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Selecting Ramp Design Speeds, Volume 1: Guide (2021)

Chapter: Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed

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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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Suggested Citation:"Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed." National Academies of Sciences, Engineering, and Medicine. 2021. Selecting Ramp Design Speeds, Volume 1: Guide. Washington, DC: The National Academies Press. doi: 10.17226/26415.
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57 Section 4. Design Tool to Evaluate Ramp Designs for Consistency with the Selected Ramp Design Speed A tool to estimate vehicle speeds along interchange ramps could help designers and traffic engineers in conducting operational analyses and making design decisions. Speed estimation on ramps requires application of calibrated speed profile models. A database of vehicle speeds observed on ramps was assembled and statistical modeling conducted to develop speed profile models for ramps (Torbic et al., 2021). The models consist of equations that contain calibration coefficients and terms to account for the influence of variables such as initial speed, ramp segment length (curve or tangent segment), curve radius, and others. To apply the models, an Excel®-based spreadsheet tool was developed that allows designers and traffic engineers to enter key variables describing the ramp of interest to obtain a speed estimate for vehicles along the length of the ramp. The spreadsheet tool is applicable to entrance and exit ramps at service interchanges including diagonal ramps, loop ramps, and outer connection ramps. Speed data were collected for ramps from several system interchanges, but modeling efforts did not yield reliable speed prediction models. Therefore, the ramp speed profile models incorporated into the spreadsheet tool are only applicable for the design and evaluation of entrance and exit ramps at service interchanges. The spreadsheet-based Ramp Speed Profile Model (RSPM) is intended for several purposes: 1. It can be used to assess the adequacy of a new ramp design during the design process. After developing an initial design for a ramp, the engineer can input key variables into the RSPM to estimate vehicle speeds along the ramp and determine if the anticipated operating speeds along the ramp are as intended (e.g., predicted operating speeds along each sections of the ramp do not exceed the design speeds of the individual ramp sections). If the anticipated operating speeds are not consistent with the design of the individual ramp sections, then the ramp could be redesigned so the anticipated operating speeds along the ramp are more consistent and align with the design speeds of the individual ramp sections or speed-reduction measures could be implemented as appropriate to reduce speeds. 2. If a ramp is being considered for reconstruction, the RSPM could be used to assess the design consistency of different design alternatives such that the anticipated operating speeds along the ramp will be consistent and align with the design speeds of the individual ramp sections. The RSPM is organized so the worksheets for entrance and exit ramps can each be printed on two pages, or one sheet of paper front and back. The first page for each type of ramp contains input data entry cells and the computed vehicle speeds in tabular format. The second page for each ramp type contains the computed vehicle speeds in graphical format, advisory notes, and acceleration rate calculations in tabular format.

58 4.1 Input Data for the RSPM The RSPM contains two analysis worksheets – one for entrance ramps and one for exit ramps. The input cells on these worksheets are color-coded blue or orange. Blue cells represent required input values, and orange cells represent optional input values. The analyst provides input values into these cells that describe key design characteristics of the freeway, freeway mainline ramp terminal, ramp proper, and crossroad ramp terminal. The RSPM also contains a Factors and Tables worksheet with various yellow-shaded cells. Yellow represents a calibration parameter. The analyst can change these values, but should do so only if the change is justified by an engineering evaluation of field data. Some of the input data cells are configured with data validation features to prevent illogical values from being entered. For example, the speed-change lane type can only be specified as “parallel” or “taper”. With other input data cells, warning messages are provided to indicate inputs that are permitted but may be outside of the range for which the models were developed. For example, curve radius values are preferred to be in the range of 0 to 2,000 ft based on the speed model calibration dataset. Curve radii greater than 2,000 ft may be entered, but a warning message will show that curves with radii greater than 2,000 ft will be treated as tangents. Some cells or data boxes in the program have comment boxes that provide a description of the input data or interpretation of the output data. Red triangles indicate the presence of these comments. The comments can be viewed by placing the cursor on top of the red triangles. RSPM Input Data – Entrance Ramps Figure 20 provides a screen shot of the data input portion of the entrance ramp analysis worksheet. The following data are needed to describe an entrance ramp. For an entrance ramp, Milepost 0.000 is always located where the ramp connects to the crossroad ramp terminal. The milepost for all other locations along the entrance ramp are measured relative to Milepost 0.000. Inputs for Entrance Ramps: • Speeds - Freeway mainline design speed, VDS Hwy (mph). Values must be in the range of 50 to 85 mph and an increment of 5 mph. - Average operating speed on the freeway mainline, VOS Hwy (mph). If this speed is not known and the input cell is left blank, the freeway mainline regulatory speed limit value will be used as the average operating speed for the freeway. - Freeway mainline regulatory speed limit, VSL Hwy (mph). Values must be in the range of 45 to 85 mph and an increment of 5 mph. Values greater than 65 mph may be entered, but calculations will be based on a maximum value of 65 mph due to calibration of the models. - Estimated vehicle speed at the crossroad ramp terminal, VXRoad (mph). This value may be based on field measurements. If field measurements are not available, a value of 15 mph is recommended where the traffic control is stop, yield, or signal controlled; otherwise, 30 mph is recommended. A minimum value of 5 mph must be entered.

59 • General Characteristics - Ramp grade (percent). This grade describes the overall ramp and is computed from the elevations of the ramp’s beginning and ending points. • Ramp Proper - Input for individual tangents: • Design speed of tangent, VDS Tan (mph). Values must be in the range of 5 to 80 mph. This information is entered into the same data row as the information for the subsequent curve. • If the entire ramp is tangent, this information is entered into the first data row for curves and tangents on the ramp proper. • If no tangent design speeds are entered, the design speed for each tangent is assumed to be equal to that of the subsequent curve, or that of the freeway mainline if the entire ramp is tangent. - Input for individual curves: • Design speed of curve, VDS Curve (mph). Values must be in the range of 5 to 80 mph. • Milepost of the beginning of the curve [i.e., point of curvature (PC)], XPC (mi). • Radius of the curve, R (ft). Values should be in the range of 0 to 2,000 ft. Curve radii greater than 2,000 ft may be entered, but a warning message will show that curves with radii greater than 2,000 ft will be treated as tangents. • Curve length, Lc (mi). Values should be in the range of 0.05 to 0.25 mi. Values outside of this range may be entered but a message box will prompt the analyst to adjust the value or continue if the input value is outside the range of the calibration dataset. • Freeway Mainline Ramp Terminal - Milepost of the gore point, XG (mi). The gore point is located where the pair of solid white pavement edge markings that separate the ramp from the intersecting roadway are 2 ft apart. If markings do not extend to a point where they are 2.0 ft apart, the gore point is found by extrapolating both markings until the extrapolated portion is 2.0 ft apart. - Gap acceptance length, LGap Acpt (mi). This length begins at the gore point and ends at the beginning of the taper. - Taper length, LTaper (mi). This length begins at the end of the gap acceptance length and ends at the end of the speed-change lane where there is no additional width for the speed-change lane. - Acceleration length on the ramp proper, LAcc Length RP (mi). This length is that portion of the acceleration length measured upstream from the gore. This length may coincide with the point of tangency (PT) of the last curve on the ramp or another location where it is believed acceleration to the freeway speed begins.

