Short note: spacing and headway

Spacing is the distance between the front of one vehicle and the front of the next vehicle in the same lane, measured in metres. Average spacing $s$ is related to density $k$ (veh/km) by

$$s = \frac{1000}{k}\ \text{m}$$

Headway is the time between the passage of the front of one vehicle and the front of the next vehicle at a fixed point, in seconds. Average headway $h$ is related to flow $q$ (veh/h) by

$$h = \frac{3600}{q}\ \text{s}$$

Spacing and headway are linked by speed: $s = v\,h$ ($v$ in m/s).

 |<------- spacing (m) ------->|
 [==== car 1 ====]     <-gap->  [==== car 2 ====]
 front              rear        front
 |<------ headway (s) at a point ------>|

• The gap is the time between the rear of one vehicle and the front of the next, and the clearance is the corresponding distance. So $h =$ gap + (vehicle length / speed) and $s =$ clearance + vehicle length.
• Headways are used in capacity (saturation headway about 2 s per vehicle at a signal gives 1800 veh/h), safety and queue analysis; short headways (below about 1 s) are unsafe. Spacing is used to compute density and to find the storage space needed for queues.
• For random arrivals the headways follow a negative exponential distribution.