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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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Suggested Citation:"Chapter 3 - Spreadsheet Tool." National Academies of Sciences, Engineering, and Medicine. 2023. Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide. Washington, DC: The National Academies Press. doi: 10.17226/27131.
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CHAPTER 3 Spreadsheet Tool 3.1 Introduction This chapter describes the spreadsheet tool that the research team developed and includes details that are useful for using the spreadsheet tool. Three examples are also presented for three different applications: an intersection with a right-turn movement of interest featuring a single right-turn lane, a dual right-turn lane group, and a shared right-turn lane. Chapter 4 provides some additional information about the methodologies used in the spreadsheet. 3.2 Limitations of the Spreadsheet Tool and Methodologies The main purpose of the spreadsheet tool that the research team developed is to allow a user to view estimated RTOR-adjusted volumes and capacities based on mathematical models devel- oped as part of this project. There are several existing tools, such as the HCM Computational Engine, and commercial products such as the Highway Capacity Software, which are capable of accommodating a wide variety of intersection configurations. Rather than replicate this capa- bility, the spreadsheet tool was designed for a more limited range of intersection configurations, while the volume models were integrated into the HCM Computational Engine to enable wider application. This section discusses the limitations of the spreadsheet tool. 3.2.1  Need for Signal Timing Data The research affirms that RTOR volumes and RTOR capacities are dependent on the vehicular and pedestrian demands that conflict with each RTOR movement. All the models of RTOR volume incorporated some variables reflecting the signal timing. Attempting to exclude all such variables did not yield useful models. When analysts estimated models excluding the variables, the variable coefficients often had counterintuitive effects. Therefore, estimating the RTOR volume requires a preliminary signal timing plan. This is also true of the HCM signalized intersection method in general, namely that it is not possible to perform the analysis without signal timing data. In some cases, signal timing data may not be available, and the analyst would need to come up with a plausible signal timing plan. To assist, the spreadsheet tool includes some features to suggest a signal timing plan using a few different methods of estimating a cycle length and splits. The process may require a few iterations. 3.2.2  Intersection Configurations The spreadsheet tool can model an eight-phase intersection with separate protected left-turn lanes, with the possibility of single, dual, or shared right-turn lanes. The spreadsheet tool does 16

Spreadsheet Tool   17   not directly support fewer phases and does not model protected/permitted left turns. Finally, the spreadsheet tool does not include a model of actuated green signal times. These capabilities were not built into the spreadsheet tool because the HCM Computational Engine already handles these other situations; instead, the RTOR equations were integrated into the HCM Computational Engine. Therefore, while the spreadsheet is able to illustrate the use of the RTOR equations for a subset of intersection situations, the modified HCM Computational Engine including the RTOR equations permits more general use. 3.2.3  Delay Equation The spreadsheet includes a basic calculation of the HCM average delay (d1 and d2) for infor- mational purposes by performing a rough estimate of the signal performance. Users may notice that, for some volume conditions, changes that increase RTOR capacity have a limited effect on the delay results. It must be remembered that the HCM delay reflects the delay to vehicles that turn right on green and thus excludes vehicles that turn right on red. As the volume on green approaches zero, the HCM delay converges on a value that is dependent entirely on the signal timing. Additional information is provided in Chapter 4. 3.2.4  Model Data Locations The data used to generate the models was obtained from 260 intersections of various types from across the United States. However, a few states had more representation in the dataset com- pared to other states, as explained in greater detail in the final report for NCHRP Project 03-136, NCHRP Web-Only Document 368: Right-Turn-on-Red Operation at Signalized Intersections with Single and Dual Right-Turn Lanes: Evaluating Performance. For this reason, local calibration may be needed to account for regional differences between the locations used for data collection and the site of interest to the analyst. 3.3  Overview of the Spreadsheet Tool The spreadsheet contains two sheets: • How To Use – contains a quick-start guide that explains how to get started using the spread- sheet. Note that cells where users should enter information are shaded yellow in the other tabs, and are labeled with Microsoft Excel notes that explain what information should be entered. • Site – contains basic information about the site, including turn-lane configurations and signal phase assignments. • Analysis – contains the LOS results and also permits entry of volume data. Calculations also take place in several hidden sheets: • Models 1A, 1B, 2, and 3 contain calculations for four alternative volume models that were developed during this study. Additional information about the models is presented in Chapter 4. • Capacity includes calculations for the modified capacity model for RTOR movements. • LOS contains definitions of signalized intersection LOS. The sheet also contains definitions of Arrival Type and Platoon Ratio for reference. • Defaults contains cell definitions that control a macro to return the workbook to its initial, default conditions. To view the hidden sheets, right-click on the sheet names at the bottom of the Microsoft Excel window and select the “Unhide . . .” option. This opens a tool that allows selection of one or all of the hidden sheets for viewing.

