Why do spaceships have a top speed?

[Cattlegod]

1 - there is NO hard cap to a rockets speed due to its exhaust exit velocity. Say you have 2 planets moving in a straight line parallel to each other. One moving at 200m/s and the other moving at 100m/s. Each planet is about to launch a rocket in the same direction they are traveling. Both the rockets have an exhaust exit velocity of 100m/s. Now, if the exit velocity of the rocket was the limiting factory, the rocket on the 100m/s planet would just sit there and hover right at its launch point (we know that isn't true because we launch rockets all the time from earth) and the other rocket would actually crash backward into the planet. You can see that having the exhaust speed be the limiting speed of the rocket fails logic.

2 - The reason you can't reach the speed of light is the faster you go your mass actually increases, eventually to the point where you have infinite mass at the speed of light. So, as the rocket propels you forward and you are losing mass and accelerating, you will reach a point where the rocket will start gaining mass even with the rocket fuel burning (if it were possible to put this much fuel on a rocket in the first place) and you would not be able to accelerate anymore.

 

[Kyanzes]

I'm not considering to add to this thread anything useful as I'm short of the required education/dedication, but certainly would like to ask something I don't really "dig". What is exactly space? I mean everyone here seem to agree that space contains small particles of matter, radiation etc. But what's there where no matter or radiation could be found? Is there such space? If so, what is it? Some gravitational field? If so, is there any place where no gravity is present? And if there are such slices of space where no gravitation is present, what is it that allows light for example to radiate (read somwehere that photons have no mass)? Also, what makes space three dimensional? Would like to understand the nature of space on a VERY basic level if it's possible.

 

[Spinne]

Originally posted by: Kalessian
I have a number of questions about physics that bother me. I mainly want to understand the limits of accelerating; why you can't just start throwing crap out the back of a vehicle and never stop going faster. I have a pretty good idea of each one, but I don't have the math to back up my thoughts.


First, I want to be able to determine the acceleration of a space ship in a vacuum given its specific impulse and its mass. We should assume the mass of the fuel is negligible, so no need to involve a lot of calculus

Now, let's take a modern chemical rocket. It has a specific impulse of 450. As I understand it, this means that 450kg of thrust is produced, for one second, for every 1kg of fuel consumed.

Since thrust = mass of the exhaust x accel. of exhaust, you get F(t)= M(e) x A(e)

Every action has equal reaction: magnitude of F(t) = Mass of Ship x Accel. of Ship?

My problem is with specific impulse and thrust, here. I want to measure thrust in Newtons, but specific impulse is giving me a mass...

But with thrust in N, I could get the acceleration of the ship if I also knew its mass, correct?

Now here is my big problem. I'm pretty sure there's a sqrt function in here, somewhere. I know the rocket's velocity can't just keep increasing - this isn't a constant acceleration problem. I imagine the rocket getting closer and closer to its max speed but never reaching it. Like at some point you hit really deminishing returns, and you can't throw stuff out the back of the rocket fast enough to propell the ship faster. I'm pretty sure it's closely related to exhaust velocity but I'd like this explained.

What's the mathematical model for this? How can I find out what time it would take to approx.(say within 5% of the asymptote) reach the rocket's max speed?

Or am I totally wrong?

What I'd like is someone saying: ok, a rocket with mass of 10 tons and a SI of 450 would take t amount of time to reach its max speed. And an explanation, please.


Ok, so now the relativity part. Let's take a flat spacetime that's completely void and empty except for person A at rest and person B in his spaceship. Person B has with him an accelerometer and a clock. Person A has a clock. Their clocks are in sync when the ship starts from rest at A's position.

The ship moves, magically, at a constant acceleration. No concerns about thrust or anything, the net force that moves the ship is external, magic, infinite. Now, as the ship approaches .9c, according to A his mass is now 2.3x as large as it was before. Then at .999c, it's 7x as large. Because of relativity, the relative mass increases.

Also, at .999c, their clocks are no longer in sync. A's clock will be much farther ahead of B's clock, correct?

So I understand what happens according the A's point of view, but what about B's?

According to B, at .999c, his ship is not any larger than it was when he started. Is everything else, such as A himself, getting much smaller to B?

