Rodel
Interactive Roundabout Design
RODEL V1-WIN
INTERACTIVE ROUNDABOUT DESIGN
Copyright © Rodel Software Ltd
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Table of Contents
Introducing Rodel............................................................................................4
Entry Capacity ...................................................................................................5
Calibration .........................................................................................................6
Arrival Turning Flows.........................................................................................6
Traffic Flows ......................................................................................................7
The traffic Flow Profile. ............................................................................................. 7
Direct Flow Profile ..................................................................................................... 8
Peak Hour Factor Flow Profile ................................................................................... 8
Synthetic Profile.......................................................................................................... 9
Flow Modifiers .................................................................................................10
Average Daily Traffic .......................................................................................11
Time-sliced Profile...........................................................................................12
Consequences of Time sliced Profile........................................................................ 12
Geometry.........................................................................................................13
Geometric Parameters ....................................................................................13
Approach Geometry ........................................................................................13
Leg name .................................................................................................14
Graphical Geometry Editor.......................................................................15
Bearing.....................................................................................................16
Grade Separation G .................................................................................16
Approach HalfWidth V..............................................................................17
Number of Approach Lanes nv.................................................................18
Entry Geometry ...............................................................................................18
Entry Width E ...........................................................................................18
Number of Entry Lanes ne .......................................................................21
Flare Length L’ .........................................................................................21
Entry Radius R .........................................................................................22
Entry Angle Phi (Ф) ..................................................................................23
Circulating Geometry.......................................................................................25
Diameter D ...............................................................................................25
Circulating Width C ..................................................................................27
Circulating Lanes nc.................................................................................27
Exit Geometry..................................................................................................28
Exit Width Ex and Exit Lanes nex ............................................................29
Exit Road Width Vx and Lanes nvx ..........................................................29
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Capacity Modifiers...........................................................................................30
Capacity +/-..............................................................................................30
Confidence Level .....................................................................................31
Cross-walk Factor ....................................................................................32
Calibration .......................................................................................................32
HCM Calibration.......................................................................................32
Empirical Calibration ................................................................................33
Calibration of Road Capacity....................................................................34
Calibration of Approach Road and Exit Road Capacity................................... 34
Bypass Geometry............................................................................................35
Bypass Approach .....................................................................................35
Bypass Types...........................................................................................35
Free Bypass Lane.............................................................................................. 35
Merge Bypass Lanes ......................................................................................... 35
Yield Bypass Lanes........................................................................................... 36
Exclusive Right Turn Lanes.............................................................................. 36
Bypass Approach Width Vb......................................................................37
Entry and Bypass – Separate (independent) Approach Widths ........................ 37
Entry and Bypass – Partial Shared Approach Road.......................................... 37
Bypass Entry Width Eb....................................................................................38
Bypass Entry Lanes neb ..........................................................................38
Bypass Effective Flare Length..................................................................38
Total Flare Lt ............................................................................................40
The Total Flare Length Lt for Yield or Exclusive Bypasses ............................ 40
The Total Flare Length Lt for Free and Merge Bypass lanes. .......................... 40
Bypass Radius Rb....................................................................................41
Bypass Entry Angle Фb ............................................................................42
Bypass and nc..........................................................................................42
Bypass Capacity Modifiers .......................................................................43
Bypass Exit Lanes nmx ...................................................................................43
The number of Exit Merge Lanes nmx ..................................................................... 43
Accident Models ..............................................................................................44
Approach Curvature R0 ...........................................................................44
Fast Path Radius R1 ................................................................................44
Economic Evaluation.......................................................................................45
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Introducing Rodel
Rodel v1-Win is a fully interactive program for the Planning, Design, Evaluation and Analysis of
Roundabouts.
The primary input and output is displayed in a single window and input data can be edited and the
results viewed in the same window during a three seconds cycle. This is very educational and
develops a good understanding of the relationships between geometry and capacity. As all input
and output is either in the single main window or in sub windows one mouse click away making
navigation extremely simple. The use of confusing nested windows has been strenuously avoided
Mode 1, the Planning Mode uses minimal existing geometric data together with an estimated
outer circle diameter to generate geometric options that achieve Target Delay, Queue or Volume
Capacity Ratios for each leg. Typically about 40 geometric options are derived for each leg
providing over 2.5 million possible layouts for a 4 leg roundabout. A geometric option is selected
for each leg that fits within the Right of Way and Cost constraints while achieving the desired
Target Delays, Queues or Levels of Service, while minimizing accidents.
Mode 2 is used for detailed Design, Evaluation and Analysis. Detailed design starts with the
selected geometry from Mode1 and refines the geometry, tailoring the design to the objectives.
Usually objectives compete and Rodel enables designers find the optimum trade-off between
competing objectives. Mode2 uses 11 geometric parameters for each leg to derive entry capacity
which is very sensitive to geometric parameters. The interactive nature of Rodel plus the strong
relationships it shows between capacity and geometry lead to unique design solutions especially
with high flows that are difficult to accommodate.
All the parameters have a pop up summary called by clicking on the parameter name. The
Geometric parameters also have graphical input that is selected by clicking any of the name of
the Geometry Grid. The data input graphically automatically update the data in the grids..
Rodel v1-Win is a dynamic model and instead of modeling the peak hour as a whole, using and
producing hourly data, Rodel divides the peak hour into small time slices and models each slice
in turn. This provides the evolution of Flows, Capacity, VC Ratios, Queues, Delays and LOS over
the hour as well as hourly averages. The evolution of queues is especially useful for checking if
queues block back critically for all or part of the hour.
Peak hour arrival flows are reshaped into a rise and fall profile using three methods including the
Peak Hour Factor method.
The model supports both Left Hand and Right Hand driving and allows either English or Metric
units for geometric definition.
It includes extensive Error, Warning and Caution checks that displaying messages to help and
guide the user, including the assessment of approach and exit road capacities, warning the user if
arrival or exit flows reach or exceed these capacities, as it is unnecessary to design for flow levels
that cannot reach or exit the roundabout.