18   Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner’s Guide 3.4  Instructions for Use of the Spreadsheet Tool These instructions are presented in the order that the input data are organized on the Site and Analysis worksheets. Figure 9 shows the Site worksheet, while Figure 10 shows the Analysis worksheet. All the cells highlighted in yellow are intended for user input. The next section will go through each of the fields on these two pages. A discussion of the contents of the hidden calculation sheets is presented at the end of this chapter. As values are entered into the cells, the cell shading will change color to indicate that a non-default value has been entered. To return all the values to their default configuration, click the “Restore Default Values” button (Figure 9, callout “vii”). 3.4.1  Configuration of the Site Worksheet This subsection explains configuration of the Site worksheet. 3.4.1.1  Basic Model Information The uppermost range of cells on the Site worksheet (Figure 9, callout i) permits the user to enter the following information: • Location Type. Select Intersection or Interchange for the appropriate location type. Inter- change is intended for signalized intersections at freeway ramps. Some of the models use this information to modify their results. • Cycle Length. Enter the cycle length used at the signal during the time period of interest, in seconds. • Analysis Period. This is the HCM analysis period. The value can be changed if desired. The default value is 0.25 hr. 3.4.1.2  Assumptions for Capacity Analysis The next section on the Site worksheet (Figure 9, callout ii) permits the user to enter estimated critical gap and follow-up time values that are used in the capacity models. Default values are given, but these can be changed. These values govern the gap acceptance behavior of RTOR vehicles for the indicated right-turn lane configurations. 3.4.1.3  Approach Configuration This range of cells on the Site worksheet (Figure 9, callout iii) contains configurable param- eters for each approach at the intersection. The four approaches are labeled WB, EB, NB, and SB for westbound, eastbound, northbound, and southbound respectively. • Left-Turn Lanes. The number of left-turn lanes on the approach (should be set to 1 or higher). • Left-Turn Saturation Flow Rate. The saturation flow rate (in veh/h/ln) to be used for the left- turn lane group. • Thru Lanes. The number of through lanes on the approach (should be set to 1 or higher). • Thru Lane Saturation Flow Rate. The saturation flow rate (in veh/h/ln) to be used for the through movement lane group. • Right-Turn Lane Configuration. Determines the number of lanes for the right-turn movement. May be set to Single, Shared, or Dual. The selection of Shared sets the number of right-turn lanes to 0, and the through movements are configured to have one through and right-turn lane in addition to any through-only lanes. • Right-Turn Saturation Flow Rate. The saturation flow rate (in veh/h/ln) to be used for the right-turn lane group.

Figure 9. Site worksheet showing locations for site and signal configuration entry.

A Figure 10. Analysis worksheet showing locations for volume entry and LOS results.

