Performance Criteria for Retroreflective Pavement Markers (2022)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

185   Field Speed Study A P P E N D I X D Study Objective The objective of the study was to quantify the effects of RPMs on a motorist’s speed. The desired goal was to study roadways where only RPMs were replaced in order to isolate the effects of RPMs. Another desired goal was to observe the effects of RPMs on motorists’ speed under wet pavement and adverse weather conditions. Study Methodology Roadways having RPMs installed for the first time would be the ideal location for a before/after study; however, all highways and major arterials under the jurisdiction of TxDOT have RPMs installed. Thus, to investigate the possible effects of RPMs on TxDOT roadways, data were collected only where RPMs had recently been replaced. No other maintenance work, such as road resurfacing or road improvements, was being done at the sites of interest. The research team had the assumption that if only RPMs were being replaced on a segment, then the current visibility levels of the RPMs would be similar to no RPMs present. The research team contacted maintenance engineers in 17 different counties in three different regions of TxDOT for possible sites. Site Selection The research team found four roadways where RPMs were being replaced. The four roads were the following: • FM 1971, near Carthage, Texas • FM 2517, near Carthage, Texas • SH 47, near Bryan, Texas • SH 21, near Bryan, Texas Replacement of RPMs was taking place along certain segments of the roadways listed above. The research team wanted to collect speed data along tangent and curve segments. The research team deployed road tube counters to measure speeds at the midpoint on curves, and placed counters at least 200 ft away from intersections with other highways. The following sections describe where counters were placed and the characteristics of the roads. Farm to Market Road 1971 FM 1971 is a two-lane rural road located near Carthage, Texas. The road provides access to Lake Murvaul, and the surrounding area is mostly farmland. The speed limit for this road is 55 mph, with 2-ft wide shoulders and an average lane width of 10 ft. There is no overhead

186 Performance Criteria for Retroreflective Pavement Markers lighting on this road. Road tubes were placed over 1,000 ft from the start of the curve. Figure D-1 shows an aerial view and photo of the installation. (a) (b) Figure D-1. FM 1971 data collection site location (Map Data: Google). Two counters were placed along the road. One counter was placed along the maintenance segment, and another counter was placed outside the maintenance segment. The second counter was to serve as a control site for the road segment; however, the counter malfunctioned and all before data could not be downloaded. During the after period, a counter was not placed at the control site. Speed data were collected during the first week of March 2017 for the before period and then during the last week of June 2017. The RPMs were replaced in April 2017.

Field Speed Study 187   Farm to Market Road 2517 Counters were placed at two data collection sites on FM 2517: one location was on a tangent segment, and the other location was at a horizontal curve. This road is a two-lane rural highway with a speed limit of 75 mph. At the curve, there were no other delineation treatments other than the RPMs. Figure D-2 shows an aerial view and a street view of the data collection site. (a) (b) Figure D-2. (a) Aerial view and (b) street view of the data collection site on the curve at FM 2517 (Map Data: Google). The horizontal curve had rumble strips on each side of the shoulder. The lane width measured at the site was 11.5 ft, with a shoulder width of 3 ft for the westbound (WB) direction and 2 ft for the eastbound (EB) direction. The horizontal curve does not have a sharp radius or

188 Performance Criteria for Retroreflective Pavement Markers degree of curvature. The curve has a steep drop-off for vehicles traveling through the outside of the curve. Figure D-3 shows the location of the second data collection site on FM 2517. (a) (b) Figure D-3. (a) Aerial view and (b) street view of the data collection site at the tangent section of FM 2517 (Map Data: Google). The road tubes were placed 320 ft upstream from the intersection with County Road 405. The location was also located over 3,000 ft from a four-way intersection. The lane width at this site was 10.25 ft for EB traffic and 11 ft for WB traffic. The paved shoulder was around 2 ft on both sides of the road. Both sites at FM 2517 were restricted passing zones. At both sites, researchers measured speeds during the first week of March 2017 for the before period and then during the last week of June 2017. The RPMs were replaced in April 2017.

