Incorporating Truck Analysis into the Highway Capacity Manual (2014)

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

81 S e c t i o n 8 Section 8 focuses on development of improved methodologies for predicting the speeds of trucks on freeways under varying vertical grade conditions. 8.1 Existing HCM Treatment of Trucks on Freeways The current HCM freeway procedures are not designed to predict truck speeds on freeways. The current HCM freeway procedures use passenger car equivalent (PCE) values to create equiv- alent passenger-car-only flow rates corresponding to the observed mixed vehicle flow rates. This transformation leads to performance metrics (e.g., density and speed) based on automobile-only flow conditions that are asserted to pertain to the mixed flow condition—that is, the PCE values produce passenger-car-only flow rates that have densities (the LOS measure) and overall average traffic speeds that are consistent with those that would result from the actual flow rates and traffic (especially truck) mixes. There is no provision in the HCM for predicting truck speeds separately from that of mixed flow traffic. So that HCM users do not have to develop PCE values for every analysis situation, the HCM presents suggested values for a variety of conditions. Exhibit 52 shows the values suggested for freeway analyses in level, rolling, and mountainous terrain. A more expansive set of suggested values is provided for specific conditions, as shown in Exhibit 53. This table gives PCE values for combinations of grade, grade length, and heavy- vehicle percentage. For example, a PCE of 3.0 is recommended for a 5–6% grade of length 0.75–1.00 mile where the percentage of trucks and buses is 20%. The HCM presents a graph that shows how truck speeds vary for different segment lengths, grades, and starting speeds (see Exhibit 54). The graph is nominally predicated on a truck with a weight-to-horsepower ratio of 200 lbs/hp entering an upgrade at 55 mph or accelerating from 8 mph on either an upgrade or a downgrade. Otherwise, no information about truck speeds is given in any of the HCM procedures. Rather, the HCM reports an average speed for the traffic stream as a whole. Moreover, that speed is technically for a PCE traffic stream. Hence, if the trucks have a different speed, that speed is not identified. 8.2 Research Objective and Approach The objective of this task within the research project was to develop a methodology for pre- dicting truck speeds on freeways under varying vertical grade conditions. This methodology has been developed using a seven-step process: 1. Conduct a preliminary analysis of available field observation of freeway performance to gain a sense of what should emerge from the methodological development. Prediction of Freeway Truck Speeds

82 incorporating truck Analysis into the Highway capacity Manual Passenger Car Equivalent Level Terrain Rolling Terrain Mountainous Terrain ET (trucks and buses) 1.5 2.5 4.5 ER (RVs) 1.2 2.0 4.0 Source: Exhibit 11-10, Highway Capacity Manual (TRB, 2010). Exhibit 52. PCE values for trucks, buses, and rvs. Proportion of Trucks and Buses Upgrade(%) Length (mi) 2% 4% 5% 6% 8% 10% 15% 20% ≥25% ≤2 All 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 >2–3 0.00–0.25 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 >0.25–0.50 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 >0.50–0.75 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 >0.75–1.00 2.0 2.0 2.0 2.0 1.5 1.5 1.5 1.5 1.5 >1.00–1.50 2.5 2.5 2.5 2.5 2.0 2.0 2.0 2.0 2.0 >1.50 3.0 3.0 2.5 2.5 2.0 2.0 2.0 2.0 2.0 >3–4 0.00–0.25 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 >0.25–0.50 2.0 2.0 2.0 2.0 2.0 2.0 1.5 1.5 1.5 >0.50–0.75 2.5 2.5 2.0 2.0 2.0 2.0 2.0 2.0 2.0 >0.75–1.00 3.0 3.0 2.5 2.5 2.5 2.5 2.0 2.0 2.0 >1.00–1.50 3.5 3.5 3.0 3.0 3.0 3.0 2.5 2.5 2.5 >1.50 4.0 3.5 3.0 3.0 3.0 3.0 2.5 2.5 2.5 >4–5 0.00–0.25 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 >0.25–0.50 3.0 2.5 2.5 2.5 2.0 2.0 2.0 2.0 2.0 >0.50–0.75 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.5 2.5 >0.75–1.00 4.0 3.5 3.5 3.5 3.0 3.0 3.0 3.0 3.0 >1.00 5.0 4.0 4.0 4.0 3.5 3.5 3.0 3.0 3.0 >5–6 0.00–0.25 2.0 2.0 1.5 1.5 1.5 1.5 1.5 1.5 1.5 >0.25–0.30 4.0 3.0 2.5 2.5 2.0 2.0 2.0 2.0 2.0 >0.30–0.50 4.5 4.0 3.5 3.0 2.5 2.5 2.5 2.5 2.5 >0.50–0.75 5.0 4.5 4.0 3.5 3.0 3.0 3.0 3.0 3.0 >0.75–1.00 5.5 5.0 4.5 4.0 3.0 3.0 3.0 3.0 3.0 >1.00 6.0 5.0 5.0 4.5 3.5 3.5 3.5 3.5 3.5 >6 0.00–0.25 4.0 3.0 2.5 2.5 2.5 2.5 2.0 2.0 1.0 >0.25–0.30 4.5 4.0 3.5 3.5 3.5 3.0 2.5 2.5 2.5 >0.30–0.50 5.0 4.5 4.0 4.0 3.5 3.0 2.5 2.5 2.5 >0.50–0.75 5.5 5.0 4.5 4.5 4.0 3.5 3.0 3.0 3.0 >0.75–1.00 6.0 5.5 5.0 5.0 4.5 4.0 3.5 3.5 3.5 >1.00 7.0 6.0 5.5 5.5 5.0 4.5 4.0 4.0 4.0 Source: Exhibit 11-11, Highway Capacity Manual (TRB, 2010). Exhibit 53. PCEs for specific grades.

