highway capacity manual 2000

___________________________________________________Highway Capacity Manual 2000

Chapter 24 – Freeway Weaving Page 24-1 06/08/99

I. INTRODUCTION

This chapter contains detailed procedures for the analysis of operations in freeway weaving areas.Guidelines are also given for the application of these procedures to weaving areas on multilane highwaysand collector distributor roadways.

For a discussion of basic concepts and definitions, please consult Chapter 13, Freeway Concepts.This section contains a complete discussion and definition of the three types of weaving configuration –Type A, Type B, and Type C, and of unconstrai ned and constrained operations in weaving areas.Understanding these concepts and definitions is critical to correctly applying the methodology of thischapter, and to adequately interpreting the results of analysis.

II. METHODOLOGY

WEAVING AREA PARAMETERS

Exhibit 24-1 illustrates and defines the variables that are used in the analysis of weaving areas.These variables are used in the various algorithms that make up the analysis methodology. In addition tothese variables, weaving areas are classified into one of three types of geometric configurations, defined asfollows:

• Type A Weaving vehicles in both directions must make one lane-change to successfullycomplete a weaving maneuver.

• Type B Weaving vehicles in one direction may complete a weaving maneuver withoutmaking a lane-change, while those in the other direction must make on lane-change to successfully complete a weaving maneuver.

• Type C Weaving vehicles in one direction may complete a weaving maneuver withoutmaking a lane-change, while those in the other direction must complete two ormore lane-changes to successfully complete a weaving maneuver.

The methodology presented in this chapter has five distinct components:

• Models predicting the space mean speed (average running speed) of weaving and non-weaving vehicles in the weaving area. Models are specified for each configuration type andfor unconstrained and constrained operations.

• Models describing the proportional use of lanes by weaving and non-weaving vehicles thatare used to determine whether operations are unconstrained or constrained.

• An algorithm that converts predicted speeds to an average density within the weaving area.

• Definition of level of service criteria based upon density within the weaving area.

• A model for the determination of the capacity of any weaving area.

These components are discussed in the sections that follow.


Chapter 24 – Freeway Weaving 4-2 06/08/99

EXHIBIT 24-1. PARAMETERS AFFECTING WEAVING AREA OPERATION

Symbol DefinitionLNNw

Nw (max)

Nnw

vvo1

vo2

vw1

vw2

vw

vnw

VRR

Sw

Snw

SD

Ww

Wnw

Length of weaving area, m.Total number of lanes in the weaving area.Number of lanes to be used by weaving vehicles if unconstrained operation is tobe achieved.Maximum number of lanes that can be used by weaving vehicles for a givenconfiguration.Number of lanes used by non-weaving vehicles.Total rate of flow in the weaving area, pcph.Larger of the two outer, or non-weaving, flows in the weaving area, pcph.Smaller of the two outer, or non-weaving, flows in the weaving area, pcph.Larger of the two weaving flows in the weaving area, pcph.Smaller of the two weaving flows in the weaving area, pcph.Total weaving flow in the weaving area, pcph (vw=vw1+vw2).Total non-weaving flow in the weaving area, pcph (vnw=vo1+vo2).Volume ratio; the ratio of weaving to total flow in the weaving area (VR=vw/v).Weaving ratio; the ratio of the smaller weaving flow to total weaving flow(R=vw2/vw).Speed of weaving vehicles in the weaving area, km/h.Speed of non-weaving vehicles in the weaving area, km/h.Speed of all vehicles in the weaving area, km/h.Density of all vehicles in the weaving area, pc/km/ln.Weaving intensity factor for prediction of weaving speed.Weaving intensity factor for prediction of non-weaving speed.

PREDICTION OF WEAVING AND NON-WEAVING SPEEDS

The heart of the weaving area analysis procedure is the prediction of space mean speeds ofweaving and non-weaving flows within the weaving area. They are separately predicted because undersome conditions, they can be quite dissimilar, and the analyst needs to be aware of this.

The algorithm for prediction of average weaving and non-weaving speeds may be generally statedby Equation 24-1.

[24-1]i

i W

SSSS

+−+=

1minmax

min

vo1 or v o2

vw1 or v w2

vo1 or v o2

vw1 or v w2



whereSi = average speed of weaving (i=w) or non-weaving (i=nw) vehicles,

km/h.

Smin = minimum speed expected in a weaving area, km/h.

Smax = maximum speed expected in a weaving area, km/h.

Wi = weaving intensity factor for weaving (i=w) and non-weaving(i=nw) flows.

For the purposes of these procedures, the minimum speed, Smin is set at 24 km/h. The maximum speed,Smax, is taken to be the average free-flow speed of the freeway segments entering and leaving the weavingarea plus 8 km/h. The addition of 8 km/h to the free-flow speed adjusts for the tendency of the algorithm tounderpredict high speeds. Setting the minimum and maximum speeds in this way constrains the predictionrange of the algorithm to a reasonable range. With these assumptions incorporated, the speed prediction isgiven by Equation 24-2.

[24-2]

whereSFF is the average free-flow speed of the freeway segments entering and leaving the section.

The weaving intensity factors (Ww, Wnw) are a measure of the impact of weaving activity on theaverage speeds of weaving and non-weaving vehicles, respectively. These factors are computed byEquation 24-3.

[24-3]

whereWi = weaving intensity factors for weaving (i=w) and non-weaving (i=nw)

flows.

VR = volume ratio.

v = total flow rate in the weaving area (equivalent pcph).

N = total number of lanes in the weaving area.

L = length of the weaving area, m.

a,b,c,d = constants of calibration.

Constants of calibration (a,b,c,d) are given in Exhibit 24-2. They vary on the basis of three factors:

• whether the prediction is for the average speed of weaving or non-weaving vehicles,• configuration type (A, B, or C), and• whether the operation is unconstrained or constrained.

i

FFi W

SS

+−+=

1

1624

d

cb

i L

NvVRaW

)28.3(

)/()1( +=



EXHIBIT 24-2. CONSTANTS FOR COMPUTATION OF WEAVING INTENSITY FACTORS

General Form:

W = a (1+VR)b (v/N)c / (3.28 L)d

Configuration Constants for Weaving SpeedSw

a b c d

Constants for Non-Weaving SpeedSnw

a b c dTYPE AUnconstrainedConstrained

0.15 2.2 0.97 0.80 0.35 2.2 0.97 0.80

0.0035 4.0 1.3 0.75 0.0020 4.0 1.3 0.75

TYPE BUnconstrainedConstrained

0.08 2.2 0.70 0.50 0.15 2.2 0.70 0.50

0.0020 6.0 1.0 0.50 0.0010 6.0 1.0 0.50

TYPE CUnconstrainedConstrained

0.08 2.3 0.80 0.60 0.14 2.3 0.80 0.60

0.0020 6.0 1.1 0.60 0.0010 6.0 1.1 0.60

Initial estimates of speed are always based upon the assumption of unconstrained operation. Thisassumption is later tested, and speeds are re-computed if operations turn out to be constrained.

The combination of Equations 24-2 and 24-3 yields sensitivities that are consistent with observedoperations of weaving areas:

• As the length of the weaving area increases, speeds also increase, as the intensity of lane-changing declines.

• As the proportion of weaving vehicles in total flow (VR) increases, speeds decrease,reflecting the increased turbulence caused by higher proportions of weaving vehicles in thetraffic stream.

• As average total flow per lane (v/N) increases, speeds decrease, reflecting more intensedemand.

• Constrained operations yield lower weaving speeds and higher non-weaving speeds thanunconstrained operations. This reflects the fact that weaving vehicles are constrained to lessspace than equilibrium would require, while non-weaving vehicles have correspondinglymore than their equilibrium share of space. In Exhibit 24-2, this is reflected by changes in theconstant a.

