Incorporating Truck Analysis into the Highway Capacity Manual (2014)

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115 S e c t i o n 1 0 This section describes the research relating to the effects of trucks on the capacity of freeways, arterial street segments, roundabouts, and signalized intersections. Recommended updates to the current HCM passenger car equivalents (PCEs) for capacity are provided. 10.1 The Freeway Truck PCE Models The procedures for estimating truck PCEs can be described in a simple example. Exhibit 77 shows a plot of 1-min flow-density data points for the experimental scenario that involves a 6% upgrade and 30% Class 9 trucks with a weight-to-horsepower ratio of 150 lbs/hp. It is immediately apparent that the data points for the mixed traffic stream lie well below those for the all-automobile condition. This is consistent with the findings from analysis of the I-40 data. In addition, the speeds are very different (the slopes of the relationships). Moreover, the maximum density achieved by the mixed flow is greater than that for the all-automobile flow. Clearly, Exhibit 77 shows the need for a PCE-based adjustment to the flow rates. The scatterplot labeled “PCE Adj” re-plots the 30% truck data points so that the maximum flow rate matches that for the all-automobile case. As shown by the sequence of solid black lines, the initial data point (35, 1500) is transformed into one that is scaled to the automobile-only maximum flow (35, 1500), and then the point on the automobile-only relationship is found that has the same flow rate (22, 1500). The resulting density is then used to determine the LOS for the mixed flow condition. Presently, the HCM procedure converts the existing mixed flow into an equivalent all-automobile flow so that an all-automobile density can be assigned and a LOS determined. This is what the fig- ure shows: first, the squares show the locus of the density/flow points for the actual mixed flow conditions. An appropriate PCE value was identified by determining what adjustment factor needed to be applied to create an equivalence between the 95th-percentile mixed flow rate (about 1500 veh/hr/lane) and the all-automobile 95th-percentile flow rate (about 2400 veh/hr/lane). The effect of this mapping is illustrated by the triangular data points. The flow rates have been upward adjusted, but the densities have been unchanged. This shows how the mixed flow conditions get mapped by the HCM procedure into the all-automobile conditions, by showing that the flow rates are upward adjusted. Note that the densities are not adjusted. The current HCM procedure assumes that this mapping of the flow rates allows one to determine where the mixed flow condi- tion lies along the continuum of all-automobile flow rates and then, based on the all-automobile conditions, to determine what equivalent all-automobile density pertains and, thereby, the LOS to assign. For example, in the case of the black lines shown, an actual mixed flow operating condition of a flow rate of 1000 veh/hr/lane and 34 veh/mile/lane is treated as being equivalent to an all-automobile condition of 1500 veh/hr/lane and 21 veh/mile/lane. This happens because the mixed flow rate of 1000 veh/hr/lane is upward adjusted to 1500 veh/hr/lane (by the PCE conversion) and then based on Predicting the Effect of Trucks on Capacity

116 incorporating truck Analysis into the Highway capacity Manual that flow rate, an all-automobile density of 21 veh/mile/lane is identified and based on that, assign a density-based LOS. The densities observed in the field are likely to always be higher than those antici- pated by the all-automobile model. For practitioners, this means that they cannot take the HCM- derived density as an indication of what they should observe in the field—that is, the mixed flow rate density they observe in the field (if they observe it) will be significantly higher than the one predicted by the HCM procedure. This does not mean that the LOS is actually worse than that predicted by the HCM procedure, nor does it necessarily mean that the HCM procedure is wrong; rather, it is a reflection of the fact that the operating conditions for mixed flows (in terms of speeds and densities for a given flow rate) will be significantly different than those for an all-automobile traffic stream. The 637 scenarios were used to create a function that predicts PCE values. The important independent variables proved to be weight-to-horsepower ratio, percent trucks, grade, and truck type (we assume because of vehicle length). First, for each of the 520 mixed flow scenarios, a PCE value was estimated. The 95th-percentile flow rate from the automobile-only runs was used as an estimate of the facility’s automobile-only capacity. The 95th-percentile flow rate from the mixed traffic runs was used as the mixed traffic capacity. These two values were then used in combination with the automobile and truck percent- ages to compute the PCE value: Equation 63( )= + = −f f p p PCE or PCE f p f p f ao s m s a t ao s a m s t m s where faos = 95th-percentile flow rate from automobile-only VISSIM runs (veh/hr); fms = 95th-percentile flow rate from mixed traffic VISSIM runs (veh/hr); Note: +6% grade, 30% Class 9 trucks with 150 lbs/hp and an all-automobile traffic stream. 0 500 1000 1500 2000 2500 3000 0 10 20 30 40 50 60 70 Fl ow R at e pe r L an e (v eh /h r) Density per Lane (veh/mi) Flow-Density for Class 9, 150 lb/hp, 30% trucks Auto Only 30% Truck PCE Adj Fl ow R at e pe r L an e (v eh /h r) Exhibit 77. Flow-density relationships on a +6% grade.

