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Chapter 15: Weaving, Merging, and Diverging Movements on Freeways and Multilane Highways Chapter objectives: By the end of this chapter the student will be able to: Describe weaving configurations Describe merge and diverge configurations Become familiar with the steps of conducting a weaving area analysis Become familiar with the steps of conducting a merge/diverge area analysis Conduct these analyses manually and by HCS2010 Discuss the limitations of these models Chapter 15 1 I-215 and 21st South, SLC Chapter 15 2 15.1 Turbulence areas on freeways and multilane highways Turbulence as characterized by the additional lane-changing these maneuvers cause: i.e. one movement must make at least one lane change. Other elements: the need for greater vigilance on the part of the driver, more frequent changes in speed, and average speeds that may be somewhat lower than on similar basic sections. The maximum length over which weaving movements are defined varies (2,500ft in HCM 2010). Beyond that, analyze as separate ramps. The maximum length over which merging and diverging movements are defined is 1,500 ft. Chapter 15 3 15.2 Level-of-service criteria Just like the basic section, density is used as MOE. For merge and diverge areas, densities reflect the “merge/diverge influence area which consists of lanes 1 and 2 (right & next-to-right lane) and the acceleration or deceleration lane 1,500 ft upstream of a diverge or downstream of a merge. For weaving areas, the density reflects an average for all vehicles across all lanes of the segment between the entry and exit points of the segment. Chapter 15 4 Compare the upper boundaries of the LOSs between Basic Freeway Segments and Weaving/Merging/Diverging Segments. C-D Roadways = CollectorDistributor Roadways Chapter 15 LOS Basic Fwy Segment 5 15.3 A common point: converting demand volumes to flow rates Both procedures rely on algorithms stated in terms of demand flow rates in passenger car units for base conditions. This time as a group, not by lane. Make sure you read the introductory section of 15.4 for the history of the weaving analysis method. Vi vi PHF * f HV * f p We have seen the definitions of these terms in Chapter 14. Heavy vehicle and driver population factors are the same ones used for basic freeway and multilane highway segments in Chapter 14. Chapter 15 6 15.4 Weaving Segments: Basic characteristics and Variables 15.4.1 Flows in a weaving area vw vw1 vw 2 vnw vo1 vo 2 Weaving flows (pc/hr) vs. Nonweaving flows (pc/hr) Subscript 1 means the larger flow; subscript 2 means the smaller flow of the two. v vw vnw VR vw v R vw 2 vw Chapter 15 VR = Volume Ratio R = Weaving Ratio 7 15.4.2 Critical geometric variables Three influential variables Lane configuration Length of the weaving area, ft Width (number of lanes) in the weaving area Lane configuration classifications One-sided vs. two-sided weaving segments Ramp-weave vs. major weaving segments One-sided vs. two-sided? A one-sided weaving segment is one in which no weaving maneuver requires more than two lane changes. A two-sided weaving segment is one in which a one-lane on-ramp on one side of the facility is closely followed by a one-lane off-ramp on the other side of the facility. Chapter 15 8 Numerical characteristics of two-sided weaving configurations (p.322) • In two-sided configurations, ramp-to-facility and facility-toramp movements are NOT the weaving flows (they are merge and diverge flows). • Ramp-to-ramp vehicles weave across facility-to-facility vehicles. But facility-to-facility (meaning freeway to freeway) vehicles do not have to make lanes changes. • So, only the ramp-to-ramp vehicles are considered to be “weaving.” • In (d), LCRR = 3 and NWV = 0; in (c). LCRR = 2 and NWV = 0. Chapter 15 9 Numerical characteristics of one-sided weaving configurations (p.323) LCRF = Min # of lane changes that a R-to-F weaving vehicle must make to complete the movement. LCRF = LCFR = 1, NWV = 2 LCFR = Min # of lane changes that a F-to-R weaving vehicle must make to complete the movement. LCRF = 1, LCFR = 0, NWV = 2 LCRF = 0 or 1, LCFR = 1, NWV = 3 NWV = # of lanes from which a weaving maneuver may be completed with one lane change, or no lane change. “Lane balance”: When # of exit lanes = # of entry lanes + 1 Chapter 15 10 Length of the weaving area (p.324) Short length (ft) Base length (ft) LS = 0.77*LB Width of a weaving area (p.325) The total width of the weaving area is measured as the total number of lanes available for all flows, N. In the above figure, N = 4. Chapter 15 11 15.5 Computational procedures for weaving area analysis Chapter 15 See Fig 15.7. p.326 12 Chapter 15 13 Fig. 15.8: Weaving Variables Defined for One-Sided Weaving Segments Chapter 15 14 Fig. 15.8: Weaving Variables Defined for One-Sided Weaving Segments (continued) Nwv Chapter 15 15 Fig. 15.8: Weaving Variables Defined for One-Sided