Spreadsheet Tool   21   • Conflicting Pedestrians. The number of pedestrians crossing the approach, in pedestrians per hour. • Right-Turn Adjustment Type. This range allows the selection of the type of adjustment to be made for right turns on this approach. Six options are available, as explained below: – NTOR. No adjustments will be made to either the volume or the capacity. This would be appropriate for an approach where RTOR is not allowed or to assume that all right-turn traffic proceeds on green. – Volume Model 1A. The right-turn volume will be adjusted by a zero-inflated negative binomial model that incorporates certain variables that are not always available in field count data. – Volume Model 1B. The right-turn volume will be adjusted by a zero-inflated negative binomial model that is restricted to variables that are more likely available in field count data. – Volume Model 2. The right-turn volume will be adjusted by subtracting estimated RTOR volumes based on a multiple-variable negative binomial model that incorporates conflict- ing volumes. – Volume Model 3. The right-turn volume will be adjusted using a logistic regression model that uses the proportion of red time and the total right-turn flow rate. • Capacity. The right-turn volume will not be adjusted; instead, the movement capacity will be adjusted according to a model that incorporates conflicting movement volumes and a gap acceptance model for RTOR. The user should select NTOR in the case that the movement does not permit RTOR. Otherwise, the user may select any of the other options to estimate the effect of RTOR. The four volume models have different included variables and expression forms that yield slightly different results. These provide RTOR values that can be used to adjust the total right turn volume. Selecting the capacity model will produce estimates of the RTOR capacity that could be used for volume-to-capacity ratio calculations. As the spreadsheet notes, the delay calculations based on estimated capacity are not valid because the form of the existing delay equation is not able to fully capture the effect of increasing the RTOR capacity, as explained in more detail in Chapter 4. • The following settings are only applicable to Model 1A. These adjustments are difficult to obtain in the field and are limited to use with Model 1A only. If not using Model 1A, the default values can be retained. – Presence of Parallel Ped Crosswalk. Enter “TRUE” if there is a pedestrian crossing to the right of the right-turn movement, and “FALSE” if not. – Presence of Conflicting Bike Lane. Enter “TRUE” if there is a bicycle lane crossing the right-turn movement, and “FALSE” if not. – Percent Conflicting Thru Flow Rate in Red. Model 1A uses some flow rates specific to the red interval. The default values are 100% or 0% for most of these parameters, but they may be changed if that the local intersection has characteristics that would reduce the conflicting flow during red. – Percent Opposing Left-Turn Flow Rate in Red. This would typically be lower than 100% if the opposing left turn is protected/permitted. – Percent Shadowed Left-Turn Flow Rate in Red. This might be lower than 100% if the shadowed left turn is protected/permitted. – Conflicting U-Turn Flow Rate in Red. A flow rate value for conflicting U-turn movements can be entered here. – Percent Conflicting Pedestrian Flow Rate in Red. This refers to the pedestrian movement crossing the subject right turn. This might be lower than 100% if some pedestrians are expected to cross in different intervals besides the red interval for the subject right turn. – Percent Parallel Pedestrian Flow Rate in Red. This refers to the pedestrian movement to the right of the subject right turn. This might be higher than 0% if some pedestrians are expected to cross while the subject right turn is red.

22   Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner’s Guide Some details of the models are provided in Chapter 4. Additional technical details are con- tained in NCHRP Web-Only Document 368. Full calculation details are available in the hidden calculation worksheets. Results of the calculations are displayed in the Analysis worksheet. 3.4.1.4  Signal Timing and Phase Configuration The next range of cells (Figure 9, callout iv) controls the properties of each phase at the inter­ section. The model assumes that an eight-phase scheme is used, and eight divisions are arranged into the form of a ring diagram labeled with phases 1–8. In each range the properties are as follows: • Approach. This assigns the phase number to a particular approach. • Movement. This assigns the phase number to the left-turn or through and right-turn move- ments for the selected approach. • Split. This sets the amount of split (in seconds) assigned to the phase. • Platoon Ratio. This factor permits the adjustment of delay to account for signal coordination. This is used to determine the progression factor (PF) that is used in the HCM delay calculation, and to determine the queue service time of conflicting movements in the modified capacity model. – For random arrivals, a value of 1.0 should be used. – To model good progression, use a value greater than 1.0, and to model poor progression, use a value less than 1.0. If the data are available, the value can be related to the percent on green, green time, and cycle length by the following equation: P CP Rp = = (3) g C g where: Rp = platoon ratio, P = proportion of vehicles arriving on green during the cycle, C = cycle length, and g = green time. If the data are not known, suggested values for platoon ratio are provided in Table 5, which includes given platoon ratio values for different qualitative arrival types. • Incremental Delay Factor, k. This permits the setting of a factor to account for actuation. This is used in the calculation of the d2 term in the estimated delay. The default value is 0.5, Table 5.   Arrival type and platoon ratio. Arrival Type Description Platoon Ratio Value Very poor progression. Dense platoon (representing over 80% 1 of traffic) that arrives at the start of red. 0.333 Unfavorable progression. Moderately dense platoon (40–80% 2 of traffic) arriving during the red phase. 0.667 Random arrivals. Sparse platoon (less than 40% of traffic), or 3 coordinated operation with minimal benefit from progression. 1.000 Favorable progression. Moderately dense platoon (40–80% of 4 traffic) that arrives during the green phase. 1.333 Highly favorable progression. Dense platoon (representing 5 more than 80% of traffic) arriving at the start of green. 1.667 Exceptional progression. Near-ideal progression characteristics. Very dense platoons progressing through closely spaced 6 intersections with minimal or negligible side street entries. 2.000 Source: Adapted from the HCM (TRB 2016).

