiter WF:0.9278 Description:3 hr Loiter \n",
      "Segment:5 Name:Cruise WF:0.8581 Description:1500 nm range \n",
      "Segment:6 Name:Loiter WF:0.9917 Description:20 minute loiter \n",
      "Segment:7 Name:Land WF:0.9950 Description:None Provided \n",
      "Misson Weight Ratio 0.6440\n",
      "Fuel Fraction 0.3773\n",
      "Empty Weight Fraction 0.43607 based on TGW W_0 estimate 50000.000 lb\n",
      "Takeoff Gross Weight W_0 57882.726 lb\n",
      "Landing Gross Weight W_x 37277.185 lb\n",
      "Fuel Burned 20605.540 lb\n"
     ]
    }
   ],
   "source": [
    "\n",
    "ASW_LD_max = 16\n",
    "cruise_LD_ratio = ASW_LD_max * 0.866\n",
    "loiter_LD_ratio = ASW_LD_max\n",
    "cruise_velocity = 596.9 # ft/s\n",
    "cruise_SFC = high_bypass_turbofan_cruise_SFC\n",
    "loiter_SFC = high_bypass_turbofan_loiter_SFC\n",
    "mission_loiter = 10800 # 3h in s\n",
    "landing_loiter = 1200 # 20 min in s\n",
    "cruise_range = 9114000 # 1500nm in ft\n",
    "\n",
    "ASW_Mission = AircraftMission()\n",
    "ASW_Mission.append_segment('Warmup and Takeoff',0.97)\n",
    "ASW_Mission.append_segment('Climb',0.985)\n",
    "ASW_Mission.append_segment('Cruise',cruise_WF(cruise_range,cruise_SFC,cruise_velocity,cruise_LD_ratio),seg_description='1500 nm range') \n",
    "ASW_Mission.append_segment('Loiter',loiter_WF(mission_loiter,loiter_SFC,loiter_LD_ratio),seg_description='3 hr Loiter') \n",
    "ASW_Mission.append_segment('Cruise',cruise_WF(cruise_range,cruise_SFC,cruise_velocity,cruise_LD_ratio),seg_description='1500 nm range') # 1500 nm\n",
    "ASW_Mission.append_segment('Loiter',loiter_WF(landing_loiter,loiter_SFC,loiter_LD_ratio),seg_description='20 minute loiter') #20 mins\n",
    "ASW_Mission.append_segment('Land',0.995)\n",
    "ASW_Mission.display_mission()\n",
    "\n",
    "MWR_tmp = ASW_Mission.mission_weight_ratio()\n",
    "print(\"Misson Weight Ratio %.4f\" % (MWR_tmp,))\n",
    "FF_tmp = FF(MWR_tmp)\n",
    "print(\"Fuel Fraction %.4f\" % (FF_tmp,))\n",
    "TakeoffG_W_estimate = 50000\n",
    "EWF_tmp = EWF(TakeoffG_W_estimate,0.93,-0.07)\n",
    "print(\"Empty Weight Fraction %.5f based on TGW W_0 estimate %.3f lb\" % (EWF_tmp,TakeoffG_W_estimate))\n",
    "TGW_tmp = TGW(EWF_tmp , FF_tmp, Crew_Weight, Payload_Weight)\n",
    "print(\"Takeoff Gross Weight W_0 %.3f lb\"  % (TGW_tmp))\n",
    "LGW_tmp = ASW_Mission.landing_weight(TGW_tmp)\n",
    "print(\"Landing Gross Weight W_x %.3f lb\"  % (LGW_tmp))\n",
    "fuel_burn = TGW_tmp-LGW_tmp\n",
    "print(\"Fuel Burned %.3f lb\"  % (fuel_burn))\n",
    "\n",
    "\n",
    "    \n",
    "def calc_WG0(WGV,Fuel_F,Crew_W, Payload_W, HS_metric,WeightS_E,VWS=False,VWS_penalty=1.04):\n",
    "    EWF_calc = EWF(WGV,HS_metric,WeightS_E,VWS=False,VWS_penalty=1.04)\n",
    "    return TGW(EWF_calc, Fuel_F, Crew_W, Payload_W)\n",
    "\n",
    "def diff_calc_WG0(WGV,Fuel_F,Crew_W, Payload_W, HS_metric,WeightS_E,VWS=False,VWS_penalty=1.04):\n",
    "    tmp_wgv = calc_WG0(WGV,Fuel_F,Crew_W, Payload_W, HS_metric,WeightS_E,VWS,VWS_penalty)\n",
    "    result = WGV - tmp_wgv\n",
    "    if result < 0:\n",
    "        mag_result = result * -1\n",
    "    else:\n",
    "        mag_result=result\n",
    "    return mag_result\n",
    "    \n",
    "\n",
    "def calc_WG0_array(WGV_list,Fuel_F,Crew_W, Payload_W, HS_metric,WeightS_E,VWS=False,VWS_penalty=1.04):\n",
    "    WG0_array=[]\n",
    "    EWF_array=[]\n",
    "    diff_array=[]\n",
    "    for a in range(0,len(WGV_list)):\n",
    "        WG0_array.append(calc_WG0(WGV_list[a],Fuel_F,Crew_W, Payload_W, HS_metric,WeightS_E,VWS,VWS_penalty))\n",
