Megastructures can speed up interstellar travel, but they have to be HUUUUGE

In this blog we consider using megastructures to speed up an interstellar ship and whether we can beat the estimates provided by rockets. Previously I spoke about rockets, (also on substack) which can reach on the order of 1-10%c and really struggle beyond that either due to the rocket equation, energy density or heat dissipation issues reducing the potential acceleration.

Megastructures need to be used in “established” systems only and have to be used to both speed up and slow down ships. Megastructures have very high theoretical limits, so I will attempt to give a sense of scale required to accelerate a ship around to 0.1c. I am going to consider the following structures: light or laser arrays, mass drivers, proton beams and giant slings (yes, really).

Light array or lasers.

A light array is a structure that focuses sunlight from a particular area into a beam that then drives the sail. It is similar to a laser, but can be a lot more efficient, since one doesn’t have to go through a an intermediate step of light->electricity -> light. This means the sail can be smaller and still receive a substantial amount of light.

We consider a focusing light array of A square meters than can exert all of its pressure onto a nearly perfectly reflective solar sail that moves a ship of mass M. The light array is at certain distance from the Sun, where the light exerts a certain amount of pressure. Around H portion of light is transferred to the surface as heat.

There is a big issue of this setup, which is light diffraction and dissipation over large distances. I am basically going to ignore this effect entirely and assume that we can solve this technologically by creating advanced lenses along the pathway which refocus the light into a point (this may or may not be possible).

The nice part of this setup is that the bigger the array, the more momentum one can transfer onto a ship. So, hypothetically you can move a ship arbitrarily fast if you focus enough of a stars energy onto its sail. The problem is once again heat dissipation. No surface is perfectly reflective. Some amount of light will always get inside the surface and become heat. While the amount of reflectivity of a surface is much higher than engine efficiencies, it is still not 100%.

If we wish to accelerate a ship of mass M at an acceleration of 1 G, the amount of total light power we would need is: (m * g * c) / 2 and the amount of heat needed to be dissipated is (m*g*c) *h /2.

Plugin in m = 1 kg, g = 10m/s^2 and h = 0.001 (a very optimistic reflective surface), we get heat = 1.5Mw

Once again, this is beyond anything we could plausibly expect radiators to handle, but if we drop acceleration to 0.01 g (0.1 m/s^2), we get a reasonable amount of 15 kw per kilogram of spaceship mass, which gets into a theoretically realistic range (see previous post).

The issue with such a small acceleration is that the amount of time that the light needs to be active becomes immense. The distance that this acceleration needs to be active is given by the formula of (v^2 / 2 a), which for v = 0.1c and a = 0.1m/s^2 is equal to (0.1 * 3 * 10^8) ^2 / (0.2) = 4.5 * 10^15 meters, which exactly 1000 times the distance between the sun and Neptune. This term v^2 / a shows up everywhere in the concept of megastructures and gives you a sense of the problem.

We don’t just need a hefty laser with a few lenses floating around in the solar system, we would need to extend this system of lasers and lenses far into interstellar space.

Another important concern is how large each laser need to be or consider how big the surface area needs to be to get this level of laser pressure from sunlight.

At m = 10 ^8 kg (around the size of an aircraft carrier) and acceleration of 0.01g (0.1ms^2), we need about 10^7 N of force. The solar pressure around earth is around 10^-5 N per square meter, which means we need about 10^12 square meters= 10^6 square kilometers. This means a laser or a solar lens would need to concentrate around 1000 by 1000 km worth of sunlight on an aircraft carrier sized ship to move it at around 0.01g. If we a just considering one specific mirror, this seems doable, however, this level of sunlight pressure needs to be maintained from a specific point in the solar system outwards till around 1000 times the distance to Neptune.

Mass drivers

Image is NOT to scale. For our purposes, the ring would has to be WAAY larger.

Mass drivers is basically “train tracks in space.” There are tons of potential designs for such train tracks. Coilguns have a nice property that they don’t create much heat in the ship and don’t have to deal with rail deformation. Railguns are another option, though large material and electrical pressures mean they are harder to keep using over and over again. Current maglevs are similar to coil guns, regular train tracks are more similar to railguns. The design space is rather large, so we’ll consider the general issues core to every design. Using many mass drivers is not constrained by heat, however it is constrained by the ability of the payload to handle high G forces.