Predicting the effect of trucks on capacity 117 pa = proportion of automobiles in traffic stream (decimal); pt = proportion of trucks in traffic stream (decimal); and PCE = passenger car equivalent (unitless). These PCE values and the corresponding attributes of each scenario (truck type, weight-to- horsepower ratio, etc.) were then used to derive an equation that predicted the PCE values. The result was the following equation: 0.922 0.7632 0.00799 0.00582 % 0.1300 % Equation 64PCE TT TT WtHp T G( ) = + + − + where PCE(TT) = passenger car equivalent for truck type TT (unitless); TT = truck type (enter the FHWA Vehicle Class Number 4–13 as an integer); WtHp = weight-to-horsepower ratio (lbs/hp); T% = truck percentage (as a decimal); and G% = grade percentage (as a decimal). The t statistic values for the coefficients are all greater than 1.97; therefore, all of the indepen- dent variables are relevant in predicting the PCE value. The Pearson’s correlation coefficient for the equation as a whole, R2, has a value of 0.8976, indicating a good correlation between the equation and the model run results. Note that while the PCE of a truck will vary depending on the total flow of all vehicles on the facility, the procedure described above is designed to estimate PCEs only for capacity flow. 10.2 Arterial Segment Truck PCEs All of the 637 scenarios have been used to create a function that predicts PCE values. The impor- tant independent variables are truck type, weight-to-horsepower ratio, percent trucks, and grade. For each of the 520 mixed flow scenarios, a PCE value has been estimated. The 95th-percentile flow rate from the automobile-only runs, fao s , is used as an estimate of the facility’s automobile- only capacity. The 95th-percentile flow rate from the mixed traffic runs, fm s , is used as the mixed traffic capacity. These two values are then used in combination with the automobile and truck percentages, pa and pt, to compute the PCE value: Equation 65( )= + = −f f p p PCE or PCE f p f p f ao s m s a t ao s a m s t m s These PCE values and the corresponding attributes of each scenario (truck type, weight-to- horsepower ratio, etc.) were then used to estimate an equation to predict the PCE value. The result was the following equation: 0.5006 0.08447 0.004475 .01224 % 0.07621 % 0.7005 Equation 66 5.54 10.4 15.4 10.87 9.70 2 = + + + + = − PCE TT WtHp T G R where The numbers shown below each coefficient = their respective t-statistics; TT = the truck type (the FHWA vehicle class); WtHp = the lbs/hp; T% = the truck percentage (as a decimal); and G% = the grade percentage (as a decimal).

118 incorporating truck Analysis into the Highway capacity Manual The t-critical value is 1.97. The t-statistic values for the coefficients are all greater than this value; therefore all of the independent variables are relevant in predicting the PCE value. The R2 is 0.7005 as shown. Note that while the PCE of a truck will vary depending on the total flow of all vehicles on the facility, the procedure described above is designed to estimate PCEs only for capacity flow. 10.3 Creating Composite Trucks for Capacity Analysis While an actual traffic stream is a mixture of trucks from Classes 4–13, there is no expectation that an HCM user will actually use PCE values for each type of truck when doing analyses; rather, a composite PCE should be employed. The HCM 2010 uses Equation 11–3 (in Chapter 11) (copied as Equation 67) to compute the heavy-vehicle adjustment factor: 1 1 1 1 Equation 67( ) ( )= + − + −f P E P EHV T T R R where PT = the percentage of trucks in the traffic stream, PR = the percentage of RVs, ET = the PCE for trucks, and ER = the PCE for RVs. More generally, if the trucks and RVs are regarded simply as vehicles of type k, then the heavy- vehicle adjustment factor can be rewritten as Equation 68: 1 1 1 Equation 68∑ ( )= + −f P EHV k k k Simply put, k = 1 is for trucks and k = 2 for RVs. Without loss of generality, these thoughts can be extended to a condition where there are a number of different truck types. Then Equation 68 can be rewritten as Equation 69 or Equa- tion 70, depending upon whether there is a desire to differentiate the RVs from the trucks: 1 1 1 1 Equation 69∑ ( ) ( )= + − + −f P E P EHV T T R R T i i i 1 1 1 Equation 70∑ ( )= + −f P EHV T T T i i i In Equation 70, the RVs are simply another truck type. The objective of such a composite truck PCE is to create the following equivalence: 1 1 Equation 71∑( ) ( )− = −P E P ET T T T T i i i  where E˜T is the composite truck PCE. Solving Equation 71 for E˜T results in the following: 1 1 1 1 Equation 72 ∑ ∑ ∑ ( ) ( ) = − + = − +E P E P P E P T T T T T T T T T T i i i i i i i i 

