Force vector calculation for mecanum drive

[ndurvasula]

Hi everyone,

This is my first thread on Delphi so I'm really new here. I'm on team 449, and I am making a VR Practice field for use with Google Cardboard, and I am trying to make it as physically accurate as possible. Right now, I am trying to implement different kinds of drives, but mecanum seems to be the most difficult. I would like to know how to calculate the magnitude of a vector given it's direction. To make this more clear, I have a value f, that represents the amount of force that would be applied to the robot in a given time frame if it is going directly forward/backward. I also have vector v containing the horizontal and vertical vectors representing the direction of the robot (both between -1 and 1). How do I calculate the magnitude of the force that needs to be applied to the robot given f and v (hopefully accounting for internal roller friction as well)? Keep in mind that this formula has to run every frame, and it is going to be run on a phone. If there is any lag in a VR application, it kills the user's eyes.

Thanks a lot, any help would be really appreciated!