Our new Indie Games subforum is now open for business in G&T. Go and check it out, you might land a code for a free game. If you're developing an indie game and want to post about it, follow these directions. If you don't, he'll break your legs! Hahaha! Seriously though.

Our rules have been updated and given their own forum. Go and look at them! They are nice, and there may be new ones that you didn't know about! Hooray for rules! Hooray for The System! Hooray for Conforming!

## Posts

Nope, for the 100 kg probe its all the energy which arrives on the earth for 4 minutes given a 100% efficient antimatter factory. For a 20 tonne spaceship, its more energy than has ever been used in the history of mankind.

tbloxhamongo to the atomic rockets site

http://www.projectrho.com/rocket/

they have a lot of information like that there.

AeolusdallasonAeolusdallasonBuilding giant solar panels near mercury would probably require even more power. Not to mention the "antimatter factories".

Pi-r8onusthere seem to require such an energy expenditure that we're better off building some local infrastructure first. Which means moon-base, mars-base, and then on to figuring out how to get quintillions of Joules of solar energy easily.durandal4532onAeolusdallasonI can't find the flaw in your reasoning at the moment (and it is

reallystarting to bother me; I've been typing this post for an hour and a half), but your conclusion is false.CycloneRangeronA given velocity increment is worth more kinetic energy at higher speed; consequently, when you are going, say, 100 m/s, and accelerate fuel combustion products out the back of your ship at 10 m/s, your fuel has lost 950 J of energy per kilogram from the perspective of someone here on the Earth (in whose reference frame your spaceship's velocity was measured). Your spacecraft has to get that much energy back for conservation of energy to not have been violated. The faster you go, the more energy is added. You get a partial refund on the deposit you made to accelerate that fuel, basically.

The closer you get to c, of course, the more energy you get back from a given increment of velocity change in your exhaust—but the cost of a given increment of acceleration is even

more, so you still run into a barrier. But it's not at 0.8c, or at any given number less than c, even for a fueled vehicle.CycloneRangeronYou're going 100m/s. The fuel is ALSO going 100m/s. Whether you're at rest or moving it comes out relative to you at 10 m/s.

And KE increases fairly linearly, IIRC. It does become very hard to accelerate further as you near c, but that's because of time dilation, not losing effective energy (you're accelerating at the same rate by your clock, but according to the rest of the universe your clocks are running slower)

Phoenix-DonKE = (1/2)*m*V^2

So, not linear. And it gets even weirder when you throw in relativity (the above is the Newtonian approximation).

No, you've got it partly wrong. You are indeed accelerating at the same rate by your clock, but this is exactly equivalent to an increased energy cost. Remember, energy is force*distance.

CycloneRangeronIf you by your clock are accelerating at a steady rate- the force*distance seems like it should be the same. (to your point of view)

Phoenix-DonThe discussions you guys are having are, at times, largely ignoring relativity in such a way that it makes more sense to think of it not as reaching c, but rather reaching an infinite velocity. The discussion's going to need to be a bit more rigid if we want to talk about limitations in any concrete manner.

ElJeffeonI make tweet.

That site is almost all for in solar system stuff, you can see that they haven't used the relativistic corrections which you have to do for any kind of interstellar mission. In the solar system 1 g is indeed not very hard acceleration and you would wish you could accelerate harder. In an interstellar mission the force output of the engines is pretty much unimportant above a certain threshold, effectively your ship will be at max speed well before halfway.

tbloxhamonHey, I'm not ignoring relativity, thats why everything in my posts is going so grindingly slowly despite requiring such ridiculous levels of supertech

tbloxhamonbig.Throw on a bussard ramjet as a brake, and collect fuel while you're at it.

[Tycho?]onI'm not sure where you think we disagree. We're not ignoring relativity (I'm not, at least), it's just that we don't have any way of getting to the very high velocities where it starts to really make a difference.

CycloneRangeronI don't think a "light sail" would work. Unless you are saying that the lasers are independent of the craft. In which case it would only work for a short distance and then likely have the light blocked or diffused by somthing.

Otherwise it would just sit in place, because the light emitted from the laser would push back and then be canceled out by the light hitting the said.

JebusUDonGuess it always comes down to.

CycloneRangeronThat sounds like it would be difficult to control the rate of acceleration finely, though, and how does the breaking mechanism work?

AJAlkaline40onBraking is accomplished by use of a magnetic sail once you reach your destination star system. There are other ways to do it as well, but a magnetic sail is the usual proposal.

CycloneRangeronOkay, so, I don't really know dick about theoretical physics, but couldn't you use the same principles that govern a Bussard ramjet to scoop up the matter-half of your reaction fuel? That'd

hugelycut down on your mass.Salvation122onWhy not send out probes to drop a "route", basically stationary platforms in space that shoot laser beams till the next spot or as far as they remain viable. Then said craft would be pushed by these lasers until reaching it's destination. Obviously the initial setup is slow (and costly), but wouldn't the next trips then be much more efficient and less costly?

