Artist rendering of orbital ring system, from 1982 paper by Paul Birch

Dynamic Structures

Introduction

I've decided to use the term "dynamic structures" for a host of ideas that rely on a momentum stream to provide forces that help support a structure. Imagine shooting a fire hose upward at a flat plate. The plate is tied to the ground with ropes. With careful aim and a steady stream of water, one can achieve a state in which the plate is suspended in the air with the ropes taut. This is the basic idea for a host of concepts. I would like to eventually examine several of these in detail, but for now a bibliography will suffice. One variant, the earth-circling ring is described in a bit more detail below. This provides a motivation for the single study available to date, "Stability of an Earth-Circling Ring".

Examples of Dynamic Structures

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Earth Circling Rings

A mass stream can orbit around the earth. The stream can be kept coherent either by using a continuous cable (see study below), or by levitating discrete masses inside of a tube. Now you can do several interesting things with this momentum stream. One, by altering the orbital path of the stream you can create a force that will support a stationary cable to the earth. The top of the tower rides on the ring using some form of levitation. The figure below (taken from Birch [1]) shows an exaggerated view of the stream path with two stationary towers. The paths are truncated sections of an elliptical orbit. Alternatively, a vertically launched spacecraft can "land" on the ring and be accelerated to orbital velocity, again using a combination levitation and a linear electric drive. A small fraction of the ring's momentum is transferred to the spaceship.

Nikola Tesla proposed a ring around the earth in the 1870's. It appears that Tesla's ring was rigid and did not move at orbital speed [link]. This is rather like Larry Niven's "Ring World" stories. Alexander Bolonkin gives some basic analysis for an earth-circling ring to hold up towers [see Ref 1 in bibliography list below]. The most thorough analysis of the concept that I've seen comes from Paul Birch in a series of articles in the Journal of the British Interplanetary Society [2-4]. Birch describes ways of dealing with precession and non-equatorial orbits. He also provides an analysis that supports the claim that a ring/tower system is stable. The study below shows that a free ring (no connecting towers) is unstable.

Ring Bibliography

  1. Alexander Bolonkin, Non-Rocket Space Launch and Flight, Chapter 3,Elsevier, 2006
  2. Paul Birch, "Orbital Ring Systems and Jacob's Ladders- I", JBIS Vol 35, pp 475-497, 1982.
  3. Paul Birch, "Orbital Ring Systems and Jacob's Ladders- II", JBIS Vol 36, pp 115-128, 1983.
  4. Paul Birch, "Orbital Ring Systems and Jacob's Ladders- III", JBIS, Vol 36, pp 231-238, 1983.

Studies

Stability of an Earth-Circling Ring

Stability of Earth Circling Ring Computable Document Format

First published; 7/27/2012

Consider a continuous cable that circles the entire earth. The cable has a rotational velocity equal to, or greater than the velocity for a circular orbit at the cables altitude. The cable would be in an orbit and in equilibrium with gravity. The study question is what happens if there is a small perturbation in velocity applied to one part of the cable. For a unconnected stream of masses, the perturbed mass would simply move into a slightly elliptical orbit. For a continuous cable, the behavior is quite different. The study demonstrates that a continuous orbital ring is not stable without the application of outside forces.

In order to perform the analysis, a Mathematica code was written for the dynamic analysis of a connected chain of points. The chain of points is a discretized representation of the continuous cable. The code is general, and can be used to examine a wide range of tether and flexible-structure problems. Links for the code (chainDynamicModel.m) and the users guide can be found on the Resources page.

Only a CDF (Wolfram Computational Document Format) of the study is available. Because of the animated results, a PDF version would not be of much use.

The animation below comes from the study. It will be visible and interactive if you have the Wolfram CDF player installed on your browser. The image shows the case of an orbital ring that is moving 1% faster than orbital velocity so that the ring is under tension. A small (10 m/sec) radial velocity "bump" is applied to the red node. The animation shows the evolution of the disturbance. The series of dots are the analysis nodes. The red node is shown larger simply to highlight the perturbed point - it is not heavier or any different than the other nodes. Also, there is an illusion that the black nodes are not moving, or moving backwards. The red node is showing the overall rotation of the ring.

The blog page for leaving comments or questions on this work is here.

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