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NCHRP 3-78b: Final Project Report April 2016 71 5 MODELING AND APPLICATIONS This chapter presents an overview of nine of the methodological steps from the crossing assessment methodology shown in Chapter 7 of the NCHRP 03-78b guidebook. A list of these models is presented in Table 5-1, followed by more detailed discussion. The table illustrates in which step in the Guidebook Chapter 7 method the models are used, as well as the form of the model. Table 5-1: Overview of Predictive Models Model Type and Name Methodology Step Model Form Details in Section Free-Flow Speed Model 2 Traffic Flow Theory 5.1 Crossing Sight Distance 3 Traffic Flow Theory 5.2 Gap Opportunity Model 5 Traffic Flow Theory 5.3 Yield Opportunity Model 5 Regression 5.4 Gap Utilization Model 6 Table 5.5 Yield Utilization Model 6 Table 5.6 Audible Environment 7 Expert Judgment 5.7 Delay Model 8 Regression 5.8 Risk Performance Model 10 Regression 5.9 The results of this research are based on field data collection in several states across the country, but performance measures can vary significantly based on the local context of a specific site. This research recognizes the significance of different driver behaviors in different states, and it has attempted to identify and quantify the factors that are related to local context of the study locations. These include enforcement level, land use, and general level of driver courtesy in a particular area. However, caution should be taken when generalizing the models to other geographic regions or even specific municipalities that can have very unique driver and pedestrian cultures. It is highly recommended that as many parameters as possible are locally calibrated, and that the accessibility performance is verified through local and regional accessibility observations. 5.1 Free-Flow Speed Model The first model is used to predict the vehicular free-flow speed in the vicinity of a crosswalk at roundabouts or CTLs. The model is a function of the geometric design of the roundabout or CTL, with the controlling variable being the fastest path radius at the crosswalk. High vehicular speed has been linked to a low probability of yielding through research, and so the estimate of free-flow speed is important to estimate for example a base yielding probability at the crosswalk in free-flow or non-congested conditions. The model used to predict the speed of the crosswalk is the theoretical Fastest Path Speed model described in NCHRP Report 672 for roundabouts. This model in turn is adapted from speed-radius relationships found in the AASHTO Green Book. The free-flow speed model uses the following equations to show the speed-radius relationship for curves for both +0.02 super elevation: V = 3.4415 R0.3861, e = + 0.02 The equation predicts the 85th percentile free-flow speed expected at the crosswalk as a function of fastest path radius (in ft.) that is believed to control the speed at the crosswalk. For roundabout entries, this speed is generally equal to the R1 term as shown in Figure 5-1. For roundabout exits, the radius of the corresponding movement (left, through, or right) is used, along with an acceleration constraint.
NCHRP 3-78b: Final Project Report April 2016 72 Figure 5-1: Roundabout Vehicle Path Radii (Source: NCHRP Report 672) At a roundabout entry, this speed is principally a function of the R1 radius shown in Figure 5-1. For exiting vehicles, the analyst can estimate an equivalent composite radius from terms R2, R4, and R5 depending on whether the conflicting movement is a right-turning vehicle from the immediate upstream entry, or a through or left-turning vehicle from another entry. Since vehicles have an opportunity to accelerate leaving the roundabout, their actual speeds at the crosswalk are expected to be higher than those predicted by the respective controlling radii. As such, the speed is estimated at the fastest path radii, adjusted by acceleration of vehicles as described in NCHRP Report 672. For CTLs, the equivalent of the R1 radius is used to estimate the speed. The equivalent radius computations are summarized in Table 5-2. Table 5-2: Equivalent Composite Radius for Speed Estimation Approach Vehicle Movement Equivalent Composite Radius RBT Entry Right, Through and Left R1 RBT Exit Right R5 with acceleration constraint RBT Exit Through R2 with acceleration constraint RBT Exit Left R4 with acceleration constraint CTL Right R1 equivalent at CTL The model was compared to free- flow speed data for roundabout entries, roundabout exits, and channelized turn lanes. In particular, the model results were compared to the 85th percentile free-flow speeds at the crosswalk derived from a sample of at least 30 free-flowing vehicle speeds measured with a radar device. Figure 5-2 shows the fastest path equation above as a function of radius, with field-measured validation data for roundabouts and channelized turn lanes. Sites with raised crosswalks were excluded from the graph since speeds at those sites is not a function of radius alone.
