Is it possible to get a spacecraft into earth orbit using Linear Eddy Current Braking on an orbital runway?

Question

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/

Answer 1

https://lifeboat.com/em/arrestor.pdf

"An Orbiting Magnetic Arrest System for Rocket-Free Transportation to Earth Orbit"

If transport to earth orbit could be decoupled into the two separate tasks of reaching orbital altitude and maintaining an orbit, rocket-free transportation to orbit would be possible with straightforward improvements to existing technology. The capability to achieve the first task, reaching orbital altitude, has been demonstrated by several cannon-launch systems. The second task, maintaining an orbit by compensating for atmospheric drag and other disturbances, can be performed by available low power, high-efficiency propulsion methods, such as plasma or ion thrusters. However, a link between these two tasks is required, namely, capturing a payload at orbital altitude and accelerating it to orbital speed. A magnetic arrest system can fulfill this critical role.

and otherwise search the writings of Phil T. Putman, for example:

"Capture Dynamics of Coaxial Magnetic Brakes", https://sci-hub.se/10.1109/ELT.2008.20

D. Centering force In order for capture of a hypervelocity projectile by a magnetic brake to be nondestructive, the projectile must not contact the walls of the catch tube. Fortunately, a centering force is also generated in the coaxial brake geometry

This thing about a centering force generated by coaxial geometry is a key reason to consider a coaxial (tube) design. Putnam also highlights the benefits of using a passive tube with a magnet on the moving particle:

for the method based on a projectile-mounted magnet, the catch tube uses only passive components, resulting in a nondestructive hypervelocity brake with minimal initial and operating costs.

Answer 2

I'm just going to add some considerations about tidal forces, thanks to @Steve Linton for mentioning this:

Crushed by the moon

The tidal force (https://en.wikipedia.org/wiki/Tidal_force) from the moon is rather small, about $10^{-12} m/s^2/m$. This is not a serious problem.

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Crushed by the spacecraft

When a spacecraft lands on the runway, it exerts various forces. In particular there is a braking force, and for longer runways the spacecraft needs to be supported against gravity as well. For long runways, buckling is a problem. Also it is problematic to deal with supersonic and transsonic ships (see below).

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Rigid runways

These considerations suggest that the runway should be made rigid. A 100km long runway is probably too long. Cutting the length by 3 to 30km would reduce the effect of the curvature of earth to be negligible (the deviation between a chord and a circular arc of 30km is a mere 16 meters). 30km increases the acceleration that the spacecraft feels:

$a = v^2/2s = 7800^2/(2 × 30,000) ≈ 1000 m/s^2 $

$1000 m/s^2$, or $100g$ was used for the Sprint Missile which carried a relativelty delicate nuclear warhead, so it is reasonable to assume that a spacecraft can be built to withstand such an acceleration without causing large mass penalties. Indeed, the quicklaunch project planned to have an acceleration of 1800g for a projectile that included a rocket motor.

A long pipe can be rigidified by adding a ring at the centre and cables - the 1km long quicklaunch gun (under the sea in this case) looked like this:

30 km will be more difficult than 1km, but in space some aspects of structures are easier, e.g. vastly smaller air resistance, and spacecraft landing decelleration will be 0.3g. Aluminium alloys are capable of withstanding the forces involved so the structure should hold as long as it is rigid enough to not buckle. However a greater safety margin might be needed, increasing the mass from 300x to 1000x the spacecraft mass.

There is a tradeoff here - if the runway is shorter, it can be less massive without being crushed or buckling. However a shorter runway makes it harder to build an efficient spacecraft to interact with it.

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Destroyed by shockwaves

Another problem which perhaps wasn't immediately obvious when considering the design is that the spacecraft in the reference design travels at $7800 m/s$ with respect to the runway, which is greater than the speed of sound in aluminium ($6300 m/s$).

If the spacecraft is supersonic or transsonic with respect to the metal of the runway, harmful shockwaves might build up in front of it. It is not clear to me whether this is a "game over" problem.

There is also the speed of sound of transverse waves in aluminum, about $3000 m/s$.

Beryllium has better performance in these respects - $12800 m/s$ and $8000 m/s$ respectively. But sourcing a large amount of beryllium could be costly - 1 ton of beryllium costs \$500,000 (meaning that \$1 billion buys you 2000 tons of it... though this is more than the current annual production of beryllium!).