Field Speed Study 189   State Highway 47 SH 47 is a four-lane highway with a speed limit of 75 mph. The facility has higher traffic volumes compared to FM 1971 and FM 2517. The travel lanes are separated by a grass median. The research team placed one counter for each direction of traffic. Figure D-4 shows an aerial view of the data collection sites. Figure D-4. Data collection sites at SH 47 (Map Data: Google). Due to the high traffic volumes and high speeds, the research team used Google Earth to measure the median, lane, and shoulder width. For northbound (NB)/WB traffic, the average lane width was 11.5 ft, and the shoulder width was 7 ft. The NB/WB traffic traveled down a 2% downhill slope toward the location of the speed counter. For southbound (SB)/EB traffic, the average lane width was 11 ft, with a paved shoulder width of 9 ft. The roadway leading to the counter was relatively flat. For the before period, counters were placed on April 17, 2017. For the after period, counters were placed on August 22, 2017. State Highway 21 SH 21 is a four-lane highway with a speed limit of 75 mph. The corridor runs in the east– west direction. The highway intersects with SH 47, and traffic is separated by a grass median that is over 5 ft wide. The research team placed one counter for each direction of traffic. Figure D-5 shows an aerial view of the data collection sites.

190 Performance Criteria for Retroreflective Pavement Markers Figure D-5. Data collection sites for SH 21 (Map Data: Google). The counters were placed over 400 ft from the intersection with the Texas OSR highway. Due to the high traffic volumes and high speeds, the research team used Google Earth to measure the median, lane, and shoulder width. For EB traffic, the average lane width was 11.5 ft, and the shoulder width was 10 ft. For WB traffic, the average lane width was 12 ft, with a paved shoulder width of 10 ft. For the before period, counters were placed on April 17, 2017. For the after period, counters were placed on October 5, 2017. Summary There were a total of seven counters placed at four different sites. Six of the counters were placed on tangent segments, and only one counter was placed on a curve. Table D-1 gives a summary of the data collection sites and roadway characteristics.

Field Speed Study 191   Table D-1. Summary of data collection sites. Site Number Road Segment Direction Average Lane Width (ft) Shoulder Width (ft) Speed Limit (mph) 1a FM 1971 Tangent NB 11.30 1.25 55 1b FM 1971 Tangent SB 8.80 1.67 55 2a FM 2517 Curve EB 11.50 2.42 75 2b FM 2517 Curve WB 11.50 3.42 75 3a FM 2517 Tangent EB 10.25 2.10 75 3b FM 2517 Tangent WB 11.20 1.67 75 4 SH 47 Tangent NB 11.5 0 7.00 75 5 SH 47 Tangent SB 11.00 9.00 75 6 SH 21 Tangent EB 11.50 10.00 75 7 SH 21 Tangent WB 12.00 10.00 75 Data Collection The research team let the traffic counters collect data for at least seven nights. There were some sites that due to extreme weather or equipment failure, did not record data for the whole data collection period. The road tube counters provided speed of vehicle, number of axles, vehicle class, time of day, and date of the data point. Table D-2 shows the dates for the data collection periods. Table D-2. Data collection periods for all sites. Site Number Road Segment Study Period Date Placed Date Removed 1 FM 1971 Tangent Before 3/2/2017 3/9/2017 After 6/20/2017 6/28/2017 2 FM 2517 Curve Before 3/2/2017 3/9/2017 After 6/20/2017 6/28/2017 3 FM 2517 Tangent Before 3/2/2017 3/9/2017 After 6/20/2017 6/28/2017 4 SH 47 Tangent Before 4/17/2017 4/21/2017 After 8/22/2017 8/29/2017 5 SH 47 Tangent Before 4/17/2017 4/21/2017 After 8/22/2017 8/29/2017 6 SH 21 Tangent Before 4/17/2017 4/21/2017 After 10/5/2017 10/13/2017 7 SH 21 Tangent Before 4/17/2017 4/21/2017 After 10/5/2017 10/13/2017 In addition to the speed data, the research team used online sources to collect sunlight and weather data. Weather data were collected from the website www.weatherunderground.com. The website provides historical weather data that include date, time of day for reading, precipitation,

