[hrench]

Originally Posted by asid61

Wouldn't the rotation speed of the gear also come into effect (hence why I said mech. power)?

I think you're being fooled because the rotation speed is a backwards-way to correlate torque. I agree with FrankJ, motor torque is the only concern and it doesn't matter the speed. In my gear design handbook, even when figuring the max horsepower a gear train can do, it takes it straight back to Force on the gear teeth, which is all from torque.

Originally Posted by asid61

this is a mathematical question, not a practical one. Not really sure how I can make that more clear

Yeah I understand, but if you're optimizing the weight of the gears, I think you'll still be concerned about the weight of the plates and shafts. Unless you're mostly concerned about the angular momentum of rotating mass, which can be important sometimes.
Yes, you can write excel sheets to compare different areas of gear-sets and it might help us all learn a few things, but you'll have to make assumptions about lightening and material (or probably assume no change on both).
Another interesting side effect of one-pass (or fewer passes) is with a very large bull gear you'll decrease the Force on each tooth appreciably, such that you'll need less gear face width, making the gear lighter in another way. But the interior of the bull gear will still need to be as strong for the torque--you'll only save weight near the circumference.
Multiple passes won't benefit from this, they'll still need wide face-width gears for higher torque.

So you'll need equations for area, but also thickness (which can be varied from face to center) because weight is from volume.

Originally Posted by asid61

I have designed gearboxes before (look through my submitted images) and weight is rarely my constraint. If you don't like the constraints, then I can't help you.

I've looked at your gear boxes and they're amazing and creative. I particularly like the cycloidal and drill press swerve. But it does look like you pay attention to weight.