4×100m Relay: Baton Exchange Timing

Team Speed

Base top speed 10.0 m/s

Go-Signal Timing

Exchange 1 (leg 1→2) 12 m early

Exchange 2 (leg 2→3) 12 m early

Exchange 3 (leg 3→4) 12 m early

How many metres before the exchange mark the incoming runner is when the outgoing runner takes off. Too small = caught from a standstill near the back of the zone. Too large = the outgoing runner sprints clear before being caught.

Live Readouts

Total team time

— s

Baton speed

0.0 m/s

Exchanges legal

— / 3

EX 1

EX 2

EX 3

How it works

Each sprinter accelerates toward a personal top speed following the standard exponential sprint model used in athletics biomechanics:

v(t) = v_max · (1 − e^(−t/τ))
x(t) = v_max·t − v_max·τ·(1 − e^(−t/τ))

τ is the acceleration time constant (≈1–1.3 s for a trained sprinter) — small τ means the runner reaches top speed almost immediately, large τ means a slower build-up.

By IAAF rule, the baton may legally change hands only inside a 20 m changeover zone (10 m either side of the exchange mark). The outgoing runner waits at the back edge of that zone and takes off once the incoming runner crosses a trigger point — the "Go-Signal Timing" slider sets how far before the mark that trigger point sits.

Trigger too close to the mark → the outgoing runner is still nearly stationary when caught, an easy but slow pass.
Trigger too far before the mark → the outgoing runner is already at speed and may outrun the incoming runner clear through the front of the zone — an illegal exchange (+2.0 s penalty here, disqualification in real competition).
The fastest legal total time comes from timing the trigger so the two runners are both moving near top speed exactly as they meet, deep in the zone.

Total team time = sum of the four legs run continuously by whoever is holding the baton, plus a 2 s penalty for every illegal exchange.

Baton (current holder) Changeover zone (20 m)

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