MAE 155A, Aerospace Engineering Design I
Winter 2007
Homework Assignment 2, Part B
1. Do 4.2 and also figure the delta Vee if the thruster burns 100 lbs of propellant moving
a 4000 lb spacecraft. (initial mass
2. Do 4.4 and also figure the same problem is the ISP =350 sec
Note the following problems are first order design estimates, so the answers don’t have
to be accurate to more than 10% All the hints are to make them gradable in a class of
50+)
3. For a rocket plane based on Learjet 24, with mass 9000 lb at end of burn and 18000 lb
full, with and engine thrust of 30K lbf and an Isp of 300 sec, Determine the maximum
altitude reached, ignoring drag. Determine the effect on max altitude of a 1 lb
increase in empty weight or a 1 second decrease in specific impulse. Average angle is
90 degrees straight up Hint: R is mass ratio (full mass over burnout mass) tb is burn
time U.e is exhaust velocity. (Equation from Hill and Petersen, Mechanics and
thermodynamics of propulsion) Should be close to 100 km
2
hmax 
Ue  ln( R)
2 g
2
 Ue tb 
R
R1
 ln( R)  1 

4. Design a single stage rocket for Mars orbital insertion (liftoff from Mars). Required
DeltaVee=3.5 km/sec using monopropellant hydrazine. The key to this problem is
that higher chamber pressures lead to higher Isp, but they make the propellant tank
heavier. Higher pressures also make the rocket engine easier to design. To make it
easy on the grader, you should Use Isp=250, pc=50 psi (or .35 Mpa) as a starting
point. Determine mass ratio, chamber pressure and area ratio (Use above estimates at
first, then check for consistency later), use tank mass for spherical composite or
titanium tanks. (You can figure the tank mass from sec 4.4.4 or use a hydrazine tank
from (http://www.psi-pci.com/) Assume structural mass 10% of tank mass. Engine
mass=2% of thrust on Earth. (i.e. 100 lbf engine weight 2 lb) What is the exhaust
pressure? (Answer: Mars Ambient=700 Pa, source
http://mars.jpl.nasa.gov/MPF/science/atmospheric.html ) Determine chamber pressure
to be significantly higher than exhaust ambient pressure on Mars, and pick an
expansion ratio. Use these numbers to figure Isp from equation 4.8 Some typical real
numbers for pressure and Isp can be found at
(http://cs.space.eads.net/sp/SpacecraftPropulsion/MonopropellantThrusters.html#Mod
elCHT400) Your number should be close (~20%)
For this case, assume that the pressure losses in the injector etc. are neglected.
Determine required mass ratio given hydrazine Isp, make sure that the numbers add
up. Neglect the weight of the pressurization system. For a robust system, determine
the max pressure that will still achieve orbit. No need for multiple iterations.
5. Conduct a preliminary design of a two-stage pressure fed rocket to put a 10 kg
payload into a 250 km circular orbit. Use a composite fuel tank (stress=200 ksi,
Rho=1.5) and 2219 aluminum (stress=36 ksi, Rho=2.8) LOX tanks.
Research existing system design and use the data for your design. See for example:
NLV paper
Use LOX/RP1 for the first stage and LOX/LH2 for the second stage.
Use data in table 4.2 and equation 4.8 to calculate exactly the Isp at beginning and
end of burn
Total deltavee required is 10 km/sec (4 km/sec for the first stage, 6 km/sec for the
second)
Ignore drag and gravity losses (already accounted for)
Determine Po for each stage use average Pe over flight for thrust. Figure out throat
area and estimate area ratio for each stage
Determine burnout altitude for first stage, use pressure at that altitude for second
stage engine design.
Determine each engine thrust at beginning and end of burn
Determine acceleration at beginning and end of burn.
Hint: Use Tsiolowski equations 4.19-4.21 to determine required mass ratio for each
stage. Assume Isp for LOX RP(kerosene) (sea level 265 sec (F-1 engine) and Isp for
LOX –LH2 is 421 (j2 engine)
Determine tank mass, assume structure is 10% of tank mass, Determine starting mass
of complete second stage, Use this mass to determine mass of first stage, then repeat.
Second stage design
Then figure out the engine isp data using assumed pressures and determine if the
whole system closes: i.e. Higher pressures make for higher isp but then the tanks get
heavier. There is a pretty good estimate of the required pressure in the NLV paper.