{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Questions and Solutions\n", "\n", "The following comprises the theory that I expect you to have absorbed and be fluent in over the preceding module. Some questions have *wordy* answers whilst others have *numerical answers*. The numerical answers are provided, and the method is hidden in dropdowns in some cases, and completely hidden in the source ipynb notebooks in other cases.\n", "\n", "A lot of the theory questions ask you to _derive_ something. I do not include solutions to these questions - they are all 'bookwork' which is included in the notes. If you're not able to answer them, ask on Slack.\n", "\n", "Remember that you are expected to be writing your own code snippets rather than simply using this website as a calculator. I might be a real bastard and turn off the _live code_ functionality during certain exams to enforce that.\n", "\n", "## Background Questions\n", "\n", "These are not directly taught in this course, *per se*, but will prove your abilities to analyse aircraft data in order to even start the problems in Module 1. The following will test your understanding of the drag polar.\n", "\n", "### WT Data\n", "\n", "A test is carried out on a 1:20 scale model of an aircraft in an atmospheric wind tunnel (ie $\\rho = \\rho_{SL}$ in the working section) at a speed of 20m/s. The model has a rectangular wing with a span of 1.70m and a chord of 0.24m. \n", "\n", "| $\\alpha/^\\circ$ | \\-6 | \\-3 | 0 | 3 | 6 | 9 | 12 | 15 | 18 |\n", "|----------------------|------|------|------|------|------|------|------|-------|-------|\n", "| $L\\,\\text{N}^{-1}$ | \\-25 | 0 | 25 | 50 | 75 | 100 | 125 | 135 | 115 |\n", "| $D\\,\\text{N}^{-1}$ | 1\\.9 | 1\\.6 | 1\\.9 | 2\\.8 | 4\\.3 | 6\\.4 | 9\\.1 | 13\\.8 | 19\\.2 |\n", "\n", "Perform the following data analysis and presentation:\n", "- Evaluate $C_L$ and $C_D$ for each incidence. \n", "- Plot $C_D$ against $C_L$.\n", "- Plot lift/drag ratio $C_L$/$C_D$ against $C_L$\n", "- Plot $C_D$ against $C_L^2$.\t\n", "\n", "and **using these graphs**, estimate:\n", "\n", "- The lift curve slope $a$.\n", "- The zero-lift incidence $\\alpha_{0L}$.\n", "- The lift coefficient at zero lift, $C_{L0}$\n", "- The induced drag factors $K$ and $k$.\n", "- The zero lift drag $C_{D0}$ (you can assume camber is negligible) \n", "- The maximum lift/drag ratio.\n", "- The approximate stall angle $\\alpha_s$.\n", "- The maximum lift $C_{Lmax}$\n", "\n", "{admonition} Answers\n", ":class: dropdown\n", "$$a= 4.78/rad$$\n", "$$\\alpha_{0L}= -3^\\circ$$\n", "$$C_{D0} = 0.016, K = 0.048, k=1.07$$\n", "$$L/D_{max}\\simeq 18$$\n", "$$\\alpha_S\\simeq 15^\\circ$$\n", "$$C_{Lmax}\\simeq 1.35$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false, "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "data": { "text/html": [ "