Conservation of momentum

[sol invictus]

I strongly suspect that there's a force on the tapered walls of the cavity that balances out the difference exactly, but I'd have to revise a lot of stuff I haven't looked at for a quarter of a century before I could work it out.

It depends a little on what the initial state of the of the microwaves is.

Think of some marbles in a can in space (make the can tapered if you want, or any shape). You can imagine a configuration where the can is at rest, but all the marbles are flying towards one end. When they hit, they'll scatter in many directions, and the thing will settle down to a state where the whole can moves in the direction the marbles were originally going (since the average momentum carried by the marbles themselves after they have time to scatter a few times will be close to zero).

(You could do this experiment - take a basin of water, shake it once to make a wave, and quickly set it down on ice or some other slippery surface before the wave hits the side. The whole thing will slide off, jolting a little as the waves settle down.)

Contrast that with the case where the can is at rest and the marbles are flying around randomly. It's obvious that no matter what the shape of the can is, it will never start accelerating off in some direction (or even move much except for some little vibrations from bouncing marbles).

So you could probably arrange a configuration of EM fields that would give the thing a little kick at the beginning, but only because you started off with that momentum. You can't change the net momentum so long as nothing leaves the can, and the shape is totally irrelevant to that. So yes, there's a force on the tapered sides exactly that cancels the one he computed. No work necessary.

 

[Dancing David]

Because nothing leaves the cavity. Firing photons out of one end is a perfectly viable way of creating thrust. The concept of a lightsail is based on this, although it gets double the momentum per photon because they're reflected back on themselves. The EM drive doesn't fire photons out of one end; it's based on the principle that the photons bounce harder off one end of the cavity than they do off the other. I strongly suspect that there's a force on the tapered walls of the cavity that balances out the difference exactly, but I'd have to revise a lot of stuff I haven't looked at for a quarter of a century before I could work it out.

Dave

Thanks! I didn't realize it was sealed.

We can move this house on three, everyone push! (inside)

 

[Dave Rogers]

I just took a look at the paper by Roger Shawyer, the inventor. It's at http://emdrive.com/theorypaper9-4.pdf, because I was interested to see how he calculates the axial component of the force on the walls of the cavity.

From Shawyer's FAQ on the EmDrive:

Q. Why does the net force not get balanced out by the axial component of the sidewall force?

A. The net force is not balanced out by the axial component of the sidewall force because there is a highly non linear relationship between waveguide diameter and group velocity. (e.g. at cut off diameter, the group velocity is zero, the guide wavelength is infinity, but the diameter is clearly not zero.) The design of the cavity is such that the ratio of end wall forces is maximised, whilst the axial component of the sidewall force is reduced to a negligible value.​

He's clearly implying here that he has calculated the axial component of the sidewall force and found it to be negligible. However, in the paper, which he claims gives the full theory of the device, he doesn't bother to do so. He demonstrates that the group velocity of the microwaves is changing as they propagate down the cavity, but he's not even attempted to determine whether this results in a force exerted on the sidewalls by the radiation field. He's simply calculated the radiation pressure on the two end walls, found that it's greater on the larger wall because of the greater group velocity of the microwaves at the wider end of the cavity, and concluded that the difference is a real net force.
​

There's a longer version of the paper at http://www.newscientist.com/data/images/ns/av/shawyertheory.pdf from the New Scientist, where he tries to handwave away the sidewall forces, effectively pretending that they only act at right angles to the direction of propagation. This is incorrect; photon pressure from specular reflection can only possibly act at a right angle to the reflecting surface. Having pretended the axial component doesn't exist, Shawyer therefore doesn't bother to calculate it.

Shawyer is either lying, or is unable to comprehend simple vector summation.

Dave

 

[GreyICE]

Because nothing leaves the cavity. Firing photons out of one end is a perfectly viable way of creating thrust. The concept of a lightsail is based on this, although it gets double the momentum per photon because they're reflected back on themselves. The EM drive doesn't fire photons out of one end; it's based on the principle that the photons bounce harder off one end of the cavity than they do off the other. I strongly suspect that there's a force on the tapered walls of the cavity that balances out the difference exactly, but I'd have to revise a lot of stuff I haven't looked at for a quarter of a century before I could work it out.

Dave

No. No it does NOT depend on this. The momentum of photons would NEVER move a ship at any appreciable velocity.

A lightsail works by catching the solar wind. It's a gigantic version of the ships Columbus used. It most certainly does not propel itself with photons.

 

[Dave Rogers]

No. No it does NOT depend on this. The momentum of photons would NEVER move a ship at any appreciable velocity.

A lightsail works by catching the solar wind. It's a gigantic version of the ships Columbus used. It most certainly does not propel itself with photons.

