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92 Section 5. Case Studies This section demonstrates through several case studies how to evaluate the consistency of a ramp design based on the selected ramp design speed. It brings together information presented in three previous sections (Section 2.14, Section 3, and Section 4) to demonstrate how designers can assess the adequacy of a new ramp design during the design process or if an existing ramp is being considered for reconstruction how the guidelines herein can be used to evaluate the adequacy of design alternatives. Several case studies are first presented for entrance ramps, followed by several case studies for exit ramps. The case studies are of actual ramps recently designed and/or built. When designing the ramps used in the case studies, agencies would have used design guidance from the 2011 Green Book or a manual with similar guidance. When gathering information for the case studies, the ramp design speed for each of the ramps was requested; however, none of the agencies provided the actual ramp design speeds from which the designs were based. Therefore, the ramp design speeds reported below in the case studies are inferred ramp design speeds based on the information available. As such, the case studies may illustrate potential differences that could arise when designing a ramp based on design guidance from the 2011 Green Book and design guidelines presented herein. In addition, other assumptions were made about the design of the ramp and/or characteristics of the connecting roads if the agencies did not provide the information. 5.1 Evaluating the Consistency of a Ramp Design for an Entrance Ramp at a Service Interchange Based on the Selected Ramp Design Speed With entrance ramps, several key issues related to the selection of an appropriate ramp design speed should be considered during the design process and while evaluating the consistency of a ramp design: ⢠Because the controlling feature of an entrance ramp is towards the end of the ramp near the freeway mainline ramp terminal, ramp design speeds for entrance ramps are generally at least 35 mph or greater. ⢠Vehicle acceleration is a primary design control for entrance ramps. On the ramp proper, each tangent and curve section should be designed with sufficient length to accommodate the acceleration expected to occur over its length. Green Book Figure 2-33 may be used as a guide for determining minimum practical lengths of individual tangent and curve sections along the ramp proper. ⢠As vehicles transition from the ramp proper to the freeway mainline ramp terminal of an entrance ramp, the primary design criterion provided within AASHTO policy addresses minimum acceleration lengths along the freeway mainline ramp terminal (see Green Book Table 10-4). Vehicles should be able to attain a speed within 5 mph of the operating speed of the highway (or freeway) by the time they reach the end of the acceleration length.
93 ⢠Drivers tend to begin the merge, acceleration process only after gaining a clear view of the freeway right-traffic lane. If the driverâs view from the ramp is obstructed, the acceleration length will not begin until near the ramp gore where the view of the freeway becomes unobstructed (Hunter and Machemehl, 1999). ⢠In general, the acceleration length begins at the end of the controlling curve or feature of the ramp proper. However, if the radius of the final curve of the ramp is greater than 1,000 ft or a tangent is present upstream of the gore point and drivers on the ramp have a clear view of traffic in the right lane of the freeway, the beginning of the acceleration length may be located upstream of the gore point (i.e., along the final curve of the ramp proper). Below are two case studies of entrance ramps to demonstrate how to evaluate the consistency of a ramp design based on the selected ramp design speed. Case Study No. 1: Loop Entrance Ramp in Suburban Area Background Information This case study features a loop ramp in a highly developed suburban area. Figure 31 provides a schematic and characteristics of the ramp. The loop ramp is part of a partial cloverleaf interchange. It begins at a signalized ramp terminal on a divided arterial. The speed limit on the crossroad is 45 mph. A ramp meter is present on the ramp, and a high-occupancy vehicle lane is adjacent to the travel lane leading up to the ramp meter. The ramp consists of a compound curve with radii of 182 ft and 224 ft, respectively, in the direction of travel. A third horizontal curve with a radius of 3,000 ft is located near the gore point. Based on the design speeds of Curves 1 and 2 and guidance in the 2011 and 2018 editions of the Green Book, the likely ramp design speed used for the design of this loop ramp is 25 mph.
94 Interchange type: Service Conditions: Constrained Area type: Urban/Suburban Ramp configuration: Loop Freeway characteristics Design speed: 70 mph Operating speed: 65 mph Speed limit: 65 mph Crossroad characteristics Type of roadway: Primary/major rd Speed limit: 45 mph Type of traffic control at terminal: Signal Ramp Proper Ramp grade: 1 % downgrade Max superelevation (emax): 12 % Curve 1 PC milepost: 0.044 mi Curve length: 0.076 mi Curve radius 182 ft Superelevation: 12 % Design speed 25 mph Curve 2 PC milepost: 0.120 mi Curve length: 0.036 mi Curve radius 224 ft Superelevation: 10 % Design speed 25 mph Curve 3 PC milepost: 0.223 mi Curve length: 0.032 mi Curve radius 3000 ft Superelevation: 4 % Design speed 50 mph Freeway Mainline Ramp Terminal Milepost of gore point 0.338 mi Acceleration length (upstream of the gore point) 0.083 mi Gap acceptance length 0.057 mi Taper length 0.110 mi Speed-change lane type Parallel Figure 31. Case Study No. 1 (Entrance Ramp: General Ramp Characteristics and Dimensions) Design Consistency Assessment Based on the design guidelines presented herein, given the freeway design speed is 70 mph, the crossroad is a divided arterial, and the ramp is located in a highly developed suburban area, Table 4 indicates the ramp design speed for a loop ramp should be between 25 and 35 mph. Since space is limited, a lower ramp design speed of 25 mph seems logical for this ramp. Thus, the design speed of the last curve encountered along the ramp proper that significantly affects vehicle speed should be 25 mph. The design speed of Curve 2 is 25 mph; so as designed, the ramp design speed of this ramp is consistent with the design guidelines presented herein. All