Answer 3

Notes On Prior Art

I have had this concept up at wikiversity for a while now, and recently initiated a conversation with the OP on twitter, which is how this question got started.

What inspired me to start thinking about it at first was a reddit comment from Dani Eder about the possibility of landing on the Moon using a metal coated track and magnetic induction + joule heating (which is sometimes referred to as magnetic friction, and is also the principle of an Eddy Current Brake). This got me thinking about ways to more economically land on asteroids by using high tensile strength cables secured to them by harpoon, or some such mechanism, with a metal coating to enable eddy current braking. I realized the logical place to use this is earth orbit, about halfway through writing the wikiversity page.

Since then a few people mentioned Kingsbury and Arnold as having the same basic idea, but I could not locate an issue of the article, and the only summaries I could find referred to that as an orbital coilgun. Recently, I did find a copy of the article here, and was able to confirm my suspicion that they indeed were talking about a coilgun that catches and fires craft, not a simple eddy current track. I believe their version suffers from too much complexity.

Others here have mentioned similar looking ideas. The Eddy Current Brake to Lunar Orbit from Lunarpedia seems like the same idea, but for lunar orbit.

What to Call It

This has been put through a lot of evolution because a lot of people seem to have originated the idea separately, and it isn't really a popular enough idea to have a common term yet. I was calling this a Hypervelocity Landing Track at one point (HLT-LEO for the low earth orbit version), but 'Space Runway' also fits. It could also be an Orbital Track (analogous to Birch's Orbital Ring). Roger Arnold and Donald Kingsbury called it a Spaceport, and Phil T. Putman called it an Arrestor. It can also be considered a soft version of Edward F. Marwick's idea of crashportation.

How Much Mass To Bootstrap From?

I think the 5000 ton starting point in the OP (note: 100x smaller than Arnold & Kingsbury) is probably too big of a system to attract much interest, but this concept can be scaled down considerably from there. It could be as little as 100 tons, or even 1 ton. The main reason you wouldn't go 1 ton would be because payloads of a kilogram or so are hard to punch through the atmosphere.

On the other hand, the OP makes a good point that recent advances in reusable rockets do lower the cost for a 5000-ton structure substantially. So a system this large is not inconceivable, and may make more economic sense for a company like SpaceX.

How Should It Be Shaped?

One relatively simple idea is to use a tube. The craft flies into the tube, and electromagnetic induction causes it to be repelled from the walls. Another way would be to have a magnetic track that the craft wraps a tube around. Alternately, it may be possible to use a nonmagnetic metal track which the craft extends coils around with in a u-shape (upside-down U,so that gravity pushes it in tension with the magnetic field).

One of the most interesting ideas could be a linear swarm of satellites that acts as a track, without being physically connected. The issue here might be that they need to not be spaced too far apart, as the craft would not be under acceleration when its coils are not interacting with anything. One way to work around this would be to make the coils long in the direction of travel. So picture a flat sheet of coils that is bent into an upside down U, long enough that it is always covering at least one satellite.

The main advantage of swarm is a "constructionless" bootstrapping method. You can start with 1000 satellites, then over the course of 100 days with 10 launches per day, increase the swarm to double, without having to solve problems of space based construction (welding and so forth). The components would be equipped with programmable ion thrusters, and would fly themselves into place.

Even if we assume a tube shape, the track can be segmented into many tubes positioned end-to-end, with just enough separation to prevent them from colliding before ion thrusters redirect them to their original positions. This would be one way to approach issues having to do with the speed of sound in aluminum (6700 m/s) being lower than the initial difference in velocity (7800 m/s).

Another way to configure the track would be as a tensegrity structure. The speed of sound/mechanical forces through high-strength fibers under tension tends to be higher than orbital velocity, so the reduction in tension caused by the craft inertia being transferred to the early part of the track gets picked up by the later part of the track, distributing the momentum more quickly.

Should Superconductors be Used?

According to Lofstrom, superconductors are difficult to deal with. So while they may be useful in some of the larger scale designs, I think this prohibits smaller scale designs and probably introduces unneeded engineering complexity. But without them, there's the question of how to make the magnetic field, and whether you have to use permanent magnets (which perhaps doesn't work so well for some of the design possibilities above).