60 - Proportion of gap acceptance length used by merging vehicles, PGap Acpt [From a design perspective, PGap Acpt = 1.0 meaning merging vehicles are expected to use the entire gap acceptance length. However, field data show that many drivers use only a portion of the gap acceptance length prior to merging onto the freeway. PGap Acpt = 0.5 is provided as a default based on Torbic et al. (2012)]. This quantity is a calibration parameter and can be adjusted by the analyst. Figure 21 illustrates the elements and dimensions in red text of the freeway mainline ramp terminal that are input into the RSPM for an entrance ramp. This figure is also included on the Factors and Tables tab within the spreadsheet tool. Figure 20. Input Data for RSPM for Entrance Ramps

61 Figure 21. Elements and Dimensions of Freeway Mainline Ramp Terminals Input into RSPM for Entrance Ramps RSPM Input Data – Exit Ramps Figure 22 provides a screen shot of the data input portion of the exit ramp analysis worksheet. The following data are needed to describe an exit ramp. For an exit ramp, Milepost 0.000 is located at the gore point where the ramp diverges from the freeway mainline. Mileposts for all other locations along the exit ramp are measured relative to Milepost 0.000. Locations upstream of the gore point along the freeway mainline ramp terminal have negative milepost values, and locations downstream of the gore point have positive milepost values.

62 Inputs for Exit Ramps: • Speeds - Freeway mainline design speed, VDS Hwy (mph). Values must be in the range of 50 to 85 mph and an increment of 5 mph. - Average operating speed on the freeway mainline, VOS Hwy (mph). If this speed is not known and the input cell is left blank, the freeway mainline regulatory speed limit value will be used as the average operating speed for the freeway. - Freeway mainline regulatory speed limit, VSL Hwy (mph). Values must be in the range of 45 to 85 mph and an increment of 5 mph. - Estimated vehicle speed at the crossroad ramp terminal, VXRoad (mph). This value may be based on field measurements. If field measurements are not available, a value of 15 mph is recommended where the traffic control is stop, yield, or signal controlled; otherwise, 30 mph is recommended. A minimum value of 5 mph must be entered. • General Characteristics - Ramp grade (percent). This grade describes the overall ramp and is computed from the elevations of the ramp’s beginning and ending points. - Ramp type. Permissible types are diagonal, loop, or outer connection. • Freeway Mainline Ramp Terminal - Speed-change lane type. Permissible types are parallel or taper. - Taper length, LTaper (mi). This length begins at the beginning of the speed-change lane where there is no additional width for the speed-change lane and ends at the beginning of the divergence zone (i.e., where the taper is at least 12 ft). - Divergence zone length, LDiv Zone (mi). This length begins at the end of the taper and ends at the gore point. Values should be in the range of 0.0 to 0.14 mi. Values outside of this range may be entered but a message box will prompt the analyst to adjust the value or continue if the input value is outside the range of the calibration dataset. - Proportion of speed-change lane length located upstream of the diverge point, PSCL. From a design perspective, vehicles are expected to diverge from the freeway at the end of the taper and the beginning of the divergence zone length. However, field data show that drivers diverge at different locations along the speed-change lane. PSCL = 0.1 is provided as a default based on Torbic et al. (2012). This quantity is a calibration parameter and can be adjusted by the analyst. Note that the speed-change lane length equals the taper length plus the divergence zone length (LSCL = LTaper + LDiv Zone). - Deceleration length on the ramp proper, LDec Length RP (mi). This length is that portion of the deceleration length measured downstream from the gore point. This length may coincide with the PC of the first curve on the ramp proper or another location where it is believed deceleration to the speed on the ramp proper transitions.

63 • Ramp Proper - Input for individual tangents: • Design speed of tangent, VDS Tan (mph). This information is entered into the same data row as the information for the preceding curve. - If the entire ramp is tangent, this information is entered into the first data row for curves and tangents on the ramp proper. If no tangent design speeds are entered, the design speed for each tangent is assumed to be equal to that of the preceding curve, or that of the freeway mainline if the entire ramp is tangent. - Input for individual curves: • Design speed of curve, VDS Curve (mph). Values must be in the range of 5 to 80 mph. • Milepost of the beginning of the curve (i.e., PC), XPC (mi). • Radius of the curve, R (ft). Values should be in the range of 0 to 2,000 ft. Curve radii greater than 2,000 ft may be entered, but a warning message will show that curves with radii greater than 2,000 ft will be treated as tangents. • Curve length, Lc (mi). Values should be in the range of 0.05 to 0.25 mi. Values outside of this range may be entered but a message box will prompt the analyst to adjust the value or continue if the input value is outside the range of the calibration dataset. • Crossroad Ramp Terminal - Milepost of the crossroad ramp terminal, XXRoad (mi). - Queue storage length, LQ Storage (mi). The queue storage length consists of the specified length (if any) at the end of the ramp where stopped vehicles are likely to queue because of traffic control at the ramp terminal intersection. Figure 23 illustrates the elements and dimensions in red text of the freeway mainline ramp terminal that are input into the RSPM for an exit ramp. This figure is also included on the Factors and Tables tab within the spreadsheet tool.

64 Figure 22. Input Data for RSPM for Exit Ramps

65 Figure 23. Elements and Dimensions of Freeway Mainline Ramp Terminals Input into RSPM for Exit Ramps RSPM Input Data – Error Checks and Warning Messages The RSPM performs several checks of the input data to determine if any errors were made or inconsistent values entered into the spreadsheets. On the entrance ramp worksheet, the following error checks and warning messages are provided: • If any required data elements are not entered, a note will appear above the output graph to remind the analyst to “Provide all missing data elements and re-run the analysis.” • If the analyst specifies a beginning milepost for a curve that is less than the previous curve’s ending milepost, the analyst will receive a message box that reads “Invalid data entry. The beginning milepost for curve x is located upstream of the end of curve x-1.” A

66 message will also appear to the right of the curve input data stating “Check milepost and length data,” and a message will appear above the output graph stating “Check curve data.” • If the analyst specifies a milepost for the gore point that is less than the previous curve’s ending milepost, the analyst will receive a message box that reads “Invalid data entry. The last curve cannot extend past the gore point.” A message will also appear to the right of the input data stating “Check milepost and length data” and “Check gore location data”, and a message will appear above the output graph stating “Check location data for gore and last curve.” On the exit ramp worksheet, the following error checks and warning messages are provided: • If any required data elements are not entered, a note will appear above the output graph to remind the analyst to “Provide all missing data elements and re-run the analysis.” • If the analyst specifies a beginning milepost for a curve that is less than the previous curve’s ending milepost, the analyst will receive a message box that reads “Invalid data entry. The beginning milepost for curve x is located upstream of the end of curve x-1.” A message will also appear to the right of the curve input data stating “Check milepost and length data,” and a message will appear above the output graph stating “Check curve data.” • If the analyst specifies a milepost for the ramp endpoint that is less than the last curve’s ending milepost, the analyst will receive a message box that reads “Invalid data entry. The last curve extends past the ramp endpoint.” A message will also appear to the right of the input data stating “Check milepost and length data” and “Check ramp endpoint location data,” and a message will appear above the output graph stating “Check location data for ramp endpoint and last curve.” • The worksheet will display error messages if the specified queue storage length exceeds half the ramp length or extends upstream of the PT of the last curve. In addition, various data entry cells on both worksheets are programmed with data validation checks to prevent entries that are erroneous or outside the range of the calibration dataset for the speed profile models. If the analyst enters an improper value, a message box will appear specifying the proper range of input values or prompt the analyst to adjust the value or continue if the input value is outside the range of the calibration dataset. 4.2 Output Data from the RSPM The RSPM provides the capability to predict speeds for a given ramp design and visually compare predicted speeds for alternative designs. Section 4.2.1 describes the output for an initial ramp design. Section 4.2.2 describes the output to visually compare predicted speeds of alternative designs. Output Data - Calculate The analyst obtains output data by clicking the Calculate button after entering the input data (see Figures 20 and 22). Output data are provided in tabular and graphical form. The output includes estimated vehicle speeds and acceleration rates along the ramp and comparisons of estimated acceleration rates against design values from the Green Book.

