This relationship applies to fast movements with no well-defined target width

What it is

The linear growth of error with speed describes only movements that have no bounded target to hit and must be completed within a fixed time — swinging an arm toward a rough direction, executing a swing in time with a metronome, drawing a line of a specified length within a set duration. What's being measured for these tasks is the continuous deviation of the endpoint from the intended direction or distance, not a binary judgment of whether it landed "inside a boundary or not." As soon as a task carries a bounded target to hit, it falls outside what this relationship describes.

Why it happens

This boundary condition matters because whether a target width exists determines both how error gets defined and whether there's any opportunity for correction during the movement. A movement with no target width is measured by how far the trajectory itself deviates from the intended heading or distance — a continuous quantity that directly reflects the variability of the neural drive signal at the moment the impulse was generated; such movements are also typically short enough that they're already over before visual or proprioceptive feedback could act on them, so the measured deviation is essentially pure noise from the motor-planning stage, undiluted by any mid-course correction. A discrete pointing task with a defined target width, by contrast, cares about the binary outcome of landing inside the boundary or not, and as long as the movement is slow enough, the user has time to correct as they approach the target, smoothing away some of the deviation that speed alone would otherwise have produced.

Studying it

The first step in deciding whether a task should be described by this linear relationship or by some other model is to look at how the task itself is structured: if it requires completion "within a given time" (time is an externally imposed constraint, and speed is derived from it) and the endpoint is scored as a continuous spatial deviation, it falls within this relationship's scope; if instead the task requires hitting a target of fixed width and position with time left as a free variable that the participant weighs on their own, it does not.

Methodological note: some interface actions look "timed" on the surface but are really just a soft suggested duration (implied, say, by an animation's pacing), and the user is still free to go slower and more carefully. In that case speed is still a self-selected operating point, and the governing logic is still the speed-accuracy trade-off, not this linear relationship — the key distinguishing question is whether the time constraint is genuinely non-negotiable.

Where it stops holding

If a task originally matches the conditions described here (no target width, time-constrained) but the time actually allowed in practice is more generous than intended, participants get room to insert feedback-based correction near the end of the movement, and the measured error-versus-speed relationship will be flatter than a pure linear one — this conclusion can no longer be applied directly to predict error magnitude in that case.

Related

• Same group: A8.10.1 For a movement completed within a fixed time, error grows in proportion to speed · A8.10.3 Not to be confused with the logarithmic pointing law — the applicable conditions differ
• Nearby: A8.08 The two-phase structure of target acquisition · A8.06 Open-loop control
• Search terms: Schmidt's Law · impulse-variability theory · timed movement