Interstellar travel with rockets

[jrphilps]

Hello everyone, I have a question that is only vaguely related to the kerbal gaming experience. It revolves around the issue of interstellar travel, and whether such journeys can be completed in a human life time. My personal belief is that, in the far future, our descendants may be able to create ships that can reach 10% light speed or so (a delta v of 30,000 km/s). Some people scoff at the mere suggestion that this may be so. One example would be this video:

In it, the narrator takes a look at the movie avatar, and critiques the venture stars design (starting at 5:25). He does some estimates on the joules and watts expended over the course of its journey, but then makes the strange claim that any craft attempting to accelerate at greater than 1 g will vaporise itself! He didn't actually say that, but this is the essence of what his argument boils down to: Even if you scale the engine down, the heat it emits will exceed the crafts specific heat. Can anyone find a flaw in his math or reasoning?

[vexx32]

Moved to the Science labs.

[nhnifong]

Very interesting video.

[architeuthis]

Well, getting 1.5 g acceleration with an anti-matter rocket does strike me as unrealistic, .1 g maybe, but there are several faults in his argument. For one thing 100,000 tons wet mass seems way too high, interstellar rockets are not built like aircraft carriers. My guess would be less than 10,000 tons wet mass. He also gives 99.99% efficient as a reducto ad absurdum, but an antimatter rocket would be open-cycle, the main sources of heat transfer would be absorbed gamma radiation in the radiation shield from the matter-antimatter reactions and the inefficiency of the magnet used in the nozzle. I think 99% efficient might actually be plausible in this case. If you're running a radiator at 1500K, which is plausible if the radiation shield is made out of tungsten, and with an emissivity of .9 you'd need 540 km^2 of radiator panels to get rid of the waste heat. This is a lot bigger than what is pictured in the movie, I'd guess that the ISV Venture Star has maybe a tenth of a square kilometer of radiator area; perhaps its radiator runs hotter than 1500K or the efficiency of the rocket is greater than 99%. If the rocket was 99.99% efficient the radiator area would only need to be 5.4 km^2 to discharge the waste heat. At any rate 540 km^2 seems like a lot but it's not at all impossible, especially if you're using something like a droplet radiator, certainly more plausible than his 1000 year Noah's Arc idea.

BTW, nhnifong, if you're the same PSU system science grad student, we've met. We talked about evolving go players using genetic algorithms for a project in our alife class, and you showed me a mancala player you had made in python. Small world:)

Edited January 13, 2014 by architeuthis

[Nuke]

the phrase 'planet sized fuel tank' keeps echoing through my mind.

[DaveofDefeat]

As implausible as the star ship is, I do disagree with the weight of the ship. he compares the weight of the spaceship to the weight of a fully armed, fueled and armored aircraft carrier. I really do not believe a spaceship would be built so inefficiency and would only use the strongest most lightweight components available. Surely in the future they can afford to put something a little more practical than steel in their anti matter space ship.

-And WACO! I went to college there once.

Edited January 13, 2014 by DaveofDefeat

[jrphilps]

For one thing 100,000 tons wet mass seems way too high, interstellar rockets are not built like aircraft carriers. My guess would be less than 10,000 tons wet mass. He also gives 99.99% efficient as a reducto ad absurdum, but an antimatter rocket would be open-cycle, the main sources of heat transfer would be absorbed gamma radiation in the radiation shield from the matter-antimatter reactions and the inefficiency of the magnet used in the nozzle.

Well, even if the ship gets scaled down, the only thing you are doing is decreasing the absolute amount of energy involved in propelling it: The relative amount remains the same, and that is a crucial point his argument (since the energy would supposedly vaporise the ship). For interstellar travel to be plausible, his math must be shown to be in error, and I believe it is.

If the engines have a mass of 10,000 tons, and a specific heat of 4.9E10 joules, raising its temperature by 600 celcius would require 2.9E12 joules, which is likely the maximum operating limit. Of course, since I don't know the rate at which steel radiates heat away in a vacuum, I don't yet have a figure on the watts required...

Lets look at the numbers separating the venture star from a more contemporary craft like the saturn v. Assume that both ships are already in orbit, firing one stage after another (and ignore the differences in propulsion efficiency). What is the energy budget?

-Venture star: Mass of 100,000 tons, delta v of 210,000 km/s, and a burn time of 15,768,000 seconds.

