Thermal Effects On A Long Tether

Paper number

IAC-07-C1.I.16

Author

Prof. Maurizio Parisse, Aerospace Engineering School, University of Rome La Sapienza, Italy

Coauthor

Prof. Fabio Curti, Aerospace Engineering School, University of Rome La Sapienza, Italy

Coauthor

Dr. Francesco Longo, Italian Space Agency (ASI), Italy

Year

2007

Abstract

In the study here proposed, a simple model of a very long tether system orbiting the Earth is defined, in order to analyze the coupling mechanisms between the pitch and thermal dynamics and between the thermal dynamics and the transverse vibrations of the wire connecting the tip masses of the tether. 
The system, initially aligned along the local vertical because the gravity gradient torque, experiences a periodic thermal load depending on the orbital position; the consequence of such variable thermal input is a thermal elongation of the wire with a significative displacement of the tip masses. The radial movement of the masses triggers a pitch libration due to the Coriolis forces. The thermal input is therefore depending not only on the true anomaly but also on the attitude so that a two ways interaction between attitude and thermal dynamics is established.
The focus is, however, on the aerodynamic force acting on the lower mass of the tether which is flying through the ticker layers of the atmosphere. 
Since the thermal elongation of the wire does not move the c.m. of the system, the downward movement of the lower tip mass due to wire heating increases the aerodynamic torque; in the cooling phase, f.i. during the eclipse time, the wire shrinks, the lower mass moves upward and reduces its drag and arm with respect to the c.m.
The effect of the thermal dynamics is, therefore, a pulsating aerodynamic torque which acts as a forcing term in the pitch equation. The stability of the system is studied making use of the Floquet theory; the periodic coefficients coming from the input of the thermal equation.
The other relevant dynamics object of study have been the transverse vibrations of the tether, modelled as a tight rope under the action of transverse non uniform distributed force which arises from Coriolis effect during the thermal transient of the wire. Under the assumption of uniform heating or cooling, the distributed time depending Coriolis force, is represented by a butterfly diagram. It is worthwhile to notice that thermal input variations due to attitude and orbital dynamics are almost instantaneously sensed as temperature rate because the very low thermal inertia. The spectral analysis of such forcing term has been performed and the results compared with the natural frequencies of transverse vibrations of the wire.

Abstract document

IAC-07-C1.I.16.pdf