• Type B sections are the most efficient for handling large weaving flows. For such highweaving flows, weaving speeds are higher than for Type A and C sections of equal length andwidth.

• The sensitivity of speeds to length is greatest for Type A sections, as weaving vehicles areoften accelerating or decelerating as they traverse the weaving area.

• The sensitivity of non-weaving speeds to the volume ratio (VR) is greatest for Type B and Csections. Because these sections can accommodate higher proportions of weaving vehicles,



and because each has a through lane for one weaving movement, non-weaving vehicles aremore likely to be sharing lanes with weaving vehicles than in Type A sections, where theopportunity to segregate is greater.

The last point is important, and serves to highlight the essential difference between Type Asections (particularly ramp-weaves) and others (Types B and C). Because all weaving vehicles must crossa crown line in Type A sections, weaving vehicles tend to concentrate in the two lanes adjacent to thecrown line, while non-weaving vehicles gravitate to outer lanes. Thus there is substantially moresegregation of weaving and non-weaving flows in a later section in this chapter.

This difference makes Type A sections behave somewhat differently from other configurations.Speeds tend to be higher in Type A sections than in Type B or C sections with the same length, width, anddemand flows. This does not, however, suggest that Type A sections always operate better than Type B orC sections for similar lengths, widths, and flows. Type A sections have more severe restrictions on theamount of weaving traffic that can be accommodated than other configurations. This is discussed further inthe section on “Capacity of Weaving Areas.”

DETERMINING THE TYPE OF OPERATION

The determination of whether a particular section is operating in an unconstrained or constrainedstate is based upon the comparison of two variables that are defined in Chapter 13. The two variables are:

Nw = number of lanes that must be used by weaving vehicles in order to achieveequilibrium, or unconstrained, operation; and

Nw (max) = maximum number of lanes that may be used by weaving vehicles for a givenconfiguration.

Fractional values for lane use requirements of weaving vehicles may occur because weaving andnon-weaving vehicles share some lanes. Cases for which Nw < Nw (max) are unconstrained, because thereare no impediments to weaving vehicles using the number of lanes required for equilibrium. Where Nw >Nw (max), weaving vehicles are constrained to using Nw (max) lanes, and therefore cannot occupy as muchof the roadway as would be needed to establish equilibrium operations.

Exhibit 24-3 provides algorithms for the computation of Nw, and shows the values of Nw (max),which are discussed more fully in Chapter 13.

EXHIBIT 24-3. CRITERIA FOR UNCONSTRAINED VS CONSTRAINED OPERATIONOF WEAVING AREAS

Configuration Number of Lanes Required for UnconstrainedOperation, Nw

Nw (max)

TYPE A 1.21 N VR0.571 L0.234 / Sw0.438 1.4

TYPE B N [0.085 + 0.703 VR + (71.57/L) – 0.0112 (Snw-Sw) ] 3.5TYPE C N [0.761 + 0.047 VR – 0.00036 L – 0.0031 (Snw-Sw) ] 3.0*

* For two-sided weaving areas, all freeway lanes may be used by weaving vehicles.

The algorithms of Exhibit 24-2 are interesting. They rely on the prediction of unconstrainedweaving and non-weaving speeds. The equations take these results, and predict the number of lanesweaving vehicles would have to occupy to achieve unconstrained speeds. If the result indicates thatconstrained operations exist, speeds would have to be recomputed using constrained equations.

The limit on maximum number of weaving lanes, Nw (max), is most restrictive for Type Asections, and reflects the need for weaving vehicles to cluster in the two lanes adjacent to the crown line.The through weaving lane in Type B and C configurations provides for greater occupancy of lanes byweaving vehicles.



Type A sections have another unusual, but understandable, characteristic. As the length of a TypeA section increases, it is more likely that constrained operation will result. As the length increases, thespeed of weaving vehicles is also able to increase. Thus, weaving vehicles are using more space as lengthincreases, and the likelihood of requiring more than the maximum of 1.4 lanes to achieve equilibrium alsoincreases.

Type B and C sections show an opposite trend. Increasing length has less of an impact onweaving speed than for Type A sections. First, acceleration and deceleration from low-speed ramps is lessof an issue in Type B and C sections, which are, by definition, major weaving areas. Second, thesubstantial mixing of weaving and non-weaving vehicles in the same lanes makes the resulting speeds lesssensitive to length. In Type B and C sections, the proportion of lanes needed by weaving vehicles toachieve unconstrained operation decreases as length increases.

The user should note that under extreme conditions (high VR, short length), the equation for TypeB sections can predict values of Nw >N. While this is not practical, and reflects portions of the researchdata base with sparse field data, it may always be taken to indicate constrained operations.

CONVERTING SPEED PREDICTIONS TO AN AVERAGE DENSITY

Once speeds have been estimated, and the type of operation determined (which may cause a re-computation of estimated speeds), the speed results may be converted to an average density for all vehiclesin the weaving area. Before a density is computed, it is necessary to estimate the average space meanspeed of all vehicles in the section:

[24-4]

where

S = space mean speed of all vehicles in the weaving area, km/h.

Sw = space mean speed of weaving vehicles in the weaving area, km/h.

Snw = space mean speed of non-weaving vehicles in the weaving area, km./h.

v = total flow rate in the weaving area, equivalent pcph.

vw = weaving flow rate in the weaving area, equivalent pcph.

vnw = non-weaving flow rate in the weaving area, equivalent pcph.

The average speed for all vehicles may now be converted to a density:

[24-5]

)()(nw

nw

w

w

S

v

S

vv

S+

=

S

NvD

/=



where:D = average density for all vehicles in the weaving area, pc/km/ln.Other variables as previously defined.

LEVEL-OF-SERVICE CRITERIA

Level-of-service criteria for weaving areas are based upon the average density of all vehicles inthe weaving area. The criteria are shown in Exhibit 24-4.

EXHIBIT 24-4 LEVEL-OF-SERVICE CRITERIA FOR WEAVING AREAS

Maximum Density (pc/km/ln)Level ofService Freeway Weaving Area Multilane and C-D Weaving Areas

A 6.0 8.0B 12.0 15.0C 17.0 20.0D 22.0 23.0E 27.0 25.0F > 27.0 >25.0

In general, these criteria allow for slightly higher densities at any given level of service thresholdthan on a comparable base freeway segment or multilane highway segment. This follows the philosophythat drivers expect and will accept higher densities in weaving areas relative to those on basic freeway ormultilane highway sections. The level of service E/F boundary does not follow this approach. Rather, itreflects densities that are somewhat less than that identified for basic freeway or multilane highwaysegments. Due to the additional turbulence in weaving areas, it is believed that breakdown occurs atsomewhat lower densities than for basic segments.

CAPACITY OF WEAVING AREAS

The capacity of a weaving area is any combination of flows that causes the density to reach theLOS E/F boundary condition of 27.0 pc/km/ln for freeways or 25.0 pc/km/ln for multilane highways or C-D roadways.

Thus, capacity varies with a number of variables: configuration, number of lanes, free-flow speedof the freeway, length, and volume ratio. Because of the form of predictive algorithms, it is not possible togenerate a simple closed-form solution for capacity given the specification of the other variables. Rather, atrial-and-error process must be used. In the applications section of this chapter, such computations havebeen made for freeways, and the results are tabulated for ease of use.

The tabulated capacities reflect some other limitations on weaving area operations that reflect fieldobservations:

• The capacity of a weaving area may never exceed the capacity of a similar basic freeway ormultilane highway segment.

• Field studies indicate that weaving flow rates should not exceed the following values: 2,800pcph for Type A sections; 4,000 pcph for Type B sections; 3,500 pcph for Type C sections.Higher weaving flows are likely to cause failure regardless of the results of analysis using theprocedures herein.

