Eddy Current Brake to Orbit

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This device is the central feature of a spacecraft carrier that receives spacecraft into orbit as an aircraft carrier receives aircraft that land on its deck. It works by having a long slotted aluminum tube in orbit and having the shuttle vehicle that is launched to orbital altitude enter this slot while the tube is moving by at orbital speed. The shuttle only needs to reach orbital altitude to enter the eddy current brake tube. That can be 10 kilometers on Luna at the perilune, an altitude that can be reached with 188 meters per second mission delta v, including gravity loss, a few seconds maneuvering fuel, and a small safety margin. Magnetic flux from permanent magnets deployed by the shuttle is directed at the walls of the tube causing a repulsive force and a retarding force.[1][2] By reducing the speed of the shuttle relative to the orbiting aluminum tube, the shuttle is brought up to near orbital speed. Since eddy current braking loses effectiveness at low relative speeds, friction braking is used to give the shuttle the last 18 meters per second to reach orbital speed and match velocity with the aluminum tube. During all the time that the relative speed of the shuttle and the aluminum tube is greater than 18 meters per second, there is no contact between the material of the shuttle and the material of the aluminum tube.

Eddy current concept.png

In the illustration of the Eddy Current Brake Device, the rectangle and dot to the left represent the spacecraft carrier and shuttle approaching rendezvous The dot and rectangle to the right are the spacecraft carrier and shuttle moving off together.

Motivation

Such an orbiting spacecraft carrier ought to be economic in transferring large quantities of cargo from the surface of a celestial body into orbit. If it is first used successfully in delivering lunar materials for building space based solar power satellites, then it could possibly be developed further to allow mass emigration from Earth and to deliver lunar materials to orbit for building the homes for emigrants, space habitats.

Orientational Stability

The aluminum tube requires electrically enhanced orientational stability because the tube needs to have extremely slight deviation from the absolute orbital path to not communicate radial or transverse motions to the shuttle. This is achieved by shifting masses along the length of the spacecraft carrier to counter any tendency to pitch up or down. Electrically enhanced rigidity is achieved with electromagnets varying the tension on selected tension members in the structure as is determined to be necessary by continuous laser measurements. Other sorts of transducers could also provide the needed effect. Fine yaw control is provided by reaction wheels sized for adjusting the yaw of the spacecraft carrier. Course yaw control is provided by steering with the electric thrusters to unload the reaction wheels.

Vibration Damping

The structural material holding the aluminum in place varies from aluminum to steel as necessary to avoid having the speed of sound in the structure match the speed of the shuttle as it moves through that portion of the spacecraft carrier. This avoids having a destructive shock wave move through the structure. Compression waves could be generated in a controlled way to cancel harmful vibrations. The same active structural system that provides enhanced rigidity would also generate the controlled compression waves for canceling harmful vibrations. In particular the structure of the spacecraft carrier is an active truss structure.[3] The study of active structures is an actively developing field. [4] [5]

Maintaining Orbital Momentum

The spacecraft carrier requires high specific impulse electric thrusters to maintain orbital momentum when donating some momentum to the less massive shuttle. Thrusters of sufficient force are possible because they can be made very massive since they would not be supporting their own weight, just restoring the small number of meters per second the tube loses by interaction with the shuttle. A spacecraft carrier in orbit around Luna would use oxygen as reaction mass for the electric thrust because oxygen is readily available on Luna. VASIMR[6] thrusters can use oxygen as a reaction mass because the VASIMR thruster has no electrode in contact with the heated plasma and will not have the problem of electrode oxidation. A magnetoplasmadynamic thruster[7] using hydrogen that NASA is developing would have problems with electrode oxidation if switched to oxygen reaction mass. The use of oxygen will also have an effect of lowering the maximum achievable specific impulse. A guestimate is 25,000 m/sec exhaust velocity instead of the 100,000 m/sec anticipated for NASA's thruster. This is the result of oxygen having 16 times the atomic weight of hydrogen. Still, the oxygen fueled VASIMR would be able to generate sufficient momentum to bring a 2.5 metric ton shuttle up to orbital speed using only 170 kg of oxygen reaction mass. So bringing up oxygen from Luna to fuel the thrusters should not be an intractable problem. A spacecraft carrier orbiting Earth would use hydrogen fueled thrusters as above.