67 RSPM Output Data – Entrance Ramps Figure 24 shows the graph containing estimated vehicle speeds along an entrance ramp based on the inputs in Figure 20. In this example, the ramp consists of four tangents and three curves in alternating series, followed by the speed-change lane. The speed profile is shown as a solid blue line, and the design speeds of individual sections are shown as a broken red line. Vehicle speeds are either input by the analyst or estimated for the following key points on the speed profile: • The beginning point of the ramp at the crossroad ramp terminal. • The beginning and ending mileposts for each tangent or curve segment. • The midpoint of each curve segment. • The gore point, labeled as Point G. • The point on the speed-change lane where most vehicles are expected to merge into mainline traffic. By default, the location of this point is specified as 0.5 of the gap acceptance length in the direction of traffic flow but can be changed by adjusting the calibration factor in the worksheet. • The endpoint (i.e., taper point) of the speed-change lane. Figure 24. Graphical Illustration of Vehicle Speeds for Sample Entrance Ramp Notes: Alternate Profile The merge speed is more than 5 mph below the freeway operating speed. OffOff

68 Design speeds for the ramp components are plotted as follows: • The design speed for each curve is shown as the specified value for the curve. • The design speed for each tangent is shown as the specified value for the tangent, or for the next downstream curve if no value is specified, or the freeway mainline if there is no downstream curve. • Along the speed-change lane, the design speed of the freeway mainline is shown as an upper limit. Two types of tabular outputs are provided with the RSPM. The predicted speeds used to generate the graphical output are provided in tabular form (Table 10), and acceleration calculations associated with the output are also generated (Table 11). The acceleration calculations are organized by segment, starting with the first tangent between the crossroad ramp terminal and the first curve, continuing through each successive curve and tangent, and ending with the last portion of the speed-change lane. Curves are treated as two segments because the speed prediction models provide speed estimates for the midpoint and end of each curve. The speed- change lane is treated as two segments because acceleration occurs only on the specified portion of its length prior to the merge (the first half, by default) but the specified portion can be adjusted. The following calculations are provided: • Segment length, mi. • Initial and final speed on the segment, mph. • Average acceleration rate on the segment (computed from length and initial and final speeds), mph/s and ft/s2. These values are provided in the purple-shaded cells. • Design acceleration rate, computed using Equation 29, ft/s2. • Notes comparing the estimated average acceleration rates to design acceleration rates. If the estimated average acceleration rate exceeds the design rate, a message will indicate “accel > design”. Otherwise, the message will indicate “OK”. Table 10. Plotted Speed Data for Sample Entrance Ramp Point Type Milepost Profile, mph Milepost Design, mph Xrd 0.000 15.00 0.000 20 Tan 0.020 15.00 0.020 20 Cmc 0.045 15.67 0.020 25 Cpt 0.070 19.27 0.070 25 Tan 0.120 26.46 0.070 28 Cmc 0.145 25.74 0.120 28 Cpt 0.170 25.79 0.120 30 Tan 0.260 32.58 0.170 30 Cmc 0.290 32.09 0.170 35 Cpt 0.320 32.27 0.260 35 Tan 0.400 38.92 0.260 40 SCm 0.435 44.77 0.320 40 SCe 0.470 44.77 0.320 65 Tpr 0.520 44.77 0.520 65

69 Table 11. Acceleration Rate Calculations for Sample Entrance Ramp RSPM Output Data – Exit Ramps Figure 25 shows the graph containing vehicle speed calculations for an exit ramp based on the inputs in Figure 22. In the example, the ramp consists of a speed-change lane followed by four tangents and three curves, with queue storage space at the end of the last tangent segment. Speeds are provided for the following key points: • The beginning point of the speed-change lane, at the beginning of the taper from the freeway mainline. • The point on the speed-change lane where most vehicles are expected to diverge from the mainline traffic. The location of this point is specified as 0.1 of the speed-change lane length in the direction of travel but can be changed by adjusting the calibration factor in the worksheet. • The beginning and ending mileposts for each tangent or curve segment. • The midpoint of each curve segment. • The beginning point of the queue storage length. • The endpoint of the queue storage length and the ramp. Segment Data Speed, mph Average Acceleration Design Acceleration Number Type Length, mi Initial Final mph/s ft/s2 ft/s2 Notes 1 Tangent 0.020 15.000 15.000 0.000 0.000 7.500 OK 2 Curve 0.025 15.000 15.667 0.114 0.167 7.500 OK 3 Curve 0.025 15.667 19.266 0.698 1.024 7.181 OK 4 Tangent 0.050 19.266 26.464 0.914 1.341 5.839 OK 5 Curve 0.025 26.464 25.735 -0.211 -0.310 4.251 OK 6 Curve 0.025 25.735 25.793 0.017 0.024 4.371 OK 7 Tangent 0.090 25.793 32.579 0.611 0.897 4.362 OK 8 Curve 0.030 32.579 32.087 -0.147 -0.216 3.453 OK 9 Curve 0.030 32.087 32.272 0.055 0.081 3.506 OK 10 Tangent 0.080 32.272 38.917 0.821 1.205 3.486 OK 11 Speed-change 0.035 38.917 44.772 1.944 2.852 2.891 OK 12 Speed-change 0.035 44.772 44.772 0.000 0.000 2.513 OK 13 Taper 0.050 44.772 44.772 0.000 0.000 2.513 OK

70 Figure 25. Graphical Illustration of Vehicle Speeds for Sample Exit Ramp Design speeds for the ramp components are plotted as follows: • Along the speed-change lane and the first tangent, the design speed of the freeway mainline is shown as an upper limit. • The design speed for each curve is shown as the specified value for the curve. • The design speed for each subsequent tangent is shown as the specified value for the tangent, or the specified value for the previous upstream curve if no value is specified, or the freeway mainline if there is no upstream curve. Two types of tabular outputs are provided for exit ramps. The predicted speeds used to generate the graphical output are provided in tabular form (Table 12), and deceleration calculations associated with the output are also generated (Table 13). The deceleration calculations are organized by segment, starting with the speed-change lane, continuing through each successive curve and tangent, and ending with the queue storage space on the last tangent segment. Curves are treated as two segments because the speed prediction models provide speed estimates for the midpoint and end of each curve. The speed-change lane is treated as two segments. The first portion is where a vehicle begins the diverge maneuver from the freeway mainline onto the Notes: Alternate Profile OffOff

71 freeway mainline ramp terminal. The second portion begins where the diverge maneuver is complete and the vehicle is positioned within the speed-change lane. Similar calculations are provided as for entrance ramps, except design deceleration rates are computed using Equation 30. If the estimated average deceleration rate exceeds the design rate, a message will indicate “decel > design” for exit ramps. Otherwise, the message will indicate “OK”. Table 12. Plotted Speed Data for Sample Exit Ramp Table 13. Deceleration Rate Calculations for Sample Exit Ramp Output Data - Revise In addition to the previously described calculations, the analysis worksheets provide the capability to easily compare results after the analyst changes some input values to evaluate an alternative design. This feature is invoked by clicking the revise button (see Figures 20 and 22). Point Type Milepost Profile, mph Milepost Design, mph Tpr -0.100 60.00 -0.150 55 SCd -0.090 55.90 0.050 55 Gor 0.000 42.86 0.050 45 Tan 0.050 41.43 0.100 45 Cmc 0.075 41.43 0.100 40 Cpt 0.100 36.55 0.180 40 Tan 0.180 36.55 0.180 35 Cmc 0.205 36.55 0.230 35 Cpt 0.230 30.24 0.230 30 Tan 0.260 29.38 0.260 30 Cmc 0.290 29.38 0.260 20 Cpt 0.320 22.14 0.320 20 Qst 0.350 0.00 0.320 15 Xrd 0.400 0.00 0.400 15 Segment Data Speed, mph Average Acceleration Design Acceleration Number Type Length, mi Initial Final mph/s ft/s2 ft/s2 Notes 1 Speed-change 0.010 60.000 55.900 -6.600 -9.680 -10.648 OK 2 Speed-change 0.090 55.900 42.864 -1.987 -2.914 -9.920 OK 3 Tangent 0.050 42.864 41.434 -0.335 -0.491 -7.607 OK 4 Curve 0.025 41.434 41.434 0.000 0.000 -7.353 OK 5 Curve 0.025 41.434 36.546 -2.117 -3.106 -7.353 OK 6 Tangent 0.080 36.546 36.546 0.000 0.000 -6.486 OK 7 Curve 0.025 36.546 36.546 0.000 0.000 -6.486 OK 8 Curve 0.025 36.546 30.242 -2.339 -3.431 -6.486 OK 9 Tangent 0.030 30.242 29.381 -0.237 -0.348 -5.367 OK 10 Curve 0.030 29.381 29.381 0.000 0.000 -5.214 OK 11 Curve 0.030 29.381 22.145 -1.726 -2.532 -5.214 OK 12 Tangent 0.030 22.145 0.000 -2.270 -3.330 -3.930 OK 13 Queue 0.050 0.000 0.000 0.000 0.000 0.000 OK

