Rodel v1.96 User Guide
Table of Contents Introducing Rodel... 4 Entry Capacity... 5 Calibration... 6 Arrival Turning Flows... 6 Traffic Flows... 7 The Traffic Flow Profile... 8 Direct Flow Profile... 8 Peak Hour Factor Flow Profile... 9 Synthetic Profile...10 Flow Modifiers...11 Average Daily Traffic...12 Time-sliced Profile...13 Consequences of Time sliced Profile...13 Geometry...14 Geometric Parameters...14 Approach Geometry...15 Leg name...15 Graphical Geometry Editor...16 Bearing...17 Grade Separation G...18 Approach Half Width V...18 Number of Approach Lanes nv...19 Entry Geometry...20 Entry Width E...20 Number of Entry Lanes ne...23 Flare Length L...23 Entry Radius R...24 Entry Angle Phi (Ф)...25 Circulating Geometry...28 Diameter D...28 Circulating Width C...29 Circulating Lanes nc...30 2
Exit Geometry...31 Exit Width Ex and Exit Lanes nex...31 Exit Road Width Vx and Lanes nvx...32 Capacity Modifiers...33 Capacity +/-...33 Confidence Level...34 Crosswalk Factor...35 Calibration...36 HCM Calibration...36 Geometric Calibration...37 Calibration of Road Capacity...38 Bypass Geometry...39 Bypass Approach...39 Bypass Types...39 Bypass Approach Width Vb...40 Bypass Entry Width Eb...42 Bypass Entry Lanes neb...43 Bypass Effective Flare Length...43 Total Flare Lt...45 Bypass Radius Rb...46 Bypass Entry Angle Фb...47 Bypass and nc...48 Bypass Capacity Modifiers...48 Bypass Exit Lanes nmx...48 Accidents...49 Accident Models...49 Accident Geometry...49 Approach Curvature R0...49 Fast Path Radius R1...50 Economics...51 Economic Evaluation...51 3
Introducing Rodel Rodel 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-second cycle. This is very educational and develops a good understanding of the relationships between geometry and capacity; 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. Geometric options are derived for each leg providing alternative layouts. A geometric option is selected for each leg that provides the best fit within available constraints while achieving the desired Target Delays, Queues or Levels of Service, while minimizing accidents. Mode 2 is used for finalizing the Evaluation and Analysis. A more refined design starts with the selected geometry from Mode 1 and refines the geometry, tailoring the design to the objectives. Usually objectives compete and Rodel enables designers to find the optimum trade-off between competing objectives. Mode 2 uses six geometric parameters for each leg to derive entry capacity. Rodel s interactive user interface plus the strong relationships it shows between capacity and geometry lead to unique design solutions. 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 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. This High Definition Queuing Theory also allows for accuracy in Queue and Delay predictions at high v/c conditions up to and exceeding 1.0. 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 display messages to help and guide the user, including the assessment of approach and exit road capacities, warning the user 4
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 separate approach lanes, but share the approach width partially or fully. Three 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 range of models is used from NHCRP Report 672 Roundabouts: 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 The current version of Rodel incorporates two capacity options: Geometric and HCM (6 or 10). HCM uses the Capacity Equations from the Highways Capacity Manual. The geometric Rodel Capacity Algorithms are an extension of Kimber s equations that model US conditions. The enhanced geometric capacity model has been developed to model North American roundabouts; for example, 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 geometric capacity model has also been applied to situations where the number of opposing circulating streams differs from 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 enhanced model: 5
1. 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 significantly but this effect can be reflected manually by using other Capacity Modifier as it depends on specific local conditions and cannot be generalized. 2. 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 AM or PM peak only leaving the capacity intercept unchanged for the other peak hours. 3. 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. 4. 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 tradeoff between risk and increases in geometry. However, each roundabout is case specific in this respect. Calibration Calibration is allowed in the geometric model 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. HCM model calibration - matches HCM procedures (follow-on time) Calibration must be used with extreme caution and must be fully understood and based on sufficiently 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 and can be used to produce Annual Economic Evaluation data for both Delays and Accidents. The Arrival Turning Flows are modified in several ways: 6
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 with direct flow input, 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 (1, 3, 5 or 15-minute intervals). 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 more coarse representation of the peak hour profile and is consistent with HCM procedure. 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 histogram of the rise and fall in peak hour traffic. It uses three Flow Times and three Flow Ratios 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. 7
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 (southbound 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 coarse for assessing queues and delays. Consequently it is necessary to convert the 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. 1. 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. 8
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 an 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. 2. 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. 9
This profile is divided into 8 Time Slices of 7.5 minutes. 3. 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 0, 30 and 60 to create any shape. For example the profile for the short intense discharge from a school or factory can easily be created. The profile can also be skewed by moving the Time 2 off center. 10
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. 11