Spreadsheet Tool   23   Table 6.   Incremental Delay Factor based on passage time (unit extension) and degree of saturation. Passage Time Movement Degree of Saturation (s) ≤ 0.50 0.60 0.70 0.80 0.90 ≥ 1.0 ≤ 2.0 0.04 0.13 0.22 0.32 0.41 0.50 2.5 0.08 0.16 0.25 0.33 0.42 0.50 3.0 0.11 0.19 0.27 0.34 0.42 0.50 3.5 0.13 0.20 0.28 0.35 0.43 0.50 4.0 0.15 0.22 0.29 0.36 0.43 0.50 4.5 0.19 0.25 0.31 0.38 0.44 0.50 5.0 0.23 0.28 0.34 0.39 0.45 0.50 Pretimed movement 0.50 0.50 0.50 0.50 0.50 0.50 Source: Adapted from the HCM (TRB 2000). representing pretimed control. Lower values can be used to represent other conditions. A table of k values is provided in Table 6. This shows values that could be selected based on the movement’s degree of saturation and passage time. If the type of control is not known, then k = 0.5 should be used. • Upstream Metering Factor, I. This permits the setting of a factor to account for upstream metering of traffic on the movement. This is used in the calculation of the d2 term in the estimated delay. The default value is 1.0, representing that no metering occurs. A table of recommended values for this factor is included in Table 7. If there is no upstream signal or it is not anticipated to meter downstream traffic, then I = 1.0 should be used. • Yellow Time. The amount of time configured for the yellow change interval for this phase. • Red Clearance Time. The amount of time configured for the red clearance interval for this phase. • Green Time. This cell shows the amount of effective green time resulting from the split, subtracting the yellow and red clearance times. The calculation uses the standard HCM assumption that the start-up lost time and extension of effective green are equal. The cells to the right of this block (Figure 9, callout v) provide a series of checks to assist the user in properly configuring the splits and phase assignments. When all are properly configured, all of these checks should read OK. Several different errors are possible for the numerical values of the splits. The splits must add up to the cycle length in each ring (i.e., phases 1, 2, 3, 4 and 5, 6, 7, 8). In addition, the splits in one ring must equal the splits in the other ring within each concurrency group (i.e., the phases on the same side of the barrier: 1 + 2 = 5 + 6 and 3 + 4 = 7 + 8). Details of the trial calculations are provided to assist with setting the splits. The phase assignment check will return an error whenever the same movement is assigned to more than one phase. Exactly eight possible combinations of approach and movement are possible, and each combination must be uniquely assigned to one phase. Sometimes, the signal timing for a location is not known in advance. For this situation, a tool is included with the spreadsheet that will suggest a cycle length and splits appropriate for the given Table 7.   Recommended upstream metering factors. Degree of Saturation at Upstream Intersection 0.40 0.50 0.60 0.70 0.80 0.90 ≥ 1.0 I 0.922 0.858 0.769 0.650 0.500 0.314 0.090 Source: Adapted from the HCM (TRB 2000).

