CE 141 2 nd Long Exam Topics Examples 2 nd Semester AY 2014-2015 Moving Observer Example A bicycle racer practices every day at different times. Her route includes a ride along a 0.5mi bikeway and back. Since she is a traffic engineer, she made it a habit to count the number of cars in lane A that she meets while riding southward , the number of cars in lane A that overtake her while riding northward , and the number of cars in lane A that she overtakes while riding northward .
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Time of The Day 8:00 9:00 A.M. 9:00 10:00 10:00 11:00 11:00 12:00
107 113 30 79
– – –
10 25 15 18
74 41 5 9
Given that the bicyclist travels at a constant speed of 20 mi/h, (a) Find the traffic stream conditions for each period of the day (b) Calibrate the and plot the relationship, and (c) Estimate the capacity of lane A.
= +
Moving Observer Example Solution (a) It takes the bicyclist computed as:
hr, to traverse the half mile distance where in is 0.5 = 0.025 ℎ = 20 /ℎ
Since the bicyclist is traveling at a constant speed (constant speed in moving against and moving with the flow) Using the formula:
= = = 0.025 ℎ = + +
= and = Computing for the time interval 8:00 – 9:00 AM, + 10 74 = 860 ℎ/ℎ = 107 0.025+ 0.025 = 1940 ℎ/ℎ = 800 ℎ/ℎ = 1760 ℎ/ℎ = ∑ = ∑ = 107 + 113 + 30 + 79 = 329 = ∑ = ∑ = 1074 + 25 41 + 155 + 18 9 = 61 = ++ = ∑ = 5360 Using the formula: = = 0.5 0.5 = 5 /ℎ = = 74 107 0.025 0.025 10 860 860 = 15 /ℎ = 40 /ℎ = 25 /ℎ Using the formula: = / = 860 5 = 172 ℎ/ = 129 ℎ/ = 20 ℎ/ = 70 ℎ/ where in
Summary of Answers:
1 2 3 4
860 1940 800 1760
5 15 40 25
172 129 20 70
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(b) Using linear regression(u as y and k as x), a linear equation representing the u k relationship can be generated as: where
= 43.02
= 43.02 0.22
= 0.22
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To get the q k relationship multiply the equation above by k
= = 43.02 0.22
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(c)
= = = 43.02 /ℎ = = = 43.02 = 195.54545454 0.22 = 43.02∗195.54545454 = 2103.09 ≈ 2104 ℎ/ℎ 4
. , where s is the spacing in miles and u is the speed in mph, derive the = − relationships u –k, u – q, and q – k. Also, estimate the capacity (i.e., ) of the roadway. A study of the traffic using a tunnel showed the following u – k relationship applies: = 17.2ln 228 The following relationship applies to a particular urban highway: = 273 70ln
1. Given
2.
3.
4. A moving observer conducted two test runs on a 5-mi stretch of roadway. Both tests were in the direction of the traffic. Given the following measurements, calculate the flow, concentration, space mean speed, average spacing, and average headway of the traffic stream.
Test Run 1 2
Test vehicle speed (mi/h) 10 20
vehicles 100 -150
5. While taking measurements by the moving-observer method, a test vehicle covered a 1-mi section in 1.5 min going against traffic and 2.5 min going with the traffic. Given that the traffic flow was 800 veh/h and the test vehicle passed more than 10 vehicles than passed it when going with traffic, find (a) Number of vehicles encountered by the test vehicle while moving against traffic (b) The speed of the traffic being measured (c) The concentration of the traffic stream (d) Whether on its run with the traffic the test vehicle was travelling faster than the traffic stream 6. Given the following u k relationship
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= 30ln(300 )
Find the jam concentration, the capacity of the roadway, and the speed of the shockwave between conditions and 7. A line of traffic moving at a speed of 30 mph and a concentration of 50 veh/mi is stopped for 30s at a red light. Clculate (a) The velocity and direction of the stopping wave (b) The length of the line of cars stopped during 30s red (c) The number of cars stopped during the 30s of red.
= 60 ℎ
= 40 ℎ
= 250 ℎ/ A vehicular stream at = 1200 ℎ/ℎ and = 100 ℎ/ is interrupted by a flag-person for 5 min beginning at = . At time = + 5 vehicles at the front of the stationary platoon begin to be released at = 1600 ℎ/ℎ and = 20 ℎ. Assuming = 240ℎ/ Assume
8.
(a) Plot the location of the front of the platoon vs time and location of the rear of the platoon versus time (b) Plot the length of the growing platoon versus time. 9. A 15-mi/h school zone is in effect from 7:30 to 9:00 am. Traffic measurements taken on October 10,1985, showed that at precisely 9:00 am, the conditions presented in the figure prevailed. How long did it take for the 3-mi platoon to disappear, and what was the speed of the shock wave that commended at the moment when the platoon dissipated completely?
10. You were the driver of the sixth car to be stopped by a red light. Ten seconds elapsed after the onset of the following green light before you were able to start again. Given that the release flow was 1200 veh/h, calculate the release concentration and the release mean speed. Assume an average car length L=18 ft and a safety margin of
= 2 .
