Reaction engines and relativistic travel

[Frank]

If you keep on accelerating with 1g for close to a year, you're so close to the speed of light that you can zap just about anywhere while little subjective time is occuring. So, you can go effectively anywhere in our galaxy in two years subjective time (as you have to decelerate as well).

That raises two questions for me:

1) What is the total amount of mass and energy required to do that

2) Why are reaction engines considered to be most efficient when the exhaust more or less stops dead in space, and why would the speed of the ejection mass set an upper limit to the speed you can accomplish?

I don't get the second point. Because any mass you eject at the back should increase your speed, no matter what. Yes, the faster you go, the less your speed increases by the same amount of thrust, but there should be no lower boundary. As far as I get it.


And what would be the minimum requirements for such a relativistic space ship?

 

[StefanS]

2) Why are reaction engines considered to be most efficient when the exhaust more or less stops dead in space, and why would the speed of the ejection mass set an upper limit to the speed you can accomplish?

I don't get the second point. Because any mass you eject at the back should increase your speed, no matter what. Yes, the faster you go, the less your speed increases by the same amount of thrust, but there should be no lower boundary. As far as I get it.

The exhaust mass doesn't stop in space.

You don't look at the whole picture. The mass you eject needs to be expelled from your space craft. Thus, there is a limit to the maximum mass you can eject. So what you want is that the mass you eject is in fact ejected with maximum speed.


Same basic things from wiki (relativistic Tsiolkowsky eq.)

 

[Frank]

Yes, I agree. And when the speed of the exhaust mass is close enough to c, time dilation will just about cancel out the diminishing returns, subjectively. At least, that's how I get it. So, either the "specific impulse" thing is not relevant for that case, or it's meant for atmospheric travel only.

But even if the speed of the exhaust is a lot less than c, you're still accelerating, even when you "go faster" than that in relation to the vector of your point of origin.

That's why I don't get the idea, that the exhaust is most efficient when it's about equal to your relative speed. Relative to what? You're your own origin, when traveling through space. And faster is better, although it requires more energy to be expended to speed it up.

And while a slow exhaust might do wonders for your energy quotum, it's not helping getting you there faster.



On the other hand, if mass is no problem, you could disect a large body, and throw the chuncks backwards at relatively low speed for the same relative increase.


Edit: Ok, I get it. As you said, the total amount of mass you carry is limited. The faster you fire it away, the larger the increase in speed. Stupid of me.

 

[Frank]

Then again, that doesn't take the amount of energy into account. Unless you count that as the maximum amount you can extract from the mass available, in exhaust speed. Which actually might make fusion better than anti-matter annihilation, as it's much easier to put the energy provided by fusion to good use.

Ok. I get the point. Thanks. So, back to my question: what would be the minimal requirements for such a ship?

 

[StefanS]

Twhat would be the minimal requirements for such a ship?

That depends I am not that knowledgable on the matter of the exotic nuclear propulsion systems. I did however, work on "electrical" propulsion systems. Though again, I did only work on micro thrusters (FEEP) and since I am still bound by NDA I can't say too much about the work we did there, except producing them was kind of voodoo.
For electrical propulsion you basically have a few problems (little thrust & long acceleration time) and benefits (less fuel, continuous acceleration). The main problem, however, is you run into is the size of the power supply which adds hefty weight penalties to your space-craft.

EDIT: I've got an easy script on the subject of electrical propulsion lying around somewhere. I'll see if I can dig up the electronic version.

EDIT2: Found it. Two links at the bottom. it covers basic S/C propulsion as well and is pretty easy.