# Speed Reduction Capabilities of Two-Geometry Roundabouts

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experiment Design and Methodology

_{c}), circulatory roadway width along the major axis (x), circulatory roadway width along the minor axis (y), and carriageway edge design elements (R

_{entry}, R

_{exit}, R′

_{entry}, and R′

_{exit}). The entry width was set to 3.5 m, while the exit width was set to 4.0 m (Figure 1c).

- the entry path radii (R
_{1}and R′_{1}), which are the minimum radii on the fastest through paths before the entrance line; - the circulating path radii (R
_{2}and R′_{2}), which are the minimum radii on the fastest through paths around the central island; and - the exit path radii (R
_{3}and R′_{3}), which are the minimum radii on the fastest through paths into the exit.

_{1}along R

_{1}and V′

_{1}along R′

_{1}, Figure 3c), the circulating speed (V

_{2}along R

_{2}and V′

_{2}along R′

_{2}, Figure 3c), and the exit speed (V

_{3}along R

_{3}and V′

_{3}along R′

_{3}, Figure 3c). The resulting relative speed between the consecutive fastest path elements on the entrance path, the path around the central island (V

_{1}–V

_{2}), and elements on the path around the central island exit path (V

_{3}–V

_{2}) was also investigated.

**Condition 1:**circulatory roadway width in single-lane roundabouts (x and y) should be smaller than 5.5 m so that drivers do not use a wide roadway as two lanes and sufficient deflection is achieved [1].**Condition 2:**circulatory roadway width in the direction of the minor axis (y) should be between 4 and 6 m [22].**Condition 3:**vehicle path deflection around the central island (D) should be greater or equal to double the entrance width (which is 7.0 m in this investigation) for the roundabout’s design to be deemed satisfactory [10].**Condition 5:**the calculated expected driving speed through the roundabout for the major and minor axis directions (V) should be lower than 35 km/h [14].**Condition 6:**for vehicles to safely negotiate the roundabout, the maximum relative speed between consecutive fastest path elements (V_{1}–V_{2}and V_{3}–V_{2}) should not exceed 25 km/h [16].

_{i}and R′

_{i}, where i = 1–3), and the axis length, these values along both the major and minor axis were plotted for all analyzed roundabout schemes. One hundred simple linear regression models were defined taking the major axis (a) as an independent variable and measured values (L, L′, U, U′, R

_{i}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 roundabout’s design. Their purpose is to provide the visualization of the investigation results in as simple a way as possible.

## 3. Results

#### 3.1. Roundabout Schemes with Variable (y)

**Condition 1 (x, y < 5.5 m)**, as they were up to two times wider than the recommended value. This was expected, due to the applied swept path construction. Namely, swept paths for the circular movement were constructed based on a front axle center point path shaped as an arc around the circular central island for a long design vehicle. This arc was constructed with a radius that was offset by 2 m from the roundabout’s minor axis. Only one resulting circulatory roadway width along the minor axis (y) was smaller than 5.5 m—the one for the largest analyzed (a) and (b/a = 0.90). At the same time, Condition 1 was met by three standard geometry roundabout schemes with variable (y) and (a = b = 23–25 m), as shown in Table 2.

**Condition 2 (y < 6.0 m)**was met by 13 two-geometry roundabout schemes with variable (y). At the same time, Condition 2 was met by seven standard geometry roundabout schemes with variable (y) (Table 2). It can be noted that the resulting circulatory roadway width along the minor axis (y) was inversely proportional to the roundabout size, namely, the major and minor axes (a and b). This was not the case with the resulting circulatory roadway width along the major axis (x), as these values for (b/a = 0.75, 0.80, and 0.85) after initial reduction started to rise (Table 2).

_{i}, and R′

_{i}, where i = 1–3) for different (b/a) relations as dependent variables (Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8). It should be emphasized here that these simple linear regression models were not intended for use in the two-geometry roundabout’s design. The modeled simple linear dependency of the distance between the tangent of the entry radius and the tangent of the exit radius along the major axis (L), the distance between the tangent of the entry radius and the tangent of the exit radius along the minor axis (L′), the deflection along the major axis (U), and the deflection along the minor axis (U′) and the major axis length (a) for roundabout schemes with variable (y) is shown in Figure 4 and Figure 5. It can be noted that the parameters (L) and (U) were significantly influenced by (a) for every designed roundabout scheme with variable (y), while this dependency is less significant for the parameters (L′) and (U′), especially for (b/a = 0.80) and (b/a = 0.90a).