NCHRP 3-78b: Final Project Report April 2016 73 Figure 5-2: Free-Flow Speed Model Validation with Field Data The figure shows a data plot with fastest path radius (in feet) on the x-axis and vehicle speed (in mi/h) on the y-axis. Four data series are plotted. The first series plots the fastest path radius and speed relationships for superelevation of +0.02 as a solid line. The remaining three data series show field measured data for roundabout entries (gray filled triangles), roundabout exits (black filled circles), and channelized turn lanes (black non- filled diamonds). The graph shows that the free-flow speed data collected from most sites, excluding the ones with raised crosswalks, can reasonably be approximated by the fastest path speed model. The proposed free-flow speed model therefore represents a reasonable approximation of the expected free-flow speeds at the crosswalks for sites without available speed data. 5.2 Crossing Sight Distance In the AASHTO publication, A Policy on the Geometric Design of Highways and Streets, also known as the âGreen Book,â many design principles are based on the concept of sight distance calculations. Specifically, AASHTO distinguishes three types of sight distance: (1) stopping sight distance, (2) intersection sight distance, and (3) decision sight distance. These sight distances are used to guide the design of features such as minimum radii for horizontal and vertical curves, or to limit landscaping and sight obstructions at intersections and serve to reduce impedances to the driverâs line of sight. The resulting design principles are also reflected in roundabout design guidelines (Rodegerdts et al., 2010), and apply equally to CTLs. To assure adequate design for vehicular movements, sight distance needs to be provided, and more specific guidance is available in aforementioned references. In this section, crossing sight distance is introduced as the distance required by pedestrians to recognize
NCHRP 3-78b: Final Project Report April 2016 74 the presence of conflicting vehicular traffic and determine crossing opportunities at intersections and roundabouts. The distance is established through sight triangles that allow a pedestrian to evaluate potential conflicts with approaching vehicles. Similarly, the resulting sight triangles also assure that the driver has a clear view of a pedestrian waiting to cross or approaching the crosswalk. For pedestrians who are blind, the crossing sight distance applies in that any visual obstructions are also expected to impact the audible environment at the crosswalk and the ability to hear approaching vehicles without sound obstructions or deflections. Although sight triangles are traditionally bound by linear vehicle paths, the roadway geometry of roundabouts and CTLs is non-linear. Therefore, sight distances are derived along the curvature of conflicting vehicular travel paths using the estimated vehicle speed and crossable gap times. This provides the distance for vehicles to travel along a path toward the crosswalk at their current speed in the amount of time needed for a pedestrian to cross the road safely. In other words, adequate crossing sight distance assures that a pedestrian can identify vehicles far enough away to provide sufficient time to cross the road. Adequate crossing sight distance also assures that drivers can see the pedestrian as he or she steps off the curb and into the roadway with sufficient time to react. The methodology developed to determine crossing sight distance adequacy at a roundabout or CTL has been adapted from the sight distance performance check for vehicles at roundabouts from NCHRP Report 672: Roundabouts: An Informational Guide â Second Edition (Rodegerdts et al., 2010), calculations and definitions from the AASHTO âGreen Bookâ (AASHTO, 2011), and the pedestrian mode methodology in Chapter 19 of the 2010 Highway Capacity Manual (TRB, 2010). 5.2.1 Assumptions and Inputs The estimation of crossing sight distance requires several input variables and assumptions to execute the calculations. First, the calculation requires the estimation of a prevailing vehicle speed. This speed is estimated from site geometry (design radii), as well as speed prediction equations described in the previous section. Second, the calculation requires the estimation of a crossable gap time, which is a function of crossing distance, pedestrian walking speed, and any decision latency. A methodology for performing the crossable gap time estimation adapted from Highway Capacity Manual methods is shown below. Finally, the calculation requires some assumption of pedestrian and vehicle heights. In this chapter, an assumed height of 4 feet for pedestriansâ eyes is used, as well as an assumed object height of 2.5 feet, consistent with AASHTO recommendations (AASHTO, 2011). 5.2.2 Crossing Sight Distance at Roundabouts In general, there are two scenarios for pedestrians crossing approaches at roundabouts: (1) the pedestrian begins by crossing the entry lane(s) and ends by clearing the exit lane(s), and (2) the pedestrian begins by crossing the exit lane(s) and ends by clearing the entry lane(s). The presence of a splitter island at roundabout approaches encourages a two-stage pedestrian crossing, a process in which each direction of vehicular travel is crossed independently. Consequently, there are four locations at which a pedestrian must evaluate gaps in vehicular traffic to determine crossing opportunities. Given the particular traffic pattern at roundabouts, crossing from curb to splitter island, crossing from splitter island to curb, and crossing at entry versus exit approaches all are different for several reasons, including: â¢ Traffic is approaching from the left when crossing from the curb, but from the right when crossing from the splitter island; â¢ Traffic is moving only in front of the pedestrian when crossing from the curb (quiet behind the pedestrian), while it is moving both in front of and behind the pedestrian when crossing from
