Sublight Propulsion

[Lazar]

I'm trying to understand sublight propulsion for some personal scifi projects. My thing is, I've always had trouble getting my head around speed in space - reconciling the fact that speed is relative, with the fact that c is an absolute speed limit. Just to start off, for measures of performance, do you think it would make more sense for sublight drives to be rated by acceleration rather than by some notion of "top speed"?

[Captain Seafort]

Absolutely. The only way "top speed" has any relevence is as a legal limit to avoid any relatavistic wierdness.

[Lazar]

So in space - say, traveling from one side of a solar system to the other - it would make sense to talk about speed as a multiple of c, but not in terms of stuff like m/s?

[Graham Kennedy]

I'm trying to understand sublight propulsion for some personal scifi projects. My thing is, I've always had trouble getting my head around speed in space - reconciling the fact that speed is relative, with the fact that c is an absolute speed limit. Just to start off, for measures of performance, do you think it would make more sense for sublight drives to be rated by acceleration rather than by some notion of "top speed"?

Depends on what you are trying to compare. As you said, speed is indeed relative so there's no "top speed" in space as such. There is something called "delta vee", which is how much something can change its velocity by. So for instance if yous ship can accelerate at 10 m/s/s, and it can hold that acceleration for two hours before it runs out of fuel, then its delta vee is 72,000 m/s. Depending on practical issues in how the engines work, delta vee should be reasonably constant for a given ship design. Meaning that if it runs the engines at half thrust for half acceleration, the fuel will last twice as long and thus give the same delta vee.

Acceleration is also an important measure of a ships engines since it indicates how rapidly it can change its velocity.

Things get more complicated as your velocity gets towards an appreciable fraction of light, though.

[Sionnach Glic]

"Top speed" means nothing in terms of space, because there is no top speed. There's acceleration, which is a whole different thing, and which Graham's explained better than I can. If you hear people talking about top speed in space, then it's a good bet they don't know what they're talking about.

[Sionnach Glic]

By the way, is this discussion just about impulse drives, or sublight drives in sci-fi in general? If the latter, this'll be moved elsewhere.

[Lazar]

By the way, is this discussion just about impulse drives, or sublight drives in sci-fi in general? If the latter, this'll be moved elsewhere.

No, it's not about ST impulse drives in particular. You're right, it should be moved.

"Top speed" means nothing in terms of space, because there is no top speed.

But then there's the speed of light. I've never been able to get my head around the fact that speed is relative in space (which it obviously is, because there are no fixed points of reference), but that there's an absolute speed limit which is defined as (roughly) 300 million m/s. Like, if I can't say objectively that I'm traveling at 10 000 km/h in space, then how could I say objectively that I'm traveling at .5c or .99c?

[Sionnach Glic]

IIRC, that's actualy light's acceleration and not its speed. Could be mistaken though, my last physics class was long ago, and I didn't do too well.

Thread moved to Other/General.

[Lazar]

IIRC, that's actualy light's acceleration and not its speed.

No, I checked - the speed of light in a vacuum is defined as 299 792 458 m/s. It's definitely a speed. I think the whole point of modern physics is just to try to put all kinds of contradictory stuff together in order to mess with us - relative speed versus absolute speed limit; relativity versus physics...

Could be mistaken though, my last physics class was long ago, and I didn't do too well.

Science and math have never been my strong suits.

[Sionnach Glic]

Ah, right. Well, just ignore me.

[Mikey]

The issue is not with speed as such, but rather with one of the determining factors of speed. Speed is distance per time; and because of time dilation at significant fractions of c, that measure becomes inconstant. Therefore, it is easier and more valid to measure speed relative to a constant - c - because it's really the only definitive way to compare two speeds.

[Graham Kennedy]

It's not that speed is relative just because you express it in fractions of lightspeed. If I say "I am going at 150,000 km per second", I have to say what I am doing that speed compared to. But if I say instead "I am going at 0.5 c", that's exactly the same thing, and I still have to express what it is compared to.