_{i}(i = 1–3) for the variable circulatory roadway width along the minor axis (y) are given in Appendix A, Table A1. The modeled simple linear dependency of the personal vehicle’s fastest path radii (R

_{i}and R′

_{i}, where i = 1–3) and the major axis length (a) for roundabout schemes with variable (y) is shown in Figure 6, Figure 7 and Figure 8. It can be noted that:

- radii for (b/a = 0.75) showed the greatest discrepancy caused by large path radii values in roundabouts with the smallest major and minor axes,
- for (b/a = 1.00), either no influence could be noted, or radii were inversely proportional to (a), and
- for the rest of the roundabout schemes, either no influence could be noted, or radii were proportional to (a).

**Condition 3 (D > 7.00.m)**was met by 88% of the designed two-geometry roundabout schemes with variable (y) and by all standard roundabout schemes with variable (y) (Appendix A, Table A2). Condition 3 was not met by the two-geometry roundabouts with the smallest major and minor axes:

- major axis (a) of 18 m and (b/a = 0.75, 0.80), and
- major axis (a) of 19 and 20 m and (b/a = 0.75).

**Condition 4 (R**was not met by one analyzed two-geometry roundabout with variable (y) (Appendix A, Table A1): the one with a major axis (a) of 18 m and (b/a = 0.75) for both directions. This condition was met by all analyzed standard roundabout schemes.

_{1}< 100 m)**Condition 5 (V < 35 km/h)**was not met by all analyzed roundabout schemes with variable (y) (Appendix A, Table A2). The results of the estimation of vehicle speed based on the fastest through paths (V

_{2}) showed that these values were over 35 km/h in five analyzed two-geometry roundabout schemes for the major axis direction and three analyzed two-geometry roundabout schemes for the minor axis direction (Appendix A, Table A2). Therefore, this condition was not met for (V

_{2}) in the two-geometry roundabouts with the smallest major and minor axes:

- major axis (a) of 18 m and (b/a = 0.75, 0.80) for both directions,
- major axis (a) of 19 m and (b/a = 0.75) for both directions, and
- major axis (a) of 20 and 21 m and (b/a = 0.75) for the major axis direction.

**Condition 6**, regarding the relative speed between consecutive fastest path elements on exit and around the central island (V

_{3}–V

_{2}), was not met by 98% of analyzed paths constructed in two-geometry roundabout schemes (Appendix A, Table A2). Regarding the relative speed between consecutive fastest path elements on entry and around the central island (V

_{1}–V

_{2}), this condition was not met by 6% of analyzed paths. These paths were constructed in two-geometry roundabouts with variable (y) with the smallest major and minor axes (Appendix A, Table A2):

- major axis (a) of 18 m and (b/a = 0.75) for both directions,
- major axis (a) of 18 m and (b/a = 0.80) for the major axis direction, and
- major axis (a) of 19 m and (b/a = 0.75) for the major axis direction.

#### 3.2. Roundabout Schemes with Fixed (y)

_{i}, and R′

_{i}, where i = 1–3) for different (b/a) relations as dependent variables (Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13). It should be emphasized here that these simple linear regression models were not intended for use in the two-geometry roundabout’s design. The modeled simple linear dependency of the distance between the tangent of the entry radius and the tangent of the exit radius along the major axis (L), the distance between the tangent of the entry radius and the tangent of the exit radius along the minor axis (L′), the deflection along the major axis (U), and the deflection along the minor axis (U′) and the major axis length (a) for roundabout schemes with fixed (y) is shown in Figure 9 and Figure 10. It can be noted that compared to the roundabout schemes with variable (y), the parameters (L) and (L′) remained the same and that parameters (U) and (U′) were slightly larger. Their dependency on (a) remained the same.

_{i}(i = 1–3) for the variable circulatory roadway width along the minor axis (y) are given in Appendix A, Table A3. The modeled simple linear dependency of the personal vehicles’ fastest path radii (R

_{i}and R′

_{i}, where i = 1–3) and the major axis length (a) is shown in Figure 11, Figure 12 and Figure 13 for roundabout schemes with fixed (y). It can be noted that compared to the roundabout schemes with variable (y), these radii were smaller. Radii for (b/a = 0.75) showed the greatest discrepancy, caused by large path radii values at roundabouts with the smallest major and minor axes.

