Traffic Engineering, 4 Edition Roess, R.P., Prassas, E.S., and McShane, W.R. FALL 2012
Solutions to Homework No. 4 – Chapter 9 Problem 9-1 A limited network counting study was was conducted for eth network shown here, Because Because only two sets of road tubes were available, the study was conducted over a period of several days, using Station A as a control location. The network is shown here. Figure 9.19 1
Using the data from the study, shown in the tables estimate the 12-hour volume (8 am to 8 PM) at each station for the average day. Table 9.14: Axle Counts for Control Station A
DAY Monday Tuesday Wednesday Wednesda y
TIME PERIOD 8:00-11:45 am 12:00 - 3:45 PM 3,000 2,800 3,300 3,000 4,000 3,600
4:00 -7:45 PM 4,100 4,400 5,000
Table 9.15: Axle – Counts for Coverage Stations Station 1 2 3 4 5 6 7 8 9
Day Monday Monday Monday Tuesday Tuesday Tuesday Wednesday Wednesday Wednesday
The problem calls for estimating a total 12‐hour volume for the study data shown. There is one control‐count station (Station A, Figure 9.19) and 9 coverage‐count stations (Stations 1‐9, Figure 9.19). There are several issues that must be addre ssed in the estimation process: • Data was taken in three four‐hour periods: 8 AM to 12 Noon, 12 Noon to 4 PM, and 4 PM to 8PM. To allow for movement of data crews, however, actual counts were taken for 3.75 hours out of each 4‐hour period. All counts, therefore, must be multiplied by 4.00/3.75 = 1.067 to estimate the actual 4‐hr counts. • Counts were taken using road tubes, and thus represent axle‐counts, not vehicle‐counts. Sample data on traffic composition (Table 9.16) must be used to estimate the average number of axles per vehicle, which can than be used to convert axle‐counts to vehicle‐counts. vehicle‐counts. • Counts taken during one 4‐hour period must be expanded t o estimate counts for the 12‐hour target period. • Counts were taken across three days. All counts must, therefore, be adjusted to reflect the average day of the count.
These conversions can be done in almost any order, and are best done using a spreadsheet. As all results must be rounded to the nearest vehicle, the order of computations and the rounding mechanism used may cause small discrepancies in final answers. In this solution, rounding is done only in the final step, although most of the spreadsheet tables will appear to be rounded at each step.
Table 1, which follows, computes the average number of axles per vehicle from the sample data of Table 9.16. The total number of axles observed is divided by the total number of vehicles observed to determine the conversion factor.
Table 1: Computing the Average Number of Axles Per Vehicle
Average Axles/Vehicle = 2,780/1,276 = 2.18
The data from the Control Count Station A must now be manipulated to produce conversion values for coverage counts. Two conversions must be conducted: a) from 4‐hr counts to 12‐hr counts, and b) from 12‐hr counts on a particular day to 12‐hr counts representing the average of the three days of the study. The first is accomplished by calibrating the percentage of 12‐hour volume that occurs in each 4‐hour period. For each day of the study, the percentage is computed as (V4/V12)*100. There will be different values for each day of the study. These can be
applied separately to coverage counts on the same day, or the average percentages can be applied to all three days. The second conversion is accomplished by calibrating “daily variation factors” for each of the three days of the study. These factors are defined as V AVE/VDAY. The calibration
of these values can be based directly on the 3.75 ‐hr axle‐counts of Table 9.15. These values could be could be converted to 4‐hr vehicle‐counts and used, but the conversions would affect every number equally, and none of the conversion values would be changed. Table 2 illustrates the computation of these conversion values in spreadsheet form. In terms of expanding counts from 4 hours to 12 hours, the percentages do not vary greatly for each day of the study. Therefore, percentages based upon the average data will be used. Coverage counts are now expanded to full 12 ‐hour vehicle counts in Table 3, using the following equation:
V 12i = 1.067 V 3.75i * DF j Pk Where: V12i = 12‐hour vehicle count for Station i, vehs V3.75i
= 3.75‐hour axle count for Station i, axles
1.067 = expansion factor, 3.75 hrs to 4 hrs DF j = daily adjustment factor for day j pk
= percentage of volume volume occurring during time period k, expressed expressed as a decimal
Table 2: Calibration of Conversion Values from Control ‐Count Data
Table 3: Expansion and Adjustment of Coverage Counts to 12‐Hour Vehicle‐Counts Station
Exp To 4 hr
Exp To 12 hrs
Veh Count (/2.18) 872
Daily Adjustment Factor 1.118
8:00 – 11:45
12:00 – 3:45
4:00 – 7:45
8:00 – 11:45
12:00 – 3:45
4:00 – 7:45
8:00 – 11:45
12:00 – 3:45
Problem 9‐2 The following control counts were made at state maintained permanent count station. From the information given, calibrate the daily volume variation factors for this station. Table 9.1: Data for Problem 9-2 Day of Week Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Average Annual Volume for Day 3,500 4,400 4,200 4,300 3,900 4,900 3,100
Daily variation factors may be computed as:
DF = VAVE V AVG Where: VAVE = average daily count for all days of the week, vehs VDAY = average daily count for each day of the week, vehs These computations are carried out in Table 4. 4 ,.
