1. Ramps & Weaving

2. Hmwk Go thru Example Problems 15-1, 15-2, 15-3 and understand
Ch 15 # 1, 2, 4 can use HCS+

3. Merging & Diverging movements
Cause turbulence in the traffic stream
More lane changing, changes in speed, lower average speeds
F 15-1 Paths of Ramps and weaves

4. Merging
Occurs when 2 separate traffic streams form a single stream (not lane)
Can occur at on ramp, 2 facilities joining
Merging vehicles change lane to enter traffic stream
Non merging traffic changes lanes to avoid merging traffic

5. Diverging
One stream separates into 2
Off ramps and major highway splits
Diverging vehicles must align themselves in proper lane
Non diverging vehicles must change lanes to avoid diverging vehicles

6. Weaving Occurs when merge and diverge are spaced closely to each other
2500’ is max spacing for weave
But must have a continuous auxiliary lane connecting the two ramps

7. LOS Criteria Measure of effectiveness = density T15.1 For weaving
Density is an average of all vehicles across all lanes between exit & entry point
Merge & diverge influence areas F15.2
Density is 2 right hand lanes + auxiliary lane
Can have overlap
Use worst case for LOS

8. Converting Demand Volumes
Must convert all component volumes to a demand volume
vi = Vi/(PHF*fHV*fp)
vi = demand volume under base conditions
Vi= volume under prevailing conditions (vol found with count)

9. Analysis of Weaving Areas
Flows in a weaving area
F15.3 do on board
vo1 = larger outer flow – non weaving
vo2 = smaller outer flow – non weaving
vw1 = larger weaving flow
vw2 = smaller weaving flow
All in pc/h base conditions
By convention traffic flow is L->R

10. Analysis of Weaving Areas
vw = total weaving flow = vw1 + vw2
vnw = total non weaving flow = vo1 + vo2
v= total flow = vw + vnw
VR volume ratio = vw /v
R = weaving ratio vw2 / vw

11. Geometric Variables Lane configuration
How entry and exit lanes connect
4 configurations
F15.4
Ramp weave F15.4(a)
1 lane on ramp followed by 1 lane off ramp connected with auxiliary lane
Every weaving vehicle must make a lane change
Ramps have lower speed than highway
All weaving vehicles make 1 lane change

12. Geometric Variables Major weave – F 15.4(b)
All weaves must take place within weave area
Major weave – F 15.4(b)
Lane changing pattern similar
3 of 4 entry lanes have 2 lanes
Vehicles accel or decel thru weave area
Ramps and weaves on 1 side of road

13. Geometric Variables 2 sided ramp weave F 15-4(c)
Single lane on ramp followed by 1 lane off ramp on opposite side of road
Vehicles must traverse all lanes
Vehicles occupy all lanes for a period of time

14. Major Weave – F 15-4(d) 3 of 4 entry/exit lanes have 2 lanes
Ramps on opposite sides of freeway
Vehicles must traverse all lanes
Vehicles occupy all lanes for a period of time

15. One sided weaves Fig 15-5 shows critical parameters
LCRF =minimum # of lane changes ramp ->facility vehicle must make
Usually 0, 1
LCFR =minimum # of lane changes facility -> ramp vehicle must make
Nwv = # of lanes from which a maneuver may be completed with 1 or no lane changes
Nwv = either 2 or 3
What are values for Fig 15-5?

16. One sided weaves
Nwv = # of lanes from which a maneuver may be completed with 1 or no lane changes
Nwv = either 2 or 3
What are values for Fig 15-5?

17. Two sided weaves LCRF , LCFR =>not weaving flows
LCRR = minimum # of lane changes ramp ->ramp vehicle must make
Nwv = 0 by definition
What are values for Fig 15-5?

18. Length of Weaving Area
Length is critical in determining intensity of lane changing
Fig 15.6 shows 2 ways to measure length
LS is used in calculations

19. Width of Weaving Area
Measured as # of lanes available for all flows (N)
Width of weave has impact of total number of lane changes that drivers can choose to make
Proportional use of lanes by weaving and non-weaving vehicles
Normal conditions – vehicles compete for space and operations across all lanes reach equilibrium
All drivers experiencing similar conditions

20. In weaving areas
Always some segregation of weaving and non-weaving flows
Non-weaving drivers stay to the outside lanes to avoid turbulence
Weaving drivers need to occupy lanes for maneuver
Non-weaving and weaving vehicles do share lanes
Will share in a manner that provides them with similar operating quality

