Can magnetic field expand faster than light?

[Tominator]

I still don't get your "wall" comments. Perhaps you can work out a concrete example.

Btw, relativistic momentum is a non-linear function of velocity: p=mv/sqrt(1-v²/c²) which increases without bound as the velocity approaches c.

Yes, I was totally wrong with the "wall" comments, cos I did not realize that I can not bounce of, or push off something traveling almost at the speed of light in the oposite direction. On the other hand, isn't it more efficient to push off something in fraction of a second rather than slowly?
Recently, I have done some calculations. I wanted to know, how heavy could the ship, powered by 150MW nuclear reactor be, to be able to lift of and accelerate at 15m/s.sqrt (at 5m/s.sqrt, if we count the gravitational acceleration). I found out, that even with engine efficiency at 50%, the ship can weight around 670tuns. Am I correct?
If yes, why arent we using it, the ion engine shoul be in principal able to do the job.

 

[Dale]

Hi Tominator,

You may want to read the https://www.physicsforums.com/showthread.php?t=199087" by D_H, one of our resident rocket scientists.

Acceleration of a rocket is not just a function of engine power and vehicle mass, it also depends on the exhaust velocity and exhaust mass flow rate. Specifically, if you look at the last two equations on D_H's page you can combine them to determine the required exhaust velocity and the mass flow rate of the exhaust given a specific power, acceleration, and vehicle mass.

For your scenario, with a 75 MW power, 15 m/s² acceleration, and a 670 tonne vehicle, you find that the required exhaust velocity is 15 m/s and the required mass flow rate is 673 tonne/s. That exhaust velocity is unrealistically low and the mass flow rate is unrealistically high (the rocket burns all its fuel in less than 1s).

For a more realistic exhaust velocity of 4000 m/s, with the same 75 MW power plant, and the same 15 m/s² acceleration, your maximum vehicle mass is 2.5 tonne and your ehxaust mass flow rate is 9 kg/s. Even that mass flow rate will use up the entire load of fuel in less than 5 minutes.

 

[Tominator]

Hi DaleSpam,

Thanks for the link, but I did not mean any particular type of engine, such as rocket engine that is why I wrote ship. The nuclear reactor's output is elecricity, so there would be an engine running on electricity required. Rockets are very inefficient, because the exhaust gases are heated, thus major part of the energy is consumed by heating the gases.

I counted the possible weight of the ship with 150MW reactor from these equations: W=F.s, P=W/t and s=a.tsqrt/2 (15m/s.sqrt is the acceleration of the ship)
from these, considering time=1s, you got m=2W/a.sqrt

You might say, that the ship needs to exhaust something to gain momentum but till it is in the atmosphere, it can use the air around to repell off, above the atmosphere it might use ion engines.

The exhaust velocity of ion engine is around 40 000m/s in vacum. The energy here is used to push off the ions, so it should be much more efficient than conventional rocket engines.

 

[Dale]

So using an exhaust velocity of 40 km/s, a power of 75 MW, and an acceleration of 15 m/s² we get that the vehicle mass is 250 kg and that it consumes fuel at a rate of 94 g/s.

So, the point is that an engine with a higher exhaust velocity provides less thrust for a given power than an engine with a lower exhaust velocity. It is more efficient in terms of delta-v/kg of fuel (the exhausted fuel has more momentum per kg of fuel), but produces less thrust in terms of N/W (more of the energy is in the exhaust).

 

[Tominator]

That is strange, because I have heard about concept called NERVA, which is actually nuclear powered rocket. It never flew, because of the radioactive pollution it would cause. But it was certainly, according to what I know, able to fly. But the amount of fuel was almost like with normal rocket.
On the other hand, I still do not know, why are those equations, I have used, incorrect. I have read the link, you have sent me, but I still can not figure out, why am I getting different answer by the euation, I have mentioned in previous post.
If one object applies force on another object the reaction has to be equivalent, no matter, what the weight ratio is between the two objects. If the force is the same, the momentum has to be the same too. So how can the possible weight of the ship depend on the weight of the fuel exhausted per second?

 

[Dale]

I still do not know, why are those equations, I have used, incorrect. I have read the link, you have sent me, but I still can not figure out, why am I getting different answer by the euation, I have mentioned in previous post.

The first clue that something is wrong in that equation is that you just randomly specified t=1s. That should clue you in that your result depends on time and is only valid at one time point.

If one object applies force on another object the reaction has to be equivalent, no matter, what the weight ratio is between the two objects. If the force is the same, the momentum has to be the same too.

Yes, that is correct. That is what Newton's 3rd law says.

So how can the possible weight of the ship depend on the weight of the fuel exhausted per second?

Because you specified a power, not a force. For a given fixed power the thrust force is a function of the exhaust velocity. Once you have fixed the power and the exhaust velocity then the exhaust mass flow rate and the thrust are uniquely determined by conservation of momentum (derived by D_H in the tutorial). Then if you further fix the acceleration that uniquely determines the vehicle mass by Newton's 2nd law.

 

[Dale]

Hi Tominator,

I hope my previous post was not too terse. Anyway, I wanted to explain a little more. I really recommend that you read the rocket tutorial in depth and ask me any specific questions that you have.

