Guidance for the Design and Application of Shoulder and Centerline Rumble Strips (2009)

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119 S E C T I O N 9 The dimensions of rumble strips used in practice vary from state to state. No typical standard design for either shoulder or centerline rumble strips is used in every state. This is logi- cal because shoulder and centerline rumble strips are being installed along numerous roadway types with a range of oper- ating conditions (i.e., vehicular speeds), cross-sectional charac- teristics (e.g., lane widths, shoulder widths, clear zone widths), and potential users (e.g., motor vehicles and bicyclists). It seems reasonable to believe that the optimum dimensions for a given roadway should vary based upon these three elements (i.e., operating conditions, cross-sectional characteristics, and potential users). For shoulder rumble strips the dimension that varies the most among states is the length. Table 6 shows a range in this dimension from 6 to 36 in. (152 to 914 mm). For milled rumble strips groove lengths are commonly between 12 and 16 in. (305 and 406 mm), and for rolled rumble strips groove lengths of 24 to 36 in. (610 to 914 mm) are common. Recently, at least one transportation agency (i.e., Arizona DOT) has adopted a policy that allows groove lengths as short as 6 in. (152 mm) for milled rumble strips. The desire to install milled rumble strips with groove lengths less than the typical 12 to 16 in. (305 to 406 mm) is: 1. To keep this dimension as narrow as possible to provide additional lateral clearance for bicyclists, 2. Due to pavement performance issues when rumble strips are installed on roadways with narrower shoulders, or 3. Simply to install rumble strips on roadways with narrow or nonexistent shoulders where rumble strips might not otherwise be installed. The primary concern about narrowing the groove length is whether the rumble strip will still provide sufficient noise and/or vibration levels to arouse an inattentive, distracted, drowsy, or fatigued driver. Research conducted in Kansas (36) is the only research that has investigated this issue to any degree. Results of the research indicate that longer rumble strip lengths generally produce higher noise levels in the passenger compartment; it was suggested that one reason for this find- ing could be that with the shorter patterns there was a lower probability of the vehicle’s tires making full contact with the pattern. The Kansas research, and most previous rumble strip research where noise data were collected in the field, collected noise levels while driving the motor vehicles over extended portions of the rumble strip patterns (i.e., parallel to the rumble strips). However, when errant vehicles encounter rumble strips, the vehicle tires cross the rumble strips at an angle so the inter- action between the rumble strip pattern and the tires is differ- ent than what has typically been evaluated. This difference in the way vehicles encounter rumble strips during actual roadway departures (i.e., at angles) and the way rumble strip noise levels are typically collected in the field (i.e., parallel to the rumble strips) may or may not change the magnitude of the sound level generated in the passenger compartment for a given rum- ble strip. The probability that there could be a difference in the magnitude of the sound levels between the two types of encounters likely increases when the groove length is shortened because there is less opportunity for the tire to completely drop into the groove. To determine optimum dimensions for both shoulder and centerline rumble strips for a range of operating conditions, a field experiment was conducted where noise data were collected and statistical models developed to predict noise responses within the passenger compartment of a passenger car while it traversed various rumble strip patterns. The remainder of this section is organized as follows: Field Data Acquisition Methodology, Field Data Collection, Analysis Methodology, and Analysis Results. Next, Application of the Noise Models provides examples of how agencies can apply several predictive models for developing recommended dimensions for use within their rumble strip policies. This section concludes with a Summary of Key Findings from the study. Optimum Dimensions for Rumble Strips

Data Acquisition Methodology This field experiment involved driving a mid-size passenger car over a variety of rumble strip patterns at various speeds and departure angles. Data were collected in six states using a Chevrolet Impala. The decision was made to include only passenger cars in this experiment primarily because the crash data suggest that passenger cars (and light trucks) are involved in the majority of crashes that could be remedied by shoulder and centerline rumble strips. Heavy vehicles are involved in a relatively significant portion of head-on crashes, but it is not known what portion of these crashes actually involved the heavy vehicle crossing the centerline into oncoming traffic. In summary, the field experiment was designed with the intention of developing rumble strip patterns that generate sufficient stimuli to alert drivers in passenger cars. To collect the noise data, a portable data acquisition sys- tem was developed using a laptop personal computer (PC), a global positioning system (GPS) module, a hand held sound level meter (SLM), and a USB analog-to-digital (A-D) con- verter module, as illustrated in Figure 13. Interface software for the GPS and A-D modules was written in MATLAB. The laptop PC was also used for manual record keeping by the observer. The SLM was mounted on the centerline of the vehicle facing forward at approximately the same height and same fore-aft location as the driver’s ear. The GPS module was mounted on the roof of the vehicle with a magnetic base. The USB A-D module was mounted into a plastic junction box. The junction box was carried on the floor of the vehicle, and the PC was carried on the lap of the observer. Figure 14 shows a photograph of the data acquisition system. Ten seconds of raw data were collected for each test. Raw data information is provided in Table 76. Data acquisition was initiated manually by the observer before the driver initiated the steering maneuver. Analog voltages from the SLM for sound level (A weighting) and direct microphone output were measured at 5 KHz by the USB A-D module. Global position, vehicle speed, and vehicle heading were transferred in standard NMEA 0183 text at 5 Hz using a 19,200 baud RS-232 serial interface and held in the serial buffer for interrogation after the test. Raw data for each test were immediately recorded into a standard MATLAB data file. Raw data were post-processed to record results for each test into a tab-delimited ASCII file as shown in Table 77. Vehicle heading at the start of the test was subtracted from all vehicle heading measurements to provide relative heading during the maneuver. Maximum relative heading was recorded as angle of departure. Ambient sound level at the start of the test and maximum sound level while traversing the rumble strips were recorded. Ambient sound level was defined as the average over the first 0.5 seconds of the test. Duration of the sound event was meas- ured whenever the sound level rose above the mean sound level plus 1.5 standard deviations over the entire test. A Fast Fourier Transform (FFT) of sound intensity was computed to deter- mine the dominant frequency of the sound event. A TXT file for a single typical trial at 59 mph (95 km/h) and 4 degrees angle of departure is provided in Table 78. Sample plots of vehicle speed and relative heading are shown in Figure 15. Plots of sound level in dBA (Channel 0), raw sound intensity (Channel 1), and fre- quency spectrum are shown in Figure 16 for the test in Table 78 at 59 mph (95 km/h) and 4 degrees angle of departure. Field Data Collection The in-vehicle sound field data collection effort focused on milled rumble strips; however, a sample of rolled rumble strip patterns was also included in the experiment. All field data collection was performed using a Chevrolet Impala passenger car because it is representative of the current vehicle fleet and was readily available at all data collection locations. Data were collected in six states. Separate vehicles were used in several states. Each vehicle had low mileage with relatively new tires. Most field data collection was performed during dry, daylight 120 LAPTOP PC USB A-D MODULE GPS MODULE SOUND LEVEL USB RS-232 ANALOG +5 VDC Figure 13. Block diagram of data acquisition system. Figure 14. Photograph of data acquisition system.

