# 61 Virginis Mission Design: Solar System-sized Rail Gun for Ship Acceleration?

In this answer to another question, solar system-scale rail gun acceleration (and deceleration) was brought up as an alternative, and I found this intriguing. It's worth another question at least.

Basic Idea

In a mass accelerator (rail gun), an object is drawn through a ring using an electromagnet, the ring is turned off, and the accelerated object heads off to the next ring for another boost. In space (essentially zero gee), this would mean that the object would experience acceleration while it was within the range of effect of the ring and coast between rings.

Acceleration Range

I understand the inverse square law, where $I = 1/r^2$, however I don't understand how that relates to how well a giant electromagnet ring is going to effectively pull on an object (say 100 tonnes) that's moving at some fraction of $c$ toward it. Each successive ring is going to have less time to pull on the object, and thereby the speed gain incremental is going to be smaller each time.

Acceleration Force

Presuming you could get a powerful enough magnetic ring to do the job, human passengers could stand high $g$ acceleration for brief periods of time ($10g$ for several minutes, $2g$ for 24 hours). If the average effect time from the Acceleration Range problem above were one second, I presume each ring would only add 9.8 m/s to the speed, which means it would take a lot of rings to get up to a useful fraction of $c$.

Number of Rings

So, how many rings would it take to accelerate an object to greater than $.5c$? How about $.7c$? How much acceleration time would each ring have on the object? Let's put a limit of $10g$ for five minutes and $2g$ for 24 hours, with some sort of curve between those two values.

Travel Time

If you're quickly boosting to $.5c$, then coasting for a while, then decelerating at the same rate on the other end, I presume a $27.9ly$ trip would take somewhere on the order of 56 years, and at $.7c$ it would take around 40 years. Is this correct?

I'm aware there are lots of questions and lots of variables here. I think, though, that the problem space is boxed in enough for a creative answer to come out. My apologies if this isn't the case.

• A nitpick. You are almost certainly talking about a coilgun (or Gauss gun) rather than a railgun. – WhatRoughBeast Apr 6 '16 at 2:52
• Per the answer below, I'm not talking about any of it. But yeah, you're right, coil gun. – J.D. Ray Apr 6 '16 at 15:08

The inverse square law will apply no matter how great the speed, because as the payload gets closer to a powered ring, the pull (and hence the acceleration) gets stronger. It's true that as the payload accelerates, each ring will affect the payload for less time, and thus impart less acceleration. But the inverse square law still holds, because although the time for each acceleration drops, the distances remain the same.

Now, your question contains a contradiction; you first say each successive ring would have less time to pull on the payload, suggesting a fixed distance between the rings; but then you say each acceleration toward a ring will impart the same 9.8 m/s to the speed. In the latter case, the spacing between the rings would increase, but the required power for each successive ring would go up substantially.

I'm going to assume the former case is true, because the latter case would require exponentially increasing levels of power, which at some point would become impractical for any conceivable engineering project.

So, let's take the theoretical and simple case -- repeat, theoretical (not practical) case: The rings are 9.8 meters apart, the acceleration is 2g (19.62 m/s^2), and the exit velocity is 0.7c, or (0.7 x 299,800,000 meters/second =) 209,900,000 m/s. Ignoring relativistic effects, that gives us* a liner accelerator 1,122,783,127,661.8 km (0.11867827023672889 light-years) in length, and a transit time of 2971:44 hrs:minutes, or 123 days + 19 hrs 44 minutes.

How many rings? Well, it's 102.04 rings per kilometer. That's a lot of rings!

Now, for practical matters... aside from the obviously enormous engineering problem of constructing anything that long, even in deep space... is the fact that as the payload gets up to very high speeds, switching the electromagnets off at the precise instant the payload passes becomes increasingly more difficult. In fact, realistically, I think the magnetic field wouldn't die away instantly; it would persist for some small fraction of a second. Bottom line: The faster the payload goes, the less effect the linear cannon is going to have. As the payload goes faster and faster, the acceleration will drop away towards zero.

The law of diminishing returns suggests to me that the actual exit speed is likely to be only a fraction of what the theoretical speed should be. Just what fraction? I couldn't even give an educated guess, but my wild guess is less than 1/4 of the theoretical speed.

As an alternative, I'd suggest using a lightsail and laser cannons for acceleration, as that wouldn't have nearly as bad a (practical) dropoff in acceleration as the payload accelerates to very high speeds. It also means you don't have to build a 1.1 trillion kilometer long liner accelerator!

*using the online calculator at http://keisan.casio.com/exec/system/1224829579

Travel time: Obviously, at 0.7 lightspeed, the payload will travel at 0.7 light-years per year, or 27.9 ly in 39.86 years; slightly longer due to acceleration and deceleration times at the ends, so yes, as you say, a stationary observer would see the trip taking about 40 years travel time.

However, at a speed of 0.7 lightspeed, the time dilation is significant. For someone traveling in the capsule, the trip would take (39.86 / 1.4 =) 28.47 years, plus the times for acceleration and deceleration at the ends.

• Lasers and lightsails is where this whole thing started when someone mentioned linear accelerators. It seemed worth investigating. Thanks for the calculator link. – J.D. Ray Apr 6 '16 at 2:02
• iirc the gauss/coil guns (accelerators with the power switching problem) have a practical upper limit of exit velocity. This was less than Earth's orbital velocity and may have been around 6-7 km/sec (but I don't recall the source). Railguns, which use a different mechanism for imparting acceleration and don't do switching, don't have the same limit, however, they are far more destructive to the launcher. – Jim2B Apr 7 '16 at 5:29
• I mentioned in a comment on this question that there's another way a coilgun might be used--instead of accelerating the craft itself, accelerate a stream of small pellets (which can be small in mass and therefore gain a larger velocity boost from each ring) to push along a starship in a similar way to pushing a starship with photons from a laser. There's some discussion of this here and here. – Hypnosifl Apr 7 '16 at 19:10