Speed Reduction Capabilities of Two-Geometry Roundabouts

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper deals with interesting and important issue of vulnerable road users (motorcyclists) on and in general is well prepared and structured. However, it's worth considering some modifications.

First of all the title of the second section could be changed as the Authors in their paper do not prepare any laboratory tests were different materials are being used. Maybe it‘d be better to call it Experiment design and methodology (or something else).

 On page 5, line 179 there is given a formula of the expected driving speed in relation to the vehicle path radius – it is not clear for what position of a vehicle this formula applies to (the inlet/outlet or central point on the circulatory roadway of the roundabout).

 It’s also known that speed on the circulatory roadway of the roundabout is related to the initial speed of a vehicle at the entrance point so it is worth to provide such information if any assumptions have been made in these terms.

 It would be good to add some information about traffic conditions under which the speed was measured – possibly it was under free flow traffic but it should be clarified.

 For the estimation of the relative speed Authors used speed values marked as V₁, V₂, V₃ but it’s not clear where exactly are located these check points.

 Please review the paper to make sure that the description of the minor and major axes is unified throughout the paper (see page 13 l. 390 and 392).

 As the manuscript refers to the speed at roundabouts it is worth to mention some additional publications that deal with this issue (i.e. Chen et al. Investigation of models for relating roundabout safety to predicted speed; Ziolkowski. Roundabouts as an Effective Tool of Traffic Management; Macioszek. The road safety at turbo roundabouts in Poland; Surdonja et al. Analyses of maximum-speed path definition at single-lane roundabouts)

Author Response

Dear Reviewer, thank you for your valuable input. We hope that we have successfully addressed all raised issues. Revisions made to the manuscript are marked up using the “Track Changes” function and highlighted in yellow.

Comment 1: First of all the title of the second section could be changed as the Authors in their paper do not prepare any laboratory tests were different materials are being used. Maybe it‘d be better to call it Experiment design and methodology (or something else).

Answer 1: Thank you for the input, we have changed the title to “Experiment design and methodology”.

Comment 2: On page 5, line 179 there is given a formula of the expected driving speed in relation to the vehicle path radius – it is not clear for what position of a vehicle this formula applies to (the inlet/outlet or central point on the circulatory roadway of the roundabout). It’s also known that speed on the circulatory roadway of the roundabout is related to the initial speed of a vehicle at the entrance point so it is worth to provide such information if any assumptions have been made in these terms.

Answer 2: According to “CROW: Eenheid in Rotondes; CROW publication no.126; CROW: Ede, The Netherlands, 1998”, this formula applies to the “expected driving speed through the roundabout” – it gives a single value of vehicle speed for every location on the through path - the inlet/outlet and central point on the circulatory roadway. This is because the vehicle path radius (R) is assumed to be constant along the vehicle through path and it is calculated using two measured values: the distance between the tangent of entry radius and the tangent of the exit radius (L) and the deflection (U). Due to this limitation, the second approach to speed estimation in our investigation included the construction of fastest through paths on final roundabout schemes described in “ROUNDABOUTS: An Informational Guide, 2nd Edition, TRB, Washington, D.C., 2010” (FHWA approach). By utilizing fastest through paths radii on entry, exit and on circulatory roadway (constructed according to the FHWA approach) and the CROW model for the expected driving speed on each location, the entry, circulating and exit speed were calculated and compared. We edited the Introduction as follows.

Lines 35–50: “The influence of deflection on roundabout performance is evaluated either by measuring the deflection provided by roundabouts’ design elements (for example, using procedure given in [10]) or by defining the radius (or radii) of the centerline of a vehicle traveling along the so-called fastest path through the roundabout and then calculating the vehicle speed [11]. This theoretical fastest path is representative of most used trajectory by drivers under free flow conditions when minimizing their driving discomfort [12]. In the latter approach, speed prediction models that are based on fundamental functions of vehicle dynamics are used. For example, FHWA model, described in [13], predicts the speed for five locations on the fastest paths (right-turn, left-turn, through circulating, exit or entry movements), based on the vehicle path radii, side friction factor, and superelevation on these locations. On the other hand, CROW model, described in [14], gives a single value of vehicle speed for every location on the through path: the entry, around the central island, and the exit. It predicts the expected driving speed through the roundabout based on the vehicle path radius that is calculated using measured design elements and the vehicle path radius is assumed to be constant along the vehicle through path.”.

Lines 106–114: “The investigation included the determination of the vehicle path deflection provided by the designed central island and the determination of passenger vehicle speed through the designed roundabout schemes based on following approaches: (1) by measuring the deflection provided by designed roundabout’s geometry features; (2) by measuring the designed roundabout’s geometry features and calculating the fastest path radii and vehicle speed using CROW model; (3) by constructing the fastest through paths, measuring the path radii on entry, around the central island, and exit (according to FHWA model), and then calculating the vehicle speed for each location using CROW model.”.