**Condition 3 (D > 7.00.m)**was not met by one analyzed two-geometry roundabout (Appendix A, Table A4): the one with a major axis (a) of 18 m and (b/a = 0.75) for both directions. This condition was met by all analyzed standard roundabout schemes with fixed (y).

**Condition 4 (R**was met by all analyzed two-geometry roundabouts (Appendix A, Table A3) and by all analyzed standard roundabout schemes with fixed (y).

_{1}< 100 m)**Condition 5 (V < 35 km/h)**was not met by all analyzed paths (Appendix A, Table A4). The results of the estimation of vehicle speed based on the fastest through paths (V

_{2}) showed that Condition 5 was met by all analyzed paths.

**Condition 6**, regarding the relative speed between consecutive fastest path elements on entry and around the central island (V

_{1}–V

_{2}), was met by all analyzed paths (Appendix A, Table A4). This condition regarding the relative speed between the consecutive fastest path elements on exit and around the central island (V

_{3}–V

_{2}) was not met by 92% of analyzed paths (Appendix A, Table A4).

## 4. Discussion

_{entry}, R

_{exit}, R′

_{entry}, and R′

_{exit}, Figure 1c), designed according to the design vehicles’ swept paths, resulted in values of the expected driving speed through the roundabout (V) higher than the recommended 35 km/h [14] in every analyzed roundabout scheme, including the standard roundabouts. These differences were especially pronounced for two-geometry roundabout schemes with smaller major axis (a) values (up to 16 km/h on schemes with (a) of 18 m). Here, it should be noted that this recommended speed limit at roundabouts is conservative compared to the ones given in roundabout design guidelines and regulations used worldwide. For example, Swiss and American guidelines limit the speed to 40 km/h, and French and Italian guidelines to 50 km/h [19]. At the same time, the CROW model (Equation (3)), used in this investigation for the estimation of vehicle speed, results in higher speed values compared to the FHWA model given in [13], which includes superelevation and side friction factors [16,19].

_{1}–V

_{2}), while only 1 (2%) of the analyzed paths met the requirement for a maximum relative speed on exit (V

_{3}–V

_{2}). For roundabouts that did not meet these requirements, lower speed for the fastest entering and exiting movements should be provided. It is relatively simple to reduce the speed for the fastest entering movements in single-lane roundabouts. Possible options are the introduction of a truck apron (thus adjusting the design vehicle’s swept path and designed entry width/radii parameters) or shifting the approach alignment to the left. Shifting the approach alignment to the left would increase the speed for the fastest exiting movements. Therefore, the issue of relative speed was addressed by fixing the circulatory roadway widths (y) to 5.5 m in the second part of the investigation. This intervention completely fixed the issue of maximum relative speed on entry (V

_{1}–V

_{2}); however, 92% of the analyzed paths at the exit did not meet the condition of maximum relative speed (V

_{3}–V

_{2}< 25 km/h).

_{entry}, R

_{exit}, R′

_{entry}, and R′

_{exit}, Figure 1c) closer to the outer edge of the circulatory roadway. The expected driving speed through the roundabouts will be estimated by a procedure that includes superelevation and side friction factors. Furthermore, designed two-geometry roundabout schemes will be compared with standard single-lane roundabouts according to their capacity and the surface they occupy. The roundabouts’ capacity will be determined according to the regression Swiss Bovy model, which considers the joint influence of geometric parameters on the capacity [28].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Calculated vehicle path radius (R) and measured personal vehicle fastest paths radii R

_{i}and R′

_{i}(i = 1–3) for the variable circulatory roadway width along the minor axis (y).

Major Axis | Minor Axis | Major Axis Direction (Axis a) | Minor Axis Direction (Axis b) | Standard Geometry (b = a) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a (m) | b (m) | R (m) | R_{1}(m) | R_{2}(m) | R_{3}(m) | R′ (m) | R′_{1}(m) | R′_{2}(m) | R′_{3}(m) | R = R′ (m) | R_{1} = R′_{1}(m) | R_{2} = R′_{2}(m) | R_{3} = R′_{3}(m) |

18 | 13.50 | 48.05 | 130.92 | 40.51 | 371.82 | 45.69 | 150.86 | 34.53 | 315.26 | 29.47 | 45.66 | 14.85 | 67.69 |

