Review Reports - A Design Model for Urban Single-Lane Roundabouts with Offset Approaches

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article proposes a design model for single-lane urban roundabouts in which the approach legs do not intersect the geometric center (lateral offset). Through swept path analysis using a 12-meter bus and fastest path analysis, the authors defined the maximum offset limits for outer radii ranging between 17.5 and 25 meters.

From the analysis of the content and methodology described in the sources, the following critical points emerge:

The study is entirely based on theoretical examples created in a CAD environment. There is no direct comparison with traffic data from real existing roundabouts with offset approaches to verify whether the calculated speeds correspond to actual speeds.
The model assumes that all approach legs intersect at a strict 90° angle. In urban practice, offset roundabouts are often required precisely where space is irregular and the angles between approach legs are oblique or acute. The research could be expanded to include approach legs with angles other than 90°, providing guidelines for oblique approaches, which are very common in urban redevelopment projects.
The analyses were conducted using only one type of vehicle: a 12-meter, two-axle bus. Although common, this does not cover the needs of smaller roundabouts (where light commercial vehicles might allow greater offsets) or roundabouts that must accommodate longer articulated vehicles.
The validation of the model was carried out by randomly selecting three additional theoretical outer radii (18.5, 21.5, and 23.5 m) and testing them using the same procedures. This approach confirms the internal consistency of the equations, but not the external validity of the model in real-world conditions. The model could be applied to an existing roundabout experiencing safety or operational issues due to offset, comparing current parameters with those suggested by the model.
The study excluded roundabouts with an outer radius of 15 meters because the offset caused overlapping of the roadway edge arcs. However, in dense urban areas, a 15-meter radius is very common, and the lack of a solution for this size limits the applicability of the model.

Author Response

COMMENT 1: The study is entirely based on theoretical examples created in a CAD environment. There is no direct comparison with traffic data from real existing roundabouts with offset approaches to verify whether the calculated speeds correspond to actual speeds.

ANSWER 1: Please see the attachment.

Thank you very much for your comments and suggestions; they have been very helpful. As you noted, we did not compare the calculated speeds to actual speeds in our study, as this has been done in other similar studies, described in the revised version of the manuscript, Lines 74–101 and 604–608.

Lines 74–101: “Speed analysis is usually conducted by measuring the roundabout geometric characteristics and checking the obtained deflection [31, 32, 37, 38], by measuring the geometric characteristics of the roundabout and calculating the path radii and vehicle speed [30, 39], or by drawing the fastest vehicle path, measuring the path radii and estimating the vehicle speed based on the radii [28, 29, 33–36]. If the initial roundabout geometric design does not meet the requirements of the selected design vehicle and required vehicle speed, the initial design is revised. Predicting speeds at roundabouts in urban areas, where severe spatial and environmental constraints dictate layouts that do not conform to design standards, is challenging and can lead to inconsistent speed analysis results. As a result, standardised speed prediction models have been tested in several studies. For instance, design and operating speeds were evaluated for several urban roundabouts in the Municipality of Cuneo, Italy [40]. The observed speeds were comparable to those derived from the US guidelines' speed model [34], despite certain discrepancies that arose from local driver behaviour, vehicle performance, and design practices. Only one roundabout presented in this study strictly adhered to the Italian design standards [38]. Consequently, this was the only case in which the variance between observed speeds and those predicted by the US guidelines [33] remained below 10 %. According to the findings of a study [41] conducted on urban roundabouts in Zagreb, Croatia, deviations between design speeds calculated using US guidelines [33] and measured speeds ranged from -45.69% to +13.07%. As in the Italian study, these deviations were attributed to various factors, including intersection geometry, vehicle characteristics, and driver behaviour. Another recent study [42] analysed connected vehicle (CV) trajectory speeds at 56 roundabouts in Carmel, Indiana. Comparing passenger vehicle speeds with theoretical models revealed that certain aspects of the US guideline speed model [36] require updating. Specifically, future models should account for lower entry speeds and higher speeds within the circulatory and departure sections for vehicles approaching slowly. Notably, however, deceleration and acceleration values remained consistent across both the theoretical approach and the sampled data, suggesting that current modelling of speed change rates remains accurate.”

