Mecanum wheel equations

i would like to design a 3d model of a mecanum wheel to 3d print but i dont know where to start. is there some formulas/equations i need to follow. is their a certain ratio for the rollers, how much space is needed between rollers etc. please help a rookie out

Unfortunately we do not have any equations at our disposal for calculating the forces / speeds needed for motion in a Mecanum setup. Friction coefficients will likely ne used since there is still rubbing as well as rolling.
Most designers opt for fairly powerful motors, and restrict the motion to very flat surfaces.
You do need to ensure you use two left wheels and two right wheels in the correct configuration, and each wheel has its own gear motor.
If you can give us an idea of the size / weight, we can see if we can find comparable platforms to get an idea of what motors they use.

I need it to be 80 mm in diameter and as light as possible

We offer a selection of Mecanum wheels here:
robotshop.com/en/robot-wheel.html
Two manufacturers in particular have a nice selection:
robotshop.com/en/robot-wheel … d=AndyMark
robotshop.com/en/robot-wheel … exus+Robot
3" and 60mm or 80mm seem to be the closest options.