121 Raw data Device Data rate Value Date/time stamp PC once per test date and time Global position GPS 5 Hz latitude and longitude Vehicle speed GPS 5 Hz miles/hour Vehicle heading GPS 5 Hz degrees CW from north Sound level (A weighting) SLM 5 KHz dBA (10 mV per db) Sound intensity SLM 5 KHz voltage Table 76. Raw data collected by data acquisition system. etoNstinUeciveDdleifataD CPemaneliF tsetfotratstadedroceRCPraeY tsetfotratstadedroceRCPhtnoM tsetfotratstadedroceRCPyaD tsetfotratstadedroceRCPruoH tsetfotratstadedroceRCPetuniM tsetfotratstadedroceRmm.mmddSPGedutitaL Longitude GPS ddmm.mm Recorded at start of test Vehicle speed GPS miles/hour Recorded at start of test Angle of departure GPS degrees Maximum difference in heading from start of test Ambient sound level SLM dBA Average over first 0.5 seconds Maximum sound level SLM dBA Maximum value during test Duration of sound event SLM seconds Time when sound level is above mean plus 1.5 standard deviations Dominant frequency of sound event MIC Hz FFT peak frequency File Yr Mo Day Hr Min Lat Lon pilot_east1 2006 10 12 9 18 4048.97 7754.65 Speed Ang_Dep Amb_SL Max_SL Dur Freq 59.67 4.10 66.22 79.83 1.05 172.20 Table 77. Sound-level data acquisition fields. Table 78. Sample text file for a typical trial. 0 1 2 3 4 5 6 7 8 9 55 56 57 58 59 60 Sp ee d [m ph ] 0 1 2 3 4 5 6 7 8 9 -2 0 2 4 6 R el at iv e he ad in g [de g] Time [sec] Figure 15. Typical vehicle speed and relative heading.

conditions. In situations where the pavement surface was wet or where light rainfall occurred, the data collection team noted the occurrence in the data acquisition system. Two observers collected the in-vehicle noise data. One observer drove the test vehicle, while the other executed the data acquisition system described in the previous section. The following variables were collected in the field: • Pavement surface type (asphalt or concrete); • Travel speed; • Roadway departure angle; • Rumble strip dimensions (length, width, depth, and spac- ing); and • Location of rumble strip pattern (shoulder or centerline). The survey conducted in this project produced informa- tion about the dimensions of milled rumble strip patterns being used by various transportation agencies. From the survey, for milled shoulder rumble strip patterns the length dimension ranged from 6 to 18 in. (152 to 457 mm); the width dimension ranged from 5 to 8 in. (127 to 203 mm); the groove depth dimension ranged from 0.375 to 0.75 in. (10 to 19 mm); and the spacing dimension ranged from 11 to 19 in. (280 to 483 mm). For centerline rumble strip patterns the length dimension ranged from 6 to 24 in. (152 to 610 mm); the width dimension ranged from 5 to 7 in. (127 to 178 mm); the depth dimension ranged from 0.375 to 0.625 in. (10 to 16 mm); and the spacing dimension ranged from 12 to 48 in. (305 to 1,220 mm). The states included in the field data collection efforts were selected based on the desire to develop a database with a balance of rumble strip pattern locations (shoulder vs. centerline) and pattern dimensions. The states included in the sound level testing were Arizona, Colorado, Kentucky, Minnesota, Pennsylvania, and Utah. A list of data collection locations, rumble strip pattern and type, and pavement sur- face type are shown in Table 79. It was anticipated that the dimensions reported in the agency survey may be different than those constructed in the field because the state standards typically include tolerances. As such, the observers sampled the dimensions in the field to verify the field dimensions matched the dimensions provided by the transportation agencies for the given locations. If the dimensions did not match those anticipated, the observers recorded the dimension in the field and updated the analysis database. Sound level data were collected using the data acquisition system described above. To closely approximate typical driv- ing speeds on roadways with rumble strips, the test vehicles were driven at speeds ranging from approximately 40 to 65 mph (65 to 105 km/h). Chen (48) collected sound level data using a 5 degree angle of departure, while Mak and Sick- ing (96) indicate that highest run-off-road encroachment angle probabilities are 7.5 and 12.5 degrees on high-speed roadways (> 45 mph [70 km/h]). The roadway departure angles collected during experimentation ranged from 1 to nearly 10 degrees. Steeper angles were not possible because either shoulder widths were not wide enough or roadside hardware were adjacent to the shoulder, thus preventing maneuvers at larger angles. In many cases, left-side encroach- ments over centerline rumble strips were limited to 5 degrees 122 0 1 2 3 4 5 6 7 8 9 10 60 70 80 Time [sec] Ch an ne l 0 [d bA ] 0 1 2 3 4 5 6 7 8 9 10 -5 0 5 Time [sec] Ch an ne l 1 [V ] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0.01 0.02 Frequency [Hz] Am pl itu de [V ] Figure 16. Typical sound level, sound intensity, and frequency spectrum.

