Guide to the Jartrek Universe Physics.

The Laws of Physics (more work needed here)

Let's face it the writers original 'Startrek' series pretty much ignored Newtonian physics so we will do the same. Ships have mass and you clearly need more power to move a bigger ship. So :-

Motion at 'Sub Warp' speeds.

'Sub warp' travel is powered by 'impulse*' engines. These give a ship velocity (not acceleration) as follow :-

Velocity = Impulse Power / Ship mass

*Nothing to do with the use of the word 'impulse' in classical physics.

Motion at Warp speeds.

For a ship to get into 'warp space', 'hyperspace' or whatever it needs 'warp engines'. Doubling the number of warp engines does seem to half the time it takes to get anywhere but it does not double the 'wrap factor'. Most ships can make warp 5 but very few can make warp 8. From this we get:-

Warp Velocity = Warp Power / Ship mass

but

Warp Factor = Fudge Factor X log( Warp Velocity )

Coordinate system

Jartrek universe (or will be) a multi dimensional space. Locations in this space are uniquely identified in a coordinate system.