NCHRP 3-78b: Final Project Report April 2016 75 the splitter island; and â¢ Entering traffic is decelerating as drivers approach the yield line and circular roadway, while exiting traffic is accelerating as drivers exit the roundabout. Since traffic patterns at each conflicting approach are judged independently, there are sight distances and sight triangles associated with each location and their conflicting approaches. The entry crossing locations have one potential conflict with vehicles entering the roundabout. The exit crossing locations are subject to two conflicting movements: traffic from the immediate upstream entry approach (right turns) and traffic circulating from other upstream approaches (through and left-turn movements). To figure out the minimum intersection sight distance, two parameters should be known. The first parameter is the critical headway, tn,c, for the pedestrian. The critical headway describes the minimum amount of time necessary for a pedestrian to cross the roadway. The critical headway calculation is directly derived from the pedestrian analysis method covered in the two-way stop-controlled intersection methodology of the Highway Capacity Manual 2010 (TRB, 2010). tn,c = (Ln / Sp) + ts where, Ln = crosswalk length for a specific traffic stream, ft; Sp = average pedestrian walking speed, ft/s, could be measured in the field with a maximum value of 3.5 ft/s; ts = pedestrian start-up time and end clearance time, s (default is 2 seconds). In the context of this analysis, the pedestrian start-up and end clearance time estimate should include any decision latency by a blind pedestrian. In field observations and direct comparisons of decision-making by blind and sighted pedestrians at CTLs (Schroeder et al., 2004), it is evident that a sighted person makes the crossing decision much more quickly compared to a blind person, who must often wait for the sound of a vehicle crossing the crosswalk to subside before being able to determine whether there is a gap, or there is another vehicle following the first. The second parameter is the vehicle speed. The analyst can either measure or make an assumption about the speed, V, of vehicles along the approach of interest. For vehicles entering or exiting the roundabout, the speed can be determined using the speed prediction models presented in the previous section. Using the speed (V) and critical pedestrian headways (tn,c), the length of the conflicting vehicle paths (d) are calculated using the equations below. The different vehicle paths are shown graphically in Figure 5-3. d1 = (1.467) (V1,entering) (t1,c) d2,e = (1.467) (V2,entering) (t2,c) d2,c = (1.467) (V2,circulating) (t2,c) d3,e = (1.467) (V3,entering) (t3,c) d3,c = (1.467) (V3,circulating) (t3,c) d4 = (1.467) (V4,entering) (t4,c) where, d1 = distance along entry leg upstream of the entry crosswalk for crossing from curb, ft; d2,e = distance along previous entry upstream of the exit crosswalk for crossing from island, ft; d2,c = distance along circulating lane upstream of the exit crosswalk for crossing from island, ft; d3,e = distance along previous entry upstream of the exit crosswalk for crossing from curb, ft; d3,c = distance along circulating lane upstream of the exit crosswalk for crossing from curb, ft;
NCHRP 3-78b: Final Project Report April 2016 76 d4 = distance along entry leg upstream of the entry crosswalk for crossing from island, ft; Vn,stream = design speed of conflicting movement, mph; tn,c = critical headway required by a pedestrian crossing a specific traffic stream, depends on the number of lanes and lane width. Once the minimum distance, d, is determined for all possible conflicting movements, the designer should plot the distance along the actual vehicle path that is driven (i.e. the fastest path). Figure 5-3 shows the necessary sight distance, d, for each crossing location at the entry and exit of a roundabout. Note that the length of each d may be longer or shorter than shown relative to the roundabout geometry, depending on the speed and critical headway times used in the calculation. Figure 5-3: Minimum Sight Distance along the Actual Vehicle Path for Roundabouts This figure shows a schematic of a roundabout with calculated sight distances drawn for entry and exit legs, and for both crossings from the curb and crossings from the splitter island. After plotting the distance from the pedestrian location, the sight triangle is determined as shown in Figure 5-4. Any sight obstruction should be eliminated from the sight triangles for better pedestrian visibility and enabling pedestrians who are blind to hear approaching vehicles more clearly.
NCHRP 3-78b: Final Project Report April 2016 77 Figure 5-4: Pedestrian Sight Triangles for each Crossing Location (Sidewalk and crosswalks will be added to this figure) This figure shows a schematic of a roundabout with estimated sight triangles drawn based on the calculated sight distances. Sight triangles are drawn for entry and exit legs, and for both crossings from the curb and crossings from the splitter island. For each entry and exit approach to a roundabout, three traffic streams should be checked that correspond to the pedestrian crossings of a roundabout: 1. Entering stream, which is composed of vehicles approaching the roundabout and not yet circulating. The speed for this movement can be approximated using the fastest path methodology for the entry path R1 as presented in NCHRP Report 672. 2. Exiting stream, adjacent approach, which is composed of vehicles that enter the roundabout at the adjacent (counterclockwise) approach and exit at the approach of interest. The speed for this movement can be approximated based on the right turn path radius R5 in NCHRP Report 672. 3. Exiting stream, circulating, which is composed of vehicles that enter the roundabout prior to the immediate upstream entry and are thus completing either a through or left-turn maneuver prior to reaching the exit crosswalk. The speed for this movement can be approximated by taking an average of the radius terms R2, R3, and R4 as an approximation, with the exiting speed in most cases limited by acceleration from circulating speeds (see NCHRP Report 672 for further discussion). 5.2.3 Crossing Sight Distance at Channelized Turn Lanes Pedestrians crossing at CTLs are conceptually similar to crossing scenarios at roundabouts. Depending on the geometry and lane configuration of the intersection adjacent to the channelized turn lane, the facility may either perform similar to an entry (CTL with downstream yield control) or an exit approach of a
NCHRP 3-78b: Final Project Report April 2016 78 roundabout (CTL with a downstream acceleration lane). To make a safe crossing at a CTL, a pedestrian must consider the vehicular traffic approaching the CTL and attempting to complete the right-turning movement. At CTLs, the pedestrian is either crossing from the splitter island to the curb (scenario 1) or from the curb to the splitter island (scenario 2). Similar to the roundabout methodology, the length of the traffic stream for approaching vehicles is calculated along its path (d) to determine how each sight triangle will be bound. Figure 5-5 shows the length of each path as it relates to each potential pedestrian crossing location. The figure shows the two locations at which the pedestrian must assess vehicular traffic in order to determine whether a safe crossing can be made. Note that the two crossing points are shown on different approaches for simplicity only. Figure 5-5: Minimum Sight Distance along the Actual Vehicle Path for CTLs This figure shows a schematic of a CTL with calculated sight distances drawn for both crossings from the curb and crossings from the splitter island. As with the case of roundabouts, sight triangles bound by non-linear conflicting paths must be determined to provide adequate sight and auditory distances. Figure 5-6 shows the sight triangles associated with each crossing scenario.