when opposing traffic volumes were high or when sight dis- tance was limited. The data acquisition team manually recorded or validated the rumble strip pattern dimensions (length, width, depth, and spacing), rumble strip pattern type (milled or rolled), rumble strip location (shoulder or centerline), pavement surface type (concrete or asphalt), and pavement surface condition (dry or wet). The portable data acquisition system recorded the time (year, month, day, hour, minute), location (latitude and longitude), travel speed, angle of departure, ambient and max- imum sound levels, and duration and frequency of rumble strip noise generated in the vehicle. The observers provided a unique file name for each measurement so the location (state, route number, and milepost/segment location) of the observa- tion was recorded. There were 990 sound level measurements recorded in the field during the experiment. This included 204 measurements in Arizona, 175 measurements in Colorado, 147 measurements in Kentucky, 101 measurements in Min- nesota, 251 measurements in Pennsylvania, and 112 measure- ments in Utah. 123 State Route Begin End Shoulder or centerline Milled or rolled Pavement type Length (in.) Width (in.) Depth (in.) Spacing (in.) Number of observations PA 220 77 83 Shoulder Milled Concrete 17 7.5 0.5 12 14 PA 80 165 221 Shoulder Milled Asphalt & Concrete 16.5– 17.0 6.5–7.0 0.375 12.0–12.5 61 PA 219 41 68 Shoulder Milled Asphalt 16.5 6.0 0.5 11.5-12.0 41 PA 989 180 180 Centerline Milled Asphalt 12.0 7.0 0.5 12.0 3 PA 837 190 190 Centerline Milled Asphalt 12.0 7.0 0.5 12.0 3 PA 79 59 73 Shoulder Milled Asphalt 16.0 5.0 0.375 6.0 28 PA 51 550 550 Centerline Milled Asphalt 12.0 7.0 0.5 24.0 2 PA 48 Centerline Milled Asphalt 12.0 7.0 0.5 24.0 3 PA 288 90 90 Centerline Milled Asphalt 12.0 7.0 0.5 24.0 2 PA 22 11 13 Shoulder Milled Asphalt 16.0 5.0 0.375 6.0 7 PA 18 160 170 Centerline Milled Asphalt 12.0 7.0 0.5 24 6 PA 108 60 60 Centerline Milled Asphalt 12.0 7.0 0.5 24 3 PA 80 95 152 Shoulder Milled Asphalt 16.5 7.0–8.0 0.5 12 35 PA 28 6 221 Shoulder Milled Asphalt 16.0–16.5 5.0–7.0 0.375/0.5 6/12 43 MN 23 212 231 Centerline Milled Asphalt 8 8 0.5 20 18 MN 25 97 142 Centerline Milled Asphalt 8 8 0.5 20 30 MN 95 9 28 Centerline Milled Asphalt 8 8 0.5 20 20 MN 65 51 54 Shoulder Milled Asphalt 12 7 0.5 12 9 MN 65 55 56 Centerline Milled Asphalt 8 8 0.5 20 6 MN 169 216 219 Centerline Milled Asphalt 8 8 0.5 20 6 MN 18 16 19 Shoulder Milled Asphalt 12 7 0.5 12 12 CO 70 294 304 Shoulder Milled Concrete 24 4 0.375 4.75 35 CO 6 262 271 Centerline Milled Asphalt 12 5 0.375 12 5 CO 70 189 237 Shoulder Milled Asphalt 12 4.5 0.375 12 28 CO 70 172 179 Shoulder Rolled Asphalt 24 1 0.375 9 15 CO 70 163 163 Shoulder Milled Asphalt 12 4.5 0.375 12 3 CO 70 133 142 Shoulder Rolled Asphalt 24 1 0.375 9 18 CO 70 86 114 Shoulder Milled Asphalt 12 4.5 0.375 12 45 CO 70 79 86 Shoulder Milled Concrete 24 4 0.375 4.75 9 CO 70 41 78 Shoulder Milled Asphalt 12 4.5 0.375 12 21 UT 70 207 212 Shoulder Milled Asphalt 12 12 0.5 12 6 UT 70 201 203 Shoulder Milled Asphalt 24 8.5 0.5 9 15 UT 70 160 192 Shoulder Milled Asphalt 12 8 0.625 12 30 UT 6 294 298 Shoulder Milled Asphalt 9 5 0.5 12 9 UT 6 283 285 Shoulder Milled Asphalt 10 9 0.5 12 9 UT 6 274 275 Shoulder Milled Asphalt 8 8 0.5 12.5 8 UT 6 188 188 Shoulder Milled Asphalt 15 6 0.375 12 3 UT 6 179 257 Shoulder Rolled Asphalt 12 8 0.75 12 32 AZ 89 458 – Shoulder Milled Asphalt 8 7 0.375 12 8 AZ 89 – – Shoulder Milled Asphalt 9 5.5 0.75 11 45 AZ 89 – 495 Centerline Milled Asphalt 6 7 0.375 12 68 AZ – – – Shoulder Milled Asphalt 12 7 0.375 12 5 AZ 40 318 342 Shoulder Rolled Asphalt 24 2 1 8 44 AZ 40 290 317 Shoulder Milled Asphalt 12 7 0.375 12 35 KY 31 9 24 Centerline Milled Asphalt 24 7 0.625 24 46 KY 9006 4 55 Centerline Milled Asphalt 24 7 0.5 24 102 Table 79. Rumble strip locations, patterns, and dimensions.

Analysis Approach In previous research Khan and Bacchus (97) used both linear and nonlinear regression models to estimate in-vehicle noise generated when traversing various rumble strip patterns. In the present study, ordinary least squares (OLS) linear regression was used to model sound level differences. Sound level differ- ence was defined as the difference between the maximum and ambient sound levels generated during each test. The OLS estimator assumes the following: • The explanatory variables are nonstochastic, • No omitted or irrelevant variables are included in the model specification, • The disturbance has a mean value of zero and is normally distributed, • Homoskedastic disturbances, • No autocorrelation between disturbances, • No perfect multicollinearity, • Correctly specified model, and • Zero covariance between the disturbance and explanatory variables. Violating the assumptions of the OLS estimator can result in biased, inconsistent, or inefficient parameter estimates. As such, several diagnostic measures were applied to test the OLS assumptions. The Anderson-Darling test was used to test the normality assumption of the disturbances. This test compares the cumulative distribution of the residuals to those of a the- oretically normal distribution. The null hypothesis is that the residuals follow a normal distribution. A Breusch-Pagan/ Cook-Weisburg test was used to assess the residuals for hetero- skedasticity. The null hypothesis (χ2 test) is that the residuals have a constant variance. The autocorrelation assumption was tested using the Durbin-Watson statistic. The null hypothesis is that the residuals are not autocorrelated. Variance inflation factors (VIFs) were used to determine the presence of multi- collinearity. VIFs are a measure of multicollinearity among the explanatory variables in a model; values exceeding 10 indicate that multicollinearity is present. Last, the Ramsey RESET test was used to assess the model for omitted variable bias. The null hypothesis (F test) is that the model has no omitted variables. When assumption violations result from the analysis, various treatments can be applied. These are discussed in the follow- ing section. The independent variables considered in the sound level difference model are as follows: • Vehicle speed (mph); • Vehicle angle of departure (degrees); • Pavement type (concrete vs. asphalt); • Pavement condition (wet vs. dry); • Rumble strip location (shoulder vs. centerline); • Rumble strip type (milled vs. rolled); and • Rumble strip length, width, depth, and spacing (in.). The general model form used in the analyses was as follows: where SLDiff = sound level difference (dBA), β = regression parameter estimates for sound level difference model, X = vector of explanatory variables for sound level difference model, and ε = disturbance term for sound level difference model. Using the general form shown in Equation (4), several dif- ferent models were estimated. These include an aggregate model using all data collected in the experiment with the rum- ble strip dimensions, speed, and departure angle all in con- tinuous form. Additionally, disaggregate models using only the milled rumble strip data were estimated. In the analysis approach, the dependent variable used in the model specification is the sound level difference. The sound level difference was computed as the difference between the maximum sound level generated as the test vehicle traversed the rumble strip pattern minus the ambient sound generated in the passenger compartment of the test vehicle prior to encroaching the rumble strips. Separate models for the max- imum and ambient sound levels were not specified because the sound level distributions obtained on the travel lane (ambient sound) and as the vehicle traversed the rumble strip pattern (maximum sound) were different. Specifically, the variability of these distributions differ; therefore, using predictions from separate ambient and maximum sound level models will either over- or underestimate the sound level difference experienced by drivers who leave the roadway and pass over a rumble strip pattern. A model of the sound level difference is based only on a single distribution. Analysis Results The response and explanatory variables used in the sound level difference model, and their descriptive statistics, are shown in Table 80. Nearly 44 percent of the sound level measurements were recorded on shoulder rumble strips. Approximately 8 percent of the sound level measurements were recorded on concrete pavement, while nearly 89 percent were recorded on the milled rumble strip pattern. Modeling results are presented in Table 81. Each of these variables was statistically significant in the model at the 10 percent confidence level. A normal probability plot of SLDiff (4)= +β εX 124

