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.

Since warp theory is not exactly physics but sci-fi, I don't think there's any point looking for a formula for that. However, these might be of some help:

http://memory-alpha.org/wiki/Warp_factor
http://en.wikipedia.org/wiki/Warp_speed#Warp_velocities
and especially the plot by Okuda:
http://en.wikipedia.org/wiki/File:Warptable.gif
The axis on the right shows the megawatts (10^9 watts) that correspond to each warp factor. Since the plot doesn't mention a specific ship, my guess is that the energy requirements do not vary that much with the size. As I said all this is very speculative.

Yes, C_P, it's all speculative. But, hey, that's what's fun for me: speculation! I like speculation.

The wiki chart you linked to is a nice recreation of the warp factor/power usage chart found in the TNG tech manual, pg 55. The obvious errors of the original table (eg, "power usage in megajoules per cochrane") were corrected (eg, "power usage in *megawatts* per cochrane") in the wiki chart and the resolution slightly enhanced. It has its own problems, of course, but it's a nice one none the less. Indeed, it is from this very chart I used to calculate the power usages quotes for the Galaxy Class, above. And, yes, IMHO, I think it's safe to say the chart is for the Galaxy Class specifically. How that chart changes for different ships is up for debate... Which is exactly what I want to do!

...I just need to find a place that has done/is doing it. Which is why the question.

Thanks for the other links. I'll check them out when I'm not at work.