Figure 5-6: Sight Triangles Associated with Crossing Locations at CTLs This figure shows a schematic of a CTL with estimated sight triangles drawn based on the calculated sight distances. Sight triangles are drawn for both crossings from the curb and crossings from the splitter island. NCHRP 3-78b: Final Project Report A pril 2016 79 Consistent with the roundabout methodology, the two parameters of critical headway and vehicle speed should be measured or calculated. As stated in the prior section on roundabouts, the critical headway for a pedestrian crossing a traffic stream is based on the amount of time needed for a pedestrian to safely cross a specific traffic stream, plus a buffer time of 2 seconds. The critical headway calculation is consistent with the description above for roundabouts. Once adapted to channelized turn lanes, the length of the conflicting vehicle paths (d) are calculated using the equations below. d1 = (1.467) (V1, entering) (t1,c) d2 = (1.467) (V2, entering) (t2,c) where, d1 = distance along approach upstream of crosswalk for crossing from curb, ft; d2 = distance along approach upstream of crosswalk for crossing from island, ft; Vn,stream = design speed of conflict movement, mph; tn,c = critical headway required by a pedestrian crossing a specific traffic stream, s, depends on the number of lanes and lane width. 5.3 Gap Opportunity Model The availability of crossable gaps can be estimated using traffic flow theory concepts based on traffic volume and an assumed headway distribution. Assuming random arrivals, the analyst can use the negative exponential distribution to estimate the probability of observing a time-headway greater than tc seconds
80 NCHRP 3-78b: Final Project Report April 2016 (May 1990). The term tc in this case corresponds to the critical gap needed for a pedestrian to cross the street, measured in seconds. This equation assumes random arrivals of vehicles. For non-random arrivals, including platooning effects from upstream signals, other distributions are available (May 1990). The use of this equation for estimating the probability of crossable gaps for pedestrians was first introduced by Schroeder and Rouphail (2010) for estimating pedestrian delay at roundabouts, and was also referenced in NCHRP Report 674. Equation 1 shows the equation that can be used to estimate the probability of encountering a gap greater than the critical gap. Equation 1: Estimating P(CG-Opp) from Traffic Flow Theory (May 1990) tc tavg P(CG â Opp) = P(headway â¥ tc ) = e where, tc = critical headway for crossable gap (sec.) tavg = average headway, defined as tavg=(3,600sec/hour) / (V vehicles/hour) In the absence of pedestrian platoons, the critical gap for pedestrians can be calculated by equation 2 following the pedestrian delay methodology at two-way stop-controlled intersections in the 2010 Highway Capacity Manual (TRB, 2010). Equation 2: Pedestrian Critical Gap after HCM2010 Chapter 19 L tc = + tsS p where, L = crosswalk length (ft) Sp = average pedestrian walking speed (ft/s) default = 3.5ft/s, and ts = pedestrian start-up and clearance time (s), default = 2s. Using the above relationship, the probability of observing a crossable gap in a stream of 400 vehicles per hour at a 14-foot lane at a roundabout (or a CTL) and a corresponding critical headway of tc=14/3.5+2=6 seconds is: tc tavg P(CG â Opp) = P(headway â¥ 6sec.) = e = e = 51.3% As an alternative to this theoretical estimation of the availability of crossable gaps, an analyst may be able to measure an empirical headway distribution, or develop such distribution from simulation. The gap opportunity model was tested against field data collected at roundabouts and channelized turn lanes in this project. These data points are plotted against the volume of traffic and compared to the theoretical model. For more accurate results, only sites which had a total of more than ten available gaps were compared to the model since that represented a better sample size. The results are shown for two-lane roundabouts in Figure 5-7 and for channelized turn lanes in Figure 5-8. Calculated R-squared for the models are 0.59 and 0.23 respectively. The critical headway for crossable gap used for a two-lane roundabout entry and exit was calculated as 10 sec and for channelized turn lanes was calculated as 7 sec using the guidance above. 9 6 â
81 NCHRP 3-78b: Final Project Report April 2016 Figure 5-7: Gap Opportunity Validation for Roundabout Entry and Exit The figure shows a data plot with traffic volume on the studied roundabout approach (in vehicles per hour) on the x-axis and gap opportunities (in %) on the y-axis. Three data series are plotted. The first series plots the predicted rate of gap opportunities as a solid line. The remaining two data series show field measured data for roundabout entries (gray filled triangles) and roundabout exits (black filled circles)
82 NCHRP 3-78b: Final Project Report April 2016 Figure 5-8: Gap Opportunity Validation for Channelized Turn Lanes The figure shows a data plot with traffic volume on the studied roundabout approach (in vehicles per hour) on the x-axis and gap opportunities (in %) on the y-axis. Two data series are plotted. The first series plots the predicted rate of gap opportunities as a solid line. The other data series show field measured data for channelized turn lanes (black non- filled diamonds). From Figure 5-7, it can be concluded that the theoretical model works well for roundabout entry and exits, which is confirmed by the reasonable R-Square value of 0.59. One outlier site in Greenbelt, MD was removed, because of the siteâs proximity to a metro station, which resulted in high vehicle platooning depending on the arrival and departure of trains at the metro station. That site consistently showed higher availability of gap opportunities than predicted by the model. Analysts should consider this when applying the model for roundabouts where vehicle arrivals may not be random, for example due to upstream signals. For channelized turn lanes, Figure 5-8 shows that the theoretical model works for low volumes of traffic. At higher volumes (more than 500 vehicles/hour) the model appears to underestimate the availability of gap crossing opportunities. This could be the result of vehicle platooning from upstream signals and due to blockage. Hence, this model can only estimate crossing opportunities for random arrivals of vehicles and does not take into account the platooning effect that can be caused at higher volumes. 