the residuals is shown in Figure 17. The residuals generally appear normally distributed. The Anderson-Darling test (A2 = 0.623; p-value = 0.104) indicates that the null hypothesis of a normal distribution is not rejected. The Breusch-Pagan/ Cook-Weisberg test for heteroskedasticity is not rejected (χ2(1) = 2.63; p-value = 0.105); therefore, the assumption of homoskedastic disturbances is met. The Durbin-Watson statistic was 1.106, which indicates positive autocorrelation. This suggests that the disturbance terms are correlated. Auto- correlation occurs for a variety of reasons, including specifica- tion bias (omitted variables or incorrect functional form), lags, or data manipulation (interpolation or extrapolation). The Ramsey RESET test was used to assess the linearity assumption of the explanatory variables in the model specification. The null hypothesis (F test) is that the model specification is linear (as opposed to nonlinear). The null hypothesis that the model is correctly specified using linear explanatory variables is not rejected (F[3, 976] = 2.43; p-value = 0.064), thus no omitted variable bias is present in the model. No data interpolation or extrapolation occurred so the likely reason for autocorrelation 125 Variable name Minimum Maximum Mean Standard deviation Ambient noise level (dBA) 56.40 77.57 63.43 2.90 Maximum noise level (dBA) 67.12 90.02 79.41 4.08 Sound level difference (dBA) 2.63 26.26 15.98 4.32 Location indicator 1: shoulder rumble strips ; 0: centerline rumble strips 0 1 0.44 0.50 Pavement type indicator 1: concrete; 0: asphalt 0 1 0.08 0.27 Rumble strip type indicator 1: milled 0: rolled 0 1 0.86 0.35 Pavement condition indicator 1: wet surface 0: dry surface 0 1 0.20 0.40 Vehicle travel speed (mph) 39.5 66.6 52.2 7.5 Angle of departure (degrees) 0.6 9.6 2.8 1.9 Length of rumble strip (in.) 6 24 15.4 6.2 Width of rumble strip (in.) 1 12 6.2 1.9 Depth of rumble strip (in.) 0.375 1.0 0.5 0.2 Spacing of rumble strip (in.) 4.75 24 13.6 5.7 95% confidence interval Variable Parameter estimate Standard error t– statistic P > |t| Lower Upper VIF A/N612.11480.6000.026.6703.1056.8tnatsnoC Speed (mph) 0.027 0.017 1.60 0.109 –0.006 0.060 1.03 Location indicator (1: shoulder; 0: centerline) –1.689 0.337 –5.01 0.000 –2.351 –1.028 1.79 Angle of departure (degrees) –0.271 0.082 –3.30 0.001 –0.432 –0.110 1.53 77.1023.0412.0000.009.9720.0762.0).ni(htgneL 76.2689.0755.0000.050.7901.0177.0).ni(htdiW 74.1234.6655.2000.055.4889.0494.4).ni(htpeD Spacing (in.) –0.394 0.035 –11.31 0.000 –0.462 –0.326 2.49 Rumble strip type indicator (1: milled; 0: rolled) 2.652 0.560 4.74 0.000 1.553 3.751 2.43 Pavement type indicator (1: concrete; 0: asphalt) –1.391 0.534 –2.60 0.009 –2.439 –0.343 1.37 Pavement condition indicator (1: wet; 0: dry) –2.596 0.363 –7.15 0.000 –3.309 –1.883 1.33 Number of observations: 990. R2: 0.179. Radj2: 0.171. Root MSE: 3.936. Table 80. Descriptive statistics of variables included in noise database. Table 81. Regression model of sound level difference.

is the potential lag of the dependent variable (sound level dif- ference). In the presence of autocorrelation, the standard errors are inefficient. To treat the problem of autocorrelation, the Newey-West method to obtain the standard errors was applied. The results of the regression estimation, corrected for autocorrelation with a single lag, are shown in Table 82. Based on the results shown in Tables 81 and 82, the results of the model can be interpreted as follows: • A one unit increase in travel speed (mph) increases the sound level differential by 0.027 dBA. • Rumble strips encountered on the shoulder by the right- side tires of a passenger car are associated with lower sound level differences when compared to centerline rumble strips encountered by the left-side tires of a passenger car. • A one unit increase in the vehicle angle of departure (degrees) is associated with a 0.271 dBA decrease in the sound level differential. • A one unit increase in the rumble strip length (in.) is associ- ated with a 0.267 dBA increase in the sound level difference. • A one unit increase in the rumble strip width (in.) is associ- ated with a 0.771 dBA increase in the sound level difference. 126 Pe rc en t Residual Normal Probability Plot of the Residuals (response is sldiff) 99.99 99 95 80 50 20 5 1 0.01 -15 -10 -5 0 5 10 15 Figure 17. Normal probability plot of sound level difference residuals. Table 82. Regression model of sound level difference with Newey-West standard errors. 95% confidence interval Variable Parameter estimate Standard error t– statistic P > |t| Lower Upper 728.11474.5<0.00143.5916.1056.8tnatsnoC 360.0900.0–0.14084.1810.0720.0)hpm(deepS Location indicator (1: shoulder; 0: centerline) –1.689 0.398 –4.25 <0.001 –2.470 –0.909 121.0–124.0–<0.00155.3–670.0172.0–)seerged(erutrapedfoelgnA 323.0112.0<0.00153.9920.0762.0).ni(htgneL 810.1525.0<0.001 <0.001 31.6621.0177.0).ni(htdiW 001.7788.10.00183.3823.1494.4).ni(htpeD 413.0–474.0–07.9–140.0493.0–).ni(gnicapS Rumble strip type indicator (1: milled; 0: rolled) 2.652 0.811 3.27 0.001 1.060 4.244 Pavement surface type indicator (1: concrete; 0: asphalt) –1.391 0.685 –2.03 0.043 –2.736 –0.046 Pavement surface condition indicator (1: wet; 0: dry) –2.596 0.465 –5.58 <0.001 –3.509 –1.683 Number of observations: 990. R2: 0.179. Radj2: 0.171. Root MSE: 3.936.