192 Performance Criteria for Retroreflective Pavement Markers temperature, and weather condition (e.g., cloudy, foggy). During parts of the study, there were days with heavy rain and light rain. In order to categorize periods of heavy and light rainfall, the research team calculated the rate of rainfall per hour and used the following scale (1): • Less than 0.1 inch of rain per hour equals light rainfall. • 0.1 to 0.3 inch of rain per hour equals moderate rainfall. • More than 0.3 inch of rain per hour is heavy rainfall. For collecting times for sunrise, sunset, night, and daylight, the research team used an Internet source (2). To account for the glare during sunrise/sunset conditions, the research team classified sunrise and sunset times to occur 30 minutes before and 30 minutes after the reported sunrise/sunset times. Hours of the day 30 minutes before sunrise and 30 minutes after sunset were considered nighttime hours. Daytime was considered to take place 30 minutes after sunrise and 30 minutes before sunset. During data collection, rainfall was observed during both study periods at all sites. Table D-3 shows the recorded amounts of precipitation according to light condition. Table D-3. Precipitation amounts according to time of day. Road Study Period Date Precipitation (in./hr) According to Daylight Condition Night Day Average Max Min Average Max Min FM 1971 and FM 2517 Before 3/4/2017 3/5/2017 3/6/2017 3/7/2017 0.02 0.02 0.08 0 0.02 0.04 0.12 0 0.01 0.01 0.04 0 0.02 0.07 0.04 0.23 0.03 0.17 0.08 0.38 0.02 0.01 0.01 0.08 After 6/22/2017 6/24/2017 0.02 0.62 0.03 1.83 0.01 0.03 0.11 0.01 0.27 0.01 0.01 0.01 SH 47 Before 4/17/2017 4/18/2017 0.14 0.06 0.48 0.40 0.01 0.01 0.09 0.01 0.32 0.01 0.04 0.01 After 8/23/2017 8/25/2017 8/26/2017 8/27/2017 1.09 0.01 0.31 0.83 1.76 0.01 1.03 1.21 0.16 0.01 0.01 0.36 5.00 0 0.69 0.98 5.00 0 1.89 1.26 5.00 0.03 0.47 8/28/2017 0.29 0.97 0.01 0.23 0.47 0.07 8/29/2017 0.03 0.03 0.02 0 0 0 SH 21 Before 4/17/2017 0.14 0.48 0.01 0.09 0.32 0.04 4/18/2017 0.06 0.40 0.01 0.01 0.01 0.01 After NA NA NA NA NA NA NA Total 0.41 1.83 0.01 0.36 5.00 0.01 Precipitation amounts ranged from 0.01 in/hr to 5 in/hr. For FM 1971 and FM 2517, there were more days with precipitation in the before period than the after period. The opposite was observed for SH 47. The research team assumed that 0.01 inch of precipitation was the minimal amount of rainfall needed for wet pavement conditions. During nighttime hours, half of the days experienced light rainfall on average. Four days experienced heavy rainfall during nighttime hours. There was no rainfall at SH 21 during the after period of the study.

Field Speed Study 193   Descriptive Statistics The raw data from the road tubes had entries for unclassified vehicles (i.e., no axle count) and entries with no speed recorded. These entries were omitted from the database, in addition to sunset and sunrise data entries. Over 114,000 recorded speeds were part of the initial database. Table D-4 shows average, maximum, and minimum speeds of the initial database. Table D-4. Initial database speed statistics (speed in mph). Road Segment DIR Before After Count Average Speed Max Speed Min Speed Count Average Speed Max Speed Min Speed FM 1971 Tangent NB SB 1,197 1,180 59.00 58.40 87 85 10 11 1,296 1,341 58.30 59.10 96 99 8 13 FM 2517 Curve EB WB 6,062 6,101 66.30 66.60 151 110 19 21 7,175 7,395 67.40 67.10 100 103 20 16 Tangent EB WB 4,534 3,681 60.90 58.90 114 145 11 10 1,315 1,155 62.20 56.60 99 87 13 14 SH 47 Tangent NB SB 15,176 13,352 71.70 70.80 134 108 22 18 27,190 16,673 72.10 69.10 118 132 14 17 SH 21 Tangent EB WB 24,834 20,500 71.23 70.81 114 117 15 18 55,883 17,626 70.46 69.35 116 105 10 15 Grand Total 96,617 67.80 151 10 137,049 69.20 132 8 The initial database showed that on some sites, the speeds decreased after RPMs were replaced, while on other sites, the average speed increased. The highest decrease in average speed was 2.28 mph observed for WB traffic at FM 2517 on the tangent section. The highest increase in average speed was 1.29 mph for EB traffic at FM 2517 on the tangent section. Speeds as high as 151 mph and as low as 8 mph were observed. The low values for the minimum speeds could be due to farming equipment or construction trucks coming out of the RELLIS Campus at the SH 47 sites. A box plot was used to help determine the minimum and maximum speeds that should be considered for analysis. The difference in vehicle count at SH 21 was due to broken equipment that was observed when the research team picked up the counter. Figure D-6 shows a box plot of the data found in the initial database.

