CHAPTER 24 FREEWAY WEAVING CONTENTS I. INTRODUCTION... 24-1 Scope of the Methodology...24-1 Limitations of the Methodology...24-1 II. METHODOLOGY...24-1 LOS...24-2 Weaing Segment Parameters...24-3 Determining Flow Rates... 24-3 Weaing Segment Diagram... 24-3 Weaing Segment Configuration...24-5 Determining Weaing and Nonweaing Speeds... 24-5 Determining Weaing Intensity... 24-7 Constants for Computing Weaing Intensity Factors... 24-7 Determining Type of Operation...24-7 Determining Weaing Segment Speed...24-8 Determining Density... 24-9 Determining Weaing Segment Capacity... 24-9 Multiple Weaing Segments... 24-19 Collector-Distributor Roadways...24-19 III. APPLICATIONS...24-19 Computational Steps...24-20 Planning Applications... 24-20 Analysis Tools...24-20 IV. EXAMPLE PROBLEMS...24-22 Example Problem 1...24-23 Example Problem 2...24-26 Example Problem 3...24-29 Example Problem 4...24-32 Example Problem 5...24-37 V. REFERENCES...24-39 APPENDIX A. WORKSHEET... 24-39 Freeway Weaing Worksheet EXHIBITS Exhibit 24-1. Freeway Weaing Methodology...24-2 Exhibit 24-2. LOS Criteria for Weaing Segments... 24-3 Exhibit 24-3. Parameters Affecting Weaing Segment Operation... 24-4 Exhibit 24-4. Construction and Use of Weaing Diagrams... 24-4 Exhibit 24-5. Determining Configuration Type...24-5 Exhibit 24-6. Constants for Computation of Weaing Intensity Factors... 24-6 Exhibit 24-7. Criteria for Unconstrained Versus Constrained Operation of Weaing Segments... 24-8 Exhibit 24-8. Capacity for Various Weaing Segments... 24-10 Exhibit 24-9. Freeway Weaing Worksheet...24-21 24-i Chapter 24 - Freeway Weaing
I. INTRODUCTION SCOPE OF THE METHODOLOGY Detailed procedures for the analysis of operations in freeway weaing segments are contained in this chapter. Guidelines are also gien for the application of these procedures to weaing segments on multilane highways. A discussion of basic concepts and definitions is gien in Chapter 13, Freeway Concepts. This section contains a complete discussion and definition of unconstrained and constrained operations in weaing segments and of the three types of weaing configuration: Type A, Type B, and Type C. An understanding of these concepts and definitions is critical to the correct application of the methodology of this chapter and to adequately interpret the results of analysis. The procedures of this chapter hae been assembled from a ariety of sources and studies. The form of the speed prediction algorithm was deeloped as a result of a research project in the 1980s (1). Concepts of configuration type and type of operation were deeloped in an earlier study (2) in the 1970s and updated in another study of freeway capacity procedures published in 1979 (3). The final weaing procedures for the 1997 HCM are also documented (4). Seeral other documents describe the deelopment of weaing segment analysis procedures (5 7). Background and concepts for this chapter are gien in Chapter 13, Freeway Concepts LIMITATIONS OF THE METHODOLOGY The methodology in this chapter does not specifically address the following subjects (without modifications by the analyst): Special lanes, such as high-occupancy ehicle lanes, in the weaing segment; Ramp metering on entrance ramps forming part of the weaing segment; Specific operating conditions when oersaturated conditions occur; Effects of speed limits or enforcement practices on weaing segment operations; Effects of intelligent transportation system technologies on weaing segment operations; Weaing segments on collector-distributor roadways; Weaing segments on urban streets; and Multiple weaing segments. The last subject, which has been treated in preious editions of this manual, has been deleted. Multiple weaing segments must now be diided into appropriate merge, dierge, and simple weaing segments for analysis. II. METHODOLOGY The methodology presented in this chapter has fie distinct components: Models predicting the space mean speed (aerage running speed) of weaing and nonweaing ehicles in the weaing segment (models are specified for each configuration type and for unconstrained and constrained operations); Models describing the proportional use of lanes by weaing and nonweaing ehicles, used to determine whether operations are unconstrained or constrained; An algorithm that conerts predicted speeds to an aerage density within the weaing segment; Definition of leel-of-serice (LOS) criteria based on density within the weaing segment; and A model for the determination of the capacity of a weaing segment. Exhibit 24-1 summarizes the methodology for freeway weaing segments. 24-1 Chapter 24 - Freeway Weaing Introduction
EXHIBIT 24-1. FREEWAY WEAVING METHODOLOGY Input - Geometric data - Weaing and nonweaing olumes - Free-flow speed of freeway segment before and after the weaing segment Volume Adjustment - Peak-hour factor - Heay ehicles - Drier population Compute flow rates Establish weaing segment configuration type Compute unconstrained weaing and nonweaing speeds Check for constrained-flow operation If unconstrained If constrained Compute constrained weaing and nonweaing speeds Compute aerage space mean speed within the weaing segment Compute density within the weaing segment Determine LOS LOS The LOS of the weaing segment is determined by comparing the computed density with the criteria of Exhibit 24-2. A single LOS is used to characterize total flow in the weaing segment, although it is recognized that in some situations (particularly in cases of constrained operations) nonweaing ehicles may achiee higher-quality operations than weaing ehicles. Chapter 24 - Freeway Weaing 24-2 Methodology