Lines 604–608: “Given that no single model perfectly predicts roundabout speeds, our study employed established European and US guidelines that have remained industry standards for over two decades. This study found the German and US guidelines to be robust indicators for bus-related and RCV restrictions. Furthermore, this research provides the specific parameters required for the prevention of inconsistent design outcomes.”

COMMENT 2: The model assumes that all approach legs intersect at a strict 90° angle. In urban practice, offset roundabouts are often required precisely where space is irregular, and the angles between approach legs are oblique or acute. The research could be expanded to include approach legs with angles other than 90°, providing guidelines for oblique approaches, which are very common in urban redevelopment projects.

ANSWER 2:

As mentioned in the manuscript Lines 135-136 (references [45] and [46]), research on roundabout angles other than 90° was conducted for roundabouts without offset approaches. In this study, we analysed 95 roundabout layout combinations (64 for the bus and 31 for the RCV). Combining different approach offsets with varying approach angles requires preparing a significantly larger number of schemes. For example, incorporating angles between 70° and 90° in 5° increments would yield approximately 400 schemes, 1,600 trajectories, and 1,600 speed and deflection tests. This is planned for future research, as mentioned in the Discussion section of the revised manuscript, Lines 667–675: “The limitations of this study were that it was not conducted on real examples of urban single-lane roundabouts with offset approaches, that the approach axes on the analysed roundabouts were all positioned at right angles, and only the triangular splitter island was evaluated. To help identify potential shortcomings in the roundabout design model, future research will include analysis of roundabout schemes with approach angles ranging from 70° to 90° in 5° increments, as well as one approach offset, two design vehicles, and other splitter island types. The model will be applied to a real-world roundabout experiencing safety or operational issues due to offset, and current parameters with those suggested by the model will be compared.”

COMMENT 3: The analyses were conducted using only one type of vehicle: a 12-meter, two-axle bus. Although common, this does not cover the needs of smaller roundabouts (where light commercial vehicles might allow greater offsets) or roundabouts that must accommodate longer articulated vehicles.

ANSWER 3:

The research has been expanded to include Refuse Collection Vehicles (RCVs) to bridge the gap and obtain approach offset results for roundabouts with outer radii of 15–20 m.

COMMENT 4: The validation of the model was carried out by randomly selecting three additional theoretical outer radii (18.5, 21.5, and 23.5 m) and testing them using the same procedures. This approach confirms the internal consistency of the equations, but not the external validity of the model in real-world conditions. The model could be applied to an existing roundabout experiencing safety or operational issues due to offset, comparing current parameters with those suggested by the model.

ANSWER 4:

Thank you for your valuable input. We will consider this in future research, as stated in the Discussion (Lines 667-675).

COMMENT 5: The study excluded roundabouts with an outer radius of 15 meters because the offset caused overlapping of the roadway edge arcs. However, in dense urban areas, a 15-meter radius is very common, and the lack of a solution for this size limits the applicability of the model.

ANSWER 5:

The research has been expanded to include Refuse Collection Vehicles (RCVs) to bridge the gap and obtain approach offset results for roundabouts with outer radii of 15–20 m.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper addresses a practical problem in urban intersection design: how lateral offsets of approach centerlines affect the geometry and safety performance of single‑lane roundabouts. The authors stated a clear objective, presented a systematic methodological sequence, conducted swept‑path and fastest‑path analyses using a 12 m two‑axle bus, and developed a validated, user‑oriented design model. Although the topic is relevant to practitioners working within tight urban constraints and the paper has a good organization, the authors should clarify the novel contribution relative to the existing literature (where 49 referenced works are few): what specific gap does this study fill, and what is its scientific advance?

Several considerations follow:

- The analyses used a single, relatively narrow design vehicle (a 12 m bus). While conservative for many urban contexts, this choice excluded smaller vehicles and larger articulated buses and trucks. The authors should indicate whether allowable offsets depend on vehicle type and size.