• A one unit increase in the rumble strip depth (in.) is associated with a 4.494 dBA increase in the sound level difference. • A one unit increase in the rumble strip spacing (in.) is associated with a 0.394 dBA decrease in the sound level difference. • Milled rumble strips are associated with a higher sound level difference when compared to rolled rumble strips. • A concrete pavement surface is associated with a lower sound level difference when compared to an asphalt pavement surface. • A wet pavement surface is associated with a lower sound level difference when compared to a dry pavement surface. The adjusted R2 value of 0.171 indicates that the regression line does not fit the sample data very well. Because interior vehicle noise is a complex measurement, there are several possible explanations for this low value, including the following: • Vehicle tires used on the test vehicles may have had different inflation pressures or tread wear; • Pavement surface temperatures were different among and within experimental locations. The research team attempted to collect pavement surface temperature during field test- ing but could not safely stop the vehicle on many high- speed roadways during each test to consistently record this information; • Rumble strip pattern wear differs within experimental test locations, particularly on asphalt pavement surfaces; and • Pavement surface texture can vary considerably between test locations. As noted in the Analysis Approach discussion above, addi- tional models of sound level difference were estimated using linear regression. These models were estimated with two specific purposes in mind: 1. Can more of the variability of the data be explained by accounting for the use of different test vehicles in the different states, and 2. To determine statistical differences between certain rumble strip dimensions. Only data collected on milled rumble strips were considered in developing these additional models. Table 83 shows a model developed to account for the use of different test vehicles in different states. Table 83 shows the parameter estimates with Newey-West standard errors to correct for autocorrelation. All other assumptions of the lin- ear regression model were met. The signs of the parameter 127 Table 83. Linear regression with state indicator variables. 95% confidence interval Variable Parameter estimate Standard error t- statistic P > |t| Lower Upper 642.01871.5<0.00179.5192.1217.7tnatsnoC Speed (mph) 0.057 0.016 3.58 <0.001 0.026 0.089 Location indicator (1: shoulder; 0: centerline) –1.116 0.335 –3.34 <0.001 –1.773 –0.459 Angle of departure (degrees) –0.275 0.079 –3.50 <0.001 –0.429 –0.121 524.0972.0<0.00154.9730.0253.0).ni(htgneL 378.0321.0900.016.2191.0894.0).ni(htdiW 140.6271.0830.080.2594.1601.3).ni(htpeD Spacing (in.) –0.300 0.050 –5.97 <0.001 –0.398 –0.201 Pennsylvania indicator* (1: Pennsylvania; 0: otherwise) 2.197 0.513 4.28 <0.001 1.189 3.205 Minnesota indicator* (1: Minnesota; 0: otherwise) 1.165 0.752 1.55 0.122 –0.310 2.641 Arizona indicator* (1: Arizona; 0: otherwise) 4.039 0.713 5.66 <0.001 2.639 5.439 Utah indicator* (1: Utah; 0: otherwise) –3.219 0.937 –3.43 0.001 –5.058 –1.379 Pavement type indicator (1: concrete; 0: asphalt) –3.065 0.568 –5.40 <0.001 –4.179 –1.950 * Kentucky and Colorado are the baseline, and set to zero. State effects in the table should be interpreted using Kentucky and Colorado as a baseline. State effects with a negative sign are expected to have lower sound level differences than the baseline, while state effects with a positive sign are expected to have higher sound level differences than the baseline. Number of observations: 850. R2: 0.332. Radj2: 0.323. Root MSE: 3.452.

estimates in Table 83 are the same as those in Tables 81 and 82. The magnitudes of the parameter estimates are also similar. The Pennsylvania, Arizona, and Utah state indicators in Table 83 are statistically significant, and the Minnesota state indicator is marginally significant. Wet pavement in Arizona and Utah may explain the large parameter estimates for these state indicators when compared to the baseline of Kentucky and Colorado (both set to zero). The vehicle type, tire tread wear, and air temperature may also be influencing sound levels in all four states. When interpreting the meaning of the state indicator variables, the intention is that states would not have to select a given state (i.e., Arizona, Colorado, Kentucky, Minnesota, Pennsylvania, or Utah) that they are somehow most similar to, but rather the state indicator variables should be viewed as separate vehicles. By including these different vehicles in the model, more of the variability in the data can be explained, so there is greater reliability in the predictions. Efforts were also made to use indicator variables to determine the relative effects of different rumble strip dimensions on sound level difference. To create the dimension indicator vari- ables, construction tolerances were considered. For example, if a state standard indicated a milled rumble strip pattern of 16 in. (L) × 7 in. (W) × 0.5 in. (D) × 12 in. (S) [406 mm (L) × 178 mm (W) × 13 mm (D) × 305 mm (S)], contractors may be permitted a tolerance of ± 1 in. (25 mm) for the length, width, and spacing dimensions, and a tolerance of ± 0.25 in. (6 mm) for the depth dimension. This was confirmed based on the field measurements. As such, efforts to group dimen- sions into bins based on tolerances were undertaken. At least 10 percent of the observations for any binned dimension cate- gory were sought. The descriptive statistics for the binned dimension data are shown in Table 84. A linear regression model was estimated using the categor- ical dimension data. State indicator variables were not con- sidered because of the multicollinearity problems created by the including both state and dimensions indicators in the same model. Several dimensions were unique to a single state; thus perfect multicollinearity (a linear regression assumption violation) resulted. All remaining regression assumptions were met using the categorical dimension data, except the auto- correlation assumption. As such, the standard errors were estimated using the Newey-West method. The regression model estimates are shown in Table 85. Interpretation of the parameter estimates in Table 85 indi- cates the following: • The trends for travel speed, rumble strip location (shoulder vs. centerline), angle of departure, pavement type, and pavement surface are consistent with findings reported in Table 82, but changes in the magnitude of the estimators do occur. • The rumble strip length dimension indicator is highly sig- nificant and negative when compared to the baseline con- dition (length > 14 in. [356 mm]). This indicates that longer rumble strips are associated with a higher sound level dif- ference than shorter patterns. Rumble strips with length dimensions less than or equal to 14 in. (356 mm) generate approximately 3.5 dBA of less sound above the ambient level than rumble strips greater than 14 in. (356 mm) in length. • The rumble strip width dimension indicator is highly signif- icant and positive when compared to the baseline condition (width > 6 in. [152 mm]) indicating that rumble strips with narrower widths produce greater sound level differences. However, the interaction between the width and depth dimension indicators is highly significant and negative, suggesting that width and depth are jointly associated with sound level difference. For a given milling machine, cutting heads are a given diameter so increasing the width of a rum- ble strip consequently increases the depth of the rumble strip as well, and vice versa. • The depth indicator is not statistically significant in Table 85 (t-stat = 0.79) when compared to the baseline (width > 0.5 in. [13 mm]). As noted previously, however, the depth- width interaction has a negative parameter estimate. • The rumble strip spacing indicator is highly significant and positive when compared to the baseline condition (spacing > 12 in. [305 mm]). This indicates that closely spaced rum- 128 Variable name Minimum Maximum Mean Standard deviation Length 6–10 in. indicator 0 1 0.240 0347 Length 12–14 in. indicator 0 1 0.250 0.433 Length > 14 in. indicator 0 1 0.489 0.500 Width 4–6 in. indicator 0 1 0.802 0.398 Width > 6 in. indicator 0 1 0.198 0.398 Depth < 0.5 in. indicator 0 1 0.864 0.343 Depth > 0.5 in. indicator 0 1 0.136 0.343 Spacing 4–8 in. indicator 0 1 0.135 0.260 Spacing 10–12 in. indicator 0 1 0.586 0.493 Spacing > 12 in. indicator 0 1 0.279 0.357 Table 84. Descriptive statistics of categorical rumble strip dimension data.

