How a Tether Works

For an introduction to tethers we recommend an article in Scientific American.

The main problem to be solved is getting off Earth cheaply. To do this we propose a "momentum exchange tether". This tether is a long cable, 500 km long, rotating around its own center of mass and orbiting the Earth. At one end of the tether is a mass called the ballast. A suborbital rocket would rendezvous with the other end of the tether (we call the payload end) when the tether is vertical with the ballast at the end farther from Earth and the rocket has matched speed and location with the tether. The ballast has enough extra momentum that even though it looses some in picking up the payload the tether stays in orbit.

Materials

The strongest commercial fiber in 2000 is Spectra-2000. Spectra-2000 is less dense than water at 0.97 grams/cc. It can handle 3.51 billion newtons per square meter (Gpa). Pound for pound, Spectra-2000 is 10 times stronger than steel. It is very resistant to fatigue, abrasion, and ultraviolet. It is cheap enough to be used as kite string or fishing line. Indications are that stronger fibers could be made at higher costs, if there was a real demand. Improvements over the last 20 years have been substantial and continued progress is expected. So while we use Spectra-2000 numbers for this discussion, there could well be something better by the time a SSTT and tether are actually in operation.

Another material is dyneema which looks interesting, in part because it is used in fotino / YES2 project. It can handle 1 million cycles to 70% of peak. After 2 years exposure to sunlight (on Earth) it has 80% of strenght. This is said to be better than other fibers. Sunlight in space will be harsher, so how long a tether lasts is an issue to watch out for. Wikipedia says chemically identical to Spectra, just another brand name. A third brand name is TIVAR.

Mass of the Tether System

The initial tether system will be launched on an existing rocket. Existing rockets charge around $2,000 per lb. This means that the more mass the initial tether has the more it is going to cost to get it into orbit. Initially we plan to have a small mass.

The mass of the tether and ballast will be increased for larger payloads, and faster tip speeds. The strength of the tether material has a significant impact on the mass of the tether. This is not only because the tether must hold up the payload, but it must hold up its own weight which is usually much more than the payload. The faster the tip speed the more the centripetal acceleration, and the stronger the tether needs to be. The following graph shows how the ratio of the tether mass to payload mass depends on the tip speed and safety factor for a spectra-2000 tether. This is only for the mass of the tether from the center of mass to the payload. In the normal case where the ballast is large these numbers for tether mass are just a bit low. As an example, for a 2.5 km/sec tip speed and a safety factor of 2, the tether mass as shown in the graph would be about 13 times the mass of the payload. For reasonable sized ballast the tether might be 14 times the mass.

Tether Taper

A tether needs to hold its own mass as well as the payload mass. Because of this tethers used for higher tip speeds need to be tapered. The following graph illustrates the taper of a tether.

Some speeds

A rotating tether can offer a grapple speed of 5 km/sec. The SSTT needs to be able to achieve that speed. You can experiment with the tether java applet to try different tethers. The earth is spinning at 1000 MPH and an airlaunched SSTT can give you another 500 MPH for a total of 1,500 MPH. This is about 0.67 km/sec. The SSTT just needs to supply about 4.23 km/sec plus what is lost to drag and gravity (less than 0.5 km for airlaunch, so the SSTT target DV is about 4.73 km/s).

To get to orbit, without a tether, a rocket needs to have a delta-V of about 9 km/s. With the help of a tether, the SSTT only has to provide about half the speed of a full orbiter.

Ballast

The ballast can consist of lead weights, solar arrays, batteries, fuel tanks, tele-operated robots, space-junk, or whatever. At some point it could be a space hotel, or a space farm. Because it is not at the center of mass it will have some small artificial gravity.

One interesting source of initial ballast is the spent rocket stage that got your initial payload to orbit. This can be a significant source of free ballast. As mentioned above, a Zenit 2 second stage, empty, has a mass of 10.6 tons.