A Scheme Notes utility has been added to enable key information to be recorded with the scheme
data. This can be used to record the evolution of the design, especially key decisions and to
communicate this information to other Planners, Designers, Analysts or Clients. These notes are
included in the printout together with any outstanding Warning or Caution messages..
A recent addition is the explicit modeling of all types of bypass lanes. The model includes the
interaction between yield line entry capacity at the roundabout and the bypass lane capacity
when they do not have seperate approach lanes, but share the approach width partially or fully..
A range of accident models are included. There are Intersection Level Models that use global
intersection geometry and flow data and Approach Level Models that use detailed entry geometry
and detailed turning flows. A Ronge of models is used from NHCRP Report 672 ‘Roundabouts:
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An Informational Guide’ and also the UK Injury accident models. The user can select any model
and can compare their results.
Arrival Turning Flows for the am peak, off peak and pm peak are modeled in a single Rodel file
and the results used to derive annual delay costs and annual accident costs for Economic
evaluation.
The output is on tabbed fields. Any field can be active while the others are one mouse click away.
Entry Capacity
Rodel v1-Win uses two capacity options. Empirical or HCM.
‘HCM’ uses the Exponential Capacity Equations from the Highways Capacity Manual or NCHRP
Report 672.
The ‘Empirical’ or new Rodel Capacity Algorithms are an extension of Kimbers equations that
model US conditions.
The enhanced capacity model has been developed to specifically model US style single lane
roundabouts with very wide single lane entries (to accommodate large trucks) that are wider than
the receiving section of the circulating road. (Entries wider than the circulating road are not
permitted in the UK)
The empirical capacity model has also been applied to situations where the number of opposing
circulating streams differs (more or less) than the number of entry streams. The effect on entry
capacity is modest with low circulating flows but increases as circulating flows increase. (This was
not in the original model as UK Roundabout Guides required that the number of circulating lanes
were not less than the number of entry lanes, which is now no longer the situation, so the model
has been updated)
Several Capacity Modifiers have been added to the model:
1. Location. This lowers the capacity intercept for relaxed ‘Rural’ locations. This rises slowly
through ‘Outer Urban’ and ‘Urban’ to a maximum for more assertive ‘Central Urban’ driver
behavior.
2. The capacity Intercept is adjusted by the Light / Dark parameter as capacity is reduced
by about 5% in dark conditions. Snow and icy conditions reduce capacity very
significantly but this effect can be reflected manually by using other Capacity Modifier as
it depends on specific local conditions and cannot be generalized.
3. Capacity Intercept modification alters the intercept for temporary reasons such as parked
cars on an approach during the peak hour only. The adjustment to the intercept can be
applied for the PM peak only leaving the capacity intercept unchanged for the other peak
hours.
4. The effect of Crosswalks on capacity is also included. This uses the capacity factors from
the tables in Exhibits 4-7 and 4-8 of NCHRP Report 672 ‘Roundabouts: An Informational
Guide’
5. The Confidence Level modifies the Capacity Intercepts to test the effects of pessimistic
capacity on Queues, Delays and LOS. Roundabout intercepts are the mean of a normal
distribution. All models implicitly use the mean value. Rodel uses the mean when the
Confidence level is set at 50%. However, higher confidence levels can be used to test the
consequences of sub mean capacities. If queues and delays on any leg become
unacceptable with the sub-mean capacity then small modifications to geometry can
increase capacity to remedy the situation. This produces more robust designs that will
work acceptably even if the capacity turns out to be significantly sub-mean. The
Confidence Level range is from 50% to 99%. Typically designing at 85% confidence level
is considered a good trade off between risk and increases in geometry. However, each
roundabout is case specific in this respect.
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The Location parameter is permanent altering the capacity in all peaks. It is not a variable for a
specific roundabout but only varies between roundabouts in different environments. However, the
Crosswalk, Capacity Intercept Modifier and the Confidence Level can be applied differently to
each peak hour.
Calibration
Calibration is allowed in Rodel v1-Win by adjusting either or both the Capacity Intercept and
Capacity Slope. This alters the capacity for all peaks and is considered a permanent change that
applies at all times to all peaks.
Calibration must be used with extreme caution and must be fully understood and based on
sufficient sound data. The detailed section on calibration must be read and understood to use
Rodel appropriately.
Arrival Turning Flows
The Arrival Turning Flows (veh/hr) are displayed for Right Hand Drive with the right turning flows
in the right column. Bypass flows are stored in a separate column. AM Peak, Off Peak and PM
Peak flows are used in Rodel v1-WIn and can be used to produce Annual Economic Evaluation
data for both Delays and Accidents.
The Arrival Turning Flows are modified in several ways
1. The Arrival flows are converted to passenger car equivalent flows using the Percentage
of Trucks. This is essential as capacity equations use passenger car equivalent flows.
This includes the effect of trucks on capacity..
2. A Flow Factor, provided for each leg, is a utility factor for modifying flows for any reason.
Usually it is used to growth the flows up or down to a different year, or for sensitivity
testing of flow variation on Capacity Queues, Delays and Level of Service..
3. Rodel includes Start Queues, (the queues existing at the start of the peak hour) for both
the Roundabout yield line and the Bypass lane. When VC Ratios are low -medium, Start
Queues are minimal and can be ignored. However at higher VC ratios they can be
significant and ignoring them can lead to an underestimation of Delays, Queues and
Level of Service, when they are most critical. The Start Queue input is primarily used
when modeling existing observed flows, as the start queues are known. If the start
queues are not known, (future year flows), then zero is input and Rodel estimates the
Start Queues by automatically modeling a pre peak period before modeling the peak
hour. The start queues are added to the peak hour flows as these wish to cross the yield
line during the peak hour.
The Arrival Flows are the average flow rate for the peak hour and must modified to create the
varying flow rate due to the rise and fall in flows over the peak hour. This can be done three
ways:
1. Direct Flows can be input. These are observed flows counted for short equal time periods
during the peak hour.