Predicting the Effect of Trucks on Capacity 119 However, since 1∑ ∗ =P PT T T i i , then Equation 72 can be simplified to: 1 1 1 Equation 73 ∑ ∑ ∑ ∑ ∑ = = − +       = − +      E P E P P E P P P P E P T T T T T T T T T T T T T T T T T i i i i i i i i i i i i i Hence, E˜T is given by the percentage weighted average of the ETi values. Application of this technique is illustrated in Exhibit 78 for a freeway. An application to an arterial would proceed similarly. Shown is the distribution of trucks by class for a situation where the trucks compose 6.1% of the overall traffic stream and the grade is level (0%). For each truck class, the table in Exhibit 78 shows the raw percentage in the traffic stream, the average weight, average length, average horsepower, ratio of average weight to average horse- power, PCE value, and percentage of total trucks. For example, trucks in Class 5 represent 2.5% of the overall traffic stream; their average weight is 10,322 lbs; their average length is 23.23 ft.; their average horsepower is 188; their average weight to average horsepower ratio is 55; they have a PCE of 2.10; and they compose 41.2% of the trucks. The weights, lengths, and distribution of vehicle classes in this table (Exhibit 78) were obtained from a year’s worth of weigh-in-motion (WIM) data obtained from the North Carolina DOT Exhibit 78. Developing composite PCE values for a freeway. Note: The above example is applicable for 6% trucks on level terrain (0% grade). Class ClassVar Raw Pct AvgWt AvgLngth AvgHp Wt/Hp Grade PCE TrkPct 4 4 0.7% 21325 31.75 180 118 0% 2.17 12.1% 5 5 2.5% 10322 23.23 188 55 0% 1.73 41.2% 6 6 0.5% 25733 30.09 279 92 0% 2.11 8.5% 7 7 0.1% 51879 30.46 279 186 0% 2.94 1.7% 8 8 0.8% 26090 51.09 293 89 0% 2.24 14.0% 9 9 1.1% 52670 65.20 370 142 0% 2.74 18.6% 10 10 0.0% 55095 73.64 370 149 0% 2.87 0.3% 11 11 0.0% 55554 77.74 370 150 0% 2.96 0.1% 12 12 0.2% 61147 60.79 370 165 0% 3.16 3.0% 13 13 0.0% 76439 64.67 370 207 0% 3.56 0.5% All 6.4 6.1% 25782 38.2 252 93 0% 2.12 100.0% 4 4 0.7% 21325 31.7 180 118 0% 2.17 12.1% 5-7 5.2 3.1% 14244 24.6 206 69 0% 1.86 51.4% 8-10 8.6 2.0% 41745 59.8 340 123 0% 2.55 32.9% 11-13 12.1 0.2% 63093 61.8 370 171 0% 3.21 3.6% All 6.4 6.1% 25896 38.4 253 96 0% 2.15 100.0% 4-7 5.0 3.9% 15597 26.0 201 78 0% 1.90 63.5% 8-13 8.9 2.2% 43521 59.5 340 128 0% 2.61 36.5% All 6.4 6.1% 25782 38.2 252 96 0% 2.14 100.0% 4-13 6.4 6.1% 25782 38.2 252 93 0% 2.12 100.0% All Classes Four Composite Trucks Two Composite Trucks One Composite Truck

120 incorporating truck Analysis into the Highway capacity Manual for the WIM station located on U.S. 421 just south of the interchange with U.S. 64 in Siler City, North Carolina, for the 2004 calendar year. A total of 654,826 vehicles were included in the sample (Stone, 2011). Weights are averages of loaded and unloaded vehicles for each vehicle class. Weights include vehicle plus cargo. The horsepower ratings by vehicle class were obtained from a doctoral thesis by Ahanotu (1999). The percentage of trucks is for the New York State Route 7 freeway at the Hudson River Bridge (Burke, 2012). The bottom half of the table shows four different composite representations of the traffic stream. The first comprises four truck groups: 4 by itself (buses); 5–7 (single-unit trucks); 8–10 (tractors with single trailers); and 11–13 (tractors with multiple trailers). The second has two composite categories: 4–7 (single-unit vehicles) and 8–13 (tractors with one or more trailers). The third category lumps the trucks together into one group. The overall composite PCE is 2. This overall composite is the one currently recommended by the HCM procedure for freeways in level terrain. 10.4 Signalized Intersection Truck PCEs This research task focused on development of improved truck PCEs for signalized inter- sections. The objective was to replace the existing single PCE value for trucks at signals with a method for estimating truck PCEs for saturation flow rate calculation at signals that enables the analyst to estimate PCE values that are sensitive to the percent of trucks (0%–100%) and the specific grade (–30% to +30%) on the approach to the signal. 10.4.1 Current HCM Method The current HCM method for evaluating the operation of signalized intersections uses a flat 2.0 PCE for trucks in the computation of the approach saturation flow rate. There is no adjust- ment to the PCE value for the approach grade or different mixes of truck types (single-unit or semitrailer). 10.4.2 Approach Several studies have investigated the discharge characteristics at signalized intersections and proposed PCE values. Most of these studies involved field data collection of saturation headways of passenger cars and trucks at the intersection approaches to determine PCE values. There was no investigation of truck characteristics or intersection design features (notably approach grade) on the PCE values. A comprehensive review is provided by Washburn and Cruz-Casas (2010). They developed and applied a custom simulation tool to investigate the impact of the proportion of trucks, truck size, and truck position in the queue. They suggested PCE values of 1.8, 2.2, and 2.8 for small, medium, and large trucks, respectively. Boltze (2006) reported saturation flow rates for the approaches to signalized intersections under different grades. He found an effect with both grade and the percent trucks. A major challenge in empirical studies for determining truck impacts on saturation flows at signalized intersections is the difficulty of finding appropriate study locations: measurements of saturation flow per HCM require at least eight vehicles in the queue plus a significant proportion of truck traffic in order to have multiple trucks in the queue for a sufficient number of cycles. These conditions are difficult to be met especially at locations with high grades. So, the simulation approach was chosen to determine how truck proportion and approach grade affect the satura- tion flow rates at signals. Field data collected at the two intersections near the port terminals in