• Field studies indicate that there are also limitations on the proportion of weaving flow (VR)that can be accommodated by various configurations:



• Configuration Maximum practical VR

Type A – 2 lanes 1.00Type A – 3 lanes 0.45Type A – 4 lanes 0.35Type A – 5 lanes 0.20Type B – all 0.80Type C – all 0.50

At higher volume ratios, stable operations may still occur, but operations will be worse thanthose anticipated by the methodology, and failure could occur.

• For Type C sections, the weaving ratio, R, should not exceed 0.40, with the larger weavingflow being in the direction of the through weaving lane. At higher weaving ratios, or wherethe dominant weaving flow is not in the direction of the through weaving lane, stableoperations may still occur, but operations will be worse than those anticipated by themethodology. Breakdown may occur in some cases.

• The maximum lengths for which weaving analysis is conducted is 600 m for Type A sectionsand 750 m for Types B and C. Beyond these lengths, merge and diverge areas are separatelyconsidered using the methodology of Chapter 25, Ramps and Ramp Junctions.

III. APPLICATIONS

OPERATIONAL ANALYSIS

In operational analysis, all input variables are specified: demand flows and characteristics and allgeometric characteristics. The application of the methodology results in a determination of the expectedlevel of service under the specified conditions. The steps in such an analysis are specified and discussed inthe sections that follow.

Establish Roadway and Traffic Conditions

All existing or projected roadway and traffic conditions must be specified. Roadway conditionsinclude the length of the section, the number of lanes, the type of configuration under study, and type ofterrain or grade conditions. Where freeway free-flow speeds are not known, then the characteristics of thefreeway (or multilane highway) must be specified to allow their determination using the appropriatealgorithms.

Configuration is based upon the number of lane-changes required of each weaving movement. Acomplete discussion of this concept is found in Chapter 13. Exhibit 24-5 may be used as a helpful guide inestablishing configuration type.

Traffic conditions include a specification of each flow in the section: vo1, vo2, vw1, and vw2. Theheavy vehicle composition and peak-hour factor that apply to each should also be known. In most cases,hourly volumes are specified. Peak-hour factors will then be used to estimate maximum 15-minute flowrates, which are used in analysis. This procedure, however, assumes that all component flows peak duringthe same 15-minute period. This may not be the case. Thus, whenever possible, 15-minute flow ratesshould be directly observed, so that the worst period can be identified and analyzed. Use of peak-hourfactors to estimate flow rates results in a worst case analysis based upon all flows peaking at the same time.



EXHIBIT 24-5. DETERMINING CONFIGURATION TYPENumber of Lane Changes Required by Movement vw2Number of Lane

Changes RequiredBy Mvt vw1 0 1 >2

0 Type B Type B Type C1 Type B Type A NA

> 2 Type B NA NA NA = not applicable; configuration is not feasible.

Convert Hourly Traffic Volumes to Peak Flow Rates Under Base Conditions

All of the models and equations of this chapter are based upon peak 15-minute flow rates inequivalent pcph. Thus, hourly volumes must be converted to this basis:

[24-6]

whereV = hourly volume, vph.v = peak 15-minute flow rate in hour, equivalent pcph.fHV = heavy vehicle adjustment factor (from freeway or multilane highway

methodology).fp = driver population adjustment factor (from freeway or multilane

highway methodology).

When 15-minute flow rates are specified initially, set the PHF to 1.00 before applying this conversion.

Construct a Weaving Diagram

After volumes have been converted, it is useful to construct a weaving diagram of the typeillustrated in Exhibit 24-6. All flows are shown as flow rates in equivalent pcph, and critical analysisvariables are identified and placed on the diagram. The diagram may now be used as a reference for allrequired input information during the remaining steps in the solution.

Estimate Unconstrained Weaving and Non-Weaving Speeds

Compute the weaving intensity factors for the appropriate configuration, assuming that operationsare unconstrained. This is done using the algorithm and constants shown in Exhibit 24-2. Use the weavingintensity factors to estimate average speed of weaving and non-weaving vehicles (assuming unconstrainedoperations) as shown in Equation 24-2.

Check for Constrained Operation

Using the equation for the appropriate configuration from Exhibit 24-3, compute the number oflanes weaving vehicles must occupy to achieve unconstrained operation (Nw). If this value is less than orequal to the value of Nw (max) shown in Exhibit 24-3 (for the appropriate configuration), then operationswill be unconstrained, and the speeds estimated in the previous step are correct. If Nw > Nw (max),operations are constrained. In this case, the speeds must be recomputed using constants of calibration forconstrained operations (from Exhibit 24-2).

pHV fxfxPHF

Vv =



THEN:vW1 = WEAVING FLOW WITH THE HIGHEST NUMERIC VALUE (500)vW2 = WEAVING FLOW WITH THE SMALLEST NUMERIC VALUE (300)vW = TOTAL WEAVING FLOW (500 + 300 = 800)v = TOTAL FLOW IN THE WEAVING AREA (500 + 300 + 1500 + 400 = 2700)VR = VOLUME RATIO = vW/v (800/2700 = 0.296)R = WEAVING RATIO vW2/vW (300/800 = 0.375)L = WEAVING LENGTH = 370mN = NUMBER OF LANES = 4

EXHIBIT 24-6. CONSTRUCTION AND USE OF WEAVING DIAGRAMS

Compute Average Space Mean Speed and Density of All Vehicles in the Weaving Area

The space mean speed for all vehicles in the weaving area is computed using Equation 24-4.Density may then be computed using Equation 24-5.

Determine Level of Service

The level of service for the weaving area is determined by comparing the computed density to thecriteria of Exhibit 24-4. A single level of service is used to characterize total flow in the weaving area,although it is recognized that in some situations (particularly in cases of constrained operations) that non-weaving vehicles may achieve better operational quality than weaving vehicles.

Special Application – Multiple Weaving Areas

Multiple weaving areas are formed when one merge point is closely followed by two divergepoints, or where two merge points are closely followed by a single diverge point. In such cases, severalsets of weaving movements take place over the same segment of the freeway, and lane-changing turbulencemay be higher than that found in the simple weaving sections referred to in previous sections.

The two types of multiple weaving areas are shown in Exhibits 24-7 and 24-8. Figure 24-7depicts a single merge area followed by two diverge areas, and shows weaving diagrams for the twosegments of the weaving area. The weaving of movement 5 with movements 3 and 4 must take place inthe first segment, as movement 5 exits at the first diverge. The weaving of movement 2 with movement 3can take place anywhere in the weaving area. However, to avoid the turbulence of weaving that must takeplace in the first segment, these latter weaving movements will tend to concentrate in the second segmentof the weaving area.



EXHIBIT 24-7. WEAVING FLOWS IN A MULTIPLE WEAVE FORMED BY A SINGLE MERGEFOLLOWED BY TWO DIVERGES

EXHIBIT 24-8. WEAVING FLOWS IN A MULTIPLE WEAVE FORMED BY TWO MERGESFOLLOWED BY ONE DIVERGE



Exhibit 24-8 depicts two merge areas followed by a single diverge. In this case, the weaving ofmovements 3 and 4 with movement 5 must take place in the second segment of the section, as movement 5only enters at the second merge point. Although the weaving of movement 2 with movement 3 could takeplace anywhere in the section, it will tend to be concentrated in the first segment as drivers seek to avoidthe turbulence of other weaving movements that must take place in the second segment.

The analysis of multiple weaving sections involves the construction of appropriate weavingdiagrams for each segment, as illustrated in Exhibits 24-7 and 24-8. Once these diagrams are established,each segment may be analyzed as a simple weaving section, using the six steps as previously described.The type of weaving area for each segment is determined by the required lane changes of weaving vehicles,as presented in Exhibit 24-5.

