By router I assume a woodworking machine rather than a CNC mill. This one if you search has a blog, a long one, by someone who made it and improved it over a year or more. There is someone in the Bristol ME club who displayed one about 4 years ago at their show and might be able t give you some measurements of friction etc.
If you really want to calculate it you need to look at the ball screw specifications for the torque required to overcome internal friction, likewise the slides. then examine the energy needed to pull the cutter blade, on each revolution, into the material as it will be trying to push itself back off the job rather than cut into it. Some of this energy comes from the rotational inertia of your intended spindle, which you can measure. And so on. I could give you full details for a suitable fee – my father was from Bradford and my grandfather from Aberdeen.
Baz – south of Watford