Predicting the effect of trucks on capacity 121 Oakland, California, and Miami, Florida, were used to develop and calibrate the VISSIM micro- simulation program. The calibrated simulation was then applied in several scenarios to develop the truck PCE sensitive to the truck proportion and the grade at signalized intersections. 10.4.3 Simulation Development Steps The previously discussed microsimulation model development work to develop the freeway and arterial speed models investigated and calibrated the truck footprint and speed-acceleration profiles in the VISSIM simulation. Truck acceleration profiles (acceleration versus speed) were developed for two truck classes: single-unit trucks (FHWA Vehicle Class 5) and semitrailer/ combination trucks (FHWA Vehicle Class 9). A VISSIM simulation model was coded and calibrated for each signalized intersection test site based on flows and queue lengths collected at the test sites as described in the next section. The number of required simulation replications was next determined to account for stochastic variability (10 simulation runs were used per scenario). The calibrated VISSIM simulation was applied to obtain saturation flows for different scenarios of truck types, proportions, and approach grades. The following issues had to be addressed: • Truck position in the queue: Previous research has shown that the start-up lost time and saturation flow depend on the truck position in the queue in addition to the type and pro- portion of trucks. Different PCE values result for different combinations of truck positions in the queue (Washburn and Cruz-Casas, 2010). However, such data are difficult to collect in practice. Furthermore, queue position by vehicle type and the associated discharge headway are not standard outputs by VISSIM and other simulation programs. • Number of queued vehicles: HCM requires that there are at least eight vehicles in the queue to reliably obtain saturation flows, of which the first four vehicles (headways) are used in the calculation of the start-up lost times. In typical undersaturated conditions, stochastic volume variations may result in shorter queues and result in errors in the predicted saturation flows. To account for both these issues, the predicted discharge rate (in veh/h) of the through move- ment from the simulation was used as the primary output for getting the PCE values. To obtain the discharge rate from the VISSIM simulation, the input approach volume was increased to exceed capacity to ensure a continuous queue. The discharge rate or capacity (c) is then obtained from the detector recorded volume. The detector is placed just downstream of the intersection stop line. The saturation flow rate S (veh/h/green) is calculated from Equation 74( )=S c g C where c is the discharge rate (veh/h) and g/C is the green time per cycle ratio for the intersection approach. The heavy-vehicle adjustment factor fhv is calculated from Equation 75=f S S hv b where S is the saturation flow rate (veh/h/green) and Sb is the baseline saturation flow (0% trucks on flat grade). The PCE value is calculated from the heavy-vehicle adjustment factor fhv as follows: PCE 100 f P 100 P 1 Equation 76 hv hv hv = × −   + where Phv is the proportion of heavy vehicles (%) and fhv is the heavy-vehicle adjustment factor.

122 incorporating truck Analysis into the Highway capacity Manual Selection of Test Sites Two test sites were selected, both at major maritime ports, so as to obtain high semitrailer truck volumes. The Maritime Street site is located on a major access road to the Port of Oakland, California. The Biscayne Boulevard site is located on the main access road to the Port of Miami. Being maritime port sites, both sites had flat (0%) level grades. Field observations at both sites indicated that queues rarely approached eight vehicles in length; thus, field measurement of saturation flow rates was ruled out. Test Site 1: Maritime Street, Oakland, California. Field data were collected on Wednesday, March 13th, 2013, at a signalized intersection at Maritime and 14th Streets close to the port of Oakland, California. The site had a very high proportion of trucks (83% of the total volume), most of which were semitrailer trucks. A VISSIM simulation of the test site was developed and calibrated based on the field collected data. The calibration consisted of adjustment of driver model parameters and truck fleet characteristics based on the approach described in the previ- ous section. Comparison of the measured and VISSIM predicted counts and saturation flows showed close agreement. Most of the discrepancies were found on movements not essential for this application (e.g., left turns). Note that VISSIM predicted higher saturation flows for 100% passenger cars (2,200 vehicles per hour of green [vphg]/lane vs. the ideal saturation flow of 1,900 vphg/lane in the HCM 2010). The northbound approach of Maritime at 14th Street was selected to obtain the discharge flow rate, saturation flows, and PCE values according to the above described approach. Test Site 2: Biscayne Boulevard, Miami, Florida (Validation Site). The above described meth- odology was applied at a second location, Biscayne Boulevard in Miami, Florida. All trucks to and from the port of Miami pass through the intersection of Biscayne Boulevard with NE 5th Street and NE 6th Street. Data were collected at the inter sections of eastbound NE 5th Street with south- bound Biscayne Boulevard and westbound NE 6th Street with northbound Biscayne Boulevard on Tuesday, April 16th, 2013, between 8 a.m. and 10 a.m. The data collection at this site consisted of • Turning movement counts; • Length of green time, red time, and amber time for individual cycles (in seconds); • Total number of departures for the cycle (i.e., number of vehicles crossing the stop bar, including through, left, and right turning vehicles) broken down by vehicle class; • Stopped vehicles in queue at the start of green (i.e., number of vehicle in queue before the first vehicle crosses the stop bar at the beginning of green) broken down by vehicle class; • Stopped vehicles in queue at the start of red (i.e., number of vehicles in queue at the end of green which could not be serviced during the cycle); and • Other events (crashes, double parking, jay-walking, etc.). A VISSIM simulation was created for the Miami site for the intersection at Biscayne Boulevard (north-south) and Port Boulevard/NE 6th Street (east-west). The truck characteristics and other settings were identical to the Maritime Street VISSIM simulation. Comparison of field measured flows and queues in the westbound direction indicates that the simulation model reasonably replicates observed conditions. The differences between measured and simulated volumes were less than 1%, and the difference in simulated and field observed queue lengths was about 8%. Exhibit 79 shows the simulation model predicted sample saturation flows and PCE values obtained at the two test sites. It can be seen that they are in close agreement. Sample Tests First, a series of tests were performed to verify that the simulation was working cor- rectly for one scenario of weight-to-horsepower ratio (equal to 150 lbs/hp). These tests are described below.