194 Performance Criteria for Retroreflective Pavement Markers Figure D-6. Box plot of initial database. The box plot in Figure D-6 shows that for all sites, many of the outlier speed readings fell below 40 mph for all sites. For higher speeds, many of the outlier higher speeds were above 90 mph. The database for analysis included speeds in the range of 40 to 100 mph. After filtering speeds below 40 mph and above 100 mph, there were over 113,000 speed readings. Table D-5 shows the descriptive statistics of the database with speeds ranging from 40 to 100 mph.

Field Speed Study 195   Table D-5. Final database speed statistics. Road Segment DIR Before Replacement Speeds (mph) After-Replacement Speeds (mph) Count Average Std. Dev. 85th Percentile Count Average Std. Dev. 85th Percentile FM 1971 Tangent NB SB 1,160 1,150 60.10 59.20 7.80 7.50 68 67 1,244 1,296 59.3 60.0 7.6 7.8 67 68 FM 2517 Curve EB WB 6,027 6,080 66.50 66.70 7.10 7.10 73 73 7,143 7,356 67.6 67.3 7.2 7.1 74 74 Tangent EB WB 4,349 3,429 62.10 60.90 8.00 8.40 70 69 1,269 1,060 63.3 58.8 8.2 7.4 71 66 SH 47 Tangent NB SB 15,164 12,994 71.70 71.90 5.80 7.70 77 79 27,145 16,247 72.2 70.1 6.9 7.4 78 77 SH 21 Tangent EB 24,474 71.81 7.63 78 55,711 70.57 5.74 76 WB 20,424 70.93 6.5 77 16,838 71.12 7.93 78 Grand Total 95,251 69.82 7.92 77 135,309 70.2 7.11 76 The average speeds increased after removing the lower speed values. The observations about changes in average speed depended on the road and on the direction of traffic; however, the changes in speed were within +/- 3 mph. For WB traffic on SH 21, the average speed increased in the after period of the study once the lower speed values were filtered out. The increase was less than 0.5 mph. The standard deviation ranged between 6 and 8 mph, with the exception of SH 47. The statistics in Table D-6 show the average speeds at each site during all times of the day. Table D-6 shows the average speed, standard deviation, 85th percentile speed, and number of recorded speeds according to daytime and nighttime conditions.

196 Performance Criteria for Retroreflective Pavement Markers Table D-6. Speed statistics according to daytime and nighttime conditions. Period of the Day Study Period Speed Values FM 1971 Tangent FM 2517 SH 47 Tangent SH 21 Tangent Curve Tangent NB SB EB WB EB WB NB SB EB WB Night After Count 200 178 1,177 1,070 188 126 3,173 2,612 12,279 2,583 Average 59.1 59.4 68.1 66.2 64.2 56.6 70.5 69.3 69.86 69.98 Std. dev. 6.9 8.1 8.2 7.8 8.5 8.7 7.3 7.4 5.9 8.2 85th per. 66 68 76 73 73 65 77 76 75 77 Before Count 238 246 1,412 1,068 953 620 1,875 1,378 3,679 4,134 Average 60.9 58.5 66.8 65.3 62.8 59.3 70.4 71.9 70.9 71.2 Std. dev. 8.3 7.9 7.2 7.7 8.3 9.4 6.5 7.9 8.21 7.4 85th per. 70 67 74 73 71 69 76 78 77 76 Day After Count 1,044 1,118 5,966 6,286 1,081 934 23,972 13,635 43,432 14,255 Average 59.4 60.1 67.5 67.4 63.2 59.1 72.4 70.3 70.8 71.3 Std. dev. 7.8 7.7 7.1 7.00 8.1 7.2 6.8 7.3 5.7 7.9 85th per. 67 68 74 74 71 66 78 77 76 78 Before Count 922 904 4,615 5,012 3,396 2,809 13,289 11,616 20,795 16,290 Average 59.9 59.4 66.4 66.9 61.9 61.2 71.9 71.9 72.2 71.5 Std. dev. 7.6 7.4 7.0 6.9 7.9 8.2 5.7 7.7 7.5 6.2 85th per. 67 67 73 74 69 69 77 79 78 77 FM 2517 at the curve segment showed an increase of around 1 mph during nighttime conditions. The highest increase in average speed on tangent segments was 1.4 mph, also observed at FM 2517 for EB traffic. Overall, the increase in average speeds ranged from 0.1 to 1.4 mph for all times of the day. For the nighttime, a decrease in average speeds depended on the direction of traffic and road. All tangent segments observed a decrease in average speed during the nighttime after the RPMs were replaced in at least one direction. The highest decrease in average speed during nighttime was around 3 mph, observed at FM 2517 WB on the tangent segment. The decrease in average speeds ranged from 1.1 to 2.7 mph. For SH 21, the reported average speed excluded speeds recorded during the wet conditions. At FM 1971, the speed limit was 55 mph; however, all measured 85th percentile speeds were at least 10 mph or more over the speed limit. During the before period of the study at nighttime, the 85th percentile speed was the

