# What would be the size of the biggest possible space ship? [closed]

In a story I am making, I want the main character to face the largest government organisation. To make them seem more intimidating, I need the biggest ship possible. So, what would be the maximum space ship size, with it being structurally stable?

Tech available would be around the time before (but not of) FTL drives. They can go near the speed of light, but not faster yet. Also, no "Ancients" involved in this one (except for maybe power source, if it is needed to power the giant).

## closed as too broad by ArtOfCode, bowlturner, March Ho, James♦, congusbongusJan 27 '15 at 6:17

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• Biggest space ship under what constraints? If I slap an ion drive onto Jupiter using a power source from the ancients, does that count as a space ship? With enough materials, I can build a Shkadov thruster around the biggest star i can find, but I'm not sure that's what you're looking for, either. – ckersch Jan 26 '15 at 19:17
• Reconsider the size as intimidation thing. The larger you build it, the bigger the target :-) – jamesqf Jan 27 '15 at 4:00
• Seehttps://www.google.es/search?q=night+sky+from+another+planet&biw=1024&bih=611&source=lnms&tbm=isch&sa=X&ei=WlHKVNXeEsWtU7m9gPgG&ved=0CAYQ_AUoAQ#tbm=isch&q=largest+science+fiction+space+ships – Barnaby Jan 29 '15 at 15:35
• If you can and do, survive going .9c, making it out of handwavium is on the table. So the real question is what safety factor should you scale back to, from a ship slightly less than the mass of a black hole? ;p – Mazura Feb 14 '18 at 21:52
• May I remind you that a huge spaceship is not required to make a government or an organization intimidating. There are much more subtle and scary ways to accomplish that... – MauganRa Feb 18 '18 at 21:37

## That's No Moon, That's a Space Station Ship!

The first fundamental limitation to a space vessel's size is material strength. Beyond a certain point, whatever material your ship is made of will collapse under its own weight without exotic active materials.

We can do some estimates using the Lane-Emden equation to predict the stresses the spacecraft will have to endure. I assume a spherical, incompressible ($n=0$) spacecraft in a vacuum. The math is a bit complex but the results are simple. Given a density $\rho$ and a maximum stress $\sigma$ the maximum size of the spacecraft is: $$M=\sqrt{\frac{6\sigma^3}{\pi G^3\rho^4}} \\ R=\sqrt{\frac{3\sigma}{2\pi G\rho^2}}$$ Let's try three different materials:

• 4142 carbon alloy steel: $\rho=7900~\text{kg}/\text{m}^3,\ \sigma=85~\text{ksi}$
• 6061 aluminium alloy: $\rho=2700~\text{kg}/\text{m}^3,\ \sigma=35~\text{ksi}$
• Grade 5 titanium: $\rho=4400~\text{kg}/\text{m}^3,\ \sigma=155~\text{ksi}$

Only a portion of the spacecraft will consist of structure, let's say $5\%$ of the total volume. We will multiply both the density and the yield strength by this fraction.

• Steel: $M=0.035~\text{M}_\text{Moon},\ R=0.67~\text{R}_\text{Moon}$
• Aluminium: $M=0.079~\text{M}_\text{Moon},\ R=1.3~\text{R}_\text{Moon}$
• Titanium: $M=0.28~\text{M}_\text{Moon},\ R=1.6~\text{R}_\text{Moon}$

We can see that from a mechanical standpoint a spaceship can be almost unimaginably huge, comparable to the size of the Moon (although much less dense). The gravity inside the spacecraft increases proportionally to the distance from the center, reaching a maximum at the surface of: $$g=\frac{GM}{R^2}=\sqrt{\frac{8\pi G\sigma}{3}}$$ For our test spacecraft the surface gravities are on $0.013~g$, $0.008~g$, and $0.018~g$, so you'll still be pretty much floating on the inside.

## I Feel the Need... the Need for Speed!

The second limitation is power. If a moon-size spacecraft is insulated well enough that its surface is a frosty $-200~^\circ C$, then the power requirement to maintain the internal temperature due to heat loss is about $60~\text{TW}$, or about four times global energy consumption.

However, this pales in comparison to the energy needed to move around the solar system. Moving a tenth-moon-mass spacecraft from Earth orbit to Mars orbit will require at least $2\times 10^{30}~\text{J}$ of energy (the Sun's entire energy output for two hours). Even assuming $99\%$ efficiency, that the energy is slowly applied over a year, and radiators cover the entire surface of the spacecraft, you'd need to maintain a temperature of $4200~\text{K}$ to reject the waste heat.