    "        EWF_array.append(EWF(WGV_list[a],HS_metric,WeightS_E,VWS=False,VWS_penalty=1.04))\n",
    "        diff_array.append(diff_calc_WG0(WGV_list[a],Fuel_F,Crew_W, Payload_W, HS_metric,WeightS_E,VWS,VWS_penalty))\n",
    "    return WG0_array, EWF_array, diff_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have created a function for the the formulas and a way to store and interrogate mission profiles we can find the ideal $W_0$ using the iteration method Raymer shows. "
   ]
  },
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    {
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2pu/Y8dx3X6al8Xg8Hk+qeEOROHyy6hNOeKwzu0xeRpfj6nHvvTZF6fF4Kibe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa2ef048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "WGV_array = [50000]\n",
    "for a in range(0,250):\n",
    "    WGV_array.append(WGV_array[a]+50)\n",
    "    \n",
    "calc_WG0_tmp, calc_EWF_tmp, diff_array = calc_WG0_array(WGV_array,FF_tmp,Crew_Weight, Payload_Weight, bomber_HS_metric,bomber_weight_sensitivty_e)\n",
    "best_guess_index = numpy.argmin(diff_array)\n",
    "fig, ax = plt.subplots()\n",
    "axes = [ax, ax.twinx(), ax.twinx()]\n",
    "fig.subplots_adjust(right=0.75)\n",
    "axes[-1].spines['right'].set_position(('axes', 1.2))\n",
    "axes[0].plot(WGV_array,calc_WG0_tmp,c='b')\n",
    "axes[0].set_title('Estimated vs Calculated Takeoff Gross Weight for\\nASW Mission Best Guess $W_0$:%.3f lb EWF:%.4f' % (WGV_array[best_guess_index],calc_EWF_tmp[best_guess_index]))\n",
    "axes[0].set_ylabel('Calculated $W_0$ (lb)',color='b')\n",
    "axes[0].set_xlabel('Estimated $W_0$ (lb)')\n",
    "axes[0].tick_params('y', colors='b')\n",
    "axes[1].plot(WGV_array,calc_EWF_tmp,c='r')\n",
    "axes[1].set_ylabel('Empty Weight Fraction',color='r')\n",
    "axes[1].tick_params('y', colors='r')\n",
    "axes[2].plot(WGV_array,diff_array,c='g')\n",
    "axes[2].set_ylabel('|difference|',color='g')\n",
    "axes[2].tick_params('y', colors='g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimisation\n",
    "In contrast to the method expressed in Raymers book because we have expressed the formulas as python functions we can use the powerful optimisation methods available to us.  Here we use the scipy library minimize method to efficently find the ideal $W_0$ for the mission as defined.\n",
    "\n",
    "Because python has these libraries it makes it much easier to create functions that call other functions and explore the solution space to create optimal aircraft designs.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimised Takeoff Gross Weight W_0 found 56718.073 lb with EWF 0.4322\n"
     ]
    }
   ],
   "source": [
    "import scipy.optimize as optimize\n",
    "minimum_W_0 = optimize.minimize(diff_calc_WG0,50000, args = (FF_tmp,Crew_Weight, Payload_Weight, bomber_HS_metric,bomber_weight_sensitivty_e))\n",
    "min_EWF = EWF(minimum_W_0.x,0.93,-0.07)\n",
    "print(\"Optimised Takeoff Gross Weight W_0 found %.3f lb with EWF %.4f\" % (minimum_W_0.x,min_EWF))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": ["print('Difference between the Takeoff Gross Weight W_0 estimations: {} lbs'.format((WGV_array[best_guess_index] - minimum_W_0.x)[0]))\n",
              "print('Difference between the Empty Weight Fraction EWF estimations: {} %'.format(100*((calc_EWF_tmp[best_guess_index] - min_EWF)[0])))"]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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