Prediction of Freeway Truck Speeds 83 2. Select a test site with a calibrated microsimulation model for investigating the relationship between volumes, truck percentages, the mix of truck types, and vertical grade on sustained automobile and truck speeds. 3. Develop acceleration functions (acceleration versus speed, one for each truck type) that can be used as inputs into the microsimulation model so that the effects on truck speed could be tested for various grades, truck percentages, and mixes of semitrailer and single-unit trucks. Compare the trajectory predictions (speed versus distance) from these functions with those from prior studies. 4. Develop and apply a microsimulation model of a single-lane freeway with a constant grade to see whether any model parameter values need to be adjusted to generate speed-distance trajec- tories that are consistent with the findings from Steps 1 and 2 above. The use of a single-lane simulation at this point eliminates possible passing effects on the observed average link speed. 5. Conduct simulations of a wide range of truck types, weight-to-horsepower ratios, truck percentages, flow rates, and grades using a simulation model of a three-lane freeway with constant grades. Do this initially for one truck type (focused principally on FHWA Classes 5 and 9) and then for mixes of truck types and weight-to-horsepower ratios. The use of three- lane simulation at this point allows vehicle passing effects to be incorporated into the results. 6. Determine what predictive relationships can be used for truck PCEs and speeds based on the data from Step 4. 7. Test the resulting treatments for truck PCEs and speeds using a quasi-real case study whose setting is based on a real-world facility, but whose design and traffic mix details have been treated parametrically to allow tests of the effects of various other conditions (e.g., flow rates, truck mix percentages, and grades). The findings from this process are described below. 8.3 Initial Field Assessment Freeway performance for different truck percentages was examined based on data from I-40 in Raleigh, North Carolina. The intent was to gain a sense of what the methodology should predict. This stretch of freeway is basically level, it is three-lanes wide in each direction, and its geometry is consistent with the ideal conditions employed in the HCM. Source: Exhibit 11-A1, Highway Capacity Manual (TRB, 2010). Exhibit 54. Performance curves for 200 lb/hp truck.

84 Incorporating Truck Analysis into the Highway Capacity Manual Exhibit 55 shows a plot of the 15-min observations of flow and density. It is obvious that the truck percentage does have an effect on both the maximum flow rate that is achieved and the density that corresponds to that maximum flow rate. The maximum flow rates are lower and the densities are higher than those that arise when the truck percentage is less than 5%. The plot also shows that the freeway speeds are influenced by the truck percentage. As is well known, the slope of the line from the origin to any data point is the speed that pertained when that data point was recorded. Hence, it appears that the interplay of the trucks with other vehi- cles creates slower speeds, higher densities, and lower capacities than for (nearly) all-automobile conditions. Exhibit 56 shows a plot of the corresponding 15-min observations of speed and flow. In this case, the data points for different truck percentages are shown in separate graphs. The most significant observation from Exhibit 56 is perhaps that the percentage of trucks has an influence on the speeds achieved at or near capacity. This is consistent with the insights emerging from the flow-density plot. Since this section of freeway is basically level, grade cannot be the cause. It must be the interaction of the trucks with the other vehicles. This effect may arise more generally; not just here. The second observation is that the percentage of trucks has an influence on the 15-min aver- age speeds during times of low flow. Since vehicle interactions are not likely to be the cause—it may be that the trucks using the freeway when the volume-to-capacity (V/C) ratio is low cannot or choose not to travel at the speed of the other vehicles. These trends suggest that the influence of the trucks may be significant, especially at higher truck percentages. Moreover, the trucks are likely to affect both speed and density across the range of V/C ratios. Particularly, higher truck percentages are likely to result in higher densities and lower speeds than those that typify predominantly automobile conditions. Exhibit 55. Flow-density relationships on I-40 for various truck percentages.

Prediction of Freeway Truck Speeds 85 8.4 The Freeway Test Bed The investigation of the freeway speed flow effects of trucks on extended grades was per- formed on a hypothetical facility consisting of 8 miles of level three-lane freeway followed by 5 miles of three-lane freeway with a grade. The grade on the 5-mile section varied from –6% to +6% in 1% increments (13 grades total). The hypothetical facility was simulated using the VISSIM microsimulation model (PTV Group, n.d.). 8.5 Calibration of Acceleration Profiles Steps 2 and 3 in the analysis process were for developing the truck acceleration functions (relationships between the maximum acceleration and speed) that would be used in the micro- simulation model—in this case, VISSIM. Step 2 focused on developing the functions themselves. Step 3 aimed to incorporate those functions into VISSIM and then to see what results were pro- duced and whether any other VISSIM parameters needed to be adjusted to generate trajectories (predictions of speed versus distance) that were consistent with expectations from other research efforts. It seemed best to do these two steps simultaneously because there might be iterations, which proved to be true: two iterations were needed to reach closure. 8.5.1 Background on Truck Acceleration and Deceleration Profiles In the HCM 2010, there are truck performance curves (Exhibit 11-21, HCM) for trucks with a weight/power ratio of 200 lb/hp. The reference data used to develop this truck performance Exhibit 56. Speed-flow relationships on I-40 for various truck percentages.

