FACULTY OF ENGINEERING AND COMPUTER SCIENCE
DEPARTMENT OF MECHANICAL AND INDUSTRIAL ENGINEERING
COURSE
NUMBER
Space Flight Dynamics and Propulsion Systems
EXAMINATION
MECH 485/6251
DEADLINE SUBMISSION
Midterm Quiz
October
SECTION
XX
# of pages (including title page)
15th
, 2013 @ 18:00
PROFESSOR
Dr. Hoi Dick Ng
SPECIAL INSTRUCTIONS:
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Closed books, closed notes
Faculty approved calculators allowed
Write everything on the exam paper, please circle your final answer
Read each question carefully and answer all questions
State clearly any assumptions you make
Good luck!
Name: ____________________________________
Surname, given names
Signature: ___________________________________
I.D.: ___________________________
Problem #1 [Rocket fundamentals] (10 pts)
a) An electrostatic thruster produces 0.5 N of constant thrust over a 3 hour duration and
consumes a total of 0.5 kg of propellant while using 4 kW of power. What is the specific impulse
of the thruster?
b) Find the ratio of the velocities of two vehicles, one powered by a liquid chemical rocket and
the other by a solid chemical one, when they are used for acceleration of a 10,000 kg payload in
a zero-gravity field. Both vehicles have a total initial mass of 510,000 kg. The liquid propellant
rocket has 60% greater specific impulse and 30% greater mass of empty vehicle (without
propellant and payload), and the solid-propellant rocket has a structural coefficient of  = 0.080.
Problem #2 [Multi-stage rocket]
Our discussion of staging in class suggested it as a solution if a single-stage rocket was not
capable of reaching the desired velocity. Assume a rocket of total mass 100 tons, carrying a
spacecraft payload of 1 ton. The engines develop a constant exhaust velocity of 3,000 m/s. The
structural mass is assumed to be 10% of the fuel mass.
1) Determine the velocity of this configuration as a single stage rocket
2) If the rocket is divided into two smaller stages, each with half the fuel, and the
structural mass also shared equally, and the payload being the same, determine the
total velocity increment for the two stage configuration.
Question #3 (20 Points):
A rocket has the following parameters:
 Thrust = 6,000 N
 Isp = 200 seconds
 Initial mass = 200 kg
 Burn time = 10 seconds
Assume that the exit pressure is equilibrated with the atmospheric back pressure at all times,
neglect drag and assume gravity is a constant (use g = 10 m/s2 if you want).
1. The condition of maximum propulsive efficiency for a rocket engine is the case where the
flight speed is equal to the exhaust speed of the material exiting the engine. Does this
rocket see such a condition of maximum propulsive efficiency at any time during a
vertical launch?
2. What is the velocity at burnout?
3. How much additional height does the rocket attain after burnout?
4. Extra Credit (do this part only if you have completed the rest of the exam). If the burn
time may be taken as much longer than 10 seconds and the propellant mass is kept
constant, at what time in the flight does the condition of maximum propulsive efficiency
occur?
Question #4 (20 Points):
Consider the Boeing X-37B Orbital Test Vehicle shown in the picture below. In this picture the
vehicle is circumnavigating the Earth at a Low Earth Orbit 200 km above the Earth’s surface.
Because of a change in the mission profile, the X-37B needs to raise its orbit by 50 km (to a new
orbit of 250 km above the surface of the Earth) and the engines on the vehicle are sufficient to
accomplish this task.
The following information is provided:
 Radius of the Earth=6,378 km
 G=6.670x10-11 N m2/kg2
 Mass of the Earth = 5.975x1024 kg
 Mass of the Sun = 332,488 times the mass of the earth
 Mass of the X-37B = 10,000 kg
1. Determine the mission velocity increments that are needed from the X-37B’s engine
burns for an orbital transfer of the vehicle with the least fuel consumption.
Question #5 (20 Points):
During a secret space mission, two individual orbital maneuvers are required by the spaceship to
reach the final destination. The required V for each change are: V1 = 200 m/s and V2 = 1500
m/s. Each V can be achieved by firing A two-stage thruster system with:
Stage 1: Isp = 260 sec
Stage 2: Isp = 280 sec
 = 0.95
 = 0.85
where  is defined as  = Mp/(Mp + Minert) where Minert is the mass of the structure and Mp is the
propellant mass. Assuming the gross initial mass of the spaceship is 2,000 kg. Determine the
propellant masses for each stage and the payload capabilities of this system.