Car-Following Simulator

20.0 m/s +0.00 m/s² Lead

20.0 m/s +0.00 m/s² Follower

Slow Free-flow lead vehicle color = its current speed

Δx = space gap (follower's front to lead's rear) shaded zone = minimum gap g_min

Speed

–

Relative speed Δv

–

Space gap Δx

–

Time gap

–

Acceleration

–

Lead vehicle

Target speed 20.0 m/s

Max acceleration 3.0 m/s²

Caps how fast the lead car can speed up or brake — it ramps toward the slider, it doesn't jump.

Car-following model

Following policy

Time gap: desired distance grows with speed. Space gap: desired distance is a fixed constant — one fewer parameter (no τ).

α — sensitivity 0.50 /s

τ — desired time gap 1.50 s

g_des — desired gap 20.0 m

A fixed following distance, independent of speed — much larger than g_min, which stays a separate, small safety floor.

dΔx/dt = v_lead − v_follower
dv/dt = α · [Δx − (g_min + τ·v_follower)]

L — vehicle length 4.5 m

g_min — minimum gap 2.0 m

Δx = space gap, front bumper (follower) to rear bumper (lead)
equilibrium: Δx* = g_min + τ·v · stop if Δx ≤ g_min
L only draws the vehicle bodies: center spacing = Δx + L