86 Incorporating Truck Analysis into the Highway Capacity Manual curve is found in the paper “Survey of Uphill Speeds of Trucks on Mountain Grades” (Willey, 1949). Trucks with weight/power ratios of about 200lb/hp were selected to develop the model since they would have acceptable operating characteristics from the standpoint of the highway users. However, applying a single truck performance curve for one weight/power ratio for all trucks reduces the accuracy of any analysis conducted. To develop multiple truck performance curves for specific weight/power ratios, the following procedure can be followed: • Find representative weight/power ratios according to the probability distributions of weight/ power ratios. Figures D-5 through D-10 in NCHRP Report 505: Review of Truck Characteristics as Factors in Roadway Designs (Harwood et al., 2003) are distributions for several states. The figures also show the 25th-, 75th-, 85th-, and 90th-percentile ratios that could be used to get the specific values of weight/power ratios (see Exhibit 57). • Apply specific values of the weight/power ratio to develop truck performance curves. Differ- ent weight/power ratios lead to different acceleration rates. Table 29 in Chapter 5 of NCHRP Report 505 (reproduced in Exhibit 58) shows the acceleration rate with a given weight/power ratio and speed. The speed profile computations in Appendix E of NCHRP Report 505 can be used to determine acceleration rates for different grades (Harwood et al., 2003). NCHRP Report 505 (Harwood et al., 2003). Source: Adapted from Figure D-5: Distribution of Estimated Weight-to-Power Ratios for California Freeways, Exhibit 57. Weight-to-horsepower ratio distribution example. Weight-to- Power Ratio (lb/hp) Acceleration rate (fpss) 0 mph 10 mph 20 mph 30 mph 100 1.87 1.70 1.47 1.29 200 1.22 1.08 0.96 0.79 300 0.91 0.81 0.72 0.58 400 0.71 0.61 0.50 0.36 *Average acceleration capabilities of trucks accelerating from specified speed to 64 km/hr (40 mph). Source: NCHRP Report 505 (Harwood et al., 2003). Exhibit 58. Average truck acceleration capabilities.*

Prediction of Freeway truck Speeds 87 8.5.2 Approach to Calibrating VISSIM Truck Profiles Steps 2 and 3 started with a review of the literature on truck performance. The review showed that the procedure described in NCHRP Report 505 (Harwood et al., 2003) would be a good start- ing point for developing a predictive model. The procedure described in the report could predict the performance of various truck types on specific grades or sequences of grades. Moreover, the procedure was codified in an Excel spreadsheet on a floppy disk that was included with the report. The spreadsheet produced speed-versus-distance trajectories based on user-specified inputs. (In the text that follows, this model is referred to as the “NCHRP Report 505 spreadsheet.”) It was found that the NCHRP Report 505 spreadsheet did produce the results presented in NCHRP Report 505—for example, if the weight-to-power ratio was set to 200 lb/hp and the weight-to-frontal-area ratio was set to 580 lb/ft2, the graphs and tables shown in the report could be produced. (It is interesting, however, that this value for the weight-to-frontal-area ratio was different from the default value that the spreadsheet would have selected automatically.) A check of the NCHRP Report 505 spreadsheet’s predictions with other sources suggested that it was likely to be a valid representation of truck performance. It could generate the acceleration and deceleration curves shown in the AASHTO Green Book. (We assume this is because the intent was to use the NCHRP Report 505 findings in the AASHTO Green Book.) However, it could not generate the trajectories shown in the HCM. This is probably due to differences in assumptions about truck characteristics. However, creation of the acceleration functions revealed a problem: a marked and abrupt decrease in acceleration arose at a speed of 10 ft/sec. The report and the logic called for different equations to be used to predict the tractive effort (acceleration produced by the engine) above and below this speed, but there was no indication that the acceleration value should change dra- matically. It seemed to make more sense for the values to match where the logic changed (which we believe is what was intended). It seemed that a logic error was made in creating the program. Assuming this was the case, a change was to rectify this anomaly, and the trajectory predictions of the new code were compared with the old. The difference was very small. With an expectation that the spreadsheet would now produce acceptable acceleration func- tions, Step 4 commenced. The acceleration functions were coded into VISSIM and simulations were conducted. However, the results did not match. VISSIM predicted significantly lower crawl speeds on the upgrades. A check of VISSIM logic showed that it automatically adjusted the acceleration rates up or down by 1% of gravity for every 1% change in grade (decreasing it for upgrades and increasing it for downgrades). This is consistent with the effect that should arise from changes in grade. A check of the NCHRP Report 505 spreadsheet revealed three more problems, two major and one minor. The first was that the influence of grade was omitted even though its influence was described correctly in the report. A grade term did appear in the formula for predicting the trac- tive effort (inconsistent with the text of the report), but the influence of grade did not appear in the resistance equations. (Moreover, the way in which grade appeared in the tractive effort equation did not make logical sense.) The second problem was that there was no upper bound on the tractive effort due to the weight on the powered axles and/or the friction between the tire and the road. The third was that the coefficient for the V ′ term in the resistance equation used a value of 0.0004, while the report showed 0.004. Using 0.004 in the spreadsheet produced illogical results, so it was concluded that the value shown in the text was a typographical error. In light of these findings, it was necessary to make two significant changes to the NCHRP Report 505 spreadsheet. First, the effect of grade was introduced in the resistance equations; second, a limit on the tractive effort was added based on the percentage of truck weight on the powered axles and the coefficient of friction.