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. 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-hour 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. 12
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. 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 13
arrival flows, capacity, flow / capacity ratios, queues and delays in addition to the usual hourly results. 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. 14
Approach Geometry Approach Geometry has six parameters displayed in the main window on the first data table. HCM does not use the Grade Separation (G) or the number of approach lanes (n). 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 counterclockwise for right hand driving. Leg 1 can be chosen arbitrarily, but it helps avoid mistakes if a convention is adopted. 15
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. 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. 16
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 counterclockwise 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. 17
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 (130 m). For such roundabouts and for roundabouts terminating freeways G should be set to 1 for all legs disregarding the lack of grade change. 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 geometric model has a range from 6.5 ft (2 m) to 40 ft (12 m) 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. Geometric 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 which is actually used by approaching traffic) should be used as input, otherwise capacity may be significantly overestimated. The following graph shows the variation in capacity with V (for with fixed circulating flows) at a three lane entry. 18
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. Number of Approach Lanes nv A maximum of 4 lanes (40 ft) 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 10 ft (3 m) although capacity can be derived for lanes as narrow as 6.5 ft (2 m). The geometric model uses nv for checks and warnings. 19
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. E has a range of 12 ft (3.65 m) to 54 ft (16.5 m) 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. 20
The graph below shows capacity related to Entry Width with flow and all other parameters fixed. E is typically 14 ft (4.2 m) to 18 ft (5.5 m) 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%. The geometric 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 21
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 geometric 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 geometric equations to any combination of entry and circulating lanes. The effect on entry capacity is modest at low circulating flows but increases as circulating flow rise. The graph to the right shows capacity for circulating flows on 1 4 lanes. 22
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 (4.25 m) but needs to be wider for trucks. The minimum multilane width is 10 ft (3.0 m). 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 halfway point in the approach. 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 300 ft. 23
With L = ~312 ft (100 m) the capacity is 95% of the capacity achieved by widening V to match E. The Capacity / Flare length graph above is with V = 13 ft (4 m) and E = 26 ft (8 m) so E-V is 13 ft (4 m). Increasing L produces a sharp capacity increase that starts to level off after about 230 ft (70 m). 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 HCM does not use the entry radius R. The geometric capacity model has a range for the entry radius of 6 ft (2 m) to infinity. 24
Entry Radii greater than about 65 ft (20 m) gives little increase in capacity. However reducing R below 65 ft (20 m) reduces capacity at an increasing rate as shown at the right. In practice R ranges from about 33 ft (10 m) to about 132 ft (40 m). Entry Angle Phi (Ф) The Phi angle for an entry is the angle between the mean path of the entering traffic and the mean path of the circulating traffic. The HCM model does not use the entry angle Phi. Phi has a range in the geometric model from 10 to 60 degrees. Values between 20 and 40 degrees are recommended. Entry angle Phi has a minor capacity effect. However, there is limited scope for changing Phi, as low values below 20 degrees should be avoided as this makes visibility to the left more difficult especially with larger diameter roundabouts. Capacity Effects of Phi Angle (Ф) 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. Mean Path The mean path of the entering traffic is considered as it crosses the yield. (This is the centerline of an approach, single- to multi-lane). The circulating traffic is the mean circulating path of the traffic that is first crossed by the mean entering traffic. 25
Measuring Phi Two Methods There are two methods for measuring Phi: Method 1: 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 It is used with a nearby exit, as the entering traffic first conflicts with the exiting traffic that has diverged from the circulating traffic. In this case, the angle between the two streams is 2Phi, so Phi is the angle/2 as illustrated in the graphic below. Source excerpted from the UK TRRL Laboratory Report 942, Transport and Road Research Laboratory 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. 26
Method 2 is used if the mean path of the entering traffic first conflicts with the mean path of the circulating traffic (before exiting traffic has diverged). The angle between the two streams is Phi (not the 2Phi of method 1) as illustrated in the graphic below. The second method applies where an entry and exit are too removed from each other to use the above method. This is shown below. 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. Discussion The Phi Angle for an entry is a proxy for the conflict angle between the entering traffic on each entry lane and the circulating traffic. Usually, if Phi for an entry is within the acceptable range, then the Phi for each lane is also within the range (the proxy represents each lane well). However, for multilane entries with 3 and 4 lanes, the Phi for each lane can be very different from the Phi for the whole entry (the proxy Phi), with the outside lanes (3rd or 4th lanes) having a very small unacceptable Phi even when Phi for the other lanes, and for the entry as a whole, is within the accepted range. In addition, a design may have the lane Phi on all lanes within the acceptable range, but have an unacceptably poor view-angle to the left. In such cases, realignment and adjustment of the approach can significantly mitigate, if not remove, these problems. 27