95 other sections and elements of the ramp should be designed consistent with this ramp design speed to provide appropriate speed transitions along the ramp. To evaluate the adequacy and consistency of the existing ramp design, the ramp proper should be divided into individual tangents and curves. Design speeds and anticipated operating speeds should be evaluated for these tangents and curves on the ramp proper, along with the acceleration length and anticipated operating speeds for the freeway mainline ramp terminal. In Figure 31, the design speeds of the curves are presented, but the design speeds for the tangents were not provided for the ramp so this information is assumed as follows. With entrance ramps, the first check of the adequacy of the ramp is to assess whether the design speeds increase in a stepwise manner between the contiguous segments on the ramp proper. For this case study, the first tangent begins at the crossroad ramp terminal and extends to the PC of Curve 1 at MP 0.044. Since the design speed of Curve 1 is 25 mph, it is logical for the design speed of the first tangent to be 20 mph. From MP 0.044 to MP 0.156, the design speeds of the individual curves for the compound curve are both 25 mph. The second tangent begins at the end of Curve 2 (i.e., MP 0.156) and extends to the PC of Curve 3 at MP 0.223. Since the design speed of Curve 3 is 50 mph, it is logical for the design speed of the second tangent to be 45 mph. From MP 0.233 to MP 0.255, the design speed of Curve 3 is 50 mph. The third tangent begins at the end of Curve 3 (i.e., MP 0.255) and extends to the gore point at MP 0.338. Since the design speed of Curve 3 is 50 mph, it is logical for the design speed of the third tangent to be 55 mph. Based on the assumed design speeds for the individual tangents and the design speeds of the curves as specified, the existing design of the ramp proper appears adequate as the design speeds of contiguous segments either increase or are the same in the direction of travel, and the change in design speed between adjoining sections is at most 5 mph. The next step to evaluate the adequacy of the ramp proper is to confirm that sufficient distance is provided for a vehicle to accelerate as intended along the length of the ramp. A quick assessment that could be made is to simply compare the overall length of the ramp proper (i.e., from the crossroad ramp terminal to the gore point) with the length necessary to accelerate from the assumed entry speed of a vehicle at the crossroad ramp terminal and the design speed of the final segment of the ramp proper. The length from the crossroad ramp terminal to the gore point is 0.338 mi (1785 ft). The assumed entry speed of a vehicle onto the ramp proper from the crossroad ramp terminal is 15 mph, and the design speed of the tangent immediately upstream of the gore point is 55 mph. From Table 5, the minimum length required to accelerate from a speed of 15 mph to 55 mph is 0.179 mi (945 ft). This initial check suggests that sufficient distance is provided along the ramp proper for a vehicle to accelerate from a speed of 15 mph to 55 mph prior to entering the speed-change lane at the gore point. However, this assessment does not account for the individual tangent and curve sections that comprise the ramp proper. Therefore, further assessments should be made in reference to both the design speeds of the individual components and the anticipated operating speeds along the individual components. In reference to design speeds and evaluating the ramp proper to confirm that sufficient distance is provided for a vehicle to accelerate as intended along the length of the ramp, Table 18 shows the beginning and ending mileposts and actual length of the individual components, the beginning and ending design speeds of the individual segments for this assessment, and the minimum acceleration lengths necessary to accelerate from the beginning and ending design speeds based upon acceleration capabilities of lower performance vehicles (see Green Book
96 Figure 2-33). For this assessment, the design speed of the upstream segment is used as the beginning design speed for the adjacent downstream segment. Table 18. Case Study No. 1: Assessment of Design Speeds for Individiual Segment of the Ramp Proper and Minimum Acceleration Lengths Section Mileposts (MP) Actual Length (mi) Design Speeds (mph) Minimum Acceleration Length (mi) Begin End Begin End Tangent 1 0.000 0.044 0.044 15 20 0.009 Curve 1 0.044 0.120 0.076 20 25 0.013 Curve 2 0.120 0.156 0.036 25 25 0.000 Tangent 2 0.156 0.223 0.067 25 45 0.084 Curve 3 0.223 0.255 0.032 45 50 0.038 Tangent 3 0.255 0.338 0.083 50 55 0.040 For this ramp, the lengths of the individual tangents and curve sections all exceed the minimum accelerate lengths required based on the initial and ending design speeds, except for Tangent 2 and Curve 3. As designed, the length of Tangent 2 is 0.067 mi, and the minimum length for a vehicle to accelerate from 25 to 45 mph is 0.084 mi. Similarly, the length of Curve 3 is 0.032 mi, and the minimum length for a vehicle to accelerate from 45 to 50 mph is 0.038 mi. Before deciding that this ramp design is inadequate and should be redesigned, it should be recognized that the alignment of Curve 3 is fairly gentle with a radius of 3,000 ft so this curve is not expected to significantly affect vehicle speeds. With this in mind, the actual length from the beginning of Tangent 2 (MP 0.156) to the end of Tangent 3 (MP 0.338) is 0.182 mi. For a beginning design speed of 25 mph at the beginning of Tangent 2 and an ending design speed of 55 mph at the end of Tangent 3, the minimum length for a vehicle to accelerate from 25 to 55 mph is 0.162 mi. Thus, as designed, it appears that sufficient length is provided for vehicles to accelerate exiting Curve 2 up to the gore point at the end of Tangent 3, before entering the speed- change lane. However, before such a decision is made, further assessment should be made to evaluate minimum acceleration lengths based on the anticipated operating speeds along the individual components. To do so requires the use of speed prediction models to estimate vehicle speeds along the ramp. Figure 32 illustrates the inputs that would be specified to estimate speeds along the ramp using the RSPM. For this ramp, since the radius of Curve 3 is greater than 2,000 ft, from the end of Curve 2 (MP 0.156) to the gore point (MP 0.338), the predicted speed along the ramp is calculated assuming a tangent section. Figure 33 shows the predicted speed profile along the ramp, including additional information in tabular form. Plotted speed data are provided as output from the RSMP as well as acceleration data as follows: ⢠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.