88 incorporating truck Analysis into the Highway capacity Manual After making these changes, the new model’s predictions were compared with those from a model developed by Rakha et al. (2001). Rakha et al.’s model differed in subtle ways from that contained in the revised NCHRP Report 505 spreadsheet, but it seemed like the two models should produce similar results. To check its logic, Rakha et al.’s model was codified in an adapta- tion of the NCHRP Report 505 spreadsheet. The finding was that not only was the code capable of producing the results shown in Rakha et al., but its parameter values could also be adjusted to produce the results predicted by the revised NCHRP Report 505 spreadsheet and vice versa. Hence, it was concluded that the modified NCHRP Report 505 spreadsheet was producing defen- sible results. A return to Step 3 now showed that the truck trajectories (speeds versus distance) predicted by the revised NCHRP Report 505 spreadsheet agreed with the predictions from VISSIM. This was true across the entire range of grades and weight-to-horsepower ratios. 8.6 Truck Footprint for VISSIM A side effort involved creating VISSIM footprints (i.e., lengths, widths) of the Class 5 and 9 trucks. The effect of these footprints was two-fold in the main simulations. First, the footprints affected the length of the trucks in the car-following and lane-changing behavior. Second, from a display standpoint, the footprints determined the appearance of trucks in the animations. 8.7 VISSIM Simulations and PCE and Speed Model Development Steps 4 and 5 were focused on conducting the VISSIM simulations and developing the pre- dictive models for PCEs and truck speeds. At first, the expectation was that these steps would be done in series. However, as was the case with Steps 2 and 3, the results from the VISSIM simulations suggested useful ways to think about the predictive equations, so the two steps were done in parallel. About 6,552 combinations of truck mix, grade, and traffic flow rate were simulated. The parameters that defined each simulation were as follows: • FHWA Class 5 (single-unit trucks) and 9 (semitrailer trucks); • Weight-to-horsepower ratios of 50, 100, 150, and 200 lbs/hp; • Grades from –6% to 6% (13 grades total); • Truck percentages of 0%, 10%, 20%, 30%, 40%, 50% and 100%; and • Flow rates of 240, 600, 1200, 1800, 1920, 2040, 2160, 2280, and 2400 vehicles per hour per lane (veh/hr/lane). The flow rates are equivalent to V/C ratios of 10%, 25%, 50%, 75%, 80%, 85%, 90%, 95%, and 100% for the all-automobile (no truck) condition. Rather than work with each simulation separately, scenarios were formed in which the nine V/C conditions associated with each combination of FHWA class, weight-to-power ratio, grade, and truck percentage were grouped together. This resulted in 637 scenarios: 520 mixed scenarios (2∗4∗5∗13) and 13 all-automobile scenarios plus 104 all-truck scenarios (2∗4∗13). The methodology was developed based on the simulation results from these scenarios.

Prediction of Freeway truck Speeds 89 8.8 The Speed Prediction Models The steps in the procedure that focus on predicting the truck speed are motivated by Exhibit 59. It shows the speed-flow plot for this same condition. In fact, the plot also shows the speed-flow relationships for the truck and automobile speeds separately (in the 30% trucks case) as well as two other cases: automobiles-only and trucks-only. The data points marked “Scenario” are the average mixed speeds for the 30% truck condition. At low flow, they are scattered between 40–70 mph, but they quickly drop to around 30 mph (the truck crawl speed) as the flow rate increases. The automobile speeds, marked “Autos,” follow a similar trend (as they should since 70% of the traffic stream is automobiles). This motivates a prediction model that allows the values to drop from the all-automobile condition to the all- truck condition. This is a new idea in the context of the HCM procedures. The trucks speeds, marked “Trucks,” are all at the crawl speed for the 6% grade, as they should be given the length of the segment (5 miles). The data points marked “Auto Only” are for an all-automobile condition. To make the V/C ratios match, the automobile-only flow rates can be downward adjusted so that the automobile-only maximum flow rate matches that of the mixed scenario. The automobile-only speeds stay at or near 70 mph until capacity is reached. The data points marked “truck only” are from the simulation of a traffic stream involving 100% trucks. To make the V/C values match in this instance, the flow rates have been upward adjusted so that the actual maximum flow rate in the all-truck circumstance (855 veh/hr/lane) maps to the maximum flow rate in the case under study (again, 1,500 veh/hr/lane). 0 10 20 30 40 50 60 70 80 0 200 400 600 800 1000 1200 1400 1600 1800 Sp ee d (m ph ) Flow Rate per Lane (veh/hr) Speed-Flow Relationship Auto Only Scenario Autos Trucks Truck Only Exhibit 59. Truck and automobile speed-flow relationships on a +6% grade.

