How do you build Drives?

[prestidigitator]

Re: How do you build Drives?

 

Question:

 

I linked that Bob Lazaar "Gravity Generator" stuff that I'm loosely basing my FTL on and am curious.

 

Let's say this drive system is plausible; does it break either or both of those laws? General idea is a nuclear reaction that turns the energy into a gravity wave and either pushes or pulls against other gravity fields. So the 'thrust' is provided by gravity, not the exhaust of reaction mass. Is that a reactionless drive? Or no, because there is a nuclear reaction that requires fuel, albeit a tiny amount?

 

Gravity does not act on a single mass, but is an attraction between different masses. I'm not sure what a gravity "wave" is supposed to be, but it's lovely rubber physics. A mass out in front of your ship (for example) would serve to accelerate the ship forward, but that useful mass out front would be accelerated back toward your ship in return, rather than accelerating along with your ship. If somehow the mass being used to accelerate your ship also accelerates with your ship, then conservation of momentum is definitely being violated. Conservation of energy may or may not be, I suppose, though it is hard to consider each of those conservation laws in isolation when in reality both must hold.

[Zeropoint]

Re: How do you build Drives?

 

Not always.

They violate conservation of momentum, but can be made so that they obey conservation of energy.

These don't obey either.

 

Well, I'm going to attempt to convey my understanding of the situation. Here goes:

 

As we all know, the kinetic energy of a moving object is equal to 0.5 * mass * velocity^2.

 

That "squared" bit is where the complications come in, since it means that the same absolute change in velocity does NOT always produce the same change in kinetic energy. For example, a one kilogram mass at rest has zero joules of kinetic energy, while the same mass moving at ten meters per second has 0.5 * 1 * 10^2 = 0.5 * 1 * 100 = 50 joules of kinetic energy. Accelerate that same mass to 20 m/s and it now has 0.5 * 1 * 20^2 = 0.5 * 1 * 400 = 200 joules of kinetic energy.

 

Okay, no problem so far--that just means that our drive, be it a rocket or reactionless thruster, consumes more energy over that second acceleration. But, there are a couple of problems that creep in. First, is this mass undergoing a constant acceleration? If so, that means that the drive's consumption of energy is increasing with every passing second. That's . . . odd, but not a violation of conservation of energy.

 

The second issue is worse: as Einstein taught us, there are no privileged observers, i.e. we cannot designate any frame of reference as being "correct" or "stationary". In a reference frame where the mass is stationary to begin with, an observer sees the tiny rocket expend 50 joules worth of stored energy to add 50 joules of kinetic energy, and then in the next second (or however long) expend 200 joules of stored energy to add 200 joules of kinetic energy. No problem, it's changed 250 joules of some form of potential energy into kinetic energy.

 

However, consider a second frame of reference, in which the rocket in question is initially moving with a velocity of -10 m/s. In this case, the rocket BEGINS with 50 joules of kinetic energy, and over the first second of acceleration, it comes to rest . . . losing 50 joules of potential energy AND 50 joules of kinetic energy. In the next second, the rocket accelerates to 10 m/s, expending that same 200 joules and gaining . . . 50 joules of KE.

 

Note that thus far, I have not distinguished between a newtonian rocket and a reactionless thruster--I'm simply dealing with spent fuel and the change in kinetic energy.

 

And that, in fact, is the source of the error: I have ONLY been considering the motion of the rocket itself, and ignoring the exhaust. When the rocket accelerates, the exhaust also accelerates (in the opposite direction, of course). When the exhaust is included in the calculations, it turns out that in any frame of reference, the total kinetic energy of the rocket/exhaust system changes by the same amount as the energy expended by the rocket.

 

For a reactionless thruster, fuel energy spent = kinetic energy gained ONLY for a specific frame of reference; in any other frame of reference--which are equally valid, the change in kinetic energy is NOT equal the the fuel energy spent.

