Mach Effect progress

GIThruster · Post by **GIThruster** » Mon Dec 10, 2012 9:05 pm

You're on a red herring. It does not matter what it takes to get the rocket to any specific velocity. Since V is relative, all rockets are always at sufficiently high V to have this seeming conservation violation. The propellant is not the issue. The issue is that simple kinematics cannot give you the proper answer. You have to sum the instantaneous frames of reference--whatever that is--and I can't help with that. It's graduate level GR. I can only note to you that Steven Feurst did not make this objection, and neither did anyone who has peer reviewed this.

If you think the propellant is the issue, then do the calculation with the rocket on a flywheel, with it's propellant supplied through the moment arm, same as with Roton. You'll see you get the same absurd result. If you spin up the flywheel with an electric motor, and your Hall thruster on the flywheel has the same velocity and thrust efficiency as that in chris' example, you get the same result.

tomclarke · Post by **tomclarke** » Mon Dec 10, 2012 9:19 pm

OK - lets do the math.

a rocket thruster will use energy to create velocity differential dV between the craft and its ejected fuel. For a mass flow dm/dt we have force:
dV(dm/dt)
and power:
(1/2)(dV^2)(dm/dt)

You will notice that we can reduce the power for given force arbitrarily by reducing dV at the cost of increasing dM.

That tells you that something is hapenning here to the energy equation. It is easiest to see this in the instantaneous rest frame of the rocket

after time dT let:
M0 = dTdm/dt
M1 = def rocket mass

dV1 = dV(M0/M1)
dV0 = -dV

E = (1/2)dV^2(M0/M1+1)M0

We are assuming M1 >> Mo (otherwise the power eqn needs modifying) so the energy expened balances the KE after the dT interval of thrust.

Now consider ME drive doing the same thing. In this case for a given force F the energy (measured in instantaneous rest frame) will be different from the energy (measured in some different frame). That is problemtic. You have to invoke some energy transfer with "all mass in universe" etc for it to balance.

Note taht teh rocket case energy balances in a moving frame because the higher rocket delta E balances the higher ejected fuel deltaE so all is still OK. With ME we have a force without the material acted on so things do not balance. Unless as I say you reckon something about all mass in universe etc so it is not really reactionless.

GIThruster wrote:I don't have that previous explanation handy. It is however not necessary.

chris' contention that rockets don't demonstrate this problem is bullshit. Put a rocket on a flywheel and feed it propellant through the moment arm just as with Roton and you have precisely the same curiosity pop up. That's because we don't normally do the math properly. Just as when we do vector addition, we can normally use Newtonian mechanics and get away with it, we can for short periods of time get away with doing the math improperly in this instance. However, the same objection chris, goatguy, Andrew Palfreyman and others at NSF have had has been answered several times now over the years, and it's important to note that it will come up several more times in the coming years. (Steven Feurst's objection is a different one. It's not fair to say he made this mistake.)

This is because the people making the complaint don't understand the relevant math. Rather, they in general understand how to be a troll. When you have a simple counter-example that clearly demonstrates the method being used to come up with a conservation violation generates an absurd conclusion that applies equally as well to all rockets, it is obvious that the method is wrong. And that is enough an answer.

Just take the simple case chris offered: "If a craft was moving at 100,000 m/s then would a 130uN thrust not mean that its rate of kinetic energy gain would be 13 J/s, and if so is this not a contradiction to an input energy of 1 W?" Substitute the thruster in this example with a Hall or Ion thruster and you have THE SAME RESULT. It doesn't matter how the thruster gets to 100,000 m/s. All satellites in GSO are moving a lot faster than this in the Earth reference frame they were launched in and their Hall thrusters are putting out this kind of thrust. Are they all violating conservation? Of course not. What about Deep Space 1? Calculating in the manner chris is recommending, it has been over-unity since it first had its Ion engines kick in.

I should note to you here, that Jim never defends himself against cranks like chris. He knows there are still nut cases out there that think Newton and Einstein were wrong. Especially trolls like chris, think they're going to prove themselves clever by peeing on the leg of an elephant. If there are still whack jobs who claim Newton and Einstein are wrong, there are most certainly going to be trolls who say Woodward is wrong, and they are not worth answering past showing conclusively they are doing the math wrong.