-Saturn v: Mass of 2800 tons, delta v of 12.33 km/s, and a burn time of 1010 seconds.

If the venture star is travelling at 17,031.6 times the velocity, but has a burn time 15,611.8 times longer... Where did he get the idea that the heat would melt the engines? If you make both ships the same size *, the venture star is running only slightly hotter than the saturn v! Thus, there is an error in his math somewhere. The figures of 1.4E17 watts (venture star) and 1.9E11 watts (saturn v) cannot be accurate. The difference between them cannot possibly be more than two orders of magnitude, even accounting for the fact that the venture star is 35.7 times more massive than the saturn v.

*Allowing us to measure the proportion of energy to mass, which will determine whether the ships melts or not

[jrphilps]

As implausible as the star ship is, I do disagree with the weight of the ship. he compares the weight of the spaceship to the weight of a fully armed, fueled and armored aircraft carrier.

Aircraft carriers are actually rather flimsy when compared to other sea going vessels, but of course, not comparable to a conservative (I.E, structurally flimsy) design like the venture star. Reaching such a high velocity (70% of light) means you have to sacrifice even the pretense of durability. Modern carriers have torpedo bulkheads and kevlar spall liners, but cannot in any sense be considered armored.

I really do not believe a spaceship would be built so inefficiency and would only use the strongest most lightweight components available. Surely in the future they can afford to put something a little more practical than steel in their anti matter space ship.

I think the mass estimate is fairly accurate, given all the equipment they are hauling around. And most of the ships mass would still need to be devoted to the matter/anti-matter fuel in order to get up to 70% of light velocity, which is a major bummer... Maybe if teleportation proves feasible in the future, thats one way we could avoid carrying outrageous amounts of propellant: Beam it directly onto the ship through a local space station.

[magnemoe]

Venture star was not designed to be realistic, just to look realistic, pretty much like the spaceship in 2001.

As I understand they use an laser pumped solar sail to accelerate, then antimatter for braking.

Main issue for me was the power requirements for the ship. Was in the magnitude of the total amount of sunlight who fall on earth.

Yes its a lots of power, not impossible but kind of kill the plot in the movie hard. Your only serious pollution problem would be heat pollution and it might be an very serious issue. No others it might be cost effective to turn vaste into plasma and separate the elements, power would be to cheap to meter anyway.

If power is not to cheap to meter they would run the ship on 1g instead of 1.5g.

Edited January 13, 2014 by magnemoe

[Aghanim]

Venture star was not designed to be realistic, just to look realistic, pretty much like the spaceship in 2001.

As I understand they use an laser pumped solar sail to accelerate, then antimatter for braking.

Main issue for me was the power requirements for the ship. Was in the magnitude of the total amount of sunlight who fall on earth.

Yes its a lots of power, not impossible but kind of kill the plot in the movie hard. Your only serious pollution problem would be heat pollution and it might be an very serious issue. No others it might be cost effective to turn vaste into plasma and separate the elements, power would be to cheap to meter anyway.

If power is not to cheap to meter they would run the ship on 1g instead of 1.5g.

Agreed. Everyone seems to forget the solar sail part, they only include pure antimatter beamed core rocket

But....... 1.5g pure photon beamed propulsion? That laser is emitting power like crazy, imagine if Earth accidentally got into the beam path, say bye bye to the world as you know it

[crazyewok]

No we will not do instersteller travel with rockects. Impossible.

If we want to do that we need to man up and to bite bullet and go nuclear with or spacehips.

[Ralathon]

No we will not do instersteller travel with rockects. Impossible.

If we want to do that we need to man up and to bite bullet and go nuclear with or spacehips.

You do realize we're discussing antimatter rockets here right? The term rocket is not restricted to chemical engines, a nuclear rocket is still a rocket.

Anyway, after doing some digging on the Avatar wiki for the specs of the ship I figured out that it supposedly injects extra hydrogen in its exhaust for additional thrust. Making it essentially a NERVA fuelled by antimatter-matter annihilation. This could also help fix the cooling issues, it can use the hydrogen fuel as a coolant before injecting it in the engine. Most chemical rockets use the same principle to stop them from melting. That way you can dump loads of heat so you can get away with a smaller radiator.

If you do the maths on it you'll probably find out that the ship is still ridiculous. Interstellar trips in human lifetimes simply require really really big numbers to work. But the heating issue should be solvable.