24   Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner’s Guide volumes (which need to be entered in the Analysis worksheet, as explained in the next section). To use this tool, first select the desired method (callout vi). The three methods available are as follows: • Webster determines a cycle length using Webster’s equation. • Intersection Saturation determines a cycle length using the degree of intersection saturation (XC), using the desired value of XC provided by the user. The value must range between 0.65 and 0.95. Whereas it is possible to attain values outside this range, such values tend to yield unreasonable cycle lengths. The selection of the value represents the degree to which the inter- section operation should be close to capacity. That is, a higher value will favor “tighter” operation, with a shorter cycle length and greater odds for phases to be served their maximum green time, while a lower value will favor “looser” operation but requires a longer cycle length. The value will influence the cycle length resulting from the analysis. It is recommended to start by using a value of 0.85, and then adjust higher or lower if the resulting cycle lengths are too high or too low. • User Cycle uses whatever value for cycle length is entered in the Cycle Length field (callout i). The resulting cycle length will range between 30 and 180 seconds (based on internal limits), and splits will be provided that are proportional to the volume-to-saturation ratios of each phase, subject to minimum green times. The yellow and red clearance times entered in the Signal Timing fields (callout iv) are also relevant. Finally, after signal timing has been entered, it is possible to preview the results for RTOR volumes using both the single-variable and multi-variable models (callout viii). This information is included here for users who are only interested in seeing estimated RTOR volumes. The results are dependent on volume data, as explained in the next section. These single-variable and multi- variable RTOR volume model results are presented for each approach, ignoring the selection of the right-turn adjustment type (callout iii). 3.4.2  Configuration of the Analysis Worksheet This subsection explains configuration of the Analysis worksheet. 3.4.2.1  Volume Entry The Analysis worksheet contains a table with 12 lane groups labeled as left turns (LTs), throughs (Ths), and right turns (RTs). These are organized by approach. In the case where a shared through and right-turn lane group is configured, the corresponding right-turn lane will be empty, as illustrated by the westbound approach shown in Figure 10. Vehicle volumes can be entered in the upper range of cells in the Analysis worksheet (Figure 10, callout ix). The peak hour factor (PHF) is entered in the row just below this. This is the only data entry needed on this worksheet. The remainder of the cells will automatically update and provide results based on the selected models and other site characteristics on the Site worksheet. 3.4.2.2  Results of Calculations The remaining cells on the Analysis worksheet show the results of various steps in the calcu­ lation process. Some of the calculations are carried out on hidden sheets (explained at the end of this chapter). The following is a description of the meaning of each row in this worksheet. • PHF-Adjusted volume. The volume and PHF entered by the user in the preceding two rows are used to provide an adjusted volume that accounts for the variability in traffic within the time period of interest.