5.4 Yield Opportunity Model The probability of encountering a yield opportunity is a function of different variables such as driver courtesy, potentially explained by factors such as making eye contact and other nonverbal communication between driver and pedestrian. It is also dependent on the geometry of the site, particularly the resulting vehicle operating speeds. More yields are expected where vehicle speeds are low and where drivers expect
83 NCHRP 3-78b: Final Project Report April 2016 the presence of pedestrians, including university campuses and downtown areas. Most field studies estimate the probability of yielding based on the number of vehicles that could have yielded, P(Yield). Note that this is different than the probability P(Y-Opp) used in here, which is calculated on the basis of all encountered vehicles. The latter term is thus a better representation of the yield encounter rate that a pedestrian is likely to experience. A reasonable approach for estimating P(Y-Opp) from P(Yield) is to subtract the probability of crossable gaps from the total number of vehicle events, as was illustrated in NCHRP Report 674 (see Equation 5-1): Equation 5-1: Estimating Yield Opportunities from Yield Probabilities PY âOpp = PYield * (100% â PCGâOpp ) This approach assures that the sum of PY-Opp and PCG-Opp is less than or equal to 1.0 as is required by definition. The team developed models that predict driver yielding behavior, P(Yield) at midblock crossings using logistic regression models from earlier studies (Schroeder 2008; Schroeder and Rouphail, 2011b), and work was recently completed on expanding the yielding prediction models to application for multi-lane roundabouts (Salamati et al., 2013). The modeling of driver yielding behavior in these earlier studies showed several factors with a significant effect on the likelihood of yielding: â¢ Drivers that exit the roundabout have lower likelihood of yielding to a pedestrian than drivers entering the roundabout. â¢ At the exit leg of the roundabout, drivers who are turning right from the adjacent leg to the approach where the pedestrian is standing have lower propensity of yielding to pedestrians than drivers who are exiting from other directions. â¢ Drivers tend to yield more often to a pedestrian who is carrying a white cane compared to a sighted pedestrian. â¢ Drivers located in the far lane relative to the pedestrian location have lower likelihood of yielding to a pedestrian standing at the curb than a driver located in the near lane. â¢ As the speed of the vehicle entering or exiting the roundabout increases, the likelihood of driver yielding decreases. The yield model development in this project used a total of 55 data points for two-lane roundabouts from nine states in the United States. There was not sufficient data available to develop a separate yield model for single-lane sites. From the data, multivariable linear regression models were generated to predict driver yielding rates to âblindâ and âsightedâ pedestrians at two-lane roundabouts in nine U.S. states. Statistical testing showed no significant difference between yielding rates to âblindâ and âsightedâ pedestrians, and as such final models were created through manual selection informed by full modeling efforts and correlation analysis using the dependent variable of interest, driver yielding rate to all pedestrians (YIELDR). Several models were tested that focused on geometric and behavioral predictors for driver yielding behavior. The final selected model with the highest adjusted R2 value includes fastest path radius and RRFB as explanatory factors for driver yielding behavior (Table 5-3).
84 NCHRP 3-78b: Final Project Report April 2016 Table 5-3: Recommended Model to Predict Yielding Rates to Pedestrians YIELDR Regression Coefficient Std Error p 95% Conf Interval RDS -0.065 0.011 0.000* -0.088 -0.042 RRFB 11.947 6.619 0.077** -1.335 25.229 Constant 82.535 6.057 0.000 70.380 94.690 Prob > F 0.000 R2 0.392 Adj. R2 0.369 *p<0.05, **p<0.10 The final model to predict yields is also shown in Equation 5-2, and is a function of approach fastest path radius (RDS) and the presence of an RRFB at the approach. The fastest path radius (in ft.) is a continuous variable, and RRFB is a binary variable that is 1 if a roundabout approach is equipped with RRFB. Equation 5-2: Estimating Probability of Yielding P(Yield) = (-0.065)*(RDS) + (11.9)*(RRFB) + 82.6 The model predicts a base yield probability of 82.6%, which is reduced by 6.5% for each one hundred foot increase in the fastest path radius. The presence of an RRFB increases the yield probability by 11.9% after controlling for radius. The model has been calibrated from data at two-lane roundabouts only. It is expected, that yield rates at single-lane roundabouts are higher than the estimate from Equation 5-2, while yield rates at three-lane roundabouts are lower. It is noted that the difference between roundabout entry and exit does not show up as a variable in the model, even though previous research found those to have significantly different yielding rates. In the current yield model the RDS variable accounts for these differences, with exit legs oftentimes having faster radii (and thus less yielding) than entry legs. This effect of fastest path radius is graphically illustrated in Figure 5-9.