Table 3: Calibration of Daily D aily Adjustment Factors e.g. 4,043/3,500 4,043/3,500 = 1.155 etc
Problem 9 ‐3 What count period would you select for a volume only study at an intersection with a signal cycle length of (a) 60 seconds, (b) 90 seconds, and (c) 120 seconds.
5 minutes minutes or 15 minutes. Count Count 4 of 5 or 13 of 15. 15. The counting period period and the actual count time must be multiples of 1 minute.
6 minutes minutes or 15 minutes. minutes. Count 4.5 of 6 or 12 of 15. 15. The counting period and the actual count time must be multiples of 90 seconds or 1.5 minutes.
6 minutes minutes or 18 minutes. Count Count 4 of 6 or 16 of 18. 18. The counting period period and the actual count time must be multiples of 2 minutes.
Problem 9 ‐4 The following control counts were made at an urban count station to develop daily and monthly factors. Calibrate these factors given the data shown here.
Daily adjustment factors are based upon the data in Table 9.18. The factors, which use the same equation noted in Problem 9‐2, are based upon the average of the 4 weeks of data provided. Monthly adjustment factors are based upon the data in Table 9.19, and are computed using the following equation: MFi = AADT ADTi Where: MFi = monthly adjustment factor month i AADT = average annual daily traffic , vehs/day (estimated as the average of 12 monthly ADTs) ADTi = average daily traffic for month i, vehs/day Daily adjustment factors are calibrated in Table 4. Monthly adjustment factors are calibrated in Table 5. Monthly variation factors must be themselves “adjusted” to reflect the middle of each month.
x 31 = 69,750 x 28 = 61,600 x 31 = 62,000 x 30 = 63,000 x 31 = 60,450 x 30 = 55,500 x 31 = 55,800 x 31 = 52,700 x 30 = 60,000 x 31 = 65,100 x 30 = 64,500 x 31 = 71,300 741,700
AADT = 741,700/365 = 2,032 veh/day Monthly factor = 2032/2250 2032/2250 = .904, .904, 2032/2200 = .924 etc. These are factors of the third week of the month as per the data not the middle as requested. You would need to plot these out to the end of the third week of the month and then using the graph locate the end of the second week (middle of the month and obtain the slightly adjusted monthly factor. It ain’t worth it. Lol
Problem 9 ‐ 5 The four control stations shown nearby have been regrouped for the purposes of calibrating calibratin g daily variation factors. Is the group appropriate? IF not, what would be an appropriate grouping be? What are the combined daily variation factors for the approximate group(s)? The stations are located sequentially along a state route. Table 9.20: Daily Variation Factors for Individual Individual Stations Stations Station 1 2 3 4
Mon 1.04 1.12 0.97 1.01
Tues 1.00 1.07 0.99 1.00
Wed 0.96 0.97 0.89 1.01
Thurs 1.08 1.06 1.01 1.09
Fri 1.17 1.02 0.86 1.10
Sat 0.90 0.87 1.01 0.85
Sun 0.80 0.82 1.06 0.85
The four control count stations of text Table 9.20 are proposed to form a single “group” for the purpose of calibrating Daily Adjustment Factors DF. To be an appropriate grouping, the “average” factor for each day of the week cannot differ from the factors at each station by more than ± 0.10. The grouping is evaluated in Table 7. Table 7: Average Daily Factors for Group and Assessment
Obviously, four of the factors lie outside the acceptable range. It appears that Station 3 most likely should be eliminated. Assuming that they are still spatially contiguous, Stations 1, 2, and 4 may be grouped, and must again be tested, as shown in Table 8. Table 8: Re‐Grouped Stations Tested
The re‐grouping meets the acceptability criteria, and would be used.