EvigilantonI was under the impression that braking for these sorts of systems was generally done by orbital capture, which is extremely fuckin' slow but utterly dependable (assuming you do the math right.)

Salvation122onHmm, that might help a bit. But remember that I'm using the relativistic calculations here, so even things that seem hugely helpful only give you a tiny scrap more speed. Using a ramscoop effectively lets you carry just the antimatter, and thus doubles your total fuel mass. Now, the calculations for this are very complicated to do exactly, but you can get a 'theoretical maximum' from using the equation for the relativistic kinetic energy of a kg of fuel travelling at the target speed and then dividing that by the possible liberated KE from that fuel. When the amount of energy required to accelerate that fuel to a given speed is greater than the energy released by that fuel, you have your maximum speed, since no amount of extra fuel of that sort will make you go any faster. You just accelerate for longer at a slower rate.

Relativistically..

KE = (mc^2)/(1-v^2/c^2)^0.5 - mc^2

liberated KE = ship efficiency * fraction of ship which is fuel * fuel to energy conversion factor * mc^2

Using a ship efficiency of 0.25, and 90% of the ship being fuel, and a fuel to energy conversion factor of 2 (assuming we can somehow scoop up the mass with our ramscoop for free, it will actually be less than this) our speed tops out at 72% c.

tbloxhamonIt absolutely is. Look up the relativistic kinetic energy of an object on wikipedia, or look up at my previous post where I laid it out. As soon as the amount of energy required to accelerate that fuel to that speed is greater than the amount of energy you can liberate from the fuel then you would have been better off building a lighter spacecraft and not bringing the fuel. If the fuel requires more energy to accelerate than it gives back then its not fuel, its simply dead weight. True once the fuel is there you may as well burn the fuel, but it wont do any good since you will never get to that maximum speed powered by that type of fuel, you'll just get exponentially closer and closer as your fuel gets more and more useless. I suppose yes, no piece of fuel is ever totally useless, but you'd soon get to the point where you would be burning as much energy for the last m/s as you did for the 2e8 m/s before it.

edit - oh, and the reason you dont get your deposit back, is that you need to do the work on the fuel to shoot it out the back. To you you would think nothing had happened, but from earth it would look like you were shooting out your fuel really slowly and at a hugely decreased rate. You never get a single erg of that kinetic energy used to accelerate the fuel back, its all wasted.

tbloxhamondoesimpose a velocity limit since time for you is running much more slowly relative to someone who is moving at nearly c relative to you. But the phenomenon you are postulating applies, at varying speeds for varying fuel enthalpies, regardless of relativistic effects. So let us ignore them for the moment.Say you are near your "maximum velocity". In fact, say you have reached it, or come infinitesimally close. Your claim is that burning a mass of fuel will not accelerate you (or will accelerate you a negligible amount) because the energy will be contained in the exhaust's kinetic energy exclusively. So, the exhaust plume travels away from you at (whatever your exhaust speed is for this type of rocket), and you don't accelerate at all. This is impossible, however, because it violates conservation of momentum. Whatever momentum is given to the exhaust plume must be recovered with an opposite sign in the spacecraft.

Looked at another way, you are essentially telling our spacecraft crew that they will fire their engines, a plume of exhaust will erupt out the back of their ship, and... nothing will happen. If this were true, they'd be able to infer their "absolute" speed as the speed at which this happens (or the speed at which it begins to have a measurable effect; I think the point is clear). But again, the notion of an "absolute" speed contradicts relativity, so again we have arrived at an impossibility.

CycloneRangeronThe idea is that you're not better off having the fuel on board to begin with. Instead of thinking of that moment 2 years into the mission when you're firing your rockets, think of the entire trip. Your acceleration across that entire trip will be lower because of all that fuel you brought on. As such, the cumulative effect of all that fuel tops out at a given velocity.

ElJeffeonI make tweet.

From your perspective (on the spaceship), a given quantity of fuel burned will produce a given force (and an acceleration proportional to your fuel mass). You are correct in that the fuel required to gain an additional velocity increment at the end of your burn is larger the higher that end-of-burn velocity is, but there is no "hard limit". If you start with more fuel, you have a lower acceleration to begin with. The cost of obtaining a given velocity increases exponentially (and faster than exponentially at relativistic speeds), but it does not increase towards an asymptote (except at c, of course).

CycloneRangeronfjafjanon- "Proving once again the deadliest animal of all ... is the Zoo Keeper" - Philip J Fry

Agreed.

AJAlkaline40onCan you prove mathematically that this is the case? Because I don't think you can.

Meanwhile, tbloxham spelled out the precise equations you need to calculate the maximum speed for a bit of fuel. Look:

A) For a given chunk of fuel mass, it will take a given amount of energy to accelerate it to some speed, V. Call that energy K.

B) For a given chunk of fuel mass, there will be some maximum amount of energy you can get out of it, given the nature of your propulsion system. Call that energy P.

C) If, for a given V, K > P,

you cannot reach that velocity. It is impossible.ElJeffeonI make tweet.