97 ⢠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, the message will indicate âaccel > designâ. Otherwise, the message will indicate âOKâ. Figure 32. Case Study No. 1 (Entrance Ramp: Inputs to RSPM)
98 Plotted Speed Data Acceleration Data Figure 33. Case Study No. 1 (Entrance Ramp: Outputs from RSPM) Notes: Alternate Profile The merge speed is more than 5 mph below the freeway operating speed. OffOff Point Type Milepost Profile, mph Milepost Design, mph Xrd 0.000 15.00 0.000 20 Tan 0.044 28.75 0.044 20 Cmc 0.082 29.10 0.044 25 Cpt 0.120 29.51 0.120 25 Cmc 0.138 29.91 0.120 25 Cpt 0.156 30.35 0.156 25 Tan 0.338 44.96 0.156 70 SCm 0.366 47.89 0.505 70 SCe 0.395 47.89 Tpr 0.505 47.89 Segment Data Speed, mph Average Acceleration Design Acceleration Number Type Length, mi Initial Final mph/s ft/s2 ft/s2 Notes 1 Tangent 0.044 15.000 28.750 1.899 2.785 7.500 OK 2 Curve 0.038 28.750 29.098 0.074 0.108 3.913 OK 3 Curve 0.038 29.098 29.514 0.089 0.131 3.866 OK 4 Curve 0.018 29.514 29.908 0.180 0.265 3.812 OK 5 Curve 0.018 29.908 30.352 0.207 0.303 3.762 OK 6 Tangent 0.182 30.352 44.963 0.840 1.232 3.706 OK 7 Speed-change 0.028 44.963 47.892 1.326 1.944 2.502 OK 8 Speed-change 0.029 47.892 47.892 0.000 0.000 2.349 OK 9 Taper 0.110 47.892 47.892 0.000 0.000 2.349 OK
99 A couple of points are worth noting from the speed profile illustrated in Figure 33: ⢠The predicted operating speed at the end of the first tangent (28.75 mph) is greater than the design speed of Curves 1 and 2 (25 mph). Because this is an entrance ramp and speeds are intended to increase along the ramp, having the predicted operating speeds entering and along Curves 1 and 2 being greater than the design speeds for the individual sections may not be much of a concern. However, if it is a concern, several options are to either decrease the length of tangent entering Curve 1 or install signing (e.g., an advisory speed sign in advance of Curve 1 and/or chevrons along the curve) to warn drivers of the sharpness of the curves. ⢠The predicted merge speed (47.89 mph) is approximately 17 mph below the operating speed of the freeway (65 mph). The goal is for vehicles to enter the highway at a speed within 5 mph of the speed of traffic on the highway. That is not expected to happen here, at least based on the current assumptions (see note above the speed profile). As input, it is assumed that vehicles merge on the highway at MP 0.366, using only half of the gap acceptance length (PGap Acpt = 0.50). This assumption is based on merging behavior observed in the field (Torbic et al., 2012). According to the design guidelines, vehicles 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), not the middle of the gap acceptance length, so the predicted speed at the end of the gap acceptance length should be looked into further. ⢠The actual acceleration length (LAcc Length) is 0.111mi (0.057 mi + 0.054 mi). From Table 6, given the design speed of the final tangent is 55 mph and the design speed of the highway is 70 mph, the minimum acceleration length is 0.066 mi (350 ft). Thus, as designed, the actual acceleration length meets the design criteria for minimum acceleration length, but several inconsistencies exist between the predicted speed profile and design criteria as specified in Table 6. The design speed for the final section of the ramp proper is 55 mph, and from Table 6 the assumed operating speed for a design speed of 55 mph is 48 mph. However, the predicted operating speed at the end of the tangent is 45 mph, slightly less than the assumed operating speed corresponding to a design speed of 55 mph. Similarly, in Table 6, for a freeway design speed of 70 mph, the assumed merge speed is 53 mph. In this example, it is given that operating speed and speed limit of the highway are both 65 mph. Thus, the desirable merge speed is 60 mph (i.e., 5 mph below the operating speed of the highway). Assuming an initial entry speed of 45 mph as predicted from the RSPM and a final merge speed of 60 mph, the minimum acceleration length is approximately 0.227 mi (1,200 ft) (i.e., more than double the actual acceleration length). Considering these inconsistencies between the predicted speed profile and the assumed initial entry and merge speeds from Table 6, this ramp should potentially be redesigned to allow for a longer acceleration length between 0.189 and 0.227 mi (1,000 and 1,200 ft). Assuming an acceleration length of 0.220 mi (1,160 ft), the RSPM predicts an operating speed of 60 mph at the end of the acceleration length and gap acceptance length. Figure 34 shows the revised inputs to the RSPM. The gap acceptance length was increased to 0.166 mi (which by default increases the acceleration length) and the PGap
100 Acpt was changed to 1.0. Figure 35 shows the revised speed profile with a merge speed of 60 mph at the end of the acceleration length and gap acceptance length (MP 0.614). Figure 34. Case Study No. 1 (Entrance Ramp: Revised Inputs to RSPM)
101 Plotted Speed Data Acceleration Data Figure 35. Case Study No. 1 (Entrance Ramp: Revised Outputs from RSPM) Notes: Alternate Profile OffOff Point Type Milepost Profile, mph Milepost Design, mph Xrd 0.000 15.00 0.000 20 Tan 0.044 28.75 0.044 20 Cmc 0.082 29.10 0.044 25 Cpt 0.120 29.51 0.120 25 Cmc 0.138 29.91 0.120 25 Cpt 0.156 30.35 0.156 25 Tan 0.338 44.96 0.156 70 SCe 0.504 60.05 0.614 70 Tpr 0.614 60.05 Segment Data Speed, mph Average Acceleration Design Acceleration Number Type Length, mi Initial Final mph/s ft/s2 ft/s2 Notes 1 Tangent 0.044 15.000 28.750 1.899 2.785 7.500 OK 2 Curve 0.038 28.750 29.098 0.074 0.108 3.913 OK 3 Curve 0.038 29.098 29.514 0.089 0.131 3.866 OK 4 Curve 0.018 29.514 29.908 0.180 0.265 3.812 OK 5 Curve 0.018 29.908 30.352 0.207 0.303 3.762 OK 6 Tangent 0.182 30.352 44.963 0.840 1.232 3.706 OK 7 Speed-change 0.166 44.963 60.049 1.326 1.944 2.502 OK 8 Taper 0.110 60.049 60.049 0.000 0.000 1.873 OK
102 Case Study No. 2: Diagonal Entrance Ramp in Rural Area Background Information This case study features a diagonal entrance ramp to a high-speed rural freeway. Figure 36 provides a schematic and characteristics of the ramp. The ramp begins at a minor-road stop- controlled intersection and consists of three curves with radii of 8,056 ft, 2,497 ft, and 2,856 ft. The posted speed limit on the freeway is 85 mph, and the average operating speed on the freeway is 72 mph. Based on the design speeds of the three curves on this ramp and guidance in the 2011 and 2018 editions of the Green Book, it is difficult to assess what ramp design speed would have been selected for the design of this diagonal ramp.