14.40 | 38.71 | 91.76 | 29.73 | 99.72 | 33.89 | 64.38 | 24.93 | 101.60 | |||||

15.30 | 35.07 | 65.64 | 22.84 | 94.27 | 31.58 | 59.00 | 19.45 | 94.89 | |||||

16.20 | 33.61 | 59.84 | 19.58 | 88.86 | 30.04 | 48.54 | 18.12 | 92.57 | |||||

19 | 14.25 | 42.23 | 83.36 | 29.92 | 138.70 | 36.51 | 68.39 | 24.89 | 168.35 | 30.66 | 49.90 | 14.60 | 70.50 |

15.20 | 36.38 | 65.94 | 22.83 | 96.03 | 30.78 | 52.76 | 18.93 | 81.92 | |||||

16.15 | 31.91 | 60.28 | 20.73 | 78.96 | 29.49 | 47.90 | 16.00 | 76.77 | |||||

17.10 | 31.21 | 53.41 | 17.81 | 69.81 | 31.40 | 48.39 | 15.84 | 67.25 | |||||

20 | 15.00 | 37.06 | 68.11 | 25.21 | 103.99 | 32.16 | 56.33 | 20.84 | 114.37 | 29.31 | 44.69 | 13.47 | 88.76 |

16.00 | 33.45 | 55.07 | 20.34 | 85.04 | 31.80 | 51.71 | 17.78 | 84.18 | |||||

17.00 | 31.94 | 53.82 | 18.43 | 71.26 | 28.98 | 47.00 | 17.00 | 74.80 | |||||

18.00 | 30.02 | 51.13 | 17.10 | 71.38 | 28.77 | 46.91 | 15.57 | 75.42 | |||||

21 | 15.75 | 39.27 | 59.77 | 24.96 | 157.55 | 29.94 | 49.33 | 17.92 | 79.59 | 30.51 | 43.29 | 14.74 | 88.76 |

16.80 | 32.00 | 53.36 | 20.32 | 79.49 | 28.49 | 42.22 | 15.13 | 64.06 | |||||

17.85 | 30.87 | 51.23 | 17.45 | 65.08 | 27.97 | 40.78 | 15.00 | 60.47 | |||||

18.90 | 26.75 | 47.83 | 17.29 | 57.12 | 26.92 | 43.37 | 16.68 | 66.65 | |||||

22 | 16.50 | 35.04 | 59.72 | 21.45 | 80.99 | 30.50 | 44.36 | 15.84 | 68.63 | 30.92 | 47.46 | 14.13 | 59.25 |

17.60 | 32.22 | 53.04 | 20.17 | 73.93 | 29.35 | 47.44 | 14.45 | 58.97 | |||||

18.70 | 31.30 | 50.24 | 16.96 | 63.65 | 28.80 | 43.70 | 14.85 | 61.35 | |||||

19.80 | 32.04 | 49.63 | 16.00 | 66.26 | 29.72 | 44.17 | 15.93 | 60.10 | |||||

23 | 17.25 | 32.70 | 55.51 | 21.70 | 68.36 | 28.90 | 54.55 | 17.13 | 70.06 | 31.82 | 50.04 | 14.20 | 85.30 |

18.40 | 31.94 | 53.99 | 20.39 | 65.73 | 28.48 | 43.66 | 14.73 | 62.15 | |||||

19.55 | 30.57 | 47.12 | 16.11 | 60.73 | 28.35 | 42.11 | 15.25 | 57.34 | |||||

20.70 | 30.61 | 47.74 | 14.97 | 58.53 | 29.38 | 44.67 | 14.64 | 56.25 | |||||

24 | 18.00 | 33.27 | 54.61 | 20.22 | 72.43 | 28.40 | 43.16 | 15.01 | 54.66 | 32.91 | 52.95 | 14.69 | 65.82 |

19.20 | 32.09 | 50.17 | 18.49 | 63.01 | 29.73 | 39.81 | 17.92 | 55.36 | |||||

20.40 | 31.61 | 48.64 | 16.43 | 58.72 | 29.27 | 47.30 | 14.80 | 57.27 | |||||

21.60 | 31.59 | 45.62 | 15.42 | 60.27 | 32.29 | 50.89 | 14.98 | 58.21 | |||||

25 | 18.75 | 34.02 | 53.65 | 19.81 | 68.22 | 28.01 | 41.56 | 13.81 | 55.61 | 33.96 | 52.93 | 14.70 | 68.15 |