CAPACITIES AND SERVICE VOLUMES

As noted previously, the capacity of a weaving area is represented by any set of conditions thatresults in an average density of 27 pc/km/ln (for freeways) or 25 pc/km/ln (for multilane highways and C-Droadways). Thus, capacity varies with the configuration, the length and width of the weaving area, theproportion of total flow that weaves (VR), and the free-flow speed of the freeway. For any given set ofconditions, the algorithms described herein must be solved iteratively to find capacity.

For freeway facilities, such capacities have been determined, and are shown in Exhibit 24-9.These capacities represent maximum 15-minute flow rates under equivalent base conditions, and arerounded to the nearest 10 pcph. To find a capacity under a given set of prevailing conditions:

[24-7]

where:c = capacity under prevailing conditions, stated as a rate of flow for the peak 15-

minutes of the hour, vph.

cI = capacity under base conditions, stated as a rate of flow for the peak 15-minutesof the hour, pcph. (Exhibit 24-9).

fHV = heavy vehicle adjustment factor (basic freeway segments or multilanehighways).

fp = driver population adjustment factor (basic freeway segments or multilanehighways).

If a capacity in terms of an hourly volume is desired, it may be computed as:

[24-8]

wherech = capacity under prevailing conditions, expressed as an hourly volume, vph.PHF = peak hour factor.

PHFcch =

pHVI ffcc =



EXHIBIT 24-9. CAPACITY FOR VARIOUS WEAVING AREAS

(A) TYPE A WEAVING AREAS – 120 km/h FREE-FLOW SPEED

Length of Weaving Area, m.VolumeRatio, VR 150 300 450 6001

Three-Lane Sections0.10 6050 6820 72004 72004

0.20 5490 6260 6720 70500.30 5040 5780 6240 65700.40 4660 5380 5530 58003

0.452 4430 50003 52703 55503

Four-Lane Sections0.10 8060 9010 96004 96004

0.20 7320 8340 8960 94000.30 6710 75203 80903 85103

0.355 63703 71603 77003 80009

Five-Lane Sections0.10 10080 11379 120004 120004

0.206 9150 105403 112703 117903

(B) TYPE A WEAVING AREAS –110 km/h FREE-FLOW SPEED


Three-Lane Sections0.10 5770 6470 6880 70504

0.20 5250 5960 6380 66800.30 4830 5520 5940 62400.40 4480 5150 52503 55303

0.452 4190 47903 50203 53103

Four-Lane Sections0.10 7690 8630 9180 94004

0.20 7000 7940 8500 89000.30 6440 71803 77103 80903

0.355 60803 68303 73603 77303

Five-Lane Sections0.10 9610 10790 11470 117504

0.206 8750 100303 106903 111603

(C) TYPE A WEAVING AREAS – 100 km/h FREE-FLOW SPEED


Three-Lane Sections0.10 5470 6110 6480 67300.20 5000 5640 6020 62900.30 4610 5240 5620 59000.40 4290 4900 49903 52503

0.452 4000 45203 47903 50403

Four-Lane Sections0.10 7300 8150 8630 89700.20 6660 7520 8030 83800.30 60803 68303 73103 76503

0.355 57803 65203 69903 73303

Five-Lane Sections0.10 9120 10180 10790 112100.206 8330 95003 100803 105103



Exhibit 24-9 (Continued)

(D) TYPE A WEAVING AREAS – 90 km/h FREE-FLOW SPEED


Three-Lane Sections0.10 5160 5730 6050 62700.20 4730 5310 5650 58800.30 4380 4950 5290 55400.40 4090 44203 47303 49603

0.452 3850 42403 44703 4780Four-Lane Sections

0.10 6880 7640 8070 83500.20 6310 7080 7530 78400.30 57903 64603 68903 71903

0.355 55203 6180 65903 69103

Five-Lane Sections0.10 8600 9550 10080 104400.206 80603 89303 94603 98203

(E) TYPE B WEAVING AREAS – 120 km/h FREE-FLOW SPEED

Length of Weaving Area, m.VolumeRatio, VR 150 300 450 600 7507

Three-Lane Sections0.10 72004 72004 72004 72004 72004

0.20 6830 72004 72004 72004 72004

0.30 6120 6690 7010 72004 72004

0.40 5550 6100 6430 6670 68500.50 5100 5630 5950 6180 63700.60 4750 5260 5570 5800 59800.70 4180 4990 5290 5520 56900.808 3900 4820 50009 50009 50009

Four-Lane Sections0.10 96004 96004 96004 96004 96004

0.20 9110 96004 96004 96004 96004

0.30 8170 8910 9350 96004 96004

0.40 7400 8140 8570 8890 91300.50 66703 7500 7930 80009 80009

0.60 60703 66709 66709 66709 66709

0.70 55803 57609 57609 57609 57609

0.808 50009 50009 50009 50009 50009

Five-Lane Sections0.10 120004 120004 120004 120004 120004

0.20 11390 120004 120004 120004 120004

0.30 10210 11140 11690 120004 120004

0.40 92703 100009 100009 100009 100009

0.50 80009 80009 80009 80009 80009

0.60 66709 66709 66709 66709 66709

0.70 57609 57609 57609 57609 57609

0.808 50009 50009 50009 50009 50009



Exhibit 24-9 (continued)

(F) TYPE B WEAVING AREAS – 110 km/h FREE-FLOW SPEED



0.20 6460 6950 70504 70504 70504

0.30 5810 6320 6620 6830 69800.40 5280 5790 6090 6300 64700.50 4860 5350 5650 5860 60300.60 4550 5010 5300 5510 56800.70 4320 4770 5050 5250 54100.808 3650 4600 4880 50009 50009


0.20 8610 9270 94004 94004 94004

0.30 7750 8430 8820 9100 93100.40 7040 7720 8120 8400 86200.50 63703 7140 7530 7820 80009

0.60 58103 66709 66709 66709 66709

0.70 53503 57609 57609 57609 57609

0.808 50009 50009 50009 50009 50009


0.20 10760 11590 117504 117504 117504

0.30 9690 10540 11030 11370 116400.40 88303 9650 100009 100009 100009

0.50 79603 80009 80009 80009 80009

0.60 66709 66709 66709 66709 66709

0.70 57609 57609 57609 57609 57609

0.808 50009 50009 50009 50009 50009

(G) TYPE B WEAVING AREAS – 100 km/h FREE-FLOW SPEED



0.20 6070 6510 6750 69004 69004

0.30 5490 5950 6210 6400 65400.40 5010 5470 5740 5930 60700.50 4620 5070 5340 5530 56800.60 4330 4760 5020 5220 53600.70 4120 4530 4790 4970 51200.808 3600 4380 4630 4820 4960


0.20 8100 8680 9010 92004 92004

0.30 7320 7930 8280 8530 87100.40 6680 7290 7650 7900 81000.50 60603 6760 7120 7370 75800.60 55403 6340 66709 66709 66709

0.70 51303 56403 57609 57609 57609

0.808 48003 50009 50009 50009 50009


0.20 10120 10850 11260 115004 115004

0.30 9150 9910 10350 10660 108900.40 83703 9110 9560 9880 100009

0.50 75703 80009 80009 80009 80009

0.60 66709 66709 66709 66709 66709

0.70 57609 57609 57609 57609 57609

0.808 50009 50009 50009 50009 50009




(H) TYPE B WEAVING AREAS – 90 km/h FREE-FLOW SPEED



0.20 5670 6050 6270 6410 65200.30 5150 5560 5790 5950 60700.40 4720 5130 5370 5540 56700.50 4370 4770 5010 5190 53200.60 4110 4500 4730 4900 50300.70 3910 4290 4520 4690 48200.808 3440 4150 4380 4540 4670


0.20 7560 8070 8360 8550 86900.30 6870 7410 7720 7940 81000.40 6290 6840 7160 7390 75600.50 57403 6360 6680 6920 70900.60 52703 5990 6310 6530 66709

