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X-Drive Speed & Strafe

An X-drive is faster than the same parts on a tank drive, but not in the direction most people assume, and not for free.

Inputs

Diameter across the wheel. Mecanum and flex wheels share a diameter with the plain ones, so pick by name rather than by size. Anything not listed can be typed in.

°

0 is straight forward, 45 is diagonal, 90 is straight sideways.

Results

Forward or sideways

—ft/s

The X-drive's fastest directions.

Diagonal (45°)

—ft/s

Its slowest.

At your chosen heading

—ft/s

Same parts on a tank drive

—ft/s

Speed change vs tank

—×

Forward push vs tank

—×

Before accounting for omni grip.

Which way is it fast?

Which way is it fast?
0°

The robot seen from above, its four omni wheels at 45°, with the gray outline showing how fast it can go in every direction at once. Swing the arrow round: it is longest straight forward, sideways and backward, and shortest on the diagonals, which is the opposite of what most teams expect from the name. The dotted circle is what the same parts would give on a tank drive.

The speed envelope

How fast the drive can go in every direction. The corners point forward, back, left and right. The flat edges are the diagonals.

Diamond-shaped speed envelope of an X-drive, longest forward, back, left and right, shortest along the diagonals forwardrightbackleftdiagonal

X-drive   tank drive, same parts

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:

forward speed = wheel speed ÷ cos 45° = wheel speed × √2 ≈ 1.414 × wheel speed

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. Traveling 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:

diagonal speed = wheel speed × 1.0

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:

forward force = 4 × wheel force × cos 45° ≈ 2.83 × wheel force (a tank drive with four wheels gives 4 × wheel force)

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 valuable for lining up. Whether that beats being able to win a shoving match depends entirely on the game.

Sources & assumptions

Cartridge speeds and wheel diameters are VEX published figures. The √2 and cos 45° factors are geometry, not measurements. They follow from wheels mounted at 45° and are exact.

Assumes a true X-drive: four omni wheels at exactly 45°, equally spaced, no slip, all four motors identical. It ignores scrub, roller friction and the grip difference between omni and traction wheels, all of which make a real X-drive worse than these figures rather than better.

Every source the site uses, and when it was checked

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                                Drivetrain Type Comparatorfills in your gear sizes here

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                                X-Drive Speed & Strafe

                                Where your answer goes

                                Track Width & Turning Geometrysee how quickly that drive spins and finishes a 90-degree turnbrings your top speed with itAutonomous Time Estimatorcheck an auton route at that speed fits in the timebrings your top speed with itPushing Force & Traction Limitomni wheels grip less, so find out how much push is leftbrings your gear sizes with it

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