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OK, I'll bite. Frankly I don't get the objection. ...
Please search for the posts by Frobnicat (preferably using "Google Advanced Search", who has thoroughly dealt with this, including frame-indifference, and the issues you discuss. Frobnicat has a lot of posts discussing this in previous threads.
ok, found this article:
http://forum.nasaspaceflight.com/index.php?topic=37438.msg1369806#msg1369806
Now I get it. Yes. I don't see this as constant acceleration for constant power in. But then even from SR I didn't see how acceleration could be constant either if mass is increasing and force is not. That's just basic SR coupled with Newton's first law. A variant of the rotating EMDrives I've also seen proposed as a perpetual motion machine was the "infinite oscillator". Two EMDrives that are cross coupled so that they oscillate in distance between them by using gravity to attract to each other, storing up the electrical energy produced by the motion induced by gravitational acceleration and then prior to collision, switching each device "on" to drive them apart until the stored electrical power is consumed and then back off again, thus completing the cycle.
Breaking my silence for once. A "over unity" scheme does not need constant acceleration with constant power, it needs constant
force with constant power input. Because acceleration is relative (what you say of acceleration in SR depends on reference frame, from the spacecraft itself there is no decrease in acceleration at constant force...) there is always a great confusion with interpretation in delta kinetic energy. And a force can be applied at
constant velocity,
no acceleration, as in a tractor pulling a plow at constant velocity (wrt to ground), as in a turbojet thrusting for a plane moving against aerodynamic drag at constant velocity (wrt to air mass). Such a force F applied at a given constant velocity V relative to a support will release a power of FV if F is in same direction as V and will absorb a power FV in the opposite direction. More generally the power given from the thrusting system at constant velocity V wrt to some support will be the scalar product F by V (the power given is negative, ie absorbed, if vector are opposite directions). The power
will not change any kinetic energy as we are talking
constant velocity, so it must go elsewhere. I'm heavily insisting on that because it seems hard to get through, as many want to think as the emdrive as some kind of "electric energy to kinetic energy converter". This is
not the principle of the proposed overunity scheme.
The proposed scheme derives from the fact that (most of) the claims so far measure a thrust against a proportional restoring force, a spring or such, and damped, being that after a short transient of acceleration (as expected from a force) the system stabilizes (more or less) in a static equilibrium (as expected from a constant force). In other words, the proposed device is claimed to give a constant force (at least for a few tens of seconds) for a constant power input when acceleration is 0, ie at constant velocity (of 0 wrt ground). So far so good, that's what we would expect from a thruster after all.
What I'm proposing is to put this phenomenon of constant thrust at constant power
and constant velocity to do work on a generator (a mechanical energy to electric energy converter). Well, the overunity then appears immediatly for a propellantless system thrusting above 1/c = 3.33 µN/kW, because at a
constant velocity above the inverse of this figure_of_merit (and the inverse of something that is above 1/c is a velocity that is below c, hence physically attainable, at least in principle), at such a velocity V wrt to the generator that recovers some power (I illustrate the case on a rotating shaft, but could be linear all the same), then one sees that the mechanical power output by the thrusting system is FV while the electric input is F/figure_of_merit<FV, given that we chose V such that V>1/figure_of_merit.
The only caveat I see is if the phenomenon somehow "knows" its velocity relative to what it is pushing, or more generally that it "knows" some kind of absolute velocity, and that the "figure_of_merit" is different depending of V, even while acceleration=0. Different
constant velocities (wrt to what ?) would yield different figure_of_merit, in such a way to render such overunity scheme impossible. Notice that, the higher the figure_of_merit as measured in some frame (say, the lab) the lower the range of velocities around this hypothetical 0 velocity frame is allowed before the figure_of_merit is degraded. Basically, an hypothetical 1N/kW Emdrive thruster in the lab could certainly not thrust at such performance above 1km/s (wrt to the lab) in all directions. If there is such a thing as an aether defining a priviledged physical reference frame against which the phenomenon is "pushing" or "grabbing", one would indeed see a very strong directionality of the efficiency of the effect, presumably relative to the stars, and one would see such strong directionality all the more with higher figure of merit. At 1N/kW measured in the lab, the directionality could hide only if the aether wind wrt the lab would be below 1km/s. Such an "aether" would clearly be earth bound, as no other thing that is not earth bound moves at such small pace relative to labs on earth. Which would ask the applicability to
deep space use of an effect that depends on an earth bound (or any local planetary) field to reach its nominal efficiency. What I'm saying is that, should static experiments show consistent results (we are far from that) and dynamical experiments show some kind of lowering of figure_of_merit when velocity wrt lab is higher, say for instance that figure_of_merit is shown to be always below 1/velocity (as is the case for other means of propulsion, when taking into account all the flows, see link below), then we would understand that the system is indeed unable to be used in overunity schemes, but also that it is pushing on the walls of the lab or some other nearby part, and is useless as a mean of revolutionary deepspace propulsion, where there are no walls to push on.
For the full constant velocity treatment please refer to
https://forum.nasaspaceflight.com/index.php?topic=39004.msg1461319#msg1461319To be fair, only the most extravagant claims of figure of merit in the 1N/kW range and above would make it practical to put such "power harvesting property" (of constant power constant thrust at
constant velocity propellantless propulsion) in a reasonably sized box. Given the efficiencies in conversion and the difficulty to put material at 2km/s tangential speed, I guess the practicallity of such device would start with 2N/kW and above. At 5N/kW there is no question it is possible, the frustum is solid state after all (and the RF generator can be put near the axis...). With mega engineering I see a solution also to extract continuous excess power from the overunity scheme with only 0.1N/kW with two contra-rotating rings in LEO... power would have to be beamed elsewhere... don't know if it would be more economical that massive spatial solar infrastructures...
On the other hand, practical engineering and potential tremendous economic impact apart, the theoretical "problem" of the apparent over unity remains even for figures of merit as low as 4µN/kW, even though we can't really build devices with macroscopic parts approaching relativistic relative velocities needed. Thank you for reading.