ble strip patterns are expected to have a higher sound level difference than patterns spaced further apart. The decision was made to model the difference between the ambient sound level while traveling in the travel lane and the maximum sound level generated while traversing the rumble strips either on the shoulder or on the centerline. This decision was based on the fact that the sound level distribu- tions for the ambient sound levels and the maximum sound levels were different. Several models were developed (but are not included here within the report) that predicted ambient sound levels and maximum sound levels separately. These models explained approximately 26 to 32 percent (i.e., the adjusted R2 values were on the order of 0.26 and 0.32) of the variability of the ambient and maximum sound levels. These models provide credibility to the data collection effort indicat- ing that the data were collected in a reasonable manner and the correct data were collected. These models also illustrated the complexity in modeling the sound level difference between the interaction of a passenger car, its tires, the pavement sur- face, and the rumble strip dimensions. Application of the Noise Models This section provides several examples of how the noise prediction models developed as part of this research can be used to establish rumble strip dimensions for different types of rumble strip applications. The examples demonstrate how to use the noise prediction models presented in Tables 82 and 83. The advantage of using either of these models is that the rumble strip dimension variables are included as continuous variables. Therefore, agencies can perform sensitivity analyses by varying the rumble strip dimensions to determine desirable or optimal dimensions for their policies. The disadvantage of using the noise prediction model from Table 83 is that an agency has to assume whether its roads are most like the states of Kentucky and Colorado (i.e., the base condition of the model) or more like roads in Pennsylvania, Minnesota, Arizona, or Utah. A simple recommendation on how agencies should assess which state their roads most closely resemble cannot be pro- vided because there is much information that is confounded within this indicator variable such as (a) the differences in the individual cars used to collect data within that given state; (b) Arizona was the only state where data were collected during wet pavement conditions; and (c) the condition of the rumble strips in the varying states (i.e., whether the rumble strips were recently installed or had been in place for several years), etc. Because of the type of information confounded within the state indicator variables, unless an agency is from one of the four states represented in the model, it is recommended that the agency assume the base conditions when using the model from Table 83. Three examples are presented below. The first two exam- ples make use of the noise prediction model in Table 82. The third example makes use of the noise prediction model in Table 83. 129 Table 85. Linear regression model with categorical rumble strip dimension data. 95% confidence interval Variable Parameter estimate Standard error t–statistic P > |t| Lower Upper 907.61358.11<0.00155.11732.1182.41tnatsnoC 580.0020.0100.091.3710.0350.0)hpm(deepS Location indicator (1: shoulder; 0: centerline) –1.468 0.334 –4.39 <0.001 –2.124 –0.812 Angle of departure (degrees) –0.373 0.081 –4.63 <0.001 –0.531 –0.215 Pavement type indicator (1: concrete; 0: asphalt) –2.599 0.562 –4.63 <0.001 –3.703 –1.500 Pavement condition indicator (1: wet; 0: dry) –2.515 0.382 –6.58 <0.001 –3.264 –1.765 Length < 14 in.a 139.2–240.4–<0.00123.21–382.0784.3– Width < 6 in.b 991.5460.2<0.00155.4897.0236.3 Depth < 0.5 in.c 641.2619.0–134.097.0087.0516.0 Spacing < 12 in.d 494.4930.3<0.00161.01173.0667.3 Width < 6 x Depth < 0.5 in interaction –4.245 0.870 –4.88 <0.001 –5.952 –2.538 a Length > 14 in. is the baseline. Since the length < 14 in. effect has a negative sign, rumble strip pattern lengths > 14 in. are expected to have higher sound level differences. b Width > 6 in. is the baseline. Rumble strip widths > 6 in. are expected to have lower sound level differences than narrow rumble strip patterns (< 6 in.). c Depth > 0.5 in. is the baseline. This parameter is not statistically significant. d Spacing > 12 in. is the baseline. Rumble strip spacing > 12 in. are expected to have lower sound level differences than closer spaced patterns (< 12 in.). Number of observations: 850. R2: 0.283. Radj2: 0.274. Root MSE: 3.573.

Example No. 1: Designing Shoulder Rumble Strip Dimensions for Freeways Suppose a state transportation agency wants to establish a policy for the design of milled shoulder rumble strips on rural and urban freeways with posted speed limits between 55 and 65 mph (88 and 105 km/h). On freeways, the shoulders can consist of either concrete or asphalt pavement. Horizontal curves on freeways are relatively flat due to the higher design speeds, so the typical angle of departures can be assumed to be relatively low. Because a wet pavement surface produces lower sound level differentials than dry pavement surfaces, a wet pavement surface will be assumed. Because the policy will be for freeways, the shoulders will be relatively wide, and in most cases bicycles will not be permitted on the roadways; thus the length dimension of the rumble strip can be determined inde- pendent of the shoulder width and bicycle considerations. Also, because bicycles are not permitted on freeways in most states, the rumble strips can be designed for the higher ranges of desirable maximum sound level difference. Because asphalt surfaces generate higher sound level differences, asphalt sur- faces will be considered first in the analysis. In this first example, the noise prediction model from Table 82 is used to establish potential rumble strip dimensions: where Speed = vehicle speed (mph); Location = location indicator (1 = shoulder; 0 = centerline); SLDiff = + − −8 650 0 027 1 689 0 271. . . .Speed Location Angle Length Width Depth+ + + − 0 267 0 771 4 494 0 . . . .394 2 652 1 391 Spacing RS Type PVMT Surface + − − . . 2 596. PVMTCondition (5) Angle = angle of departure (degrees); Length = length of rumble strip (in.); Width = width of rumble strip (in.); Depth = depth of rumble strip (in.); Spacing = spacing between rumble strips (in.); RS Type = rumble strip type indicator (1 = milled; 0 = rolled); PVMT Surface = pavement surface type indicator (1 = concrete; 0 = asphalt); and PVMT Condition = pavement surface condition indicator (1 = wet; 0 = dry). It will be assumed the rumble strip dimensions will be estab- lished first for the right (outside) shoulder of the freeway. The process could be repeated for establishing desirable dimensions for the left (median) shoulder of the freeway. The following are known based upon the information given above: • Location: Right (outside) shoulder rumble strips (Indica- tor = 1); • Rumble strip type: Milled (Indicator = 1); • Pavement type: Asphalt (Indicator = 0); and • Pavement condition: Wet (Indicator = 1). Inputting the variables above into the sound level difference model yields the following: The dimensions for three different rumble strip patterns, two vehicle speed levels (assuming 55 and 65 mph [88 and 105 km/h] posted speeds), and three angles of departure are shown in Table 86. Pattern 1 can be assumed to be an edgeline SLDiff = + − +7 017 0 027 0 271 0 267. . . .Speed Angle Length Width Depth Spacing+ + −0 771 4 494 0 394. . . (6) 130 Table 86. Rumble strip dimensions and parameters considered in example no. 1. Rumble strip dimensions Rumble strip pattern Length (in.) Width (in.) Depth (in.) Spacing (in.) Speed (mph) Departure angle (degrees) Sound level difference (dBA) 1 6 5 0.375 12 55 1 10.70 2 12 6 0.375 12 55 1 13.09 3 16 7 0.5 12 55 1 15.51 1 6 5 0.375 12 55 3 10.16 2 12 6 0.375 12 55 3 12.55 3 16 7 0.5 12 55 3 14.97 1 6 5 0.375 12 55 5 9.62 2 12 6 0.375 12 55 5 12.58 3 16 7 0.5 12 55 5 14.43 1 6 5 0.375 12 65 1 10.97 2 12 6 0.375 12 65 1 13.93 3 16 7 0.5 12 65 1 15.78 1 6 5 0.375 12 65 3 10.43 2 12 6 0.375 12 65 3 13.39 3 16 7 0.5 12 65 3 15.24 1 6 5 0.375 12 65 5 9.89 2 12 6 0.375 12 65 5 12.85 3 16 7 0.5 12 65 5 14.70