72 For example, the speed profile shown in Figure 25 is for an exit ramp with three curves (see input data in Figure 22). Figure 26 shows the revised speed profile if the radius of the first curve is decreased from 1,000 ft to 600 ft. The original speed profile is shown as a broken blue line and the revised speed profile is shown as a solid blue line. If the data inputs for design speed are adjusted, only the revised design speed plot is displayed. Figure 26. Revised Graphical Illustration of Vehicle Speeds for Sample Design Alternative (Exit Ramp) 4.3 RSPM Speed Calculations This section describes the speed calculation framework used by the RSPM. The calculation framework is a direct implementation of curve and tangent speed profile models for ramps. The framework involves estimating the initial speed at the beginning of the ramp, and then estimating speeds on each successive ramp segment as a function of the speed at the end of the preceding segment. The RSPM estimates vehicle speeds along the full length of a ramp, from the crossroad ramp terminal through the full length of the speed-change lane. A ramp is described linearly, with mileposts at the beginning and end of each ramp segment. For entrance ramps, Milepost 0.000 is located where the ramp proper connects to the edge of traveled way at the crossroad ramp terminal, and the ramp endpoint is located at the end of the speed-change lane of the freeway

73 mainline ramp terminal. By definition, the speed-change lane includes the tapered area. For exit ramps, Milepost 0.000 is located at the gore point which is defined as the location where the pair of solid white pavement edge markings that separate the ramp from the intersecting roadway are 2.0 ft apart. A ramp with n segments is generally analyzed as follows: • Obtain an estimate of the initial speed at the beginning of the ramp. For entrance ramps, a default estimate of the initial speed is based on the type of traffic control at the crossroad ramp terminal. The analyst may also input an initial speed at the crossroad ramp terminal. For exit ramps, a default estimate is based on the regulatory speed limit on the freeway mainline, and the length and type of speed-change lane where the ramp diverges from the mainline. The analyst may also input the average operating speed of the freeway mainline in the vicinity of the speed-change lane. Then, the diverge speed is based on the average operating speed of the freeway mainline rather than the regulatory speed limit, taking into consideration the length and type of speed-change lane. • If Segment 1 is a curve, apply a curve speed model to estimate vehicle speed at the curve midpoint (MC) and PT. If Segment 1 is a tangent, apply a tangent speed model to estimate vehicle speed at the end of the tangent. • For each successive segment (Segment 2 through Segment n), use the vehicle speed at the end of the preceding segment and the appropriate speed model (curve or tangent) to estimate the vehicle speed at the end of the segment. If the segment is a curve, estimate vehicle speeds at the MC and the PT. • Estimate the vehicle speed at the end of Segment n based on the appropriate speed model (curve or tangent) and the conditions at the end of the ramp. For entrance ramps, this speed is influenced by the length and type of speed-change lane of the freeway mainline ramp terminal. For exit ramps, this speed is influenced by the type of traffic control at the crossroad ramp terminal. • Compute the average acceleration rate on every ramp segment based on the segment lengths and estimated vehicle speeds. Compare the average acceleration rate to design acceleration rates from the Green Book and note any cases where the estimated average acceleration rate exceeds the design value. The vehicle speed calculations for entrance and exit ramps are described in greater detail in the following subsections, followed by a discussion of acceleration rate calculations used to assess the adequacy of the design and other checks of the design performed within the RSPM. Speed Calculations for Entrance Ramps Applicable speed calculations are presented in the order of the primary components of an entrance ramp based on the direction of travel: • The crossroad ramp terminal. • The ramp proper. • The freeway mainline ramp terminal.

74 Crossroad Ramp Terminal The vehicle speed at the beginning point of an entrance ramp at the crossroad ramp terminal, VXRoad, is estimated based on the traffic control at the crossroad ramp terminal or is input by the analyst. Default speeds are based on the traffic control type at the crossroad ramp terminal as follows: • Stop, yield, or signal: 15 mph. • Other traffic control types: 30 mph. The default speed values are based on engineering judgement and recommendations by Bonneson et al. (2012). Ramp Proper – Preliminary Speed Profile A preliminary speed profile is computed for the ramp proper to determine if the ramp proper has a “controlling curve” that is sufficiently sharp to affect vehicle speeds. Preliminary speeds are computed for the PC, midpoint (MC), and PT for each curve assuming that the curves are sufficiently gradual that their geometry does not affect vehicle speeds. The following equations are used to compute the preliminary speed estimates at the PC, MC, and PT of each curve: 𝑉 , , = 1.0118𝑉 + 78.3087𝑋 ; 𝑉 (5) 𝑉 , , = 0.9667𝑉 + 143.9664𝑋 − 5.3122𝐼 − 2.6028𝐼 + 7.9150𝐼 ; 𝑉 (6) where: Vi,j,NC = Predicted vehicle speed for curve i at point j (j = PC, MC, or PT), by applying the model for tangents with no downstream curve (see Section 4.3.1.3), mph. Vi,j,C = Predicted vehicle speed for curve i at point j (j = PC, MC, or PT), by applying the model for tangents with a downstream curve (see Section 4.3.1.3), mph. VXRoad = Vehicle speed at the crossroad ramp terminal (provided by the analyst), mph. VOS Hwy = Average operating speed on the highway (or freeway) mainline, mph. Xj = Milepost for point j, mi. I55 = Indicator variable for 55-mph regulatory speed limit on the highway (or freeway) mainline (= 1 if the regulatory speed limit is 55 mph, 0 otherwise). I60 = Indicator variable for 60-mph regulatory speed limit on the highway (or freeway) mainline (= 1 if the regulatory speed limit is 60 mph, 0 otherwise). I65 = Indicator variable for 65-mph regulatory speed limit on the highway (or freeway) mainline (= 1 if the regulatory speed limit is 65 mph or above, 0 otherwise).