Field Speed Study 197   highest. After RPMs were replaced, the 85th percentile speed was similar to the 85th percentile speed observed during the day. At all other sites, the difference in 85th percentile speed was +/- 3 mph according to time of day, road, and direction of traffic. A goal of this study was to observe the speed of motorists during rainfall events before and after replacement of the RPMs. Table D-7 shows the average speeds during recorded rainfall events at night for each road. Table D-7. Average speeds at nighttime during recorded rain events. Study Period Speed Values FM 1971 Tangent FM 2517 Curve FM 2517 Tangent SH 47 Tangent After Count Average 32 57.97 140 65.42 30 58.10 1598 67.02 Std. Dev. 7.06 7.87 9.37 7.85 Before Count Average 53 56.79 260 64.06 140 59.55 299 66.57 Std. Dev. 8.12 8.05 8.89 8.09 For rainfall events, the average speed does not take into account different directions of traffic. Three of the four roads had an increase in average speed after the RPMs were replaced. The increase in average speeds ranged from 0.45 to 1.36 mph. The tangent section at FM 2517 saw a decrease of 1.45 mph in average speed after RPMs were replaced. Data Analysis The study used two methods to analyze the data. The first method used was an ANOVA to identify if the difference in mean speeds was statistically significant. The second method consisted of using linear regression to assess the impact of the RPMs and if there were other factors that affected speeds at the sites. The results of the analysis are discussed in the sections below. ANOVA For the ANOVA, the research team looked at the nighttime speeds. In order for the posted speed limit and the highway geometrics to not be a factor in the analysis, each site was analyzed separately. In addition to the nighttime analysis, an analysis was conducted for speed of motorists during nighttime hours during rainfall events. Table D-8 shows the difference between the calculated mean speed before and after RPMs were replaced during nighttime hours. Table D-8. ANOVA for nighttime speeds under clear weather conditions. Road Segment Mean Speed (before) Mean Speed (after) Difference (after – before) ANOVA p-value FM 1971 Tangent 60.05 59.37 -0.68 0.22937 FM 2517 Tangent 61.60 61.44 -0.16 0.77349 FM 2517 Curve 66.45 67.34 0.89 0.00014*

198 Performance Criteria for Retroreflective Pavement Markers SH 47 NB Tangent 71.09 71.99 0.90 0.00001* SH 47 SB Tangent 71.86 70.13 -1.73 < 0.00001* SH 21 EB Tangent 70.94 69.86 -1.08 < 0.00001* SH 21 WB Tangent 71.24 69.98 -1.26 < 0.00001* * Statistically significant. The ANOVA showed that the differences in mean speeds were statistically significant for FM 2517 at the curve, SH 21, and SH 47. The differences between the measured means were around 1 to 1.5 mph. At the tangent section at SH 47, there was a decrease between before and after, whereas at FM 2517, there was an increase of 1 mph. This could mean that there were other factors influencing the speed of traffic. The sites at SH 21 experienced a decrease in average speeds during clear nighttime conditions after RPMs were replaced. The ANOVA results for wet-weather conditions during nighttime hours are shown in Table D-9. Table D-9. ANOVA of nighttime speeds during rain events. Road Segment Mean Speed (before) Mean Speed (after) Difference (after – before) ANOVA p-value FM 1971 Tangent 56.79 57.97 1.18 0.499 FM 2517 Tangent 59.55 58.10 -1.45 0.423 FM 2517 Curve 64.06 65.42 1.36 0.104 SH 47 NB Tangent 66.57 67.40 0.83 0.115 SH 47 SB Tangent NA 66.35 NA NA SH 21 EB Tangent 71.48 NA NA NA SH 21 WB Tangent 69.83 NA NA NA * Statistically significant. The differences in mean speeds ranged from about 0.5 to 1.5 mph. The tangent section on FM 2517 was the only site that saw a decrease in mean speed after the new RPMs were placed. The ANOVA showed that the differences between mean speeds during wet conditions were not statistically significant. Linear Regression Model After the ANOVA, the research team used linear regression to quantify the impact of RPMs and other factors on traffic speed. The analysis was conducted only for nighttime conditions. SH 47 and SH 21 were analyzed separately from all other roads because they had a median separating the different directions of traffic and both roads had a higher speed limit. The correlation between higher speeds and presence of a median may have led to false assumptions if all sites were analyzed together. Linear Regression Model for SH 47 and SH 21, Nighttime Conditions There were two models used for analysis. The first model used data for nighttime, clear weather conditions, which included data from both SH 47 and SH 21. The second model