Where to Deploy the Device

This sort of device may be possible for the moon, Mars, and Earth. A similar device would work for moving from orbital speed to a stop on the lunar surface. The first place and the easiest place to deploy an eddy current brake to orbit device is on Luna. To deploy it at Mars and Earth the device should already be operating on Luna to supply low cost materials in orbit or another source of materials should be available. Demonstrating the device at Luna will not guarantee success in deploying it at Mars or Earth.

Power Conservation

Replacing the simple aluminum of the tube with electrically conductive wires, insulation, and electrical power storage would recover some of the energy lost in the momentum transfer from the tube to the shuttle. The eddy current brake to orbit device could be built when it becomes economical to ship large masses of construction material from Luna to lunar orbit.

There have been objections to mass drivers because of large current switching requirements needed to have drive coils first attract the bucket then turn off to not retard the bucket on the way to orbital velocity. There is no such current switching requirement for the eddy current brake to orbit device.

Orientation in Orbit

Shifting mass from the ends toward the middle of the tube causes a decrease in the moment of inertia, so the angular rate of the tube (which averages about one rotation per orbit) increases to maintain constant angular momentum. This causes a pitch down movement relative to the horizon. Shifting mass from the middle towards the ends causes the opposite effects.

Because the entire tube moves at the speed of the center of the tube rather than at the speed dictated by the radial distance from the center of the elliptical orbit, the cross sections of the tube from leading end to trailing end all follow similar orbits but with the perilune shifted forward for leading cross sections and rearward for trailing cross sections. The slotted tube that interacts with the shuttle occupies a circular arc centered on the center of Luna at all times to maintain unstable equilibrium with respect to pitch. A child hopping on a pogo stick is another example of dynamically rebalanced unstable equilibrium.

Landing on Luna

Setting down on the lunar surface by eddy current braking has some advantages over using tethers. With a rotating tether, for example one that rotates four times while orbiting the moon once, each end of the tether touches down on the moon three times per orbit. There are six opportunities for momentum exchange launch to orbit. A vehicle to land must achieve the correct orbital speed at the correct position at the correct time to rendezvous with the tether and be dropped to the moon. The tether provides both launching to orbit and landing from orbit, but both must be scheduled with matching masses for every launch. There might be some fill-in cargo that is sent when other cargo does not match the incoming mass, such as bricks or fiber glass. With the eddy current braking device, the vehicle to be landed only requires the correct position and correct direction of movement with respect to the slotted aluminum tube to properly enter the eddy current braking device and brake to a stop. It is much like landing an airplane on a runway. The differences are that an airplane does not have such a high relative speed to the runway, the runway is somewhat wider than the eddy current braking slot, and the airplane must contend with varying wind conditions which would not affect eddy current braking on Luna. Also for an eddy braking slot there is no requirement for super strong structural materials as for a tether. There is no mass matching requirement for incoming and outgoing cargo. Unused cargo capacity on any particular shuttle would still be likely to be filled with bulk cargo being sent at a lower freight rate. A tether fastened to the lunar surface and extending up through L2 would be a nice way to handle cargo and would not require matching incoming and outgoing cargo mass, but it would be well in excess of 64500 kilometers long. It would be a major engineering project that would not be the first thing undertaken by industry on Luna.

Potential for Future Expansion

Just one orbiting spacecraft carrier would be a large thing. It would need to include a space station with amenities for crews of spacecraft passing through the station. Artificial gravity of perhaps 8 meters per second squared would be provided by an internal centrifuge. The closed system life support problems will need to have been solved before building the spacecraft carrier because closed system life support would be needed on Luna before people achieve the extensive industrial capabilities needed to build an orbiting spacecraft carrier.