90 incorporating truck Analysis into the Highway capacity Manual Predicting the truck speeds proved to be relatively simple. In all 636 scenarios involving trucks (including the 100% truck case), the truck speed proved to match that which is derivable from the acceleration function, the deceleration function, and the length of the grade: , , Equation 27s L t L g s t o( )= ω where st = truck speed (mi/hr); L = length of segment with grade; and t(L|g,s0,w) = the time required to travel the distance, L, given the grade involved, g, the truck’s initial speed upon entering the segment, s0, and the truck’s acceleration capabilities, w. The specific equations employed in simulating the movement of the truck through time are adapted from Appendix E of NCHRP Report 505 (Harwood et al., 2003): • Computation of total resistance: If v >10 ft/sec then: 0.2445 0.0004 222.6 Equation 28Rr v WtHp v ele = − − − ∗β ∗ If v ≤ 10 ft/sec then: 0.2445 0.0004 Equation 29Rr v= − − 0.021 Equation 302Ra v WtFaele= − ∗ α ∗ 32.17 Equation 31Rg g= − ∗ Equation 32R Rr Ra Rg= + + • Computation of tractive effort: 15368 10, 14080 10. Equation 33TE WtHp Max v Max v ENG ele ( ) ( )= ∗β ∗ + 32.2 1 Equation 34TE ABS gADH ( )( )= ∗ µ ∗ρ ∗ − , Equation 35TE Min TE TEENG ADH( )= • Computation of vehicle position (d), velocity (v), and acceleration (a) at time t: Equation 36a t TE R( ) = + Equation 370v t v a t dt∫( ) ( )= + Equation 380d t d v t dt∫( ) ( )= + where v = the speed at a given point in time (ft/sec); g = the grade (as a decimal); WtHp = the weight-to-horsepower ratio (lb/Hp);

Prediction of Freeway truck Speeds 91 WtFa = the weight-to-frontal-area ratio (lb/ft2); aele = an altitude-related adjustment factor for air resistance for converting sea-level aerodynamic drag to local elevation is equal to (1 – 0.000006887 ∗ ft. elevation)4.255; bele = an altitude-related adjustment factor for rolling resistance; µ = the coefficient of friction between the tire and the road; r = the percentage of the truck’s weight on the powered axles; Rr = the acceleration due rolling resistance (ft/sec2); Ra = the acceleration due to air resistance (ft/sec2); Rg = the acceleration due to grade-related resistance (ft/sec2); R = the total acceleration due to resistance (ft/sec2); TEENG = the tractive effort acceleration provided by the engine (ft/sec 2); TEADH = the tractive effort acceleration that can actually be applied given the limitation imposed by µ and r (ft/sec2); TE = the actual tractive effort applied expressed as acceleration (ft/sec2); a(t) = the acceleration at any given point in time (ft/sec2); v(t) = the velocity at any given point in time (ft/sec); d(t) = the distance the truck has gone (ft.); and dt = the increment of time (e.g., 1 second) being used in the simulation. 8.8.1 Predicting Automobile Speeds An interesting and important finding is that automobile speed is affected by the trucks, especially when the truck percentage is high and the grade is steep. Hence, for high truck percentages, the automobile speeds need to be estimated as well as the truck speeds. The reason is that when the truck percentage is high and the grades are steep, the automobiles cannot easily overtake the trucks. The automobiles are constrained and in the limit have a speed that converges to the truck speed—that is to say, they become entirely (or effectively) constrained by the truck performance. Exhibit 10 illustrates this in the case of 30% trucks on a 6% upgrade. A method was developed to predict the automobile speed as a function of the scenario condi- tions. Examination of the individual scenario runs suggested the following trends: • The automobile speed is always high when the V/C ratio is low. Often, the speed at zero flow is the auto-only free-flow speed, but not always. • When the truck percentage is low as on downgrades and on the level, the automobiles are able to follow a speed curve that closely matches the all-automobile condition. • When the truck percentage is high and on upgrades, the automobile speeds decline to the truck speed as the V/C ratio increases. • The pattern of decrease follows that of a logistics curve (as is commonly used in logit models). As the V/C ratio increases, the automobile speeds decline slowly at first, then more rapidly, and then more slowly as the truck speed is reached. Hence, the automobile speed asymptoti- cally approaches limiting speeds for both low and high V/C ratios. This pattern can be seen in Exhibit 10. • There is variation in the range of V/C ratios (or flow rates) over which this decline occurs. It is a wide range (say from V/C = 0.1 to V/C = 0.9) when the grade is slight, the truck percentage is low, and the weight-to-horsepower ratio is low (e.g., a 2% grade, 10% trucks, and a truck with only 50 lb/hp. It is narrow (say, from V/C = 0.1 to V/C = 0.2) when the grade is steep, the truck percentage is high, and the weight-to-horsepower ratio is high (e.g., a 6% grade, 30% trucks, and a truck with 200 lb/hp). Exhibit 59 shows the condition for a 6% grade, 30% trucks, and 150 lb/hp.

