Assume you are observing traffic in a single lane of a highway at a specific location. You measure the average headway and average spacing of passing vehicles as 3.2 seconds and 165 ft, respectively. Calculate the flow, average speed, and density of the traffic stream in this lane?

Respuesta :

Answer:

Traffic flow = 1125 veh/hr

Average speed = 35.15 mi/hr

Traffic density = 32 veh/mi

Explanation:

Given Data:

average headway= h =3.2 sec

average spacing = s = 165 ft

Required:

Traffic flow, average speed and density of traffic

Solution:

a. Traffic flow

It cn be calculated through relation

[tex]q=1/h[/tex]

[tex]q=1/3.2=0.3125 veh/sec\\q=0.3125*60*60veh/hr\\q=1125veh/hr[/tex]

b. Average Traffic Speed

It can be calculated by the equation

[tex]v=s/h\\v=165/3.2\\v=51.56ft/sec\\v=51.56*3600/5280\\v=35.15mi/hr[/tex]

c. Traffic Density

It can be calculated by

[tex]K=q/u\\K=1125/35.15\\K=32 veh/mi[/tex]

Following are the calculation to the given points:

Given:

average headway [tex](h) =3.2\ sec[/tex]

average spacing[tex](s) = 165 \ ft[/tex]

To find:

Traffic flow=?

average speed=?

The density of traffic=?

Solution:

Traffic flow [tex](q)= \frac{1}{\text{average headway}}=\frac{1}{3.2} = 0.3215\ \frac{veh}{sec}= 1125\ \frac{veh}{hour}[/tex]

Density of traffic[tex]= \frac{1}{\text{average spacing}}= \frac{1}{165}= 0.006\ \frac{veh}{ft}= 32 \ \frac{veh}{mile}[/tex]

Average speed[tex]= \frac{\text{Traffic flow}}{\text{density of traffic}}= \frac{1125}{32} \ = 35\ mph[/tex]

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