Spreadsheet Tool   25   • Movement(s). This row indicates which movements are represented by the column. This mainly indicates whether the through-lane group represents only the through movement or both the through and right-turn (Th+RT) movements. • Group Volume. This row shows the PHF-adjusted volume for the lane group prior to any adjustment for RTOR. This mainly presents the combined through and right-turn volumes for lane groups with shared through and right-turn lanes. • RTOR-Adjusted Volume. This row presents one of the main model results and is highlighted (Figure 10, callout x). In the case where a volume adjustment for RTOR is selected, the adjusted volume for the lane group will be provided here. The adjustment is made according to the model selected by the user (single-variable or multiple-variable) as well as the lane configura- tion (single, shared, or dual). If the approach is configured for NTOR or if capacity adjustment is selected, this volume will be the same as the group volume in the above row. • Number of Lanes. This gives the number of lanes for the lane group. For a shared through and right-turn lane group, it is assumed that the rightmost lane is the shared lane and that no additional right-turn-only lanes exist. • Saturation Flow Rate. The next two rows show the saturation flow rate for the movement in units of veh/h/ln and veh/h. The saturation flow rates are carried over from the Site worksheet for the relevant approach. • Effective Green Duration. The duration of green for the phase controlling the movement is determined using the data provided in the Analysis worksheet. It is assumed that right-turn movements are controlled by the same phase as the through movements. • Green-to-Cycle Ratio. This provides the g/C ratio that is used extensively in delay calculations. This represents the proportion of time that the signal is green for the associated phase. • Capacity. This shows the capacity of the lane group, prior to any adjustment for RTOR. • Adjusted Capacity. This row shows the adjusted capacity for right-turn lane groups. An adjustment is made if the capacity option for the approach is selected in the Site worksheet. No adjustment is made if the approach is configured as NTOR or as one of the two volume options. This is also another one of the main outputs of the models developed in this research, so it is highlighted (Figure 10, callout xi). • Volume-to-Capacity Ratio. This presents the ratio of adjusted volume to adjusted capacity for the lane group. • Platoon Ratio. This shows the platoon ratio for the phase assigned to the lane group. • Proportion on Green. This shows the proportion of vehicles arriving on green, as calculated from the platoon ratio and green-to-cycle ratio using Equation 3. • PF. This shows the calculated PF term, which is determined from the green-to-cycle ratio and percent on green. The PF is used as a modifier for the HCM d1 term, either decreasing delay in the case of better progression or increasing it in the case of worse progression. • HCM Delay terms. The next few rows show the variables used to calculate delay using the HCM delay equation. The d1 term is computed as a function of the volume-to-capacity and green-to-cycle ratios and it includes an adjustment for PF (a multiplier). The k and I factors are brought from the Site worksheet for the associated phase; these are used in the d2 delay term. This model assumes no significant delay from the third HCM delay term for initial queuing (d3). • Average Delay and LOS. The bottom two rows (Figure 10, callout xii) show the results of the HCM delay calculation using the d1 and d2 formulas. The average delay for each vehicle is indicated along with the corresponding LOS. The LOS is set to F if the volume exceeds the capacity, regardless of the average delay. Note that the HCM delay equation represents the delay of vehicles stopped during green, so for right-turn movements, the delay equation excludes RTOR vehicles. Thus, even if the volume of a movement is set to zero, some baseline delay exists from the d1 term, which can be

26   Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner’s Guide thought of as the expected delay of one randomly arriving vehicle, assuming that it arrives in the middle of the red interval and the driver has to wait until the start of green. In addition, capacity adjusted for the possibility of RTOR will have little effect on delay, because the delay equation still uses the existing g/C ratio. Thus, the delay results and LOS are mainly provided for reference, as the main products of this research are the estimated volume and capacity. 3.5  Example Application and Comparison of Results To discuss the use of the spreadsheet tool and examine the resulting changes to volume or capacity associated with the three provided models, this section shows results from the example data included in the spreadsheet tool. The intersection layout, volumes, and signal timing are presented in Figure 11. This is a hypothetical scenario selected with different right-turn configurations on each approach to facilitate a comparison of model results. Note that the eastbound approach in this example does not include RTOR. Figures 9 and 10 illustrate how this intersection would be coded in the spreadsheet. 6 6 6 6 1 200 450 100 8 (NTOR) 150 150 8 150 3 7 150 300 4 100 4 250 400 1250 Cycle Length = 100 s P1 P2 P3 P4 5 5 2 2 2 17 s 45 s 18 s 20 s P5 P6 P7 P8 17 s 45 s 18 s 20 s Figure 11.   Example intersection configuration used for discussion of results.

