MECH1907 – Introduction to Aerospace Engineering
Fall 2021–2022
Mini Assignment 1 – Due date: September 21, 2021
Common conversions and parameters
• 1 ft = 0.3048 m
• 1 lbm = 0.454 kg
• Gravitational acceleration g = 9.81 m/s2 (32.2 f t/s2 )
Note: Only short answers are required for grading, but feel free to elaborate if you want.
Qn. 1 Calculus exercise. Force is defined as the rate of change of momentum,
F =
d (mV )
.
dt
(1)
(a) Write the full form of the expression for Force, derived based on Equation 1 (10 points).
(b) Under which assumption do we get the Newton’s second law from this Force equation?
(10 points)
Qn. 2 Calculus exercise. Finding the distance traveled (s) during acceleration caused by a net
force F . Assume we start at time t = 0, and the vehicle is at rest, V = 0. Derive the
expression for the distance traveled when the vehicle reaches the final velocity, Vf , assuming
constant force F and mass m (20 points).
Note: Show how you get the answers, using differentiation and integration. The answers
need to be expressed in terms of the independent variables, e.g., Vf , m, and F .
Hint: start by expressing a in terms of dV and dt, and similarly, V in terms of ds and dt.
Qn. 3 Find out the differences between the speeds below (10 points):
(a) Indicated airspeed (IAS)
(b) Calibrated airspeed (CAS)
(c) True airspeed (TAS)
And which one would be particularly useful for:
(a) Pilots
(b) Aircraft design engineers
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Qn. 4 Units. There are some unusual units used in the field of aerospace engineering. Provide
brief descriptions of the units below (i.e., what are they for) and their conversion to SI units
(if applicable) (15 points).
(a) Nautical mile (nmi)
(b) Astronautical units (AU)
(c) Knot (nautical miles/hour)
(d) Bar
(e) Flight level
(f) Drag count
(g) Smoot
Which one(s) from the above is/are not related to aerospace engineering, if any?
Qn. 5 Unit conversion exercises. Show how you arrive at the answer, step-by-step. Use the
common conversion given on the first page.
(a) How much lbm is 1 slug? (10 points)
(b) How much N is 1 lbf ? (10 points)
(c) The thrust specific fuel consumption (TSFC) is an engine property defined as the amount
of fuel burned (in terms of mass or weight) per unit thrust per unit time. It is therefore
crucial to use the right unit in the calculation, to ensure a correct and safe aircraft
performance assessment. How much is, then, 0.7 lbm /(lbf · h) in g/(kN·s) (h and s refer
to hours and seconds, respectively)? (15 points)
Bonus question (OPTIONAL)
Understanding forces. Aircraft engine provides Thrust (T ) that makes it possible for the aircraft
to move forward. Similarly, when you swim, your arms and legs act as the “propeller” that allows
you to move forward. Nowadays, there are some alternative means to swim in a limited space, such
as: tethered swimming, resistance swimming, countercurrent swimming. How do you think these
alternatives can “replace” conventional swimming? In a way, countercurrent swimming shares the
same principles as wind-tunnel experiments for, say, aircraft wing. How are these two related?
(5 points)
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