103 Interchange type: Service Conditions: Unconstrained Area type: Rural Ramp configuration: Diagonal Freeway characteristics Design speed: 85 mph Operating speed: 72 mph Speed limit: 85 mph Crossroad characteristics Type of roadway: Local/minor rd Speed limit: 45 mph Type of traffic control at terminal: Stop control Ramp Proper Ramp grade: 0.17 % Maximum superelevation (emax): 6 % Curve 1 PC milepost: 0.123 mi Curve length: 0.055 mi Curve radius 8056 ft Superelevation: 3.51 % Design speed 80 mph Curve 2 PC milepost: 0.179 mi Curve length: 0.062 mi Curve radius 2497 ft Superelevation: 3.51 % Design speed 40 mph Curve 3 PC milepost: 0.272 mi Curve length: 0.078 mi Curve radius 2856 ft Superelevation: 2.50 % Design speed 35 mph Freeway Mainline Ramp Terminal Milepost of gore point 0.398 mi Acceleration length (upstream of the gore point) 0.047 mi Gap acceptance length 0.042 mi Taper length 0.094 mi Speed-change lane type Taper Figure 36. Case Study No. 2 (General Ramp Characteristics and Dimensions) Design Consistency Assessment The alignment of this ramp is relatively straight or flat, with the sharpest curve having a radius of 2,497 ft, so it is unlikely that the horizontal alignment will affect vehicle speeds. Based on the
104 design guidelines presented herein, the footnote at the bottom of Table 4 reads where the horizontal alignment of a diagonal entrance ramp is relatively straight and has little impact on vehicle speeds, the ramp design speed is dependent on the operational characteristics of the freeway mainline ramp terminal. For this situation, it is recommended that the ramp design speed be within 15 to 20 mph of the highway design speed. Thus, a logical ramp design for this diagonal ramp would be either 65 or 70 mph. For purposes of this case study, 65 mph is selected as the ramp design speed. All other sections and elements of the ramp should be designed consistent with this ramp design speed to provide appropriate speed transitions along the ramp. To evaluate the adequacy and consistency of the existing ramp design, one of the first checks for an entrance ramp is to assess whether the design speeds of contiguous segments along the ramp proper increase sequentially. Without even considering possible design speeds for the tangent sections between curves, it is apparent from Figure 36 that the design speeds of contiguous segments along this ramp do not increase sequentially in a stepwise manner. Curve 1 has the highest design speed (80 mph). Curve 2 has the second highest design speed (40 mph), and Curve 3 has the lowest design speed at 35 mph. Thus, rather than the design speeds increasing sequentially along the ramp proper, the design speeds (at least for the curves) decrease along the ramp proper as currently designed. This check does not necessarily mean that the current ramp design is inadequate and should be redesigned, but further evaluation is necessary. As indicated in the design guidelines presented herein, it is desirable but not essential that the design speeds of the contiguous segments along the ramp proper of an entrance ramp increase in a stepwise manner. It is more important that the contiguous segments along the ramp provide for appropriate speed transitions from segment to segment. To further evaluate the adequacy and consistency of the existing ramp design, the ramp proper should be divided into individual tangent and curve sections to assess if the contiguous segments along the ramp provide for appropriate speed transitions from segment to segment. In this case, because all of the curve radii along the ramp proper are over 2,000 ft, it is unlikely that the curves will significantly affect vehicle speeds so the entire ramp proper can be evaluated as a single tangential section. Thus, a quick assessment can be made to simply compare the overall length of the ramp proper (i.e., from the crossroad ramp terminal to the gore point) with the length necessary to accelerate from the assumed entry speed of a vehicle at the crossroad ramp terminal and the design speed at the gore point. For this ramp, the length from the crossroad ramp terminal to the gore point is 0.398 mi (2,101 ft). The assumed entry speed of a vehicle entering the ramp proper from the crossroad ramp terminal is 15 mph, and the design speed of the overall tangential alignment is 65 mph (i.e., the assumed ramp design speed as indicated above). From Figure 15, the minimum length required to accelerate from a speed of 15 mph to 65 mph is approximately 0.317 mi. This check suggests that sufficient distance is provided along the ramp proper for a vehicle to accelerate from a speed of 15 mph to 65 mph prior to entering the speed-change lane at the gore point. However, before such a decision is made, further assessment should be made to evaluate the anticipated operating speeds along the individual components of the ramp. To evaluate the anticipated operating speeds along the ramp, the RSPM can be used. Figure 37 shows the inputs into the RSPM for this ramp, and Figure 38 shows the predicted speed profile along the ramp and other outputs in tabular form.
105 Figure 37. Case Study No. 2 (Entrance Ramp: Inputs to RSPM)
106 Plotted Speed Data Acceleration Data Figure 38. Case Study No. 2 (Entrance Ramp: Outputs from RSPM) A couple of points of interest are worth noting here comparing the output from the RSPM and design guidelines presented herein: ⢠Although the alignment of the ramp proper shows three curves (see Figure 36), because all of the curve radii are greater than 2,000 ft, the inputs into the RSPM essentially treat the ramp proper as a single tangent section. The predicted speed at the end of this ramp Notes: Alternate Profile The merge speed is more than 5 mph below the freeway operating speed. OffOff Point Type Milepost Profile, mph Milepost Design, mph Xrd 0.000 15.00 0.000 65 Tan 0.398 46.34 0.398 65 SCm 0.419 49.29 0.398 80 SCe 0.440 49.29 0.550 80 Tpr 0.550 49.29 Segment Data Speed, mph Average Acceleration Design Acceleration Number Type Length, mi Initial Final mph/s ft/s2 ft/s2 Notes 1 Tangent 0.398 15.000 46.344 0.671 0.984 7.500 OK 2 Speed-change 0.021 46.344 49.295 1.866 2.738 2.428 accel > design 3 Speed-change 0.021 49.295 49.295 0.000 0.000 2.282 OK 4 Taper 0.110 49.295 49.295 0.000 0.000 2.282 OK
107 proper (i.e., the gore point) is approximately 46 mph, which is less than the ramp design speed of 65 mph. ⢠Although the alignment of the ramp proper is treated as a single tangent section, it is important to check that the anticipated operating speeds along each of the curves are consistent with the design speeds of the curves. From the graph in Figure 38, it can be seen that for Curves 1 and 2, the predicted operating speeds are below the design speeds of the curves; but for Curve 3 from MP 0.272 to MP 0.350, predicted speeds increase from approximately 35 to 42 mph. Considering that it is recommended that the design speed of a curve be based on the speed at the MC rather than the speeds entering or exiting the curve, the fact that vehicles are predicted to exit the curve approximately 7 mph above the design speed may be a concern. If so, several options for addressing this concern would be to potentially increase the curve radius or provide additional superelevation to increase the design speed of Curve 3. ⢠Based on previous research (Torbic et al., 2012), drivers tend to merge onto the freeway using only about half of the gap acceptance length rather than the full gap acceptance length and acceleration length. Assuming vehicles merge onto the freeway using half of the gap acceptance