EXHIBIT 24-2. LOS CRITERIA FOR WEAVING SEGMENTS Density (pc/mi/ln) LOS Freeway Weaing Segment Multilane and Collector-Distributor Weaing Segments A 10.0 12.0 B > 10.0 20.0 > 12.0 24.0 C > 20.0 28.0 > 24.0 32.0 D > 28.0 35.0 > 32.0 36.0 E > 35.0 43.0 > 36.0 40.0 F > 43.0 > 40.0 In general, these criteria allow for slightly higher densities at any gien leel-ofserice threshold than on a comparable basic freeway segment or multilane highway segment. This follows the philosophy that driers expect and will accept higher densities on weaing segments than on basic freeway or multilane highway segments. The LOS E/F boundary does not follow this approach. Rather, it reflects densities that are somewhat less than those identified for basic freeway or multilane highway segments. Because of the additional turbulence on weaing segments, it is belieed that breakdown occurs at somewhat lower densities than on basic freeway and multilane highway segments. WEAVING SEGMENT PARAMETERS Exhibit 24-3 illustrates and defines the ariables that are used in the analysis of weaing segments. These ariables are used in the algorithms that make up the methodology. All existing or projected roadway and traffic conditions must be specified when applying the methodology. Roadway conditions include length of the segment, number of lanes, type of configuration under study, and type of terrain or grade conditions. If freeway free-flow speed (FFS) is not known, the characteristics of the basic freeway segment or multilane highway must be specified to allow its determination using the algorithms of Chapter 21 or 23. DETERMINING FLOW RATES All of the models and equations in this chapter are based on peak 15-min flow rates in equialent passenger cars per hour. Thus, hourly olumes must be conerted to this basis using Equation 24-1. where = V PHF * f HV * f p (24-1) = peak 15-min flow rate in an hour (pc/h), V = hourly olume (eh/h), f HV = heay-ehicle adjustment factor (from basic freeway segment or multilane highway methodology), and f p = drier population factor (from basic freeway segment or multilane highway methodology). If 15-min flow rates are specified initially, set the PHF to 1.00 before applying this conersion WEAVING SEGMENT DIAGRAM After olumes hae been conerted to flow rates, it is useful to construct a weaing diagram of the type shown in Exhibit 24-4. All flows are shown as flow rates in equialent passenger cars per hour, and critical analysis ariables are identified and placed on the diagram. The diagram may now be used as a reference for all input information required in applying the methodology. 24-3 Chapter 24 - Freeway Weaing Methodology
EXHIBIT 24-3. PARAMETERS AFFECTING WEAVING SEGMENT OPERATION o1 or o2 w1 or w2 Symbol L N N w N w (max) w1 or w2 o1 or o2 Definition Length of weaing segment (ft) Total number of lanes in the weaing segment Number of lanes to be used by weaing ehicles if unconstrained operation is to be achieed Maximum number of lanes that can be used by weaing ehicles for a gien configuration Number of lanes used by nonweaing ehicles Total flow rate in the weaing segment (pc/h) Larger of the two outer, or nonweaing, flow rates in the weaing segment (pc/h) Smaller of the two outer, or nonweaing, flow rates in the weaing segment (pc/h) Larger of the two weaing flow rates in the weaing segment (pc/h) Smaller of the two weaing flow rates in the weaing segment (pc/h) N nw o1 o2 w1 w2 w Total weaing flow rate in the weaing segment (pc/h) ( w = w1 + w2 ) nw Total nonweaing flow rate in the weaing segment (pc/h) ( nw = o1 + o2 ) VR R S w S nw S D W w W nw Volume ratio; the ratio of weaing flow rate to total flow rate in the weaing segment (VR = w /) Weaing ratio; the ratio of the smaller weaing flow rate to total weaing flow rate (R = w2 / w ) Speed of weaing ehicles in the weaing segment (mi/h) Speed of nonweaing ehicles in the weaing segment (mi/h) Speed of all ehicles in the weaing segment (mi/h) Density of all ehicles in the weaing segment (pc/mi/ln) Weaing intensity factor for prediction of weaing speed Weaing intensity factor for prediction of nonweaing speed A B EXHIBIT 24-4. CONSTRUCTION AND USE OF WEAVING DIAGRAMS 1500 500 300 400 Segment and flows C D A 300 1500 500 C B 400 Weaing diagram D Chapter 24 - Freeway Weaing 24-4 Methodology
WEAVING SEGMENT CONFIGURATION Weaing segment configuration is based on the number of lane changes required of each weaing moement. A complete discussion of this concept is found in Chapter 13. Exhibit 24-5 may be used to establish configuration type. See Chapter 13 for diagrams and concepts of the three weaing segment configurations EXHIBIT 24-5. DETERMINING CONFIGURATION TYPE Number of Lane Changes Required by Moement w2 Number of Lane Changes Required by Moement w1 0 1 2 0 Type B Type B Type C 1 Type B Type A N/A 2 Type C N/A N/A Note: N/A = not applicable; configuration is not feasible. The three types of geometric configurations are defined as follows: Type A Weaing ehicles in both directions must make one lane change to successfully complete a weaing maneuer. Type B Weaing ehicles in one direction may complete a weaing maneuer without making a lane change, whereas other ehicles in the weaing segment must make one lane change to successfully complete a weaing maneuer. Type C Weaing ehicles in one direction may complete a weaing maneuer without making a lane change, whereas other ehicles in the weaing segment must make two or more lane changes to successfully complete a weaing maneuer. DETERMINING WEAVING AND NONWEAVING SPEEDS The heart of the weaing segment analysis procedure is the prediction of space mean speeds of weaing and nonweaing flows within the weaing segment. They are predicted separately because under some conditions they can be quite dissimilar, and the analyst must be aware of this. The algorithm for prediction of aerage weaing and nonweaing speeds may be generally stated by Equation 24-2. S i = S min + S max S min 1 +W i (24-2) where S i = aerage speed of weaing (i = w) or nonweaing (i = nw) ehicles (mi/h), S min = minimum speed expected in a weaing segment (mi/h), S max = maximum speed expected in a weaing segment (mi/h), and W i = weaing intensity factor for weaing (i = w) and nonweaing (i = nw) flows. For the purposes of these procedures, the minimum speed, S min, is set at 15 mi/h. The maximum speed, S max, is taken to be the aerage free-flow speed of the freeway segments entering and leaing the weaing segment plus 5 mi/h. The addition of 5 mi/h to the free-flow speed adjusts for the tendency of the algorithm to underpredict high speeds. Setting the minimum and maximum speeds in this way constrains the algorithm to a reasonable prediction range. With these assumptions incorporated, the speed prediction is gien by Equation 24-3. S i =15 + S FF 10 (24-3) 1 +W i 24-5 Chapter 24 - Freeway Weaing Methodology
