Studies on the performance of a rocket propelled orbiting missile
Creators: name: Halvorson, George Grandchamp
name: Sledge, Edward Cress
Publisher: name: California Institute of Technology
Year: 1946
Subjects: Aeronautics
Aeronautical Engineering

description: NOTE: Text of symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.


This report is a study of the performance requirements necessary to launch a rocket propelled missile into a circular orbit about the earth. Various trajectories by which a missile can be launched into such an orbit are investigated and an estimation is made of the minimum propellant-gross weight ratio required to reach stable orbital conditions at various altitudes.

The velocity of a projectile traveling about the earth in a circular orbit must be such that its weight is exactly balanced by the centrifugal force acting upon it. The expression for the required velocity, relative to a non-rotating earth, can be derived from the following figure.

[...].


By the law of Conservation of Energy, such an orbit, once obtained, must remain circular unless influenced by additional forces. The action of atmospheric drag would be to cause a continual loss of energy; this loss would be made up at the expense of potential energy, causing the projectile to move in toward the earth in a contracting spiral. It can be shown (of. ref. 2) that, for altitudes greater than one hundred and twenty miles, the rate of this contraction is negligible.

The practical applications of an orbiting missile are numerous. A few are as follows:

a) A radio relay station for television and other high frequency communication.
b) To carry instruments for continuous measurement of upper atmospheric phenomena.
c) A military weapon of unlimited range, provided it can be brought back to earth at will.

The possibility of launching a vehicle into a circular orbit by means of rocket propulsion depends primarily upon the conditions of propellant consumption which are required to reach a stable orbital velocity. These conditions are:

a) Propellant characteristics (in particular, specific impulse).
b) Rate of propellant consumption.
c) Propellant-gross weight ratio.
	
The velocity necessary for a circular orbit is in the neighborhood of 26,000 ft/sec. For an unboosted rocket with an uniform burning rate the terminal velocity (neglecting drag and gravity forces) is given by [...] where [...] is assumed constant. If we take [...] to be equal to 400 sec., a representative value for a rocket fuel consisting of oxygen and hydrogen, the value of [...], the propellant-gross weight ratio, corresponding to [...] =26,000 ft/sec., is [...]=. 0.867. Thus, even with the most powerful rocket fuel, the required propellant gross weight ratio is very high, and the importance of a more careful estimation of this ratio is evident.

A comprehensive analysis of the important factors which influence the performance of an orbiting rocket has been made by W. Z. Chien of GALCIT. In this analysis, Dr. Chien considered a vertical trajectory as a first approximation in obtaining estimates of the altitude of the circular orbit and of the propellant-gross weight ratio required (cf. ref. 2).

This report extends the considerations of Chien's work to oblique trajectories of various types, all of which terminate at the end of burning with the proper velocity conditions for a circular orbit. The first part of the report is a recapitulation of Chien's analysis. The second part deals with the characteristics of various oblique trajectories by which a rocket may be launched directly into a circular orbit; and the third part analyses a procedure whereby the rocket is launched into an elliptical orbit near its perihelion, is allowed to travel as a free body around the earth to the aphelion of the ellipse and then, by an additional boost of velocity, is projected into a circular orbit.