...
more energy to go from 100 to 101 than to go from 0 to 1. Because of the square.
100˛ to 101˛ -> needs to add 201
0˛ to 1˛ -> needs to add 1
Wow, again, seems paradoxical, as this is the same "thing", just seen from a different way...
Please, please Frobnicat, you are going too fast for me.
- Nobody should add kinetic energy in different reference frames. That's not a paradox, that's plain and classical mechanics. A consequence is that nobody should use trust/power ratio.
This is not what is going on. What is going on is choosing a given arbitrary inertial frame, and working from there. I know there is no paradox. Anybody can use thrust/power ratio in a given arbitrary inertial frame and it will give correct results if the system is losing enough mass in the process. Thrust/power is ok because the power is from the onboard generator, and thrust has an effect of the variable of interest (velocity) that is linear.
Onboard generator -> given power OK (don't depend on frame)
given power -> given Thrust (from Ts) OK (don't depend on frame)
given Thrust -> given acceleration OK a = F / m ( don't depend on frame)
acceleration -> (Vf - Vi)/delta_t OK ( don't depend on frame)
For the last : Vf and Vi magnitudes do depend on frame, but the difference Vf-Vi dont.
So, this is not a problem with using Thrust/Power
The problem in Appendix A is that there is an error, a huge error, when calculating the Hall thruster in the frame of CMB : the change in kinetic energy is given by initial state minus final state. Which yields a value higher than the spent onboard energy. BUT but but, the change in kinetic energy should be the other way around, final state minus initial !!!
Which would yield a negative value, that is obviously less than spent energy. So their calculation is plain wrong, so is their conclusion that a Hall thruster is as much paradoxical as a Q thruster. The calculation done properly show quite the opposite : the Hall thruster has a perfectly sane energetic behaviour in whatever frame, even when using Thrust/Power as a mean to know its acceleration, and the same calculation for Q-thruster (not done in the paper) show it has a pathological behaviour in some frame, giving more kinetic energy than energy spent.This is as simple as that, this is gross (playing on a sign convention) and subtle (relativity, even Newtonian, has interpretation subtleties, and nobody really like to check sign conventions). But in money terms maybe it's more clear : doing a financial operation where a cash investment of 1000$ (spent energy) makes that your portfolio values (kinetic energy) goes from 100000$ before to 10000$ after you would not say that the change in portfolio value is before-after 100000-10000=90000 and you had 90 over unit gain factor. You would do after-before and see that you have a change of -90000 and
lost 90 times the cash invested : this is not really over unit gain. The difference probably fell into someone else pocket. Financial system is not exactly conservative but see the point :
change is not initial-final, it's final-initial, this is gross, and turns the conclusion on it's head.
- There is no ongoing conspiracy at NASA, only usual business in an agency that consumes 2 billions each years and wants to survive. To survive it needs people support.
People enjoy Startrek stuff (I am not joking, I really mean it). So NASA (and Discovery TV, and a handful of SF authors and some NASA consultants) feed people with the stuff they ask. That's a profitable business.
Yeah, I do enjoy Startrek a lot too. But when you see people signing under NASA stamp EM simulations showing net asymmetry in momentum of photons bouncing inside cavity, while Greg Egan a "hard" science fiction author does a perfect job at showing how EM waves bouncing in an asymmetric cavity yields a perfectly symmetric result of 0 net thrust, then you see there is a problem. I would be tempted to give more credits to wild speculation of scifi authors than to scientists working on propellentless schemes. We'd better see how to fix the polarized negative power coupling axis on the Falcon Millenium...
I'd rather stick with working on more concrete hypothesis for explaining the apparent experimental results, but when I saw this Appendix A I couldn't keep silence : there is a huge error in this paper, and there is a completely wrong conclusion drawn from this huge error. This would need at least a public acknowledgement and proper correction from the authors if they are serious about doing science.
If one want serious science papers, there are many reputable sources. Science journals mostly, not conference papers, not pre-print servers, not self cited papers.
I know it may sound harsh, I don't want to be harsh, sorry for my lack of writing gift. This whole thread is going too far, intelligent people see artifacts and meaning where there is none. I am very sorry about that.
I am sorry that people working on those advanced concepts are doing such mistakes and bad methodology. There should be room for speculations and bold experiments. Appears there is no "serious science paper" dealing with energy conservation for propellentless schemes (is there ?). We would be very happy to see more than conference papers, pre-prints, self cited papers, on the subject. Appears the public production of people involved is kept at that level.
So what do we do ? Leave the subject altogether ? Don't tempt me.
If we want to keep on discussing propositions of the proponents then we are left with no options but to read and comment publications of that level.