Attributes of weaing segments captured by the model where S FF is the aerage free-flow speed of the freeway segments entering and leaing the weaing segment (mi/h). Initial estimates of speed are always based on the assumption of unconstrained operation. This assumption is later tested, and speeds are recomputed if operations turn out to be constrained. The combination of Equations 24-2 and 24-3 yields sensitiities that are consistent with obsered operations of weaing segments. As the length of the weaing segment increases, speeds also increase, and the intensity of lane changing declines. As the proportion of weaing ehicles in total flow (VR) increases, speeds decrease, reflecting the increased turbulence caused by higher proportions of weaing ehicles in the traffic stream. As aerage total flow per lane (/N) increases, speeds decrease, reflecting more intense demand. Constrained operations yield lower weaing speeds and higher nonweaing speeds than unconstrained operations. This reflects the fact that weaing ehicles are constrained to less space than equilibrium would require, whereas nonweaing ehicles hae correspondingly more than their equilibrium share of space. In Exhibit 24-6, this is reflected by differences in the constant a. EXHIBIT 24-6. CONSTANTS FOR COMPUTATION OF WEAVING INTENSITY FACTORS General Form c a(1+ VR) b N W = L d Constants for Weaing Speed, S w Constants for Nonweaing Speed, S nw a b c d a b c d Type A Configuration Unconstrained 0.15 2.2 0.97 0.80 0.0035 4.0 1.3 0.75 Constrained 0.35 2.2 0.97 0.80 0.0020 4.0 1.3 0.75 Type B Configuration Unconstrained 0.08 2.2 0.70 0.50 0.0020 6.0 1.0 0.50 Constrained 0.15 2.2 0.70 0.50 0.0010 6.0 1.0 0.50 Type C Configuration Unconstrained 0.08 2.3 0.80 0.60 0.0020 6.0 1.1 0.60 Constrained 0.14 2.3 0.80 0.60 0.0010 6.0 1.1 0.60 Type B configurations are the most efficient for handling large weaing flows. Weaing speeds of such flows are higher than for Type A and C configurations of equal length and width. The sensitiity of speeds to length is greatest for Type A configurations, because weaing ehicles are often accelerating or decelerating as they traerse the weaing segment. The sensitiity of nonweaing speeds to the olume ratio (VR) is greatest for Type B and C configurations. Because these configurations can accommodate higher proportions of weaing ehicles and because each has a through lane for one weaing moement, nonweaing ehicles are more likely to share lanes with weaing ehicles than in Type A configurations, where the opportunity to segregate is greater. The last point is important and seres to highlight the essential difference between Type A configurations (particularly ramp-weaes) and others (Types B and C). Because all weaing ehicles must cross a crown line in Type A segments, weaing ehicles tend to concentrate in the two lanes adjacent to the crown line, whereas nonweaing ehicles Chapter 24 - Freeway Weaing 24-6 Methodology
graitate to outer lanes. Thus there is substantially more segregation of weaing and nonweaing flows in Type A configurations. This difference makes Type A segments behae somewhat differently from other configurations. Speeds tend to be higher in Type A segments than in Types B or C gien the same length, width, and demand flows. Howeer, this does not suggest that Type A segments always operate better than Types B or C for similar lengths, widths, and flows. Type A segments hae more seere restrictions on the amount of weaing traffic that can be accommodated than do other configurations. Determining Weaing Intensity The weaing intensity factors (W w and W nw ) are a measure of the influence of weaing actiity on the aerage speeds of both weaing and nonweaing ehicles. These factors are computed by Equation 24-4. a(1 +VR) b c N W i = L d (24-4) where W i = weaing intensity factors for weaing (i = w) and nonweaing (i = nw) flows; VR = olume ratio; = total flow rate in the weaing segment (pc/h); N = total number of lanes in the weaing segment; L = length of the weaing segment (ft); and a, b, c, d = constants of calibration. Constants for Computing Weaing Intensity Factors Constants for computation of weaing intensity factors (a, b, c, d) are gien in Exhibit 24-6. Values for these constants ary on the basis of three factors: Whether the aerage speed prediction is for weaing or nonweaing ehicles, Configuration type (A, B, or C), and Whether the operation is unconstrained or constrained. DETERMINING TYPE OF OPERATION The determination of whether a particular weaing segment is operating in an unconstrained or constrained state is based on the comparison of two ariables that are defined in Chapter 13: N w = number of lanes that must be used by weaing ehicles to achiee equilibrium or unconstrained operation, and N w (max) = maximum number of lanes that can be used by weaing ehicles for a gien configuration. Fractional alues for lane use requirements of weaing ehicles may occur because weaing and nonweaing ehicles share some lanes. Cases for which N w < N w (max) are unconstrained because there are no impediments to weaing ehicles using the number of lanes required for equilibrium. If N w N w (max), weaing ehicles are constrained to using N w (max) lanes and therefore cannot occupy as much of the roadway as would be needed to establish equilibrium operations. Exhibit 24-7 proides algorithms for the computation of N w and shows the alues of N w (max), which are discussed more fully in Chapter 13. Definition of constrained weaing segment 24-7 Chapter 24 - Freeway Weaing Methodology
EXHIBIT 24-7. CRITERIA FOR UNCONSTRAINED VERSUS CONSTRAINED OPERATION OF WEAVING SEGMENTS Configuration Number of Lanes Required for Unconstrained Operation, N w N w (max) Type A 0.74(N) VR 0.571 L 0.234 /S 0.438 w 1.4 Type B N[0.085 + 0.703VR + (234.8/L) 0.018(S nw S w )] 3.5 Type C N[0.761 + 0.047VR 0.00011 0.005(S nw S w )] 3.0 a Note: a. For two-sided weaing segments, all freeway lanes may be used by weaing ehicles. The equations of Exhibit 24-7 rely on the prediction of unconstrained weaing and nonweaing speeds. The equations take these results and predict the number of lanes weaing ehicles would hae to occupy to achiee unconstrained speeds. If the result indicates that constrained operations exist, speeds must be recomputed using constrained equations. The limit on maximum number of weaing lanes, N w (max), is most restrictie for Type A segments and reflects the need for weaing ehicles to cluster in the two lanes adjacent to the crown line. The through weaing lane in Type B and C configurations proides for greater occupancy of lanes by weaing ehicles. Type A segments hae another