Awesome. I like you're thinking with regards to just scaling the Teradynes to match the warp factor, however the formula is a linear scale, whereas it appear that warp factor is exponential.
In Doc#4, page 25 onward I describe the fuel usage of the Enterprise. In this I define the formula for Deuterium per hour as:
Cubic Meters per hour = 3 * Warp Speed ^ 2
or to put it another way:
= 3 * Warp Speed * Warp Speed
This gives us our exponential scale:
Warp 1 = 3 cubic meters per hour
Warp 2 = 12 cubic meters per second
Warp 3 = 36 cubic meters per second
Warp 4 = 48 cubic meters per second
Warp 5 = 75 cubic meters per second
Warp 6 = 108 cubic meters per second
Warp 7 = 147 cubic meters per second
Warp 8 = 192 cubic meters per second
Warp 9 = 243 cubic meters per second
This fits in well with the fact that the warp scale is also exponential.
On page 35 onward of Doc#04 I describe power generation. In this I use the formula for MegaWatts being produced by the warp core in any given second as:
cubic meters of deuterium per second * 204,000,000
or
Warp 1 = 170,000 MW
Warp 2 = 680,000 MW
Warp 3 = 2,040,000 MW
Warp 4 = 2,720,000 MW
Warp 5 = 4,250,000 MW
Warp 6 = 6,120,000 MW
Warp 7 = 8,330,000 MW
Warp 8 = 10,880,000 MW
Warp 9 = 13,770,000 MW
These are the stupendous amounts of power required to throw the ship through space and it explains why it is so difficult for the NX-01 project to advance from a Warp 4 ship to a Warp-5 one.
Now, to switch this around, what we are really saying is that in order to drive the ship at Warp 8 we need to produce 10,880,000 MW of power. Ships power is taken off this total (which will reduce the overall speed), and things like shields and lasers will take a huge amount of power off this value.
So to calculate the current warp speed of the ship we use the formula SQRT((MegaWatts * TotalWarpEngineEfficiency) / 17,000,000)
TotalWarpEngineEfficiency is 100% when the warp engine is undamaged.
So, if we produce 10,880,000 MW of power from teh warp core, say 100,000 MW goes to other ships systems first (life support, lights etc.) then we end up with:
Warp Speed = SQRT((10,780,000 * 100) / 17,000,000)
which gives us warp 7.96.
What I want to model is that if the captain uses a bit less power by shutting down systems, then this will increase the speed of the ships marginally.
It appears that the warp core is also used to power the shield and phasers which would also explain why they can't be used at warp.