If we consider a “train track” simply floating in space that needs to accelerate a spacecraft from 0 to 0.1c using 1g of acceleration, the train track needs to be: d = (v ^ 2 / 2 a) long, which is 10 times the distance between the Sun and Neptune. It’s extremely challenging to “mount” a continuous structure like this in the Solar system (and outside) without it getting deformed by diverging orbital speeds at different points of the system. It is plausible to use a “piece-wise” coilgun, where the pieces in separate orbits have to align only once during a flight and then diverge. It’s not really re-usable until the orbits converge again or are corrected by orbital maneuvers.

Note that the distance increases with the square of velocity, so getting 1% the speed of light needs a track 10 times less than the distance between Sun and Neptune. Getting higher speed requires to get not only the v^2 factor but also the hyperbolic relativistic adjustment factor.

If we want a stable megastructure in a star system, we need something circular: either an orbital ring or a ring world. While being circular solves the problem of the track not being long enough and not being stable enough to reuse, it creates a new problem of centripetal acceleration. In order to have a maximum centripetal acceleration equal to 1G, at the point of accelerating to 0.1c, the radius need to be (v^2 / a) (yes, here it is again) twice the length of a straight train track (20 times the sun/Neptune distance).

Note, that given the maximum centripetal acceleration of 1G and a maximum forward acceleration of 1G is additive. Given that they are orthogonal, this would already require 1.4G of force on a person.

So once, again, a megastructure *can* speed up a craft but it has to be HUGE.

Given how much the 1G constraint on the crew directly trades off against the length of the megastructure, one might ask: how could we get humans to endure more than 1G. There are lots of creative (and horrifying) ways to do so. Shorter people handle Gs better, as do muscular (but not too muscular) people (think Tolkien dwarfs). Specialized suits can aid certain organs in function, they might include pumps around calves and arms syncing to your heart to move blood). Exoskeletons with very soft padding can hold individual parts of you.

Submerging a person in a liquid (including filling their lungs) will also improve your ability to handle Gs. This was portrayed well in Neon Genesis Evangelion with a special liquid called LCL. And while its primary purpose was meant to be pilot syncing, it would have an massive added bonus of getting the pilot to withstand much higher Gs from flight or falls for longer. Atomic Rockets has a long list of ways that fiction and reality tried to improve human ability to handle G-forces.

Now, evolving a sub-race of humans to specialize in ring-world-assisted interstellar travel is an interesting idea. They might be space dwarfs, who easily breathe underwater because they are part fish. This may sound exciting to some, but may not be an ideal solution for lots of other reasons.

Proton beams

Proton beams are usually explored in sci-fi as potential ways to implement rockets or as potential weapons. However, they offer a number of advantages over the previous option which makes them one of the best megastructures for interstellar travel.

The setup is as follows: the megastructure shoots protons at the ship. The ship uses a positively charged magnet to “bounce” the protons off without touching them. This way, you can gain momentum WITHOUT any transfer of matter or heat. This means using external proton launchers doesn’t really have any of the major constraints of rockets or light. The only major issue is that the protons have to be much faster than your ship and will lose effectiveness if the speeds begin to close up.

Given that you don’t need to worry about heat, you can accelerate at 1G (or any acceleration really), which means mounting fewer stations than the light version.

While I say protons, in reality any atom core stripped of electrons can do. There are some tradeoffs involved in using heavier atoms, in that you can pack more mass densely in space than protons, but at the same time it’s harder to strip electrons out of an atom, the more they have. The exact tradeoffs are somewhat beyond the scope here.

Protons do suffer from electrostatic diffraction and that is a big problem if you are sending large beams of protons far away. However, there are a number really creative solutions to this problem: having more stations that hit the ship from slightly different angles, having stations pre-placed very close to the path of the spaceship also helps. Even using missile-like single-use mobile sub-stations, which use a shaped explosion to launch protons is also possible.

Proton launchers preplaced close to the path of the interstellar ship do resemble isolated coilgun sections. In both cases, the structures are using magnetic forces to move the ship without “touching” it. The advantages of proton launchers is that they don’t have to be as close to the ship and have much higher margins of error.

From an energy perspective, slower protons are more energy efficient than light. Light momentum and energy are related by p = E /c formula. For a non-relativistic proton, p = E / (s/2), meaning a proton at 0.1c is ~20 times more energy efficient at transferring momentum than light. As the proton becomes relativistic, it approaches the efficiency of the photon.