Doing the math (again, too complicated to waste space here) we find that the maximum size for a spacecraft radiating at a given temperature and power is: $$M=\frac{36\pi\sigma^3 T^{12}}{D^3\rho^2}\\ R=\frac{3\sigma T^4}{D\rho}$$ Where $\sigma$ is now the Stefan-Boltzmann constant, not stress, and $D$ is the waste power generated per unit mass. In our case (a year-long trip to Mars using a $99\%$-efficient reactionless drive) $D\approx 0.1~\text{W}/\text{kg}$ and $\rho\approx 200~\text{kg}/\text{m}^3$. Assuming we maintain a comfortable exterior temperature of $300~\text{K}$, this gives us: $$M=270\,000~\text{t} \\ R=70~\text{m}=230~\text{ft}$$ This is actually a minimum estimate of the maximum size, since a sphere is the least-efficiently radiating shape. You can get much larger by extending radiative surfaces out from your craft. As a rule of thumb, at the energy density mentioned above you need one square meter of radiator for every five tonnes of spacecraft, or one square foot for every half-ton. (Remember if you have "wings" that radiate on both sides the area is doubled!)

So while a spacecraft could structurally be the size of a small moon, the energy requirements would make it impossible to manage. You should be much safer with a ship in the million- to billion-tonne range, with a size from a few hundred meters to a few kilometers: think battlestar size.

• While your math looks right (and I am no expert), there must be something missing b/c we can't even build a 100km tether for a space elevator. You suggest it would be possible to build a titanium ship that is 5,560 km long. If the math is sound it must only be possible if in the middle of deep space and never moved. Like a very delicate flower. Any external stresses would damage the structure. Not sure how to adjust you formulation, but at the very least I also suspect 5% is an underestimation since the mass the of people and objects inside would also add a substantial amount of stress. – trans Mar 18 '15 at 19:14
• @trans, You are correct, looking back on this I see some mistakes. If we use 5% strength (fraction of cross-section that is load bearing) and 20% density (fraction of volume which is filled), we reduce the mass by 1/16 and the size by 1/4. Also, I'm using the upper limit/yield stress, so you are correct that it would be fragile. But, note that materials are generally stronger under compression than tension, and the the actual gravity of the ship is very low, so the large size does make sense. They wouldn't be able to approach a planet due to the tidal forces, however. – 2012rcampion Mar 18 '15 at 19:57
• Did you ever read Mutineers Moon? – Christian Sauer Feb 25 '17 at 12:06
• A space elevator is being pulled on by earths gravity and be much longer than 100km @trans – Donald Hobson Jul 24 '17 at 19:39

There is no upper limit other than those given by the propulsion technology available and the ability of your dockyards to build. Size would have effects on the geometry and design of the ship.

The reason for this that without gravity, atmosphere or other external factors there are no real forces other than the thrust of the engines the spaceship needs to be rigid against. And those forces are part of the design, so it would be a question of what compromises are you willing to make, not an absolute upper limit. So your technology might put a limit on mass per engine before you start experiencing structural issues. So you increase the number of engines, which makes your ship "flatter" and has effects on manoeuvrability... and so on.

Even tidal effects on orbit, which might be significant for a large ship, would be simply design parameters. Probably they'd simply give up on orbital manoeuvres? Closest thing to an absolute limit I can think of is that a massive enough ship would have a non-trivial gravity field of its own. This is not a problem by itself since you could build the ship to be in hydrostatic equilibrium. But if the ship uses a propellant based propulsion, significant part of that mass would be transient. At that point I think people would just build more ships instead of bigger ones.

Also, given the presumed difficulties of radiating heat in space, a very large ship would probably have very large area for its mass. So the construction might be something like a bubble. Discrete modules kept together by cables, connected by flexible tubes and pushed apart by pneumatics. A structure like that could be very large. The modular construction would make it reasonably simple to build in any size as well.

I think that there probably is some specific technology you want to use that imposes a much stricter size limit, though.

• Presumably there's a size limit where the gravity of the ship itself would overwhelm the material it's constructed of, which would be the final limit - build bigger then that and it all collapses into itself. Although I suspect there might be a sufficiently light/strong material that it would overcome that and you could just build to an indefinite size. – Dan Smolinske Jan 26 '15 at 19:26
• @DanSmolinske Sure, but as I said (3rd paragraph) that is solvable in itself since the "collapsed" state would be stable and could be "built around". Of course having that gravity core would kill your mass to thrust ratio... But I honestly think people would give up on making bigger ships for other reasons before that is an issue. I probably should have said it outright in the answer, but basically I think the bigger ships will need to have lower density in order to have the surface area to radiate all their waste heat. If that is true, the "gravitic collapse" would not be a problem. – Ville Niemi Jan 26 '15 at 19:35
• @DanSmolinske Because the waste heat would scale with "active" volume, which scales similar to mass. So area would scale roughly the same speed as the mass, probably by having more empty space in the core. Which would keep the gravity roughly constant regardless of size. I might be wrong about this as I really don't think anyone would build ships large enough for this to crop up, so I haven't really thought that much about it. – Ville Niemi Jan 26 '15 at 19:40