Dynamics of a Partial Elevator with Multiple Climbers
- Paper number
IAC-08.D4.2.2
- Author
Ms. Pamela Woo, McGill University, Canada
- Coauthor
Prof. Arun Misra, McGill University, Canada
- Year
2008
- Abstract
The use of a space elevator has been proposed as an alternate way of transporting cargo into space. For a full elevator – with its base anchored to the Earth, and the structure extending out to 144 000 km – the tension developed in the tether requires a material much stronger than any now in existence. On the other hand, the construction of a partial elevator is more feasible. This partial structure will be shorter in length, and will not be attached to the Earth. A payload can dock at its lower end, and then use a climber to ascend to higher altitudes, while saving in fuel consumption. Many believe that over the upcoming decades, this partial elevator can be constructed and implemented, providing an alternative method for space travel. For this purpose, the dynamics of a partial elevator with multiple climbers is studied.
The proposed methodology is as follows. The partial elevator is modelled as an N-body tethered system, consisting of two end masses and N–2 climbers, joined by N–1 tether segments. In the case of payload transportation, the total length of the tether segments is kept constant, and the climber masses are significantly smaller than the end masses. For in-plane motion, the N–1 generalized coordinates are the angles formed between each tether segment and the local vertical. For a prescribed motion of the climbers, the governing equations of motion are derived, following the Lagrangian approach outlined in previous research. Since the partial elevator is a large structure, the mass of the tether must be included in the analysis. In addition, a distinction is made between the system’s centre of mass and its centre of orbit.
The equations of motion are solved numerically to find the variation of the tether angles over a period of time during and after the movement of the climbers. Since these angles introduce perturbations in the motion of the climbers, different system parameters and various climbing schemes are considered in order to determine the ideal conditions resulting in minimal libration angles for the elevator. Many simulations are performed, and extensive results are presented in this paper.
- Abstract document
- Manuscript document
IAC-08.D4.2.2.pdf (🔒 authorized access only).
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