We have also changed the Figure 3b to illustrate this issue better (adding the dimension R on the vehicle path).

Comment 3: It would be good to add some information about traffic conditions under which the speed was measured – possibly it was under free flow traffic but it should be clarified.

Answer 3: The speed was not measured in this investigation because there aren’t any two-geometry roundabouts in our country, and their number is low worldwide, so there is not yet enough experimental data collected. Because of that, our investigation was based only on roundabout schemes designed in AutoCAD. The speed was predicted (calculated) according to the instructions given in “CROW: Eenheid in Rotondes; CROW publication no.126; CROW: Ede, The Netherlands, 1998.”

We have added the following text to Introduction section (lines 35–41), introducing the new reference regarding the assumed traffic flow conditions: “The influence of deflection on roundabout performance is evaluated either by measuring the deflection provided by roundabouts’ design elements (for example, using procedure given in [10]) or by defining the radius (or radii) of the centerline of a vehicle traveling along the so-called fastest path through the roundabout and then calculating the vehicle speed [11]. This theoretical fastest path is representative of most used trajectory by drivers under free flow conditions when minimizing their driving discomfort [12].”.

Comment 4: For the estimation of the relative speed Authors used speed values marked as V₁, V₂, V₃ but it’s not clear where exactly are located these check points.

Answer 4: We edited this paragraph as follows (lines 228–234): “Finally, estimations of vehicle speed based on the speed-radius relationship (3) were conducted for every path radius: the entry speed (V₁ along R₁ and V’₁ along R’₁, Figure 3c), the circulating speed (V₂ along R₂ and V’₂ along R’₂, Figure 3c), and the exit speed (V₃ along R₃ and V’₃ along R’₃, Figure 3c). The resulting relative speed between consecutive fastest path elements on the entrance path and the path around the central island (V₁-V₂) and elements on the path around the central island the exit path (V₃-V₂) was also investigated.”

Comment 5: Please review the paper to make sure that the description of the minor and major axes is unified throughout the paper (see page 13 l. 390 and 392).

Answer 5: We have reviewed the paper to make sure that the description of the minor and major axes is unified throughout the paper. Changes were not made in the text you are referring to (lines 483– 488: “In the second part of the investigation, the circulatory roadway width along the minor axis (y) was fixed to 5.5 m to meet the requirements of Condition 1 and Condition 2. This intervention in the initial roundabout schemes reduced the circulatory roadway widths along the major axis (x) and increased deflection around the central island, which is favorable in terms of traffic safety and speed reduction.”) because major axis (a) and minor axis (b) are not mentioned there. The parameters that are described are “circulatory roadway width along the minor axis (y)” and “circulatory roadway widths along the major axis (x)”.

Comment 6: As the manuscript refers to the speed at roundabouts it is worth to mention some additional publications that deal with this issue (i.e. Chen et al. Investigation of models for relating roundabout safety to predicted speed; Ziolkowski. Roundabouts as an Effective Tool of Traffic Management; Macioszek. The road safety at turbo roundabouts in Poland; Surdonja et al. Analyses of maximum-speed path definition at single-lane roundabouts)

Answer 6: Thank you for your input. We rewrote the Introduction and mentioned these publications (lines 30–57: “The benefits of modern roundabouts result from the fact that they are designed to control traffic speeds [8,9]. This control is achieved through the selection of appropriate design elements that result in adequate vehicle path curvature on entry, around the central island, and exit. It is considered that the driving speed through the roundabout is mostly influenced by the deflection of the vehicle path that is caused by the roundabout’s central island. The influence of deflection on roundabout performance is evaluated either by measuring the deflection provided by roundabouts’ design elements (for example, using the procedure given in [10]) or by defining the radius (or radii) of the centerline of a vehicle traveling along the so-called fastest path through the roundabout and then calculating the vehicle speed [11]. This theoretical fastest path is representative of the most used trajectory by drivers under free flow conditions when minimizing their driving discomfort [12]. In the latter approach, speed prediction models that are based on fundamental functions of vehicle dynamics are used. For example, the FHWA model, described in [13], predicts the speed for five locations on the fastest paths (right-turn, left-turn, through circulating, exit, or entry movements), based on the vehicle path radii, side friction factor, and superelevation on these locations. On the other hand, the CROW model, described in [14], gives a single value of vehicle speed for all specific locations on the through path: the entry, around the central island, and the exit. It predicts the expected driving speed through the roundabout based on the vehicle path radius. This radius is calculated using measured roundabout design elements and it is assumed to be constant along the vehicle through path. There are also empirically derived speed prediction models, such as a multiple linear regression model developed for Italian roundabouts (described in [15]) or a model for speed prediction that includes central island diameter, and the average of entry, circulating, and exit width as derived variables (described in [8]). The investigations that led to the development of these models showed that the FHWA model overestimates entry and exit speed values. At the same time, investigation results given in [16] showed that the CROW model results in an even larger estimated speed compared to the FHWA model and that these differences are proportional to the path radius.”).