Field Speed Study 199   analyzed nighttime data under wet-weather conditions. The second model used data for SH 47 because there was no rain event in the after period of the study for SH 21. The first linear regression model equation was: SPD = B_or_A + LW + SW + PC_TT Where, B_or_A = study period. LW = lane width. SW = right shoulder width. PC_TT = passenger vehicles or heavy trucks. Vehicles with more than two axles were classified as heavy trucks (TT), and all others were classified as passenger vehicles. The lane width in the model ranged from 11 to 12 ft, and the right shoulder width ranged between 7 to 10 ft. The research team plotted a histogram of the subset data to check for normality. Figure D-7 shows the histogram of the speed distribution. Figure D-7. Histogram for data from SH 21 and SH 47, under nighttime, clear weather conditions. The histogram shows a normal distribution of the speed measurements. The subset had a total of 28,103 speed readings; 20,962 speed measurements were from SH 21 and 7,141 were

200 Performance Criteria for Retroreflective Pavement Markers from SH 47. The average speed of the subset was 70.49 mph, and the median value was 71. The data set included over 3,300 vehicles that were classified as heavy trucks. Table D-10 shows the linear regression model results. Table D-10. First linear regression model coefficients for nighttime speeds at four-lane highways. Variable Estimate Std. Error t value Pr(>|t|) Intercept 65.40 1.608 40.66 <0.0001 B_or_A: Before 0.918 0.084 10.91 <0.0001 LW 0.751 0.141 5.153 <0.0001 SW -0.349 0.371 -8.763 <0.0001 PC_TT: TT -4.845 0.119 -40.25 <0.0001 Residual standard error: 6.466 on 28098 degrees of freedom. Multiple R-squared: 0.06374; Adjusted R-squared: 0.06361. F-statistic: 478.2 on 4 and 28098 DF; p-value: < 2.2e-16. The base conditions for the model were (1) after RPMs were replaced, and (2) passenger vehicles. According to the estimates, heavy vehicles drive around 5 mph slower than passenger vehicles. Speeds were around 1 mph higher before RPMs were replaced than after RPMs were replaced. The shoulder width decreased the speed of motorists around one-third mph per foot of shoulder width. A quantile-to-quantile (Q-Q) plot was used to help assess whether the dependent variable (speed) was normally distributed. Figure D-8 shows the Q-Q plot. Figure D-8. Q-Q Plot of linear model for clear, nighttime conditions on four-lane highways.

Field Speed Study 201   Normally distributed data plots a roughly straight line on a Q-Q plot. The line shown in Figure D-8 is roughly straight, meaning that the data are adequate for linear regression. The low R-squared could be due to the range of speeds imposed on the data set. From the model, it could be inferred that the new RPMs had a statistically significant impact on motorists’ speeds during nighttime conditions under clear weather. The magnitude of the coefficient shows that although the influence was found to be statistically significant, the influence may not be significant in a practical sense. For the second model, which considered nighttime data under wet conditions, the following equation was used: SPD = B_or_A + DIR + RN_SC + PC_TT Where, B_or_A = study period. DIR = direction of travel lane. RN_SC = precipitation scale. PC_TT = passenger vehicles or heavy trucks. Only SH 47 had rain events occur before and after the RPMs were replaced. Because both directions had similar lane widths and shoulder widths, geometric characteristics were not included in the model; however, preliminary analysis of the data showed that there were differences in average speeds according to direction of travel. The precipitation scale included four outcomes: • No rainfall. • Light rainfall. • Moderate rainfall. • Heavy rainfall. The criteria for each scale were explained in a previous section. The subset had a total of 9,038 speed measurements. Figure D-9 shows a histogram of the speed data collected.