length as input in Figure 37 (i.e., PGap Acpt = 0.5), vehicles are expected to merge onto the freeway at MP 0.419 at a speed of approximately 49 mph, which is 23 mph below the average operating speed of the freeway. If PGap Acpt = 1.0, vehicles are expected to merge onto the freeway at MP 0.440 at a speed of approximately 52 mph, which is still 20 mph below the average operating speed of the freeway. With either scenario (i.e., PGap Acpt = 0.5 or PGap Acpt = 1.0), vehicles are not predicted to merge onto the freeway at a speed within 5 mph of the freeway operating speed. ⢠The actual acceleration length (LAcc Length) is 0.089 mi (0.047 mi + 0.042) mi). From Table 6, given the design speed of the final tangent is 65 mph and the design speed of the highway is 85 mph, the minimum acceleration length is 0.095 mi (500 ft). Thus, as designed, the actual acceleration length meets the design criteria for minimum acceleration length, but several inconsistencies exist between the predicted speed profile and design criteria as specified in Table 6. The overall ramp design speed assuming a simple tangential ramp proper is 65 mph, and from Table 6 for a design speed of 65 mph the assumed operating speed entering acceleration length is 56 mph. However, the predicted operating speed at the gore point is 46 mph, which is less than the assumed operating speed corresponding to a design speed of 65 mph. Similarly, from Table 6, for a freeway design speed of 85 mph, the assumed merge speed is 59 mph. However, in this example, it is given that operating speed is 72 mph. Thus, the desirable merge speed is 67 mph (i.e., 5 mph below the operating speed of the highway). Table 6 (even as adapted) does not provide sufficient information to estimate the minimum acceleration length assuming a merge speed of 67 mph. In the absence of sufficient information from Table 6, Figure 15 could be used to estimate the minimum acceleration length based on an initial speed of 46 mph and a final speed of 67 mph (Note: 46 mph is the predicted speed at the gore point MP 0.398. To be more accurate, the predicted speed at MP 0.351 where the actual acceleration lane begins should be used for determining the minimum acceleration length). From Figure 15, the minimum acceleration length is approximately 0.227 mi (1,200 ft), compared to the
108 actual acceleration length of 0.089 mi. Considering these inconsistencies between the predicted speed profile and the assumed initial and merge speeds from Table 6, this ramp should potentially be redesigned to allow for a longer acceleration length, gap acceptance length, and/or speed-change lane length. Based on speed predictions from the RSPM, the acceleration length and gap acceptance length should extend to MP 0.573 for vehicles to merge onto the freeway at a speed of 67 mph (i.e., within 5 mph of the freeway operating speed). Figure 39 illustrates the revised inputs into the RSPM, and Figure 40 shows the revised output for the design alternative that predicts a merge speed of 67 mph by extending the acceleration length and gap acceptance length. In Figure 39, the gap acceptance length was increased from 0.042 mi to 0.175 mi, and PGap Acpt was changed from 0.5 to 1.0. Figure 39. Case Study No. 2 (Entrance Ramp: Revised Inputs to RSPM)
109 Plotted Speed Data Acceleration Data Figure 40. Case Study No. 2 (Entrance Ramp: Revised Outputs from RSPM) 5.2 Evaluating the Consistency of a Ramp Design for an Exit Ramp at a Service Interchange Based on the Selected Ramp Design Speed With exit ramps, several key issues related to the selection of an appropriate ramp design speed should be considered during the design process and while evaluating the consistency of a ramp design: ⢠A wide range of ramp design speeds are applicable to exit ramps because the controlling feature may be towards the upstream end of the ramp (i.e., near the freeway mainline Notes: Alternate Profile OffOff Point Type Milepost Profile, mph Milepost Design, mph Xrd 0.000 15.00 0.000 65 Tan 0.398 46.34 0.398 65 SCe 0.573 67.08 0.398 80 Tpr 0.683 67.08 0.683 80 Segment Data Speed, mph Average Acceleration Design Acceleration Number Type Length, mi Initial Final mph/s ft/s2 ft/s2 Notes 1 Tangent 0.398 15.000 46.344 0.671 0.984 7.500 OK 2 Speed-change 0.175 46.344 67.078 1.866 2.737 2.428 accel > design 3 Taper 0.110 67.078 67.078 0.000 0.000 1.677 OK
110 ramp terminal) or the downstream end of the ramp (i.e., associated with the crossroad ramp terminal). For example, where the horizontal alignment of the ramp is curvilinear and the first curve encountered on the exit ramp is the controlling feature, ramp design speeds will likely be higher, but if the horizontal alignment of the ramp is relatively straight and the operational characteristics of the crossroad ramp terminal are the controlling feature, ramp design speeds will be lower. Ramp design speeds for exit ramps may range from 15 mph to 65 mph or higher. ⢠As vehicles transition from the freeway to the freeway mainline ramp terminal to the ramp proper of an exit ramp, the primary design criterion provided within AASHTO policy addresses minimum deceleration lengths along the freeway mainline ramp terminal (see Green Book Table 10-6). Vehicles should be able to maintain their speed on the freeway, diverge from the freeway onto the freeway mainline ramp terminal, decelerate at a comfortable rate within the freeway mainline ramp terminal, and enter the ramp proper at a speed consistent with the design of the ramp proper. ⢠The deceleration length begins where the width of the auxiliary lane increases to 12 ft or greater (i.e., the end of taper) and extends at least to the gore point. If the first curve that significantly affects vehicle speed begins at the gore point, then the boundary between the freeway mainline ramp terminal and the ramp proper is at the gore point. However, if the beginning of the first curve that significantly affects vehicle speed is downstream of the gore point, then the boundary between the freeway mainline ramp terminal and the ramp proper may be downstream of the gore point. It may be assumed that any curve radius less than or equal to 1,000 ft will significantly affect vehicle speed. ⢠Vehicle deceleration is a primary design control for exit ramps. On the ramp proper, each tangent and curve section should be designed with sufficient length to accommodate the deceleration expected to occur over its length. Green Book Figure 2-34 may be used as guide for determining minimum practical lengths of individual tangent and curve sections along the ramp proper. ⢠At the downstream end of the ramp, the ramp should be designed so that vehicles enter the functional area of the crossroad ramp terminal at relatively low speeds (e.g., between 15 and 20 mph); and as appropriate, sufficient distance should be provided for a vehicle to come to a complete stop at the end of the queue storage length near the crossroad. Below are two case studies of exit ramps to demonstrate how to evaluate the consistency of a ramp design based on the selected ramp design speed. Case Study No. 3: Loop Exit Ramp in Suburban Area Background Information This case study features a loop ramp in a suburban area. Figure 41 provides a schematic and characteristics of the ramp. The ramp ends at a signalized intersection. The ramp consists of a compound curve, with radii in the following order: 525 ft and 265 ft. Based on the design speeds of Curves 1 and 2 and guidance in the 2011 and 2018 editions of the Green Book, the likely ramp design speed used to design this loop ramp was either 25 or 30 mph.