0.70 48903 53503 57609 57609 57609

0.808 45903 50009 50009 50009 50009


0.20 9450 10090 10440 10680 108600.30 8580 9260 9650 9920 101200.40 78903 8550 8950 9230 94500.50 71703 7960 80003 80003 80003

0.60 65803 66709 66709 66709 66709

0.70 57609 57609 57609 57609 57609

0.808 50009 50009 50009 50009 50009

(I) TYPE C WEAVING AREAS – 120 km/h FREE-FLOW SPEED



0.20 6590 72004 72004 72004 72004

0.30 5890 6540 6930 7200 72004

0.40 5530 5960 6350 6620 68400.5010 4890 5500 5870 6140 6360


0.20 8780 96004 96004 96004 96004

0.30 7850 8720 9230 9590 96004

0.40 7110 7950 8470 87509 87509

0.5010 6520 70009 70009 70009 70009


0.20 115203 120004 120004 120004 120004

0.30 101403 111703 116709 116709 116709

0.40 87509 87509 87509 87509 87509

0.5010 70009 70009 70009 70009 70009




(J) TYPE C WEAVING AREAS – 110 km/h FREE-FLOW SPEED



0.20 6240 6830 70504 70504 70504

0.30 5610 6200 6550 6790 69800.40 5090 5670 6020 6270 6470

0.5010 4680 5240 5590 5840 6030Four-Lane Sections

0.10 9350 94004 94004 94004 94004

0.20 8320 9100 94004 94004 94004

0.30 7470 8270 8730 9060 93000.40 6240 7560 8030 8360 8620

0.5010 5830 6990 70009 70009 70009


0.20 109003 117504 117504 117504 117504

0.30 96303 105703 10910 11320 116300.40 85903 87509 87509 87509 87509

0.5010 70009 70009 70009 70009 70009

(K) TYPE C WEAVING AREAS – 100 km/h FREE-FLOW SPEED



0.20 5890 6410 6700 6900 69004

0.30 5310 5850 6160 6370 65400.40 4840 5370 5680 5910 6080


0.10 8760 92004 92004 92004 92004

0.20 7850 8540 8930 9200 92004

0.30 7080 7790 8210 8500 87200.40 6450 7150 7580 7880 8110

0.5010 5950 6630 70009 70009 70009


0.20 102503 110503 11170 11500 115004

0.30 91103 99603 10260 10620 109000.40 81703 87509 87509 87509 87509

0.5010 7000( 7000( 7000( 7000( 7000(




(L) TYPE C WEAVING AREAS – 90 km/h FREE-FLOW SPEED



0.20 5510 5970 6230 6400 65200.30 5000 5480 5750 5940 60900.40 4570 5050 5330 5530 5680


0.10 8150 8700 8980 90004 90004

0.20 7350 7960 8300 8530 87000.30 6660 7300 7670 7920 81100.40 5640 6730 7110 7370 7580

0.5010 5300 6260 6640 6900 70009


0.20 95803 102703 10380 10660 108700.30 85703 93103 9580 9900 101400.40 77203 84703 87509 87509 87509

0.5010 70009 70009 70009 70009 70009

Notes for Exhibit 24-9:

1. Type A weaving sections longer than 600 m are treated as isolated merge and diverge areas using the procedures ofChapter 25, Ramps and Ramp Junctions.

2. Three-lane Type A sections do not operate well at volume ratios greater than 0.45. Poor operationsand some local queuing is expected in such cases.

3. Capacity occurs under constrained operating conditions.

4. Capacity constrained by basic freeway segment capacity.

5. Four-lane Type A sections do not operate well at volume ratios greater than 0.35. Poor operations andsome local queuing are expected in such cases.

6. Five-lane Type A sections do not operate well at volume ratios greater than 0.20. Poor operations andsome local queuing are expected in such cases.

7. Type B and C weaving sections longer than 750 m are treated as isolated merge and diverge areasusing the procedures of Chapter 25, Ramps and Ramp Junctions.

8. Type B weaving sections do not operate well at volume ratios greater than 0.80. Poor operations andsome local queuing are expected in such cases.

9. Capacity constrained by maximum allowable weaving flow rate: 2,800 pcph (Type A), 4,000 (TypeB), 3,500 (Type C).

10. Type C weaving sections do not operate well at volume ratios greater than 0.50. Poor operations andsome local queuing are expected in such cases.



Service volumes for other levels of service are given in Chapter 13, Freeway Concepts. Theseservice volumes are in terms of full-hour volumes for an assumed PHF of 0.90, and include 5 percenttrucks on level terrain. Service volumes are tabulated only for freeways with a free-flow speed of 120km/h.

For other peak-hour factors and truck percentages, the service volumes of Chapter 13 can bemodified and expressed as Equations 24-8 and 24-9.

[24-8]

[24-9]

where: SVTi = service volume for LOS i, from Chapter 13, for the standardconditions of PHF = 0.90 and 5 percent trucks on level terrain.

SFi = service flow rate for LOS i under prevailing conditions.

SVi = service volume for LOS i, under prevailing conditions.

To find service flow rates or service volumes for multilane highways, or for freeways with free-flow speeds other than 120 km/h, trial-and-error computations would have to be made to find conditionsyielding the appropriate density for the desired level of service. Such a trial and error procedures wouldalso be necessary to find capacity values for multilane highways. It is recommended that suchcomputations be programmed using a spreadsheet for convenience.

IV. EXAMPLE PROBLEMS

The following sample calculations illustrate the application and interpretation of the methodologypresented in this chapter.

Example Problem 1 – Analysis of a Major Weaving Area

The weaving area illustrated in Exhibit 24-10 serves the following traffic volumes: A-C = 1,815vph, A-D = 692 vph, B-C = 1,037 vph, B-D = 1,297 vph. Traffic volumes include 10 percent trucks, andthe PHF = 0.91. The section is located in generally level terrain. The driver population is composedprimarily of commuters, and the observed free-flow speed of the freeway is 110 km/h. What level ofservice is to be expected, and what is the capacity of the section?

EXHIBIT 24-10. WEAVING AREA FOR EXAMPLE PROBLEM 1

PHFxSFSV

fxx

SVSF

ii

HVTi

i

=

=)90.0976.0(

L = 450 m

SFF = 110 km/h



Calculations for this case are summarized in Exhibit 24-11.

EXHIBIT 24-11. COMPUTATIONS FOR EXAMPLE PROBLEM 1

Configuration: Type B (A-D requires on lane change; B-C, none)

Convert Volumes: PHF = 0.91 (given)ET = 1.5 (basic freeway, level terrain)fHV = 1/[1+0.10(1.5-1)] = 0.95fp = 1.00 (commuters)

v(A-C) = 1,815/(0.91x0.95x1.00) = 2,100 pcphv(A-D) = 692/(0.91x0.95x1.00) = 800 pcphv(B-C) = 1,037/(0.91x0.95x1.00) = 1,200 pcphv(B-D) = 1,297/(0.91x0.95x1.00) = 1,500 pcph

Weaving Diagram: 2,100

800

1,200

1,500

Critical Variables: vw = 1,200 + 800 = 2,000 pcphv = 2,000 + 2,100 + 1,500 = 5,600 pcphR = 800/2,000 = 0.40VR = 2,000/5,600 = 0.357

Unconstrained Speeds: Ww = 0.08 (1+0.357)2.2 (5,600/4)0.70/(3.28x450)0.50 = 0.650Wnw = 0.002 (1+0.357)6.0 (5,600/4)1.0/(3.28x450)0.50 = 0.455

(Exhibit 24-2)

Sw = 24 +[(110-16)/(1+0.650)] = 81.0 km/hSnw = 24 = [(110-16)/(1+0.455)] = 88.6 km/h

Check Type of Operation: Nw = 4 [0.085+(0.703x0.357)+(71.57/450)-0.0112(88.6-81.0)] = 1.64 lanes < 3.5 lanes (unconstrained)

(Exhibit 24-3)

Constrained Speeds: Not needed, operation is unconstrained.

