In CateCATS1 the thrust for the LEO-Tether comes mostly from an EDT. However, the LEO-Tether is a rotating tether so the thrust is complicated somewhat. We investigate the issues here.

Rotating EDT

A rotating EDT loses some of its opportunity for thrust by the rotation. Thrust is perpendicular to the wire (and current). Useful thrust is the component parallel to the orbit velocity vector. This component is proportional to the cosine of the angle of the tether relative to the local radius. At 45 degrees the cosine is 70%, at 0 the cosine is 100%. The average from 0 to 45 degrees is about 90%.

If the Electrodynamic Tether (EDT) has the ability to push current both ways, it can apply power for 90 degrees (plus and minus 45), charge the batteries over the next 90 degrees, apply (reversed) power for 90 degrees, and charge the batteries again for the last 90 degrees. This pattern gives a thrust program of 50%.

Power within 45 degrees on an EDT that only has solar cells, produces a net thrust of about 90% of 50% or 45% of what the solar cell power available on the tether could theoretically produce. It would be nice to use the solar cells during the other 50% of the rotation. Batteries offer a way to save that electricity and use it during the near vertical portion of rotation.

In (?) by Robert Hoyt (and Forward?), they made the observation that they charged their batteries while above 1000 km altitude, and applied power (both battery and solar cells) while under 1000 km and when the tether was within 45 degrees of the local vertical.

A tether designed for support of SSTT to LEO traffic will be in circular or near circular orbit. The tether design offered in this book is in orbit between 500 and 700 km altitude. This tether will not have an apogee above 1000 km altitude. This tether will essentially be ‘under power’ all the time the tether is in sunshine (about 62% of the time).

With the parameters for supporting an SSTT, the tether rotates about once every 24-25 minutes. This will produce an on – off cycle of about 6 minutes under power, and 6 minutes where the angle is poor for power, so the battery can be charged. This cycle allows us to calculate how much battery capacity is needed for the tether.

One question is how should the battery be used? One simple choice is to charge the battery for the poor power angles, (~6 minutes) then apply battery and solar power during the power phase. This program could double the power applied during the power phase, giving thrust of 90% of theoretical optimum.

Unfortunately, when you charge and discharge a battery, something is lost. NiCd batteries return about 80% of the power used to charge them. This gives a total thrust from a simple cycle of about 81% of maximum power. This is graphed below as the simple use line (line 1). This pattern requires 2.29 kg of battery per kW of solar cells.

Since a NiCd battery returns only 80% of the charge, and the cosine of 38 degrees is about .8, it would be a waste of electricity to charge NiCd batteries after the tether is within 38 degrees. The pattern of charging the battery for 52 degrees, then run both solar cells and batteries for 38 degrees gives a net thrust of 82% of maximum. This is a slight improvement. Line 2 in the graph shows a shorter arc, slightly above the simple case. This pattern requires 2.63 kg of battery per kW of solar cells.

Since the useful thrust varies as the cosine of the angle, the battery could be used for power during a smaller arc, when the thrust is better. For line 3, the battery is charged for 52 degrees, then the solar cells provide thrust until the tether is within 5 degrees, and the battery kicks in for the 5 degrees within vertical, the EDT gets 85.4% of theory. This profile has a peak with a lower, long arc in the graph. Again this takes 2.63 kg of battery per kW.

Unfortunately pulsing the power in one tenth of the time requires a current of 10 times the current the solar cells would drive. This forces the mass of the conductor up (about 10 times). A tradeoff of some increase in current, but slightly lower total thrust makes some sense.

Curve #4 in the graph is a pattern of charging the battery for 52 degrees, using solar cells for from 38 degrees down, and adding the battery at 20 degrees. This combination provides 84.5% of theory. It has three times the peak current.

We think this is a good tradeoff of thrust, mass of battery and mass of conductor. For design purposes we have used this fraction in calculating the solar cells needed on the tether.

Li-ion batteries only return about 70% of the power used to charge them. Li-ion batteries in simple use produce about 75% thrust over a rotation of the EDT. It would not make sense to charge a Li-ion battery after the tether is within 45 degrees. The best tradeoff for Li-ion batteries gets just under 79.7%. They have higher power storage per kg, so Li-ion batteries may be the right choice.

Self Shade

During the equinox, the plane of the tether’s orbit will include the sun. This means that the solar panels on the end of the tether can shadow panels not on the end. A megawatt of solar cells needs about 5100 m^2 of area. Two panels (one on each side of the tether) would be about half that. If they are square, they need to be about 51 meters on a side.

By spreading out these arrays, the angle during which the shadow will cost power generation can be reduced. If the next array is a kilometer up the tether, it will be in shade only 40 seconds out of a 24 minute rotation (about 1.67%).

These arrays need a two axis rotation, one to compensate for the rotation of the tether, the other to track the plane of the sun. They need a clamp to the tether, leverage to hold a 160 foot panel along the tether, and a frame.