# ENAE 483/788D

Principles of Space Systems Design

Fall, 2002

Question 10:

**For both ENAE 483 and ENAE 788D:**

a) The NERVA rocket engine used hydrogen (H_{2}) as
propellants, heated by a nuclear reactor. Assuming the Isp for
an ideally expanded NERVA engine was 900 sec, reverse engineer
the engine to estimate the temperature of the hydrogen in the
reactor. (Hint: since no combustion takes place, assume the ratio
of specific heat for H_{2} is the ideal value of 1.4)

b) It would be nice to use a simple, easy to handle material
like water as propellant for a nuclear engine. Based on the data
for the NERVA from (a), estimate the Isp available using water
for the propellant.

c) You need to design a pressure-fed system to supply LOX to
a hybrid rocket engine. The LOX tank contains 10,000 kg initially.
You need to pressurize the tank to 300 psi. Due to the regulator
used, the minimum pressure drop between the helium pressurant
tank and the LOX tank is 100 psi. Find the volume and mass of
helium required for this pressurization, assuming the initial
He tank pressure is 3000 psi and the initial temperature is 300°K.

**For ENAE 788D only:**

d) An upper stage (operating in vacuum) contains 15,000 kg
of LOX/LH2 at a stochiometic mixture ratio. The inert mass of
the stage, including everything except the rocket nozzle, is 1000
kg. Assume the throat diameter of the rocket engine is 0.1 m,
and the nozzle is a hollow cone with a 15° half-angle. The
nozzle has a mass of 10 kg per square meter of surface area. The
rocket engine has a chamber pressure of 1000 psi and a combustion
temperature of 3800°K. Find the exit pressure Pe and expansion
ratio Ae/At that maximizes total delta-V for the stage. What is
the maximum delta-V?