Predicting the effect of trucks on capacity 123 Sample Test 1—Variation of Truck Proportion under a Fixed Truck Mix. In this test the impact of the truck proportion was investigated for 0 grade. The truck mix was kept fixed as was observed in the Maritime Street test site: 10% single-unit trucks and 90% semitrailers. The proportion of trucks varied from 0% to 83%. The predicted PCE values are shown in Exhibit 80. The predicted PCE values are higher than the HCM 2010 value of 2.0 and the difference of PCE values is small for a wide range of truck proportions. Note that the predicted PCE values are reasonably close to the PCE value of 2.8 proposed by Washburn and Cruz-Casas (2010) for the given vehicle mix. Sample Test 2—Variation of Truck Mix under a Fixed Truck Proportion. In this test, the proportion of trucks was kept fixed at 25% and 0 grade. The truck mix was varied from 100% to 10% single-unit trucks. The results are shown in Exhibit 81. The results indicate as expected that PCE values are generally lower for a higher proportion of single-unit (smaller) trucks. Developing Truck PCE Values at Signalized Intersections Following the calibration and validation of VISSIM simulation at the two test sites and the initial simulation results, a series of simulation runs at the Maritime Street site was performed to obtain PCE values for different truck proportions, approach grades, and truck mix. Each % Trucks Maritime Street Biscayne Boulevard Sat. Flow fhv PCE Sat. Flow fhv PCE 0 2,224 1.00 1.00 2,166 1.00 1.00 25 1,735 0.78 2.13 1,634 0.75 2.30 Exhibit 79. VISSIM predicted saturation flows and PCE values at the two test sites. Exhibit 80. Sample Test 1—effect of truck proportion on PCE values. 1.00 2.46 2.49 2.70 0.00 0.50 1.00 1.50 2.00 2.50 3.00 0 25 50 83 % Trucks PC E VA LU ES

124 incorporating truck Analysis into the Highway capacity Manual simulation run was replicated 10 times to account for the stochastic variability of the micro- simulation program. The following scenarios were tested: • Weight-to-horsepower ratio: 150 lbs/hp; • Truck mix: 50% single-unit trucks, 50% semitrailer trucks; • Truck proportion: 10%, 20%, 30%, 40%, 50%; and • Grade: –4%, –2%, 0, 2%, 4%, 6%, 8%, 10%. Effect of Grade and Truck Proportion. Exhibit 82 shows the impacts of truck proportion and grade on the base saturation flow rate (all passenger cars, flat grade). These findings are close to results reported earlier in the literature. Several statistical models were fitted to the resulting simulation data to predict the reduction in the saturation flow rate because of the truck propor- tion and grade. The following model was selected based on the best goodness-of-fit (R2) value and reasonable behavior for both negative and positive grades. A comparison of simulated and predicted values for this model is shown in Exhibit 83. • For Negative Grades (G<0%) % Base Saturation Flow 100 0.79 T 2.07 G= − ∗ − ∗ • For Positive Grades (G≥0%) % Base Saturation Flow 100 0.78 T 0.31 G Equation 772( )= − ∗ − ∗ where % Base Saturation Flow = the change in saturation flow rate from standard conditions (0% grade, 0% truck); T = % of heavy vehicles in traffic stream (expressed as %)(e.g., 1% trucks is expressed as 1.00); and G = grade (%) ratio of vertical climb to horizontal reach (+ for upgrade, – for downgrade) expressed as a percent (e.g., 1% grade is expressed as 1.00). Exhibit 81. Sample Test 2—effect of truck mix on PCE values. 2.05 2.09 2.13 2.45 0 0.5 1 1.5 2 2.5 3 100 90 50 10 TRUCK MIX (% SINGLE UNIT TRUCKS) PC E VA LU ES

Predicting the effect of trucks on capacity 125 Exhibit 82. Saturation flow rate by grade and truck% for 50:50 mix Class 5 and Class 9 trucks. 10 20 30 40 50 -4 -2 0 2 4 6 8 1 0 0 10 20 30 40 50 60 70 80 90 100 % B as e Sa tu ra ti on F lo w % Trucks % Grade 90-100 80-90 70-80 60-70 50-60 40-50 30-40 20-30 10-20 0-10 % Base Sat Exhibit 83. Comparison of the predicted and simulated reductions in saturation flow. 0 10 20 30 40 50 60 70 80 90 100 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 SIMULATED % BASE SATURATION FLOW PR ED IC TE D % BA SE S AT UR AT IO N FL O W