Reviewer 2 Report

Comments and Suggestions for Authors

The present article is of considerable interest. However, it would be advantageous to have empirical data that quantifies the manoeuvrability of the design vehicle in an actual roundabout, even if the characteristics of the real roundabout differ slightly from your design. This would enable a comparative analysis to determine how your proposed design could enhance the safety of heavy vehicles as they enter and exit the roundabout.

Author Response

Dear Reviewer, thank you for your valuable input. Revisions made to the manuscript are marked up using the “Track Changes” function and highlighted in yellow.

Comment 1: The present article is of considerable interest. However, it would be advantageous to have empirical data that quantifies the maneuverability of the design vehicle in an actual roundabout, even if the characteristics of the real roundabout differ slightly from your design. This would enable a comparative analysis to determine how your proposed design could enhance the safety of heavy vehicles as they enter and exit the roundabout.

Answer 1: We agree that the investigation of the maneuverability of long vehicles in an actual roundabout could be a valuable next step in our investigation, especially because previous research by the members of our department was conducted only on a test polygon by testing turning vehicles equipped with water tanks (Džambas et al. (2021): Reliability of vehicle movement simulation results in roundabout design procedure based on the rules of design vehicle movement geometry, reference [23]). In this investigation, the swept path was obtained directly on the dry surface by turning on the taps installed on the vehicles’ chassis during the maneuver. GPS positioning system was used for reconstructing vehicle swept paths. To our knowledge, this is the most used and reliable method for the investigation of the vehicles’ maneuverability. Unfortunately, investigation of the actual roundabout would require closing the intersection for other traffic due to safety concerns, so the real traffic conditions would not be captured in this test. Furthermore, previous studies (Korlaet and Dragčević (2010): Designing criteria of acute angle four-leg intersection at grade, Pecchini and Giuliani (2013): Experimental Test of an Articulated Lorry Swept Path, Džambas et al. (2021): Reliability of vehicle movement simulation results in roundabout design procedure based on the rules of design vehicle movement geometry) have indicated following issues concerning field measurements.

• Field tests offer incontrovertible results as they are conducted in real environments and traffic conditions. At the same time, they require significant financial resources and extensive preparation, so much so that they cannot be seen as a systematic tool for investigating vehicle swept paths.
• Simulated swept paths may be difficult to replicate exactly under actual driving and traffic conditions.

According to the abovementioned research, the comparison between the area covered by the vehicle as estimated by the software and the real one obtained by GPS data, denotes that the former was conservative, with wider swept paths than the real ones. Therefore, we have based our research on simulations for this investigation. At the same time, according to the simulation software manufacturer’s instructions, simulated swept paths are geometrically idealized results that should be used conservatively, with ample allowances added for clearances between vehicle tire track and roadway edge. Because of that, in our investigation, lateral safety clearances of 0.25 m were added between the simulated vehicle tire track and designed roadway edge (along the elevated splitter islands, central island, and outer carriageway edge). This is mentioned in the second section of the paper, lines 182–184: “Minimal safety lateral widths of 0.25 m were ensured along the elevated splitter islands, central island, and outer carriageway edge in every roundabout scheme, according to the instructions given in [26].”

Reviewer 3 Report

Comments and Suggestions for Authors

Although this paper belongs to the classic field of transportation design, I believe its academic significance is not enough to be published in this journal.This is mainly because the introduction of relevant calculation methods in the paper is too simple, and the setting of some model parameters is not in line with reality to my knowledge. For example, the relationships between the variables expressed in Figures 4 to 13 are all linear, which makes me feel very puzzled and surprised.

Comments on the Quality of English Language

Minor editing of English language required.

Author Response

Dear Reviewer, thank you for your input. We hope that we have successfully addressed all raised issues. Revisions made to the manuscript are marked up using the “Track Changes” function and highlighted in yellow.

Comment 1: The introduction of relevant calculation methods in the paper is too simple.

Answer 1: We have rewritten the Introduction and included the following paragraph on speed calculation methods and included additional references.