unusual, but understandable, characteristic. As the length of a Type A segment increases, constrained operation is more likely to result. As the length increases, the speed of weaing ehicles is also able to increase. Thus, weaing ehicles use more space as length increases, and the likelihood of requiring more than the maximum of 1.4 lanes to achiee equilibrium also increases. Types B and C show the opposite trend. Increasing length has less effect on weaing speed than in Type A configurations. First, acceleration and deceleration from low-speed ramps are less of an issue for Types B and C, which are, by definition, major weaing segments. Second, the substantial mixing of weaing and nonweaing ehicles in the same lanes makes the resulting speeds less sensitie to length. In Type B and C segments, the proportion of lanes needed by weaing ehicles to achiee unconstrained operation decreases as length increases. The analyst should note that under extreme conditions (high VR, short length), the equation for Type B segments can predict alues of N w > N. While this is not practical and reflects portions of the research database with sparse field data, it may always be taken to indicate constrained operations. DETERMINING WEAVING SEGMENT SPEED Once speeds hae been estimated and the type of operation determined (which may cause a recomputation of estimated speeds), the aerage space mean speed of all ehicles in the segment is computed according to Equation 24-5. S = w S w + (24-5) nw S nw where S = space mean speed of all ehicles in the weaing segment (mi/h), S w = space mean speed of weaing ehicles in the weaing segment (mi/h), S nw = space mean speed of nonweaing ehicles in the weaing segment (mi/h), = total flow rate in the weaing segment (pc/h), w = weaing flow rate in the weaing segment (pc/h), and nw = nonweaing flow rate in the weaing segment (pc/h). Chapter 24 - Freeway Weaing 24-8 Methodology
DETERMINING DENSITY The aerage speed for all ehicles may be used to compute density for all ehicles in the weaing segment as shown in Equation 24-6. N D = S where D is the aerage density for all ehicles in the weaing segment (pc/mi/ln). (24-6) DETERMINING WEAVING SEGMENT CAPACITY The capacity of a weaing segment is any combination of flows that causes the density to reach the LOS E/F boundary condition of 43.0 pc/mi/ln for freeways or 40.0 pc/mi/ln for multilane highways. Thus, capacity aries with a number of ariables: configuration, number of lanes, free-flow speed of the freeway or multilane highway, length, and olume ratio. Because of the form of predictie algorithms, generation of a simple closed-form solution for capacity gien the specification of the other ariables is not possible. Rather, a trial-and-error process must be used. Exhibit 24-8 shows tabulated alues of weaing segment capacity for a number of situations. As a rough estimate, straight-line interpolation may be used for intermediate alues. The tabulated capacities reflect some other limitations on weaing segment operations that reflect field obserations: The capacity of a weaing segment may neer exceed the capacity of a similar basic freeway or multilane highway segment. Field studies suggest that weaing flow rates should not exceed the following alues: 2,800 pc/h for Type A, 4,000 pc/h for Type B, and 3,500 pc/h for Type C configurations. Een though higher weaing flows hae been obsered, they are likely to cause failure regardless of the results of analysis using the procedures in this manual. Field studies indicate that there are also limitations on the proportion of weaing flow (VR) that can be accommodated by arious configurations: 1.00, 0.45, 0.35, or 0.20 for Type A with two, three, four, or fie lanes, respectiely; 0.80 for Type B; and 0.50 for Type C. At higher olume ratios, stable operations may still occur, but operations will be worse than those anticipated by the methodology, and failure could occur. For Type C segments, the weaing ratio, R, should not exceed 0.40, with the larger weaing flow being in the direction of the through weaing lane. At higher weaing ratios or where the dominant weaing flow is not in the direction of the through weaing lane, stable operations may still occur, but operations will be worse than those estimated by the methodology. Breakdown may occur in some cases. The maximum length for which weaing analysis is conducted is 2,500 ft for all configuration types. Beyond these lengths, merge and dierge areas are considered separately using the methodology of Chapter 25, Ramps and Ramp Junctions. As noted preiously, the capacity of a weaing segment is represented by any set of conditions that results in an aerage density of 43 pc/mi/ln (for freeways) or 40 pc/mi/ln (for multilane highways). Thus, capacity aries with the configuration, the length and width of the weaing segment, the proportion of total flow that weaes (VR), and the free-flow speed of the freeway. For any gien set of conditions, the algorithms described herein must be soled iteratiely to find capacity. Capacity of a weaing segment defined Capacity attributes of weaing segments 24-9 Chapter 24 - Freeway Weaing Methodology
Volume Ratio, VR EXHIBIT 24-8. CAPACITY FOR VARIOUS WEAVING SEGMENTS (A) Type A Weaing Segments 75-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 6,030 6,800 7,200 b 7,200 b 7,200 b 0.20 5,460 6,230 6,680 7,010 7,200 b 0.30 4,990 5,740 6,210 6,530 6,790 0.40 4,620 5,340 5,480 c 5,790 c 6,040 c 0.45 d 4,460 4,840 c 5,240 c 5,540 c 5,780 c Four-Lane Segments 0.10 8,040 9,070 9,600 b 9,600 b 9,600 b 0.20 7,280 8,300 8,910 9,350 9,600 b 0.30 6,660 7,520 c 8,090 c 8,520 c 8,830 c 0.35 e 6,250 c 7,120 c 7,690 c 8,000 f 8,000 f Fie-Lane Segments 0.10 10,050 11,340 12,000 b 12,000 b 12,000 b 0.20 g 9,100 10,540 c 11,270 c 11,790 c 12,000 b Volume Ratio, VR (B) Type A Weaing Segments 65-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 5,570 6,230 6,620 6,890 7,050 b 0.20 5,070 5,740 6,130 6,410 6,620 0.30 4,670 5,320 5,720 6,000 6,220 0.40 4,330 4,950 5,090 c 5,360 c 5,570 c 0.45 d 4,190 4,520 c 4,870 c 5,140 c 5,340 c Four-Lane Segments 0.10 7,430 8,310 8,830 9,190 9,400 b 0.20 6,760 7,660 8,170 8,550 8,830 0.30 6,180 c 6,970 c 7,470 c 7,830 c 8,110 c 0.35 e 5,870 c 6,620 c 7,120 c 7,470 c 7,760 c Fie-Lane Segments 0.10 9,290 10,390 11,040 11,490 11,750 b 0.20 g 8,450 9,700 c 10,320 c 10,760 c 11,090 c Notes: Refer to the last page of Exhibit 24-8. Chapter 24 - Freeway Weaing 24-10 Methodology