92 incorporating truck Analysis into the Highway capacity Manual A simple logistics function is used to predict these automobile speed trends: 1 Equation 39s s s s e e a to ao to v v V v v V m m ( )= + − +       −β − ∆ −β − ∆ where sa = the automobile speed at flow rate v; sao = the automobile-only speed that would arise at flow rate v (taking into account the PCE value); sto = the truck-only speed that would arise at flow rate v (again taking into account the PCE values for the mixed flow case and the all-truck case); vm = the flow rate at which the automobile speed has accomplished half of its transition from sao to sto, DV = the range of flow rates over which the transition occurs; and b = a calibration coefficient that ensures the following holds true: 2 5 2 5 Equation 40 v V V and v V V m m −β − ∆ ∆ = − β + ∆ ∆ = − This ensures that the logit term within the large parentheses is approximately equal to 1 when v = vm – DV/2 and equal to 0 when v = vm + DV/2. In Exhibit 60, vm is approximately 250 veh/hr/lane and DV is about 500 (from 100 to 600). 0 10 20 30 40 50 60 70 80 0 500 1000 1500 2000 2500 Sp ee d (m ph ) Flow Rate per Lane (veh/hr) Speed-Flow Relationship Auto Only Scenario Autos Trucks Truck Only Auto Model vm = 250 Note: +6% grade for a mixed traffic stream involving 30% Class 9 Trucks with 150 lbs/hp. Exhibit 60. A model for estimating the automobile speed relationships on a +6% grade.

Prediction of Freeway truck Speeds 93 Grade >= 1%? Grade < 4% AND TrkType-9 AND Wt/Hp=50 %Trks >= 30% Yes No Yes vm = 150 vm = 1000 - 0.3475∗%Trk - (1.226 + 0.07∗%Trk)∗Wt/Hp + 21.75∗TrkType Yes vm = 200 vm = 1050 No No Exhibit 61. Logic for determining vm values. Exhibit 60 shows the automobile speed function that has been fitted to the automobile speed trends in the exhibit. The smooth line represents the automobile speed estimated by Equation 39 and appropriate values of vm, DV, and b. A two-step process was involved in developing a procedure to create equations that would estimate vm, DV, and b for a given situation. First, for each of the 520 scenarios, estimates of vm and DV were obtained through statistical analysis. Then, the resulting estimates were placed in a database and curve-fitting techniques were used to develop estimates of the three parameters. Predicting vm proved to be most challenging. The logic shown in Exhibit 61 works well. Clearly, this is not the end result of a formal regression analysis; rather, it is derived from careful examination of the trends exhibited in vm in response to changes in the other variables involved. Also, to some degree, it reflects the vagaries of the simulation environment. It was clear from examining the initial results that for grades below 1% (the first seven condi- tions), the vm value is high if the truck percentage is 30% or less and low if it is greater. It was also clear that for grades of 1% or greater, the vm value is highest when the percent trucks is lowest and it declines as the percent trucks increases and that it falls sharply in response to increases in the weight-to-horsepower ratio. This logic is reflected in the “if–then” logic presented above, including the equation that predicts vm for grades of 1% and greater. A more detailed examination of the trends for grades of 1% or more revealed: • The patterns of predicted and observed vm clearly matched, especially for steeper grades. • For the less-steep grades, it was also clear that the stochasticity in the simulation process makes the trends less deterministic in appearance. Thus, the strength in the model presented in the “if–then” logic is that it converges to the simulation results observed as the grades increase in severity, which is a very good property for the model to have. The estimation of values for DV and b is far more straightforward. In this instance, a slight variation of Equation 39 is used: 1 Equation 41s s s s e e a to ao to v v v v m m ( )= + − +       − θ − θ where q reflects the combined effects of DV and b. The result is 0.2510 0.7964 Equation 42 32.68 2v Rmθ = ∗ =

94 incorporating truck Analysis into the Highway capacity Manual The t statistic, shown below the coefficient for vm, being significantly greater than 1.97, demonstrates that the effect is statistically significant. In summary, the prediction procedure for truck speed is relatively simple. Moreover, it pre- dicts defensible results not only for the density that will arise in a given situation, but both truck and car speeds. The procedure works whether the truck flows are of a single type or mixed. It is known to work for grades from –6% to +6% and for truck percentages up to 50%. 8.9 Freeway Truck and Automobile Speed Model Case Study To test the new procedures, a case study was conducted. To generate “field data” for the case study, a VISSIM simulation model of the study section was created based on data provided by New York State (NYS) DOT. The selected real-world case study site was a 3.5-mile section of New York State Route 7 just north of Albany (see Exhibit 62). This same site was used in the Highway Capacity Manual Appli- cations Guidebook (Kittelson et al., 2003). A VISSIM model (PTV Group, n.d.) was developed and calibrated for the case study site to generate the “observed” data against which the case study results could be compared. The facility is a freeway running between I-87 on the west to I-787 on the east. The percentage of trucks is about 6%. The free-flow speed is 55 mph. The test facility has the following grades: • Westbound: � +1.92% for 3,769 ft.; � +4.80% for 1,854 ft.; � +1.00% for 4,839 ft.; � +4.00% for 1,919 ft.; Source: Kittelson and Associates. Exhibit 62. New York State route 7 freeway test site.