GIThruster · Post by **GIThruster** » Mon Dec 10, 2012 9:32 pm

Wel I appreciate Tom is lending a hand here. I wish I could understand all that he wrote. The issue with propellant is not however the issue.

Consider the example of a Hall thruster in space with 1 second of propellant aboard and traveling at 100,000 m/s. The thruster fires with the same thrust efficiency as the M-E thruster for one second. You get the same result.

There is obviously something wrong with the math.

Note that irrespective of V, dV is linear and dE is quadratic. This means that at any thrust efficiency, there is some V where anything producing constant thrust will appear to violate conservation, without regard for things like propellant, and since V is relative, using this method you can show any thruster is always in violation of conservation. There is something wrong with the math, and its got nothing to do with propellant.

chrismb · Post by **chrismb** » Mon Dec 10, 2012 9:46 pm

forget the ? about travelling at 100,000m/s (the kinetic power is a function of the observed power in the static frame)

chrismb · Post by **chrismb** » Mon Dec 10, 2012 9:49 pm

93143 wrote:If you're going to assess energy conservation in a thruster, you have to account for both the thruster (and whatever's attached to it) and its propellant. This is what makes rockets conserve energy - the chemical energy in the propellant is converted into a fixed amount of kinetic energy inherent in the velocity difference between the rocket and its exhaust.

This is an argument about momentum, not of energy. In the original frame of acceleration, the total kinetic energy of the propellant and the rocket cannot be less than the kinetic energy of the rocket. So just look at the kinetic energy of the rocket. That, alone, cannot be greater than the sum energy expended, let alone some propellant floating around too.

chrismb · Post by **chrismb** » Mon Dec 10, 2012 9:50 pm

Just deal with this one...

State which line the error of premise occurs:
1) A 1 kg test thruster is subjected to a 1 W, 130 uN of thrust.
2) It accelerates for 10 years (call it 300 Ms) from a given rest frame at which it was at 0 m/s.
3) 300 MJ has been expended.
4) The test thruster is travelling at 39,000m/s (it'll have reached 3.6 bn miles by then ... a trip to Neptune!)
5) Its kinetic energy wrt the given rest frame is then 760 MJ, which is greater than the 300 MJ expended.

and if the answer is some reactive response by the 'rest of the universe', what would be the evidence to give that something else moved in the universe, such that it has a NEGATIVE kinetic energy effect!?

GIThruster · Post by **GIThruster** » Mon Dec 10, 2012 10:03 pm

You're on a red herring.

chris, use your example with any Hall or ion thruster. Thrust efficiency does not matter. Doing the math the way you are, at any thrust efficiency there will always be a seeming violation at some V, and since V is relative, doing the math the way you are will always yield a seeming violation.

Not for nothing, but Andrew brought this up more than a dozen times on Jim's list over 6 years. The trolling gets old. Fact is, if you can't do the math the right way, you should not be trying to do it at all.

93143 · Post by **93143** » Mon Dec 10, 2012 10:38 pm

chrismb wrote:So just look at the kinetic energy of the rocket. That, alone, cannot be greater than the sum energy expended, let alone some propellant floating around too.

That only works if you're hauling propellant around, and/or the propellant used throughout the acceleration is known to be initially stationary with respect to the initial reference frame (a simple solar sail breaks your method).

With the M-E thruster, you do not know this. In fact, for the thruster to work as described, it pretty much can't be true.

...

There was a recent discussion on NSF about Skylon, and someone tried to claim that the Mach 5.5 reached during the airbreathing phase only represented a few percent of the necessary orbital energy, leading to the conclusion that it wasn't worth it. This is nonsense, of course, for two reasons: (1) the mass at MECO is not the same as the mass at switchover; it's less than a quarter of it, and (2) the energy efficiency of the engines, as measured from the ground, increases dramatically and smoothly well past 100% as the vehicle accelerates. Once a rocket-propelled vehicle's velocity exceeds half the exhaust velocity, the vehicle gets more kinetic energy from the propellant than was available chemically (after inefficiencies), because the propellant after exhaustion is moving more slowly than it was in the tanks.