Volume Ratio, VR EXHIBIT 24-8 (CONTINUED). CAPACITY FOR VARIOUS WEAVING SEGMENTS (C) Type A Weaing Segments 60-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 5,330 5,940 6,280 6,520 6,700 0.20 4,870 5,480 5,850 6,100 6,280 0.30 4,490 5,100 5,460 5,720 5,920 0.40 4,180 4,570 c 4,880 c 5,140 c 5,330 c 0.45 d 4,040 4,360 c 4,680 c 4,920 c 5,120 c Four-Lane Segments 0.10 7,110 7,920 8,380 8,690 8,930 0.20 6,500 7,310 7,800 8,140 8,420 c 0.30 5,960 c 6,680 c 7,140 c 7,470 c 7,710 c 0.35 g 5,660 c 6,370 c 6,810 c 7,140 c 7,400 c Fie-Lane Segments 0.10 8,880 9,900 10,480 10,870 11,500 b 0.20 f 8,120 9,270 c 9,830 c 10,220 c 10,530 c Volume Ratio, VR (D) Type A Weaing Segments 55-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 5,080 5,630 5,940 6,140 6,300 0.20 4,660 5,210 5,550 5,770 5,940 0.30 4,300 4,850 5,190 5,430 5,610 0.40 4,010 4,360 c 4,670 c 4,890 c 5,070 c 0.45 d 3,880 4,180 c 4,480 c 4,700 c 4,880 c Four-Lane Segments 0.10 6,780 7,500 7,920 8,190 8,400 0.20 6,210 6,950 7,400 7,690 7,940 c 0.30 5,710 c 6,380 c 6,780 c 7,090 c 7,310 c 0.35 e 5,440 c 6,090 c 6,490 c 6,800 c 7,030 c Fie-Lane Segments 0.10 8,480 9,380 9,900 10,240 10,510 0.20 g 7,960 c 8,800 c 9,320 c 9,660 c 9,930 c Notes: Refer to the last page of Exhibit 24-8. 24-11 Chapter 24 - Freeway Weaing Methodology
Volume Ratio, VR EXHIBIT 24-8 (CONTINUED). CAPACITY FOR VARIOUS WEAVING SEGMENTS (E) Type B Weaing Segments 75-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 7,200 b 7,200 b 7,200 b 7,200 b 7,200 b 0.20 6,810 7,200 b 7,200 b 7,200 b 7,200 b 0.30 6,120 6,670 7,000 7,230 7,200 b 0.40 5,540 6,090 6,430 6,650 6,830 0.50 5,080 5,620 5,940 6,170 6,360 0.60 4,750 5,250 5,560 5,790 5,970 0.70 4,180 4,980 5,290 5,510 5,690 0.80 h 3,890 4,810 5,000 f 5,000 f 5,000 f Four-Lane Segments 0.10 9,600 b 9,600 b 9,600 b 9,600 b 9,600 b 0.20 9,090 9,600 b 9,600 b 9,600 b 9,600 b 0.30 8,160 8,900 9,330 9,600 b 9,600 b 0.40 7,390 8,120 8,570 8,860 9,110 0.50 6,660 c 7,490 7,920 8,000 f 8,000 f 0.60 6,060 c 6,670 f 6,670 f 6,670 f 6,670 f 0.70 5,570 c 5,760 f 5,760 f 5,760 f 5,760 f 0.80 h 5,000 f 5,000 f 5,000 f 5,000 f 5,000 f Fie-Lane Segments 0.10 12,000 b 12,000 b 12,000 b 12,000 b 12,000 b 0.20 11,360 12,000 b 12,000 b 12,000 b 12,000 b 0.30 10,200 11,120 11,670 12,000 b 12,000 b 0.40 9,250 c 10,000 f 10,000 f 10,000 f 10,000 f 0.50 8,000 f 8,000 f 8,000 f 8,000 f 8,000 f 0.60 6,670 f 6,670 f 6,670 f 6,670 f 6,670 f 0.70 5,760 f 5,760 f 5,760 f 5,760 f 5,760 f 0.80 h 5,000 f 5,000 f 5,000 f 5,000 f 5,000 f Notes: Refer to the last page of Exhibit 24-8. Chapter 24 - Freeway Weaing 24-12 Methodology
Volume Ratio, VR EXHIBIT 24-8 (CONTINUED). CAPACITY FOR VARIOUS WEAVING SEGMENTS (F) Type B Weaing Segments 65-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 6,930 7,050 b 7,050 b 7,050 b 7,050 b 0.20 6,220 6,670 6,930 7,050 b 7,050 b 0.30 5,610 6,090 6,360 6,560 6,700 0.40 5,110 5,590 5,870 6,070 6,220 0.50 4,710 5,170 5,460 5,650 5,810 0.60 4,410 4,850 5,120 5,320 5,470 0.70 4,190 4,620 4,880 5,070 5,230 0.80 h 3,650 c 4,460 4,720 4,920 5,000 f Four-Lane Segments 0.10 9,240 9,400 b 9,400 b 9,400 b 9,400 b 0.20 8,300 8,900 9,240 9,400 b 9,400 b 0.30 7,490 8,120 8,480 8,740 8,930 0.40 6,810 7,450 7,830 8,090 8,300 0.50 6,180 c 6,900 7,280 7,540 7,740 0.60 5,640 c 6,470 6,670 f 6,670 f 6,670 f 0.70 5,210 c 5,730 5,760 f 5,760 f 5,760 f 0.80 h 4,870 c 5,000 f 5,000 f 5,000 f 5,000 f Fie-Lane Segments 0.10 11,550 11,750 b 11,750 b 11,750 b 11,750 b 0.20 1,0370 11,120 11,550 11,750 b 11,750 b 0.30 9,360 10,150 10,610 10,930 11,170 0.40 8,540 c 9,320 9,790 10,000 f 10,000 f 0.50 7,720 c 8,000 f 8,000 f 8,000 f 8,000 f 0.60 6,670 f 6,670 f 6,670 f 6,670 f 6,670 f 0.70 5,760 f 5,760 f 5,760 f 5,760 f 5,760 f 0.80 h 5,000 f 5,000 f 5,000 f 5,000 f 50,00 f Notes: Refer to the last page of Exhibit 24-8. 24-13 Chapter 24 - Freeway Weaing Methodology
Volume Ratio, VR EXHIBIT 24-8 (CONTINUED). CAPACITY FOR VARIOUS WEAVING SEGMENTS (G) Type B Weaing Segments 60-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 6,540 6,890 6,900 b 6,900 b 6,900 b 0.20 5,900 6,320 6,540 6,700 6,810 0.30 5,340 5,780 6,040 6,210 6,340 0.40 4,880 5,320 5,570 5,760 5,900 0.50 4,520 4,940 5,200 5,380 5,520 0.60 4,230 4,640 4,890 5,080 5,220 0.70 4,020 4,420 4,670 4,850 4,990 0.80 h 3,520 c 4,280 4,520 4,700 4,840 Four-Lane Segments 0.10 8,720 9,190 9,200 b 9,200 b 9,200 b 0.20 7,860 8,420 8,730 8,930 9,090 0.30 7,120 7,710 8,050 8,280 8,450 0.40 6,510 7,090 7,430 7,690 7,860 0.50 5,920 c 6,590 6,930 7,180 7,370 0.60 5,420 c 6,190 6,520 6,670 f 6,670 f 0.70 5,020 c 5,520 c 5,760 f 5,760 f 5,760 f 0.80 h 4,700 c 5,000 f 5,000 f 5,000 f 5,000 f Fie-Lane Segments 0.10 10,900 11,490 11,500 b 11,500 b 11,500 b 0.20 9,830 10,530 10,910 11,170 11,360 0.30 8,910 9,640 10,070 10,350 10,560 0.40 8,170 c 8,860 9,290 9,610 9,830 0.50 7,400 c 8,000 f 8,000 f 8,000 f 8,000 f 0.60 6,670 f 6,670 f 6,670 f 6,670 f 6,670 f 0.70 5,760 f 5,760 f 5,760 f 5,760 f 5,760 f 0.80 h 5,000 f 5,000 f 5,000 f 5,000 f 5,000 f Notes: Refer to the last page of Exhibit 24-8. Chapter 24 - Freeway Weaing 24-14 Methodology
Volume Ratio, VR EXHIBIT 24-8 (CONTINUED). CAPACITY FOR VARIOUS WEAVING SEGMENTS (H) Type B Weaing Segments 55-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 6,160 6,470 6,630 6,750 b 5,750 b 0.20 5,570 5,950 6,160 6,300 5,400 0.30 5,070 5,460 5,690 5,850 5,960 0.40 4,640 5,040 5,280 5,450 5,570 0.50 4,310 4,700 4,940 5,100 5,240 0.60 4,050 4,420 4,660 4,830 4,950 0.70 3,870 4,230 4,450 4,620 5,750 0.80 h 3,390 c 4,090 4,310 4,480 4,610 Four-Lane Segments 0.10 8,210 8,620 8,850 9,000 b 9,000 b 0.20 7,430 7,930 8,210 8,400 8,540 0.30 6,760 7,290 7,590 7,800 7,950 0.40 6,190 6,730 7,040 7,260 7,430 0.50 5,660 c 6,260 6,590 6,800 6,990 0.60 5,210 c 5,900 6,210 6,440 6,610 0.70 4,830 c 5,280 c 5,760 f 5,760 f 5,760 f 0.80 h 4,520 c 4,950 c 5,000 f 5,000 f 5,000 f Fie-Lane Segments 0.10 10,260 10,780 11,060 11,250 b 11,250 b 0.20 9,290 9,920 10,260 10,500 10,670 0.30 8,450 9,110 9,490 9,750 9,940 0.40 7,770 c 8,410 8,810 9,080 9,280 0.50 7,080 c 7,830 8,000 f 8,000 f 8,000 f 0.60 6,520 c 6,670 f 6,670 f 6,670 f 6,670 f 0.70 5,760 f 5,760 f 5,760 f 5,760 f 5,760 f 0.80 h 5,000 f 5,000 f 5,000 f 5,000 f 5,000 f Notes: Refer to the last page of Exhibit 24-8. 24-15 Chapter 24 - Freeway Weaing Methodology