 

So, in conclusion, reactionless thrusters violate conservation of energy (or the principle that there are no "privileged observers, I suppose).

 

As much as I'd like to see a future with reactionless drives, as far as I can tell, they're as magical as perpetual motion machines.

[Kristopher]

Re: How do you build Drives?

 

Well, I'm going to attempt to convey my understanding of the situation. Here goes:

 

As we all know, the kinetic energy of a moving object is equal to 0.5 * mass * velocity^2.

 

That "squared" bit is where the complications come in, since it means that the same absolute change in velocity does NOT always produce the same change in kinetic energy. For example, a one kilogram mass at rest has zero joules of kinetic energy, while the same mass moving at ten meters per second has 0.5 * 1 * 10^2 = 0.5 * 1 * 100 = 50 joules of kinetic energy. Accelerate that same mass to 20 m/s and it now has 0.5 * 1 * 20^2 = 0.5 * 1 * 400 = 200 joules of kinetic energy.

 

Okay, no problem so far--that just means that our drive, be it a rocket or reactionless thruster, consumes more energy over that second acceleration. But, there are a couple of problems that creep in. First, is this mass undergoing a constant acceleration? If so, that means that the drive's consumption of energy is increasing with every passing second. That's . . . odd, but not a violation of conservation of energy.

 

The second issue is worse: as Einstein taught us, there are no privileged observers, i.e. we cannot designate any frame of reference as being "correct" or "stationary". In a reference frame where the mass is stationary to begin with, an observer sees the tiny rocket expend 50 joules worth of stored energy to add 50 joules of kinetic energy, and then in the next second (or however long) expend 200 joules of stored energy to add 200 joules of kinetic energy. No problem, it's changed 250 joules of some form of potential energy into kinetic energy.

 

However, consider a second frame of reference, in which the rocket in question is initially moving with a velocity of -10 m/s. In this case, the rocket BEGINS with 50 joules of kinetic energy, and over the first second of acceleration, it comes to rest . . . losing 50 joules of potential energy AND 50 joules of kinetic energy. In the next second, the rocket accelerates to 10 m/s, expending that same 200 joules and gaining . . . 50 joules of KE.

 

Note that thus far, I have not distinguished between a newtonian rocket and a reactionless thruster--I'm simply dealing with spent fuel and the change in kinetic energy.

 

And that, in fact, is the source of the error: I have ONLY been considering the motion of the rocket itself, and ignoring the exhaust. When the rocket accelerates, the exhaust also accelerates (in the opposite direction, of course). When the exhaust is included in the calculations, it turns out that in any frame of reference, the total kinetic energy of the rocket/exhaust system changes by the same amount as the energy expended by the rocket.

 

For a reactionless thruster, fuel energy spent = kinetic energy gained ONLY for a specific frame of reference; in any other frame of reference--which are equally valid, the change in kinetic energy is NOT equal the the fuel energy spent.

 

So, in conclusion, reactionless thrusters violate conservation of energy (or the principle that there are no "privileged observers, I suppose).

 

As much as I'd like to see a future with reactionless drives, as far as I can tell, they're as magical as perpetual motion machines.

 

My approach to such questions is that they'll work if they work, and not work if they don't, and that we don't know yet.

[prestidigitator]

Re: How do you build Drives?

 

If I recall correctly, Asimov's gravitic drives were explained as amplifying the gravitational acceleration between the ship and far off masses in the desired direction of acceleration. That would mean that those far off masses would gain some momentum toward the ship as well, but usually the masses are so humongous it wouldn't matter much. That's similar to the idea of a "slingshot" orbit about a planet to gain momentum; you don't get something for nothing, but the planet is so massive its orbit about its star isn't going to change much. "Reactionless" as far as anyone in the ship is concerned, but not an actual violation of the conservation of momentum. As for conservation of energy? Who knows. The drive would have to be expending a lot of energy certainly, but there's nothing that says it couldn't be getting that energy from some kind of nuclear reaction or stored energy or something. Eh.