- All layouts are synthetic, with approaches constrained to 90° and a single splitter‑island geometry. Real sites frequently exhibit skewed approach angles, varied splitter designs, and mixed vehicle fleets; consequently, field validation is needed.

- The authors adopt US guidance as the most restrictive standard, but some tabled speed outcomes approach or exceed recommended limits under certain offsets. The paper should better quantify safety risk or propose conservative safety buffers.

- The discussion does not assess pedestrian delay, exposure, or accessibility implications associated with increased exit crossing widths. Authors should comment these aspects..

The authors should.

- extend analyses to additional design vehicles and mixed fleets to improve applicability.

- test the model on real‑world sites with varied approach angles and splitter geometries, and include empirical crash or speed data where available;

- provide an explicit safety margin or practitioner decision rule for cases in which modeled speeds approach maximum guideline values;

- assess pedestrian crossing exposure and offer mitigation guidance when offsets increase exit crossing lengths.

Author Response

COMMENT 1: Although the topic is relevant to practitioners working within tight urban constraints and the paper has a good organization, the authors should clarify the novel contribution relative to the existing literature (where 49 referenced works are few): what specific gap does this study fill, and what is its scientific advance?

ANSWER 1: Please see the attachment.

Thank you very much for your comments and suggestions; they have been very helpful.

In the revised paper, we have proposed a design model for urban roundabouts with outer radii between 15 and 25 m and two design vehicles (a 12-m-long bus and an RCV). The model is based on an analysis of 95 single-approach offsets (64 for the bus and 31 for the RCV) and up to 377 dual-approach offset combinations (229 for the buses and 148 for the RCV), using 1.0 m increments. As far as we are aware, only one study similar to ours has been published to date (reference no. 47, described in Lines 140-144 and 610-615), but it focused solely on trigonometry and did not include swept path analysis, splitter islands, or fastest path analysis. We have highlighted our contribution to roundabout design practice in the Introduction (Lines 156-164).

Lines 145–164: “In this paper, the methodology and results of an investigation into the effects of the approach centreline offset on the geometric design and safety performance of urban single-lane roundabouts are presented. This research aimed to define the maximum lateral offset as a function of the design vehicles' swept path and fastest path analyses, and to develop a model for the design of urban single-lane roundabouts with varying outer radii and approach centreline offsets to eliminate numerous iterations in the roundabout design process. As the influence of the approach offset on the geometric design of single-lane roundabouts is particularly problematic in urban and suburban locations due to spatial constraints, the analyses conducted in this research were focused on the theoretical examples of four-legged single-lane roundabouts with geometric elements whose dimensions are in line with values given in roundabout design guidelines, standards, and recommendations [28–39] for urban and suburban roundabouts. This approach fills a gap in the fields of civil and transport engineering by eliminating the need for time-consuming, numerous iterations of swept path and fastest path analyses. These models enable the selection of outer roundabout radii or offsets beyond those specifically presented in this paper, with a high degree of certainty in the results. While most current guidelines merely suggest avoiding offset approaches without providing supporting numerical data, this study provides the specific parameters required for informed design to prevent inconsistent results, offers a clear design methodology, and shortens the time needed for quality roundabout design.”

COMMENT 2: The analyses used a single, relatively narrow design vehicle (a 12 m bus). While conservative for many urban contexts, this choice excluded smaller vehicles and larger articulated buses and trucks. The authors should indicate whether allowable offsets depend on vehicle type and size.

ANSWER 2:

Yes, the allowable offsets depend on vehicle type and size Lines 580-582, Figure 8 and 9. The research has been expanded to include Refuse Collection Vehicles (RCVs) to bridge the gap and obtain approach offset results for roundabouts with outer radii of 15 to 20 m.

COMMENT 3: All layouts are synthetic, with approaches constrained to 90° and a single splitter‑island geometry. Real sites frequently exhibit skewed approach angles, varied splitter designs, and mixed vehicle fleets; consequently, field validation is needed.

