Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 07-Mec-B7 Aero and Space Flight, National Examinations, December 2016. Three hours, open book, any non-communicating calculator permitted. Seven questions of equal value (20 marks each); any six constitute a complete paper, and the grade is (mark obtained / 120) × 100. Some questions require an essay answer, where clarity and organisation are marked. All seven questions are solved below.
Reference texts. J. D. Anderson, Introduction to Flight, 9th ed. (standard atmosphere, altitude definitions, Pitot-static measurement, airplane performance, take-off and landing, atmospheric entry); J. D. Anderson, Fundamentals of Aerodynamics, 6th ed. (finite-wing theory, induced drag, 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, maximum rate of climb, jet range and endurance); 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).
Check: standing assumptions. The paper's page-1 instruction is that "if doubt exists as to the interpretation of any question, the candidate is urged to submit… a clear statement of any assumptions made." Three assumptions are used throughout and are stated once here: (i) the International Standard Atmosphere with sea-level values $T_0 = 288.15\ \text{K}$, $p_0 = 101.325\ \text{kPa}$, $\rho_0 = 1.225\ \text{kg}/\text{m}^3$, tropospheric lapse rate $0.0065\ \text{K}/\text{m}$, $R = 287.05\ \text{J}/(\text{kg}\cdot\text{K})$ 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 $T = T_0\,(\rho/\rho_0)$ 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 $s = V^2/(2a)$. Aircraft weights use $g = 9.81\ \text{m}/\text{s}^2$; the atmosphere model itself uses the defining value $9.80665\ \text{m}/\text{s}^2$.
