Question

Occupancy data from a single loop detector was obtained from a one way street. The loop detector has a length of 6 feet and was observed to have six vehicles cross over it in a period of 30 seconds. The duration and the length of each vehicle are shown in the table below. Use the average vehicle length in your calculations. Estimate the values of q, k and u (flow, density and speed)

Vehicle	1	2	3	4	5	6
Duration (sec)	0.31	0.28	0.3	0.33	0.39	0.35
Length (ft)	17	21	22	18	24	19

Answer 1

We are given the following

So average vehicle length = 20.1667 ft

So we can calculate spot speed of each vehicle.

Each vehicle crosses a length of (6 + average vehicle length) in the duration counted for that vehicle.

So we have the spot speeds as follows and we can also compute the average speed

for example Spot Speed of vehicle 1 = (6+20.167/0.31 = 84.409 ft/sec

Spot speed of vehicle 2 = (6 +20.167)/0.28 = 93.452 ft/sec

Six vehicles are observed over a period of 30 seconds

So flow = 6/30 = 0.2 veh/sec = 720 veh/hour

Average speed = 81.039 ft/sec

So density = Flow/speed = 0.2 /81.039 = .002468 veh/ft = 8.0969 veh/km

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