Track Width & Turning Geometry
How fast the robot turns, how much space it needs to do it, and why a long drivebase fights you every time it does.
Inputs
Left wheel center to right wheel center, across the robot.
Front wheel center to rear wheel center, along the robot.
From the Drivetrain Speed calculator.
Results
Point turn rate
—°/s
Both sides driving, opposite directions.
Time for a 90° turn
—sec
Time for a 180° turn
—sec
Swing turn rate
—°/s
One side driving, the other stopped.
Swing turn radius
—in
Path of the robot's center.
Circle swept by the wheels
—in
Diameter, during a point turn.
Wheelbase to track ratio
—
When you would use this
Our autonomous turns overshoot every time.
The turn rate tells you how many degrees a second you actually spin. If your code assumes a fixed turn time, that number is what it should be built from, and it changes whenever you change wheels or gearing.
We cannot line up on the goal quickly enough in a match.
Compare the time for a 90 degree turn against your cycle time. If turning is eating a large share of every cycle, a narrower track buys more than a faster drive does.
We are choosing how wide to build the drivetrain.
Enter a couple of track widths. A wide robot is more stable and turns slower at the same wheel speed; a narrow one is the reverse. Read that against the tipping tool before committing.
The robot scrubs and judders when it turns.
Check the wheelbase against the track. A long, narrow robot fights itself in a point turn because the wheels are far from the turning axis. The shape ratio here says how bad it is.
Watch it turn
Looking down on the robot. Drag to turn it on the spot, and the dashed circle is the space it sweeps out — the corner furthest from the middle is what catches on things. A long, narrow robot sweeps a much bigger circle than a square one of the same width.
How this is calculated
In a point turn the robot spins about its own center, so each wheel runs round a circle of radius half the track width. That is all the geometry there is:
turn rate (°/s) = wheel speed ÷ (track width ÷ 2) × 180/π time for 90° = 90 ÷ turn rateWith your numbers
The useful consequence: a narrower robot turns faster at the same drive speed, because its wheels travel a shorter circle to sweep the same angle. Widening the track for stability costs turn rate directly, and that is a real trade rather than a free improvement.
A swing turn, with one side stopped, pivots about the stopped wheel instead. The moving side now runs a circle of the full track width rather than half, so the robot turns at half the rate, but it also travels forward while doing it, which is often what you actually want when lining up.
Why wheelbase makes turning harder
None of the above accounts for the thing that dominates in practice. During a point turn, wheels at the front and back of the robot are being dragged sideways across the tiles. That sideways scraping is called scrub, and it is wasted effort: motor power spent heating the floor rather than turning the robot.
The further a wheel sits from the center along the robot's length, the more sideways it has to slide. So a long, narrow drivebase scrubs badly, and a short, wide one barely at all. The ratio above is the shape indicator: above 1 means the robot is longer than it is wide, and turning will feel heavy.
The usual fixes, in rough order of how much they help:
- Omni wheels. Rollers let the wheel slide sideways freely, which removes most of the scrub. This is why so many drives run omnis on the corners.
- Shorten the wheelbase, or move to a six-wheel drive where the middle wheels sit near the turning center.
- Drop-center. Mounting the middle wheels very slightly lower rocks the robot onto a shorter effective wheelbase, so it turns about the middle pair.
Sources & assumptions
No VEX-specific constants are used on this page. The results follow from the geometry of a differential drive and your own measurements. There is nothing here to become stale between seasons.
Assumes a tank-style drive with wheels rigidly fixed, turning about the geometric center, with no wheel slip and no scrub losses. Holonomic drives (X-drive, mecanum) turn on entirely different geometry and are not covered here.
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