P=dE/dt
meaning that power is the derivation of energy, or, if the power consumption is constant, energy per time:
P=E/t
The two terms are also confused in the warp factor diagram in the TNGTM, where the "power usage" is given in megajoules (energy unit). I have been pondering whether energy or power would be correct in the diagram.
In a Newtonian propulsion a certain amount of energy is required to achieve a certain speed. The power is irrelevant in that the same speed can be achieved with a weaker engine, it will only take a longer time. Warp propulsion, however, is different. Once the warp field disapppears, the starship drops out of warp. To maintain the warp field, a continuous power output is necessary. The question is only where this energy (=accumulated power) is exactly going to, once the ship has been accelerated to its final speed. Jason Hinson suggests something like part of the energy flowing back from the subspace (what about the rest, will it eventually heat up subspace?), and, although he doesn't explicitly mention it, I think he means this energy replenishes the warp plasma in the nacelles, and this is what the horizontal slot in most nacelles is mainly about.
Anyway, I have recently changed megajoules to megawatts in the TNGTM diagram, assuming at least the factor 10^6 is "correct".
http://www.uni-siegen.de/~ihe/bs/startrek/treknology/warptable.gif
Another question is why the power is given in mega**** per cochrane. This implies that this value has to be multiplied by the warp factor (=cochrane value) to obtain the actual power consumption. One guess: The mega****/cochrane would be the power for one warp field layer, but Warp 2, for instance, would require two of them (again Hinson's theory).
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"No, thanks. I've had enough. One more cup and I'll jump to warp." (Janeway, asked if she would like some coffee in "Once upon a Time")
www.uni-siegen.de/~ihe/bs/startrek/
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"Angels and Ministers of Grace, defend us"
-Hamlet, Act I, Scene IV
In my opinion the layers are more like different fields that reach further into subspace the higher their number is. This implies that the fields are separate to some degree, meaning that they don't yield a single field by simple superposition, in which case the creation of different fields would be useless. The separate nature of the fields may explain the discontinuity of the power vs. warp factor diagram. Every time a new layer is initiated there is a threshold to cross. This would not be the case if just a single field were changed to cross the Warp x barrier.
If you, however, know of a different, probably more complicated depiction of the warp field, I would like to know.
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"Angels and Ministers of Grace, defend us"
-Hamlet, Act I, Scene IV