According to B, at .999c, his clock is still moving normally, he doesn't feel like he's in slow motion at all, but if he looked at A, would A appear to be fast-forwarded super-fast?

According to B, at .999c, what would his accelerometer read? Would it still be the same as before? I think it would be, but then how can I explain that B still hasn't reached c? Time hasn't changed for him, Mass hasn't changed for him, and Acceleration hasn't changed for him, then how can velocity not equal c and then exceed it? B MUST be noticing something changing...

Is it that time is changing so fast outside his ship that he THINKS he's going much faster at .9999c than .999c, when in reality he hasn't???

It's late and I've confused myself, I'll give up now.

You're starting off on the wrong foot, so as to speak. A very very large percentage of the rocket's mass is fuel (90%-98%). Rethink through your analysis and the answer is self evident.

 

[silverpig]

I think you can start with F = d/dt (mv) and go from there.

 

[Banzai042]

Originally posted by: Cattlegod
1 - there is NO hard cap to a rockets speed due to its exhaust exit velocity. Say you have 2 planets moving in a straight line parallel to each other. One moving at 200m/s and the other moving at 100m/s. Each planet is about to launch a rocket in the same direction they are traveling. Both the rockets have an exhaust exit velocity of 100m/s. Now, if the exit velocity of the rocket was the limiting factory, the rocket on the 100m/s planet would just sit there and hover right at its launch point (we know that isn't true because we launch rockets all the time from earth) and the other rocket would actually crash backward into the planet. You can see that having the exhaust speed be the limiting speed of the rocket fails logic.

2 - The reason you can't reach the speed of light is the faster you go your mass actually increases, eventually to the point where you have infinite mass at the speed of light. So, as the rocket propels you forward and you are losing mass and accelerating, you will reach a point where the rocket will start gaining mass even with the rocket fuel burning (if it were possible to put this much fuel on a rocket in the first place) and you would not be able to accelerate anymore.

I'd guess that cattlegood has the correct answer.
Since f=ma, if f remains constant, and m continues to increase as velocity increases (at near lightspeed) acceleration will decrease, until m is so great that a=0 due to practical limitations.

 

[thescreensavers]

Originally posted by: andyandyandy
Holy jebus im confused..

me to??

 

[gsellis]

Originally posted by: Cattlegod
...(if it were possible to put this much fuel on a rocket in the first place)...

That is where the lack of vacuum in space comes into play Bussard Ramjet BABY!

Wiki if you care

Edit - OP, btw, the wiki entry has some of the math you are looking for.

 

[imported_inspire]

Originally posted by: BrownTown

Gah, you seem to like the wrong answers more than the right ones , listen to Dr.Pizza...

I failed to see the contradiction - maybe next time you could take the time to substantiate your point and point out the error for me, rather than make some pithy comment.

 

[Eeezee]

In classical theory, the ship has no maximum speed assuming it's in a vacuum and can continue generating thrust. The only limiting factor is the amount of fuel you bring with you.

In relativity theory, massive objects can not reach the speed of light, therefore it does not matter how much fuel you bring with you. As you approach c, the force necessary to increase your velocity approaches infinity. How does one generate infinite force?

 

[Eeezee]

Originally posted by: Kyanzes
I'm not considering to add to this thread anything useful as I'm short of the required education/dedication, but certainly would like to ask something I don't really "dig". What is exactly space? I mean everyone here seem to agree that space contains small particles of matter, radiation etc. But what's there where no matter or radiation could be found? Is there such space? If so, what is it? Some gravitational field? If so, is there any place where no gravity is present? And if there are such slices of space where no gravitation is present, what is it that allows light for example to radiate (read somwehere that photons have no mass)? Also, what makes space three dimensional? Would like to understand the nature of space on a VERY basic level if it's possible.

You may want to consider making a new thread for people to discuss this topic. It's a whole new bag of marbles

 

[Eeezee]

Originally posted by: inspire

Originally posted by: BrownTown

Gah, you seem to like the wrong answers more than the right ones , listen to Dr.Pizza...

I failed to see the contradiction - maybe next time you could take the time to substantiate your point and point out the error for me, rather than make some pithy comment.

It is the exhaust relative to the rocket that is important. Let's set up an example.

