Two aerial photographs were taken 30 seconds apart over one east-bound lane of l-80 near Grand Island, NE. The following results were recorded. Position from start of road section Vehicle 2000 2300 1700 1200 600 2940 3200 2400 2100 1730 1000 2 3 4
Plot the trajectories of the vehicles on graph paper and compute the average flow (vph), density (veh/mi) and space mean speed (mph) over the 3000 ft length of the lane.

the average flow (vph) = 222.69 veh/hr.  

The average velocity = 111348 ft/hr.

density = 2 × 10⁻³ veh/ft.

Explanation:

The first thing to do in this particular question is to determine the average velocity.

The average velocity = [ ( 2940 - 2000/30) + ( 3200 - 2300/30) + ( 2400 - 1700/30) + ( 2100 - 1200) + ( 1730 - 600/30) + ( 1000 - 0/30).

The average velocity = [31.33 + 30 + 23.33 + 30 + 37.66 + 33.66]/ 6 = 30.99 ft/sec.

Thus, 30.99 ft/sec × 60 × 60 = 111348 ft/hr.

The next thing to do is to determine the density. therefore, the density = 6/ 3000 = 2 × 10⁻³ veh/ft.  

The average flow (vph) =  111348 ft/hr × 2 × 10⁻³ veh/ft.  = 222.69 veh/ hr.

Also, the space mean speed (mph) over the 3000 ft length of the lane = 6/ [ 1/31.33 + 1/30 + 1/23.33 + 1/30 + 1/37.66 + 1/33.66] = 6/ 0.1977 = 30.34 ft/sec.

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