Sorry, but you're wrong. The clue is in the title: lightsail. It works, in principle, by reflecting photons from an external source, gaining twice the momentum of the photon in doing so. There's a proposal by Robert Forward that a bank of high-powered lasers could be used for propulsion; a bit useless if it worked by trapping charged particles, don't you think?

As for "gigantic version of the ships Columbus used", you do realise, don't you, that they worked by deflecting air currents, and that the solar wind is something completely different?

Dave

 

[GreyICE]

Sorry, but you're wrong. The clue is in the title: lightsail. It works, in principle, by reflecting photons from an external source, gaining twice the momentum of the photon in doing so. There's a proposal by Robert Forward that a bank of high-powered lasers could be used for propulsion; a bit useless if it worked by trapping charged particles, don't you think?

As for "gigantic version of the ships Columbus used", you do realise, don't you, that they worked by deflecting air currents, and that the solar wind is something completely different?

Dave

Yes, instead of air, it is catching a stream of fast-moving charged particles ejected from the sun. The Solar Wind is ultra-high speed charged particles, and that is what any of the proposed sails would be catching. It is EXACTLY the same as a sail - the material stops the fast-moving particles hitting it, absorbing their momentum and propelling the ship forward.

The other way I've heard is to coat them with a thin layer of matter that boils off at remarkable velocity from the heat generated by the sun - a kind of diffuse ion drive.

The 'light sails' seem highly improbable, and are much worse than something catching particles, IMHO.

I don't know what this magical laser drive is, but I highly doubt it has anything to do with anything.

 

[Dave Rogers]

Yes, instead of air, it is catching a stream of fast-moving charged particles ejected from the sun. The Solar Wind is ultra-high speed charged particles, and that is what any of the proposed sails would be catching. It is EXACTLY the same as a sail - the material stops the fast-moving particles hitting it, absorbing their momentum and propelling the ship forward.

You're wrong. Look it up.

Dave

 

[The Man]

Sorry, but you're wrong. The clue is in the title: lightsail. It works, in principle, by reflecting photons from an external source, gaining twice the momentum of the photon in doing so. There's a proposal by Robert Forward that a bank of high-powered lasers could be used for propulsion; a bit useless if it worked by trapping charged particles, don't you think?

As for "gigantic version of the ships Columbus used", you do realise, don't you, that they worked by deflecting air currents, and that the solar wind is something completely different?

Dave

I think you mean that the radiation pressure is doubled in reflection (over absorption) not that twice the momentum of the photon is gained by reflection.

 

[sol invictus]

No. No it does NOT depend on this. The momentum of photons would NEVER move a ship at any appreciable velocity.

A lightsail works by catching the solar wind. It's a gigantic version of the ships Columbus used. It most certainly does not propel itself with photons.

Dave is correct - you have this wrong. Photon pressure from the sun is much larger than solar wind pressure.

 

[sol invictus]

I think you mean that the radiation pressure is doubled in reflection (over absorption) not that twice the momentum of the photon is gained by reflection.

What's the difference?

 

[Dave Rogers]

I think you mean that the radiation pressure is doubled in reflection (over absorption) not that twice the momentum of the photon is gained by reflection.

The photon has an initial momentum p, and a final momentum -p. The change in photon momentum is -2p, therefore the change in lightsail momentum is +2p. Twice the momentum of the photon is thus gained by reflection.

Dave

 

[Dancing David]

There's a proposal by Robert Forward that a bank of high-powered lasers could be used for propulsion; a bit useless if it worked by trapping charged particles, don't you think?

I think Crazy Eddie used ground based lasers in The Mote in God's Eye.

 

[The Man]

What's the difference?

The photon has an initial momentum p, and a final momentum -p. The change in photon momentum is -2p, therefore the change in lightsail momentum is +2p. Twice the momentum of the photon is thus gained by reflection.

Dave

Yeah, you’re both right, I posted just before I went to lunch then thought about it at lunch, specifically a radiometer and remembered the erroneous application of radiation pressure for its operation. That must have gotten my old brain cells firing again and I remembered the correct calculations for radiation pressure. The only consolation is that it is not the stupidest thing I have said or posted.

I was even thinking about a cosmic background radiation sail (black on one side and reflective on the other). You would need 2.88 X 10¹⁴ square meters (about 56% of the surface area of the Earth) to get one Newton of thrust and the blackbody radiation form the black side (at equilibrium) would match the reflected radiation from the other side so you would only get thrust as long as the sail was cooler then 2.725 K.

 

[TMiguel]

A Brittish engineer has developed an engine which claims to violate the law of momentum. Forumites are discussing it here. The engine has the supposed ability to achieve acceleration without any propellant.

Like everyone else who has taken a couse or two in physics, I was taught that momentum will always be constant. I always took this law for granted because it makes perfect sense to my experience. I wonder though, does the law of momentum share the same logical problem as stating that all swans are white? Is there a compelling reason to assume that it's true at all times?