126 incorporating truck Analysis into the Highway capacity Manual This model is valid for the range of trucks between 0% and 50% of the traffic stream, for grades between and including –4% and +10%. Exhibit 84 shows the predicted PCE values for the same mixture of grades and truck propor- tions. Note that the highest PCE value was obtained for a low proportion (10%) of trucks and the maximum grade of 10%. This has been also the case for the PCE value reported in the HCM 2010 for specific grades on freeways (see Exhibit 11-11 of HCM 2010). This is because under higher truck proportions, truck platoons are formed and the impact of a single truck in a platoon of trucks is less severe than the impact of a single truck traveling in a traffic stream of passenger cars. Note also that the PCE values are very similar for high truck percentages for all grades tested. 10.4.4 Effect of Truck Mix The simulation runs were for the repeated scenarios of truck proportions and approach grades under a different truck mix (75% Class 5 single-unit trucks and 25% Class 9 semitrailers). In addition, the simulation was run for two additional truck proportions: 1% and 5%. The result- ing PCE values are shown in Exhibit 85. The results confirmed the earlier findings that the highest PCE values for trucks are obtained under low truck proportions and high grades; as shown in Exhibit 85, the predicted PCE value for 1% trucks is 11.3. Exhibit 86 illustrates the impacts of the truck mix on the PCE values for different approach grades and 10% proportion of trucks. On the average, the difference in the predicted PCE values is about 6%. Overall the differences in the reduction of saturation flow and PCE values due to the different truck mix ranged from 5% to 8% for all combinations of truck proportions and approach grades. Exhibit 84. Signalized approach PCE values—50:50 Class 5:Class 9 trucks. 10 20 30 40 50 -4 -2 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 PC E % Trucks % Grade 7-8 6-7 5-6 4-5 3-4 2-3 1-2 0-1 PCE

Predicting the effect of trucks on capacity 127 Exhibit 85. Signalized approach PCE values—75% Class 5 and 25% Class 9 trucks. 1 5 10 20 30 40 50 -4 -2 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 11 12 PC E % Trucks % Grade 11.00-12.00 10.00-11.00 9.00-10.00 8.00-9.00 7.00-8.00 6.00-7.00 5.00-6.00 4.00-5.00 3.00-4.00 2.00-3.00 1.00-2.00 0.00-1.00 PCE Exhibit 86. Impact of truck mix on PCE values—10% proportion of trucks. 1.24 1.64 1.88 1.94 2.32 2.96 4.13 7.06 1.37 1.85 2.01 2.04 2.45 3.05 4.30 7.21 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 -4 -2 0 4 82 6 10 GRADE (%) PC E VA LU E 75% CLASS 5 TRUCKS 50% CLASS 5 TRUCKS

128 incorporating truck Analysis into the Highway capacity Manual 10.4.5 Comparison with HCM Signalized Intersection Truck PCEs The findings from the analysis of the simulation results indicate that the PCE values at signalized intersections depend on the truck characteristics, proportions, and approach grade. The impacts of trucks on saturation flows (and capacities) at traffic signals are higher than the HCM 2010 estimates under the single PCE value of 2.0. This is illustrated in Exhibit 87 where the simulated and HCM 2010 heavy-vehicle adjustment factors ( fhv) are compared for all the tested scenarios. 10.4.6 Comparison with HCM Signalized Intersection Saturation Flow Adjustment The HCM 2010 method currently has two relevant saturation flow adjustment factors related with truck effects. One factor focuses on trucks exclusively. A separate saturation flow adjust- ment factor is used for grade, and it is independent of the percent of trucks. Consequently, it is necessary to consider both the PCE and grade effects in the HCM method. In the HCM, the combined effects of the heavy-vehicle PCE and grade on signalized intersection saturation flow rates are computed according to Equation 78 using the HCM recommended PCE of 2.0 (taken from Equation 18-5 of the HCM): 100 100 % 200 % 200 Equation 78( ) ( ) ∗ = + ∗ − f f HV G HV g where fHV * fg = the combined effect of percent trucks and grade on saturation flow (ratio of adjusted to ideal saturation flow); 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SIMULATED fhv H CM 20 10 fh v Exhibit 87. HCM 2010 versus VISSIM simulated heavy-vehicle adjustment factors—all tested scenarios.

Predicting the effect of trucks on capacity 129 HV% = the percentage of heavy vehicles in traffic stream (%); and G% = the percent grade (%)(+ for upgrade, – for downgrade). Exhibit 88 compares the saturation flow rate adjustments produced by the HCM for grades and percent trucks combined (Equation 78) with the truck and grade percentages produced in the simulation (as summarized in the fitted equation, Equation 77). As can be seen in Exhibit 88: • The HCM adjustments for grade and percent trucks combined are similar to the recom- mended NCFRP model (Equation 77) in the range of 0% to 2% positive grades, as long as the percent of trucks in the traffic stream is below 40%. • The recommended model diverges significantly from the current HCM method for negative grades and for positive grades above 2%. The HCM method appears to underestimate the effects of higher grades on saturation flow rates at signals. The HCM also underestimates the effects of negative grades on saturation flow. • The recommended model diverges significantly from the HCM for truck percentages in excess of 40%, regardless of the grade or lack of grade. 10.5 Roundabout Intersection Truck PCEs 10.5.1 Existing Truck Treatment The roundabout method in the HCM uses a gap acceptance model in which the capacity of the entry (centry) is determined by the conflicting flow rate on the roundabout (vconflicting): 1,130 Equation 79.001c eentry vconflicting= ∗ − ∗ The entry capacity is in passenger cars/h and reflects an adjustment for heavy vehicles. The conflicting flow rate is in veh/h and is also adjusted for heavy vehicles. Step 2 in the methodology Exhibit 88. Recommended saturation flow adjustments compared with HCM truck and grade adjustments.

