X-Drive Speed & Strafe

How this is calculated

On an X-drive the four omni wheels sit at 45° to the front of the robot, so no wheel points where the robot is going. Each one contributes a component, and the robot's speed is set by whichever wheel is being asked to spin fastest.

Why forward is the fast direction

Driving straight forward, every wheel sits at 45° to the direction of travel, so each only needs to roll at cos 45°, about 71%, of the robot's speed. Run all four at their limit and the robot moves at:

The same is true sideways, which is what makes an X-drive strafe as fast as it drives.

Why the diagonal is the slow one

This is the part that surprises people. Travelling at 45°, the robot is moving along one pair of wheels' rolling direction. Those two must spin at the robot's full speed, while the other two contribute nothing at all:

So an X-drive is slowest diagonally and fastest along the axes, the opposite of the common assumption that the diagonals are the quick way. Half the drive is idle when you go corner-to-corner.

The √2 is not free

Force works the other way round. Each wheel pushes along its own 45° line, so only cos 45° of its effort points forward:

That is about 71% of the pushing force from the same motors, the exact reciprocal of the speed gain. An X-drive is a gear ratio dressed up as a chassis: it trades force for speed at √2, and you could get the identical trade on a tank drive by changing gears.

The real cost is grip, not geometry

All four wheels must be omni, and omni wheels grip far less than traction wheels. As the Pushing Force calculator shows, most drives are limited by grip rather than by torque, so in practice an X-drive gives up considerably more pushing power than the 71% above suggests.

What you buy is the ability to move sideways without turning, which is genuinely valuable for lining up. Whether that beats being able to win a shoving match depends entirely on the game.