85 NCHRP 3-78b: Final Project Report April 2016 Figure 5-9: Graphical Representation of Yield Probability Model 5.5 Gap Utilization Model This model describes the gap acceptance behavior by blind pedestrians at roundabouts and intersections with CTLs. It is hypothesized that the gap utilization rate is primarily a function of the size of the available gaps, and further that gaps needed by blind travelers are likely to be longer than those needed by sighted pedestrians (as described in the gap opportunity model). This corresponds to the rate of gap utilization being lower for blind travelers than for sighted travelers, given the same opposing traffic stream. For blind pedestrians, gap utilization rates lower than 100% have been observed in research (NCHRP 674). Even if a gap is theoretically large enough to cross, there is a variety of factors that may contribute to gaps not being utilized, including added decision latency time (time between previous car and being ready to step into the roadway) and, most importantly, noise sources. The gap utilization adjustment is a way to account for these effects in an aggregated format by reducing the overall probability of crossable gaps calculated above. Gap opportunity utilization is estimated from the average gap opportunity utilizations observed at study locations and are shown in Table 5-4. Table 5-4 Estimated Average Gap Utilization for Blind Pedestrians Approach Average Gap Utilization Sample Size Std. Error 1 Lane Entry 66.5% 6 2.55% 1 Lane Exit 60.8% 6 2.92% 2 Lane Entry 82.3% 12 2.21% 2 Lane Exit 65.7% 11 3.00% CTL 57.9% 12 2.05%
86 NCHRP 3-78b: Final Project Report April 2016 There is presently insufficient data in the literature to derive more sophisticated gap utilization models, but analysts are encouraged to use local data or estimates should those be available. The observed averages and standard error of gap utilization are shown graphically in Figure 5-10. Figure 5-10: Graphical Presentation of Average Gap Utilization Rates In addition to this variability by site geometry, it is emphasized that the gap utilization statistics further show a large range of values across study participants making it difficult to generalize for the entire population of blind pedestrians. If a user chooses to apply the average utilization rate, higher delays (due to lower utilization rates) can be expected for half of the population of blind travelers. 5.6 Yield Utilization Model This model evaluates the rate of utilization of yield opportunities. It is hypothesized that most sighted pedestrians would accept most or all yield opportunities. Their rates of utilization for those events would therefore be assumed to equal 1.0. For blind pedestrians, yield utilization rates much lower than 100% have been observed in NCHRP 674, as well as in prior studies. Differences between individuals (including hearing differences) and unique acoustic characteristics of different sites are expected to affect these rates. Yield opportunity utilization is estimated from the average yield opportunity utilizations observed at study locations and is shown in Table 5-5. There is presently insufficient data in the literature to derive more sophisticated yield utilization models, but analysts are encouraged to use local data or estimates should those be available. Table 5-5 Estimated Average Yield Utilization for Blind Pedestrians Approach Average Gap Utilization Sample Size Std. Error 1 Lane Entry 67.0% 6 2.79% 1 Lane Exit 68.5% 6 3.30% 2 Lane Entry 72.7% 17 22.09% 2 Lane Exit 70.5% 16 1.22% CTL 35.7% 12 1.24%
87 NCHRP 3-78b: Final Project Report April 2016 The table shows average yield utilization rates for all roundabout sites in the range of 60-80%. For CTLs, the yield utilization was found to be much lower on average at around 35%, which is likely explained by increased background noise at many CTL locations. There is presently insufficient data in the literature to derive more sophisticated yield utilization models, but analysts are encouraged to use local data or estimates should those be available. The observed averages and standard error of yield utilization are shown graphically in Figure 5-11. Figure 5-11: Graphical Presentation of Average Yield Utilization Rates The statistics further show a large range of values across study participants, making it difficult to generalize for the entire population of blind pedestrians. If a user chooses to apply the average utilization rate, higher delays (due to lower utilization rates) can be expected for half of the population of blind travelers. 5.7 Audible Environment and Noise Effects A key component of accessibility for a pedestrian who is blind is the availability of adequate audible cues to assure that a blind traveler can independently navigate the roundabout or CTL. The availability of audible cues is related to the presence of noise in the vicinity of the site, as well as obstacles that may interfere with the ability to clearly hear approaching vehicles. Such obstacles may include signs, poles, or landscaping, which may impact audibility in a matter similar to their impact on sight distances. However, in some cases obstacles may improve audibility. For example, heavy landscaping in the splitter island may help separate audible cues from the two directions of traffic, and thus enhance audibility of traffic for a blind pedestrian waiting on the splitter island (NCHRP Report 674). In general, audibility is less understood than sight distance, which makes an audibility assessment more challenging due to limited available guidance. This section introduces concepts of audibility and high- level principles that should be considered in the design of a roundabout or a CTL. The analyst should identify and flag any concerns about the audible environment. The outcome is a yes/no check on whether audibility is likely to be compromised at the site. To date, no quantitative method exists to accomplish this, but some guidance is provided below. 5.7.1 Location of Crosswalk Relative to Noise Sources