Average Speed:

Average Density:

Level of Service: Level of Service C (Exhibit 24-4)

Capacity: cI = 8,420 pcph (Exhibit 24-9 F)c = 8,420 x 0.95 x 1.00 = 8,000 vphch = 8,000 x 0.91 = 7,280 vph

hkmS /7.85

6.88

600,3

0.81

000,2

600,5 =

+

=

ln//3.167.85

4/600,5kmpcD ==



The computations of Exhibit 24-11 show that the section described operates at level of service Cin the unconstrained state, with an average density of 16.3 pc/km/ln and an average speed of 85.7 km/h.Non-weaving vehicles travel somewhat faster than weaving vehicles, which is not unexpected.

The capacity of the section, given its length, width, configuration, free-flow speed, and proportionof weaving traffic, is 8,000 vph (as a 15-minute flow rate), or 7,280 vph (as a full-hour volume).

Example Problem 2 – Analysis of a Ramp-Weaving Section

The weaving section shown in Exhibit 24-12 serves the indicated traffic flows. For convenience,all traffic flows are shown in terms of peak flow rates in equivalent pcph under ideal conditions. The free-flow speed of the freeway has been observed to be 120 km/h. At what level of service will the sectionoperate, and what is its capacity.

EXHIBIT 24-12. WEAVING AREA AND FLOWS FOR EXAMPLE PROBLEM 2

Computations for this case are summarized in Exhibit 24-13.

Exhibit 24-13 indicates that the weaving section described is expected to operate at level ofservice C in the unconstrained state. The average density is expected to be 13.3 pc/km/ln and the averagespeed is 93.8 km/h. The speed of non-weaving vehicles (97.8 km/h) and the speed of weaving vehicles(79.4 km/h) are quite different, and reflect substantial segregation of weaving and non-weaving flows in thesection. Due to the short length of the weaving area (300 m), weaving vehicles must accelerate ordecelerate as they pass through the section, restricting their average speed.

The capacity of the section under base conditions (prevailing conditions are not specified) is 8,394pcph. This is considerably less than the normal freeway capacity for four lanes (9,600 pcph), and reflectsthe impact of weaving turbulence on throughput and the fact that the small amount of ramp-to-ramp trafficpresent in most ramp-weaves prevents full use of the auxiliary lane.

L = 300 m

SFF = 120 km/h



EXHIBIT 24-13. COMPUTATIONS FOR EXAMPLE PROBLEM 2_____________________________________________________________________________Configuration: Type A, Ramp-Weave (All weaving vehicles must make one lane-change)

Convert Volumes: Not required, input specified as flow rates in pcph.

Weaving Diagram: See Exhibit 24-12.

Critical Variables: vw = 600 + 300 = 900 pcphv = 900 + 4,000 + 100 = 5,000 pcphR = 300/900 = 0.333VR = 900/5,000 = 0.18

Unconstrained Speeds: Ww = 0.15 (1+0.18)2.2 (5,000/4)0.97/(3.28x300)0.80 = 0.879Wnw = 0.0035 (1+0.18)4.0 (5,000/4)1.3/(3.28x300)0-.75 = 0.410

(Exhibit 24-2)

Sw = 24 + [(120-16)/(1+0.879)] = 79.4 km/hSnw = 24 + [(120-16)/1+0.410)] = 97.8 km/h

Check Type of Operation: Nw = 1.21 (4) (0.18)0.571 (300)0.234/(79.4)0.438 = 1.02 lanes < 1.4 lanes (Exhibit 24-3)Operation is Unconstrained.

Constrained Speeds: Not required.

Average Speed:

Average Density:

Level of Service: Level of Service C (Exhibit 24-4)

Capacity: cI = 8,494 pcph (Exhibit 24-9 A)Neither capacity under prevailing conditions nor hourly capacity canbe determined as the PHF and truck presence are not specified.

Example Problem 3 – Analysis of a Ramp-Weave Resulting in Constrained Operation

The ramp-weave section shown in Exhibit 24-14 serves the following demand volumes: A-C =975 vph, A-D = 650 vph, B-C = 520 vph, and B-D = 0 vph. Traffic includes 15 percent trucks, and iscomposed primarily of drivers familiar with the location. The PHF is 0.85. The section is located ingenerally rolling terrain. Field observations have determined that the free-flow speed of the freeway is 110km/h. At what level of service is the section expected to operate, and what is its capacity?

EXHIBIT 24-14. WEAVING AREA FOR EXAMPLE PROBLEM 3

Computations for this case are illustrated in Exhibit 24-15.

hkmS /8.93

8.97

100,4

4.79

900

000,5 =

+

=

ln//3.138.93

4/000,5kmpcD ==

300 m

SFF = 110 km/h



EXHIBIT 24-15. COMPUTATIONS FOR EXAMPLE PROBLEM 3

Configuration: Type A (Ramp-Weave, all weaving vehicles must make one lane-change)

Convert Volumes: PHF = 0.85 (given)ET = 3.0 (Basic freeway section, rolling terrain)fHV = 1/[1+0.15(3-1)] = 0.77fp = 1.00 (familiar users)

v(A-C) = 975/(0.85x0.77x1.00) = 1,490 pcphv(A-D) = 650/(0.85x0.77x1.00) = 993 pcphv(B-C) = 520/(0.85x0.77x1.00) = 794 pcph

Weaving Diagram: 1,490

794

993

Critical Variables: vw = 794 + 993 = 1,787 pcphv = 1,787 + 1,490 = 3,277 pcphR = 794/1787 = 0.44VR = 1,787/3,277 = 0.55

Unconstrained Speeds: Ww = 0.15 (1+0.55)2.2 (3,277/3)0.97/(3.28x300)0.80 = 1.396Wnw = 0.0035 (1+0.55)4.0 (3,277/3)1.3/(3.28x300)0.75 = 1.012

(Exhibit 24-2)

Sw = 24 + [(110-16)/(1+1.396)] = 63.2 km/hSnw = 24 + [(110-16)/(1+1.012)] = 70.7 km/h

Check Type of Operation: Nw = 1.21 (3) (0.55)0.571 (300)0.234/(63.2)0.438 = 1.59 lanes > 1.4 lanes (Exhibit 24-3)Operation is Constrained.

Constrained Speeds: Ww = 0.35 (1+0.55)2.2 (3,277/3)0.97/(3.28x300)0.80 = 3.256Wnw = 0.002 (1+0.55)4.0 (3,277/3)1.3/(3.28x300)0.75 = 0.578

(Exhibit 24-2)

Sw = 24 + [(110-16)/(1+3.256)] = 46.1 km/hSnw = 24 + [(110-16)/(1+0.578)] = 83.6 km/h

Average Speed:

Average Density:

Level of Service: Level of Service D (Exhibit 24-4)

Capacity: cI = 4,790 pcph (Exhibit 24-9 B, Using max VR of 0.45)c = 4,790 x 0.77 x 1.00 = 3,690 vphch = 3,690 x 0.85 = 3,140 vph

hkmS /9.57

6.83

490,1

1.46

787,1

277,3 =

+

=

ln//9.189.57

3/277,3kmpcD ==


Chapter 24 – Freeway Weaving -24 06/08/99

Exhibit 24-15 determines that the subject weaving section is expected to operate at level of serviceD in the constrained state. The average density is expected to be 18.9 pc/km/ln and the average speed is57.9 km/h.

Note, however, that the three-lane ramp-weave has a volume ratio of 0.55, which exceeds themaximum recommended for such sections (0.45). Thus, operations may actually be worse than thosepredicted. This difficulty shows up in the very large difference between the average speed of non-weavingand weaving vehicles (83.6 km/h and 46.1 km/h respectively). This is clearly not a desirable situation, andcreates obvious safety problems.