rumble strip, while patterns 2 and 3 are common shoulder rumble strip patterns used in Canada and the U.S., respectively. Assume for this example that a transportation agency would like to develop rumble strip patterns that generate sound levels differences in the range of 10 to 15 dBA (i.e., 10 dBA ≤ SLDiff ≤ 15 dBA). The last column in Table 86 shows the estimated difference in sound level generated in the passenger compartment of a passenger car by the three rumble strip patterns based on the given design parameters. The shaded rows represent designs where the rumble strip pattern, speed, and angle of departure fall outside the desired sound level difference range. When the departure angle is 1 degree, Patterns 1 and 2 are expected to generate the appropriate sound level difference for both speed ranges. When increasing the departure angle to 3 degrees, again Patterns 1 and 2 are expected to produce sound level differences in the desired range, while Pattern 3 would be expected to generate sound levels slightly below the maximum criterion for speeds of 55 mph (88 km/h) and slightly above the maximum criterion for speeds of 65 mph (105 km/h). When the departure angle is 5 degrees, rumble strip Patterns 2 and 3 are expected to produce sound levels within the desir- able range at both speeds (55 and 65 mph [88 and 105 km/h]), while Pattern 1 would be expected to generate slightly less than the desired sound level. Based on this example, Pattern 2 appears to be the most appropriate pattern based on the agency’s policy decision, but Patterns 1 and 3 are not far removed from meeting the desired design guidelines so it is conceivable that Patterns 1 and 3 would be acceptable for use by the transportation agency along urban and rural freeways. Example No. 2: Designing Shoulder Rumble Strip Dimensions for Rural Two-Lane Roads Suppose a transportation agency wants to establish a policy for the design of milled shoulder rumble strips on rural two- lane roads. In establishing such a policy, the agency will need to consider the following: • Bicyclists; • Narrower shoulders; • Sharper curves; • Intermediate and high speeds (e.g., 45 to 55 mph [70 to 88 km/h] posted speed limits); and • Nearby residents. Since most rural two-lane roads are constructed of asphalt pavement, asphalt pavement will be assumed for the design. However, bicyclists are assumed to use the roadway only when the pavement surface is dry so it is assumed that the pavement condition in this example is dry. In this second example, the model from Table 82 is used again to establish potential rumble strip dimensions. The base conditions for the model (i.e., location, rumble strip type, and pavement type) are the same as in the first example. The main difference is that the wet indicator variable shown in Equation (6) should be 0 rather than 1 as in the previous example. It is assumed desirable to develop rumble strip patterns that generate sound level dif- ferences in the range from 6 to 12 dBA (i.e., 6 dBA ≤ SLDiff ≤ 12 dBA). This sound level difference represents a compro- mise between the in-vehicle noise required to alert a drowsy or fatigued driver while attempting to provide for a reason- able level of comfort and control for bicyclists. As a starting point for developing a rumble strip policy for rural two-lane roads, research results on recommended dimensions for bicycle-tolerable rumble strips are presented in Table 87. The results of these studies are in agreement for the dimensions that are specified (i.e., rumble strip width, depth, and spacing). Essentially, rumble strips with the fol- lowing dimensions are recommended for the design of bicycle- tolerable rumble strips: • Width: 5 in. (127 mm); • Depth: 0.375 in. (10 mm); and • Spacing: 11 or 12 in. (280 or 305 mm). The dimension not addressed by the previous research is rumble strip length; on rural two-lane roads, due to bicy- clists and narrower shoulder widths, rumble strip length is a dimension of particular interest in developing such a policy. Therefore, the length of the rumble strips will be varied when 131 State Width Depth Spacing (on centers) Comments 5 in. 0.375 in. 12 in. Nonfreeway facilities with operating speeds near 55 mph. Pennsylvania (Elefteriadou et al., 2000) 5 in. 0375 in. 11 in. Nonfreeway facilities with operating speeds near 45 mph. California (Bucko and Khorashadi, 2001) 5 in. 0.3125 ± 0.0625 in. 12 in. None Colorado (Outcalt, 2001) 5 in. 0.375 ± 0.125 in. 12 in. Recommend gap pattern of 48 ft of rumble strip followed by 12 ft of gap. Table 87. Rumble strip designs recommended to accommodate motorists and bicyclists from previous research.

modeling several potential patterns. The rumble strip dimen- sions of three potential patterns and other conditions (i.e., vehicle speed and departure angle) under consideration to establish the rumble strip policy are shown in Table 88. The last column in Table 88 shows the estimated difference in sound level generated in the passenger compartment of a passenger car by the three potential rumble strip patterns for the given parameters. The shaded rows represent designs where the rumble strip pattern, speed, and angle of departure fall outside the desired sound level difference range. For the pat- terns with a 16 in. (406 mm) and 12 in. (305 mm) length, the expected in-vehicle noise levels exceed the 6 to 12 dBA design range specified in the example. However, the pattern with a 6 in. (152 mm) length does produce an expected sound level difference in the design range at a speed of 45 mph (72 km/h) and departure angles of 5 and 10 degrees, and at speeds of 55 mph (88 km/h) at departure angles of 10 degrees. With this type of information, an agency could consider several options such as the following: • Establish a single rumble strip pattern (i.e., dimensions) for all rural two-lane roads. • Establish a set of dimensions for edgeline rumble strips on roadways where bicycle traffic is expected and an alternative set of dimensions for rumble strips installed on the shoulders where bicyclists are not expected. Example No. 3: Designing Centerline Rumble Strip Dimensions for Rural Two-Lane Roads Suppose a transportation agency wants to establish a pol- icy for the design of milled centerline rumble strips on rural two-lane roads. In establishing such a policy, the agency will need to consider the following: • Sharper curves; • Intermediate and high speeds (e.g., 45 to 55 mph [70 to 88 km/h] posted speed limits); and • Possibly, nearby residents. In this example, the noise prediction model from Table 83 is used to establish potential dimensions for centerline rumble strips. where PA = Pennsylvania indicator (= 1 if located in Pennsylva- nia; = 0 if not); MN = Minnesota indicator (= 1 if located in Minnesota; = 0 if not); AZ = Arizona indicator (= 1 if located in Arizona; = 0 if not); and UT = Utah indicator (= 1 if located in Utah; = 0 if not). Since most rural two-lane roads are constructed of asphalt pavement, an asphalt pavement is assumed for the design, but because no indicator variable for pavement condition is present in this noise prediction model, no assumption needs to be made concerning whether the rumble strips will be designed for wet or dry pavement conditions. Assuming a base condition for the state indicator variable, the following SLDiff = + − −7 712 0 057 1 116 0 275. . . .Speed Location Angle Length Width Depth+ + + − 0 352 0 498 3 106 0 . . . .300 3 065 2 197 1 165 Spacing PVMT Surface PA− + + . . . MN AZ UT+ −4 039 3 219. . (7) 132 Rumble strip dimensions Length (in.) Width (in.) Depth (in.) Spacing (in.) Speed (mph) Departure angle (degrees) Sound level difference (dBA) 16 5 0.375 12 45 1 15.7 16 5 0.375 12 45 5 14.6 16 5 0.375 12 45 10 13.3 16 5 0.375 12 55 1 16.0 16 5 0.375 12 55 5 14.9 16 5 0.375 12 55 10 13.6 12 5 0.375 12 45 1 14.6 12 5 0.375 12 45 5 13.6 12 5 0.375 12 45 10 12.2 12 5 0.375 12 55 1 14.9 12 5 0.375 12 55 5 13.8 12 5 0.375 12 55 10 12.5 6 5 0.375 12 45 1 13.0 6 5 0.375 12 45 5 11.9 6 5 0.375 12 45 10 10.6 6 5 0.375 12 55 1 13.3 6 5 0.375 12 55 5 12.2 6 5 0.375 12 55 10 10.9 Table 88. Rumble strip dimensions and parameters considered in example no. 2.

