Comment on 'A re-entry control effectiveness methodology for the Space Shuttle Orbiter'

Abstract

TECHNICAL COMMENTS 189 equation of velocity reduces to (9) Equation (9) is identical, except for the "approximately equal" notation, to the well-known formula that gives the ideal velocity attained by a conventional rocket in a gravitationless vacuum,t the derivation of which assumes that the exhaust velocity and mass flow rate remain constant. Both of these items, however, are varying in the case of the cold-gas thruster. Accuracy of ApproximationBy comparing Eqs. (1) and (5), it may be seen that the terminal velocity, according to the approximate formula, is slightly overestimated. The maximum percentage error occurs with thrusters using the monatomic gases (k= 3 or j= 1.667), and amounts to about 5% in the extreme case of X= Vi. As indicated in Fig. 1, the difference between the two equations decreases as A: or X grows large, such that the error in any situation does not exceed 1 % for propellant mass fractions ranging up to 10%. tSee, for example, Ref. 5.It may be concluded that for the class of cold-gas thrusters containing small propellant mass, the approximate velocity equation closely represents the integral equation of ideal velocity. The abbreviated formula permits the effect of various design factors to be readily determined.