2. A Peak Hour Factor can be used to create three flow levels with the central 15 minute
section elevated, while the levels on either side are depressed. This results in a coarse
representation of the peak hour profile.
3. A Synthetic flow profile can be created by reshaping the peak hour traffic flows into a
Normal Distribution, that is then divided into short Time Slices to produce a fine histgram
of the rise and fall in peak hour traffic. It uses three Flow Times and three Flow Ratios
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that allow any shaped profile to be created. It is especially useful for a factory exit where
the traffic emerges for a very short but sharp peak within the peak hour.
Traffic Flows
Rodel stores and uses Peak hour turning flows (veh/hr) for the AM peak, Off Peak and PM Peak.
The turning flows include Bypass flows. A peak is selected using the dropdown menu.
For driving on the right (RHD), the legs of the roundabout are numbered counter-clockwise. The
first leg can be chosen arbitrarily, but is helps to reduce mistakes if a convention is adopted such
as leg 1 = the north leg (south bound entry).
The leg number gives each entry and each exit an absolute number.
A turning movement is the flows from an entry to an exit.
The entry of a turn is specified by the leg number.
However, the exit of a turn is not specified by leg number of the exit, as using the exit number is
confusing and leads to input error and errors reading the turns.
Instead the exit is defined relative to the entry. This is the experience of a driver using the
roundabout. The driver approaches and makes a right, through or left turn relative to the entry
used by the driver. This is easy to visualize and it stores each turn type in a column.
In the above Arrival Turning Flows table (RHD), row 1 is entry leg 1 and row 4 is entry leg 4. The
right turns are in the Exit-1 column. Exit-2 is through traffic. Exit-3 is left turns and exit 4 is U turn
traffic. The bypass traffic is in a separate column.
Leg 2 through traffic = 60 v/hr Leg 4 left = 150 v/hr
The traffic Flow Profile
The turning flows summate to the total hourly arrival flows on each leg. For example the turns on
leg 4 above 160, 150, 140, 130 (0) sum to an arrival flow of 580 v/hr.
Besides being the total hourly flow, it is the average flow rate expressed as veh/hr.
It could equally be expressed as 9.67 veh/min or 0.161 veh/sec.
However, traffic rises and falls during the peak hour so the flow rate varies and using the average
value is too course for assessing queues and delays. Consequently it is necessary to convert the
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average hourly flows into a traffic profile that represents the variation in the flow rate during the
peak hour under consideration.
There are three alternative methods, selected by the Flow Profile drop down.
Direct Flow Profile
The Direct Flow option allows observed flows to be entered for each time interval. The observed
traffic profile below shows traffic counted in 5 minute Time Slices.
Time Slices (minutes) are selected using the drop down.
This can only be done when modeling an existing situation. As the actual rise and fall can be
observed and measured there is no need to estimate the shape of the profile from average hourly
flow rates.
For future situations the average peak hour arrivals are estimated and then have to be reshaped
into a estimate of the peak hour flow profile. Two methods are provided. The first is using a Peak
Hour Factor to derive a course peak hour profile or the second method can be used to synthesize
a more detailed profile.
Peak Hour Factor Flow Profile
The Peak Hour Factor (PHF) uses a single flow ratio and single implied flow time.
A PHF of 0.9 is shown below for each leg.
This creates a central 15 minute peak flow rate that is the average rate divided by 0.9
The ‘shoulders’ either side of the 15 minute peak are reduced so that the total hourly flow is
unchanged.
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This profile is divided into 8 Time Slices of 7.5 minutes.
Synthetic Profile
The Synthetic method uses three Flow Ratios and three Flow Times to create a more detailed
and flexible profiles that give a more realistic estimate of the traffic arrival rate.
The typical profile shown above extends over the whole hour. However, the Flow Times can be
set other than o 30 and 60 to create any shape. For example the profile for the short intense
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discharge from a school or factory can easily be created. The profile can also be skewed by
moving the Time 2 off centre.
The summary below compares an observed profile with the PHF and Synthesized profiles
Flow Modifiers
The input turning flows can be modified by several flow modifiers.
Input flows are vehicles/hour capacity is derived in passenger car equivalents / hour (pcu/hr).
Trucks are equivalent to 2 cars on roundabouts. The percentage trucks are therefore required in
order to change veh/hr to pce/hr for capacity estimation.
A flow factor is provided to growth the arrivals turning flows up or down to different yearly flows or
to alter them for any other particular reason. It is especially useful for varying flow levels in small
steps to test the sensitivity of the results (queues and delays, etc) to small changes in flows.
Both the Entry Start Queue and the Bypass Start Queue are the queues at the beginning of the
peak hour. These are added to the hourly arrival flows to give the total demand flow on the entry
during the peak hour.
When VC Ratios are low to medium, Start Queues are minimal and can be ignored.
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However at higher VC ratios the Start Queues can be significant and ignoring them can cause
significant underestimates of delays, queues, etc.
Start Queues are known when modeling existing observed flows. However, when modeling future
year flows they are not known and are usually ignored.
For future situations input zero rather than guessing the start Queues and this will trigger a Start
Queue estimation procedure that derives the Start Queues by modeling the pre-peak period. The
Start Queues are then added to the peak hour flows to give the total flow wanting to cross the
yield line during the peak hour.
Average Daily Traffic
For accident estimation the 24 hour Annual Average Traffic (AADT) turning flows are needed.
This may be available for an existing situation.
For future flows, estimates are often not available or are only AADT arrival flows rather that the
required turning flows.
To help in these situations the 24 hour ADDT turns can be synthesized from the AM and PM
turning flows.
Typically, 24 hr AADT turns are synthesized by multiplying the (AM turns + PM turns) by a default
factor of 5. The default can be edited where appropriate.
If the AADT arrivals flows are known the AADT turns can be synthesized by using the AM + PM
turns multiplied by the appropriate factor per leg. This will produce the given flows / leg distributed
according to the (AM+PM) turning proportions, which are a good estimate of the 24 hour turning
proportions.
