# Tethers as momentum exchange devices

- Introduction
- Some links and papers on tethers as space propulsion
- Mass ratio for constant stress cable
- Circular orbits from a rotating tether using variable release angles
- On the Possibility of Using Whip-Action to Accelerate a Space Launch Vehicle
- Stress Waves After Payload Release for a Uniform Stress Rotovator

### Introduction

Very long tethers can be used in a variety of ways to help boost a payload to orbit or between orbits. The basic idea is attach a payload to the tip of a tether. The payload energy is then increased by reeling up the tether to a higher station, climbing the tether, or by spinning the tether and releasing the payload at a favorable point. The spinning tether is particularly interesting because it can in principal pick up a payload at zero velocity relative to the earth surface, and after a 180 deg rotation release the payload beyond earth escape velocity. However, just like the space elevator the system is limited by material strength. Picking up the payload at zero velocity may not be possible in the near future because of material limits, but the spinning tether can be adjusted to the capabilities of present-day materials while still providing a substantial energy input.

Many tether systems have been proposed that give some incremental boost to a satellite in order to reach a higher orbit. For this website, we'll be interested in systems that provide a significant portion of the total energy needed for a payload to go from low velocity relative to the earth to orbit.

Once a tether has boosted a payload, the tether drops to a lower energy orbit. For continued use it must be reboosted to it's original orbit. One method would be to lower a returning payload back to earth. Alternatively, there could be a high efficiency propulsion system such as an ion engine to slower reboost the system. The most elegant solution being considered is to drive a current through the cable which interacts with the earth's magnetic field to restore the momentum.

A good short explanation of some of the basic concepts is given at the Tethers Unlimited website.

Top### Some links and papers on tethers as space propulsion

- "Moon & Mars Orbiting Spinning Tether Transport Architecture Study" NIAC Phase II Final Report by Tethers Unlimited, Aug. 31, 2001.
- Kirk Sorensen, "Hyperbolic Injection Issues for MXER Tethers", AIAA 2003-5221, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference 20–23 July 2003, Huntsville, Alabama
- Kirk F. Sorensen, "Conceptual Design and Analysis of an MXER Tether Boost Station", AIAA 2001-3915
- M.L. Cosmo and E.C. Lorenzini, "Tethers in Space Handbook", Third Edition, 1997
- Thomas J. Bogar et al, "Hypersonic Airplane Space Tether Orbital Launch (HASTOL) System: Interim Study Results", AIAA-99-4802, 9th International Space Planes and Hypersonic Systems and Technologies Conference 1-5 November 1999, Norfolk, VA USA

### Studies

#### Mass ratio for constant stress cable

First published; 7/20/2011. Last update: 7/20/2011

This notebook goes through the derivations for the cable to payload mass for three different sets of assumptions. First, we examine a vertical cable that simply hangs down from it's own center-of-gravity (CG). A payload docks with the near-earth end, and then climbs to the CG or beyond. The operational advantage is that the docking-point velocity is less than the orbital velocity for the same altitude. The second case is the classic rotovator or Moravec wheel (named after Hans Moravec). The rotovator is a rotating cable system. The tip rotational velocity can be zero relative to the earth surface. The second mass derivation includes the rotational acceleration effects, and duplicates a result published by Moravec. The third case combines the acceleration effect and the gravity gradient. A closed-form solution cannot be obtained for this case, but a numerical integration function is provided. The function is interactive in the CDF and NB formats. None of these results are new, but it is useful to have them rederived from first principals in Mathematica.

Computable Document Format | HTML Pages | PDF Version | Notebook Version |

#### Circular orbits from a rotating tether using variable release angles

First published; 8/03/2011. Last update: 8/03/2011

A rotovator is a rotating, orbiting tether that captures a payload (we'll call a "lifter"), carries the lifter around a portion of the tethers arc, and then releases it along a new trajectory. The figure shows the basic arrangement. The operation typically consider for a rotovator assumes that the payload release occurs when the cable reaches the highest point, 180 degrees around the circle. This position gives the maximum velocity gain to the payload. Because our current interest is in rotovators that allow for a substantial reduction in the initial launch velocity as compared to LEO velocity, a 180 deg position results in the payload exceeding escape velocity. This may be the desired affect, but I'd like to examine using a rotovator for efficiently reaching a circular earth orbit. The assumption is that the majority of mass going into space will go into near circular orbits, and the large mass flow into circular orbit will justify the cost of the rotovator. The easiest way to reach a range of orbits is to vary the release point. For a range of release points, the payload will go into an elliptical orbit. At either the perigee or apogee of the ellipse, and additional rocket burn would be used to circularize the orbit. The efficiency of the system can be measured by the total rocket deltaV required. The first component is the velocity need to hook up to the rotovator, and the second component is the deltaV need to circularize at the desired altitude.

Computable Document Format | HTML Pages | PDF Version | Notebook Version |

#### On the Possibility of Using Whip-Action to Accelerate a Space Launch Vehicle

First published; 7/7/2012. Revision on 7/16/2012

This study is a quick look at the possibility of using a propagating wave along a tether to accelerate a projectile. The scenario involves endoatmospheric launch, with large subsonic transports providing the initial momentum to set up the wave. A dynamic model is used to track the tether trajectory. The results show that the whipping action can magnify the speed of the transports by up to 7 times, but the resulting tether stress far exceeds any realistic material capability. By releasing the projectile before the peak velocity, the stress level can be reduced, but the release speeds are reduced to around 3 times the initial transport speed. Aerodynamic drag was not included in the study. It is very possible that drag would make the concept impractical. The report shows the raw Mathematica input and results so that the input parameters can be varied. Animations are shown in the report and therefore it is recommended that readers download the CDF version.

Revision on 7/16/2012 changes the acceptable stress level for carbon fiber

Computable Document Format | PDF Version |

#### Stress Waves After Payload Release for a Uniform Stress Rotovator

First published; 8/4/2012.

This study examines what happens when a tip mass is released from a constant stress rotovator. The sudden release of a payload will result in a stress wave that propagates along the tether. The study uses our chain dynamic model to numerically simulate the event for a couple of different tether designs. Another simulation looks at the development of the transverse motion of the tether for the case of a spacecraft docking with the tether tip with a small relative different in speed. The results make use of the animated plots, so only the CDF version of the study is available. The document includes all of the Mathematica inputs.

Computable Document Format Version |