{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 19: Entry, Descent, and Landing (EDL)\n", "\n", "This tutorial covers the dynamics of atmospheric entry, including ballistic and lifting flight paths, and aerodynamic heating estimation.\n", "\n", "## 1. Ballistic Entry Dynamics\n", "A ballistic entry occurs when a vehicle has no lift ($L/D = 0$). The trajectory is determined by gravity and drag.\n", "\n", "$$\\dot{v} = -\\frac{\\mu}{r^2} \\hat{r} - \\frac{1}{2}\\rho v^2 \\frac{C_d A}{m} \\hat{v}$$\n", "\n", "We will simulate a simplified entry from 120 km altitude." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from opengnc.edl import ballistic_entry_dynamics, sutton_grave_heating, calculate_g_load\n", "from opengnc.environment.density import Exponential\n", "from scipy.integrate import solve_ivp\n", "\n", "# 1. Setup Vehicle Parameters\n", "mass = 1000.0 # kg\n", "area = 2.5 # m^2\n", "cd = 1.5 # Hypersonic drag coefficient\n", "rn = 0.5 # Nose radius (m) for heating\n", "\n", "# 2. Initial State (120 km altitude, 7.5 km/s velocity)\n", "alt_init = 120000.0\n", "r_planet = 6371000.0\n", "r0 = r_planet + alt_init\n", "v0 = 7500.0\n", "fpa = np.deg2rad(-2.0) # Flight path angle\n", "\n", "state0 = np.array([\n", " r0, 0, 0, # Position (m)\n", " v0 * np.sin(fpa), v0 * np.cos(fpa), 0 # Velocity (m/s)\n", "])\n", "\n", "# 3. Simulation\n", "# Note: Exponential density parameters (h0, H) are in kilometers!\n", "density_model = Exponential(rho0=1.225, h0=0.0, H=8.5)\n", "\n", "def derivatives(t, y):\n", " return ballistic_entry_dynamics(t, y, cd, area, mass, rho_model=density_model, r_planet=r_planet)\n", "\n", "# Define an event to stop at ground impact\n", "def ground_impact(t, y):\n", " return np.linalg.norm(y[:3]) - r_planet\n", "ground_impact.terminal = True\n", "ground_impact.direction = -1\n", "\n", "sol = solve_ivp(derivatives, (0, 1000), state0, rtol=1e-6, events=ground_impact)\n", "\n", "# 4. Post-processing\n", "r_mags = np.linalg.norm(sol.y[:3, :], axis=0)\n", "alts = (r_mags - r_planet) / 1000.0 # km\n", "vels = np.linalg.norm(sol.y[3:, :], axis=0)\n", "\n", "plt.figure(figsize=(10, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(sol.t, alts)\n", "plt.title(\"Altitude vs Time\")\n", "plt.ylabel(\"Altitude (km)\")\n", "plt.xlabel(\"Time (s)\")\n", "\n", "plt.subplot(1, 2, 2)\n", "plt.plot(vels, alts)\n", "plt.title(\"Velocity vs Altitude\")\n", "plt.xlabel(\"Velocity (m/s)\")\n", "plt.ylabel(\"Altitude (km)\")\n", "plt.gca().invert_yaxis()\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Aerodynamic Heating and G-Loads\n", "During hypersonic entry, the vehicle experiences extreme thermal loads. We can estimate the stagnation point heat flux using the Sutton-Grave correlation and monitoring the G-loads." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Peak Heat Flux: 152.27 W/cm^2\n", "Peak G-Load: 8.80 g\n", "Final Velocity at Impact: 65.39 m/s\n" ] } ], "source": [ "q_dots = []\n", "g_loads = []\n", "\n", "for i in range(len(sol.t)):\n", " r_vec = sol.y[:3, i]\n", " v_vec = sol.y[3:, i]\n", " v_mag = np.linalg.norm(v_vec)\n", " rho = density_model.get_density(r_vec, 0.0)\n", " \n", " # Heating (W/m^2 to W/cm^2)\n", " q = sutton_grave_heating(rho, v_mag, rn)\n", " q_dots.append(q / 10000.0)\n", " \n", " # G-load (based on non-gravitational acceleration)\n", " # The integrator derivative returns total acceleration (gravity + drag)\n", " total_acc = derivatives(sol.t[i], sol.y[:, i])[3:]\n", " # Subtract gravity to get net aero acceleration for G-load\n", " r_mag = np.linalg.norm(r_vec)\n", " mu = 3.986e14\n", " grav_acc = -(mu / r_mag**3) * r_vec\n", " aero_acc = total_acc - grav_acc\n", " g_loads.append(calculate_g_load(aero_acc))\n", "\n", "print(f\"Peak Heat Flux: {max(q_dots):.2f} W/cm^2\")\n", "print(f\"Peak G-Load: {max(g_loads):.2f} g\")\n", "print(f\"Final Velocity at Impact: {vels[-1]:.2f} m/s\")" ] } ], "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": "3.10.11" } }, "nbformat": 4, "nbformat_minor": 4 }