ANSWER 3:

COMMENT 4: The authors adopt US guidance as the most restrictive standard, but some tabled speed outcomes approach or exceed recommended limits under certain offsets. The paper should better quantify safety risk or propose conservative safety buffers.

ANSWER 4:

Thank you for your valuable input. In the revised version of the manuscript, stricter limits for the approach offsets were adopted, respecting both the US and German guidelines (Figure 8 and 9, Lines 465-473, 484-491). As a result, conservative safety buffers were not proposed.

COMMENT 5: The discussion does not assess pedestrian delay, exposure, or accessibility implications associated with increased exit crossing widths. Authors should comment these aspects.

ANSWER 5:

Thank you for your input. We have included these comments in the Discussion section (Lines 646–666).

Lines 646–666: “Based on the previous research, a pedestrian crossing at a roundabout with offset approaches that is up to 2.0 m longer than at a standard roundabout layout would not pose a problem even for the slowest pedestrians, as it would require only approximately 2 extra s for them to cross. Namely, according to Giannoulaki and Christoforou [54], the slowest measured walking speeds range from 1.2 m/s to 1.4 m/s, while for seniors, the speed drops to 0.9 m/s. Furthermore, Gates et al. [55] analysed 1,947 crossing events across eleven intersections in Wisconsin and recommended a walking speed of 0.88 m/s for areas where nearly all pedestrians are over age 65. They suggest that 1.2 m/s is only appropriate for locations with very few older or disabled pedestrians, such as college campuses, while 1.15 m/s is the general recommendation for timing clearance intervals. Consequently, an additional 1.5 to 2.0 meters of crossing distance would only require approximately 2 extra seconds for even the slowest pedestrians. To reduce pedestrian and cyclist exposure, crossings can be positioned further back from but not far away from roundabout exits (splitter island should not be narrower than 2 m in that place) or supplemented with road markings such as 'shark’s teeth' (triangular yield markings). Widely used in the Netherlands, these markings legally prioritise vulnerable road users by requiring exiting motorists to slow down and yield to those crossing their path. For the roundabouts designed for the RCV, the maximum difference in crossing lengths on the entry lane is 0.4 m, while the maximum difference on the exit lane is 0.6 m, depending on the outer radius (Ro) and the approach offset. Consequently, there are no significant changes in crossing lengths between approaches with and without an offset.”

COMMENT 6: The authors should extend analyses to additional design vehicles and mixed fleets to improve applicability.

ANSWER 6:

The research has been expanded to include Refuse Collection Vehicles (RCVs) to bridge the gap and obtain approach offset results for roundabouts with outer radii of 15–20 m. A mixed vehicle fleet is not considered in the intersection geometric design. Namely, intersection traversability (unobstructed vehicle movement) is tested for just one dedicated design vehicle - the least manoeuvrable vehicle expected to regularly use the intersection surface. Critical note has been introduced in the text lines 513-517, 631-634.

COMMENT 7: The authors should test the model on real‑world sites with varied approach angles and splitter geometries and include empirical crash or speed data where available.

ANSWER 7:

We appreciate your suggestions and intend to integrate them into our future research and model enhancements. Presently, our methodology draws on established studies and existing guidelines. Due to significant inconsistencies in Croatian urban roundabout design, comparable local examples are scarce; this research specifically addresses that gap by providing data to help standardize these designs.

COMMENT 8: The authors should provide an explicit safety margin or practitioner decision rule for cases in which modelled speeds approach maximum guideline values.

ANSWER 8:

COMMENT 9: The authors should assess pedestrian crossing exposure and offer mitigation guidance when offsets increase exit crossing lengths.

ANSWER 9:

Thank you for your input. We have included these comments in the Discussion section (Lines 646–666).

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript deals with a practical issue in the geometric design of urban single-lane roundabouts: how laterally offset approaches affect design elements and vehicle speeds. The topic is relevant, since in constrained urban environments it is often difficult to align all approach centrelines through the geometric centre of a roundabout. The paper is generally well organised, and the proposed design model may be useful for practitioners who need a more systematic way to deal with offset approaches.