A shuttle only needs to reach orbital altitude to land on a spacecraft carrier and thus obtain orbit. This requirement is modest enough that a fully reusable shuttle may be possible for Earth. It ought to be part of a two stage vehicle in which a reusable booster pushes a 2.5 metric ton shuttle up to altitude to enter the spacecraft carrier. The shuttle enters the slot with maneuvering thrusters. If the market for space transportation at reduced costs is large enough, there could be a dozen spacecraft carriers in low equatorial orbit about Earth and dozens more in orbits in various planes all 40 degrees inclined to the equator with such perigee and apogee as necessary to avoid collisions. Fail-safe engineering can be a feature in spacecraft carriers orbiting Earth as long as they are confined to equatorial orbit or some other single orbital plane. The structure can be mostly aluminum which burns on re-entry to the atmosphere. It should be made to break into small pieces if it experiences runaway pitch instability. The pieces should break up from tidal force and the heat of re-entry so as to cause minimal damage on the ground. When there are more than a threshold number of spacecraft carriers in multiple 40 degree inclined orbital planes the whole system would be subject to a cascade of debris forming collisions caused by debris. This may be beyond the capability of fail-safe engineering to mitigate.

For the case of only twelve spacecraft carriers all in a single orbital plane inclined forty degrees to Earth's equator, each spacecraft carrier could have twenty receiving tubes in parallel to handle four 2.5-metric-ton shuttles every minute. Passenger shuttles would have eight passengers, a computer pilot and one crewman to look after the safety and good behavior of the passengers. So using all passenger shuttles for all the carriers would give a maximum capacity of twenty-three-thousand passengers per hour. That is sufficient to handle the emigration from Earth of all of the population increase even considering that some passengers will be returning to their homes on space habitats after visiting Earth and some shuttles will carry cargo. So the space habitat construction business will need to tool up for making homes for 240,000 emigrants per day.

Operational Details

If the orbiting tube imparts velocity to the shuttle at a rate of 30 meters per second per second, then such a tube for Luna should be about 59 kilometers (37 miles) long. With the same three g acceleration such a spacecraft carrier in orbit about Earth would need to be 1030 kilometers (644 miles) long. As with other low cost per unit mass systems of launching to orbit, a high mass rate of launch is needed to realize the potential low cost per unit mass.

The slot shaped opening in the aluminum tube that takes a shuttle to orbit faces down. A similar tube that can be an extension of the same spacecraft carrier would be on the upper surface of the carrier with the slot facing upward. This tube would receive incoming shuttles from other celestial bodies and provide deceleration to circular orbit velocity. If all of the momentum transfers to shuttles taking cargo to cis-lunar space from Luna are balanced by momentum transfers to the spacecraft carrier from shuttles taking cargo to Luna from cis-lunar space; then there is no need to adjust spacecraft carrier momentum with electric thrusters. In this case the spacecraft carrier would become an electric power generator and excess power could be beamed to Luna by microwave for use there. In the case in which incoming and outgoing traffic do not cancel their momentum donations to the spacecraft carrier and momentum withdrawals from the spacecraft carrier; there would need to be photovoltaic arrays to generate power for the thrusters that maintain momentum. There is always likely to be some need for fine adjustment of spacecraft carrier momentum with electric thrusters, limiting the amount of power that can be beamed to Luna.

A shuttle rising to orbit rises into the slot and extends permanent magnets on struts towards the aluminum to gain lift and acceleration. Part of the momentum of the spacecraft carrier could be obtained by electrically decelerating shuttles for landing using ancillary equipment. On the moon incoming shuttles would head for a landing strip with an eddy current braking device. Shuttles returning to Earth from the spacecraft carrier would use a heat shield that could be a one time use item imported from the moon. The heat shield could be made of glass sheet and glass fiber. The slot shaped opening in the aluminum landing tube on the moon's surface faces upward.

A candidate for initially putting material into lunar orbit to build the first eddy-current-brake-to-orbit device would be a lunar rocket-sled to orbit. Such a device on a smaller scale could put shuttles up to an altitude to use a lunar spacecraft carrier. The required mission delta v to reach the altitude of an orbiting spacecraft carrier is small enough that a simple hot oxygen cannon could provide it. This could simplify operations by eliminating some rocket motors, eliminating the need to reprocess steam to recover hydrogen and oxygen, and allowing the escape of a small portion of the relatively cheaper oxygen from the muzzle of a hot oxygen cannon instead of the escape of a small portion of the steam rocket exhaust from a LRSTO.