88 NCHRP 3-78b: Final Project Report April 2016 The first and foremost audibility consideration is the location of the crosswalk relative to sources of noise. In the case of a CTL, the majority of traffic noise is generated at the main intersection. It is generally expected that smaller radius CTLs result in smaller channelization islands, which in turn place the pedestrian closer to that noise source. In a similar fashion, a crossing from the channelization island to the curb is expected to have higher levels of interfering noise (from behind the pedestrian) than crossings from the curb to that island. For roundabouts, the separation between the crosswalk and the circulatory roadway impacts the level of noise at the crosswalk. Noise levels are further expected to be different between entry legs (quiet traffic slowing down in approach of the roundabout) and exit legs (louder traffic accelerating away from the roundabout). Similar to CTLs, the splitter island is expected to have exceptionally high levels of noise, with traffic traversing in front of and behind the waiting pedestrian. Wider islands and landscaping on the island may help with reducing noise levels on the splitter islands, although this has not been documented in research. Landscaping further has the potential of limiting lines of sight from the driver to the pedestrian. Other noise sources that have a high impact on the ability to hear conflicting traffic may exist in the vicinity of the site; these make it difficult for a person to distinguish conflicting traffic from background noise. Common examples of this include nearby freeways (especially at interchanges), work zones or construction activity, and general industrial activity. Noise levels are also oftentimes amplified in locations with a high percentage of trucks and other heavy vehicles. 5.7.2 Considering Curvature and Directionality of Traffic A key commonality between roundabouts and CTLs is roadway curvature. Research has shown that pedestrians can have difficulties distinguishing noise generation from through traffic and turning traffic at a CTL, or exiting and circulating traffic at a roundabout exit leg (Grantham et al, 2012). With trajectories of these movements being similar, the sound patterns generated are also similar. As such, a blind pedestrian waiting to cross at a CTL, or at the exit leg of a roundabout, will likely have a difficult time distinguishing between vehicles that conflict directly with the crosswalk from those that proceed through the main intersection or continue to circulate. Additional separation between the crosswalk and the point where the two trajectories separate is expected to enhance the ability to identify conflicting traffic accurately. 5.7.3 Absolute and Relative Noise Levels One key principle in acoustics research is the difference between absolute and relative noise levels. Research on the ability of blind travelers to identify quiet hybrid vehicles, as well as internal combustion engine vehicles, was shown to be highly correlated to the level of ambient noise (Wall Emerson et al, 2015). In other words, even a âquietâ vehicle can be audible at low ambient noise levels. Similarly, even a âloudâ vehicle can be difficult to hear when the level of background noise is elevated. Research has shown that much of the noise generated by vehicles is tire noise, thus vehicle sound is related not only to the type of vehicle, but also its speed. The notion of relative sound levels makes the audibility assessment of a new site difficult, as the designer needs to make assumptions about the level of ambient noise. For example, a very rural location is likely to have lower ambient noise levels than a busy downtown location, although unusual noise generators like agricultural equipment or industrial developments may pose an exception to that rule. Many audible traffic control devices and audible pedestrian signal (APS) systems include adjustments for the level of ambient noise that increase the decibel level of the audible indication in loud environments. 5.7.4 Impact of Grades There is some evidence that roadway grade may impact the audibility at the crosswalk. Specifically, a
89 NCHRP 3-78b: Final Project Report April 2016 crosswalk located in a downhill portion may provide better acoustic information about an approaching vehicle than a crosswalk approached in an uphill section. This pattern was suggested by research performed at two CTLs on opposing approaches at a signalized intersection described in NCHRP Report 674. With the main roadway having a notable grade (3-4%), one CTL was approached by downhill traffic, while the other was approached by uphill traffic. Study participants who were blind, as well as researchers noted that identical sound strip treatments installed in the CTL were more audible on the downhill section than on the uphill section. A potential explanation for this is that vehicle engine noises can propagate toward the crosswalk in a downhill approach, while the sound waves get trapped between the vehicle and the roadway on uphill approaches. 5.7.5 Location and Separation of Traffic Control Devices The location of traffic control devices and the separation of two or more audible devices can impact audibility at the crosswalk, as well as how well the devices themselves can be heard and distinguished from each other. The MUTCD provides specifications for installation of APS devices at signals. Two APS devices on the same corner should have a minimum separation of 10 feet, and have a rapid tick/tone walk indication. If it is not possible to achieve the minimum separation, the walk indication should be a speech message, and additional features should inform users which crossing the walk indication is for. This guidance applies at any location where APS are installed. For the placement of other traffic control devices like crosswalk signs, the MUTCD specifies that the signs need to be placed adjacent to the crosswalk, but is silent on whether they should be placed on the upstream or downstream side. Prior research and significant feedback from blind travelers suggests that a downstream sign placement is preferable. Specifically, a downstream placement assures that the sign does not block the view or sound between the pedestrian and oncoming traffic. 5.7.6 Impacts of Landscaping and the Built Environment As discussed above, landscaping can impact the audibility of a crosswalk in two critical ways. Landscaping can block critical audible information about an approaching and conflict vehicle and can thus have a harmful impact on audibility. However, landscaping can also block unwanted or distractive traffic noise (e.g. from behind the pedestrian, or from across the other side of the roundabout) and may thus have a positive impact on audibility. The built environment surrounding the crosswalk is similarly expected to impact audibility. The presence of tall buildings close to the crosswalk can cause traffic sounds to be reflected and amplified and thereby impact the ability to clearly distinguish directionality of conflicting traffic. Bridges or expressways nearby may also affect audibility. 5.8 Delay Model Previous research showed a link between pedestrian delay and probability of crossing at a crosswalk. The probability of crossing at a crosswalk, P(Cross), is described as a function of the probability of yielding, P(Y), the probability of yield utilization, P(GO|Y), the probability of encountering a crossable gap, P(G), and the probability of utilizing that crossable gap, P(GO|G): P(Cross) = P(Y)*P(GO|Y) + P(G)*P(GO|G) The team was successful in developing models to predict pedestrian delay at single-lane roundabouts, multi-lane roundabouts, and intersections with CTLs as a function of P(Cross). This allows analysts to estimate pedestrian delay for new sites if the input variables are known (Schroeder and Rouphail, 2010). Since the models are sensitive to the utilization measures, the delay can be distinguished between blind and