20.00 | 32.21 | 49.88 | 18.17 | 60.91 | 28.10 | 48.20 | 14.51 | 53.60 | |||||

21.25 | 31.38 | 46.14 | 16.90 | 59.83 | 30.65 | 51.84 | 14.66 | 57.81 | |||||

22.50 | 32.33 | 48.26 | 15.11 | 58.62 | 31.44 | 44.28 | 14.45 | 55.48 |

**Table A2.**Investigation results for Condition 3 (D > 7 m), Condition 5 (V > 35 km/h, V

_{2}> 35 km/h), and Condition 6 (V

_{1}–V

_{2}< 25 km/h, V

_{3}–V

_{2}< 25 km/h) for the variable circulatory roadway width along the minor axis (y).

Major Axis | Minor Axis | Major Axis Direction (Axis a) | Minor Axis Direction (Axis b) | Standard Geometry (b = a) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a (m) | b (m) | D (m) | V (km/h) | V_{2} (km/h) | V_{1}–V_{2} (km/h) | V_{3}–V_{2} (km/h) | D′ (m) | V′ (km/h) | V′_{2} (km/h) | V′_{1}–V′_{2} (km/h) | V′_{3}–V′_{2} (km/h) | D (m) | V (km/h) | V_{2} (km/h) | V_{1}–V_{2} (km/h) | V_{3}–V_{2} (km/h) |

18 | 13.50 | 4.7 | 51 | 47 | 38 | 96 | 4.7 | 50 | 43 | 47 | 88 | 10.5 | 40 | 29 | 21 | 32 |

14.40 | 5.9 | 46 | 40 | 31 | 34 | 5.9 | 43 | 37 | 22 | 38 | ||||||

15.30 | 7.2 | 44 | 35 | 25 | 36 | 7.2 | 42 | 33 | 24 | 39 | ||||||

16.20 | 8.3 | 43 | 33 | 24 | 37 | 8.3 | 41 | 32 | 20 | 40 | ||||||

19 | 14.25 | 5.8 | 48 | 40 | 27 | 47 | 5.8 | 45 | 37 | 24 | 59 | 11.6 | 41 | 28 | 24 | 34 |

15.20 | 7.0 | 45 | 35 | 25 | 37 | 7.0 | 41 | 32 | 22 | 35 | ||||||

16.15 | 8.2 | 42 | 34 | 24 | 32 | 8.2 | 40 | 30 | 22 | 35 | ||||||

17.10 | 9.4 | 41 | 31 | 23 | 31 | 9.4 | 41 | 29 | 22 | 31 | ||||||

20 | 15.00 | 6.8 | 45 | 37 | 24 | 38 | 6.8 | 42 | 34 | 22 | 45 | 12.7 | 40 | 27 | 22 | 43 |

16.00 | 8.1 | 43 | 33 | 22 | 35 | 8.1 | 42 | 31 | 22 | 37 | ||||||

17.00 | 9.3 | 42 | 32 | 23 | 31 | 9.3 | 40 | 31 | 20 | 33 | ||||||

18.00 | 10.5 | 41 | 31 | 22 | 32 | 10.5 | 40 | 29 | 21 | 35 | ||||||

21 | 15.75 | 7.7 | 46 | 37 | 20 | 56 | 7.7 | 40 | 31 | 21 | 35 | 13.8 | 41 | 28 | 20 | 41 |

16.80 | 9.1 | 42 | 33 | 21 | 33 | 9.1 | 39 | 29 | 19 | 30 | ||||||

17.85 | 10.3 | 41 | 31 | 22 | 29 | 10.3 | 39 | 29 | 19 | 29 | ||||||

18.90 | 11.4 | 38 | 31 | 20 | 25 | 11.4 | 38 | 30 | 19 | 30 | ||||||

22 | 16.50 | 8.7 | 44 | 34 | 23 | 32 | 8.7 | 41 | 29 | 20 | 32 | 14.9 | 41 | 28 | 23 | 29 |