75 Equations 5 and 6 are the calibrated tangent speed models. By applying these models to the curve points, speeds are predicted along the ramp proper as if it is a tangent ramp. Once the speeds Vi,j,NC and Vi,j,C are computed for each curve point, they are compared to the design speed for the curve (VDS Curve). A controlling curve is defined where either of the predicted vehicle speeds (Vi,j,NC or Vi,j,C) exceeds the curve’s design speed (VDS Curve). If a controlling curve is identified, the preliminary speed profile is revised by applying calibrated curve and tangent speed models to all ramp proper points at or downstream of the midpoint of the controlling curve (see Section 4.3.1.3). Ramp Proper Revised Speed Profile If a controlling curve is identified, the speed profile is updated as follows. The model to estimate vehicle speed at the midpoint of a curve (MC) on an entrance ramp is described as follows: 𝑉 = −8.7255 + 1.0125𝑉 + 4.7053𝑅 − 2.0183𝑅 + 0.1316𝑉 ; VMC = Max (V OS Hwy) (7) where: VMC = Predicted vehicle speed at the MC, mph. VPC = Predicted vehicle speed at the beginning of a curve (i.e., initial point of horizontal curve – PC), mph. R = Curve radius, mi. VSL Hwy = Regulatory speed limit on the highway (or freeway) mainline, mph. The model to estimate vehicle speed at the end of a curve (PT) on an entrance ramp is described as follows: 𝑉 = −12.1179 + 1.0127𝑉 + 8.3558𝑅 − 3.5183𝑅 + 0.1882𝑉 ; VPT ≥ VMC and VPT = Max (V OS Hwy) (8) where: VPT = Predicted vehicle speed at the end of a curve (PT), mph. To obtain speed estimates at the midpoint (MC) and end (PT) of the curve, knowledge of vehicle speed at the beginning of the curve (PC) is required. If the curve is the first segment on the ramp, the speed at the beginning of the curve (VPC) is estimated based on the traffic control type at the crossroad ramp terminal or a speed entered by the analyst. If the curve follows a tangent segment, the speed at the beginning of the curve (VPC) is equal to the predicted tangent endpoint speed obtained from the tangent speed model. For tangent segments followed by a curve on an entrance ramp, the tangent endpoint speed is estimated as follows: 𝑉 ,= 𝑀𝑎𝑥 𝑉 ,0.9667𝑉 + 143.9664𝐿 − 5.3122𝐼 − 2.6028𝐼 + 7.9150𝐼 ; 𝑉 (9)

76 where: VTan-End,C = Predicted vehicle speed at the end of a tangent if the tangent is followed by a curve, mph. VTan-Begin = Predicted vehicle speed at the beginning of a tangent, mph. LT = Tangent length, mi. For tangent segments not followed by a curve on an entrance ramp, the tangent endpoint speed is estimated as follows: 𝑉 , = 𝑀𝑎𝑥 𝑉 , 1.0118𝑉 + 78.3087𝐿 ; ≤ VOS Hwy (10) where: VTan-End,NC = Predicted vehicle speed at the end of a tangent if the tangent is not followed by a curve, mph. If the tangent is the first segment on the ramp, the speed at the beginning of the tangent is estimated based on the traffic control type at the crossroad ramp terminal or the analyst input value as previously described. If the tangent follows a curve segment, the speed at the beginning of the tangent is equal to the predicted curve PT speed obtained from the curve speed model (VPT). For each tangent, the analyst can input the design speed of the tangent. The design speed of the tangent section should be consistent with the speeds that drivers are likely to travel at the end of the tangent. The tangent design speed does not affect the calculation of vehicle speeds, but the RSPM plots the tangent design speed values so the analyst can check if vehicle speeds are consistent with the design speeds. Freeway Mainline Ramp Terminal On the freeway mainline ramp terminal, drivers accelerate until they merge into the highway (or freeway) mainline traffic. With the freeway mainline ramp terminal, there are three primary points of interest: • The beginning point of the acceleration length (or Point A, with speed VAcc Length(i)). • The gore point (with speed VG). • The merge location (with speed VAcc Length(f)). Figure 27 illustrates the primary components of an entrance ramp near the freeway mainline ramp terminal and the associated speeds of vehicles at the primary points of interest.

77 Figure 27. Primary Components of an Entrance Ramp near the Freeway Mainline Ramp Terminal and Associated Speed Points of Interest The speed at the gore point (VG) is computed using one of three methods based on the following scenarios: 1. The ramp proper has one or more curves and the final curve ends at the gore point 𝑛 0 and 𝑋 , = 𝑋 . 2. The ramp has one or more curves and the final curve ends upstream of the gore point 𝑛 0 and 𝑋 , 𝑋 . 3. The ramp has no curves ( 𝑛 = 0). VG is computed in these cases as follows: 𝑉 = 𝑀𝑖𝑛 𝑉 ,𝑉 , ; 𝑛 0 and 𝑋 , = 𝑋𝑀𝑖𝑛 𝑉 , 1.0118𝑉 , + 78.3087 𝑋 − 𝑋 , ; 𝑛 0 and 𝑋 , 𝑋𝑀𝑖𝑛 𝑉 , 1.0118𝑉 + 78.3087𝑋 ; 𝑛 = 0 (11) where: VG = Predicted vehicle speed at the gore point, mph. nc = Number of curves on the ramp proper. XPT,f = Milepost for the PT of final curve on the ramp proper, mi. XG = Milepost for the gore point, mi. VPT,f = Predicted vehicle speed at the PT of final curve on the ramp proper, mph.

78 The speed calculations for Scenarios 2 and 3 apply to the tangent speed model described by Equation 11. In all cases, the upper bound for the speed at the gore point is the average operating speed on the highway (or freeway) mainline (VOS Hwy) as input by the analyst. The gap acceptance length (LGap Acpt) begins at the gore point and ends at the beginning of the taper (i.e., the last location where the taper is at least 12 ft) and should be a minimum of 300 ft. The merge location is typically about half of the gap acceptance length (Torbic et al., 2012). VMerge is estimated based on the gap acceptance length, the merge location, and field-measured acceleration rates (Torbic et al., 2012) as follows: 𝑉 = 𝑀𝑖𝑛 𝑉 , 𝑉 + 2 36005280 𝑎 𝐿 𝑃 (12) where: VMerge = Predicted vehicle speed where the vehicle merges from the speed- change lane onto the highway (or freeway), mph. aGap Acpt = Acceleration rate along gap acceptance length, ft/s2. LGap Acpt = Gap acceptance length, mi. PGap Acpt = Proportion of gap acceptance length used by merging vehicles [default = 0.50, based on Torbic et al., (2012)]. The acceleration rate along the gap acceptance length (aGap Acpt) is based on Table 27 from Torbic et al., (2012), but the table has been modified slightly for use with the spreadsheet tool and is presented here as Tables 14 and 15. Using VG as the initial speed and the design speed of the highway (or freeway) mainline (VDS Hwy), Tables 14 and 15 are used to determine the acceleration rate along the gap acceptance length (aGap Acpt) based on the following conditions: 1. Use the values from Table 14 if the absolute value of the ramp’s overall grade Gr is less than 2.5 percent and Table 14 is populated for both initial speed values bounding the computed VG value and the design speed of the highway (or freeway) mainline (VDS Hwy). For example, if the ramp grade is 1 percent and the design speed of the highway (or freeway) mainline is 60 mph, Table 14 could be used for an initial speed of 30 mph (by interpolating) but not for an initial speed of 22 mph. 2. Use the values from the body of Table 15 if Condition 1 is not met. 3. Use the values from the footer of Table 15 in all other cases. Table 14. Entrance Ramp Acceleration Rates along Gap Acceptance Length, |Gr| < 2.5 percent (adapted from Torbic et al., 2012) Design Speed of Freeway (VDS Hwy) mph Acceleration Rate along Gap Acceptance Length (aGap Acpt), ft/s2, by Initial Speed (VG), mph 0 14 18 22 26 30 36 40 44 30 35 3.39 40 3.28 2.88 45 3.22 2.97 50 3.24 2.90 2.69 55 3.40 2.72 2.68 2.47 60 2.68 2.66 2.36 1.97