An Earth orbiting spacecraft carrier should cover the same ground track repeatedly to make use of the same ground bases. A first orbiting spacecraft carrier might be built from lunar materials in an orbit at an altitude first estimated at 561.5 km and an inclination of 50 degrees. At that altitude the spacecraft carrier would make 15 orbits per sidereal day and repeat the ground track every sidereal day, if it were not for precession of the orbital plane. For a prograde orbit the orbital plane regresses, which for the purpose of maintaining the same ground track has the same effect as an increase in the rotation rate of the Earth. So, the actual orbital altitude of the spacecraft carrier would need to be a little lower to repeat the 15 orbit ground track in a little less than a sidereal day. For an equatorial orbit at an altitude near 561 km the ground track of one sidereal orbit falls 6.7% short of the length of the whole circumference of the Earth. For a polar orbit that high, the ground track is 0.33% longer than the Earth's circumference. For the intermediate case of a 50 degree inclination the ground track of one orbit is only slightly shorter than the Earth's circumference. The length of ground track for 15 orbits can be estimated as 370 thousand miles, mostly over the ocean. A closer estimate of length is left as an exercise for the student. Expansion of the cargo and passenger capacity would involve increasing the number of parallel slotted tubes to receive shuttles in orbit and increasing the number of ground bases launching shuttles to the spacecraft carrier. Ground bases in the ocean would stand on stilts above mostly submerged flotation and stabilization ballast to maintain a steady position free from rolling with waves and storm winds. Standard marine propulsion could resist the motion of currents in any water too deep to use anchor cables. When there are twenty parallel tubes in the spacecraft carrier and 32 ground stations being fully utilized, it will be time to build an additional orbiting spacecraft carrier. Each new spacecraft carrier in the same orbital plane as the original would follow a new ground track and require new ground bases. Some ground bases would be in position to launch to two or more spacecraft carriers. When there are twelve spacecraft carriers, each with twenty parallel tubes, receiving launches from a full set of ground bases there will be plenty of capacity to reduce the population of the Earth by emigration and allow the Earth to become mostly park land and tourist facilities with reduced agricultural area for the reduced population. Tourists visiting Earth would come from the space habitats holding the vast majority of humanity.

Financial Feasibility

The financial feasibility of the above spacecraft carriers in orbit about Earth is mostly dependent upon the completion of 30 or 40 ten-gigawatt space based solar power satellites from lunar materials. This would open the door to the construction of a hundred or more additional SBSP satellites and the use of industrial facilities on Luna for other projects. While it is not a sufficient condition to assure the construction of spacecraft carriers about Earth, there is very little chance that spacecraft carriers will be built if the SBSP satellites are not built from lunar materials. What is needed is a large market for freight and/or passengers from Earth into orbit and dependable access to large amounts of reasonably low cost construction materials. Developing a program of building SBSP from lunar materials provides both.

The cost of emigration from Earth might be borne in part by consortiums that use the population of space habitats as labor for mining and processing operations in the asteroid belt and other places. These consortiums could profit from using emigrant labor and from using land on Earth for tourist facilities when it is sold by emigrants or their landlords. An emigrant from Earth might have raised the cost of his trip to orbit, sold his property on Earth and bought securities negotiable in extraterrestrial solar space. The cost of living in a space habitat might be covered by a contract for labor entered into in conjunction with completing a training and evaluation program on Earth.

There are some people who do not believe that this sort of transportation system is possible at any future time, without regard to any attempted lunar development as shown in the article, Future Work for NASA#LOSERS NASA cares about. Indeed, component technical developments that must be put together for this transportation system have never been tested near the scale at which they will be needed. In particular it may be untested whether a practical arrangement of magnets deployed near the wall of the tube will achieve sufficient braking deceleration at the required relative speed. There may be fewer technical difficulties with Wheel Launch to Orbit, although this method involves some heavier structure. The purpose of this article is not to predict what will be, but to show possibilities that seem to be within physical limits, so people will not give up trying to move our civilization off of Earth.


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References

  1. Eddy current brake at Wikipedia
  2. Inductrack at Wikipedia
  3. Active structure at Wikipedia
  4. Modeling and experimental modal analysis of active truss structure at IEEEXplore
  5. Adaptive Structures: Engineering Applications at Wiley
  6. VASIMR at Wikipedia
  7. magnetoplasmadynamic thruster at nasa.gov