130 incorporating truck Analysis into the Highway capacity Manual (shown in HCM Exhibit 21-10, which is not repeated here) makes PCE-based adjustments for heavy vehicles. The PCE is always 2.0 regardless of the heavy-vehicle mix. 10.5.2 Approach The objective of this task was to update and expand the PCE values for trucks so that the gap acceptance model produces capacity estimates that are consistent with field conditions involving various mixes of trucks. Our expectation was that heavy vehicles would impact the saturation flow equation in both the intercept term (because trucks take more time to enter the roundabout even without conflicting traffic) and the slope parameter (because trucks need larger gaps in the conflicting traffic). It was further expected that the truck impact on the intercept term would be proportional to the impact on the slope term. In other words, the added time for a truck to enter the roundabout would be a function of geometry and classification only and would be independent of the volume of conflict- ing traffic. This assumption was to be tested in the data analysis and, if proven valid, would allow the use of a PCE-based flow adjustment across the entire capacity curve—albeit still being a func- tion of grade, truck classification, roundabout diameter, and other factors. If the assumption did not hold (e.g., truck gap acceptance is impacted more than the unimpeded entry headway), we would instead incorporate truck factors directly into a revised roundabout entry capacity model. To conduct these analyses, the team had access to all of the videotapes and datasets prepared as part of the research for NCHRP Report 572 (Rodegerdts et al., 2007). These data encompass information related to many single-lane roundabouts nationwide and a few multilane round- abouts. Excel workbooks were created for every approach that was studied. Moreover, one tab in each workbook shows the sequence of vehicle events that took place including a field that indicates whether each vehicle was an auto, motorcycle, small truck, or large truck. A small truck was considered to be a single-unit truck, a single-unit camper, or a delivery van. A large truck was a multiple-unit truck such as a tractor-trailer, a car or truck towing a boat or trailer, or a bus. 10.5.3 Analyses Three analyses have been conducted regarding trucks at roundabouts. The first examined move-up times to estimate truck PCEs. The second looked at the entry capacity equation to see how the percentage of trucks affected its calibration. The third examined the impact of facility geometry on truck speed. These studies have been conducted on the basis of data from two of the roundabouts studied in NCHRP Report 572: the single-lane roundabout in Lothian, MD, and the double-lane roundabout in Brattleboro, VT. These two were examined most intensely because they had the highest truck flow rates. Truck PCE Values from Move-Up Times The two-lane roundabout on US-9 in Brattleboro, VT, was used to study move-up times. An aerial view of the roundabout is shown in Exhibit 89. Since the roundabout is adjacent to I-91 and on major routes into New England, it is heavily loaded and sees high truck percentages, especially on the east-, south-, and westbound approaches. This facility was selected for the analysis because it has the highest truck percentages, ranging up to almost 50% during short periods of time. Among the three approaches, nearly 20,000 events were recorded for vehicles passing through the roundabout. The events include arrival into first position on the approach, entry into the roundabout, exit from the roundabout, and passage in front of the entry point (by vehicles on the circulating roadway). Each event has a time-stamp, a lane designation, and a vehicle type.

Predicting the effect of trucks on capacity 131 For the move-up time analysis, the events representing arrival into first position in the right- hand lane were studied. Headways were computed between successive vehicles. The headways were classified into four groups: (1) cars-following-cars, (2) cars-following-trucks, (3) trucks-following- cars, and (4) trucks-following-trucks. The inverse of these headways is the instantaneous satura- tion flow rate. The inverse of the low-percentile headways gives a sense of the maximum flow rate that is possible. Variations in that flow rate with the percentage of trucks give a sense of how trucks affect the maximum capacity (i.e., the input flow rate on the approach when the circulating flow rate is zero). The variation in these maximum input flow rates gives a sense of the truck PCEs. Exhibit 90 presents the cumulative distributions (CDFs) for the four types of event pairs that were considered. The CDF labeled CC indicates a car following a car, CT indicates a truck follow- ing a car, TC indicates a car following a truck, and TT indicates a truck following a truck. There are 3156 observations of CC headways, 348 TC headways, 342 CT headways, and 41 TT headways. At the low percentiles, these headways represent the smallest intervals at which vehicles were willing to follow one another. For the cars following cars, this ranges down to 1.6 seconds; for the trucks following trucks, about 3.0 seconds. If these headways were sustainable, this would imply a car-only capacity of 2241 veh/hr and a truck-only capacity of 1835 veh/hr. However, Source: North Carolina State University. Exhibit 89. Multilane roundabout in Brattleboro, Vermont. Exhibit 90. Move-up time distributions for right- hand lanes of roundabout, Brattleboro, Vermont. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 5 10 15 20 25 30 Cu m ul ati ve P er ce nti le Move-Up Time (sec) Move-Up Time CDFs CC CT TC TT