Spreadsheet Tool   27   The results for the different models are presented in Table 8. Table 8 shows results for all 12 movements arranged into 11 lane groups (with the westbound through and right turns combined [Th*]) and includes details about how the volumes and capacities were adjusted, as well as the resulting delay equation and LOS values in the bottom- most rows. Adjusted numerical values are only given in rows involving right-turn movements; the left-turn and through movements did not change. When examining the volume results, it is important to remember that the numbers represent the total number of vehicles served during green. The estimated RTOR volume is a reduction from the original unadjusted volumes. The eastbound approach is a shared through and right-turn lane configuration. As Table 8 shows, the volume adjustments reduce the volume on green from the lane group with the shared lane. A larger adjustment is estimated by the single-variable model. The reductions are rather small, which is what would be expected from a shared lane given that through vehicles in the traffic mix will tend to block right-turn vehicles unless the number of right turns is proportion- ately high compared to through vehicles. Very little increase in capacity is seen in the capacity adjustment. The westbound approach is configured for NTOR, so the volumes and capacities are not adjusted in any of the models. The southbound approach has a dual right-turn lane. In the volume adjustments for this approach, the single-variable model estimates a larger reduction in the right turns on green due to RTOR than the multiple-variable model. The capacity model estimates an increase in the capacity of about 14%. The northbound approach has a single right-turn lane. Here again, the single-variable volume adjustment model predicts a larger reduction in right turns on green, and the capacity is esti- mated to increase by about 25%. The impacts on delay in this case are generally rather small. However, it is again important to remember that these values reflect the average delays of vehicles in the lane group served during green and excludes RTOR vehicles. As mentioned previously, even if the volume for a Table 8.   Comparison of results for alternative models for example intersection. Approach Eastbound Westbound Northbound Southbound Movement LT Th* RT LT Th RT LT Th RT LT Th RT Lane configuration 1 2 Shared 1 1 NTOR 2 2 Single 1 2 Dual Volumes by movement 150 300 100 150 150 150 250 1250 400 100 450 200 PHF 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 Volume, No RTOR (veh/h) 158 421 158 158 158 263 1316 421 105 474 211 Volume, Model 1A (veh/h) 158 402 158 158 158 263 1316 151 105 474 180 Volume, Model 1B (veh/h) 158 366 158 158 158 263 1316 237 105 474 178 Volume, Model 2 (veh/h) 158 378 158 158 158 263 1316 234 105 474 189 Volume, Model 3 (veh/h) 158 370 158 158 158 263 1316 236 105 474 135 Delay, No RTOR (s/veh) 57.7 51.6 57.7 48.6 50.6 48.8 38.8 28.1 49.5 21.3 19.4 Delay, Model 1A (s/veh) 57.7 49.7 57.7 48.6 50.6 48.8 38.8 20.5 49.5 21.3 19.2 Delay, Model 1B (s/veh) 57.7 46.9 57.7 48.6 50.6 48.8 38.8 22.3 49.5 21.3 19.2 Delay, Model 2 (s/veh) 57.7 47.7 57.7 48.6 50.6 48.8 38.8 22.3 49.5 21.3 19.3 Delay, Model 3 (s/veh) 57.7 47.2 57.7 48.6 50.6 48.8 38.8 22.3 49.5 21.3 18.9 Capacity, no RTOR (veh/h) 228 540 228 270 255 420 1440 680 210 1440 1360 Capacity, with RTOR (veh/h) 228 555 228 270 255 420 1440 853 210 1440 1540 Note: LT=left-turn, RT-right-turn, Th=through, Th*=shared through and right turn, NTOR=no turn on red, LOS=level of service.

28   Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner’s Guide lane group is set to zero, a base amount of delay will be calculated that is a function of the signal timing, and specifically the green-to-cycle ratio. In some cases, the delay reduction is enough to reduce the LOS by a letter grade because the initial value was close to the threshold. 3.6  Calculation Sheets Details of the models are included in the hidden sheets: Model 1A, Model 1B, Model 2, Model 3, Capacity, and LOS. The last of these contains a lookup table for the HCM LOS thresh- olds (along with a table of arrival types). The others consist of a range of cells that bring in input data from the other sheets. These are followed by calculations for the single, shared, and dual configurations. All of the calculations are carried out in each case, but the relevant results are selected in the bottom row of each sheet, depending on the selected lane configuration, and are referenced by the Analysis worksheet. The blue numbers that appear in some of these sheets represent coefficient values from the models. Additional details about these calculations are provided in the next chapter. 3.7 Implementation of RTOR Models in the HCM Computational Engine The spreadsheet tool is limited to a small number of intersection configurations. To mitigate these limitations, the RTOR volume models were also incorporated into the HCM Computa- tional Engine. This section describes how the methods were included in this tool, and provides instructions on how to use the RTOR models in the tool. 3.7.1  Implementation Overview The HCM Computational Engine is a spreadsheet-based tool that uses a combination of spreadsheet functions and macro procedures to execute a LOS analysis. The signalized inter­ section methodology is a self-contained procedure that includes an input for RTOR volumes. The location of these cells in the Operations sheet of the HCM Computational Engine are illustrated in Figure 12. These cells usually take human input. These have been updated to instead accept input from a new worksheet that was added to perform the RTOR volume calculations. Figure 13 shows an overview of the new “RTOR” tab. Most of the cells on this tab are auto- generating and no input is required. There are a range of blue cells that do require user input, one special green cell requiring user input, and a series of yellow cells that are only needed to run Model 1A. The blue cells needed for all models have the following functions: • For each approach as labeled, it is possible to configure NTOR to disable any RTOR calcu­ lation. To do so, enter “1” under the subject approach of interest (Figure 13, callout “i”). • The option to tell the models that the intersection is an interchange ramp is provided in a single cell under “RTOR Model Specific Parameters” (Figure 13, callout “ii”). • The option to select the model of interest is also included in this bank of cells (Figure 13, callout “iii”). The same volume models (1A, 1B, 2 and 3) are implemented here as described previously. • The option “Signal Timing Source” is highlighted in green (Figure 13, callout “iv”). This deter- mines the source of the cycle length and phase durations, which are needed by the models to calculate the red-to-cycle ratio. – The value should initially be set to “Maximums,” which brings the value from the Opera- tions tab using the maximum green values.

