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The "Space Runway"

[I have slightly edited this to clarify some issues that have been raised]

Luke Parrish mentioned an unusual and novel space launch method to me. The idea is to get a spacecraft from ~0 velocity at ~300km altitude to full orbital velocity at the same altitude.

A 1km-100km long conductive ribbon, rod or tube (the "space runway" or just "runway") is placed in a circular low orbit around earth, with the length of the runway exactly along the orbital path.

A spacecraft equipped with a powerful electromagnet precisely coincides with the front of the runway, passing slightly below it (or within it for a tube). The spacecraft initially has 0 velocity. The plan is to use the runway to transfer momentum to the spacecraft using magnetic forces.

Precise coincidence

Reliably hitting a target with just a few tens of meters of error at 8 km/s relative velocity seems like a tall order. However it can be done to an astonishing degree of accuracy - rockets have a trajectory error of about 1 m/s, and thrusters can make up the difference. In space objects travel on very predictable trajectories.

Eddy Currents

The linear eddy current braking effect will cause the craft to accelerate. Over a period of approximately 0.25-25 seconds our craft is accelerated to orbital speed. This effect is simple and doesn't require the runway to have any active components. It's just a piece of metal, electromagnetism does the work for us.

The craft is now in orbit.

Mass ratio

The runway loses an equal and opposite amount of momentum to what the ship gained. As with other space structures the runway has an efficient way to recover its speed, such as very high ISP ion engines and solar panels. The maximum velocity loss that the runway can withstand in LEO without deorbiting rapidly is about 50 m/s, therefore the runway mass must be at least $7800/50 ≈ 150$ times the spacecraft mass.

There are other reasons that the runway must mass a lot more than the spacecraft. The interaction loses kinetic energy equal to the KE of the spacecraft, which is wasted as heat - 30MJ/kg, or about 30 times the energy to melt aluminium. Obviously this needs to be spread out over a large structure. With a mass ratio of 150, the temperature increase is 200°C.

Finally one does not want one's runway to experience a large g-force. Making it more massive reduces the g-force it experiences.

Spacecraft recovery

Once the spacecraft has delivered its cargo it is stuck in orbit; the spacecraft has expensive components (the magnet(s) and engines) so one wants to reuse it. It can either reenter using aerobraking, or use a second space runway a further up travelling retrograde.

How strong does the field need to be?

Eddy current braking is proportional to the relative speed, and to the magnetic field strength squared, something like (1):

$F ≈ Vol_{track} × B^2 × σ × v$

Where $Vol_{track}$ is the volume of runway affected by the field. We assume the spacecraft has a density of $1000 kg/m^3$.

$a_{spacecraft }$

$ = F/M_{spacecraft } $

$ = F/(ρ_{spacecraft } × Vol_{spacecraft })$

$ ≈ Vol_{track}/Vol_{spacecraft} × 1/ρ_{spacecraft } × B^2 × σ × v$

therefore:

$ B^2 ≈ a_{spacecraft } × ρ_{spacecraft } / ( σ × v × Vol_{track}/Vol_{spacecraft }) $

For a 30g acceleration (300 m/s/s), on an aluminium runway ($σ = 3.77×10^7$) with $Vol_{track}/Vol_{spacecraft })$ = $10^{-2}$ (the volume of runway affected by the field is 1% of the spacecraft's volume) at a 7800 m/sec relative speed we would need:

$ B^2 ≈ 300 × 1000 /( 37700000 × 7800 × 0.01 ) $

$B ≈ 0.01$ Tesla

This is surprisingly achievable. A superconducting electromagnet could easily reach 0.01 Tesla (the state of the art systems are 20 Tesla). As the relative velocity is reduced, either B would need to increase or $ Vol_{track}$ would need to increase, for example by the runway getting thicker and wider, with a linear increase in cross-section. We can solve for B at 500 m/s relative speed:

$B^2 ≈ 300 × 1000 /( 37700000 × 500 × 0.01 ) $

$B ≈ 0.04$ Tesla

Can it be controlled?