Lines 30–57: “The benefits of modern roundabouts result from the fact that they are designed to control traffic speeds [8,9]. This control is achieved through the selection of appropriate design elements that result in adequate vehicle path curvature on entry, around the central island, and exit. It is considered that the driving speed through the roundabout is mostly influenced by the deflection of the vehicle path that is caused by the roundabout’s central island. The influence of deflection on roundabout performance is evaluated either by measuring the deflection provided by roundabouts’ design elements (for example, using the procedure given in [10]) or by defining the radius (or radii) of the centerline of a vehicle traveling along the so-called fastest path through the roundabout and then calculating the vehicle speed [11]. This theoretical fastest path is representative of the most used trajectory by drivers under free flow conditions when minimizing their driving discomfort [12]. In the latter approach, speed prediction models that are based on fundamental functions of vehicle dynamics are used. For example, the FHWA model, described in [13], predicts the speed for five locations on the fastest paths (right-turn, left-turn, through circulating, exit, or entry movements), based on the vehicle path radii, side friction factor, and superelevation on these locations. On the other hand, the CROW model, described in [14], gives a single value of vehicle speed for all specific locations on the through path: the entry, around the central island, and the exit. It predicts the expected driving speed through the roundabout based on the vehicle path radius. This radius is calculated using measured roundabout design elements and it is assumed to be constant along the vehicle through path. There are also empirically derived speed prediction models, such as a multiple linear regression model developed for Italian roundabouts (described in [15]) or a model for speed prediction that includes central island diameter, and the average of entry, circulating, and exit width as derived variables (described in [8]). The investigations that led to the development of these models showed that the FHWA model overestimates entry and exit speed values. At the same time, investigation results given in [16] showed that the CROW model results in an even larger estimated speed compared to the FHWA model and that these differences are proportional to the path radius.”

Comment 2: The relationships between the variables expressed in Figures 4 to 13 are all linear, which makes me feel very puzzled and surprised.

Answer 2: Thank you for your input. After the systematization of the investigation results in tables (Tables 2–7 and tables in the Appendix A), we have realized that this form of presentation may not be sufficient to provide a simple representation of relationship between major and minor axes values (a) and (b) and designed values of geometry variables (L, L’, U, U’, Ri and R’i (i=1–3)). Therefore, we decided to present the data given in the abovementioned tables graphically, for the convenience of the readers. However, the graphical results representation by scatter plots showed a large data dispersion. To be able to visualize the relationship between the geometry variables and the axes values in as simple a way as possible, we have applied a simple linear regression to this data. We have obtained 100 linear regression models (with coefficients of determination and correlation coefficients that range from 0.2 to 0.99) that we have presented in the manuscript body on the diagrams in question (Figures 4–13). We have not intended to develop models that could be used in the design of two-geometry roundabouts. To clarify that, we have added the following text in the second section.

Lines 255–265: “To provide the visualization of the dependence between the measured values of the distance between the tangent of the entry radius and the tangent of the exit radius along the major and minor axis (L and L’), deflection along the major and minor axis (U and U’), personal vehicle's fastest path radii along the major and minor axis (Ri and R’i, where i=1–3), and the axis length, these values along both major and minor axis were plotted for all analyzed roundabout schemes. 100 simple linear regression models were defined for major axis (a) as an independent, and measured values (L, L’, U, U’, Ri and R’i, where i=1–3) for different (b/a) relations as dependent variables. It should be emphasized here that these simple linear regression models were not intended for use in the two-geometry roundabouts design. Their purpose is to provide the visualization of the investigation results in as simple a way as possible.”

Lines 311–316: “To provide the visualization of the investigation results (given in Tables 3 and 4, and Appendix A, Table A1 and A2) in as simple a way as possible, 50 simple linear regression models were defined for major axis (a) as an independent, and measured values (L, L’, U, U’, Ri, and R’_i, where i=1–3) for different (b/a) relations as dependent variables (Figures 4–8). It should be emphasized here that these simple linear regression models were not intended for use in the two-geometry roundabouts design.”

Lines 408–413: “To provide the visualization of the investigation results (given in Table 6 and 7, and Appendix A, Table A3 and A4) in as simple a way as possible, 50 simple linear regression models were defined for major axis (a) as an independent, and measured values (L, L’, U, U’, Ri, and R’_i, where i=1–3) for different (b/a) relations as dependent variables (Figures 9–13). It should be emphasized here that these simple linear regression models were not intended for use in the two-geometry roundabouts design.”

Also, we have added the information on measured values of the distance between the tangent of the entry radius and the tangent of the exit radius along the major and minor axis (L and L’), deflection along the major and minor axis (U and U’) in the text body (Tables 3, 4, 6, and 7; lines 294–310 and 392–407).

Comment 3: Minor editing of English language required.

Answer 3: We have proofread the manuscript and, hopefully, addressed the raised issue adequately.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Fine. It could be accepted to publish on the journal.