Page 79 - Intro to Space Sciences Spacecraft Applications

Introduction to Space Sciences and Spacecraft Applications
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elevate the payload to the orbital altitude, and redirect thrust during ascent
to steer the rocket along the desired trajectory. The rocket exhaust veloc-
ity, also assumed constant for all stages, is given by v,. Finally, n repre-
sents the number of stages of the rocket.

Example Problem:

Although orbital velocity for a circular orbit at 300 km altitude is
7.73 km/sec, a typical velocity that a launch vehicle may be required
to deliver to reach this orbit is 9.5 km/sec. Assuming use of space
shuttle main engines for the propulsion system, determine the mass
ratio for a single-stage-to-orbit (SSTO) rocket.

Solution:

Using the exhaust velocity found earlier for the SSME and
remembering to use compatible units:

MR = 14.11

This indicates that the single stage would have to have about 14
times the mass of the payload in order to reach the given orbital
velocity. This is actually a somewhat respectable mass ratio and
illustrates the effectiveness of the SSME design. However, it must
be remembered that equation 3-8 gives only a crude approximation
due to the assumptions mentioned earlier. Actual stage optimization
is a complicated, iterative process that takes into account the differ-
ent thrust and mass ratio characteristics for each stage.

Launch Timing (Windows). In the preceding chapter we saw that the
plane of an orbit is fixed inertially in space while the earth rotates beneath
this plane. If it is desired to place the spacecraft into an orbital plane with
a particular inertial orientation, the launch will have to be timed so as to
occur just as the launch site rotates beneath the desired orbital plane, as
depicted in Figure 3-6 for a launch from the Kennedy Space Center.
In most instances, a plus or minus time period around the optimum time
of launch is specified and is known as the launch window. If launch does
not occur during this time period, the launch will have to be delayed until