[Themohawkninja]

All we need is 10% c and the nearest star is within a human lifetime.

Some ion engines with a lot of xenon might pull it off with a few years acceleration, but that's quite hopeful.

Anti-matter would probably be your best bet though, since we are making it as we speak, it's got 100% efficiency, and there is as much of it as there is matter, since anti-matter is made from matter.

As for the math, sounds quite silly to me since rockets accelerate at higher than 1 G all the time.

[Ralathon]

All we need is 10% c and the nearest star is within a human lifetime.

Some ion engines with a lot of xenon might pull it off with a few years acceleration, but that's quite hopeful.

Anti-matter would probably be your best bet though, since we are making it as we speak, it's got 100% efficiency, and there is as much of it as there is matter, since anti-matter is made from matter.

As for the math, sounds quite silly to me since rockets accelerate at higher than 1 G all the time.

Do you have any idea how fast 10% of c actually is? It isn't merely "very fast". 0.1c compared to a standard orbital velocity around the earth is like comparing the distance from LA to NY with a trip to the supermarket. This is not an exaggeration, check the math if you want. It is truly mindbogglingly fast.

Lets say you take a standard magnetoplasmadynamic thruster. According to the wiki they have an exhaust velocity of 110 000 m/s. Quite impressive. Tossing that into the tsiolkovsky equation for 0.1c of dV I end up with every kg of payload needing about 3*10^118 kg of xenon. Thats about 10^65 times the observable universe...

We as humanity aren't even close to achieving 10% of the speed of light. The only technologically feasible design we have right now is the Orion drive. And I'd be seriously impressed if that would make it above 0.01c.

[K^2]

Some ion engines with a lot of xenon might pull it off with a few years acceleration, but that's quite hopeful.

Exhaust velocity of a high I_SP ion engine is around 120km/s. 10% of speed of light is 30,000km/s. There isn't enough matter for use as propellant in the known universe to accelerate a single nucleus of cargo to these speeds with an ion drive.

Does this put the statement into a little bit of a perspective for you?

Edit: It is, in principle, possible to achieve .1c with nuclear pulse drive, but even that is so far beyond feasible that it might as well be impossible. The only realistic way of reaching .1c using reaction drive of any kind is with a high efficiency matter-antimatter photon drive. And we don't have a clue how to make one, let alone get fuel for it.

Edited January 13, 2014 by K^2

[magnemoe]

Agreed. Everyone seems to forget the solar sail part, they only include pure antimatter beamed core rocket

But....... 1.5g pure photon beamed propulsion? That laser is emitting power like crazy, imagine if Earth accidentally got into the beam path, say bye bye to the world as you know it

Yes, but it is kind of an overkill for an weapon system as useful as as close air support with an deathstar.

My point was that the capabilities to build that sort of laser and the solar cell system to power it would give you far more energy than you could use on earth because of heat pollution and it would be pretty much the only sort of pollution you would have. You would have to do most of the heavy industry in orbit or on the moon anyway because of this, no issue with SSTO fusion or something shuttles they used in the movie. In short the setting on Earth made little sense. No they did not have to be nice people but they would be very rich this has effect all over like how one of the health issues for poor people is obesity.

[Themohawkninja]

Do you have any idea how fast 10% of c actually is? It isn't merely "very fast". 0.1c compared to a standard orbital velocity around the earth is like comparing the distance from LA to NY with a trip to the supermarket. This is not an exaggeration, check the math if you want. It is truly mindbogglingly fast.

Lets say you take a standard magnetoplasmadynamic thruster. According to the wiki they have an exhaust velocity of 110 000 m/s. Quite impressive. Tossing that into the tsiolkovsky equation for 0.1c of dV I end up with every kg of payload needing about 3*10^118 kg of xenon. Thats about 10^65 times the observable universe...

We as humanity aren't even close to achieving 10% of the speed of light. The only technologically feasible design we have right now is the Orion drive. And I'd be seriously impressed if that would make it above 0.01c.

Fair enough. I keep forgetting what logarithmic equations can do sometimes. I just figured that the ISP might be high enough to do it with a few hundred metric tonnes of xenon, so much for that.

And yes, I do know how fast 0.1 c is. I study astronomy, so the speed of light is used quite a bit.