Open question. Can the spacecraft be precisely controlled so that it is close enough to the runway to work, but never collides? Can we keep the spacecraft stable in all five other axes while it is accelerated?

At this point we are pushed towards the tube-runway. The spacecraft is naturally stable inside the tube due to the eddy current forces stabilizing it in all directions other than along the tube axis.

It is of course very important that the spacecraft doesn't hit the runway. It must be able to reliably get close enough to magnetically attach, but not actually hit the ribbon/tube. Making the system reliable, even if there is an electronic failure somewhere is critical. Taking into account the need for very high reliability may affect the design significantly compared to a design that assumes away the coincidence problem. For example, in a tube-runway, a significant amount of mass might be dedicated to widening the front to add margin for error.

Levitating the spacecraft under the track

One possibility for a ribbon-like runway is to make it slightly ferromagnetic, so the electromagnet provides an upward force to counteract gravity and effectively levitate the spacecraft below the runway. Calculation of the force here is complicated, but it is clear that the distance separating the spacecraft and the track would need to be < size of the spacecraft's electromagnet.

Is it naturally stable?

Open question.

No. The runway itself is in unstable equilibrium in orbit since it is long and thin, and gravity gradient makes objects in orbit want to have their long axis oriented radially. This instability can be solved by varying the direction of thrust from the runway's engines.

When the spacecraft is landing or simply due to lunar tidal forces, the runway will feel a compressive force. This depends on the mass ratio and length, longer is good for the force from the spacecraft, but bad for the tidal force (which grows as $length^2$). In order to resist crushing the runway must be rigid, and in order to resist buckling it must have some wider parts (e.g. rings and guy wires).

Could humans use it?

No! The g-forces are too big/humans are too squishy and a runway long enough for humans (700km) would easily be ripped apart by the moon's tides. However the primary task any such system is to haul truly massive amounts of cargo up.

Can it scale up or bootstrap itself?

The system might be able to bootstrap by adding more mass. As the runway gets larger it can accommodate larger spacecraft to carry up more track materials, propulsion and solar panels, which can in turn build a bigger runway.

Without going into too many details, the growth of the runway will be exponential. Assuming we use Falcon Heavy in reusable mode (35 metric ton payload), the bootstrap will start at 5000 tons and end when the rocket doesn't need to add any radial velocity (about 750 tons to low earth altitude, 0 speed), at which point the runway will be about 150,000 tons

Since smaller rockets are not actually cheaper than bigger ones at the moment (especially in bulk quantities), there is no point in starting smaller than 5000 tons for this or any other launch assist system in orbit.

The runway could continue to grow up to e.g. a megaton if enough Falcon Heavy launches (1300) were made to keep feeding it mass. The runway can also be made safer as it gets more massive, with a larger front area making accidents less likely and mitigating their effects.

What's the endgame?

If a rocket can be designed that gets 100 or so reuses (Falcon 9/Heavy), then the cost to get to orbit falls to a small multiple of the cost of the fuel for the rocket, which using the runway gives ~$0.25 per kg to orbit, albeit with some g-force and size constraints.

Without the runway the \$200,000 of fuel for the FH only delivers 35 tons, and an upper stage is expended per 35 ton load. Even in bulk (assume an upper stage is $2 million in bulk) this is about \$100 per kilogram to orbit.

Clearly the space runway is capable of radically reducing the cost of space access.

Would resources be better spent on a bolo/rotating tether/nonrotating tether?

Perhaps. Tethers are not able to provide the full delta-v to orbit, so their benefits are much lower. Also as they have been investigated further more subtle problems with them have come to light, such as the need for very large safety factors for the cable.

Nonrotating (gravity gradient) tethers have similar materials-based problems to rotating ones. The materials just aren't good enough to achieve orbital speed. The runway doesn't have this problem, it can go all the way.

Would it work?

Please let me know in an answer if you can show that this system is impossible or impractical, or if you can confirm that the concept is sound.

1: https://www.physicsforums.com/threads/calculating-the-magnitude-of-eddy-currents-retarding-force.822714/