Circulating Geometry The Circulating Geometry has three parameters: 1. Diameter D 2. Circulating Width C 3. Number of Circulating Lanes nc Diameter D The diameter D is the outer diameter or Inscribed Circle Diameter. HCM does not use the D. 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. 28
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. 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 geometric 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 Leg 1 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 29
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 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 16 ft and 20 ft. Multiple lanes should be between about 14 ft and 16 ft. 30
If the central island has a truck apron then the lane next to the central island can be narrower (13 or 14 ft) 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 four geometric parameters. These parameters are not used directly in the HCM or geometric capacity models. However it is crucial that they are consistent with other capacity and accident parameters. 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 geometric models. Exit Width Ex and Exit Lanes nex The exit width excludes gutter pans. The range is 15 ft (4.6 m) to 54 ft (16.5 m). 31
Neither the HCM model nor the geometric model use Ex for capacity estimation. However, the geometric 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 geometric 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 16.5 ft for a single lane exit and about 13 ft 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 Vx is the exit road width after any exit taper has ceased. It excludes the gutter pan and has a range from 10 ft (3 m) to 40 ft (12 m). 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 4 lanes. 32
It is used to check for geometric consistency. Capacity Modifiers There are three capacity modifiers on the main screen: Capacity +/-, Confidence Level, and Crosswalk Factor. Capacity +/- The Capacity modifier Cap is used by the HCM model and the geometric model. Capacity is increased or reduced by or + the input value. The change in capacity for both HCM and geometric 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 geometric. 33
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 geometric 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. 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%. 34
Crosswalk Factor The pedestrian crosswalk factor Xwalk Fact (XF) is applied to both HCM and geometric 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. 35
Calibration Calibration can be applied to both the HCM capacity model and the geometric model. HCM Calibration 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. The HCM capacity = A ep where p = -B v 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 0.5 ft) 3600 where tc is the observed critical headway (secs) 36
Geometric Calibration Geometric calibration applies both to the slope and intercept of the capacity line. Entries and bypasses can be separately calibrated. 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 uncalibrate than calibrate the model. 37
Calibration of Road Capacity Both HCM and geometric 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. 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. 38
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 two primary types of bypass that have different entry connections to the bypass exit road: 1) Continuous Bypasses and 2) Yield Bypasses. 1) Continuous Bypasses: Free and Merge Continuous bypasses include two types: Free Bypass Lanes and Merge Bypass Lanes. Free Bypass Lanes are ones 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. Free Bypass Lanes have the largest lane capacity. 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 than Free Bypasses. 39
2) Yield Bypass Lane and Exclusive Right Turn Lane Yield Bypass Lanes are also called Partial or Semi Bypass Lanes. They have a yield line on the entry road. They may be one or two lanes in Rodel. Yield Bypass Lanes can be two lanes and thus they may have a greater capacity than a continuous Merge or Free Bypass. Yield = raised island Exclusive Right Turn = paint only Bypass Approach Width Vb Besides the two types of bypasses, each can have different types of Approach Width Vb which may be part of or separate from the Entry Approach Width V. 40
Entry and Bypass Separate (independent) Approach Widths The Roundabout entry is fed by 12 ft of the total approach width. This is used only by Roundabout traffic. The Bypass has a separate 12 ft lane that is used only by Bypass traffic. 41
Entry and Bypass Full Lane Sharing of Approach Road The Roundabout entry is fed by the total 24 ft approach width (both approach lanes). The Bypass is fed by the 12 ft right approach lane. The roundabout traffic has two lanes: one dedicated approach lane and one approach lane shared with the bypass traffic. 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. 42
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. 43
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 lane. 44
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. 45
The Total Flare Length Lt for Free and Merge Bypass lanes 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. 46
Yield Bypass Radius is shown below. Exclusive Right Turn Radius Rb is shown below. 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. 47
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. 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. 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. 48
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. 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 (geometric) 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. Accident Geometry Approach Curvature R0 The approach curvature is 1/ R0 the approach radius. This is measured over a distance of 1600 ft (500 m) prior to the yield line. 49
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. The 24-hour Annual Average Daily Traffic Flows are explained in the Traffic Flow section. 50
Economics 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. 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 cost. 51