111 Interchange type: Service Conditions: Unconstrained Area type: Urban/Suburban Ramp configuration: Loop Freeway characteristics Design speed: 75 mph Operating speed: Unknown Speed limit: 70 mph Crossroad characteristics Type of roadway: Local/minor rd Speed limit: 35 mph Type of traffic control at terminal: Signal Queue storage length: 0.050 mi Milepost of crossroad ramp terminal 0.256 mi Ramp Proper Ramp grade: 1 % downgrade Max superelevation (emax): 8 % Curve 1 PC milepost: 0.000 mi Curve length: 0.068 mi Curve radius 525 ft Superelevation: 7 % Design speed 30 mph Curve 2 PC milepost: 0.068 mi Curve length: 0.116 mi Curve radius 265 ft Superelevation: 6.6 % Design speed 25 mph Freeway Mainline Ramp Terminal Taper length 0.057 mi Divergence zone length 0.127 mi Deceleration length (downstream of the gore point) 0.000 mi Speed-change lane type Parallel Figure 41. Case Study No. 3 (Exit Ramp: General Ramp Characteristics and Dimensions)
112 Design Consistency Assessment Based on the design guidelines presented herein, given the freeway design speed is 75 mph and the ramp is located in a suburban area, Table 4 indicates the ramp design speed for a loop ramp should be between 25 and 40 mph. Given the first curve encountered on the ramp proper that significantly affects vehicle speeds has a design speed of 30 mph, the ramp design speed would be 30 mph based on the design guidelines presented herein. All other sections and elements of the ramp should be designed consistent with this ramp design speed to provide appropriate speed transitions along the ramp. To evaluate the adequacy and consistency of the existing ramp design, one of the first checks for an exit ramp is to assess whether the design speeds of contiguous segments along the ramp proper decrease sequentially in a stepwise manner. For this case study, the design speed of the first curve from MP 0.000 to MP 0.068 is 30 mph, and the design speed of the second curve from MP 0.068 to MP 0.184 is 25 mph. A tangent extends from the end of Curve 2 to the functional area of the crossroad ramp terminal. Since the crossroad ramp terminal is signalized and vehicles would be expected to come to a stop at the end of the queue storage length, a logical design speed for this tangent is 20 mph. Based on the design speeds of the two curves and the assumed design speed for the tangent upstream of the crossroad ramp terminal, the existing design of the ramp proper appears adequate as the design speeds of contiguous segments decrease in the direction of travel, and the change in design speed between adjoining sections is at most 5 mph. The next step to evaluate the adequacy of an exit ramp design is to confirm that sufficient distance is provided for a vehicle to decelerate as intended along the length of the ramp. This involves evaluating the individual components of the freeway mainline ramp terminal, the ramp proper, and to some level the crossroad ramp terminal. First, an assessment should be made to confirm that the deceleration length is sufficiently long to allow for a vehicle to decelerate as intended along the freeway mainline ramp terminal. Using Table 8, for a highway design speed of 75 mph and a design speed of 30 mph for the first controlling feature on the ramp proper, a minimum deceleration length of 0.109 mi (575 ft) is recommended. The actual deceleration length is equivalent to the divergence zone length which is 0.127 mi in length. Thus, the existing design of the freeway mainline ramp terminal appears adequate as the actual deceleration length is greater than the minimum deceleration from Table 8. A second type of assessment that should be made is to confirm that sufficient distance is provided for a vehicle to decelerate as intended along each individual tangent and curve of the ramp proper. This assessment is best accomplished by assuming or predicting an entering speed and an exiting speed for each individual section of the ramp proper and determining if sufficient distance is provided to decelerate as intended. The RSPM provides the tools to perform such an assessment. Figure 42 shows the inputs into the RSPM for this ramp, and Figure 43 shows the predicted speed profile along the ramp and other outputs in tabular form.
