Page 74 - Intro to Space Sciences Spacecraft Applications

Propulsion
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ier to store and transport than liquid hydrogen. This is particularly demon-
strated by the hydrogedfluorine combination which has been used in
some special situations to take advantage of the higher specific impulse,
but is not used regularly due to the highly toxic nature of fluorine.

Example Problem:

The space shuttle main engine (SSME) uses a liquid hydrogedoxy-
gen propellant combination. Mass flow rate to each engine is 466.6
kg/sec and the combustion chamber pressure is 20.5 x lo6 N/m2.
Determine the standard sea-level exhaust velocity, thrust, and specific
impulse for a single SSME. (Assume pe = ps.l. = 1.01 x 16 N/m2; y =
1.2; and g = 9.8 1 ds2)

Solution:

Using the values for To, R, and M (converted to kg/mole) for the
hydrogen/oxygen fuel combination given in Table 3- 1 :

v, = 3,589.4 m/sec
I,, = 365.9 sec
T = 1.68 x lo6 N = 376,835 lbs thrust

For comparison, a fully loaded space shuttle (including fuel tank
and solid rocket motors) weighs over 4 million pounds, requiring
three SSMEs and two solid rocket motors that deliver over one mil-
lion pounds thrust each just to get off the launch pad.

Nozzle Design
If we look at a closed volume approach to the thrust equation, the situ-
ation would look like that shown in Figure 3-3. In this case our control
volume merely envelopes the rocket and we must consider forces which
interact with, and through, this boundary. Summing the forces over the
entire volume we find:

ZF = b e + (Pe - pm)& (3-7)
The first term on the right-hand side of equation 3-7 represents the force
due to the propellants passing through the control volume at velocity v,.
This should be recognized as the same as the thrust term defined earlier.