If you consider what this means in the context of the M-E thruster, you should realize that while you can still question the plausibility of the mean velocity difference between the thruster and its distant reaction mass somehow always being low or zero ([*deep breath*]), your simplistic conservation argument no longer holds water.

As for "evidence" that the rest of the universe is responding appropriately, we can assume it is if the thruster works in the lab, unless some really spiffy math or strong experimental evidence (can't imagine what) says it isn't. Conservation of momentum and energy is pretty well established and can be assumed to hold absent strong evidence to the contrary.

...

GIThruster, what's "wrong with the math" in your example is that the propellant kinetic energy is unaccounted for. The propellant question is not a red herring; it's central to the issue.

GIThruster · Post by **GIThruster** » Mon Dec 10, 2012 11:08 pm

93143 wrote:GIThruster, what's "wrong with the math" in your example is that the propellant kinetic energy is unaccounted for. The propellant question is not a red herring; it's central to the issue.

That's why I suggest one do the calculations with a Hall or Ion thruster, because the energy into the thruster is electrical and constant. The energy content of the propellant is unimportant as it is at rest with regard to the thruster. We measure thrust efficiencies for Hall thrusters just the same way we do for M-E thrusters.

The only exception is that in the case of an M-E thruster driving a wormhole condition, where dm=>m, there is an additional energy into the thruster as a contribution of negative inertia from the exotic matter. In each M-E event cycle, the mass fluctuates positive in the first and third quarter cycles, and negative in the second and fourth quarter cycles. The negative fluctuation is always a little larger than the positive one, so there is an additional power into the thruster that needs to be taken account of. This becomes significant at very large thrust efficiencies where one is driving very large dm. In a 1N/W thruster, this would be significant, just as it would be with any generation of exotic matter sufficient to build a warp drive or a wormhole generator.

But this is all a separate issue. In instances with the thrust efficiencies like what we've been talking about, one can presume the energy into the thruster is the same as the energy coming out. And like I said, if you do the math the way people suppose it ought to be done, you get precisely the same seeming violation with a Hall thruster as you do with an M-E thruster. Pick a functioning Hall thruster that's been well characterized and assume an arbitrarily high V, and you will have a seeming violation, doing the math the way proposed here.

93143 · Post by **93143** » Mon Dec 10, 2012 11:10 pm

GIThruster wrote:
93143 wrote:GIThruster, what's "wrong with the math" in your example is that the propellant kinetic energy is unaccounted for. The propellant question is not a red herring; it's central to the issue.
That's why I suggest one do the calculations with a Hall or Ion thruster, because the energy into the thruster is electrical and constant. The energy content of the propellant is unimportant as it is at rest with regard to the thruster. We measure thrust efficiencies for Hall thrusters just the same way we do for M-E thrusters.

The propellant for any rocket engine, including an ion engine, is only stationary in the thruster's reference frame. In any other reference frame, it is moving at the velocity of the thruster and spacecraft. You've suggested using a frame of reference in which the spacecraft is moving so fast that it gains kinetic energy from thrust faster than it expends electrical energy. This is because in that reference frame, the velocity of the exhausted propellant is lower than it was before it was used.

If you account for both the vehicle and its propellant both before and after the propellant is exhausted, you never get a violation.

...

The energy input to a rocket engine is constant too. It's just chemical instead of electrical, meaning it's tied to the propellant mass flow rate, but this is immaterial; the principle is the same.

GIThruster · Post by **GIThruster** » Mon Dec 10, 2012 11:34 pm

Yes, but in the example I'm falsifying--chris, Andrew, goatguy--are not looking at exhaust and indeed for that example you don't need to. You're talking about a different kind of analysis. Relative exhaust velocity is not necessary to examine, because V is relative. A Hall thruster will produce the same thrust at any given V, given it has the same electrical power in.

V is relative. It's best not to look at exhaust velocity, IMHO. The point I'm making is, this single argument that chris is making, that goatguy has made and Andrew has made countless times, neglects the fact that in order to do this math properly, you need the tools of GR.

If you account for both the vehicle and its propellant both before and after the propellant is exhausted, you never get a violation.

