Stability of the Space Cable

Paper number

IAC-06-D4.3.04

Author

Dr. John Knapman, United Kingdom

Year

2006

Abstract

Previous publications have shown the general feasibility of constructing a space cable that reaches from the ground up to high altitudes as a means of launching space vehicles. This is different from the space elevator, which reaches down from geostationary orbit. In one scenario, a space cable up to 50 km high can be used to accelerate vehicles of 100 tonnes to a velocity similar to that achieved by a first-stage rocket. Another proposed infrastructure system, the launch loop, can accelerate 3-tonne vehicles into orbit. In a new scenario, the space cable attains an altitude of 140 km and is better suited to astronomy and tourism as well as the launching of vehicles.

The space cable can be constructed using existing materials and known technology. It consists of several pairs of evacuated tubes containing bolts traveling at high speeds. The bolts support the tubes using permanent-magnet levitation, stabilized electromagnetically.

One of the issues with these designs is lateral stability. Lofstrom (1985) described how to stabilize the launch loop with wires hanging down to the ground, but the space cable can be stabilized without such heavy civil engineering. Knapman (2005) outlined an active control mechanism for ensuring lateral stability in the presence of cross winds, including powerful jet-stream winds, but no study was presented of the oscillation modes. To overcome the problem of traveling waves, the tubes must be connected to each other at regular points along their length with damped elastic struts.

The lateral motion of a pair of connected tubes is governed by the following simultaneous partial differential equations:

m _u ∂ ² z ₁/∂ t ²+ m _b V∂ ² z ₁/∂ q ∂ t +( Tu−1/2 m _b V ²)∂ ² z ₁/∂ q ²= F+ F _s

m _u ∂ ² z ₂/∂ t ²− m _b V∂ ² z ₂/∂ q ∂ t +( Tu−1/2 m _b V ²)∂ ² z ₂/∂ q ²= F− F _s

V is the bolt velocity, u is the distance between two adjacent struts, m _b is the average mass of the bolts over distance u at any time t, m _u is the combined mass of the tube and bolts over distance u, T is the tension in a tube, q is the displacement along a tube, z ₁ and z ₂ are the lateral displacements of each tube, F is an external force (typically wind), and F _s is the force in a strut:

F _s =−(∂ z ₁/∂ t−∂ z ₂/∂ t) p−( z ₁− z ₂− L)є

L is the nominal length of a strut, є is its expansion coefficient, and p is the damping coefficient. These equations have solutions of the form:

z ₁= Ae ^α t( e ^{iq/ V} − Be ^{− iq/ V} )

z ₂=− Ae ^α t( e ^{− iq/ V} − Be ^{iq/ V} )

This reduces to a quartic equation in α that also determines B. Damping causes the waves to die out over time, giving stability.

Abstract document

IAC-06-D4.3.04.pdf

Manuscript document

IAC-06-D4.3.04.pdf (🔒 authorized access only).

To get the manuscript, please contact IAF Secretariat.