Volume Ratio, VR EXHIBIT 24-8 (CONTINUED). CAPACITY FOR VARIOUS WEAVING SEGMENTS (I) Type C Weaing Segments 75-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 7,200 b 7,200 b 7,200 b 7,200 b 7,200 b 0.20 6,580 7,200 b 7,200 b 7,200 b 7,200 b 0.30 5,880 6,530 6,920 7,190 7,200 b 0.40 5,330 5,960 6,340 6,610 6,830 0.50 i 4,890 5,490 5,870 6,140 6,350 Four-Lane Segments 0.10 9,600 b 9,600 b 9,600 b 9,600 b 9,600 b 0.20 8,780 9,600 b 9,600 b 9,600 b 9,600 b 0.30 7,850 8,710 9,220 9,590 9,600 b 0.40 7,110 7,950 8,450 8,750 8,750 0.50 i 6,520 7,000 f 7,000 f 7,000 f 7,000 f Fie-Lane Segments 0.10 12,000 b 12,000 b 12,000 b 12,000 b 12,000 b 0.20 11,510 c 12,000 b 12,000 b 12,000 b 12,000 b 0.30 10,120 c 11,160 c 11,530 11,670 f 11,670 f 0.40 8,750 f 8,750 f 8,750 f 8,750 f 8,750 f 0.50 i 7,000 f 7,000 f 7,000 f 7,000 f 7,000 f Volume Ratio, VR (J) Type C Weaing Segments 65-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 6,740 7,050 b 7,050 b 7,050 b 7,050 b 0.20 6,010 6,570 6,870 7,050 b 7,050 b 0.30 5,420 5,970 6,310 6,530 6,700 0.40 4,930 5,480 5,810 6,040 6,230 0.50 i 4,540 5,070 5,400 5,640 5,820 Four-Lane Segments 0.10 8,980 9,400 b 9,400 b 9,400 b 9,400 b 0.20 8,020 8,760 9,160 9,400 b 9,400 b 0.30 7,230 7,970 8,410 8,710 8,930 0.40 6,570 7,310 7,750 8,060 8,310 0.50 i 6,060 6,760 7,000 f 7,000 f 7,000 f Fie-Lane Segments 0.10 11,500 b 11,500 b 11,500 b 11,500 b 11,500 b 0.20 10,500 c 11,320 c 11,460 11,500 b 11,500 b 0.30 9,320 c 10,180 c 10,520 10,890 11,170 0.40 8,330 c 8,750 f 8,750 f 8,750 f 8,750 f 0.50 i 7,000 f 7,000 f 7,000 f 7,000 f 7,000 f Notes: Refer to the last page of Exhibit 24-8. Chapter 24 - Freeway Weaing 24-16 Methodology
Volume Ratio, VR EXHIBIT 24-8 (CONTINUED). CAPACITY FOR VARIOUS WEAVING SEGMENTS (K) Type C Weaing Segments 60-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 6,380 6,830 6,900 b 6,900 b 6,900 b 0.20 5,730 6,230 6,490 6,680 6,830 0.30 5,170 5,690 5,990 6,190 6,350 0.40 5,720 5,240 5,540 5,740 5,910 0.50 i 4,360 4,850 5,160 5,370 5,540 Four-Lane Segments 0.10 8,500 9,100 9,200 b 9,200 b 9,200 b 0.20 7,640 8,310 8,660 8,910 9,100 0.30 6,900 7,590 7,990 8,260 8,470 0.40 6,300 6,990 7,380 7,660 7,880 0.50 i 5,820 6,470 6,880 7,000 f 7,000 f Fie-Lane Segments 0.10 11,250 11,500 b 11,500 b 11,500 b 11,500 b 0.20 9,980 c 10,720 c 10,820 11,140 11,380 0.30 8,880 c 9,680 c 9,980 10,330 10,590 0.40 7,980 c 8,750 f 8,750 f 8,750 f 8,750 f 0.50 i 7,000 f 7,000 f 7,000 f 7,000 f 7,000 f Notes: Refer to the last page of Exhibit 24-8. 24-17 Chapter 24 - Freeway Weaing Methodology
Volume Ratio, VR EXHIBIT 24-8 (CONTINUED). CAPACITY FOR VARIOUS WEAVING SEGMENTS (L) Type C Weaing Segments 55-mi/h Free-Flow Speed Length of Weaing Segment (ft) 500 1,000 1,500 2,000 2,500 a Three-Lane Segments 0.10 6,010 6,400 6,610 6,740 6,750 b 0.20 5,420 5,870 6,120 6,270 6,400 0.30 4,930 5,380 5,650 5,850 5,970 0.40 4,510 4,980 5,250 5,450 5,590 0.50 i 4,180 4,630 4,900 5,100 5,250 Four-Lane Segments 0.10 8,020 8,540 8,810 8,980 9,000 b 0.20 7,230 7,830 8,160 8,360 8,540 0.30 6,570 7,180 7,540 7,800 7,970 0.40 6,020 6,640 7,000 7,260 7,450 0.50 i 5,570 6,180 6,540 6,800 7,000 f Fie-Lane Segments 0.10 10,560 c 11,100 c 11,020 11,230 11,250 b 0.20 9,420 c 10,090 c 10,200 10,460 10,670 0.30 8,430 c 9,160 c 9,420 9,750 9,960 0.40 7,610 c 8,350 c 8,750 f 8,750 f 8,750 f 0.50 i 6,930 c 7,000 f 7,000 f 7,000 f 7,000 f Notes: a. Weaing segments longer than 2,500 ft are treated as isolated merge and dierge areas using the procedures of Chapter 25, Ramps and Ramp Junctions. b. Capacity constrained by basic freeway capacity. c. Capacity occurs under constrained operating conditions. d. Three-lane Type A segments do not operate well at olume ratios greater than 0.45. Poor operations and some local queuing are expected in such cases. e. Four-lane Type A segments do not operate well at olume ratios greater than 0.35. Poor operations and some local queuing are expected in such cases. f. Capacity constrained by maximum allowable weaing flow rate: 2,800 pc/h (Type A), 4,000 (Type B), 3,500 (Type C). g. Fie-lane Type A segments do not operate well at olume ratios greater than 0.20. Poor operations and some local queuing are expected in such cases. h. Type B weaing segments do not operate well at olume ratios greater than 0.80. Poor operations and some local queuing are expected in such cases. i. Type C weaing segments do not operate well at olume ratios greater than 0.50. Poor operations and some local queuing are expected in such cases. It is possible to do so using a spreadsheet properly programmed for such iteration. Capacities hae been determined for freeway facilities and are shown in Exhibit 24-8. These capacities represent maximum 15-min flow rates under equialent base conditions and are rounded to the nearest 10 pc/h. To find the capacity under a gien set of preailing conditions Equation 24-7 is used. c = c b * f HV * f p (24-7) where c = capacity under preailing conditions stated as a flow rate for the peak 15 min of the hour (eh/h), c b = capacity under base conditions stated as a flow rate for the peak 15 min of the hour in Exhibit 24-8 (pc/h), f HV = heay-ehicle adjustment factor (basic freeway segments or multilane highways), and f p = drier population factor (basic freeway segments or multilane highways). Chapter 24 - Freeway Weaing 24-18 Methodology
If a capacity in terms of an hourly olume is desired, it may be computed using Equation 24-8. c h = c * PHF (24-8) where c h = capacity under preailing conditions expressed as an hourly olume (eh/h), and PHF = peak-hour factor. MULTIPLE WEAVING SEGMENTS When a series of closely spaced merge and dierge areas creates seeral sets of weaing moements (between different merge-dierge pairs) that share the same segment of the roadway, a multiple weaing segment is created. In preious editions of this manual, a specific procedure for analysis of two-segment multiple weaing segments, inoling two sets of oerlapping weaing moements, was presented. Although it constituted a logical approach, it did not address cases where three or more sets of weaing moements oerlapped, and it was not extensiely supported by field data. It is recommended that such cases be segregated into merge areas, dierge areas, and simple weaing segments, as appropriate, and that each segment be analyzed