[Themohawkninja]

Exhaust velocity of a high I_SP ion engine is around 120km/s. 10% of speed of light is 30,000km/s. There isn't enough matter for use as propellant in the known universe to accelerate a single nucleus of cargo to these speeds with an ion drive.

Does this put the statement into a little bit of a perspective for you?

Edit: It is, in principle, possible to achieve .1c with nuclear pulse drive, but even that is so far beyond feasible that it might as well be impossible. The only realistic way of reaching .1c using reaction drive of any kind is with a high efficiency matter-antimatter photon drive. And we don't have a clue how to make one, let alone get fuel for it.

Is this matter-antimatter photon drive just a matter-antimatter explosion directed in the opposite direction of the desired vector of motion, or is it something else?

[K^2]

That would be absolutely horrible in terms of efficiency. At best, you are getting 25% of the total impulse, while absorbing 50% of total energy. There are no materials that can withstand that sort of energy output while still giving you anything like a decent thrust. For every 1N of thrust you gain with such a drive, you'd have to dissipate 600 megawatts of heat. If you were to build your pusher plate out of Tungsten, it would only radiate 8.5 megawatts per square meter. So you'd have to have a pusher plate that's at least 70m² per 1N of thrust. And that plate would have to be at least 10cm thick to actually absorb the radiation. (This is a very rough estimate, but the order is right.) So we are talking about 140T of tungsten in shielding for every Newton of thrust. The only place that's going fast is nowhere.

You might be able to improve on this a little bit by using different materials. Carbon will perform a lot better, but it's going to slowly evaporate at high temperatures. Maybe you could use carbon encased in tungsten? You could drop that value from over 100T to just a few tons. But we are still talking about something that can't even accelerate at 1% of g by a wide margin.

If you want a ship that can manage a 1g acceleration and an I_SP of a matter-antimatter rocket, you have to build an efficient photon drive (perhaps a variation on q-thruster, or maybe something using Mössbauer Effect) and power it with a very efficient matter-antimatter reactor. How you manage to get a nearly 100% efficient reactor that's light and produces enough power to drive a photon drive like that, I have no idea. Ok, I have some ideas, but only because I haven't done the math on them, and I'm sure they wouldn't work anyways.

Point is, we don't know how to actually build something which is both powerful enough and efficient enough to go at these sort of speeds. We know that it's physically possible, but we've got less thank bupkis on this from engineering perspective.

This is the main reason I'm keeping my eye on the warp drive development. Even if we can't beat speed of light with it, just getting to .1c with it seems more likely right now than with a rocket of any kind. And when I'm considering warp drive as the more likely scenario, you can see how things don't look good.

Edited January 13, 2014 by K^2

[jrphilps]

As another point of interest, the avatar website has never specified the exact method used to accelerate the venture star out of the solar system: All they say is that it involves massive laser batterys around mercury. But since the ship is being propelled for a total of 6 months (!), the beam efficiency would begin to attenuate due to the inverse square law. So wouldn't there have to be another laser battery on mars to pick up the slack for them at some point? * Questions, questions...

*Actually, getting all of the inner planets involved in propelling this ship is probably a good idea. One problem might be that ships can only depart or arrive when mercury, venus, earth, and mars are in alignment, which happens roughly every 2 1/2 years. Perhaps they could get around this by using a ganged array of gigantic mirrors located at each planets lagrange points?

[K^2]

A collimated beam does not follow the inverse square law. Instead it follows something like 1/(r+k)². The constant k depends on how you achieve the beam, but it can be quite large. And so long as your distance is smaller than this parameter k, you don't experience any significant drop off in power. Of course, eventually, you will get far enough from the source, and it will start going to follow inverse square law. (Because r is so much greater than k.)

[jrphilps]

A collimated beam does not follow the inverse square law.

Hmm, I did not know that!

Instead it follows something like 1/(r+k)². The constant k depends on how you achieve the beam, but it can be quite large. And so long as your distance is smaller than this parameter k, you don't experience any significant drop off in power. Of course, eventually, you will get far enough from the source, and it will start going to follow inverse square law. (Because r is so much greater than k.)

I wish I was capable of advanced math (which I lamely define as anything beyond addition, subtraction, division, and multiplication). Heh.

But if we could find out the lens size of these emitters, and know how many of them there are, that would give us a baseline on what their optimum range is! James cameron has done us a great disservice by not releasing this information... K^2, do you feel like speculating on these matters?