113 Figure 42. Case Study No. 3 (Exit Ramp: Inputs to RSPM)
114 Plotted Speed Data Acceleration Data Figure 43. Case Study No. 3 (Exit Ramp: Outputs from RSPM) Notes: Alternate Profile OffOff Point Type Milepost Profile, mph Milepost Design, mph Tpr -0.184 70.00 -0.241 75 SCd -0.166 65.60 0.000 75 Gor 0.000 43.98 0.000 30 Cmc 0.034 43.98 0.068 30 Cpt 0.068 32.50 0.068 25 Cmc 0.126 32.50 0.184 25 Cpt 0.184 15.00 0.184 20 Qst 0.206 0.00 0.256 20 Xrd 0.256 0.00 Segment Data Speed, mph Average Acceleration Design Acceleration Number Type Length, mi Initial Final mph/s ft/s2 ft/s2 Notes 1 Speed-change 0.018 70.000 65.600 -4.504 -6.605 -12.423 OK 2 Speed-change 0.166 65.600 43.982 -1.987 -2.914 -11.642 OK 3 Curve 0.034 43.982 43.982 0.000 0.000 -7.805 OK 4 Curve 0.034 43.982 32.498 -3.588 -5.262 -7.805 OK 5 Curve 0.058 32.498 32.498 0.000 0.000 -5.767 OK 6 Curve 0.058 32.498 15.000 -1.990 -2.919 -5.767 OK 7 Tangent 0.022 15.000 0.000 -1.420 -2.083 -2.662 OK 8 Queue 0.050 0.000 0.000 0.000 0.000 0.000 OK
115 Figure 43 shows that vehicles are predicted to exit the freeway mainline ramp terminal at the gore point (i.e., MP 0.000) and enter Curve 1 at a speed of 44 mph. Vehicles will continue at this speed until the midpoint of Curve 1 (MP 0.034) and then decelerate to a speed of 32 mph at the end of Curve 1 (MP 0.068). Vehicle speeds are predicted to remain constant over the first half of Curve 2 (MP 0.0126) and then decelerate to a speed of 15 mph at the end of Curve 2 (MP 0.184). As vehicles exit Curve 2 and enter into a tangent portion of the ramp and functional area of the crossroad ramp terminal, vehicle speeds are predicted to decrease from 15 mph to 0 mph at the end of the queue storage length (MP 0.206). In summary, vehicle speeds are predicted to decrease from 44 mph to 32 mph over the length of Curve 1 (LC = 0.068 mi), decrease from 32 mph to 15 mph over the length of Curve 2 (LC = 0.116 mi), and decrease from 15 mph to a stop condition over the length of the first and only tangent (L = 0.022 mi). From Green Book Figure 2-34 (see Figure 18 and associated Table 8), a minimum of 0.029 mi (154 ft) is required to decelerate from 44 mph to 32 mph, a minimum of 0.012 mi (61 ft) is required to decelerate from 32 mph to 15 mph, and a minimum of 0.011 mi (56 ft) is required to decelerate from 15 mph to 0 mph. The actual length of Curve 1 (i.e., 0.068 mi) is greater than 0.012 mi (61 ft), the actual length of Curve 2 (0.116 mi) is greater than 0.012 mi (61 ft), and the actual length from the end of Curve 2 to the end of the queue (0.022 mi) is greater than 0.011 mi (56 ft). Thus, the existing design of the individual segments of the ramp proper appears adequate for a vehicle to decelerate as intended along each section. The output from the RSPM also confirms similar findings as the final column under the acceleration data table shows that the average deceleration rates along the individual sections or subsections do no exceed the design decelerations. Although the alignment of the ramp proper appears adequate in terms of providing sufficient distance for a vehicle to decelerate as intended over the length of individual sections, the predicted speeds over the entire length of Curve 1 are above the design speed of Curve 1, and the predicted speeds over a majority of the length of Curve 2 are above the design speed of Curve 2. For both Curves 1 and 2, the design superelevations are less than the emax (i.e., 8 percent) used by the agency. Without changing the curve radius of either curve, it would be possible to increase the design superelevation of each curve such that the design speed of Curve 1 would be 40 mph and the design speed of Curve 2 would be 30 mph. By doing so, the design speeds for each curve would be more aligned with the predicted operating speeds (see Figure 44).
116 Figure 44. Case Study No. 3 (Exit Ramp: Revised Outputs from RSPM) A couple of points of interest are worth noting here comparing the output from the RSPM, design guidelines presented herein, and current AASHTO policy: ⢠AASHTO policy assumes that vehicles do not decelerate in the freeway lanes before diverging from the freeway onto the freeway mainline ramp terminal. However, field observations suggest otherwise (i.e., Torbic et al., 2012). Therefore, rather than the diverge speed being equal to the operating speed of the freeway, the predicted speed at the diverge location is less than the operating speed of the freeway. In this example, the operating speed of the freeway is unknown (see Figure 42), so within the RSPM the operating speed of the freeway is assumed equal to the posted speed limit of the freeway (i.e., 70 mph). In this case study, based on characteristics of the freeway mainline ramp terminal, the diverge speed is predicted to be 65.60 mph. ⢠Based on AASHTO design policy, vehicles diverge from the freeway at the end of the taper length and beginning of the deceleration length and divergence zone length. Within the RSPM, the diverge location is based on a percentage or portion of the speed-change lane length (i.e., PSCL) as input by the analyst. The default value within the RSPM is PSCL = 0.1. In this case study, the end of the taper length and beginning of the deceleration length and divergence zone length corresponds to a value of PSCL = 0.31.
117 ⢠Based on a highway design speed of 75 mph and a design speed of 30 mph for the controlling feature on the ramp proper, AASHTO policy assumes an average running speed of 26 mph at the end of the deceleration length entering the ramp proper. Based on the given inputs describing this ramp, the RSPM predicts a speed of 44 mph at the gore point which corresponds to the end of the deceleration length. Thus, there is an inconsistency in the predicted speed at the gore point output from the RSPM and the assumed value of running speed at the end of deceleration length in the design table from AASHTO policy (i.e., Green Book Table 10-6). Case Study No. 4: Diagonal Exit Ramp in Suburban Area Background Information This case study features a diagonal ramp in a suburban area. Figure 45 provides a schematic and characteristics of the ramp. The ramp consists of two horizontal curves in opposite directions with a tangent section in between. The ramp ends at a signalized intersection, and the queue storage is within the second horizontal curve. Based on the design speed of Curve 1 and guidance in the 2011 and 2018 editions of the Green Book, the likely ramp design speed used for the design of this diagonal ramp is 45 mph.
118 Interchange type: Service Conditions: Constrained Area type: Urban/Suburban Ramp configuration: Diagonal Freeway characteristics Design speed: 70 mph Operating speed: 62 mph Speed limit: 65 mph Crossroad characteristics Type of roadway: Primary/major rd Speed limit: 35 mph Type of traffic control at terminal: Signal Queue storage length: 0.060 mi Milepost of crossroad ramp terminal 0.368 mi Ramp Proper Ramp grade: 1 % downgrade Max superelevation (emax): 12 % Curve 1 PC milepost: 0.114 mi Curve length: 0.124 mi Curve radius 850 ft Superelevation: 10 % Design speed 45 mph Curve 2 PC milepost: 0.302 mi Curve length: 0.035 mi Curve radius 335 ft Superelevation: 10 % Design speed 30 mph Freeway Mainline Ramp Terminal Taper length 0.028 mi Divergence zone length 0.006 mi Deceleration length (downstream of the gore point) 0.114 mi Speed-change lane type Taper Figure 45. Case Study No. 3 (Exit Ramp: General Ramp Characteristics and Dimensions) Design Consistency Assessment Based on the design guidelines presented herein, given the freeway design speed is 70 mph, the crossroad is a primary/major arterial, and the ramp is located in a suburban area, Table 4 indicates the ramp design speed for a diagonal ramp should be between 35 and 50 mph. The design speed of the first curve encountered along the ramp proper that significantly affects vehicle speed is 45 mph. Thus, the ramp design speed for this ramp is 45 mph, so as designed, the ramp design speed of this ramp is consistent with the design guidelines presented herein. All other sections and elements of the ramp should be designed consistent with this ramp design speed to provide appropriate speed transitions along the ramp.