accordingly. Chapter 22 contains information on this procedure. COLLECTOR-DISTRIBUTOR ROADWAYS A common design practice often results in weaing segments that occur on collectordistributor roadways that are part of a freeway or multilane highway interchange. Although the procedures of this chapter could be applied to such cases (using appropriate free-flow speeds), whether the LOS criteria specified herein should apply is unclear. Because many such segments operate at low speeds and correspondingly high densities, stable operations may exist beyond the maximum densities specified herein, which are intended for freeway or multilane highway weaing. III. APPLICATIONS The methodology of this chapter can be used to analyze the capacity and LOS of freeway weaing segments. First, the analyst identifies the primary output. Primary outputs typically soled for in a ariety of applications include LOS, number of lanes required (N), weaing segment length required (L), and weaing segment configuration type (Type). Performance measures related to density and speed are also achieable but are considered secondary outputs. Second, the analyst must identify the default alues or estimated alues for use in the analysis. Basically, the analyst has three sources of input data: 1. Default alues found in this manual, 2. Estimates and locally deried default alues deeloped by the analyst, and 3. Values deried from field measurements and obseration. For each of the input ariables, a alue must be supplied to calculate the outputs, both primary and secondary. A common application of the method is to compute the LOS of an existing or a changed segment in the near term or distant future. This type of application is termed operational, and its primary output is LOS, with secondary outputs for density and speed. Another application is to check the adequacy of or to recommend the required number of lanes, weaing segment length, or weaing configuration gien the olume or flow rate and LOS goal. This application is termed design since its primary outputs are geometric Guidelines for required inputs and estimated alues are gien in Chapter 13 24-19 Chapter 24 - Freeway Weaing Methodology
attributes of the weaing segment. Other outputs from this application include speed and density. Another general type of analysis is termed planning. These analyses use estimates, HCM default alues, and local default alues as inputs in the calculation. LOS or weaing segment attributes can be determined as outputs, along with the secondary outputs of density and speed. The difference between planning analysis and operational or design analysis is that most or all of the input alues in planning come from estimates or default alues, whereas the operational and design analyses use field measurements or known alues for inputs. Note that for each of the analyses, FFS of the weaing segment, either measured or estimated, is required as an input for the computation. Operational (LOS) Design (N, L, Type) Planning (LOS) Planning (N, L, Type) COMPUTATIONAL STEPS The worksheet for freeway weaing computations is shown in Exhibit 24-9. The worksheet is also included in Appendix A. For all applications, the analyst proides general information and site information. For operational (LOS) analysis, all required input data are entered as input. After conerting olumes to flow rates, the unconstrained weaing intensity factor is used to estimate weaing and nonweaing speeds. The number of lanes weaing ehicles must occupy to achiee unconstrained operation is determined. If this alue is less than the maximum number of lanes, then unconstrained flow exists, and preiously computed speeds will apply to the analysis. If the number of lanes required for unconstrained operation is greater than or equal to the maximum number of lanes, then weaing and nonweaing speeds must be computed for constrained operation. Then the space mean speed for all ehicles in the weaing segment is computed followed by density. Finally, leel of serice is determined using the density alue for the weaing segment. The objectie of design (N, L, Type) analysis is to estimate the length of a weaing segment, the number of lanes, or weaing segment configuration type gien olumes and free-flow speed. A desired leel of serice is stated and entered in the worksheet. Then a weaing segment length, number of lanes, and configuration type are assumed, and the procedure for operational (LOS) analysis is performed. The leel-of-serice result with the assumed parameters is then compared with the desired leel of serice. If the desired leel of serice is not met, a new combination of parameter alues is assumed. These iterations are continued until the desired leel of serice is achieed. PLANNING APPLICATIONS The two planning applications, planning (LOS) and planning (N, L, Type), directly correspond to procedures described for operational and design analysis. The first criterion that categorizes these as planning applications is the use of estimates, HCM default alues, or local default alues on the input side of the calculation. Another factor that defines a gien application as planning is the use of annual aerage daily traffic (AADT) to estimate directional design-hour olume (DDHV). Guidelines for calculating DDHV are gien in Chapter 8. The analyst typically has few, if any, of the input alues required to perform planning applications. More information on the use of default alues is contained in Chapter 13. ANALYSIS TOOLS The worksheet shown in Exhibit 24-9 and proided in Appendix A can be used to perform operational (LOS), design (N, L, Type), planning (LOS), and planning (N, L, Type) analyses. Chapter 24 - Freeway Weaing 24-20 Applications