Prediction of Freeway truck Speeds 95 � –0.80% for 1,192 ft.; and � –2.10% for 5,299 ft. • Eastbound: opposite grades for same lengths. A vertical profile of the facility is shown in Exhibit 63. The facility has two lanes eastbound and three westbound. The third westbound lane was originally intended to be a truck climbing lane, but today it is used for all traffic. The a.m. traffic is heavier eastbound; the p.m. traffic is heavier westbound. Eastbound, vehicles enter the study section at about 40–50 mph, accelerate, and then continue eastward to the I-787 interchange. Westbound, vehicles enter at 30–50 mph coming either from the bridge across the Hudson River or one of the two I-787 ramps. Of the two ramps, the loop ramp (northbound to westbound) has the most traffic; the right-hand ramp (southbound to westbound) has very little traffic. Typi- cally, there are no queues in either direction in the a.m. peak, but in the p.m. peak, there is often a queue westbound that extends half the length of the facility. Most of the westbound traffic wants to exit via the single-lane right-hand ramp at the western end; traffic from about 2.5 lanes is converging on a single-lane exit. The facility is instrumented with speed traps about at the midpoint and video cameras at either end. Data from the speed traps is not archived. However, NYSDOT periodically does short counts including truck classifications. The a.m. and p.m. peaks for the existing conditions were studied for the test site as well as hypothetical p.m. peaks that involved 15% and 30% trucks as well as a change to the geometry at the western end so that a bottleneck would not be created. (The two-lane exit eliminates the queuing problem.) The higher truck percentages are of interest because of the new methodology. A summary of the simulated and observed network performance for these conditions is shown in Exhibit 64. The data for the real-world a.m. and p.m. peak conditions are shown in the first four columns. The performance for the hypothetical situations involving 15% and 30% trucks are shown in the right-hand four columns. The simulation model produces results consistent with observed performance. Most impor- tantly, it predicts a westbound queue in the p.m. peak that extends about half-way back to the I-787 interchange. This queuing condition is very common. The proposed analysis procedure (labeled “New HCM Model” in Exhibit 65) was applied, and its predictions were compared with the performance predictions provided by the VISSIM simulation model. Both directions were studied in detail, but the main focus in this report is on the westbound direction because it has the significant upgrades. The LOS predictions westbound were checked at the end of each section. The location reported here for the eastbound direction is at the end of the 2.1% grade. 1 3 2 45 Distance from Eastern End (mi) R el at iv e El ev at io n (ft) West (Direction) East 7 1.92% 4.80% 0123 1.00% 4.00%-0.80% -2.10% Assessment points and grades 0 200 300 100 6 -2.10% Exhibit 63. vertical profile of the NY State route 7 freeway test site.

96 incorporating truck Analysis into the Highway capacity Manual As can be seen from Exhibit 65, the proposed analysis procedure (“New HCM”) predicts auto mobile and truck speeds that are generally consistent (within 6%) with those from the VISSIM model. 8.10 Freeway Truck Travel Time Reliability Existing truck travel time reliability for one or more selected segments of a freeway can be obtained from the National Performance Management Research Data Set (NPMRDS) for the National Highway System (NHS) (FHWA, 2013, June 26). Resources did not permit the development of a model for predicting truck travel time reliability. However, the SHRP2-L08 methodology (Kittelson and Vandehey, 2012) can be used to estimate mixed flow travel time reliability. Until such time as better methods become available, the SHRP2-L08 results might be used as a proxy for truck travel time reliability (Kittelson, 2012). 8.10.1 Data on Existing Truck Reliability—NPMRDS NPMRDS contains archived data on truck travel times by highway segment on the NHS, by 5-min-long time periods of the day. It is a vehicle-probe based data set. Separate travel times are reported for FHWA Vehicle Classes 7 and 8 (labeled “trucks” in the database); all other vehicle East West East West East West East West Overall Flow Rate (vph) 2902 2228 2354 2972 2354 3024 2354 3024 Peak Hour Factor 0.83 0.81 0.89 0.92 0.89 0.92 0.89 0.92 Truck Percentages 9.18% 5.64% 6.59% 5.14% 15.00% 15.00% 30.00% 30.00% Class 4 0.93% 0.56% 0.94% 0.71% 1.53% 1.49% 4.29% 4.13% Class 5 3.91% 2.47% 2.35% 2.36% 6.39% 6.57% 10.71% 13.76% Class 6 1.02% 0.56% 0.71% 0.38% 1.67% 1.49% 3.21% 2.20% Class 7 0.25% 0.14% 0.14% 0.09% 0.42% 0.37% 0.64% 0.55% Class 8 0.93% 0.70% 1.51% 0.66% 1.53% 1.86% 6.86% 3.85% Class 9 1.70% 0.93% 0.52% 0.75% 2.78% 2.48% 2.36% 4.40% Class 10 0.42% 0.19% 0.24% 0.14% 0.69% 0.50% 1.07% 0.83% Class 11 0.00% 0.05% 0.05% 0.00% 0.00% 0.12% 0.21% 0.00% Class 12 0.00% 0.00% 0.05% 0.00% 0.00% 0.00% 0.21% 0.00% Class 13 0.00% 0.05% 0.09% 0.05% 0.00% 0.12% 0.43% 0.28% Vehicle-Miles (8 hrs) Autos 34965 55077 24659 73508 22725 68107 19266 56370 Trucks 4397 3291 2455 4124 5332 11809 10917 23391 All 39362 58369 27115 77632 28057 79915 30183 79761 Vehicle-Hours (8 hrs) Autos 499 812 350 3853 323 1037 274 986 Trucks 64 51 35 232 77 182 157 408 All 563 864 386 4085 400 1220 432 1395 Avg Speed (mph) Autos 70.1 67.8 70.4 19.1 70.3 65.7 70.3 57.2 Trucks 68.5 64.2 69.3 17.8 69.3 64.7 69.5 57.3 All 69.9 67.6 70.3 19.0 70.1 65.5 69.9 57.2 Data Item AM Peak PM Peak Base Case PM Peak 30% Trucks15% Trucks PM Peak Exhibit 64. Simulated actual and hypothetical results for higher truck percentages for NY State route 7 site.