I mentioned that your formula was only valid at one time point:
P = W/t = (F.s)/t = ((m a).(1/2 a t²))/t = ma²t/2

What this means is that if you apply a constant force on an object (starting at rest at the origin) then the power increases linearly with time.

 

[Tominator]

Hi DaleSpam,

Thanks for your answers and recomendations, you wrote it clearly, but it took me some time to process it.

Because you specified a power, not a force. For a given fixed power the thrust force is a function of the exhaust velocity. Once you have fixed the power and the exhaust velocity then the exhaust mass flow rate and the thrust are uniquely determined by conservation of momentum (derived by D_H in the tutorial). Then if you further fix the acceleration that uniquely determines the vehicle mass by Newton's 2nd law.

Well, I can not argue about that. From what I have read, the equation is for a rocket burning its fuel till it reaches desired change in velocity. But there are work-arounds, for example by using more stages the rocket will be more efficient.

I mentioned that your formula was only valid at one time point:
P = W/t = (F.s)/t = ((m a).(1/2 a t²))/t = ma²t/2

What this means is that if you apply a constant force on an object (starting at rest at the origin) then the power increases linearly with time.

If the power is fixed, will the force decrease with time?
But what if we use the energy in pulses? Can the efficiency be enhanced by pulses? (Thanks to the inertia of the exhausted fuel)
What I mean is a kind of a pulse drive
With the ion engine, it is possible, (or in recent futurre it will be possible), to generate thrust by pulses. By using more ion engines, the pulses can be synchronized like in a combustion engine.

 

[Dale]

Well, I can not argue about that. From what I have read, the equation is for a rocket burning its fuel till it reaches desired change in velocity. But there are work-arounds, for example by using more stages the rocket will be more efficient.

Yes. In that case the equations on the tutorial page apply to each stage individually. Reducing the mass of the vehicle at each stage helps with efficiency.

If the power is fixed, will the force decrease with time?

Yes.

But what if we use the energy in pulses? Can the efficiency be enhanced by pulses? (Thanks to the inertia of the exhausted fuel)
What I mean is a kind of a pulse drive
With the ion engine, it is possible, (or in recent futurre it will be possible), to generate thrust by pulses. By using more ion engines, the pulses can be synchronized like in a combustion engine.

You can certainly use the energy in pulses, and in fact it is generally optimal to do so. However, the substitution s = 1/2 a t² is only valid for uniform acceleration starting from the origin, so your equation would not apply. You would need to use the more general equations on the tutorial page.

 

[Tominator]

Hm, I was really surprised, why we do not use nuclear power to get a ship to orbit, now I understand.
Anyway, recently I have got an idea: if it is possible to generate plasma, by using high frequency EM field, it should be possible to generate plasma also by using high frequency one-way current pulses. Would this have a propulsion effect(in the atmosphere)?

 

[Dale]

Yes, this is the principle used by the ill-fated sharper image "ionic breeze". You can use that principle to build a little hovercraft called an http://en.wikipedia.org/wiki/Ionocraft" . The thrust that these generate is currently not enough to lift the high voltage power supply that they need, but I think that is probably a practical limitation rather than a fundamental one. They make good little science fair projects.

 

[Tominator]

I have heard about the Ionocrafts, but I assume, they do not use plasma. I was thinking about creating plasma by the EM field and thus making a kind of EM jet engine. Because the plasma will be generated only by using electricity and of course the air, there will be no need for fuel while in the atmosphere. On the other hand, this concept would be even more inefficient than rockets.

Is there an ionizator used in the ionocrafts?

I thought, that if ionized gas runnig around in the nozzle in the direction from the air-intake to the part, where air is exhausted was used there, than the ionized gas can make the air accelerate. The ionized gas would not be exhausted, it would only circle around grabbing some air with and accelerating it in the right direction. Would this be more efficient than today's ionocrafts?

 

[Dale]

Well, the word "plasma" isn't well defined to my knowledge. A plasma is a partially ionized gas, and an ionocraft does partially ionize the air, but the degree of ionization is so low that it doesn't have much of the "collective" behavior typical of more completely ionized plasmas.

I don't know about the efficiency of the circulating nozzle idea. You could certainly keep the ions in the nozzle longer and so perhaps get more ionization for the same ionization current, but I am not clear about how you would turn the circulation into thrust.

 

[Tominator]

Well, the word "plasma" isn't well defined to my knowledge. A plasma is a partially ionized gas, and an ionocraft does partially ionize the air, but the degree of ionization is so low that it doesn't have much of the "collective" behavior typical of more completely ionized plasmas.

I don't know about the efficiency of the circulating nozzle idea. You could certainly keep the ions in the nozzle longer and so perhaps get more ionization for the same ionization current, but I am not clear about how you would turn the circulation into thrust.

I was counting with air as a propellant. The air will be sucked in, thanks to circulation of ionized gas, then compressed and accelerated out of the nozzle. (also by the circulation) So no energy would be wasted on creating plasma. It should work like a propeller made out of gas. Would it work?

 

[Dale]

I don't know. I am having a hard time visualizing how the circulating ions would act like a propeller. I am afraid that you will have to work this one out yourself, but I can also tell you that plasma mechanics is an incredibly advanced subject. To really learn it will literally take years of serious effort.

 

[Tominator]

Anyway, thanks for all the answers

 

[Dale]

You're welcome!