21. Flow Chart
F 15.7
Variables for 1 sided weave
F 15.8
F 15.9

22. Configuration characteristics
Nwv =
LCMin = minimum rate at which weaving vehicles must change lanes to successfully complete all weaving maneuvers in lane changes per hour
LCMin = (LCFR * vFR) + (LCRF * vRF) – 1 sided
LCMin = LCRR * vRR - 2 sided

23. Max Weaving Length
1. length at which weaving turbulence no longer impacts operations in the segment
2. length at which weaving turbulence no longer impacts capacity of the segment
Use this definition
LMax = [5728*(1+VR)1.6] – (1566*NWV)
Weaving length increases as VR increases

24. Max Weaving Length If LMax => LS use weaving methodology
If LMax < LS use merge and diverge methodology

25. Capacity of Weaving Segment
Must have stable flow
NOT LOS F
2 situations where breakdown occurs
1 – demand flow > total capacity of segment
~43 pc/mi/ln in the weaving segment
2 – Total weaving flow rate > capacity of segment to handle weaving flows
Maximum values
2400 pc/hr NWV = 2 lanes
3500 pc/hr NWV = 3 lanes

26. Capacity based on Breakdown Density
cIWL = cIFL – [438.2*(1+VR)1.6] LS NWV
cIFL = capacity per lane of basic freeway segment with same FFS as weaving section
Table 15.2
cIWL = capacity per lane of weaving section under ideal conditions

27. Capacity based on Breakdown Density
cW1 = cIWL*N*fHV*fp
cW1 = capacity of weaving section based on breakdown density

28. Capacity based on Maximum Weaving Flow Rates
# of weaving vehicles hits capacity before the density of the entire segment reaches 43 pc/mi/ln
Weaving turbulence can cause a breakdown causing on-ramp vehicles to queue or off ramp queues on the freeway
cIW = 2400/VR for NWV =2 or
cIW = 3500/VR for NWV =3
cIW = capacity of weaving section under ideal conditions

29. Capacity based on Maximum Weaving Flow Rates
cW2 = cIW*fHV*fp
capacity of weaving segment based on maximum weaving flow

30. Capacity of Weaving Segment
Capacity is smaller value
cW = min(cW1, cW2)
Find v/c
v/c = vfHVfp/ cW
If v/c >= 1 then LOS F -STOP

31. Total Lane Changing Rate within the Weaving Segment
3 types of lane changing maneuvers within Weaving Segment
1. Required lane changes by weaving vehicles
Absolute minimum lane changing rate that can exist in the weaving segment for the defined demands. Must be made within the weaving segment.
Weaving segment length =
LCMin = (LCFR * vFR) + (LCRF * vRF) – 1 sided
LCMin = LCRR * vRR - 2 sided

32. Total Lane Changing Rate within the Weaving Segment
2. Optional lane changes made by weaving vehicles that choose to enter segment on a lane that is not closest to their desired destination or leave segment that is not closest to their entry leg. Requires additional lane change within the weaving segment
Increases turbulence
Use reference 15

33. Total Lane Changing Rate within the Weaving Segment
3. Optional lane change made by non-weaving vehicles.
Non-weaving vehicles never have to change lanes within a weaving segment
May choose to make lane change to avoid turbulence
Use reference 15

34. Total Lane Changing Rate for Weaving Vehicles
LCW = LCMin *[LS-300)0.5*N2*(1 +ID)0.8
LCW = Total lane changing rate for weaving vehicles within weaving segment lc/h
ID = interchange density interchanges/mi
Weave segment counts as 1, count # within 3 miles of center of weave
Multilane highways use major access points
LS-300 ->for segments shorter than 300’ weaving vehicles do not make optional lane changes (cannot be negative)

35. Total Lane Changing Rate for Non-Weaving Vehicles
LCNW1 = 0.206vNW LS-192.6N
LCNW2 = *(vNW-2000)
LCNW1 = 1st estimate of NW lane changes
LCNW2 = 2nd estimate of NW lane changes
1st equation covers most situations
As NW flow increases -> NW lane changing increases
As Length increases ->NW lane changing increases
As N increases ->NW lane changing decreases

36. Total Lane Changing Rate for Non-Weaving Vehicles
2 equations are very discontinuous so need an index to determine use
INW = (LS*ID*vNW)/10000
Explains when the second equation is used
Applies to cases with long lengths, high ID’s and/or high NW flows occur

37. Total Lane Changing Rate for Non-Weaving Vehicles
If INW <= 1300
LCNW = LCNW1
If INW => 1950
LCNW = LCNW2
If 1300<= INW <= 1950
LCNW = LCNW1 + (LCNW2 + LCNW1)*((INW-1300)/650)