202 Performance Criteria for Retroreflective Pavement Markers Figure D-9. Histogram of the speeds for wet, nighttime data for four-lane highways. The histogram shows a normal distribution of the speed measurements. The median speed in the subset was 71 mph, and the mean speed was 70.34 mph. The subset had speeds for 494 heavy trucks. There were a total of 1,897 speed measurements under wet conditions; 787 occurred during heavy rainfall, 302 under moderate rainfall, and 808 under light rainfall. Table D-11 shows the coefficients of the linear model. Table D-11. Second linear regression model coefficients for nighttime speeds at SH 47. Variable Estimate Std. Error t value Pr(>|t|) Intercept 65.320 0.252 259.300 < 0.0001 B_or_A: Before -0.013 0.157 -0.084 0.9330 DIR: SB -0.840 0.149 -5.642 < 0.0001 RN_SC: Light 3.927 0.349 11.240 < 0.0001 RN_SC: Moderate 2.528 0.469 5.380 < 0.0001 RN_SC: No Rainfall 6.641 0.268 24.800 < 0.0001 PC_TT: TT -5.346 0.321 -16.640 < 0.0001 Residual standard error: 6.932 on 9031 degrees of freedom. Multiple R-squared: 0.1009; Adjusted R-squared: 0.1003. F-statistic: 168.9 on 6 and 9031 DF; p-value: < 2.2e-16.

Field Speed Study 203   The model coefficient shows that speeds would be 0.013 mph slower with barely visible or no RPMs. This coefficient was not statistically significant in the model. The base direction for the model in Table D-11 was the NB direction. The model shows that traffic traveling in the SB direction traveled around 1 mph slower than NB traffic, which could be due to the slight downhill drop in the NB direction. The base condition for the rainfall data was heavy rainfall. The model shows that as rainfall decreased, the speeds of motorists increased during nighttime. As in the model with clear conditions, heavy trucks traveled around 5 mph slower than passenger vehicles. A Q-Q plot helped further assess whether the dependent variable (speed) was normally distributed. Figure D-10. Q-Q plot of linear model for wet, nighttime conditions at SH 47. The line shown in Figure D-10 is roughly straight, meaning that the data were adequate for linear regression. The coefficient shows that drivers drove faster after the RPMs were replaced during rain events; however, the factor was not statistically significant. The amount of rainfall was a bigger factor when it came to motorists’ speeds. When there was no rainfall, drivers traveled around 7 mph higher than when there was heavy rainfall. Because the data used included only one highway, not many conclusions could be inferred from the analysis; however, the model shows that other factors play a bigger role in the choice of a motorist’s speed when traveling during rain events at nighttime.

204 Performance Criteria for Retroreflective Pavement Markers Linear Regression Model for Two-Lane Rural Highways, Nighttime Conditions The sites at FM 2517 and FM 1917 were used in the analysis. Speed data were taken at three different sites on two different roads, allowing for geometric factors such as lane width and shoulder width to be used in the model. In addition, rain events were recorded during both periods of the study; therefore, only one statistical model was used. The subset of data for nighttime conditions had a total of 7,476 speed measurements. Figure D-11 shows the distribution of the speeds. Figure D-11. Histogram of speed measurements for two-lane rural highways. The median speed was 65 mph, and the average speed in the subset was 64.51 mph. The subset included 655 speed readings under wet conditions. From 655 data points under rain conditions, 602 occurred under light rainfall, 21 under moderate rainfall, and 32 under heavy rainfall. For vehicle classification, the database included 1,161 speed readings from heavy vehicles. The lane width ranged from 9 to 11 ft, and the shoulder ranged from 1 to 3 ft. The database included tangents and horizontal curves. The linear regression model equation was: SPD = B_or_A + LW + SW + RN_YN + SEG + PC_TT + PSL Where, SPD = speed in mph. B_or_A = before or after the RPMs were replaced.

