Unified Engineering Spring Term 2005

Problem P6. (Propulsion) L.O.’s D & E

Evaluate the performance of a single stage sounding rocket to be used for atmospheric research. You are given the following design parameters:

Combustion chamber temperature = 3500 K

Combustion chamber pressure = 5 MPa

Nozzle exit area = 0.008 m²

Nozzle throat area = 0.0006 m²

Propellant mass = 30 kg

Total mass at takeoff = 40 kg

Gas constant = 300 J/kg-K

Ratio of specific heats = 1.35

a) What are the take-off thrust and take-off Isp for this rocket?

b) What is the Isp when the nozzle is ideally expanded?

c) Assuming the rocket is launched vertically and that the nozzle is ideally expanded, and neglecting drag, how high will it go?

d) If you increase the exit area 10% at a cost of1 kg in total mass at take-off (still 30 kg fuel mass) does the rocket go higher? Why?

[Note: To solve this problem you will have to use relationships from thermodynamics (steady flow energy equation) and fluid mechanics (compressible flow relations). These can all be found in the Unified Propulsion notes (Chapters V and VI). Most of the relations are written in terms of the exit Mach number, Me. To find this you will have to try several values of Me in the relationship for A*/Ae until the equation gives you the same ratio as given in the problem statement. I also recommend doing this with Matlab or a spreadsheet. Once you have it coded in, you can do all the design trades--like part (d).]