It is essential that both the AM peak and the PM peak turning flows are correct (not template
values). To ensure this the AM and PM turns are displayed when deriving the 24 hour ADDT
turns so they can be checked before proceeding.
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It can be seen above that the PM flows are real but the AM peak has template flows with 100 for
each turn, so proceeding would produce a spurious estimate of AADT turns until the AM peak is
corrected.
Time-sliced Profile
Consequences of Time sliced Profile
Instead of using average hourly data, Rodel uses the Time Sliced peak hour profile to model each
time slice successively and to dynamically model the peak hour, deriving the evolution of arrival
flows, capacity, flow / capacity ratios, queues and delays in addition to the usual hourly results.
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The time sliced results for both entries and bypasses are displayed by using the icons on the tool
bar respectively.
Geometry
Geometric Parameters
Geometric parameters are used to derive:
1. Entry capacity
2. Bypass capacity
3. Accident frequency and rate
Some geometric parameters are used in only one group while some are used in more than one
group. Parameters in more than one group are displayed in each and changes made in one
group are mirrored in other groups.
Geometric data for entry capacity is stored under six headings:
1. Approach Geometry
2. Entry Geometry
3. Circulating geometry
4. Exit Geometry
5. Capacity Modifiers
6. Entry Capacity Calibration
The first five are displayed in grids on the main screen.
The Calibration grid is called by the Calibration button.
Approach Geometry
Approach Geometry has six parameters displayed in the main window on the first data table.
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HCM does not use the Grade Separation (G) or the number of approach lanes (nev). These
columns are blank when the HCM capacity model is selected.
The HCM capacity model does not use V, but V is used to check and warn if the approach road
has insufficient capacity to accommodate the arrival flows. Default approach road and exit road
capacities are provided (varying according to the environment selected). Default values can be
replaced with local values in the Calibration data tables.
Leg name
Legs are numbered counter clockwise for right hand driving. Leg 1 can be chosen arbitrarily, but it
helps avoid mistakes if a convention is adopted.
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Graphical Geometry Editor
A click on any of the column headers will activate the graphical geometry editor.
The button on leg 1 opens the editor on leg 1. It allows most geometric data to be input or edited
as an alternative to using the data tables.
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The entry geometry for the previous leg and the exit geometry for the next leg are included as
there is interdependency between some geometric parameters on adjacent legs. For example a
two lane entry feeding a single lane section of circulating road (at the following leg) would be very
inadvisable as two into one does not fit. The graphical representation shows this error more
clearly than the data tables.
For HCM the graphical editor does not show geometric dimensions, but only the lane numbers
used by the HCM capacity model plus some additional geometry that Rodel uses for error and
warning checks.
Data is edited by clicking the current value and using the pop-up edit field. The data tables are
updated accordingly.
Both geometric dimensions and lane numbers are shown. Either can be hidden by means of the
tick boxes. The tabs at the bottom select by leg.
Bearing
This is the whole circle bearing taken in a counter clockwise direction for right hand side driving
(RHD).
North is 0 degrees bearing
Besides giving the orientation of the legs of the roundabout it is used to derive the angle between
legs for use in the accident prediction.
Accidents increase as the angle between legs reduces below 90 degrees. Small values should be
avoided.
Grade Separation G
Grade Separation is not used in the HCM model.
The Grade Separation G is changed from zero to 1 at interchanges on approaches that changes
level (either up or down). The capacity line has a larger intercept and is steeper than at normal at
grade approaches at intersections. This increases capacity at low circulating flows and reduces
capacity at high circulating flows.
The same capacity effects apply to very large roundabouts with inscribed circle diameters greater
than 425 ft (130m). For such roundabouts and for roundabouts terminating freeways G should be
set to 1 for all legs disregarding the lack of grade change.
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Approach Half Width V
This is the narrowest width of the approach road prior to any widening (flaring) up to the
roundabout entry.
The width excludes gutter pans.
The empirical model has a range from 6.5ft (2m) to 40ft (12m)
When there is a bypass lane then V may be modified and need to be determined together with
the bypass Approach Width Vb and the Total Approach width Vt.
HCM does not use V, but the Rodel uses V in HCM mode to check and warn if the approach road
has sufficient capacity to accommodate the arrival flows.
Empirical Capacity is very sensitive to V so the presence of bus stops or parked cars are a
serious consideration and only the ∆effective value (that actually used by approaching traffic)
should be used as input, otherwise capacity may be significantly overestimated.
∇
The graph below shows the variation in capacity with V (for with fixed circulating flows) at a three
lane entry.
V is a given rather than a variable the designer can change. However, in some circumstances V
can be increased by offsetting the center line of the road provided the narrower exit road is
acceptable.
V is a parameter in the accident models.
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Number of Approach Lanes nv
A maximum of 4 lanes (40ft) is permitted.
nv should not be greater than the number of entry lanes ne at the yield line.
The HCM model does not use the number of approach lanes nv.
For multi-lanes, the lane width is V / nv and this should not be less than about 10ft (3m) although
capacity can be derived for lanes as narrow as 6.5ft (2m)
The empirical model uses nv for checks and warnings
Entry Geometry
The widths and radii of the entry lanes is an important factor in determining the queues and
delays at the roundabout.
The entry geometry has five parameters displayed in the data table below.
Entry Width E
The HCM model uses the number of entry lanes only and does not use the Entry Width.
The entry width is the narrowest width at the yield line perpendicular to the traffic path.
It excludes gutter pans.
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E has a range of 12ft (3.65m) to 54ft (16.5m)
Capacity is very sensitive to E and capacity can be increased by widening E without increasing
the number of lanes. Narrow lanes have significantly less capacity than wide lanes.
However over wide lanes should be avoided as they become inefficient and the capacity increase
from widening rapidly fades. Single lane entries can be an exception to this as discussed below.
The following graph shows capacity related to Entry Width with flow and all other parameters
fixed.