90 NCHRP 3-78b: Final Project Report April 2016 sighted pedestrians, who may be presented with the same gap and yield opportunities, but have different rates of utilizing these opportunities. Three separate models are developed for single-lane CTL approaches, single-lane roundabout approaches, and two-lane roundabout approaches. Pedestrian delay for single-lane CTL approaches is predicted as shown in Equation 5-3 as a function of P(Cross). In the development of the CTL model, four studied sites in Tucson, AZ were excluded from the analysis, as these all resulted in very low delays of approximately five seconds on average, and did not follow the general data trends in the remaining nationwide sample of sites. Equation 5-3: Calculating Pedestrian Delay for Single-Lane CTL Approaches dp= 10.75 â 9.95*LN(PCross) Pedestrian delay for single-lane roundabouts is predicted as shown in Equation 5-4 as a function of P(Cross). Equation 5-4: Calculating Pedestrian Delay for Single-Lane RBT Approaches dp= 9.37 â 9.78*LN(PCross) Pedestrian delay for two-lane approaches (two-lane roundabouts) is predicted as shown in Equation 5-5 as a function of P(Cross).. Equation 5-5: Calculating Pedestrian Delay for Two-Lane RBT Approaches dp= 6.14 â 8.53*LN(PCross) The delay term, dp, in Equation 5-3 through Equation 5-5 is measured in seconds per pedestrians. The equations are applied separately to each portion of the crossing, which in the case of a roundabout means the total delay is the sum of delay for the entry and exit legs. The quantity increases with a decreasing probability of crossing, PCross, which in turn decreases with reduced availability and utilization of gaps and yields. As such, a low-volume site (lots of gaps) or a high- yielding site are expected to result in low delay, provided that utilization of crossing opportunities is adequate. As traffic volumes increase (reducing the availability of gaps), and as vehicle speeds increase (reducing the number of yields), the delay per pedestrian is expected to increase. A graphical representation of the models developed for CTLs, single-lane RBTs, and two-lane RBTs is given in the following three figures (Figure 5-12, Figure 5-13, and Figure 5-14). For the CTL results in Figure 5-12, the four outlier sites from Tucson, AZ are shown separately from the nationwide sample of sites.
91 NCHRP 3-78b: Final Project Report April 2016 Figure 5-12: Graphical Representation of CTL Delay Model Figure 5-13: Graphical Representation of Single-Lane RBT Delay Model
92 NCHRP 3-78b: Final Project Report April 2016 Figure 5-14: Graphical Representation of Two-Lane RBT Delay Model As an alternative to this pedestrian delay methodology, the analyst may choose to refer to the method in the Highway Capacity Manual, or conduct a simulation study. However, it is emphasized here that the HCM method does not account for opportunity utilization of less than 100%. For simulation, a method for considering varying gap and yield availability and utilization distributions is described in Schroeder et al. (2013). 5.9 Risk Model The third and arguably most critical accessibility performance check is the expected level of pedestrian risk. The level of risk is determined in field studies from intervention events by a Certified Orientation and Mobility Specialist, observer ratings, time-to-contact measurements, and video observations. These risk assessment factors are correlated to characteristics of the studied crosswalk to arrive at a risk prediction model. The model predicts the likelihood of a risky decision as a function of different variables. Multivariable linear regression models were generated to predict the rate that blind pedestrians may make crossing decisions that result in intervention events. The resulting model to predict interventions includes noise level at the crosswalk (0 for low levels of noise and 1 for high levels of noise), average speed of the vehicle at the crosswalk (continuous variable for values greater than 10 mph) and sight distance (0 if pedestrian sight distance is provided and 1 if it is not provided). The intervention model predicts the likelihood that a blind pedestrian makes crossing decisions which would have resulted in intervention. The intervention model, P (INT) is predicted as shown in Equation 5-6 as a function of noise (NOISE), average crosswalk speed (XSPD_AVE), and sight distance (SIGHT_D). Variables NOISE and SIGHT_D are binary variables and equal to 1 if the noise level is high and the required crossing sight distance is not provided respectively. XSPD_AVE is a continuous variable and is defined for speeds higher than 10 mph. Equation 5-6: Estimating the Probability of Interventions
93 NCHRP 3-78b: Final Project Report April 2016 P(INT)= 0.0629*(NOISE)+ 0.0020*(XSPD_AVE)+ 0.0230*(SIGHT_D) â 0.0177 Table 5-6 shows model development details for the proposed intervention model developed. The model includes variables NOISE (p=0.0393) , XSPD_AVE(p=0.067) and SIGHT_D (p=0.044). It is important to note that the model should only be used for speeds greater than 10 mph, which is the calibrated range of the observed data. Table 5-6: Final Intervention Model INT= Coefficient Std. Err. t P>|t| [95% Conf. Interval.] NOISE 0.0629 0.0118 5.34 0 0.0393 0.0866 XSPD_AVE* 0.0020 0.0011 1.87 0.067 -0.0001 0.0041 SIGHT_D 0.0230 0.0112 2.06 0.044 0.0006 0.0455 Constant -0.0177 0.0204 -0.86 0.392 -0.0588 0.0234 Prob>F 0.00 R-squared 0.558 Adj. R-Squared 0.531 Figure 5-15 plots the predicted intervention rates against the field observed intervention rates. A 45- degree line is drawn for reference to visually compare observed and predicted interventions. Predicted Vs. Observed Intervention Rates Intervention Rate 45 Degree Line 0.25 0.2 Adj. R2 = 0.53 0.15 0.1 0.05 0 0.00 0.05 0.10 0.15 0.20 0.25 Field Observed Intervention Rates M od el P re di ct ed In te rv en tio n Ra te s Figure 5-15: Plot of Predicted Intervention Rates vs. Observed Intervention Rates
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