takeoff_sim.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Globals\n",
    "GRAVITY = 9.81\n",
    "RHO = 1.225                 # kg/m^3 @ sea lvl (air density)\n",
    "LIFT_SLOPE = 2*np.pi\n",
    "ROTATIONAL_AOA = 6          # degrees\n",
    "ROTATIONAL_V = 4.5              # m/s (ill approximate rotation speed for flow speed @ takeoff)\n",
    "\n",
    "# heres the data in the xls file i was given:\n",
    "weight = 8 * GRAVITY            # kg\n",
    "\n",
    "wingspan = 2.0                  # m\n",
    "wing_area = 0.7                 # m^2\n",
    "wing_height_above_ground = 0.3  # m\n",
    "\n",
    "aspect_ratio = wingspan**2 / wing_area\n",
    "oswald_e = 0.7\n",
    "\n",
    "fuselage_frontal_area = 0.02    # m^2\n",
    "fuselage_drag_coefficient = 1.0\n",
    "\n",
    "overall_drag_coefficient = 1.2\n",
    "wheel_rolling_resistance = 0.012\n",
    "\n",
    "\n",
    "# heres some functions for the necessary \n",
    "\"\"\" \n",
    "at the moment of takeoff i thought that the lift it would have to generate \n",
    "is exactly equal to the weight of the plane itself. also, the cL_takeoff's AoA\n",
    "should be equal to zero\n",
    "\"\"\"\n",
    "def cL(AoA):\n",
    "   cL_takeoff = 2 * weight / (RHO * ROTATIONAL_V**2 * wing_area) # AoA should be 0\n",
    "   return (LIFT_SLOPE * AoA + cL_takeoff)\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "ik the formula is T = v * (dm/dt), but at the instant of takeoff (dt) the mass isn't changing.\n",
    "if mass isnt chaning then slope is zero?????????? ill just multiply by weight for now.\n",
    "\"\"\"\n",
    "def thrust_takeoff(takeoff_velocity):\n",
    "   return takeoff_velocity * weight\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "as i was thinking in terms of instantaneous moments at takeoff, i thought thrust should\n",
    "be equal to drag at takeoff. ill try this for now\n",
    "\"\"\"\n",
    "def cD(AoA):\n",
    "   cD_takeoff = 2 * thrust_takeoff(ROTATIONAL_V) / (RHO * ROTATIONAL_V**2 * wing_area) # AoA should also be 0\n",
    "   k = 1 / (np.pi * oswald_e * aspect_ratio)\n",
    "   return (cD_takeoff + cL(AoA)**2 * k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max Speed: 0.00 m/s\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "okay so i think i got the variables and everything done... took a while cuz\n",
    "i had some package problems and accidently switched to julia for some reason.\n",
    "anyways heres some actual stuff:\n",
    "\"\"\"\n",
    "\n",
    "# max speed of an airplane is when drag = thrust, so:\n",
    "\"\"\" \n",
    "creating a list of 50 speeds for the plane starting at takeoff rotational velocity\n",
    "assuming: rotational velocity ---> 50m/s, 100 values\n",
    "\n",
    "also created lists for calculated drags and thrusts as a function of velocity so\n",
    "i can graph it after\n",
    "\"\"\"\n",
    "list_speeds = np.linspace(ROTATIONAL_V, 50, 100)\n",
    "list_drags = np.linspace(0,0,100)\n",
    "list_thrusts = np.linspace(0,0,100)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "iterating thru different speeds starting at takeoff velocity and finding drag\n",
    "thrust. when drag = thrust then max speed! this is all for takeoff so ill use\n",
    "the set takeoff\n",
    "\"\"\"\n",
    "# thrust = np.array([thrust_takeoff(ROTATIONAL_V) for ROTATIONAL_V in speed])\n",
    "def drag(speed):\n",
    "    return cD(ROTATIONAL_AOA) * 1/2 * RHO * speed**2 * wing_area\n",
    "\n",
    "# ig this is all instantaneous so instead of mass change per sec, ill use weight * change in seconds\n",
    "def thrust(speed):\n",
    "    return speed * weight\n",
    "\n",
    "    ### THIS IS DEFINTLY WRONG\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "calculating drag + thrust. iterating thru list of speeds to base calcs on \n",
    "\"\"\"\n",
    "for i in range(len(list_speeds)):\n",
    "    list_drags[i] = drag(list_speeds[i])\n",
    "    list_thrusts[i] = thrust(list_speeds[i])\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "graphing drag + thrust\n",
    "\"\"\"\n",
    "x = list_speeds\n",
    "y1 = list_drags\n",
    "\n",
    "drag_thrust = plt.plot(x,y1,'r')\n",
    "\n",
    "plt.xlabel(\"Speed (m/s)\")\n",
    "plt.ylabel(\"Drag (N)\")\n",
    "\n",
    "\"\"\"\n",
    "max speed when thrust = drag\n",
    "\"\"\"\n",
    "max_speed = 0 #?????????\n",
    "print(f\"Max Speed: {max_speed:.2f} m/s\")"
   ]
  }
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