EXHIBIT 24-9. FREEWAY WEAVING WORKSHEET General Information FREEWAY WEAVING WORKSHEET Site Information Analyst Freeway/Direction of Trael Agency or Company Weaing Segment Location Date Performed Jurisdiction Analysis Time Period Analysis Year Operational (LOS) Design (N, L, Type) Planning (LOS) Planning (N, L, Type) Inputs Sketch (show lanes, L, o1, o2, w1, w2 ) Conersion to pc/h Under Base Conditions (pc/h) AADT K D V PHF % HV f HV f p (eh/day) (eh/h) o1 o2 w1 w2 w nw Weaing and Nonweaing Speeds Unconstrained Constrained Weaing (i = w) Nonweaing (i = nw) Weaing (i = w) Nonweaing (i = nw) a (Exhibit 24-6) b (Exhibit 24-6) c (Exhibit 24-6) d (Exhibit 24-6) Weaing intensity factor, W i a(1 + VR) b (/N) c W i = (L) d Weaing and nonweaing speeds, S i (mi/h) S FF 10 S i = 15 + 1 + W i Number of lanes required for unconstrained operation, N w (Exhibit 24-7) Maximum number of lanes, N w (max) (Exhibit 24-7) If N w < N w (max) unconstrained operation If N w N w (max) constrained operation Weaing Segment Speed, Density, Leel of Serice, and Capacity Weaing segment speed, S (mi/h) S = w nw S + w S nw ( ) ( ) Weaing segment density, D (pc/mi/ln) D = /N S Leel of serice, LOS (Exhibit 24-2) Capacity for base condition, c b (pc/h) (Exhibit 24-8) Capacity as a 15-min flow rate, c (eh/h) c = c b * f HV * f p Capacity as a full-hour olume, c h (eh/h) c h = c(phf) Freeway free-flow speed, S FF = mi/h Weaing number of lanes, N = Weaing segment length, L ft Terrain Leel Rolling Weaing type Type A Type B Type C Volume ratio, VR = w Weaing ratio, R = w2 w V = PHF * f HV *f p 24-21 Chapter 24 - Freeway Weaing Applications
IV. EXAMPLE PROBLEMS Problem No. Description Application 1 Determine leel of serice of a major weaing segment Operational (LOS) 2 Determine leel of serice of a ramp-weaing segment Operational (LOS) 3 Determine leel of serice of a ramp-weaing segment with Operational (LOS) constrained operation 4 Design a major weaing segment for a desired leel of serice Design (N, L, Type) 5 Design a weaing segment using sensitiity analysis Planning (N, L, Type) Chapter 24 - Freeway Weaing 24-22 Example Problems
EXAMPLE PROBLEM 1 The Weaing Segment the worksheet. A major weaing segment on an urban freeway as shown on The Question What are the leel of serice and capacity of the weaing segment? The Facts Volume (A-C) = 1,815 eh/h, PHF = 0.91, Volume (A-D) = 692 eh/h, Leel terrain, Volume (B-C) = 1,037 eh/h, Driers are regular commuters, Volume (B-D) = 1,297 eh/h, FFS = 65 mi/h for freeway, and 10 percent trucks, Weaing segment length = 1,500 ft. Comments Use Chapter 23, Basic Freeway Segments, to identify f HV and f p. Outline of Solution All input parameters are known, so no default alues are required. Demand olumes are conerted to flow rates, and weaing configuration type is determined. Weaing and nonweaing speeds are computed and used to determine weaing segment speed. The density in the weaing segment is calculated, and leel of serice is determined. Finally, capacity is determined. Steps 1. Conert olume (eh/h) to flow rate (pc/h) (use Equation 24-1). 1a. Determine f p (use Chapter 23). 1b. Determine f HV (use Chapter 23). 2. Determine weaing segment configuration type (use Exhibit 24-5). = V (PHF)(f HV )(f p ) 1,815 (A-C) = = 2,095 pc/h (0.91)(0.952)(1.000) (A-D) = 799 pc/h (B-C) = 1,197 pc/h (B-D) = 1,497 pc/h f p = 1.000 f HV = 1 1+ P T (E T 1) + P R (E R 1) 1 f HV = 1+ 0.10(1.5 1) + 0 = 0.952 Type B (Moement A-D requires one lane change; Moement B-C requires none) 3. Compute critical ariables. w = 1,197 + 799 = 1,996 pc/h nw = 2,095 + 1,497 = 3,592 pc/h = 1,996 + 3,592 = 5,588 pc/h VR = 1,996 5,588 = 0.357 R = 799 1,996 = 0.400 24-23 Chapter 24 - Freeway Weaing Example Problems
4. Compute weaing and nonweaing speeds assuming unconstrained operation (use Exhibit 24-6 and Equations 24-3 and 24-4). 5. Check type of operation (use Exhibit 24-7). 6. Compute weaing segment speed (use Equation 24-5). S = 7. Compute weaing segment density (use Equation 24-6). 8. Determine leel of serice (use Exhibit 24-2). 9. Determine weaing segment capacity (use Exhibit 24-8 and Equations 24-7 and 24-8). a(1+ VR) b c N W i = (L) d S i = 15 + S FF 10 1+ W i 0.08(1+ 0.357) 2.2 0.70 5,588 4 W w = (1,500) 0.50 = 0.643 0.0020(1+ 0.357) 6.0 1.0 5,588 4 W nw = (1,500) 0.50 = 0.450 65 10 S w = 15 + = 48.5 mi/h 1+ 0.643 65 10 S nw = 15 + = 52.9 mi/h 1+ 0.450 N w = 4[0.085 + 0.703(0.357) + (234.8/1,500) 0.018(52.9 48.5)] = 1.65 N w (max) = 3.5, therefore unconstrained operation 5,588 w S w + = nw 1,996 S + 3,592 = 51.2 mi/h nw 48.5 52.9 5,588 N D = S = 4 = 27.3 pc/mi/ln 51.2 LOS C c b = 8,110 pc/h [Exhibit 24-8(F)] c = c b * f HV * f p = 8,110 * 0.952 * 1.000 = 7,721 eh/h c h = c * PHF = 7,721 * 0.91 = 7,026 eh/h The Results This weaing segment will operate at LOS C during the peak hour. Weaing segment density is 27.3 pc/mi/ln. The capacity of the weaing segment is estimated as 7,720 eh/h (for the 15-min olume), or 7,030 eh/h (for the full-hour olume). Chapter 24 - Freeway Weaing 24-24 Example Problems
General Information FREEWAY WEAVING WORKSHEET Site Information Analyst M.E. Freeway/Direction of Trael - Agency or Company CEI Weaing Segment Location - Date Performed 8/3/99 Jurisdiction - Analysis Time Period AM-Peak Analysis Year 1999 X Operational (LOS) Design (N, L, Type) Planning (LOS) Planning (N, L, Type) Inputs 1297 Sketch (show lanes, L, o1, o2, w1, w2 ) Conersion to pc/h Under Base Conditions o1 o2 w1 w2 w nw (pc/h) AADT K D V PHF % HV f HV f p (eh/day) (eh/h) Weaing and Nonweaing Speeds Weaing Segment Speed, Density, Leel of Serice, and Capacity Weaing segment speed, S (mi/h) S = A B w nw S + w S nw ( ) ( ) Weaing segment density, D (pc/mi/ln) D = /N S L = 1,500 ft 692 1037 1815 Leel of serice, LOS (Exhibit 24-2) Capacity for base condition, c b (pc/h) (Exhibit 24-8) Capacity as a 15-min flow rate, c (eh/h) c = c b * f HV * f p Capacity as a full-hour olume, c h (eh/h) c h = c(phf) C D Freeway free-flow speed, S FF = 65 mi/h Weaing number of lanes, N = 4 Weaing segment length, L 1,500 ft Terrain X Leel Rolling Weaing type Type A X Type B Type C Volume ratio, VR = w 0.357 Weaing ratio, R = w2 w 0.400 V = PHF * f HV *f p 1,815 0.91 10 0.952 1.000 2,095 1,297 0.91 10 0.952 1.000 1,497 1,037 0.91 10 0.952 1.000 1,197 692 0.91 10 0.952 1.000 799 1,729 0.91 10 0.952 1.000 1,996 3,112 0.91 10 0.952 1.000 3,592 4,841 0.91 10 0.952 1.000 5,588 Unconstrained Constrained Weaing (i = w) Nonweaing (i = nw) Weaing (i = w) Nonweaing (i = nw) a (Exhibit 24-6) b (Exhibit 24-6) c (Exhibit 24-6) d (Exhibit 24-6) Weaing intensity factor, W i a(1 + VR) b (/N) c W i = (L) d 0.08 2.2 0.70 0.50 0.643 0.0020 6.0 1.0 0.50 0.450 Weaing and nonweaing speeds, S i (mi/h) S FF 10 S i = 15 + 1 + W i 48.5 52.9 Number of lanes required for unconstrained operation, N w (Exhibit 24-7) 1.65 Maximum number of lanes, N w (max) (Exhibit 24-7) 3.5 X If N w < N w (max) unconstrained operation If N w N w (max) constrained operation 51.2 27.3 C 8,110 7,721 7,026 Example Problem 1 24-25 Chapter 24 - Freeway Weaing Example Problems