### Lec 12: Weaving, merging, diverging

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