79 65 3.18 2.57 2.36 1.96 70 2.62 2.49 2.05 75 2.76 2.60 2.12 Table 15. Entrance Ramp Acceleration Rates along Gap Acceptance Length, |Gr| ≥ 2.5 percent (adapted from Torbic et al., 2012) Design Speed of Freeway (VDS Hwy) mph Acceleration Rate along Gap Acceptance Length (aGap Acpt), ft/s2, by Initial Speed (VG), mph 0 * 14 * 18 22 26 30 36 40 44 30 2.46 2.46 2.83 2.94 35 2.53 2.53 3.07 3.12 3.16 40 2.48 2.48 3.07 3.18 3.16 3.17 45 2.31 2.31 3.01 3.11 3.12 3.06 50 2.41 2.41 2.97 3.08 3.04 3.00 2.78 55 2.94 2.94 2.94 3.09 3.01 2.96 2.81 2.57 60 3.00 3.00 3.00 3.10 3.02 2.99 2.89 2.83 2.48 65 3.11 3.11 3.11 3.18 3.15 3.11 2.91 2.83 2.67 70 3.10 3.10 3.10 3.27 3.28 3.21 3.07 2.91 2.80 75 3.29 3.29 3.29 3.37 3.38 3.36 3.37 3.21 3.00 Average 2.76 2.76 3.04 3.14 3.15 3.11 2.97 2.87 2.74 * Underlined numbers are extrapolated. Alternate Speed Prediction Models for Entrance Ramps In addition to the speed prediction models developed as part of this research, the RSPM spreadsheet tool includes speed prediction models developed for use with the HSM safety analysis procedures for interchange ramps (Bonneson et al., 2012). Bonneson et al. note that these speed models were not developed for the purpose of predicting vehicle speeds in the context of operational or design analyses, but the speed prediction models were incorporated into the RSPM spreadsheet tool as an alternative approach to estimating and evaluating the consistency of a ramp design as it relates to vehicle speeds. Within the RSPM spreadsheet tool, the analyst has the option to display or not display predicted speeds from the HSM safety analysis procedures. Inputs into the speed profile models included in the HSM methodology for interchange ramps are shown in Table 16. When applied, the speed profile models included in the HSM methodology yield average entry and exit speeds for each curve on a ramp. A seven-step procedure described below provides details on how the models in the HSM methodology are applied to estimate vehicle speed along an entrance ramp. The nomenclature that Bonneson et al. used to describe the methodology of the speed profile models included in the HSM methodology is repeated below with a few adaptions.

80 Table 16. Input Data for Ramp Curve Speed Prediction Procedures in ISATe (adapted from Bonneson et al., 2012) Variable Description Default Value Xi Milepost of the point of change from tangent to curve (PC) for curve i 1, mi None Ri Radius of curve i 2, ft None LC,i Length of horizontal curve i, mi None VOS Hwy Average traffic speed on freeway during off-peak periods of the typical day, mph Estimate is equal to the speed limit VXRoad Average speed at point where ramp connects to crossroad, mph 15—ramps with stop-, yield-, or signal-controlled crossroad ramp terminals 30—all other ramps at service interchanges NOTES: 1 If the curve is preceded by a spiral transition, then Xi is the average of the TS and SC mileposts, where TS is the milepost of the point of change from tangent to spiral and SC is the milepost of the point of change from spiral to curve. 2 If the curve has spiral transitions, then Ri is equal to the radius of the central circular portion of the curve. Step 1—Gather Input Data: The input data for this procedure are identified in Table 16. Step 2—Compute Limiting Curve Speed: The limiting curve speed is computed for each curve on the ramp using Equation 13. vmax,i = 3.24 (32.2 Ri)0.30 (13) where, vmax,i = Limiting speed for curve i, ft/s. The analysis proceeds in the direction of travel with the first curve encountered on the ramp designated as Curve 1 (i=1). The value of vmax is computed for all curves prior to, and including, the curve of interest. The value obtained from Equation 13 is an upper limit on the curve speed. Vehicles may reach this speed if the distance between curves is long enough or the crossroad speed is high. Step 3—Calculate Curve 1 Entry Speed: The average entry speed at Curve 1 is computed using Equation 14. vent,1 = ([1.47 VXRoad]3 + 495 × 5280 X1)1/3 ; ≤ 1.47 VOS Hwy (14) where, vent,1 = Average entry speed for Curve 1, ft/s. The boundary condition of Equation 14 indicates that the value computed (vent,1) cannot exceed the average highway (or freeway) speed (VOS Hwy). Step 4—Calculate Curve 1 Exit Speed: The average exit speed at Curve 1 is computed using Equation 15. vext,1 = (V3ent,1 + 495 × 5280 Lc,1)1/3 ; ≤ vmax,1 and ≤ 1.47 VOS Hwy (15)

81 where, vext,1 = Average exit speed for Curve 1, ft/s. The boundary conditions of Equation 15 indicate that the value computed (vext,1) should not exceed the limiting curve speed (vmax,i) or the average highway (or freeway) speed (VOS Hwy). Step 5—Calculate Curve i Entry Speed: The average entry speed at Curve 2 (and all subsequent curves) is computed using Equation 16. vent,i = ( V3ext,i-1 + 495 × 5280 [Xi – Xi-1 – Lc,i-1] )1/3 ; ≤ 1.47 VOS Hwy (16) where, vent,i = Average entry speed for curve i (i = 2, 3, ...), ft/s. vext,i = Average exit speed for curve i (i = 2, 3, ...), ft/s. Step 6—Calculate Curve i Exit Speed: The average exit speed at Curve 2 (and all subsequent curves) is computed using Equation 17. vext,i = (V3ent,i + 495 × 5280 Lc,i)1/3 ; ≤ vmax,i and ≤ 1.47 VOS Hwy (17) Step 7—Calculate Speed on Successive Curves: The entry and exit speeds for Curve 3 and successive curves are computed by applying Steps 5 and 6 for each curve. Figure 28 illustrates a sample output from the RSPM worksheet for an entrance ramp that includes the alternate speed profile from the HSM procedures.

82 Figure 28. Graphical Illustration of Vehicle Speeds for Sample Entrance Ramp with Alternate Profile Speed Calculations for Exit Ramps Applicable speed calculations are presented in the order of the primary components of an exit ramp based on the direction of travel: • The freeway mainline ramp terminal. • The ramp proper. • The crossroad ramp terminal. Freeway Mainline Ramp Terminal At the freeway mainline ramp terminal of an exit ramp, there are three points of interest associated with the speed calculations: the diverge location (with speed VDiverge), the gore point (with speed VG), and the end point of the deceleration length (or Point D, at the end of LDec Length). Figure 29 illustrates the primary components of an exit ramp near the freeway mainline ramp terminal and the associated speed points of interest. Notes: Alternate Profile The merge speed is more than 5 mph below the freeway operating speed. OnOn

83 Figure 29. Primary Components of an Exit Ramp near the Freeway Mainline Ramp Terminal and Associated Speed Points of Interest The diverge location where the vehicle enters the speed-change lane is typically about one-tenth the length of the speed-change lane (Torbic et al., 2012). The vehicle speed at the diverge location is estimated based on the average operating speed of the freeway mainline (VOS Hwy) and default speed differential values (Table 17) as follows: 𝑉 = 𝑉 + ∆𝑉 (18) where: VDiverge = Predicted vehicle speed at the diverge location, mph. ∆𝑉 = Mean speed differential between freeway mainline speed and the initial speed of vehicles entering the speed-change lane (default values are provided in Table 17 based on the ramp type and type of speed-change lane), mph. Table 17. Exit Ramp Speed Differentials (adapted from Torbic et al., 2012) Ramp Type Type of Speed-Change Lane Mean Speed Differential ΔV, mph Loop Parallel -4.4 Loop Taper -5.7 Diagonal Parallel -1.6 Diagonal Taper -4.1 Outer connection Parallel -1.6 Outer connection Taper -4.1