E is typically 14ft (4.2m) to 18 ft (5.5m) on single lane roundabouts. However larger values can be
used to accommodate a design vehicle.
The ‘effective’ entry width (that actually used by the entering traffic) should be input to avoid
possible overestimation of capacity.
If the receiving circulating width is less than E, E will be reduced to the circulating width. Even
then the effective width may be less.
Below is an example of a roundabout with an effective entry width about half the physical entry
width, as the used and non-used sections are very distinct. The poor effectiveness of the entry
has reduced capacity by about 50%.
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The empirical capacity model has been extended to model US style single lane roundabouts with
very wide entries that are wider than the receiving section of the circulating road which acts as a
constraint. The circulating width and number of circulating lanes is now input for this and other
purposes.
However, situations where the width of the receiving section of the circulating road is equal or
wider than the entry width but where the relation between the entry and the central island are
such that entry path overlap is such that the Entry Width is not fully used will not be known by
Rodel, unless this is recognized by the user and the ‘effective’ entry width is input rather than the
physical entry width. If effective entry width is not input, capacity can be significantly
overestimated.
Increasing E increases accidents so E should be kept to a minimum and capacity increased by
increasing either V and or L’. When increasing the entry width, the fast path radius must be kept
sufficiently small to control entry speeds.
Single lane Entries are a special case.
As a single lane is progressively widened capacity can increase due to three capacity
mechanisms until a full two lane entry is achieved
1. Widening a narrow lane reduces side friction, increasing capacity. Side friction soon
disappears and the increase in capacity due to further widening arises from the two
remaining capacity mechanisms. However, these two mechanisms can only occur if the
section of circulating road, fed by the single lane entry, has at least two circulating lanes.
If not the single circulating lane will act as a constraint and further widening will give no
capacity increase. If the receiving circulating road has two lanes the capacity will increase
with further widening
2. Zipper queuing arises, with vehicles staggered to the left or right of the entry lane. This
raises driver assertiveness
3. Further widening encourages occasional doubling up at the yield line which increases in
frequency as the lane is further widened until full two lane operation is achieved.
However, this is totally dependent on their being two circulating lanes to receive the traffic as the
entry morphs from one to two lanes.
The empirical capacity model has been applied to situations where the number of opposing or
conflicting circulating streams differs to the number of entering streams.
This was not included in the original model as UK Roundabout Guides required that the numbers
of circulating lanes were the same as the number of entry lanes. As this is no longer case the
enhanced model applies the empirical equations to any combination of entry and circulating lanes
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The effect on entry capacity is modest at low circulating flows but increases as circulating flow
rise. The graph below shows capacity for circulating flows on 1 – 4 lanes.
Number of Entry Lanes ne
The HCM capacity model includes ne
The number of entering streams must be accommodated by the downstream circulating lanes
between the central island and the splitter island of the next leg.
The exception is when there are exclusive right turn lanes. In such cases the number of entry
lanes excluding the exclusive right turn lanes must not be greater than the number of receiving
downstream circulating lanes.
The range is 1 to 4.
The entry lane width is E / ne. The minimum single lane width should not be less than 14 ft
(4.25m) but needs to be wider for trucks. The minimum multilane width is 10ft (3.0m).
With narrow multi lanes, trucks straddle the lanes. With very narrow lanes it is obvious that trucks
will straddle. With wide lanes, trucks can stay in lane. However, care must be taken to avoid
situations where lane widths are such that it looks as though trucks will stay in lane when in fact
they will sometimes unexpectedly straddle and clip cars.
Flare Length L’
Flare length is the distance from the entry to the half-way point in the approach.
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HCM does not use the flare length L’
When V > E then L’ = 0
When E is greater than V, increasing L’ will increase capacity.
The increase in width from V to E should be at a uniform rate.
The increase in capacity is proportional to the area (E-V) multiplied by L’/2.
Consequently if E-V is very small, even a large L’ will produce only a small increase in capacity.
Even widening V to match the slightly larger E only increases capacity a little.
When E is significantly greater than V, increasing L’ produces large increases in capacity that
level out at about 300ft.
With L’ = ~312ft (100m) the capacity is 95% of the capacity achieved by widening V to match E.
The Capacity / Flare length graph above is with V = 13ft (4m) and E = 26ft (8m) so E-V is 13 ft
(4m). Increasing L’ produces a sharp capacity increase that starts to level off after about 230ft
(70m)
If there is a parallel approach E wide for a distance d back from the yield line followed by a taper
back to the approach width V then L’ is measured from the back of the parallel section to the
width (E+V)/2 as normal. However, L’ is then increased by adding d.
This is a good way of increasing capacity when a long L’ from the yield cannot be achieved due to
ROW constraints as d + a short L’ can give the same capacity increase a longer L’ with no
parallel section. All the above depends on both E and V being effective. L’ should also be
effective with no parked cars etc.
Entry Radius R
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HCM does not use the entry radius R.
The empirical capacity model has a range for the entry radius of 6ft (2m) to infinity
Entry Radii greater than about 65ft (20m) gives little increase in capacity. However reducing R
below 65 ft (20m) reduces capacity at an increasing rate as shown below.
In practice R ranges from about 33ft (10m) to about 132ft (40m)
Entry Angle Phi (Ф)
The HCM model does not use the entry angle Phi.
It has a range in the empirical model fro 0 to 77 degrees
Values between about 10 and 40 degrees are recommended with 25 to 30 degrees desirable.
Capacity is sensitive to the entry angle phi. However, as there limited scope for changing Phi, as
low values below 15 degrees should be avoided as this makes visibility to the left more difficult
especially with large diameter roundabouts and as increasing phi reduces capacity and causes
entry path overlap, Phi is in practice limited to about 15 to 40 degrees
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Measuring Phi is complicated by having two methods each applying to different types of
roundabout. Phi is a proxy for the angle between entering and circulating traffic.