Prediction of Freeway truck Speeds 97 classes (labeled “passenger vehicles”); and all vehicles combined. The number of vehicles and the percent of trucks in the data are not reported. Historic data is available for the Interstate freeway system back to October 2011. For all other highways on the NHS, data is available back to July 2013. A moderate amount of GIS database processing is required to make effective use of the data once downloaded. 8.10.2 Predicting Truck Reliability on Freeways The SHRP2-L08 methodology can be used to predict mixed flow travel time reliability for a freeway facility. It is sensitive to recurring peak-period demands, day-to-day demand variability, the frequency and severity of bad weather, crash frequency, and the scheduling of work zones on the freeway facility. The methodology can be used to predict various travel time indices (TTIs), of which, the 50th-percentile and the 95th-percentile TTIs are required. EBD Segment Length (ft) 3769 1854 4839 1919 1192 2405 3894 4510 Grade (%) 1.92% 4.80% 1.00% 4.00% -0.80% -2.1%(6) -2.1%(7) 2.10% Observed Performance Flow Rate (vphpl) 991 991 991 991 991 991 1486 1177 Auto Speed (mph) 70 68 70 68 70 70 70 70 Truck Speed (mph) 67 62 68 64 66 70 66 68 Density (veh/mi/ln) 14 16 17 17 17 17 10 8 New HCM Model PCE 1.52 1.89 1.40 1.79 1.16 1.00 1.00 1.54 Auto Speed (mph) 68.4 66.0 70.0 68.2 70.0 70.0 66.5 67.4 Truck Speed (mph) 65.7 59.5 69.9 65.3 69.9 69.9 65.6 65.3 Density (veh/mi/ln) 13.2 13.7 14.4 13.2 12.9 12.9 21.1 16.3 Observed Performance Flow Rate (vphpl) Auto Speed (mph) 69.3 68.5 69.1 68.6 68.8 69.1 69.2 69.4 Truck Speed (mph) 67.7 62.1 67.8 63.8 65.5 69.4 66.7 67.1 Density (veh/mi/ln) 16.3 16.6 16.3 16.5 16.4 16.2 7.5 6.9 New HCM Model PCE 1.52 1.89 1.40 1.79 1.16 1.00 1.00 1.54 Auto Speed (mph) 68.3 65.3 69.9 67.9 70.0 70.0 66.5 67.0 Truck Speed (mph) 65.6 59.2 69.8 65.0 69.9 69.9 65.6 64.8 Density (veh/mi/ln) 13.3 14.0 12.9 13.3 12.9 12.9 21.1 16.5 Observed Performance Flow Rate (vphpl) Auto Speed (mph) 69.1 67.8 68.9 67.8 66.2 62.3 68.9 69.3 Truck Speed (mph) 67.4 61.5 67.5 63.1 63.0 62.1 66.0 66.9 Density (veh/mi/ln) 16.4 17.0 16.4 16.9 17.6 21.3 7.4 7.8 New HCM Model PCE 1.52 1.89 1.40 1.79 1.16 1.00 1.00 1.54 Auto Speed (mph) 68.0 63.7 69.8 67.1 69.8 69.9 65.6 66.1 Truck Speed (mph) 65.2 58.1 69.6 64.2 69.8 69.9 65.6 63.8 Density (veh/mi/ln) 13.4 14.5 12.9 13.6 12.9 12.9 21.4 16.8 PM Actual Condi”ons PM 15% Trucks Westbound Assessment Loca”on PM 30% Trucks Data Item Exhibit 65. New HCM procedure versus simulation model results for NY State route 7 case study network.

98 incorporating truck Analysis into the Highway capacity Manual The median (50th-) and 95th-percentile TTIs predicted using the SHRP2-L08 method are entered into the following two equations, which are solved for the values of the parameters k and c: 50% 2 Equation 43 1 1TTI kc( ) ( )= − 95% 20 Equation 44 1 1TTI kc( ) ( )= − The agency’s target TTI threshold for on-time arrival (1.33 is recommended for freeways) is then entered into the following Burr distribution equation (along with the previously deter- mined values of k and c) to obtain the probability P of on-time arrival for mixed flow traffic on the facility: 1 1 Equation 451.33P TTITTI c k( )= − +( )= − Until a better method becomes available, the mixed flow traffic reliability (probability of on- time arrival) is assumed to be the same as for trucks. If the analyst wishes a more precise forecast, the analyst might use the SHRP2-L08 method to predict existing reliability conditions and compare that estimate with the value obtained from the NPMRDS. The ratio of the observed truck value to the estimated mixed flow value might then be used to adjust the forecasted mixed flow reliability to obtain a calibrated prediction of truck travel time reliability. However, this approach has not been tested or validated in this research.