This is something we may want to look at in terms of how to engineer coils that can handle high heats, without getting too expensive in terms of mass requirements. Note that they are self powering once the induction start to kick in. Tungsten could perhaps conduct electricity at high enough temperatures to conduct or radiate away quickly. Another possible approach would be using 'coils' consisting of plasma, as the moving particles do not need to be electrons.

High temperature coils would likely need to not be inside the spacecraft, so I am thinking along the lines of a carriage that rides along a track with the spacecraft hanging down from it.

Should The Craft Be Moving Already?

This concept can work with the craft being stationary with respect to the earth at the point of intercept. However, as Kingsbury and Arnold point out, most of the kinetic energy is from the highest difference in velocity. Their paper suggests intercepting with half of the orbital velocity already added by the 'lighter' (rocket). This is consistent with some of the realistic projectile launchers as well. Half of orbital velocity costs 1/4th the energy to reach. Moreover, a craft moving at around 4000 m/s rather than 8000 m/s with respect to the track is moving at a subsonic speed for aluminum, and the track length could be 1/4th as long. This also allows the use of coils on the craft (or carriage that it is attached to) which do not need to handle as high of current load. The disadvantage is that this doesn't give as radical gains in terms of greater load that can be boosted per rocket launch (more like 4x instead of 15-20x).

Answer 4

This is one of a whole bunch of space launch ideas that all involve "loading up" a massive orbiting object of some kind with energy and angular momentum. Then you somehow attach it to a relatively small payload of some kind and transfer angular momentum and energy to the payload. As a rather extreme example, you could put a very small payload into orbit by simply launching it vertically from Earth so that it was in front of the ISS at just the right moment. It would end up orbiting, embedded in the meteorite shielding on the front of the ISS, which would have slowed down minutely. Generally we want something a little gentler than this, but from a physics perspective it's basically the same.

A variant are structures like a pinwheel or space elevator, that use a large rotating structure to allow you to dock without violence.

You don't get something for nothing, of course, you either need to reboost the structure, or capture incoming payloads going faster than orbital velocity from time to time or your structure deorbits.

From an engineering standpoint, the magnetic brake here seems quite feasible. The track might need to cool down for a while after each capture, as quite a bit of energy has been dissipated in it. The initial rendezvous would obviously be a bit delicate, but I think the big problem is likely to be stability. A structure that long is far from rigid, and I'm not sure what keeps it stretched out. Apart from the forces from its operation, lunar and solar tides will also be acting on it. If it gets even slightly out of shape it will either lose contact with the payload, or collide with it, neither of which is good.

Answer 5

Just posting an important update to this question. It turns out that there is some prior art here, but it is extremely well hidden.

The concept of an orbiting ring magnetically braking payloads was first conceived (as far as I know) in 1979 by Arnold and Kingsbury in "The Spaceport, Part I," Analog Science Fiction/Science Fact, Vol. 99, No. 11, November 1979, pp. 48-67 and "The Spaceport, Part II," Analog Science Fiction/Science Fact, Vol. 99, No. 12, December 1979, pp. 60-77.

Answer 6

In response to two of your questions:

Is it naturally stable? No. Tidal forces will tend to torque anything in orbit so that its long axis points in the radial direction; in order to keep your launch ribbon horizontal, you'll need active measures to counteract this. Things get worse when you realize that in the 25 seconds you need for your spaceship to get up to orbital velocity, it'll fall about 3000 meters. Your launch ribbon needs to be tilted, which will make the torque worse.

Could humans use it? No. See that 3000-meter fall for the high-acceleration version? A human-rated version, with its lower acceleration, would involve a fall of 160,000 meters before the spaceship gets up to orbital velocity, more than halfway back to Earth.

Answer 7

Could humans use it? Unlikely, but maybe. At high accelerations, what ends up killing people is the difference in density between cavities like your lungs and the rest of your body. People have theorized that with liquid breathing, humans could survive continuous accelerations of up to 1000G.

Answer 8

It is a dead idea.

1. Such a runaway has insane cost.
2. That runaway must have power.
   1. electromagnets.
   2. cooling system.
3. It has to have onboard thrusters & fuel to stabilize its orbit + keep in mind Newton's third law.
4. Orbital tug on ion thrusters o/& chemical thrusters with refueling makes a way more efficient alternative.