At this moment we don’t know how to accelerate protons in an energy cost-effective manner compared to focusing sunlight, so light looks more energy efficient with today’s tech, but this is very likely a solvable problem.

If the magnet shape gets very creative, you can potentially get more momentum out of a proton than it’s starting momentum if you send it backwards at a high speed. This effectively means “capturing a proton” temporarily inside the ship (but without touching it) and then accelerating it backwards.

Proton launchers can slow down a ship better than other structures as well. While a ring world can be used to slow down ship, this requires a really dangerous “docking step” where a 0.1c ship flying in a straight line is trying to attach itself to a static circular structure.

They also have the added bonus in scaling properly compared to a ring world. While you can’t really use a ring world until the entire ring is finished, proton launchers are useful in small numbers and can be combined with rockets. They are more useful than light / lasers because they don’t compete for the limited heat dissipation budget.

In short, given that proton (or other positively charged ions) launchers have a large number of advantages over other megastructures, I expect looking for “stay beams” of high-energy positively charged particles may be a fruitful endeavor in trying to find other civilizations.

Other, more fantastical megastructures considerations:

Helical or other unusual orbits.

Another way that we can squeeze better performance out of megastructures is unusual orbits. So far I have either considered “mostly straight” orbits, where spacecraft is pointed in a direction and accelerated along its velocity. Or we consider a mostly circular orbit on a stable megastructure. However, helical orbits where the spacecraft starts close to the sun and spins outwards as its accelerating can offer some advantages over either as the centripetal acceleration is slightly lower and you can get a tiny boost from the Sun keeping you in place. Those cannot be used with light, because light doesn’t have enough acceleration to perform these kinds of maneuvers.

It’s hard to imagine how to use this with ring worlds, as a helical megastructures might be very hard to keep gravitationaly stable (but there might be creative ways to do so). They can be used with proton launchers as they do have the required acceleration. This way, we can get slightly better performance while staying longer inside the solar system (which means energy is easier to obtain).

ChatGPT got a little stumpted trying to determine the optimal orbit based on a varying acceleration, but a couple estimates suggested it might be able to squeeze out between a 10%-20% boost over a circular orbit.

But another way to get a helical orbit is:

Giant slings

We have come to the most “vibe-engineered” part of the post. A sling is one of humanity’s oldest ways to throw rocks, what are the odds if history might rhyme and we see it come back as an megastructure. The setup is as follows: we have a rotating stellar body (let’s just say Neptune) and we attach a very very tough string to it. We can either have the space craft itself “pull” on the string, extending it as it goes. Or we can have the string already be in space being dragged by neptune’s spin and the spacecraft then accelerates along it. It would resemble a “space elevator” that instead of being straight, drags around the planet (potentially looping multiple times). In both cases you get a roughly helical orbit, which offers some advantages over a circular one. However, the advantages are not enough to get orders of magnitude and the string still needs to be on the order of 10-20 distances between Sun and Neptune to achieve the desired 0.1c. The main constraint here is material science, as the required strength of the string itself + spacecraft creates larger requirements compared to a “space elevator” and we don’t know how to build those either.

A common question / desire of the LW commenters on the previous post was: can we use megastructures to go all the way up to c? What if we are traveling intergalactically instead of interstellar and “top travel speed” is our main concern.

Well, your first problem is that slowing down from c is a massive challenge. Relativistic rocket equation means you can only max out a delta-v at c and that is only if your exhaust is near c, your mass ratio is enormous, which leaves little room for radiators that need to dump ever-increasing amounts of heat. If we drop the desired top speed to 0.5c, almost all these problems become manageable and, yes, you can *theoretically* slow down an anti-matter rocket with a very low acceleration (at most 10^-5g).

Speeding up all the way up to c is also very unlikely. Fundamentally, getting to 0.9c is already a challenge. A lot of relativistic effects kick in at that level. In addition to the already punishing v^2 factor, you need to integrate over the hyperbolic gamma.

​Protons have trouble catching up with you, meaning the amount of momentum one transfers per interaction is lower and the energy efficiency is correspondingly lower. Railgun tech depends on electricity going through the ship, which has lots of issues when trying to power something moving away from it at around c. Not to mention any friction forces dumping enormous amounts of heat on both the megastrucutre and the ship. Coilgun megastructures offer the “cleanest” acceleration, but the length of such megastructures begin to approach 1 light-year if you want to get to 0.9c with 1g acceleration felt by the crew. The amount of time needed to build such a megastructure (and keep it stable) is a subject for another post.