Field Speed Study 205   LW = lane width of the travel lane (ft). SW = right shoulder width (ft). RN_YN = presence of rain. SEG = road segment (tangent or curve). PC_TT = PC_TT = passenger vehicles or heavy trucks. PSL = posted speed limit. The posted speed limit at FM 1971 was 55 mph, and 75 mph was the posted speed limit at FM 2517. Because the majority of rainfall data was light rain, the variable showing whether there was rain was used instead of the scaled amount of rainfall. Table D-12 shows the coefficients from the linear regression model. Table D-12. Linear regression model coefficients for two-lane rural roads. Variable Estimate Std. Error t value Pr(>|t|) (Intercept) 67.290 2.396 28.090 < .0001 B_or_A: Before -0.886 0.196 -4.513 < .0001 PSL 0.209 0.025 8.499 < .0001 LW -0.929 0.197 -4.710 < .0001 SW -1.147 0.229 -5.011 < .0001 RN_YN: Y -2.186 0.325 -6.719 < .0001 SEG: Tangent -6.995 0.383 -18.240 < .0001 PC_TT: TT -3.998 0.254 -15.710 < .0001 Residual standard error: 7.932 on 7468 degrees of freedom. Multiple R-squared: 0.1523; Adjusted R-squared: 0.1515. F-statistic: 191.6 on 7 and 7468 DF; p-value: < 2.2e-16. All variables in the model were found to be statistically significant. The model shows that heavy trucks traveled around 4 mph slower than passenger vehicles. In terms of the average speeds according to direction of travel during nighttime conditions, Table D-6 shows that there were higher average speeds on road segments where the lane width and shoulder width were smaller. This explains the negative coefficients for the effects of lane width and shoulder width in the model. The model also shows that motorists traveled slower on tangent segments than on the curve segment. When there was rain or wet pavement conditions, motorists traveled around 2 mph slower than they would under dry conditions. A Q-Q plot helped further assess whether the dependent variable (speed) was normally distributed. Figure D-12 shows the Q-Q plot.

206 Performance Criteria for Retroreflective Pavement Markers Figure D-12. Q-Q plot for two-lane rural road linear regression model. The Q-Q plot shows a fairly straight line, which indicates that the data were normally distributed. The model shows that the RPMs had a statistically significant effect of around 1 mph. According to the model, drivers traveled 1 mph slower before the RPMs were replaced. This result is similar to the results for the four-lane highway model under clear conditions. Conclusion A speed study was conducted on roads where RPMs were being replaced. It was assumed by the research team that if only RPMs were replaced on a road segment, then the current RPMs were close to not visible or provided very minimal guidance to motorists. Researchers contacted different regions within TxDOT and conducted the study on four different roads. The research study sought to evaluate the effects of RPMs on driving speeds during nighttime conditions and wet pavement conditions, if possible. Rainfall data were observed for both periods of the study; however, SH 21 did not have any rain data recorded for the after-replacement period of the study. The study used an ANOVA to evaluate whether there was a statistically significant difference in average speeds before and after RPMs were replaced. Further analysis of the data included running a linear regression model to find the magnitude of the effects of RPMs.

Field Speed Study 207   The ANOVA showed that there was a significant difference in average speeds during nighttime under clear weather conditions. The statistically significant conditions were observed on four-lane highways, and on two-lane rural roads where the speed limit was 75 mph. The magnitude of the difference in average speed depended on direction of travel and road segment. A separate analysis was made for nighttime speeds under wet conditions. There was no statistically significant difference in the average speeds. Linear regression models were made for nighttime speeds during clear weather and rainy weather according to the number of lanes. The models show that when the replacement of RPMs resulted in statistically significant speed changes, the magnitude of the effect was an increase of about 1 mph. The limitations to this study include the limited number of study sites and the fact that only one curve was evaluated. The sites evaluated, however, were chosen so that only the effect of RPMs could be isolated. At the curve site, there were no other delineation devices present. For all sites, there were no other improvements made to the road including repaving and restriping the road. That the magnitude of the effect of RPMs is around 1 mph shows that even though the influence is statistically significant, the influence of RPMs on speed may not be practically significant. The inclusion of rain data into the model showed speeds were influenced by the presence of rain. Other factors on the roadway and weather conditions may have a bigger effect on a driver’s speed than RPMs. References 1. Rain Measurement. WeatherShack.com. https://www.weathershack.com/static/ed- rainhttps://www.weathershack.com/static/ed-rain-measurement.htmlmeasurement.html Accessed Aug. 31, 2017. 2. Welcome to Sunrise Sunset. http://www.sunrisesunset.com/. Accessed Aug. 31, 2017.