Well that seems to me a better way to calculate. Given we can determine the relative velocities of the active mass in an M-E thruster, you may have a handy way of looking at the matter when it comes to thrust efficiency. this is decidedly a different analysis than that offered by chris, Goatguy and Andrew. I'd be interested to see how it matches up with this GR tool.

93143 · Post by **93143** » Mon Dec 10, 2012 11:49 pm

My whole point about exhaust velocity is that the exhaust is part of the problem that you can't neglect without getting an apparent conservation violation.

This is why GoatGuy and chrismb get an apparent violation from M-E - they don't consider the reaction mass. It's the exact same reason you got an apparent violation from an ion thruster. It has nothing to do with general relativity; it's just an accounting hole. Account for everything, just using vanilla Newtonian mechanics, and the apparent violation disappears.

...

The propellant for an M-E thruster is the so-called "Far-Off Active Mass" that the inertial manipulation produces a reaction against. If you try to maintain that the local manipulated mass in the thruster is ultimately what you're pushing against, you get a violation again, because when that mass "disappears" its momentum and energy go with it. It's just a medium that the force passes through on its way to what ultimately exhibits the enduring equal and opposite reaction required for conservation.

No?

GIThruster · Post by **GIThruster** » Tue Dec 11, 2012 12:01 am

I don't think you need to account for propellant when you're not driving a wormhole condition. Jim showed that if you use the GR tool, you get the right numbers for anything. The issue is really that dV is linear and dE is quadratic, so whenever we do these calculations we'll be wrong at some V. Fact is, the Newtonian method is an approximation that works just fine most of the time, just as vector addition works well most of the time, but when V approaches C, we see more and more that the Newtonian method is not actually correct. It is never precisely correct but we don't notice most of the time.

93143 · Post by **93143** » Tue Dec 11, 2012 12:12 am

GIThruster wrote:I don't think you need to account for propellant when you're not driving a wormhole condition.

You're wrong.

Jim showed that if you use the GR tool, you get the right numbers for anything.

What GR tool?

The issue is really that dV is linear and dE is quadratic, so whenever we do these calculations we'll be wrong at some V.

Not if you account for propellant/exhaust. It always works out perfectly, as long as you've correctly identified the propellant/exhaust (trivial for rockets, not so much for M-E).

Fact is, the Newtonian method is an approximation that works just fine most of the time, just as vector addition works well most of the time, but when V approaches C, we see more and more that the Newtonian method is not actually correct. It is never precisely correct but we don't notice most of the time.

True but irrelevant. The divergence from Newtonian is quite small below about a quarter of lightspeed and is in any case the wrong functional form to 'correct' for a linear vs. quadratic mismatch.

This is not Einstein vs. Newton. It's just an accounting problem. If you've got a cash flow that isn't on the books, the books won't balance. It's really that simple.

GIThruster · Post by **GIThruster** » Tue Dec 11, 2012 12:39 am

I will take you at your word.

I should note at this juncture though, that I still believe there is a problem with the lack of relativistic corrections. Perhaps not in this separate exhaust example but in others I created.

When I first created the "One Gee Solution" Paul used in the Warpstar illustration, my thinking was all Newtonian. Create a baseline thrust efficiency and with that design a hypothetical spacecraft that could generate constant 1 gee acceleration. From that, calculate the travel times around our planetary system in order to give an illustration of what is possible. Accelerate at 1 gee half way and decelerate at 1 gee the second half of the trip. Time to the Moon is about 5 hours. To Mars at its furthest approach to Earth is 2 days. Jupiter is 7, Saturn is 9. This is a handy way to look at the consequences of a certain baseline thrust efficiency that operates continually because there's no propellant to run out.

At the time when Paul and I did this, just after STAIF '06, Jim warned us that this needs a relativistic correction. He wasn't involved in that work and didn't endorse it at any time, but he did remind us several times that this is a Newtonian approximation only, and needs to be run through GR. That's fine. The original Warpstar paper included the disclaimer that this is a Newtonian approximation only.

When Sonny picked up all that work from years earlier and endorsed it, he did not make any relativistic corrections despite he claims to be able to do that sort of thing. So the stuff from Eagleworks has this same flaw, and anyone interested in the illustration, really should make those corrections if they can. Last I looked, the disclaimer is gone and the illustration is now pretty misleading.