I'm going to assume that the exhaust velocity of some gas for a rocket is 100 m/s. Whenever I say v=, that is the velocity of the rocket, not the gas.

v=0, exhaust velocity is 100 m/s
v=100 m/s, exhaust velocity is 100 m/s
v=1000 m/s, exhaust velocity is 100 m/s
etc.

There is no such thing as an absolute velocity like in the example that was presented. If the exhaust velocity is 100 m/s, that does not mean that the rocket can't go faster than 100 m/s relative to an observer.

The speed of rockets DO depend on the velocity of the exhaust gas, but they only help determine the change in velocity, not the terminal velocity.

If, for some reason, the exhaust velocity decreased as the velocity of the rocket increased (which is not the case), then it is true that the rocket will not accelerate anymore when it reaches the exhaust velocity. It would be retaining the rest of its fuel at this point.

 

[cheesehead]

The big problem with rockets is flying near-microscopic debris.

Remember, the only different between a tiny fragment of an asteroid and a bullet is speed. Due to free-floating gas clouds, collisions, and gravity, no bit of rock is likely to be moving at too high a speed relative to anything. However, if you hit a rock the size of my thumb at 3,000mph, it'll cause some pretty serious damage. At 30,000 mph, you'll be torn apart by dust.

 

[BucsMAN3K]

Originally posted by: Cattlegod
1 - there is NO hard cap to a rockets speed due to its exhaust exit velocity. Say you have 2 planets moving in a straight line parallel to each other. One moving at 200m/s and the other moving at 100m/s. Each planet is about to launch a rocket in the same direction they are traveling. Both the rockets have an exhaust exit velocity of 100m/s. Now, if the exit velocity of the rocket was the limiting factory, the rocket on the 100m/s planet would just sit there and hover right at its launch point (we know that isn't true because we launch rockets all the time from earth) and the other rocket would actually crash backward into the planet. You can see that having the exhaust speed be the limiting speed of the rocket fails logic.

2 - The reason you can't reach the speed of light is the faster you go your mass actually increases, eventually to the point where you have infinite mass at the speed of light. So, as the rocket propels you forward and you are losing mass and accelerating, you will reach a point where the rocket will start gaining mass even with the rocket fuel burning (if it were possible to put this much fuel on a rocket in the first place) and you would not be able to accelerate anymore.

^^QFT

It was killing me to read all these posts and have people say "well of course it doesn't go faster than c but why does it stop accelerating before then?" DUH!.

 

[BucsMAN3K]

 

[Born2bwire]

Originally posted by: BucsMAN3K

Originally posted by: Cheesehead
The big problem with rockets is flying near-microscopic debris.

Remember, the only different between a tiny fragment of an asteroid and a bullet is speed. Due to free-floating gas clouds, collisions, and gravity, no bit of rock is likely to be moving at too high a speed relative to anything. However, if you hit a rock the size of my thumb at 3,000mph, it'll cause some pretty serious damage. At 30,000 mph, you'll be torn apart by dust.

Eh, I think this is a mix up in logic. If the debris hits you at 30,000mph when your stationary, then, yes your in trouble. If you hit the debris at 30,000mph while its stationary, a simple force diagram will show that you will win...infact you will obliterate the debris and never look back.

Those two situations are the same thing.

 

[RossGr]

Originally posted by: BucsMAN3K

Originally posted by: Cheesehead
The big problem with rockets is flying near-microscopic debris.

Remember, the only different between a tiny fragment of an asteroid and a bullet is speed. Due to free-floating gas clouds, collisions, and gravity, no bit of rock is likely to be moving at too high a speed relative to anything. However, if you hit a rock the size of my thumb at 3,000mph, it'll cause some pretty serious damage. At 30,000 mph, you'll be torn apart by dust.

Eh, I think this is a mix up in logic. If the debris hits you at 30,000mph when your stationary, then, yes your in trouble. If you hit the debris at 30,000mph while its stationary, a simple force diagram will show that you will win...infact you will obliterate the debris and never look back.

This is so wrong. All velocities are relative. It is impossible to say something is "stationary" since the velocity depends on who is doing the observing. A collision at 30,000mph is a collision at 30,000mph, which object is "moving" is irrelevant.