38. Total Lane Changing Rate in Weaving Segment
LCALL = LCW + LCNW

39. Average Speed of Vehicles
Find speed for both weaving and non-weaving vehicles
Affected by different factors
Speed is used to find Density which is used to determine LOS

40. Average Speed of Weaving Vehicles
SW = SMIN +(SMAX – SMIN)/(1+W)
SW = Average speed of weaving vehicles
SMIN = min ave spd of weaving veh in weaving segment
SMAX = Max ave spd of weaving veh in weaving segment
W = weaving intensity factor
W = 0.226*(LCALL/LS)0.789

41. Average Speed of Weaving Vehicles
SW = 15 +(FFS – 15)/(1+W)
Where the minimum speed = 15mph
Maximum speed = FFS

42. Average Speed of Non-Weaving Vehicles
SNW = FFS – LCMIN – v/N
LCMIN shows measure of weaving turbulence

43. Average Speed of All Vehicles
S = (vW + vNW)/((vW/SW) + (vNW/SNW))
Density
D = (v/N)/S
With Density, LOS can be determined

44. Merge & Diverge Basic Characteristics
Analysis focuses on right 2 lanes – need to know lane distribution of the freeway upstream of the ramp
Fig 15.10
Variables pg 334
La or Ld – acceleration or deceleration ramp length Fig 15.11
RFFS – ramp FFS

45. Analysis of Merge/Diverge Areas
F – flowchart

46. Analysis of Merge/Diverge Areas
Merge Areas
Find flow remaining in lanes 1&2 upstream of junction
v12 = vF * PFM
PFM = proportion of approaching vehicles remaining in lanes 1&2 immediately upstream of junction (decimal)
Varies with # of lanes on facility – T 15.3

47. Ramp Analysis Is ramp isolated?
Need to know distance apart and where equivalence distance is located
For upstream off ramps
LEQ = 0.214(vF+vR)+0.444La+52.32RFFS – 2403
If LEQ >=Lup = isolated ramp
For downstream off ramps
LEQ = vd/( La)
Vd= demand flow rate on downstream ramp pc/h
If Ldn >=LEQ = isolated ramp

48. Diverge Need to account for all diverging traffic being in lanes 1&2
v12 = vR + (vF - vR )PFD
PFD = proportion of approaching vehicles remaining in lanes 1&2 immediately upstream of junction (decimal)
Varies with # of lanes on facility – T 13.7

49. Diverge Need to determine if ramp is isolated
For adjacent upstream on-ramps
LEQ = vu/( vF vR)
vu = demand flow rate on upstream on ramp
If Lup >= LEQ = isolated ramp
For adjacent downstream off ramp
LEQ = vd/( vF vR)
If Ldn >= LEQ = isolated ramp

50. Reasonableness of Lane Distribution
Does lane distribution make sense?
1. Ave flow rate in outer lanes may not exceed 2700 pc/ln/hr
If exceeded then
V12 = VF – 2700NO

51. Reasonableness of Lane Distribution
2. Ave Flow rate in the outer lanes cannot be more than 1.5 times the ave flow rate in lanes 1&2
For NO = 1 V12 = VF/1.75
For NO = 2 V12 = VF/2.50
For NO > 2 V12 = VF/(1.5*NO + 2)
If both criterion violated, use values that satisfy both criteria

52. Capacity
Must check capacity of basic facility upstream and downstream of merge/diverge
Use T 15.5 to compare values
For merge areas – max flow occurs downstream of ramp
vFO = vF+vR
For diverge areas – max flow occurs upstream of ramp
vF upstream of ramp

53. Capacity For areas where lanes are added or dropped
compare both vF and vFO to facility capacity
For merge areas
vR12 = v12 + vR are compared to max desirable flow
For diverge areas
v12 is compared
All ramp flows must be compared to ramp capacities

54. Density and LOS Merge areas
DR = vR v12 – La
Diverge areas
DR = v12 – 0.009La

55. Speed 3 areas are checked
Ramp Influence Area – 1500’ area encompassing ramp
Outer Lanes - speed of outer lanes within ramp influence area
All Lanes – speed of all lanes within the ramp influence area

56. Speed
T 15.6, 15.7
SR = space mean speed of vehicles in ramp influence area
SO = space mean speed of vehicles in outer lanes within 1500’ length range of ramp influence area
S = space mean speed of vehicles in all lanes within 1500’ length range of ramp influence area

57. Speed MS = speed proportion factor for merge areas
DS = speed proportion factor for diverge areas
vOA = average demand flow in outer lanes
= (vF-v12)/N0 pc/h/l
NO = # of outer lanes