You are not allowed to work with any other students on this exam. INDIVIDUAL EFFORT ONLY.

MAE 5495: Launch Vehicle Analysis and Design

Spring 2008

NAME ______

MIDTERM EXAM

DUE: BY 16:30 Mountain Daylight Time, 20 March 2008

Section / Value / Grade
1 / 20%
2 / 40%
3 / 40%
Total / 100%


SECTION 1: General

1. (3%) For a rocket with a nozzle ideally expanded at sea level, what happens to the thrust as the rocket is vertically launched ? Note: Assess the performance at some particular altitude. Also, assume a constant mass flow rate during the burn. Explain how this differs from a nozzle that is ideally expanded at the particular altitude you selected.

2. (4%) For an ideal rocket with a characteristic exhaust velocity of 1220 m/sec, a mass flow rate of 73 kg/sec, a thrust coefficient of 1.5, and a nozzle throat area of 0.0248 m2, compute the effective exhaust velocity, the thrust, the combustion chamber pressure, and the specific impulse.

3. (3%) For a constant stagnation pressure, what happens to each of the other parameters you calculated in Problem #2 if the nozzle throat area is increased by 100% while maintaining the nozzle’s expansion ratio.

4. (10%) The Air Force wants a space based missile intercept weapon with the following requirements:

DV = 2.5 km/sec

Mpayload = 15 kg

The prime contractor has developed a monopropellant propulsion system to meet this requirement:

Hydrogen Peroxide Liquid Monopropellant

Reaction: (Note: g=1.3 for H2O and g=1.4 for O2)

Finert = 0.44

A.  (3%) What is the minimum Specific Impulse required for this propulsion system to be feasible for this mission?

B.  (4%) Assuming that the missile interceptor is launched from a satellite in GEO, what stagnation temperature would be required to achieve this specific impulse (assume ideal nozzle expansion)? Looking at Table 3.3 on page 128 of your course text, is there a material listed that can handle this stagnation temperature?

C.  (3%) For an Isp 10% greater than what you calculated in Section A, what would the total mass of the missile interceptor be? What happens to the interceptor mass as the Isp is increased further?

SECTION 2: Thermodynamics and Thermochemistry

5. (40%) The Space Shuttle Main Engines use the fuel rich reaction below.

5 H2 (l) + O2 (l) à 2 H2O (g) + 3 H2 (g) [Reaction 1]

A.  (2%) Write the stoichiometric reaction for this fuel combination.

A themochemistry code gives the following results for Reaction 1 (above) and the stoichiometric mixture using the SSME design. The SSME has a stagnation pressure of 22.615 MPa and an expansion ratio of 77.5.

Reaction 1 / Stoichiometric Reaction
Combustion Chamber / Throat / Nozzle Exit / Combustion Chamber / Throat / Nozzle Exit
Pressure (MPa) / 22.615 / 22.615
e / 0 / 1 / 77.5 / 0 / 1 / 77.5
Temperature (K) / 2562.83 / 3766.274
g / 1.238 / 1.245 / 1.361 / 1.189 / 1.188 / 1.200
Molecular Weight / 8.408 / 8.413 / 8.416 / 16.301 / 16.502 / 17.980
CF / 0 / .691 / 1.798 / 0 / 0.655 / 1.942
Isp (s) / 0 / 171.011 / 445.232 / 0 / 145.581 / 431.779

B.  (8%) Fill in the blanks in the Table above (Pt, Pe, Tt, Te for both reactions).

C.  (7%) Does the Isp for Reaction 1 at the exit given in the Table above assume ideal expansion in vacuum? Is this the maximum achievable Isp?

D.  (5%) Calculate the characteristic exhaust velocity for both reactions.

E.  (3%) Can you determine the thrust or mass flow of either of these systems with the data given? If so, what are the values?

F.  (5%) Does the thermochemistry code use an assumption of frozen flow losses like our analytical expressions do? Explain.

G.  (10%) As expected, the stoichiometric reaction has a higher stagnation temperature than Reaction 1. However, the specific impulse for Reaction 1 is higher than the stoichiometric reaction. Explain several of the reasons why this might be true.

SECTION 3: Systems Analysis

6. (40%) Two small solid rocket motors have been tested to assess their applicability as initial upper stages for very small payloads. The data obtained during the tests is given in the Excel Spreadsheet that accompanied this exam. In the spreadsheet you will find data on the initial and final masses of the motors and data on the nozzle geometry. A characteristic exhaust velocity for each engine has been measured. You will also find real thrust measurements as a function of time (NOTE: the absolute value of the time is arbitrary). Both engines use the same solid propellants, but have different additives.

A.  (2%) For Vulcan Motor A, you will notice that the final (after the burn) throat diameter is greater than the initial (before the burn) throat geometry. Based on this data, determine what process of cooling is used for these motors.

B.  (8%) For Vulcan Motor A, determine the following parameters: propellant mass, total propulsive impulse, specific impulse, and inert mass fraction.

C.  (8%) For Vulcan Motor B, determine the following parameters: propellant mass, total propulsive impulse, specific impulse, and inert mass fraction.

D.  (6%) Determine the average exit velocity of the products for Vulcan Motor A. Assume a constant mass flow rate throughout the duration of the burn and a ratio of specific heats of the products of 1.164 for both motors. Would you expect the exit velocity for Vulcan Motor B to be higher or lower than for Vulcan Motor A? Explain (no further calculations required).

E.  (2%) Plot the Thrust versus time for the Vulcan Motor B. Is the assumption you used in Part D of constant mass flow rate a good one?

F.  (4%) Determine the Dv for both motors while carrying a 1 kg payload.

G.  (2%) The engine with the higher Isp also has a higher inert mass fraction. List several reasons why this might be true.

H.  (8%) Calculate the ratio of specific impulse (found in Sections B and C) and the ratio of the Dv that can be achieved (found in Section F) for both motors. Are these ratios similar? If they are similar, then discuss why? If they are not similar, then discuss why they are not?

Clarification: Find and . Compare these ratios.