It is extremely easy to transform the conservation of momentum problem into conservation of energy problem (which is pretty much certain) and proving that such violation is impossible.

 

[sol invictus]

It is extremely easy to transform the conservation of momentum problem into conservation of energy problem (which is pretty much certain) and proving that such violation is impossible.

They're not equivalent, actually. You can have one without the other.

 

[PingOfPong]

It is extremely easy to transform the conservation of momentum problem into conservation of energy problem (which is pretty much certain) and proving that such violation is impossible.

I remember in my PHY lab that we performed an experiment with some pendulums that showed how momentum was conserved when two pendulums collide yet some of the kinetic energy was lost. That lost energy became sound waves (you could hear them hit).

 

[GreyICE]

Dave is correct - you have this wrong. Photon pressure from the sun is much larger than solar wind pressure.

Okay, I was always under the impression this was the exact opposite, but I'll trust you.

There's no way in heck that laser thing works though.

 

[The Man]

Okay, I was always under the impression this was the exact opposite, but I'll trust you.

There's no way in heck that laser thing works though.

The radiant pressure of the Sun in the vicinity of the Earth is about 4.6 µPa absorbed making it 9.2 µPa reflected. Unfortunately, I can find no reliable range for the dynamic solar wind pressure in the vicinity of the Earth, at this time. If you can accept that the radiant emissions of the Sun can transfer more momentum then the particulate emissions, I fail to see why you think “There's no way in heck that laser thing works though”. Being focusable and one wavelength (your sail can be designed for that specific wavelength) an intended transmission of momentum can be more efficient then just gaining momentum from some random source (like the Sun). As long as the radiant source is not carried, as part of the body being accelerated, you gain more momentum then if you were carrying that source. If the radiant source is carried then there is no advantage to reflection then just shooting it out behind you and you have to carry some source for that emission energy (fuel) or gain it somewhere at perhaps less efficiency then just reflecting incident radiation.

 

[GreyICE]

The radiant pressure of the Sun in the vicinity of the Earth is about 4.6 µPa absorbed making it 9.2 µPa reflected. Unfortunately, I can find no reliable range for the dynamic solar wind pressure in the vicinity of the Earth, at this time. If you can accept that the radiant emissions of the Sun can transfer more momentum then the particulate emissions, I fail to see why you think “There's no way in heck that laser thing works though”. Being focusable and one wavelength (your sail can be designed for that specific wavelength) an intended transmission of momentum can be more efficient then just gaining momentum from some random source (like the Sun). As long as the radiant source is not carried, as part of the body being accelerated, you gain more momentum then if you were carrying that source. If the radiant source is carried then there is no advantage to reflection then just shooting it out behind you and you have to carry some source for that emission energy (fuel) or gain it somewhere at perhaps less efficiency then just reflecting incident radiation.

If it's carried its obvious garbage.

If the concept is to station lasers in useful locations to bang cargo around, I have to ask "Why?" What possible use could such a system serve that we couldn't do more traditionally? The sail would never survive contact with a gravity well (we could, say, return it to the craft, but that rather defeats the entire laser deal). An ultra-thin enormous skin in a place where things tend to pick up orbitals is a bad idea. And they'd be useless for landing. So unless we hypothesize an entirely different landing gear, they're useless for that.

They're useless on anything that rotates. They'll be pointing the wrong way too often.

So we're left with an incredibly complicated system to ship things inbetween space stations. When its the simplest thing in the world to construct an ion drive and use solar panels.

 

[The Man]

If it's carried its obvious garbage.

If the concept is to station lasers in useful locations to bang cargo around, I have to ask "Why?" What possible use could such a system serve that we couldn't do more traditionally? The sail would never survive contact with a gravity well (we could, say, return it to the craft, but that rather defeats the entire laser deal). An ultra-thin enormous skin in a place where things tend to pick up orbitals is a bad idea. And they'd be useless for landing. So unless we hypothesize an entirely different landing gear, they're useless for that.

They're useless on anything that rotates. They'll be pointing the wrong way too often.

So we're left with an incredibly complicated system to ship things inbetween space stations. When its the simplest thing in the world to construct an ion drive and use solar panels.

Traditional is not very efficient, ion drives and gravity assists are traditionally fine but the former requires transference of energy (or bringing it with you) through less efficient systems (15% to 25% max if I remember correctly) then just reflecting that radiation and the latter increases mission time as well as risk. Transport systems work in various ways, for local transport maneuverability as well as take off and landing applications are critical. However for bulk transport, over long distances, they are not that much of a concern it is just a matter of how much power you can pour into them that you do not have to carry with you. Combined systems are always the best. Do not get too hung up on the fragility of predominant sail concepts. Rotational sails (like helicopter blades) are being considered, but I do not know what the current developmental status is.