119 To evaluate the adequacy and consistency of the existing ramp design, one of the first checks for an exit ramp is to assess whether the design speeds of contiguous segments along the ramp proper decrease sequentially in a stepwise manner. For this case study, the design speed of Curve 1 from MP 0.114 to MP 0.238 is 45 mph. A tangent begins at the end of Curve 1 (i.e., MP 0.238) and extends to the PC of Curve 2 at MP 0.302. Since the design speed of Curve 2 is 30 mph, it is logical for the design speed of the tangent between Curves 1 and 2 to be 40 mph. Thus, the existing design of the ramp proper appears adequate as the design speeds of contiguous segments decrease in the direction of travel, and the change in design speed between adjoining sections is at most 10 mph. The next step to evaluate the adequacy of an exit ramp design is to confirm that sufficient distance is provided for a vehicle to decelerate as intended along the length of the ramp. This involves evaluating the individual components of the freeway mainline ramp terminal, the ramp proper, and to some level the crossroad ramp terminal. First, an assessment should be made to confirm that the deceleration length is sufficiently long to allow for a vehicle to decelerate as intended along the freeway mainline ramp terminal. For this ramp the actual deceleration length is LDec Length = 0.120 mi (i.e., 0.006 mi + 0.114 mi) which extends beyond the gore point and ends at the beginning of Curve 1. Using Table 8, for a highway design speed of 70 mph and a design speed of 45 mph for the first controlling feature on the ramp proper, a minimum deceleration length of 0.074 mi (390 ft) is recommended. Thus, the existing design of the freeway mainline ramp terminal appears adequate as the actual deceleration length is greater than the minimum deceleration from Table 8. A second type of assessment that should be made is to confirm that sufficient distance is provided for a vehicle to decelerate as intended along each individual tangent and curve of the ramp proper. Of particular interest is the distance between the end of Curve 1 (MP 0.238) and the end of the queue storage length (MP 0.308), which measures 0.070 mi (370 ft). Assuming vehicles exit Curve 1 at its design speed of 45 mph and need to come to a complete stop at the end of the queue storage length, Table 9 indicates that 0.060 mi (314 ft) is required to come to a complete stop from an initial speed of 45 mph. Thus, the existing design of the ramp proper appears adequate as the actual length from the end of Curve 1 to the end of the queue storage length is greater than the minimum length specified from Table 9 for this design condition. However, note that the functional area of the crossroad ramp terminal extends into Curve 2, so the operational characteristics near Curve 2 and the crossroad ramp terminal are of particular interest. An assessment of the operational conditions along the entire ramp and near the crossroad ramp terminal can be performed using the RSPM. Figure 46 shows the inputs into the RSPM for this ramp, and Figure 47 shows a graphical representation of the predicted speed profile along the ramp and other outputs in tabular form. The predicted speed entering Curve 2 is 25 mph. However, the functional area of the crossroad ramp terminal extends into Curve 2 and to decelerate from 25 mph at MP 0.302 to a stop condition at MP 0.308 (i.e., the end of the queue storage length) requires a deceleration rate that exceeds the maximum design deceleration rate [in Figure 45, under Acceleration Data see the Note (i.e., last column) for Segment 7]. This raises some concerns about the consistency of the current design near the crossroad ramp terminal, but as indicated the existing design of the ramp proper provides sufficient length for a vehicle exiting Curve 1 at its design speed (i.e., 45 mph) to come to a complete stop at the end of the queue storage length. Several options could be
120 considered to redesign the ramp by either changing the horizontal alignment or lengthening the ramp to reduce speeds in proximity to the crossroad ramp terminal. Another option to consider is providing signing (e.g., Signal Ahead) as vehicles exit Curve 1 to reduce speeds in advance of the functional area of the crossroad ramp terminal. Figure 46. Case Study No. 4 (Exit Ramp: Inputs to RSPM)
121 Plotted Speed Data Acceleration Data Figure 47. Case Study No. 4 (Exit Ramp: Outputs from RSPM) Point Type Milepost Profile, mph Milepost Design, mph Milepost Alt profile, mph Tpr -0.034 62.00 -0.062 70 0.000 53.99 SCd -0.031 57.90 0.114 70 0.114 40.03 Gor 0.000 53.99 0.114 45 0.238 24.86 Tan 0.114 53.99 0.238 45 0.302 17.02 Cmc 0.176 53.99 0.238 40 0.337 15.00 Cpt 0.238 32.84 0.302 40 0.368 15.00 Tan 0.302 24.67 0.302 30 Qst 0.308 0.00 0.368 30 Xrd 0.368 0.00 0.000 0.00 Segment Data Speed, mph Average Acceleration Design Acceleration Number Type Length, mi Initial Final mph/s ft/s2 ft/s2 Notes 1 Speed-change 0.003 62.000 57.900 -20.081 -29.453 -11.003 decel > design 2 Speed-change 0.031 57.900 53.988 -1.987 -2.914 -10.275 OK 3 Tangent 0.114 53.988 53.988 0.000 0.000 -9.581 OK 4 Curve 0.062 53.988 53.988 0.000 0.000 -9.581 OK 5 Curve 0.062 53.988 32.839 -4.113 -6.033 -9.581 OK 6 Tangent 0.064 32.839 24.668 -1.020 -1.496 -5.828 OK 7 Tangent 0.006 24.668 0.000 -14.086 -20.659 -4.378 decel > design 8 Queue 0.060 0.000 0.000 0.000 0.000 0.000 OK 9 -0.368 0.000 0.000 0.000 0.000 0.000 OK