[Ralathon]

But if we could find out the lens size of these emitters, and know how many of them there are, that would give us a baseline on what their optimum range is! James cameron has done us a great disservice by not releasing this information... K^2, do you feel like speculating on these matters?

I'm fairly sure he didn't mention those on purpose. He's a film maker after all, not a physicist studying relativistic rocketry. He knows that mentioning numbers means it will be ripped to shreds by anyone who does the maths on it.

I'm already fairly impressed that the ship is at least marginally plausible, even if the numbers are way off. Most writers would simply shrug and say something technobabbly that is utterly meaningless. Kudos to the guy for listening to their tech adviser.

[K^2]

But if we could find out the lens size of these emitters, and know how many of them there are, that would give us a baseline on what their optimum range is! James cameron has done us a great disservice by not releasing this information... K^2, do you feel like speculating on these matters?

If you can give me a rough number for acceleration rate over these 6 months, I could do an estimate. Basically, we need to know the distance and power loss we are willing to tolerate.

But lets say that the beam is to extend .1ly. That would put average acceleration at about .8g. Which would probably be higher early on, and drop off as the power drops with distance. So that sounds reasonable. Also, at these powers, we probably want a nuclear-pumped X-Ray laser. There has been some research on that during the Cold War. US didn't manage to build one that's large enough to function, and Soviet research on the matter is, well, classified. (I'll just say that their goals were a little different, so their results aren't immediately applicable.) But in Avatar universe we can definitely see a giant X-Ray laser like that being built for powering propulsion of an interstellar ship. We probably couldn't get the optics for particularly hard X-Ray regardless of how big the thing is, so lets go with 500eV for the X-Ray energy. That puts us at .5nm for wavelength. And .1ly is about 1Pm. (Peta-meter, or 10¹⁵ meters.) There is a simple result in wave optics that states that h/L = λ/d. Ratio of minimum spot you can see or project onto to the distance is equal to ratio of wave length to the optics diameter.

So lets say we are willing to tolerate a 75% power loss. In other words, h = 2d. And, of course, L = 1Pm and λ = .5nm. I can re-write the above equation as hd = 2d² = Lλ = 5x10⁵m². That gives us d = 500m.

Naturally, a nuclear-pumped X-Ray laser that's 500m in diameter is kind of insane, but not all together impossible. It's not the worst idea for the "first stage" of the interstellar rocket.

[jrphilps]

If you can give me a rough number for acceleration rate over these 6 months, I could do an estimate. Basically, we need to know the distance and power loss we are willing to tolerate.

The lasers accelerate the ship at 1.5 g for 0.46 year. So thats 168 days, or 4032 hours. As for the venture stars dimensions, here they are: Length = 1502.4 meters. Width = 302.2 meters. Height = 218.3 meters. Mass is unknown (but estimated by some to be 100,000 metric tons). Apparently, it also has a 16,000 meter diameter photon sail. Should be an easy target

But lets say that the beam is to extend .1ly. That would put average acceleration at about .8g. Which would probably be higher early on, and drop off as the power drops with distance. So that sounds reasonable.

Holy crap. Thats 200 times neptunes distance from the sun! Way outside the kuiper belt... This is a serious voyage. I thought the boost phase would be done before it had gotten that far.

We probably couldn't get the optics for particularly hard X-Ray regardless of how big the thing is, so lets go with 500eV for the X-Ray energy. That puts us at .5nm for wavelength. And .1ly is about 1Pm. (Peta-meter, or 10¹⁵ meters.) There is a simple result in wave optics that states that h/L = λ/d. Ratio of minimum spot you can see or project onto to the distance is equal to ratio of wave length to the optics diameter.

So lets say we are willing to tolerate a 75% power loss. In other words, h = 2d. And, of course, L = 1Pm and λ = .5nm. I can re-write the above equation as hd = 2d² = Lλ = 5x10⁵m². That gives us d = 500m.

Naturally, a nuclear-pumped X-Ray laser that's 500m in diameter is kind of insane, but not all together impossible. It's not the worst idea for the "first stage" of the interstellar rocket.

Thank you for the detailed figures! Honestly, I thought it would have to involve a minature dysons sphere or something. But a 500 meter lens definitely sounds possible for the movies setting. As for the optics, how much energy would they be able to handle without heating up and warping? The energy requirements for propelling the ship might be as high as 1.4E17 watts!

Edited January 22, 2014 by jrphilps