Ramps & Weaving

Hmwk

• Go thru Example Problems 15-1, 15-2, 15-3 and understand

• Ch 15 # 1, 2, 4 can use HCS+

• 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

• 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

• 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

• 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

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

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)

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

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

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

Geometric Variables

• 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

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

• 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

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

• Usually 0, 1

– 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?

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?

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?

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

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

• 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

Flow Chart

• F 15.7

• Variables for 1 sided weave– F 15.8

• Variables for 1 sided weave– F 15.9

– 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

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

Max Weaving Length

• If LMax => LS use weaving methodology

• If LMax < LS use merge and diverge methodology

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

Capacity based on Breakdown Density

– cIWL = cIFL – [438.2*(1+VR)1.6] + 0.0765LS +119.8NWV

– 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

Capacity based on Breakdown Density

– cW1 = cIWL*N*fHV*fp

– cW1 = capacity of weaving section based on breakdown density

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

Capacity based on Maximum Weaving Flow Rates

– cW2 = cIW*fHV*fp

– capacity of weaving segment based on maximum weaving flow

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

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

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

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

Total Lane Changing Rate for Weaving Vehicles

– LCW = LCMin + 0.39*[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)

Total Lane Changing Rate for Non-Weaving Vehicles

– LCNW1 = 0.206vNW + 0.542LS-192.6N

– LCNW2 = 2135 + 0.223*(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

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

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)

Total Lane Changing Rate in Weaving Segment

– LCALL = LCW + LCNW

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

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

Average Speed of Weaving Vehicles

• SW = 15 +(FFS – 15)/(1+W)

• Where the minimum speed = 15mph

• Maximum speed = FFS

Average Speed of Non-Weaving Vehicles

• SNW = FFS – 0.0072LCMIN – 0.0048v/N

• LCMIN shows measure of weaving turbulence

Average Speed of All Vehicles

• S = (vW + vNW)/((vW/SW) + (vNW/SNW))

• Density

• D = (v/N)/S

• With Density, LOS can be determined

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

Analysis of Merge/Diverge Areas

• F 15.12 – flowchart

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

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/(0.1096+0.000107La)

• Vd= demand flow rate on downstream ramp pc/h

• If Ldn >=LEQ = isolated ramp

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

Diverge

• Need to determine if ramp is isolated• For adjacent upstream on-ramps

• LEQ = vu/(0.071+0.000023vF-0.000023vR)

• vu = demand flow rate on upstream on ramp

• If Lup >= LEQ = isolated ramp

• For adjacent downstream off ramp

• LEQ = vd/(1.15-0.000032vF-0.000369vR)

• If Ldn >= LEQ = isolated ramp

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

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

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

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

Density and LOS

• Merge areas– DR = 5.475 + 0.0073vR + 0.0078v12 –

0.00627La

– Diverge areas

– DR = 4.252 + 0.0086v12 – 0.009La

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

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

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