Traffic flow – theoretical maximum vehicles per hour from spacing and speed If vehicle length is L metres and the clear distance between successive vehicles is C metres, moving at a speed V km/h, the theoretical maximum flow N (vehicles per hour) is:

Introduction / Context:
The simplest headway model treats vehicles as occupying a physical length L plus a clear spacing C. Converting this space headway to a time headway at speed V gives a quick estimate of the maximum possible flow rate.

Given Data / Assumptions:

• L = vehicle length (m).
• C = clear gap between vehicles (m).
• V = speed (km/h), assumed steady and uniform.
• Single lane, no lateral interference, ideal conditions.

Concept / Approach:
Time headway t = distance headway / speed. Distance headway = L + C (m). Speed in m/s is V/3.6. Therefore t = (L + C) / (V/3.6). The flow N = 3600 / t.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional check: numerator 1000*V (m/h) divided by metres gives vehicles/h, consistent with units.

Why Other Options Are Wrong:
Options B and E ignore the km→m conversion. Option C gives vehicles/s order. Option D is the reciprocal of the correct expression.

Common Pitfalls:
Forgetting to convert km/h to m/s; misinterpreting C as time gap; overlooking acceleration/driver variability which reduce real-world capacity below this ideal value.

Final Answer:
N = 1000 * V / (L + C)