Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, December 2017 — 16-Mec-B7 Aero and Space Flight. Three hours, OPEN BOOK, any non-communicating calculator permitted. Seven questions, all of equal value; any SIX constitute a complete paper, so full marks are 120 and the percentage grade is $[(\text{mark obtained}/120)\times 100]$. Some questions require an essay answer, and clarity and organisation of the answer are explicitly marked. All seven questions are solved below, and every sub-part is addressed.
Reference texts. J. D. Anderson, Introduction to Flight, 9th ed. (standard atmosphere, altitude definitions, airplane performance, take-off and landing, atmospheric entry, rocket staging, elliptical orbits); J. D. Anderson, Fundamentals of Aerodynamics, 6th ed. (airfoil stall, high-lift devices, critical Mach number and drag divergence, wave drag and area ruling); W. F. Phillips, Mechanics of Flight, 2nd ed. (parabolic drag polar, minimum-drag speed, climb and glide angles, jet range and endurance, static and dynamic stability); H. J. Allen and A. J. Eggers, A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s Atmosphere at High Supersonic Speeds, NACA Report 1381 (1958) (ballistic entry, maximum deceleration); G. P. Sutton and O. Biblarz, Rocket Propulsion Elements, 9th ed. (liquid-propellant engine architecture, solid-propellant grain design).
Check: standing assumptions. The paper’s page-1 note invites the candidate to “submit with their answer paper a clear statement of any assumptions made.” Four assumptions are used throughout and are stated once here. (i) The International Standard Atmosphere with $T_0 = 288.15\ \text{K}$, $p_0 = 101.325\ \text{kPa}$, $\rho_0 = 1.225\ \text{kg}/\text{m}^3$, tropospheric lapse rate $L = 0.0065\ \text{K}/\text{m}$ to $11\ \text{km}$, $R = 287.05\ \text{J}/(\text{kg}\cdot\text{K})$ and $\gamma = 1.4$, giving the exponents $g/(LR) = 5.2559$ for pressure and $4.2559$ for density. (ii) Where a question needs the variation of thrust with altitude but does not state it, the fixed-geometry jet assumption $T = T_{SL}\,(\rho/\rho_0)$ is used. (iii) Ground-run accelerations are evaluated once at $V/\sqrt{2}$, the speed at which $V^2$ takes its mean value, so that $s = V^2/(2a)$. (iv) Aircraft weights use $g = 9.81\ \text{m}/\text{s}^2$; the atmosphere model itself uses the defining value $9.80665\ \text{m}/\text{s}^2$. Earth data for Question 7 use $\mu = GM = 3.986\times 10^{14}\ \text{m}^3/\text{s}^2$.