The capacity estimates must also be carefully considered. They reflect the maximum VR that istabulated for Type A, three-lane weaving areas (0.45). The actual value for a VR of 0.55 would beexpected to be lower than the values shown.

One approach to improving operations would be to change the configuration (Type A sections donot handle volume ratios of 0.55 efficiently) to a Type B by adding a lane to the off-ramp on leg D. Thislane, not needed for general purposes, would have to be dropped or designed into the ramp’s otherterminus. This calculation, in effect, emphasizes the importance of configuration. The Type Aconfiguration is not appropriate for the balance of flows presented.

Example Problem 4 – A Design Application

A weaving area is being considered at a major junction between two urban freeways. Theconfiguration of entry and exit roadways is shown in Exhibit 24-16, along with the demand flows for thesection. These demand flows are expressed as peak flow rates for equivalent ideal conditions. The free-flow speed of the freeways is 120 kph. Design constraints limit the length of the weaving area to amaximum of 300 m. A design producing level of service C operation is desired.

EXHIBIT 24-16. WEAVING AREA FOR EXAMPLE PROBLEM 4(Note: Free-Flow Speed for a design case is generally estimated from the design speed or speedlimit)

Design of weaving areas is best achieved by trial-and-error analysis of likely design scenarios. Inmost cases, scenarios are limited by constraints on entry and exit roadway designs and on available length.In this case, the maximum length of 300 m will be applied to all scenarios. Given the anticipated design ofentry and exit roadways, the most obvious design would be a five-lane section as shown in Exhibit 24-17.This design results from simply connecting each of the five entry lanes with its matching exit lane. Thisresults in a Type C configuration. Analysis computations for this scenario are shown in Exhibit 24-18.

SFF = 120 km/h

1450



EXHIBIT 24-17. INITIAL TRIAL DESIGN FOR EXAMPLE PROBLEM 4

EXHIBIT 24-18: COMPUTATIONS FOR INITIAL TRIAL DESIGN, EXAMPLE PROBLEM 4_____________________________________________________________________________Configuration: Type C (Mvt B-C requires no lane-changes; Mvt A-D requires two lane-changes)

Convert Volumes: Not required; demands stated as flow rates under equivalent ideal conditions.

Weaving Diagram: See Exhibit 24-15.

Critical Values: vw = 1,500 + 1,450 = 2,950 pcphv = 2,950 + 2,000 + 2,000 = 6,950 pcphR = 1,450/2,950 = 0.492VR = 2,950/6,950 = 0.424

Unconstrained Speeds: Ww = 0.08 (1+0.424)2.3 (6,950/5)0.80/(3.28x300)0.860= 0.944Wnw = 0.002 (1+0.424)6.0 (6.950/5)1.1/(3.28x300)0.60 = 0.766

(Exhibit 24-2)

Sw = 24 + [(120-16)/(1+0.944)] = 77.5 km/hSnw = 24 + [(120-16)/(1+0.766)] = 82.9 km/h

Check Type of Operation: Nw = 5 [0.761+(0.047x0.424)-(0.00036x300)-0.0031(82.9-77.5)] = 3.28 lanesAs 3.28 > 3.0, the section is Constrained.

(Exhibit 24-3)

Constrained Speeds: Ww = 0.14 (1+0.424)2.3 (6,950/5)0.80/(3.28x300)0.860= 1.652Wnw = 0.001 (1+0.424)6.0 (6.950/5)1.1/(3.28x300)0.60 = 0.383

(Exhibit 24-2)

Sw = 24 + [(120-16)/(1+1.652)] = 63.2 km/hSnw = 24 + [(120-16)/(1+0.383)] = 99.2 km/h

Average Speed:

Average Density:

Level of Service: Level of Service D (just missing boundary for LOS C)(Exhibit 24-4)

_____________________________________________________________________________

hkmS /9.79

2.99

000,4

2.63

950,2

950,6 =

+

=

ln//5.179.79

5/950,6kmpcD ==

L = 300 m



The trial design of Exhibit 24-17 just misses the design objective of level of service C. There areother troubling aspects of the results as well. The R value (0.492) exceeds the maximum recommended forType C sections (0.40), and the section might, therefore, operate worse than expected. The constrainedoperating condition produces a large difference in the speeds of weaving and non-weaving vehicles that isalso undesirable.

There is no additional length available, as the maximum of 300 m has already been used. Thewidth cannot be made six lanes without adding lanes to entry and exit roadways as well, where they areapparently not needed. The only other potential change would be to alter the configuration to a Type Bdesign. This is best accomplished by adding a lane to leg D, as shown in Exhibit 24-19. While this lanemay not be needed on leg D, it will make weaving more efficient, and can be dropped further downstreamon leg D. Computations for this second scenario are shown in Exhibit 24-20.

EXHIBIT 24-19. SECOND TRIAL DESIGN FOR EXAMPLE PROBLEM 4

EXHIBIT 24-20. COMPUTATIONS FOR SECOND TRIAL DESIGN, EXAMPLE PROBLEM 4_____________________________________________________________________________Configuration: Type B (see discussion).Convert Volumes: As previously.Weaving Diagram: As previously.Critical Values: As previously.

Unconstrained Speeds: Ww = 0.08 (1+0.424)2.2 (6,950/5)0..70/(3.28x300)0.50= 0.881Wnw = 0.002 (1+0.424)6.0 (6.950/5)1.0/(3.28x300)0.50 = 0.740

(Exhibit 24-2)

Sw = 24 + [(120-16)/(1+0.881)] = 79.3 km/hSnw = 24 + [(120-16)/(1+0.740)] = 83.8 km/h

Check Type of Operation: Nw = 5 [0.085+(0.703x0.424)-(71.57/300)-0.0112(83.8-79.3)] = 2.86 lanesAs 2,86 < 3.5, the section is Unconstrained.

(Exhibit 24-3)

Constrained Speeds: Not required, operation is Unconstrained.

Average Speed:

Average Density:

Level of Service: Level of Service C (at maximum boundary, Exhibit 24-4)_____________________________________________________________________________

hkmS /8.81

8.83

000,4

3.79

950,2

950,6 =

+

=

ln//0.178.81

5/950,6kmpcD ==

L = 300 m



While the level of service does improve to barely provide the desired LOS C, there are many otherbeneficial effects of providing the Type B configuration. Unconstrained operation prevails, and the speedsof weaving and non-weaving traffic are similar. Again, this calculation illustrates the advantage of a TypeB configuration in handling high proportions of weaving traffic.

Example problem 5 – A Multiple Weaving Area

Exhibit 24-21 shows a multiple weaving area. Peak flow rates, already converted to baseconditions, are as follows: A-X = 900 pcph, B-X = 400 pcph, A-Y = 1,000 pcph, B-Y = 200 pcph, C-X =300 pcph, and C-Y = 100 pcph. At what level of service is this section expected to operate ?

Exhibit 24-21 also shows weaving diagrams for the two segments of the multiple weave. Theseare in accordance with the recommendations of Exhibit 24-8 for multiple weaves formed by two mergesfollowed by a single diverge. Each of the segments of the multiple weave can then be analyzed as if theywere simple weaving areas.

The configuration for both segments of the multiple weaving area is Type B. Movement A-Y mayweave without making a lane-change, while movements B-X and C-X must make a single lane-change tosuccessfully weave.

EXHIBIT 24-21. MULTIPLE WEAVING AREA WITH WEAVING DIAGRAMS FOR EXAMPLEPROBLEM 5

SFF = 100 km/h (field measurement)

L1 = 300 m L2 = 450 m



Exhibit 24-22 shows the computations for both segments of the multiple weaving area.

EXHIBIT 24-22: COMPUTATIONS FOR EXAMPLE PROBLEM 5Configuration: Type B, both segments (see discussion)Convert Volumes: Not required; demand flows given in pcph under equivalent ideal conditions.Weaving Diagrams: See Exhibit 24-21.Critical Values: See Exhibit 24-21.