On modern style roundabouts entries are close to the following exit. Consequently the mean path
of exiting traffic diverges from the mean path of circulating traffic before the mean path of entering
traffic. Entering traffic therefore crosses circulating traffic traveling along two mean paths. In such
cases the entry angle is defined as half the angle between the mean entering path and the mean
exit path. This is shown on the following diagram.
The line A-B is tangential to the median line on the southbound entry at the point it meet the yield
line.
The line C-D is tangential to the median line of the following exit at the point where it meets the
outer circle. The angle between A-B and C-D is 2 Phi.
The second method applies where an entry and exit are too removed from each other to use the
above method. This is shown below.
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The line A-B is tangential the entry mean where it crosses the yield line, the same as the former
method. However, the line CD is tangential to the median of the circulating road at the point
where it is intersected by the line A-B. Phi is the angle between A-B and B-C
Phi is not a parameter in the accident models, but small values should be avoided to make
visibility left at the entry difficult and very large angles direct traffic towards the central island
causing entry path overlap.
Circulating Geometry
The Circulating Geometry has three parameters
1. Diameter D
2. Circulating Width C
3. No of Circulating Lanes nc
Diameter D
The diameter D is the outer diameter or Inscribed Circle Diameter.
HCM does not use the D
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The relationship between capacity and D is more complicated than other parameters
For a given circulating flow the increase in capacity, shown below, is moderate.
However, increasing D gives greater increases in capacity the larger the circulating flow as shown
below.
Capacity is a small when opposing flows are large, so having a geometric parameter that
Increases capacity most, when capacity is least is very useful.
However, moderately increasing D increases the ROW disproportionately. On the contrary,
moderately reducing the D can release enough land to widen entries and increase flare lengths
sufficiently to achieve a large net gain in capacity.
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The effect of varying D should be checked with the accident models.
Circulating Width C
The circulating width only affects capacity as it defines the number of circulating streams so
neither the HCM nor the Empirical capacity models use C for capacity estimation directly. C only
affects capacity if it changes the number of circulating traffic streams.
If C allows two circulating streams, increasing C does not increase capacity until C is wide
enough to accommodate three circulating streams.
The capacity of the Leg1 entry is affected by the number of opposing circulating streams at C.
For a fixed circulating flow past an entry, the entry capacity increases as C is widened from 1 to 2
to 3 to 4 traffic streams. At low circulating flows the capacity increase is very small, but is larger
the greater the circulating flows. The figure below shows the capacity for 1, 2, 3, and 4 opposing
streams.
Leg 1 entry capacity can also be affected by the number of receiving circulating lanes at C+.
The receiving circulating width C+ must accommodate the traffic streams feeding it from the Leg
1, otherwise the entry will be forced to reduce the number of feed streams greatly reducing entry
capacity. Sometimes the number of circulating lanes needed is determined by the number of
traffic streams from other entries.
Altering the circulating width to increase the number of streams can require serious modification
of other geometric parameters. Leaving C+ alone and changing others may be less disruptive.
However, C+ must allow lane consistency.
Circulating Lanes nc
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This section must be read in conjunction with the one above on circulating width C.
HCM uses the number circulating lanes nc
nc+ should not be less than e except when ne has exclusive right turn lanes so that the remaining
ne is not greater than nc+
C / nc = the circulating lane width.
Single lane widths should typically be between about 16ft and 20ft.
Multiple lanes should be between about 14ft and 16 ft.
If the central island has a truck apron then the lane next to the central island can be narrower (13
or 14ft) with other lane(s) wider than the inner lane. This helps reduce entry path overlap and give
wider lanes for trucks making a through movement or especially a right turn. With a truck apron
and three circulating lanes the lanes can have three different widths with the narrowest next to
the central island and widest the outer lane. The narrow lane and truck apron accommodate
trucks. The middle lane does not need to be very wide for truck through movements, and the wide
outer lane generously accommodates both through truck movements and more importantly right
turns, which are often the most difficult truck movement.
Exit Geometry
Exit geometry has 4 four geometric parameters
These parameters are not used directly in the HCM or Empirical capacity models. However it is
crucial that they are consistent with other capacity and accident parameters.
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If there are inconsistencies, they can seriously affect the performance of other parameters crucial
to capacity and safety. For example an entry with two through lanes feeding into a single lane exit
will have both capacity and accident issues. However, when they are consistent the exit geometry
then has no effect.
The exit parameters are therefore used for error checking and warning messages in both the
HCM and Empirical models.
Exit Width Ex and Exit Lanes nex
The exit width excludes gutter pans.
The range is 15ft (4.6m) to 54ft (16.5m)
Neither the HCM model nor the Empirical model use Ex for capacity estimation. However, the
empirical model uses it for checks and comparisons with other parameters.
Range = 1 – 4
nex should match the number of exit streams from the circulating lanes.
If the exit tapers, the minimum exit taper should be 1:15
Neither the HCM model nor the Empirical model use nex for capacity estimation. However, it is
used for checks and comparisons with other parameters
Lane widths are Ex / nex and these should be a minimum of about 16.5ft for a single lane exit and
about 13ft for a multilane exit. They should be more generous than entry lane widths and take
account of the sharpness of the exit radius with wider lanes with smaller radii.
Ex and nex must accommodate traffic streams from exclusive right turn lanes and semi bypass
lanes.
Exit Road Width Vx and Lanes nvx
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Vx is the exit road width after any exit taper has ceased. It excludes the gutter pan and has a
range from 10ft (3m) to 40ft (12m)
Vx is used to check and warn if the exit road has insufficient capacity to accommodate the exiting
traffic from the roundabout (and bypass). Default exit road capacities are provided (varying
according to the Environment selected). Default values can be replaced with local values in the
Calibration data tables.
The number of exit lanes nvx is after all exit taper has finished. Its range is 1 – lanes
It is used to check for geometric consistency
Capacity Modifiers
There are three capacity modifiers on the main screen.
Capacity +/The Capacity modifier Cap is used by the HCM model and the Empirical model
Capacity is increased or reduced by – or + the input value.