132 incorporating truck Analysis into the Highway capacity Manual these headways are not sustainable, as the diagram suggests. If they were, the CDFs would be vertical at those values. In terms of general trends, it is clear that the CC headways are generally smaller than the TC, CT, or TT headways. Moreover, the TT headways are the largest, and the CT and TC headways are in-between. An examination of the ratios among these headways (and their implicit flow rates) shows that the one between the car-to-car and truck-to-truck flow rate remains very stable at about 2.0 across a wide spectrum of the distribution. Hence, it seems reasonable to assume that the truck PCE value is about 2.0, as portrayed presently in the HCM. The ratio of the CC flow rates to the TC flow rates is about 1.2, and the ratio of the CC flow rates to the CT flow rates is about 1.5. Hence, depending upon the mix of the traffic stream, the PCE for trucks could range from 1.2 to 2.0. If the traffic stream involved 50% trucks (obviously a high value) and the sequence consistently alternated between cars and trucks, then the ratio of the car-only flow rate to the mixed flow rate would be about 1.25 and the truck PCE would be about 2.0. Exhibit 91 provides some insight into how the maximum entry declines with increases in the percentage of trucks. The highest rates are near 1400 veh/hr/lane at near 0% trucks, declining to about 200 veh/hr/lane for 80% trucks. The upper bound of these values is an indication of the effect that the truck percentage has on the maximum entry flow. If the entry flow rate is extrapolated to about 1400 veh/hr when the truck percentage is 0% based on Exhibit 91 and the maximum entry rate is about 1300 veh/hr for 5% trucks, then the PCE value at that flow rate is 2.54. At the flow rate involving 50% trucks, the PCE value is 3.67. While these numbers are different from those presented before (and higher), it is clear that the percentage of trucks has an impact on the capacity relationship. Capacity Equation Analysis This second analysis focuses on fitting the relationship between entry flow rate and circulating flow rate. Again, the Brattleboro roundabout is used. The relationship has been studied for both the left- and right-hand lanes of the approaches. It is assumed that the relationship between the entry capacity and the circulating flow fits the functional form presented by the HCM (see Equation 79); hence, log-linear regression can be used to obtain estimates of the coefficients involved. Specifically, this means that Equation 80= ∗ −β∗c c eentry o vconflicting 0 200 400 600 800 1000 1200 1400 0% 10% 30% 50% 70%20% 40% 60% 80% En tr y Fl ow R at e Percentage Trucks Trends in Entry Flow Rate Exhibit 91. Entry flow rates, right-hand lane, Brattleboro roundabout.

Predicting the effect of trucks on capacity 133 and the values for ln(c0) and b can be found via log-linear regression based on the following equation: ln ln Equation 810c c ventry conflicting( ) ( )= − β∗ This analysis has been conducted for the right-hand lane of the approaches. (The left-hand lane has also been examined, but the regression results have very low R2 values so the analysis has not been carried further.) To conduct the analysis, the data were processed to obtain combinations of circulating flow, entering flow (in the right-hand lane) and percent trucks (on the entry leg). Sequences of 50 vehicle events were used, with an overlap of 10 events. This is equivalent to computing moving averages. The results were then binned on the basis of the truck percentage, and regression analyses were conducted. The binned data were sorted in ascending order based on the circulating flow, and the 95th-percentile values for the circulating flow and entry flow were estimated based on sequential sets of 20 observations stepping every 10. This is equivalent to creating a moving bin and comput- ing the 95th percentile for each realization of the bin. While it does involve using the individual observations multiple times, it helps to smooth out the random variations in the data. The results of the regression analyses are as shown in Exhibit 92. First, it is clear that the maxi- mum entry flow does decline as the percentage of trucks increases. (This is shown by the “Const” value.) The maximum flow value is 1,374 for 0% trucks and declines to 1,056 for 21% or more trucks. Second, the coefficient for the circulating flow remains relatively constant at about -0.7 (which happens to be the value presently shown in the HCM because the flow rates used in the regression were in thousands). Third, the t-statistics for both the constant and the circulating flow are consistently large, meaning that the intercept should not be zero and the coefficient for the circulating flow is statistically significant and different from zero. Fourth, even though the exiting flow rate has been considered in the analysis, its t-statistic is always small, which means that the exiting flow rate does not have a significant effect on the capacity of the right-hand lane. The conclusions to draw from this analysis are threefold. First, a PCE of 2.0 for trucks is appropriate and can be applied to the circulating and entering flows in order to convert the intercept value from mixed flow rates to car-only rates and vice versa. Second, the coefficient pertaining to the circulating flow rate appears to be unaffected by the percentage of trucks in the circulating stream, so no PCE adjustment should be applied to that flow rate when computing capacity values. Third, the exiting flow rate does not seem to have an effect on entry capacity, so it can be ignored. The finding for truck PCEs at roundabouts is that the current HCM value of 2.0 is affirmed for use. However, the field data suggest that it should only be applied to adjust the intercept of the capacity equation, not the coefficient in the exponent term. Exhibit 92. Entry capacity regression results for the multilane roundabout in Brattleboro, Vermont. Circ Exit Const Circ Exit 0% 1374 -0.76558 0.009219 0.832428 372.7105 -41.5053 0.484218 1-10% 1190 -0.53551 0.027035 0.545303 281.4225 -17.4901 1.19563 11%-20% 1258 -0.83072 0.007844 0.829712 310.4256 -34.4693 0.348901 21% + 1056 -0.68267 -0.02101 0.770002 181.3466 -20.725 -0.51598 Coefficients Const 2RskcurT% t-Statistics