The methodology is largely appropriate. The authors combine swept path analysis with speed and fastest-path checks, and they compare the results against several national guidelines and standards. The scope of the model is also reasonably clear: it applies to four-leg single-lane roundabouts with outer radii between 17.5 and 25 m, perpendicular approach centrelines, flared entries and exits, and a 12 m two-axle bus as the design vehicle. The results are useful, especially the finding that the allowable offset increases with the outer radius, and that left and right offsets affect entry width, exit width, and speed in different ways.

I recommend publication after minor revision. The following points should be addressed:

1.Clarification of the contribution: The manuscript reviews previous work on radial offsets and offset or skewed approaches, but the specific contribution of this study could be stated more clearly. The authors should explain more directly how the proposed design model differs from, or improves upon, existing swept path and fastest-path based design procedures.

2.Assumptions and applicability of the model: The proposed model is based on several important assumptions: theoretical roundabout layouts, one splitter-island configuration, perpendicular approach centrelines, fixed entry and exit radii, flared entries and exits, and one design vehicle. These assumptions should be presented more prominently, preferably in a compact table or a dedicated subsection. This would make the range of applicability clearer for readers and practitioners.

3.Presentation of figures and tables: Some of the tables contain a large number of values and are difficult to read. The figures showing the offset limits and the design model are central to the paper, but they would benefit from clearer formatting, larger labels, and more explicit explanation of offset direction. The authors should also check that all symbols, units, and line types are consistently defined.

4.Equation numbering and terminology: Please check the equation numbering throughout the manuscript. In particular, the speed equations appear to contain a repeated equation number. The variables and references to equations should also be checked for consistency.

5.Language editing: The English is generally understandable, but some sentences are long and occasionally repetitive. A light language revision would improve readability and make the technical argument easier to follow.

Author Response

COMMENT 1. Clarification of the contribution: The manuscript reviews previous work on radial offsets and offset or skewed approaches, but the specific contribution of this study could be stated more clearly. The authors should explain more directly how the proposed design model differs from, or improves upon, existing swept path and fastest-path based design procedures.

ANSWER 1: Please see the attachment

Thank you very much for your comments and suggestions; they have been very helpful.

COMMENT 2: 2.Assumptions and applicability of the model: The proposed model is based on several important assumptions: theoretical roundabout layouts, one splitter-island configuration, perpendicular approach centrelines, fixed entry and exit radii, flared entries and exits, and one design vehicle. These assumptions should be presented more prominently, preferably in a compact table or a dedicated subsection. This would make the range of applicability clearer for readers and practitioners.

ANSWER 2:

Thank you for your input. We accepted your suggestions and improved the model presentation in section 3.3.

COMMENT 3: 3.Presentation of figures and tables: Some of the tables contain a large number of values and are difficult to read. The figures showing the offset limits and the design model are central to the paper, but they would benefit from clearer formatting, larger labels, and more explicit explanation of offset direction. The authors should also check that all symbols, units, and line types are consistently defined.

ANSWER 3:

Thank you for your input. We have accepted your suggestions and improved the manuscript accordingly. Some of the tables were moved to the Appendix and replaced with Figures (for example Figures 8 and 9).

COMMENT 4: 4.Equation numbering and terminology: Please check the equation numbering throughout the manuscript. In particular, the speed equations appear to contain a repeated equation number. The variables and references to equations should also be checked for consistency.

ANSWER 4:

Thank you for your input. We have accepted your suggestions and improved the manuscript accordingly. We corrected two instances of incorrect equation numbering and referencing.

COMMENT 5: 5.Language editing: The English is generally understandable, but some sentences are long and occasionally repetitive. A light language revision would improve readability and make the technical argument easier to follow.

ANSWER 5:

Thank you for your input. Although most of the sentences have been improved, unfortunately, some repetition remains in the revised version of the manuscript; replacing these instances would require the inclusion of excessively large tables or figures.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

All comments have been addressed.

Reviewer 2 Report

Comments and Suggestions for Authors

Authors introduced comments and the paper is improved. No further consierations from my side.