If you're using a magnetic sail you might as well make it a ram jet. I believe I read something a few years ago that said Bussard ram jets were not practical because the amount of drag they caused in the interstellar medium was larger than the thrust you'd get out of burning the hydrogen that you collected. But if you're breaking, then you want all the drag you can. Collect fuel while your at it; fuse it and throw it back out the front of your craft to break even faster, or just collect it for use later.

[Tycho?]onLook at it this way: if you are

at this hypothetical speed limit(or very close), what will happen when you turn on your engines? Disregard the amount of fuel it took you to get there; say you are within 0.0001 km/s or whatever of your engine's "maximum speed". What happens when you turn it on? We knowfor certainthat events from the spacecraft's perspective proceed as normal, because there are no privileged reference frames. So, your engine won't mysteriously cease to function. Given that, how can you satisfy conservation of momentum without accelerating? You cannot. Things change a little bit when time dilation is thrown in, but that has nothing to do with the limit you and tbloxham are proposing.If this is all too hard to follow, I can dig through the equations later tonight, I think I have to get to a meeting now.

CycloneRangeronNo, B is correct; you only get a certain amount of energy out of a given quantity of fuel, regardless of the speed you're going when you burn it (in the non-relativistic approximation).

The real answer to El Jeffe is that in fact tbloxham has not provided an equation. The relevant equation is the rocket equation, delta v = v.exh * ln( m0/m1). Logarythmic equations have no horizontal asymptote. Problem solved.

zakkielonin the reference frame of the spacecraft, which is what I said. It is not correct in the reference frame of the Earth, which is what ElJeffe is claiming (or postulating, I guess). Look at it in terms of velocity difference: from the perspective of Earth, that "1000 m/s" or whatever that your engine spits out in the exhaust represents a much greater total change in kinetic energy when you're already traveling at high speeds. Power is (thrust*velocity), after all, and thrust is constant in our situation. (And of course, at relativistic speeds, your engine ceases to spit out a constant exit velocity at all, at least as meaured from the Earth. But that doesn't affect the hypothetical velocity limit we're arguing about here.)As for the rocket equation—I don't think it's really an answer; it seems to be the question in fact. The accuracy of that equation is what everyone here is debating. I believe it is valid; ElJeffe and tbloxham do not. I am glad that you and I seem to agree though.

CycloneRangeronWe're saying the same thing in different ways. The chemical or nuclear or antimatter reaction will yield the same energy; you're including the additional energy the exhaust will impart to the kinetic energy of the ship. The reason that the additional energy the ship gets from the reaction is greater at higher velocities is that the fuel itself has already been accelerated, and so you get the benefit of the kinetic energy already in the fuel. When you blow it up, the impulse of the particles against the ship will include both the energy from the fuel reaction and the energy from the forward movement the fuel already had.

I don't think tbloxham and El Jeffe are intentionally opposing the rocket equation. I certainly hope not, anyway! I think they both just realized that you get diminishing returns from increasing amounts of fuel and assumed there had to be an asymptote somewhere.

zakkielonSeems likely.

CycloneRangeronHmm, I guess I am wrong as I just wrote a little program to check it. The effect of the diminishing mass of the ship has an effect that I'm not seeing in the basic assumptions.

I still think that a ship with 10J/kg energy density at the start won't go faster than 4.5 m/s and so on. I do not see how a fuel, being accelerated by the same fuel which is then discarded can end up with a greater energy density at the end of Kinetic energy than it had at the beginning in 'chemical' energy when viewed from the reference frame where it began.

edit - OK, having done the same thing again my calculations are correct for a ship which doesn't change significantly in mass, and I see how continually reducing mass will help (obviously the last drop of fuel is the most efficient at transfering KE to the payload) but I still don't quite see how the KE is 'concentrated'.

edit - And it really is definately happening, tomorrow I must sit down and solve these equations to figure it out. Effectively it seems that if the ship mass reduces to near zero (99% mass loss) then the basic Chemical Energy density at start = kinetic energy density at end equation is out by about a factor of 2.

tbloxhamonIf half the US military budget of the last 50 years had been devoted to Nasa we would probably have several thriving moon colonies, and even if not, the advances in many of the sciences would be impossible to comprehend. The advances in alternate energy alone are hard to imagine.

You're thinking too small damnit. We figure out a way to dialate time around

the entire earth, sure it might fuck with the weather having seasons go buy in like 20 minutes rather than months, and the spaceship crew would still take 80 years to get there, but at leastwewon't have to wait long.On a more serious note, I think humanity should make things like space elevators and asteroid mining an actual priority, as a species. While getting to another solar system is sci-fi maybe forever (although I'd like to think that someday, if we're still around, we figure out a way to do things that we can't even conceive of right now), intra-solar system activities are all quite possible. If we can figure out an economical way to harvest asteroids and other raw materials from within our solar system, we've effectively put an end to scarcity for a great many materials.

If the human race is still progressing a hundred years from now, inter solar system colonies and bases are an inevitability.

override367onThough I'd totally live on the moon, but not under the sea.

electricitylikesmeon