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The change in capacity for both HCM and Empirical is the input value applied over the whole
range of circulating flow, so the capacity line moves up or down but remains parallel to the
original for both HCM and Empirical.
Cap – + is not for calibration purposes but for making capacity changes for a variety of more
temporary reasons. It can have different values in each peak whereas a Calibration change
applies to all peaks equally. (Calibration follows)
Confidence Level
HCM does not use Confidence Level
Roundabout entries with identical geometry and flows do not give identical capacity but have
between site ‘error’ with some having higher and some lower capacity curves.
Models predict the mean value such capacity distributions.
For any situation the precise capacity is not known. All that is known is that it is somewhere on
the capacity distribution. As the empirical capacity model knows the between site ‘error’ capacity
distribution it can produce the capacity for any point on the distribution including the mean
capacity by using the Confidence Level. (CL)
If the CL is set to 50% the mean capacity is estimated. Higher CL gives a more pessimistic
capacity estimate. For example for an 85% CL capacity there is a probability of 0.85 that the
capacity will not be less than the estimate.
The CL is very useful for testing designs to assess the risk of large queues and delays. A design
that has acceptable queues and delays at 50% CL may be fine at 85% also or may have one leg
where the queues and delays have greatly increased. This informs the designer that there is a
risk with this leg while the others are robust. This encourages some minor redesign to achieve
acceptable queues and delays at 85% CL resulting in a far more robust design with greatly
reduced risk of failure.
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When the CL is reset to 50% the queues and delays will appear little different than the original. If
comparison is to be made with other models or any type of evaluation the CL should be set at
50%.
Cross-walk Factor
The pedestrian crosswalk factor Xwalk Fact (XF) is applied to both HCM and Empirical
capacities.
Pedestrian crossings can reduce roundabout entry capacity.
When circulating flows are large the yield line capacity is usually less than the traffic capacity of
the crosswalk so it has no effect on the entry capacity. However, when circulating flows are low
the yield line capacity is usually higher than the traffic capacity of the crosswalk so the yield line
capacity is reduced.
In NCHRP report 672 ‘Roundabouts: An informational Guide’ page 4-14 Exhibits 4-7 and 4-8 give
the capacity factors for single lane and two lane entries respectively. The crosswalk factors (XF)
depend on the circulating flows passing the entries and the pedestrian flows on the crosswalk.
Calibration
Calibration can be applied to both the HCM capacity Model and the Empirical model
HCM Calibration
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HCM calibration applies to both the exponential coefficients and to the capacity intercepts. The
standard values are shown and can be superseded by input calibrated values. The calibrated
values are applied to both entry and bypass capacity estimation.
p
The HCM capacity = A × e where p = -B vc
vc = the circulating flow (pc/hr)
A = Intercept (pc/hr)
B = Exponential Coefficient
A = 3600 ÷ t f where tf is the observed follow-up headway (secs)
B = (tc – 0.5tf ) 3600 where tc is the observed critical headway (secs)
Empirical Calibration
Empirical calibration applies both to the slope and intercept of the capacity line.
Entries and bypasses can be separately calibrated.
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The intercept in modified by an + an absolute value to achieve the measured value. The size of
the intercept change is explicit.
The slope is modified to the measured by using a slope factor. The change in the slope is explicit.
For calibration measurements roundabout entries must be at genuine saturation capacity for at
least 30 continuous minutes.
Capacity measurements must be made for large sample of roundabout entries to give the
capacity lines and their distribution.
The mean of such a distribution is the calibrated value.
Using data from one or two roundabouts is hopelessly inadequate as this gives an unknown
random point on the capacity distribution, not the mean that is needed for comparison with the
mean capacity prediction of the model. Only ‘means’ can be sensibly compared to ‘means’.
Comparing an observed random point on the capacity distribution with the predicted mean is
more likely to un-calibrate than calibrate the model.
Calibration of Road Capacity
Both HCM and Empirical models include approach and exit road capacity calibration.
Calibration of Approach Road and Exit Road Capacity
The capacity of the Approach Road (V wide) and the Exit Road (Vx wide) is approximately
estimated from V and Vx and the Environment setting.
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However, local conditions may be different and values superseding the defaults can be entered
using the Calibration table above. If the calibration is set to 0 the default is used.
Bypass Geometry
Bypass calculations and results will be enabled if there is at least one leg on the roundabout with
a defined Bypass Type and a non-zero traffic flow.
Bypass Approach
Bypass approach geometry
Bypass Types
There are four types of bypass that have different entry connections to the bypass exit road.
Free Bypass Lane
A Free bypass lane is one where the exit traffic free-flows on its own exit lane without the need to
join the traffic exiting from the roundabout. They are restricted to one lane in Rodel v1-Win. Free
Bypass Lanes have the largest lane capacity. Later versions may increase the number of Free
Bypass lanes.
Merge Bypass Lanes
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Merge Bypass lanes are similar to Free Bypass lanes except the exit lane tapers to merge the
bypass traffic with the traffic on the exit road from the roundabout
Merge Bypasses have less lane capacity then Free Bypasses
Yield Bypass Lanes
Yield Bypass lanes are also called Partial or Semi Bypass lanes. They have yield line on the exit
road. They may be one or two lane in Rodel v1-Win.
Single lane Yield Bypasses have less lane capacity than Merge Bypass but they can be two lane
so may have a greater capacity than a Merge or even a Free.
Exclusive Right Turn Lanes
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Exclusive Bypass lanes have very similar capacity to Yield Bypass lanes but less than Merge
Bypass lanes, but they can be two lane so may have a greater capacity than a Merge or even a
Free Bypass.
Bypass Approach Width Vb
Besides the four types of bypasses, each type can have different types of Approach Width Vb
which may be part of or separate from the Entry Approach Width V.
Entry and Bypass – Separate (independent) Approach Widths
The Roundabout entry is fed by 15ft of the total approach width. This is used only by Roundabout
traffic. The Bypass has a separate 15ft lane that is used only by Bypass traffic. V =15ft Vb = 15ft
Vt = V + Vb =18ft
Entry and Bypass – Partial Shared Approach Road
The Roundabout entry is fed by the total 18ft approach width.