Weaving Segments (continued) Chapter 15 16 Equations (There are 23 of them! We will learn as we work through examples.) vi Vi PHF f HV f p Eq. 15-1 In between 20 equations exist in HCM2010. S vnw vw vnw vw S nw S w Eq. 15-22 vnw vw vnw vw S nw S w S v D N S Eq. 15-23 Chapter 15 17 Example 15.1 Analysis of a ramp-weave area (p.342) We will walk through this example to learn how the weaving analysis is done. (15.8) Example 15.2 Analysis of a major weaving area Chapter 15 18 15.6 Basic Characteristics of Merge and Diverge Segment Analysis The analysis procedures focus on the merge or diverge influence area that encompasses lanes 1 and 2 (shoulder and adjacent) freeway lanes and the acceleration lane for a distance of 1,500 ft upstream of a diverge or 1,500 downstream of a merge area. Merge area: v12 vF PFM Diverge area: v12 vR vF vR PFD Chapter 15 19 Measuring the Length of Acceleration and Deceleration Lanes Chapter 15 20 15.7 Computational Procedures for Merge and Diverge Segments 1. Specify all traffic and roadway data for the junction to be analyzed: peak-hour demands, PHF, traffic composition, driver population, and geometric details of the site, including the free-flow speed for the facility and for the ramp. Convert all demand volumes to flow rates in pc/h under equivalent base conditions using Eq. 15-1. 2. Determine the demand flow in lanes 1 and 2 of the facility immediately upstream of the merge (V12) or diverge junction (V12) using the appropriate algorithm as specified. Table 15.3 (PFM) & Table 15.4 (PFD). Need to check whether the subject ramp is isolated or not first. 3. Determine whether the demand flow exceeds the capacity of any critical element of the junction. (Table 15.5) Where demand exceeds capacity, level of service F is assigned and the analysis is complete. (See the right column of page 339+.) 4. If operation is determined to be stable, determine the density (Eq. 15-40 for merge and Eq. 15-41 for diverge areas) in the ramp influence area. 5. Determine the speed of all vehicles within the ramp influence area and across all facility lanes as secondary measures of performance. Table 15.6 and 15.7. Chapter 15 21 Figure 15.12 Flow Chart for Analysis of Ramp-Facility Junctions Chapter 15 22 Figure 15.12 Flow Chart for Analysis of Ramp-Facility Junctions (continued) Chapter 15 23 Equations for Merge Eq. 15-25 is for an isolated ramp. v12 vF PFM Chapter 15 24 Isolated on-ramp or not? for upstream off ramp (eq. 15-30) LEQ 0.214vF vR 0.444La 52.32RFFS 2,403 If Lup ≥ LEQ, the subject ramp may be considered to be isolated. Use eq. 15-25. Otherwise, use eq. 15-26. for downstream off ramp (eq. 15-31) LEQ vd 0.1096 0.000107La If Ldn ≥ LEQ, the subject ramp may be considered to be isolated. Use eq. 15-25. Otherwise, use eq. 15-27. Chapter 15 25 Equations for Diverge v12 vR vF vR PFD Chapter 15 Eq. 15-33 is for an isolated ramp. 26 Isolated off-ramp or not? for upstream on ramp (eq. 15-36) LEQ vu 0.071 0.000023vF 0.000076vR If Lup ≥ LEQ, the subject ramp may be considered to be isolated. Use eq. 15-33. Otherwise, use eq. 15-34. for downstream off ramp (eq. 15-37) LEQ vd 1.15 0.000032vF 0.000369vR If Ldn ≥ LEQ, the subject ramp may be considered to be isolated. Use eq. 15-33. Otherwise, use eq. 15-35. Chapter 15 27 Checking the reasonableness of lane distribution predictions, p.339 The estimated lane distribution must meet these two conditions (to be within the data availability for the regression models): 1. Average flow rate in the outer lanes may not exceed 2,700 pc/h/ln. If not met, adjust as shown below. No = # of outer lanes. v12 v F 2700No 2. Average flow rate in the outer lanes may not be more than 1.5 times the average flow rate in lanes 1 and 2. If not met, adjust as shown below. 1.5 1 2 vF For _ N 1 : 1.75 o For _ N o 1 : v12 2 1.75 1.5 2 2 vF For _ N 2 : 2.50 o For _ N o 2 : v12 2 2.50 1.5 N 0 2 2vF For _ N 2 : Chapter 15 28 o For _ N o 2 : v12 2 1.5 N 2 0 15.7.3 Capacity Considerations Chapter 15 29 15.7.4 Determining Density and LOS in the Ramp Influence Area Merge influence area DR 5.475 0.00734v R 0.0078v12 0.00627La Diverge influence area DR 4.252 0.0086v12 0.009Ld Once Density is calculated, average speeds on ramp influence area, outer lanes, and all lanes will be estimated (section 15.7.5). Chapter 15 30 15.7.5 Determining Expected Speed Measures (Make changes to the typos.) Chapter 15 31 Example 15-3 Analysis of an isolated on-ramp We will walk through this example to learn how an LOS analysis is done step by step. Chapter 15 32 Example 15-4 Analysis of a sequence of freeway ramps We will walk through this example to learn how a sequence of freeway ramps (mix of merging and diverging areas). Read Appendix II for Special Cases in Merge and diverge Analysis. We do not cover this in this class but keep in mind this topic is discussed in this book as well as in HCM so that you know what to do when you encounter these cases. Chapter 15 33