84 Vehicle speed at the gore point is estimated based on vehicle speed at the diverge location and field-measured deceleration rates (Torbic et al., 2012) as follows: 𝑉 = 36005280 52803600𝑉 + 2𝑎 (1 − 𝑃 )𝐿 (19) where: aSCL = Deceleration rate along the speed-change lane (= -2.914 ft/s2). LSCL = Length of speed-change lane, ft. PSCL = Proportion of speed-change lane located upstream of the diverge point (default value is 0.10 based on Torbic et al. (2012)). The deceleration rate (aSCL) along the speed-change lane within the speed-change lane is derived from a weighted averaging of the deceleration rates and vehicle counts reported by Torbic et al. (2012). Ramp Proper The model to estimate vehicle speed at the MC on an exit ramp is described as follows: 𝑉 = ⎩⎪⎨ ⎪⎧−13.4726 + 0.5951𝑉 + 208.5633𝑅 − 521.3073𝑅 + 0.2361𝑉 + 2.1981𝐼+0.7507𝐼 − 2.9488𝐼 ; 𝑉 ,𝑅 1,000 𝑓𝑡 𝑉 + (𝑉 − 𝑉 ) (𝑋 − 𝑋 )(𝑋 − 𝑋 ) ; 𝑅 1,000 𝑓𝑡 (20) where: IDN = Indicator variable for downward slope (= 1 if the overall ramp slopes downward, 0 otherwise). ILV = Indicator variable for level slope [= 1 if the overall ramp is level (i.e., ± 2 percent), 0 otherwise]. IUP = Indicator variable for upward slope (= 1 if the overall ramp slopes upward, 0 otherwise). VPC-1 = Predicted speed at the point preceding the curve PC, mph. XPC-1 = Milepost of the point preceding the curve PC, mi. The model to estimate vehicle speed at the end of a curve (PT) on an exit ramp is described as follows: 𝑉 = −0.6272 + 0.8637𝑉 + 108.0929𝑅 − 265.9747𝑅 − 190.8941𝐿 ; 𝑉 (21) where: Lc = Curve segment length, mi.

85 To obtain speed estimates at the midpoint and end of the curve, knowledge of vehicle speed at the beginning of the curve (PC) is required. If the curve is the first segment on the ramp, the speed at the beginning of the curve is set equal to VG. If the curve follows a tangent segment, the speed at the beginning of the curve is equal to the estimated tangent endpoint speed obtained from the tangent speed model. If the radius of the curve exceeds 1,000 ft, the estimated speed at the MC is computed based on an extrapolation of the speed change between the curve PC and its preceding point. In this case, knowledge of the location and speed at the point preceding the curve PC is required. For each curve, the analyst inputs the design speed of the curve, the milepost of the beginning of the curve (PC), the curve radius, and the curve length. For tangent segments followed by a curve on an exit ramp, the tangent endpoint speed is estimated as follows: 𝑉 , = 0.7980𝑉 + 228.6196𝑅 − 575.2145𝑅 − 645.4397𝐿+ 6733.5203𝐿 (22) with: Rnext = Min (Rmax, radius of subsequent curve), mi. Rmax = 1,000 ft (0.189 mi). For tangent segments not followed by a curve on an exit ramp, the tangent endpoint speed is estimated as follows: 𝑉 , = 0.4890𝑉 (23) If the tangent is the first segment on the ramp, the speed at the beginning of the tangent is set equal to VG. If the tangent follows a curve segment, the speed at the beginning of the tangent is equal to the estimated speed at the end of the curve obtained from the curve speed model. For each tangent, the analyst inputs the design speed of the tangent. The design speed of the tangent section should be consistent with the speeds that drivers are likely to be traveling at the end of the tangent. Crossroad Ramp Terminals Several factors are considered in the estimation of vehicle speed where the ramp meets the crossroad traveled way at the crossroad ramp terminal. First, the same default speeds used for the beginning point of entrance ramps (15 mph for stop, yield, or signal control; 30 mph otherwise) are provided as default speeds unless a field-measured value is available. Second, if queue storage space is needed at the end of the ramp, vehicle speed is estimated as 0 mph for the entirety of the needed queue storage length. The analyst enters the queue storage length.

86 Alternate Speed Prediction Models for Exit Ramps The RSPM spreadsheet tool also includes speed prediction models developed for use with the HSM safety analysis procedures for interchange ramps (Bonneson et al., 2012) that can be used to estimate vehicle speeds on exit ramps. Within the RSPM spreadsheet tool, the analyst has the option to display or not display predicted speeds from the HSM safety analysis procedures. Inputs into the speed profile models included in the HSM methodology for interchange ramps are shown in Table 16. The speed profile models yield average entry and exit speeds for each curve on a ramp. The seven-step procedure described below details how the models are applied to estimate vehicle speeds along an exit ramp. Step 1—Gather Input Data: The input data for this procedure are identified in Table 16. Step 2—Compute Limiting Curve Speed: This step is the same as Step 2 for the entrance ramp procedure. A limiting curve speed is computed for each curve on the ramp using Equation 13. vmax,i = 3.24 (32.2 Ri)0.30 (13) The analysis proceeds in the direction of travel with the first curve encountered on the ramp designated as Curve 1 (i=1). The value of vmax is computed for all curves prior to, and including, the curve of interest. The value obtained from Equation 13 is an upper limit on the curve speed. A lower curve speed than that obtained from Equation 13 is possible as deceleration may occur along the ramp as the driver transitions from the freeway speed to the crossroad speed. Step 3—Calculate Curve 1 Entry Speed: The average entry speed at Curve 1 is computed using Equation 24. vent,1 = 1.47 VOS Hwy – 0.034 × 5280 X1 ; ≥ 1.47 VXRoad (24) The boundary condition of Equation 24 indicates that the value computed (vent,1) cannot be less than the average speed at the point where the ramp connects to the crossroad (VXRoad). Step 4—Calculate Curve 1 Exit Speed: The average exit speed at Curve 1 is computed using Equation 25. vext,1 = vent,1 – 0.034 × 5280 Lc,1 ; ≤ vmax,1 and ≥ 1.47 VXRoad (25) The boundary conditions of Equation 25 indicate that the value computed (vext,1) should not exceed the limiting curve speed (vmax,i) and should not be less than the average speed at the point where the ramp connects to the crossroad (VXRoad). Step 5—Calculate Curve i Entry Speed: The average entry speed at Curve 2 (and all subsequent curves) is computed using Equation 26. vent,i = vext,i-1 – 0.034 × 5280 (X1 – Xi-1 – Lc,i-1) ; ≥ 1.47 VXRoad (26) Step 6—Calculate Curve i Exit Speed: The average exit speed at Curve 2 (and all subsequent curves) is computed using Equation 27. vext,i = vent,i – 0.034 × 5280 Lc,i ; ≤ vmax,i and ≥ 1.47 VXRoad (27)

87 Step 7—Calculate Speed on Successive Curves: The entry and exit speeds for Curve 3 and successive curves are computed by applying Steps 5 and 6 for each curve. This step is the same as Step 7 for the entrance ramp procedure. Figure 30 illustrates a sample output for an exit ramp that includes the alternate speed profile from the HSM procedures. Figure 30. Graphical Illustration of Vehicle Speeds for Sample Exit Ramp with Alternate Profile Quality Control Checks The RSPM performs several quality control checks to assess whether the ramp design, as input by the analyst, meets or violates several general design controls and criteria for ramp design. The types of quality control checks are associated with: • Acceptable acceleration/deceleration rates associated with individual portions of the ramp. • Assessment of whether the merge speed (VMerge) is within 5 mph of the average operating speed of the highway (or freeway) (VOS Hwy). Notes: Alternate Profile OnOn