values are input into Equation 7, yielding the base model (i.e., Equation 8) for use in the sensitivity analysis for this example: • Location: Centerline rumble strips (Location = 0); • Pavement type: Asphalt (PVMT Surface = 0); and • State: KY and CO (PA, AZ, MN, and UT = 0). The rumble strip dimensions of five potential patterns and other conditions (i.e., vehicle speed and departure angle) under consideration to establish the centerline rumble strip policy for a rural two-lane road are shown in Table 89. Assume SLDiff = + − +4 647 0 057 0 275 0 352. . . .Speed Angle Length Width Depth Spacing+ + −0 498 3 106 0 300. . . (8) that it is desirable to develop rumble strip patterns that gen- erate sound level differences in the range from 10 to 15 dBA (i.e., 10 dBA ≤ SLDiff ≤ 15 dBA). The last column in Table 89 shows the estimated difference in sound level generated in the passenger compartment of a passenger car by the five potential rumble strip patterns for the given parameters. The shaded rows represent designs where the rumble strip pattern, speed, and angle of departure fall outside the desired sound level difference range. All of the rumble strip patterns considered meet the desired sound level difference for at least one of the scenarios considered in Table 89. Rumble strip patterns 1, 2, and 3 appear to be the most reasonable patterns to potentially adopt for this type of policy. It is also possible that different policies could be estab- lished for varying posted speeds. 133 Rumble strip dimensions under consideration Potential rumble strip pattern Length (in.) Width (in.) Depth (in.) Spacing (in.) Speed (mph) Departure angle (degrees) Sound level difference (dBA) 1 8 5 0.375 12 35 1 12.87 2 10 5 0.375 12 35 1 13.58 3 12 5 0.375 12 35 1 14.28 4 16 6 0.375 12 35 1 16.19 5 16 6 0.5 11 35 1 16.88 1 8 5 0.375 12 35 5 11.77 2 10 5 0.375 12 35 5 12.48 3 12 5 0.375 12 35 5 13.18 4 16 6 0.375 12 35 5 15.09 5 16 6 0.5 11 35 5 15.78 1 8 5 0.375 12 35 7 11.22 2 10 5 0.375 12 35 7 11.93 3 12 5 0.375 12 35 7 12.63 4 16 6 0.375 12 35 7 14.54 5 16 6 0.5 11 35 7 15.23 1 8 5 0.375 12 35 9 10.67 2 10 5 0.375 12 35 9 11.38 3 12 5 0.375 12 35 9 12.08 4 16 6 0.375 12 35 9 13.99 5 16 6 0.5 11 35 9 14.68 1 8 5 0.375 12 55 1 13.44 2 10 5 0.375 12 55 1 14.15 3 12 5 0.375 12 55 1 14.85 4 16 6 0.375 12 55 1 16.76 5 16 6 0.5 11 55 1 17.45 1 8 5 0.375 12 55 5 12.34 2 10 5 0.375 12 55 5 13.05 3 12 5 0.375 12 55 5 13.75 4 16 6 0.375 12 55 5 15.66 5 16 6 0.5 11 55 5 16.35 1 8 5 0.375 12 55 7 11.79 2 10 5 0.375 12 55 7 12.50 3 12 5 0.375 12 55 7 13.20 4 16 6 0.375 12 55 7 15.11 5 16 6 0.5 11 55 7 15.80 1 8 5 0.375 12 55 9 11.24 2 10 5 0.375 12 55 9 11.95 3 12 5 0.375 12 55 9 12.65 4 16 6 0.375 12 55 9 14.56 5 16 6 0.5 11 55 9 15.25 Table 89. Rumble strip dimensions and parameters considered in example no. 3.

Summary of Key Findings The present experiment was designed to collect sound level data for a variety of shoulder and centerline rumble strip appli- cations in the United States. Variables collected during the field data collection effort included rumble strip dimensions (length, width, depth, and spacing), vehicle speed, vehicle angle of departure, rumble strip location (shoulder or centerline), pavement surface type (concrete or asphalt), rumble strip type (milled or rolled), and pavement surface condition (wet or dry). Exploratory analyses revealed that the sound level differential could be modeled using ordinary least squares regression. Initial modeling results (see Table 82) indicated that all parameter estimates had plausible signs, while the variability in the sound level difference was not well explained by the model. Subsequent models for milled rumble strips included state indicator variables. Several of the state indicator variables were statistically significant suggesting that vehicle characteristics, tire tread wear, and air temperature may all influence the sound level difference generated by rumble strips. The regression model with the state indicator variables (see Table 83) improved the goodness-of-fit of the model compared to the model without the state indicators, explaining approximately 33 percent of the variability in the sound level difference generated by the rumble strips. Subsequent efforts to model rumble strip dimensions as indicator variables did not improve the goodness-of-fit from the regression model as shown in Table 85. The key finding from this noise study are as follows: • The analysis found that sound level differentials generated by rumble strips could be modeled using ordinary least squares regression. • Several prediction models were developed that included the four primary dimensions of rumble strips (i.e., length, width, depth, and spacing) as significant predictor vari- ables of sound level differences generated by rumble strips, and all of the parameter estimates had plausible signs. These are the first predictive models developed that include all four primary rumble strip dimensions. Models from pre- vious research by Khan and Bacchus (97) do not include all four primary rumble strip dimensions. • The predictive models include other independent variables such as vehicle speed, angle of departure, pavement type, and pavement condition, which logically explain some of the variability in the sound levels generated by rumble strips above the ambient level. 134