Paper format. 07-Mec-B7 Aero and Space Flight, National
Examinations, May 2016. Three hours, open book; any non-communicating
calculator permitted. Seven questions of equal value; any six constitute a
complete paper and only the first six answered are marked, so full marks are 120 and the
percentage grade is (mark obtained / 120) × 100. Several questions call for an
essay-format answer, where clarity and organisation carry marks. All seven questions
are solved here.
Reference texts. Solutions follow the conventions of the texts
recommended for this examination code:
- J. D. Anderson Jr., Introduction to Flight, 9th ed. — the standard
atmosphere and the four altitudes (Ch. 3), incompressible and compressible flow with
the Pitot-static tube (§3.4, §4.11, §8.7), airplane performance
(Ch. 6), stability and control (Ch. 7), propulsion (Ch. 9), space flight and
atmospheric entry (Ch. 8). This is the primary reference throughout.
- J. D. Anderson Jr., Fundamentals of Aerodynamics, 6th ed. — finite-wing
theory and induced drag (Ch. 5), transonic flow, drag divergence and the area rule
(Ch. 11).
- B. N. Pamadi, Performance, Stability, Dynamics and Control of Airplanes,
3rd ed. — take-off and landing distances and gust load factors (Ch. 2, Ch. 5).
- G. P. Sutton and O. Biblarz, Rocket Propulsion Elements, 9th ed. —
the ideal rocket equation and propellant-system comparison (Ch. 4, Ch. 11–12).
- H. D. Curtis, Orbital Mechanics for Engineering Students, 4th ed. —
the orbit equation, vis-viva and orbital elements (Ch. 2–3).
Check — assumptions carried through the performance questions.
The paper's page-1 note invites the candidate to "submit with their answer paper a clear
statement of any assumptions made", and three quantities the performance questions need are
never stated:
- Standard atmosphere. ISA sea-level values
$T_0 = 288.15\ \text{K}$, $p_0 = 101\,325\ \text{Pa}$,
$\rho_0 = 1.225\ \text{kg}\,\text{m}^{-3}$, troposphere lapse rate
$L = 0.0065\ \text{K}\,\text{m}^{-1}$ to 11 km, then isothermal at
$216.65\ \text{K}$; $R = 287.05\ \text{J}\,\text{kg}^{-1}\text{K}^{-1}$,
$\gamma = 1.4$. Inside the atmosphere model $g = 9.80665\ \text{m}\,\text{s}^{-2}$,
giving the exponents $g/(LR) = 5.2559$ for pressure and $4.2559$ for density; aircraft
weights use $g = 9.81\ \text{m}\,\text{s}^{-2}$.
- Thrust lapse (Questions 4 and 5). For a fixed-geometry turbojet the
thrust is taken proportional to density,
$T = T_{SL}\,(\rho/\rho_0)$. Nothing in the paper states a lapse law, and this is the
conventional first approximation.
- Ground-run averaging (Question 5b). The net accelerating force is
evaluated once at $V_{LO}/\sqrt{2}$ — the speed at which $V^2$ equals its mean over
the run — and the run is then taken as uniformly accelerated.
Compressibility corrections to lift and drag are ignored wherever the question says so
(Question 4a) and elsewhere in Questions 4 and 5, consistent with the parabolic drag polar
supplied.
