If a freeway has a traffic flow density of 60 vehicles per mile and a space mean speed of 40 mph, what is the average headway?

To determine the average headway in this scenario, the relationship between traffic flow, density, and speed must be understood. Traffic flow (in vehicles per hour) can be calculated using the formula:

Traffic Flow (q) = Density (k) x Speed (v)

Where:

• Density (k) is given as 60 vehicles per mile,

• Speed (v) is given as 40 miles per hour.

First, we will convert the density and speed values into compatible units to calculate the traffic flow. The density of 60 vehicles per mile implies that there are 60 vehicles occupying each mile of freeway. Given that the space mean speed is 40 miles per hour, we can calculate traffic flow as follows:

q = k x v = 60 vehicles/mile x 40 miles/hour = 2400 vehicles/hour.

Now, to find the average headway, which is the time gap between successive vehicles in seconds, the following formula applies:

Average Headway (h) = 3600 seconds per hour / Traffic Flow (q).

Substituting the calculated traffic flow:

h = 3600 seconds/hour / 2400 vehicles/hour = 1.5 seconds per vehicle.

This calculation leads to the conclusion that the