 

[cheesehead]

Originally posted by: BucsMAN3K

Originally posted by: Cheesehead
The big problem with rockets is flying near-microscopic debris.

Remember, the only different between a tiny fragment of an asteroid and a bullet is speed. Due to free-floating gas clouds, collisions, and gravity, no bit of rock is likely to be moving at too high a speed relative to anything. However, if you hit a rock the size of my thumb at 3,000mph, it'll cause some pretty serious damage. At 30,000 mph, you'll be torn apart by dust.

Eh, I think this is a mix up in logic. If the debris hits you at 30,000mph when your stationary, then, yes your in trouble. If you hit the debris at 30,000mph while its stationary, a simple force diagram will show that you will win...infact you will obliterate the debris and never look back.

Imagine a pike. (A pike is essentially a really long spear tipped with a very sharp bit of metal, designed for thrusting.)

The person wielding the pike may charge, and impale it into you.
Or, you could be charging, and impale yourself on it.

Either way, there's roughly 15 mph of difference, assuming that the moving party is on a horse.

 

[BucsMAN3K]

Originally posted by: RossGr

Originally posted by: BucsMAN3K

Originally posted by: Cheesehead
The big problem with rockets is flying near-microscopic debris.

Remember, the only different between a tiny fragment of an asteroid and a bullet is speed. Due to free-floating gas clouds, collisions, and gravity, no bit of rock is likely to be moving at too high a speed relative to anything. However, if you hit a rock the size of my thumb at 3,000mph, it'll cause some pretty serious damage. At 30,000 mph, you'll be torn apart by dust.

Eh, I think this is a mix up in logic. If the debris hits you at 30,000mph when your stationary, then, yes your in trouble. If you hit the debris at 30,000mph while its stationary, a simple force diagram will show that you will win...infact you will obliterate the debris and never look back.

This is so wrong. All velocities are relative. It is impossible to say something is "stationary" since the velocity depends on who is doing the observing. A collision at 30,000mph is a collision at 30,000mph, which object is "moving" is irrelevant.

I've really got to stop posting when I'm drunk.

 

[Born2bwire]

This thread is starting to turn into HT's version of the plane on a conveyor belt.

 

[SonicIce]

Originally posted by: Born2bwire
This thread is starting to turn into HT's version of the plane on a conveyor belt.

And I think we can all agree the plane won't fly

 

[Stiganator]

Originally posted by: SonicIce

Originally posted by: Born2bwire
This thread is starting to turn into HT's version of the plane on a conveyor belt.

And I think we can all agree the plane won't fly

QFT

It won't fly. There is no air moving under the wing. The first bit of physics we can all agree upon in this thread.

 

[Born2bwire]

Originally posted by: Stiganator

Originally posted by: SonicIce

Originally posted by: Born2bwire
This thread is starting to turn into HT's version of the plane on a conveyor belt.

And I think we can all agree the plane won't fly

QFT

It won't fly. There is no air moving under the wing. The first bit of physics we can all agree upon in this thread.

I hate you all...

 

[SonicIce]

hehe i was joking, it will fly. the question is flawed in the first place though.

 

[Born2bwire]

Originally posted by: SonicIce
hehe i was joking, it will fly. the question is flawed in the first place though.

Well, it depends on how you ask it. I remember that one of the later threads did pose impossible conditions or ones that defeat the purpose of the question (I think they said that the conveyor belt moved fast enough to keep the plane stationary). The Straight Dope has a pretty good discussion on the thing and mentions one of the incorrect ways of stating the problem.

EDIT: Hahahah, he had to post a follow-up to address responses that he received.

http://www.straightdope.com/columns/060303.html

It's pretty much what went on in ATOT.

 

[futuristicmonkey]

Originally posted by: Stiganator

Originally posted by: SonicIce

Originally posted by: Born2bwire
This thread is starting to turn into HT's version of the plane on a conveyor belt.

And I think we can all agree the plane won't fly

QFT

It won't fly. There is no air moving under the wing. The first bit of physics we can all agree upon in this thread.

The hell? The plane's wheels have nothing to do with its speed. The thrust of the propeller will get it moving...the wheels will just move faster while still on the ground.