Figure 12. Location of RTOR volumes on the Operations worksheet.

Figure 13. HCM Computational Engine: “RTOR” Worksheet added to the spreadsheet.

Spreadsheet Tool   31   – After evaluating the intersection one time, the signal timing data should be updated by changing the value to “Output.” This will bring the data from the tab “Output 1.” The intersection can now be reevaluated to use the new RTOR volumes. • The yellow highlighted cells (Figure 13, callout v) are only relevant to Model 1A and are not used for the other models. These represent data that is not always included in basic data types for LOS analyses. If these values are not know, the cells can be left as-is, and use of Model 1A should be avoided in favor of Models 1B, 2, and 3. These models do not make use of any of the data in the yellow cells, and are calculated entirely from data available in the Operations tab. The inclusion of the RTOR models in the HCM Computational Engine should permit a greater degree of integration with the rest of the HCM model, including options such as use of split phasing, protected/permitted left turns, configuration of a T-intersection, and so forth which are not implemented in the stand-alone spreadsheet tool. In implementing the tool, the overall composition of the HCM Computational Engine was minimally changed. The only cells outside the RTOR sheet were the RTOR volume cells in the Operations tab. None of the macros were changed. 3.7.2  Description of Procedure To use the RTOR volumes, use the following steps: 1. In the RTOR sheet, be sure that the green cell for “Signal Timing Source” is set to “Maximums.” 2. Configure the intersection by entering all data into the Operations sheet as would be done normally (except that the RTOR tabs should continue to be left as formulas). 3. Enter appropriate data into the RTOR sheet per the above descriptions. The blue cells should be adjusted for all model types, and the yellow cells should be adjusted for use of Model 1A. 4. Evaluate the model by running the macros “Read Data from Sheets” and “Evaluate Auto Performance” using the appropriate buttons in the Operations sheet. 5. In the RTOR sheet, go to the green cell for “Signal Timing Source” and change the value to “Outputs.” 6. Reevaluate the model by running the macros “Read Data from Sheets” and “Evaluate Auto Performance” using the appropriate buttons in the Operations sheet. This will run the analysis again using the new RTOR volumes. This step can be repeated until the RTOR volumes converge. The values may not require more than one update to converge.

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There is a need for improved techniques for estimating the performance of right-turn-on-red (RTOR) movements at signalized intersections.

NCHRP Research Report 1068: Right-Turn-on-Red Site Considerations and Capacity Analysis: Practitioner's Guide, from TRB's National Cooperative Highway Research Program, presents two methods for estimating RTOR volume and capacity, and a spreadsheet tool to facilitate the use of these methods. The report also presents guidance on when to prohibit RTOR at a given intersection.

Supplemental to the report is NCHRP Web-Only Document 368: Right-Turn-on-Red Operation at Signalized Intersections with Single and Dual Right-Turn Lanes: Evaluating Performance, a presentation, a spreadsheet tool, and a Computational Engine with RTOR.

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