88 • Graphical illustration of estimated speeds to design speeds of individual ramp components. Check of Acceleration/Deceleration Rates After the speeds are estimated at the beginning and end of each ramp section, the average acceleration rate for the section is computed using basic kinematics as follows: 𝑎 = 𝑉 − 𝑉2𝐿 (28) where: aavg = Average acceleration rate, ft/s2. Vi = Predicted vehicle speed at the beginning of the section, ft/s. Vf = Predicted vehicle speed at the end of the section, ft/s. L = Segment length, ft. By definition, positive acceleration (or increasing speed) is positive, and negative acceleration (or deceleration, or decreasing speed) is negative. The computed average acceleration rates are compared to acceleration rates recommended by Green Book Figures 2-33 and 2-34 for design. Green Book Figures 2-33 and 2-34, reproduced above as Figures 15 and 18 respectively, illustrate acceleration and deceleration characteristics of passenger cars suitable for design applications for design features such as intersections and freeway ramps. As part of previous research on freeways and interchanges, Bonneson et al. (2012) developed regression models to estimate the acceleration and deceleration characteristics depicted in Green Book Figures 2-33 and 2-34. These acceleration and deceleration characteristics are interpreted as vehicle performance limits. For example, on an entrance ramp, vehicles can accelerate up to a maximum acceleration rate as depicted in Green Book Figure 2-33. Acceleration rates above those depicted in Green Book Figure 2-33 are not acceptable for design purposes. Based on the assessment by Bonneson et al. (2012), the maximum design acceleration rates along freeway entrance ramps may be calculated using Equation 29 and the maximum design deceleration rates along freeway exit ramps may be calculated using Equation 30: For entrance ramps: 𝑎 = (29) For exit ramps: 𝑎 = −0.121𝑉 (30) where: aDesign = Maximum design acceleration/deceleration rate, ft/s2. The maximum design acceleration rates calculated using Equations 29 and 30 are compared to the average acceleration/deceleration rates for the individual ramp sections.

89 Check of Merge Speed on Entrance Ramps For the design of an entrance ramp, the Green Book states that motorists should attain a merge speed within 5 mph of the speed of the highway (or freeway) by the time they reach the end of the gap acceptance length (LGap Acpt). The RSPM performs a check to determine if the merge speed (VMerge) is within 5 mph of the average operating speed of the highway (or freeway) (VOS Hwy). If the difference between the average operating speed of the highway (or freeway) and the merge speed (VOS Frwy - VMerge) is greater than 5 mph, a warning message is provided. Check of Estimated Operating Speeds to Design Speeds on Individual Ramp Components Graphs provide a visual indication of any locations on the ramp where the estimated operating speed of a vehicle is greater than the design speed of the individual ramp section. 4.4 Uses and Limitations of the RSPM The RSPM is intended to be used to assess the adequacy of a ramp design or design alternatives during the design or reconstruction process. With the capability to adjust several input parameters, the RSPM can be used to predict vehicle speeds based upon anticipated driver behaviors or design conditions. The output from the RSPM should not be viewed as absolute truth but should be interpreted by the analyst or engineer to help design an interchange ramp in a consistent manner that meets driver expectations. The RSPM has several known limitations. By listing these limitations, engineers can have a better sense of the strengths and weaknesses of the tool, know the conditions for which it can best be applied, and possibly figure out best approaches to modify the inputs to address design conditions or situations for which the tool was not specifically designed. The RSPM was designed to predict vehicle speeds based upon anticipated driver behaviors but the inputs can also be adjusted to predict speeds based on assumed design conditions. The primary inputs to the tool for addressing both conditions are PGap Acpt for entrance ramps and PSCL for exit ramps. For entrance ramps, it is assumed for design purposes that vehicles use the entire acceleration length and gap acceptance length before merging onto the freeway. As such, the assumed acceleration of vehicles along the acceleration length and design values for minimum acceleration lengths are based on assumed merging speeds at the end of the deceleration length. However, field data show that many drivers use only a portion of the gap acceptance length prior to merging onto the freeway (Torbic et al., 2012). By adjusting the value of PGap Acpt, the analyst can use the RSPM to predict merge speeds based upon different merge locations. A default value of PGap Acpt = 0.5 is provided within the RSPM based on observed driver behaviors. A value of PGap Acpt = 1.0 more accurately represent assumed design conditions where vehicles merge onto the freeway at the end of the acceleration length and gap acceptance length. For exit ramps, it is assumed that vehicles diverge from the freeway mainline at the end of taper and the beginning of both the divergence zone length and the deceleration length. It is also assumed that vehicles do not decelerate in the freeway lane prior to the diverge maneuver. However, field data show that drivers diverge at different locations along the speed-change lane (Torbic et al., 2012). Noting that LSCL = LTaper + LDiv Zone, a value of PSCL = 0.1 is provided as a

90 default based on field observation. However, this value could be adjusted by the analyst so that the diverge location corresponds with the beginning of the divergence zone length and deceleration length. For the diverge speed to be equivalent with the operating speed of the freeway, the input value for the operating speed of the freeway would have to be adjusted equivalent to the mean speed differentials used in the prediction methodology (see Table 17). By understanding how the various inputs can be adjusted to more accurately model observed driver behaviors or design conditions, analyst can use the RSPM to evaluate and assess specific conditions. As with the development of most design tools, it was not possible to develop the RSPM to address all ramp design scenarios or conditions. Below is a list of several known limitations of the tool which are intended to help analyst more accurately apply the tool: Key Limitations to the RSPM: • The RSPM does not address the design of ramps for system interchanges. Speed data were collected along ramps at several system interchanges, but modeling efforts did not yield reliable speed prediction models for use with freeway-to-freeway ramps. Therefore, the RSPM was developed to address only entrance and exit ramps at service interchanges, not freeway-to-freeway ramps at system interchanges. • The RSPM was designed to address the most common types of ramps at service interchanges including diagonal, loop, and outer connection ramps. The RSMP was not designed to address other types of ramps or ramps with more complex geometrics. • The RSPM incorporates several regression models for tangents and curves that predict vehicle speeds at specific locations along the ramp including: - Entrance ramp: at the MC. - Entrance ramp: at the end of the curve (PT). - Entrance ramp: at the end of a tangent with a subsequent curve. - Entrance ramp: at the end of a tangent without a subsequent curve. - Exit ramp: at the MC. - Exit ramp: at the end of the curve (PT). - Exit ramp: at the end of a tangent with a subsequent curve. - Exit ramp: at the end of a tangent without a subsequent curve. Most of the models were developed based on observations of 500 or more vehicles across multiple sites. However, the model that predicts vehicle speeds at the end of a tangent without a subsequent curve for exit ramps is based on data for 77 vehicles at one location. Therefore, when modeling an exit ramp that includes a tangent without a subsequent curve, the analyst should be aware that predicted speeds for this design condition may be less reliable than for other design conditions. The regression models are also limited with respect to the range of site characteristics where actual speed data were collected. In most cases, the RSPM allows analysts to enter site characteristics outside of the limits from which the models were calibrated (e.g., curve length). The RSPM simply provides a message, showing the range of values for which the models were calibrated and prompts the analyst to continue or modify the input value, before estimating speeds for conditions outside of the range of site characteristics from which the models were calibrated (i.e., extrapolation of speed estimates).

91 • The 85th percentile of the distribution of observed operating speeds is a frequently used measure associated with the design of geometric features. The speed prediction models incorporated in the RSPM yield estimates of average operating speeds, not the 85th percentile of operating speeds.

Next: Section 5. Case Studies »
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Selection of a design speed should be based upon the anticipated operating speed, topography, adjacent land use, modal mix, and functional classification of the roadway.

The TRB National Cooperative Highway Research Program's NCHRP Web-Only Document 313: Selecting Ramp Design Speeds, Volume 1: Guide provides further detail for selecting an appropriate ramp design speed than presented in the 2018 Green Book, to address several overarching challenges that may lead to confusion or inconsistent interpretation of existing AASHTO guidance for selecting an appropriate ramp design speed.

Supplemental to the document are NCHRP Web-Only Document 313: Selecting Ramp Design Speeds,Volume 2: Conduct of Research Report and Ramp Speed Profile Model worksheets.

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