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The Bypass is fed by 15ft of the total approach width. Roundabout and bypass traffic share the
15ft of the approach width, V = 18ft Vb = 15ft Vt = 18ft
The above example had partial lane sharing; the example below has full lane is sharing.
The Roundabout entry is fed by the total 26ft approach width (both approach lanes).
The Bypass is fed by the 15ft right approach lane. The roundabout traffic has a single dedicated
approach lane but shares the second approach lane with the bypass traffic.
V = 26ft Vb = 13ft Vt = 26ft
Bypass Entry Width Eb
For bypass types Free and Merge Eb is the narrowest width on the single lane.
For Yield bypasses, Eb is the entry width at its yield line measured in the same way as E the
entry width on the roundabout yield line.
For Exclusive bypasses Eb is the width of the exclusive lanes at the yield line and E + Eb is the
total entry width on the yield line.
Bypass Entry Lanes neb
Free and Merge can have only a single lane.
Yield and Exclusive can have 1 or 2 lanes.
Bypass Effective Flare Length
Free and Merge bypasses have a flare length Lb = 0
Below Yield Bypass flare length Lb is defined together with L’ the Entry Flare Length.
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The widths V and Vb are found first.
If V = E L’ = 0
If Vb = Eb Lb =0
The positions of V and Vb are on the parallel section of the approach where the taper starts V to
E and Vb to Eb
In the example above V and Vb are coincident this is not always the case.
Below are examples for measuring L’ and Lb for both types of Exclusive right turn lanes
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Total Flare Lt
The Total Flare Length of the combined Roundabout Entry and Bypass is Lt
The Total Flare Length Lt for Yield or Exclusive Bypasses
Lt is the flare length of the total approach.
Et = E+Eb Vt is the total approach width at the start of the approach flare
Lt is measured from E to the width (Et+Vt)/2. This width is road width and excludes gutter pans
gore hatching or vane islands.
The Total Flare Length Lt for Free and Merge Bypass lanes.
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The entry width of the bypass Eb is the minimum width of the bypass lane. The lane should have
a uniform width but it is often necessary to widen the single lane through the bend to
accommodate trucks, so the minimum width should be at the end of the bypass lane. However, it
is possible that the minimum is at the start of the bypass lane.
Bypass Radius Rb
Free or Merge Bypass Radius Rb is shown below
Yield Bypass Radius is shown below.
Exclusive Right Turn Radius Rb is shown below
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Bypass Entry Angle Фb
Free and Merge Bypasses have zero Entry Angle
Exclusive Right Turns have the same entry angle as the Entry Geometry
Yield Bypasses have an entry angle phi as shown below.
The blue lines are the median lines of the bypass entry and the bypass exit.
The red line a-b is tangent to the entry median at the point it intersects the yield line.
The line c-d is tangent to the exit median at the point it intersected by line a-b.
The point x is the intersection of a-b and c-d. The bypass entry angle phi is c-x-a.
Bypass and nc
Exclusive right turn lanes yield to the circulating traffic.
Yield Bypass Lanes are opposed by the exiting traffic. However, drivers are unsure if traffic will
exit or circulate when deciding to cross the yield line. Observations show that drivers on Yield
bypasses yield to the circulating traffic.
For a circulating volume, the entry capacity is higher with more circulating lanes as shown below.
Capacity increase becomes significant with large circulating flows.
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Bypass Capacity Modifiers
The Bypasses have the same capacity modifiers as the Entry Capacity. Bypass capacity and
Entry Capacity can be adjusted independently.
See the explanation of the Capacity Modifiers under Entry Geometry
See also...
Capacity +/- | Confidence Level | Cross-walk Factor
Bypass Exit Lanes nmx
This is included in the bypass geometry as Exclusive Right Turns and Yield Bypasses feed into
the exit lanes and the number of exit lanes must not be less than the number of bypass lanes
feeding them.
The number of Exit Merge Lanes nmx
Merge bypasses merge traffic with the traffic on the exit Road from the roundabout.
Capacity is larger with more lanes on the exit at the merge point. However, the exit flow volumes
must be large significant capacity increase. See the capacity lines for opposing traffic on 1 2 3
and 4 lanes.
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Accidents
Accident Models
There are three accident model options.
1. NCHRP 672 Preferred Vehicle Accident Model
2. NCHRP 672 Preferred Vehicle Accident Model + UK Pedestrian Model
3. UK Empirical Accident Model (veh and Peds)
All of the Accident geometric input is used by the Empirical Capacity Model and is defined under
Approach, Entry and Circulating geometry. The exceptions are the approach curvature (1/R0 the
approach radius) and The fast path radius R1
When varying geometry for capacity reasons the effect on accidents must be checked to make a
trade off where capacity and accident aims conflict.
Approach Curvature R0
The approach curvature is 1/ R0 the approach radius. This is measured over a distance of 1600ft
(500m) prior to the yield line.
Approaching the roundabout, a left hand radius is positive, reducing accidents while a right hand
radius is negative increasing accidents
The radius is a given and cannot be changed.
Input is the + 1/R0 so a straight approach is zero rather than infinite radius.
Fast Path Radius R1
The true fastest path starts next to the median. However that radius used in the accident model
starts next to the right curb. This construction should be used in the accident model to get the
best accident estimates.
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The 24 hour Annual Average Daily Traffic Flows are explained in the Traffic Flow section.
Economic Evaluation
Data is needed for the AM Peak OFF Peak and PM Peak hours.
All peaks must be modeled to get their delays and build this up into a daily value.
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The 16 or 24 hour day is derived by summing the AM and PM results with a number of off peak
hours (typically 14)
The input Delay Cost is the economic Value of Time
The proportion of accident types is needed to divide injury accidents into fatal, incapacitating and
non incapacitating accidents. The cost of each accident type is needed to find costs by type and
total accident costs.
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