Effects of Climber Transit on the Space Elevator Dynamics

Paper number

IAC-07-D4.1.04

Author

Mr. Stephen Cohen, McGill University, Canada

Coauthor

Prof. Arun Misra, McGill University, Canada

Year

2007

Abstract

The space elevator offers an alternate and efficient method for space travel in the future. An important issue for effective operation of the space elevator will be to understand its dynamics. This paper presents a simple yet realistic dynamical model for this purpose. The model is used to determine the basic motion of the elevator ribbon caused by climber transit.  Among other things, this ribbon motion can adversely affect the orbit of a launched satellite. The paper also proposes appropriate climbing procedures to minimize this effect.

The dynamical model consists of a movable base on the surface of the earth, a ribbon extending from this base to an altitude beyond the geosynchronous altitude, a climber carrying the satellite, and a counterweight at the top of the ribbon. Only motions in the equatorial plane are considered. The elastic oscillations of the ribbon are not included. It was found that the primary response of the ribbon to ascending climbers is to rotate in the direction opposite to that of the earth. This westward tilt is due to the Coriolis force on the moving climber. For a climber transit at constant speed, the response is a sum of oscillatory terms (which decay for the ascent and grow for descent) and a linear term. For constant speed transits, the amount of libration induced on the ribbon is proportional to the mass of the climber and its cruise speed. Since both of these values have upper bounds, the ribbon libration they cause is bounded as well; it is only of the order of milliradians. Still, the ribbon experiences undamped oscillations about its vertical equilibrium position that are shown to have a non-negligible effect on the placement of satellites.

Three simple climbing procedures that aim to minimize or eliminate residual oscillation of the ribbon upon climber arrival are presented in the paper. The most promising climbing procedure, which allows for the ribbon to begin and end in the vertical equilibrium position, requires that multiple climbers undergo the same transit speed profile and be phased appropriately, i.e., separated by a specific amount of time. The paper also shows that improper phasing can add the adverse effects of different climbers.

Abstract document

IAC-07-D4.1.04.pdf

Manuscript document

IAC-07-D4.1.04.pdf (🔒 authorized access only).

To get the manuscript, please contact IAF Secretariat.