A New Chain Model and Earth-Circling Rings

Once again, instead of a logical progression on any of the topics that I’ve already started, I got interested in the dynamic analysis of flexible structures using a chain model. A “chain model”, is a discretization into a series of point masses connected by elastic bars. Using numerical integration, the trajectory of each of the masses can be tracked in time. The model is useful for a more detailed look at various tether problems, and for the whole class of dynamic structures. I wrote a Mathematica software package to perform this type of analysis in a fairly general way.  The package is called chainDynamicModel.m, and it is available for download on the website Resources page.

I’ve been meaning to address the whole world of dynamic structures; sometimes called kinetic structures. These concepts use changes in the direction of a momentum stream to generate forces that can be used to support a structure. For example. consider a stream of high-speed projectiles that move vertically through an evacuated tube, using some form of levitation to avoid touching the walls. At the top, we somehow reverse the direction of the stream and pass the projectiles downward through another tube. The reversal in direction must be balanced by a force that in turn keeps the tubes in tension. A neat way to make a tall tower. Besides towers, it is easy to envision giant loops that are partially on the ground and partially high in the atmosphere. The largest loop would encircle the entire earth. I give a bibliography of some papers and other sources on a new website page devoted to dynamic structures.

An earth-circling ring has been proposed by a several authors, starting with Tesla. Tesla (and Larry Niven in Ringworld) conceived of a rigid ring. More realistically, consider a cable spinning at, or just above, the orbital speed at the cable altitude. At the orbital speed, the cable would be tension-free. So far, so good. But now consider a small perturbation in velocity, applied to a small portion of the cable. The numerical simulations show that without a restoring force, the cable trajectory grows increasing distorted. A 10 m/sec radial velocity applied to one node of the model results in the cable crashing in less than a revolution. The new page includes a brief study of these stability issues using the new chain model. The animation below (visible if you have the Wolfram CDF player installed) shows the evolution of the cable distortion over time. In this particular simulation, the cable is assumed to have the properties of graphite fiber. It is spinning at 1% above orbital velocity, which corresponds to a tensile force near the working limit for graphite. A 10 m/sec radial velocity perturbation is applied to the red node at the beginning of the simulation. Because of strobe effects, it may look like the black nodes are not moving, but the whole ring has a uniform tangential velocity.

I’m having fun with the chain model at the model. Expect to see several studies addressing the dynamic response of tethers and other long, flexible structures.