Has anyone here read or worked on a speculative mathematical formula for estimating how power requirements for a warp field reduces compared to size?
I mean, Defiant couldn't possibly use up as much energy getting over the warp 1 threshold as Galaxy does. (~14e9 Watt) Or to cruise at warp 9, for that matter. (~1.21e18 Watts) I mean, where would Defiant store all that M/AM? It doesn't have the volume. So power has to scale by size, right?
Ok, for example, it could be that for the same field geometry, it scales to the volume of the field... Which is to say, approximately as the cube of the length (L^3). So that Defiant would use on the order of (171/641)^3 = 1.9% that of Galaxy, or 270e6 and 23e15 watts for wf1 threshold and wf9 cruise, respectively...
Of course, the problem with this is the giantism of starships in star trek. If energy usage increased as the cube, than the same percentage of volume used as fuel in any size ship would get you the same range. So there'd be no real advantage for larger and larger ships.
Maybe, instead, it scales approximately to the area of the field; IE, approximately to the square of the length (L^2). This would translate to on the order of (171/641)^2 = 4.8% energy usage by Defiant compared to Galaxy; or 680e6 and 58e15 watts for wf1 threshold and wf9 cruise.
All this, as opposed to a linear scaling where defiant would use on the order of (171/641) = 27% of Galaxy's usage or, even worse, 100% of Galaxy's usage.
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This is the kind of analysis I'm looking for. Has anyone come across anything like it?
Attempting to find an approximate scaling factor for power usage?
Maybe on another forum?
Anywhere?
I mean, I have my own opinions, as you can tell, but I'd like to see what others have written on the subject.
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