Ok,
Admittedly, the math for this a\has finally gotten WAY beyond me.
Could someone give me an idea of the power to motion ratio that seems to be being generated with this system, verses, say, a regular chemical rocket?
What I am trying to find out is simple; Is this system somehow generating more motion than should be possible, assuming a direct conversion of energy to motion?
In other words, is 1 calorie of energy somehow rasing 1 cubic centimeter of water's temprature higher than 1 degree celcius, or is the amount of power being used within a reasonable ratio of energy effecient conversion, say, 70% of power applied is being converted to motion, as an example?
For the moment, set aside HOW it appears to be doing what it is doing, and let's see if it violates any of the Laws of Thermodynamics.
Sorry, but you guys have gone so far beyond me mathematically, (plus, I think I may have missed a couple of equations that would have made it simpler to follow) that I am having the devil's own time trying to keep up with this thread.
My take on that : it does very clearly violate the laws of thermodynamic unless :
- It gets energy from an "exterior" source. (1/ or 2/ in post linked)
- It emits tachyons (particles of imaginary mass and negative energy) as a way to get rid of an energetic debt. (3/ in post linked)
That it
needs more energy than it takes from its onboard generator for a given result can be shown with relatively basic Newtonian mechanics and thought experiment :
Assume a long "railway" in otherwise empty space and a small 1kg ship accelerating along this path by conventionally pushing with wheels. This is the most favorable situation to get momentum from energy. At some time, the ship is going 1km/s=1000m/s (pretty fast for wheels... use whatever magnetic coupling to "rails") and want to go faster. The power it takes to push against a moving thing (the rails are moving relative to the ship) is power=speed*force. Say we want a force of 1N, then it takes 1000*1 = 1000 Watts (1kW) of power. At 1N, a mass of 1kg experiences an acceleration = force/mass = 1/1 = 1m/s˛ (that is roughly 0.1g since 1g=9.81m/s˛). Ok so, at this 1kW power, at this speed of 1000m/s, 1kW gives an added 1m/s each second.
So after 1s at 1kW we now have a 1kg ship at 1001m/s (speed relative to rails). The energy amount of 1kW during 1s is energy_used = power * time = 1000 * 1 = 1000 J. We are far from c speeds so kinetic energy is accurately given by energy_kinetic = 0.5*mass*speed˛.
Before the acceleration : energy_kinetic_before = 0.5*1*1000˛ = 500000 J
After the acceleration : energy_kinetic_after = 0.5*1*1001˛ = 501000.5 J
energy_gained = energy_kinetic_after - energy_kinetic_before = 1000.5 J
So we have used 1000 J and we have gained 1000.5 J Alles ist gut.
All right, there is an annoying .5 J excess which is due to neglecting the fact that it gets a little bit harder to accelerate when going from 1000m/s to 1001m/s. For instance at 1000.5 m/s it would already take 1000.5*1 = 1000.5 W to get the same 1N force that we had at only 1000W when going 1000m/s. So in average we would have to spend exactly 1000.5 J to augment the kinetic energy by 1000.5 J Now consider the same experiment with a "propellantless system" that would have a thrust to power ratio of 1N/kW, that is in the ballpark of what are claiming the proponents when they are designing their mission profiles. We have the same force of 1N for the same power of 1kW that will get us from 1000m/s to 1001 m/s in 1 second,
at the energetic cost of exactly 1000J we gained exactly 1000.5 J in kinetic energy.
This speed of 1000m/s was not chosen randomly by me: the inverse of thrust to power ratio of a propellantless scheme (that is the power to thrust ratio) is the
speed beyond which the thruster gives more energy than it takes. It only gets worse (from a conservation of energy standpoint) or better (from a mission profile point of view) when higher speeds are considered :
Same values as above except we are going from 10000 m/s to 10001 m/s :
Gained kinetic energy = 0.5*1*10001˛ - 0.5*1*10000˛ = 10000.5 J
Used energy by conventional wheels = (average_speed*force) * time = (10000.5*1)*1 = 10000.5 J
Used energy by propellantless scheme = power*time = 1000*1 = 1000W (you read well, ten times less)
So in effect,
with any propellantless scheme of fixed thrust/power ratio we have over unit efficiencies in converting power to kinetic energy the over unit factor being speed/(power/thrust). And the mission profiles do exploit this over unit factor to the maximum extent permitted by their law (but forbidden by Usual law). And the attempts at explaining how the thrust/power would not be constant but would depend on "speed" to respect energy conservation fail at showing what is the "railway" : what frame would be used as a reference in the vacuum ? Vacuum has no intrinsic "rest speed".
In conclusion, proponents say that energy could be conserved, but they fail to explain how, and worse from an "ethical" standpoint, all their mission profiles critically depend on the fact that energy is not conserved (or is otherwise tapped from "somewhere", the local vacuum or the walls of the Universe, whatever).