Unconstrained Speeds: Segment 1

Ww = 0.08 (1+0.560)2.2 (2,500/3)0.7/(3.28x300)0.50= 0.752Wnw = 0.002 (1+0.560)6.0 (2,500/3)1.0/(3.28x300)0.50 = 0.766

(Exhibit 24-2)

Sw = 24 + [(100-16)/(1+0.752)] = 72.0 km/hSnw = 24 + [(100-16)/(1+0.766)] = 71.6 km/h

Segment 2

Ww = 0.08 (1+0.517)2.2 (2,900/3)0.7/(3.28x450)0.50= 0.641Wnw = 0.002 (1+0.517)6.0 (2,900/3)1.0/(3.28x450)0.50 = 0.614

(Exhibit 24-2)

Sw = 24 + [(100-16)/(1+0.641)] = 75.2 km/hSnw = 24 + [(100-16)/(1+0.766)] = 76.0 km/h

Check Type of Operation: Segment 1

Nw = 3 [0.085+(0.703x0.560)-(71.57/300)-0.0112(71.6-72.0)] = 2.16 lanes

Segment 2

Nw = 3 [0.085+(0.703x0.517)-(71.57/450)-0.0112(76.0-75.2)] = 1.79 lanes

(Exhibit 24-3) As both values are less than 3.5 lanes, both segments operate in theunconstrained mode.

Constrained Speeds: Not required, operations are unconstrained.

Average Speed:

Average Density:

Level of Service: Segment 1: Level of Service BSegment 2: Level of Service C

_____________________________________________________________________________

hkmSegS /8.71

6.71

100,1

0.72

400,1

500,2)1( =

+

=

ln//6.118.71

3/500,2)1( kmpcSegD ==

hkmSegS /6.75

0.76

400,1

2.75

500,1

900,2)2( =

+

=

ln//8.126.75

3/900,2)2( kmpcSegD ==



Exhibit 24-22 shows that each segment of the multiple weave operates at densities very close tothe level of service B/C boundary. Segment 1 is barely in LOS B, while segment 2 falls just over theboundary in level of service C. While speeds are somewhat higher in segment 2 (due primarily to its longerlength), the density is higher (as are flows), yielding a slightly lower level of service.

Example Problem 6 – Sensitivity Analysis with Design Application

A major interchange is to be built to join two major freeways in a suburban area. The issue ofhandling some of the interchanging movements in a weaving section is to be investigated. The flows inquestion are shown in Exhibit 24-23, and are given in terms of flow rates in pcph under base conditions.Because the interchange joins two future facilities, there is considerable flexibility in both the length andwidth that may be considered for the section. Level of service C operations are desired.

EXHIBIT 24-23. WEAVING FLOWS FOR EXAMPLE PROBLEM 6

Since the length, width, and configuration to be used are open to question, as is the issue ofwhether to use a weaving section at all, trial computations must be made. Speeds, densities, and levels ofservice can be determined for a range of conditions covering three, four, and five lanes, lengths from 150 mto 750 m, and all three types of configuration. Although this is a time-consuming process, it is easily set upon a programmable calculator or spreadsheet. The results of such an analysis are shown in Exhibit 24-24.

A number of points should be made concerning these results and their impact on a final designdecision.

1. Before all of the potential solutions that yield LOS C are examined, the configuration of entryand exit legs should be considered. To provide for level of service C on each of the entry andexit legs, using the criteria for basic freeway sections, each entry and exit leg would have tohave two lanes. With this consideration, all 5-lane solutions are impractical, and are thereforeeliminated from serious consideration. Five lanes is excessive, given that four lanes isadequate to handle all input and output flows.

2. If the lanes from the above legs are simply connected, a 4-lane Type A configuration results.All of the 4-lane Type A configurations produce LOS C, but all are constrained, indicatingserious imbalance between weaving and non-weaving operating quality. Also, the VR for thisproblem, 0.405, is higher than the maximum recommended for Type A, 4-lane sections (0.35),and operations may be worse than predicted here.

3. There is no easy way to produce a Type C configuration given the need for entry and exitlegs. No such configuration would be practical.

4. A Type B configuration can be created by adding a lane to leg C. The resulting 4-lane TypeB section would operate within all recommended parameters, and produces level of service Cor better for all lengths. Three-lane Type B configurations result if a lane is merged at the

SFF = 120 km/h



entrance and diverged at the exit to the section. If longer than 300 m, these also produce LOSC operations.

There are clearly judgments to be made here. The results don’t yield a clear answer, but rathergive a significant amount of information to help the analyst make the required judgment. Obviously, thebest operations would come with a long, 4-lane, Type B section. However, economic and environmentalconsiderations may also have an impact on the final choice of design.

EXHIBIT 24-24. RESULTS OF WEAVING ANALYSES, CALCULATION 6

Type A Configurations Type B Configurations Type C ConfigurationsNo ofLns

L(m) S

km/hD

pc/k/lLOS Cons

?S

km/hD

p/k/lLOS Cons

?S

Km/hD

p/k/lLOS Cons

?3 150 59.3 23.6 E N 74.3 18.8 D N 71.2 19.7 D N

300 72.6 19.3 D N 83.3 16.8 C N 81.9 17.1 D N450 80.6 17.4 D N 88.3 15.8 C N 88.1 15.9 C N600 79.3 17.6 D Y 81.8 15.2 C N 92.2 15.1 C N750 na na na na 94.4 14.8 C N 95.3 14.7 C N

4 150 61.9 16.9 C Y 80.8 13.0 C N 78.4 13.4 C N300 73.8 14.2 C Y 89.5 11.7 B N 88.9 11.8 B N450 81.2 12.9 C Y 94.2 11.1 B N 94.6 11.1 B N600 86.5 12.1 C Y 97.4 10.8 B N 98.4 10.7 B N750 na na na Na 100.3 10.2 B N 101.2 10.4 B N

5 150 66.9 12.5 C Y 83.3 10.1 B Y 82.6 10.2 B Y300 79.2 10.6 B Y 94.0 8.9 B N 92.2 9.1 B Y450 86.6 9.7 B Y 98.4 8.5 B N 99.3 8.5 B Y600 91.8 9.2 B Y 101.4 8.3 B N 102.7 8.2 B Y750 na na na na 103.5 8.1 B N 105.2 8.0 B Y

V. REFERENCES

The procedures of this chapter have been assembled from a variety of sources and studies thathave been conducted over the years. The speed prediction algorithm form was developed as a result of aresearch project in the 1980’s (1). Concepts of configuration type and type of operation were developed inan earlier study (2) in the 1970’s and updated in another study of freeway capacity procedures in 1978 (3).The final weaving procedures for the 1997 HCM were documented in Reference 4. Several otherdocuments describe the historic development of weaving area analysis procedures (References 5,6).

1. Reilly, W, et al, Weaving Analysis Procedures for the New Highway Capacity Manual, TechnicalReport, JHK & Associates, Tucson AZ, 1983.

2. Pignataro, L, et al, Weaving Areas – Design and Operation, NCHRP Report 159, TransportationResearch Board, Washington DC, 1975.

3. Roess, R, et al, Freeway Capacity Analysis Procedures, Final Report, Project DOT-FH-11-9336,Polytechnic University, Brooklyn NY, 1978.

4. Roess, R, McShane, W, and Prassas, E, Traffic Engineering, 2nd Edition, Prentice-Hall, Salt Lake CityUT, 1998.

5. Leisch, J, Completion of Procedures for Analysis and Design of Trafic Weaving Areas, Final Report,Federal Highway Administration, Washington DC, 1983.

6. Roess, R, Development of Weaving Procedures for the 1985 Highway Capacity Manual,Transportation Research Record 1112, Transportation Research Board, Washington DC, 1988.

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