Page 78 - Intro to Space Sciences Spacecraft Applications

STAGING Propulsion 65

Figure 3-6. Orbit insertion. The launch vehicle must intersect the desired
orbit at the proper altitude and with the proper velocity (magnitude and
direction).

Staging. Multistage rockets are used to more efficiently (and practically)
accelerate payloads to the high orbital velocities required. The separate
stages are designed to optimize the burn-out velocity of each stage with
respect to the overall mass the stage is accelerating. Upon burn-out, the
empty stage is discarded and the next stage, optimized with respect to the
remaining mass, takes over. The process is repeated until the desired
velocity is achieved.
A relatively simple relationship can be used to get an approximation of
the number of stages required to deliver a payload to a particular orbit
using a propulsion system of known characteristics:
mo - (k)
MR=--e (3 - 8)
*bo
In equation 3-8, MR represents the mass ratio or ratio of the original
mass (m,) to the mass at burn-out (mb) for each stage. Use of equation
3-8 assumes that this ratio is constant for all stages of the rocket. The
velocity required to establish the orbit is represented by v,. This number
will be higher than the orbital velocity of the desired orbit because it takes
into account the excess thrust needed to operate through the atmosphere,