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Solution Chapter 8

# Solution Chapter 8 - 1 Traffic Engineering 4th Edition...

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Unformatted text preview: 1 Traffic Engineering, 4th Edition Roess, R.P., Prassas, E.S., and McShane, W.R. Solution to Problems in Chapter 8 Problem 8‐1 The counts shown are for 12 out of 15 minutes. Thus, each count will be multiplied by 15/12 = 1.25 to get the estimated full 15‐minute count. Note that all values will be rounded to the nearest vehicle. Missing cells will then be estimated using straight‐line interpolation, or extrapolation at the end points. These results are shown in the table below. Table: Expanded Count Table EXPANDED COUNTS ORIGINAL COUNTS East Bound Westbound Eastbount Westbound Count Lane Lane Lane Lane 2 1 2 2 Time Lane 1 Lane 2 Lane 1 Lane 1 4:00‐4:12 360 310 426 450 345 388 4:15‐4:27 350 285 438 463 356 401 4:30‐4:42 380 330 451 475 366 413 4:45‐4:57 370 300 463 469 375 419 5:00‐5:12 370 340 447 463 363 425 5:15‐5:27 345 280 431 444 350 407 5:30‐5:42 340 310 416 425 338 388 5:45‐5:57 320 260 400 406 325 369 Italics indicate an interpolated or extrapolated cell. To answer part b of the question, lane volumes have to be added to get a total directional volume; then, the two directions are added to get a total freeway volume. Each direction is then analyzed to determine the peak hour, the peak hour volume, and the PHF. This is repeated for the highway as a whole. This analysis is shown in the table that follows. 1 2 Table: Directional and Freeway Peak Hour Time Period 4:00-4:15 4:15-4:30 4:30-4:45 4:45-5:00 5:00-5:15 5:15-5:30 5:30-5:45 5:45-6:00 Lane 1 426 438 451 463 447 431 416 400 EASTBOUND Lane 2 Total 450 876 901 463 475 926 932 469 910 463 444 875 425 841 406 806 Cum Lane 1 345 356 366 375 363 350 338 325 WESTBOUND Lane 2 Total 388 733 401 757 413 779 794 419 788 425 407 757 388 726 369 694 Cum FREEWAY Total Cum 1609 1658 1705 1726 6696 6785 1698 1632 6760 1567 6622 1500 6396 The peak hours occur as shown, although for the westbound direction, two different hours produce the same peak hourly flow. In that case, either on can be used. As shown, for the EB direction, the peak hour occurs between 4:15 and 5:15 PM, the peak hour volume is 3,668 veh/h, and the PHF is 3668/(4*932) = 0.984. For the WB direction, the peak hour occurs between 4:30 and 5:30 PM (or between 4:15 and 5:15 PM); the peak hour volume is 3,118 veh/h, and the PHF (for 4:30‐5:30) is 3118/(4*794) = 0.982. For the freeway as a whole, the peak hour occurs between 4:15 and 5:15 PM, the peak hour volume is 6,785 veh/h, and the PHF is 6785/(4*1726) = 0.983. Flow rates are simply the 15‐minute volumes divided by 0.25 hours (or multiplied by 4). Flow rates by direction are shown in the table that follows. Table: Flow Rates by Direction and Period Time Period 4:00-4:15 4:15-4:30 4:30-4:45 4:45-5:00 5:00-5:15 5:15-5:30 5:30-5:45 5:45-6:00 EASTBOUND Vol Flow Rate (veh/h) (veh/h) 876 3504 901 3604 926 3704 932 3728 910 3640 875 3500 841 3364 806 3224 WESTBOUND Vol Flow Rate (veh/h) (veh/h) 733 2932 757 3028 779 3116 794 3176 788 3152 757 3028 726 2904 694 2776 3634 3668 3642 3557 3432 3062 3118 3118 3065 2965 2 3 Problem 8‐2 The sample data must be used to estimate the average number of axles per vehicle, as shown in the following table. Table: Axles vs. Vehicles Axle Per Veh 2 3 4 5 6 Total Vehs Obs (veh) 157 55 50 33 8 303 Axles Obs 314 165 200 165 48 892 The average number of axles per vehicle is 892/303 = 2.944. The estimated number of vehicles in the count period is therefore 11,250/2.944 = 3,821 vehs. Problem 8‐3 The manually‐measured time is actually recorded of an effective distance because of the sight lines involved. This effective distance is: d eff = d 1 * Tan θ = 60 * Tan (80.4) = 60 * 6.013 = 360.78 ft The observed speed is, therefore, 360.78/8.3 = 43.5 ft/s = 43.5/1.47 = 29.6 mi/h. 3 ...
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