It's light itself that always has the same speed, no matter what.

Okay, thought experiment. A man is in a train, he fires a shot from one end of a carriage to the other, 10 metres away. It takes 1 second to get there. He calculates the speed as 10 m/s. Right?

Now, the train is moving at 10 m/s also. So to a guy on the side of the tracks, he will look at this and he will see that the bullet still covers the distance in 1 second. But because of the motion of the train, the distance covered by the bullet is twice as long, and therefore he will measure the speed as being twice as fast.

Point being, in this example we have the equation speed = distance / time. The time is the same, but the distance is different for each observer, so the speed is different.

Now swap the gun for a torch. You would expect to get the same result, that both guys would get a different distance in the same time and so a different speed. But you don't. What you find is that for each person, the speed of the light ray from the torch is exactly the same. That's the odd thing about light - its speed is always the same regardless of who is measuring it or what frame of reference they are in.

So here's the thing. Given that speed = distance / time, then if the distance is different for each observer, and the speed is same for each observer, then that can only work out if time itself is different for each observer.

And that's really all that relativity is; time and distance vary according to each observer - they have to, because they always have to work out in a way that makes the speed of light the same for everybody.

[Captain Seafort]

The thing that's always confused me is what happens when summ velocities add up to greater than c.

Take, for example, one object (A) approaching another (B) at 200,000 kps. Directly opposite B from A another object (C) is also approching B at 200,000 kps. Therefore A and C are approaching each other at 400,000 kps - 1/3 greater than c. Relativity says this is impossible, so how fast are they approaching each other, and why?

[Graham Kennedy]

When you add velocities, you use something called the Lorentz transform.

At speeds very much less than c, you just add speed u to speed v (I'm using the word speed all the time here by the way, I really should be saying velcocity. But whatever.) So in your example, w = u + v = 200,000 + 200,000 = 400,000

But in fact, because of relativistic dilation what you have to do is this :

w = ( u + v ) / ( 1 + ( uv / c^2 ) )

You can see it's basically w = u + v, but then that total is modified by dividing it by 1 + ( uv / c^2 ).

So what can we say about 1 + ( uv / c^2 )? Well note ( uv / c^2 ) - the product of the speeds, divided by the square of the speed of light. If your two objects were stationary, this fraction would work out to 0.

If u and v are both above zero but less than c, then the product of uv has to be less than c^2, and so this fraction has to have some value above 0 but less than 1.

It can't go above 1 - the only way for that to happen is for the speed of at least one object to be above c.

And if uv / c^2 must always be between 0 and 1, then 1 plus that value must always be between 1 and 2.

So you can hopefully see what this means. If both speeds are zero, then the speeds are added and then divided by 1+0; the division makes no difference. That's just a mathematical way of saying that at zero speed there is no relativity effect.

But as the speed of both objects rises to c, the fraction you divide them by rises to 2. So if both were doing light speed, then you would add their speeds together, but then you divide by 2 - halving them again! So even in the most extreme case, with each object going at lightspeed their speeds still add up to lightspeed.

So now let's look at your example and do a Lorentz transform on it.

u = 200,000,000 m/s, v = 200,000,000 m/s. So it becomes :

w = ( 200,000,000 + 200,000,000 ) / ( 1 + ( (200,000,000 x 200,000,000) / (300,000,000)^2 ) )

w = 400,000,000 / (1 + (4e+16 / 9e16))

w = 400,000,000 / (1 + 0.444)

w = 400,000,000 / 1.444

w = 276,923,076.923

Which is 0.923 c. So if two objects approach one another, each doing 2/3 c, then time and space will distort themselves so that their total closing rate is 0.923 c.

Try it, it's not that hard - basic algebra, and there is no combination of u and v you can enter where they are less than c and the combined speed is greater than c.

[Mikey]

Actually, speed is better in this case than velocity. If the direction portion of the velocity vector of u is opposite to that of v, wouldn't the sum of the velocities just be the difference of the speeds?