17.60 | 10.0 | 42 | 33 | 21 | 30 | 10.0 | 40 | 28 | 23 | 29 | ||||||

18.70 | 11.3 | 41 | 30 | 22 | 29 | 11.3 | 40 | 29 | 20 | 29 | ||||||

19.80 | 12.6 | 42 | 30 | 23 | 31 | 12.6 | 40 | 30 | 20 | 28 | ||||||

23 | 17.25 | 9.6 | 42 | 34 | 21 | 27 | 9.6 | 40 | 31 | 24 | 31 | 16.1 | 42 | 28 | 24 | 40 |

18.40 | 11.0 | 42 | 33 | 21 | 27 | 11.0 | 39 | 28 | 20 | 30 | ||||||

19.55 | 12.3 | 41 | 30 | 21 | 28 | 12.3 | 39 | 29 | 19 | 27 | ||||||

20.70 | 13.6 | 41 | 29 | 22 | 28 | 13.6 | 40 | 28 | 21 | 27 | ||||||

24 | 18.00 | 10.5 | 43 | 33 | 21 | 30 | 10.5 | 39 | 29 | 20 | 26 | 17.1 | 42 | 28 | 25 | 32 |

19.20 | 11.9 | 42 | 32 | 21 | 27 | 11.9 | 40 | 31 | 15 | 24 | ||||||

20.40 | 13.3 | 42 | 30 | 22 | 27 | 13.3 | 40 | 28 | 22 | 28 | ||||||

21.60 | 14.6 | 42 | 29 | 21 | 28 | 14.6 | 42 | 29 | 24 | 28 | ||||||

25 | 18.75 | 11.3 | 43 | 33 | 21 | 28 | 11.3 | 39 | 27 | 20 | 28 | 18.2 | 43 | 28 | 25 | 33 |

20.00 | 12.8 | 42 | 32 | 21 | 26 | 12.8 | 39 | 28 | 23 | 26 | ||||||

21.25 | 14.2 | 41 | 30 | 20 | 27 | 14.2 | 41 | 28 | 25 | 28 | ||||||

22.50 | 15.6 | 42 | 29 | 23 | 28 | 15.6 | 41 | 28 | 21 | 27 |

**Table A3.**Calculated vehicle path radius (R) and measured personal vehicle fastest paths radii R

_{i}and R′

_{i}(i = 1–3) for the fixed circulatory roadway width along the minor axis (y).

Major Axis | Minor Axis | Major Axis Direction (Axis a) | Minor Axis Direction (Axis b) | Standard Geometry (b = a) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a (m) | b (m) | R (m) | R_{1}(m) | R_{2}(m) | R_{3}(m) | R′ (m) | R′_{1}(m) | R′_{2}(m) | R′_{3}(m) | R = R′ (m) | R_{1} = R′_{1}(m) | R_{2} = R′_{2}(m) | R_{3} = R′_{3}(m) |

18 | 13.50 | 35.54 | 63.89 | 22.51 | 94.80 | 31.23 | 48.43 | 20.93 | 98.98 | 28.14 | 41.43 | 13.52 | 59.55 |

14.40 | 30.11 | 55.88 | 19.78 | 89.05 | 26.56 | 41.43 | 17.18 | 81.73 | |||||

15.30 | 30.02 | 52.71 | 17.62 | 68.98 | 27.99 | 43.34 | 14.29 | 63.58 | |||||

16.20 | 30.37 | 49.41 | 16.39 | 70.01 | 27.21 | 41.36 | 14.78 | 70.97 | |||||

19 | 14.25 | 32.36 | 61.38 | 20.54 | 81.97 | 28.44 | 42.98 | 16.99 | 80.96 | 29.66 | 45.95 | 14.17 | 60.26 |

15.20 | 30.75 | 55.47 | 18.24 | 62.73 | 26.20 | 39.80 | 14.74 | 70.03 | |||||

16.15 | 28.59 | 50.60 | 16.45 | 54.14 | 26.52 | 42.21 | 13.11 | 66.55 | |||||

17.10 | 29.17 | 49.54 | 15.96 | 63.04 | 29.38 | 43.68 | 13.83 | 56.75 | |||||

20 | 15.00 | 30.78 | 56.47 | 19.36 | 72.59 | 27.00 | 42.44 | 13.47 | 58.32 | 29.01 | 42.42 | 14.12 | 58.06 |

16.00 | 29.86 | 51.24 | 18.09 | 60.79 | 28.53 | 42.45 | 14.03 | 55.19 | |||||

17.00 | 29.63 | 50.22 | 16.57 | 57.28 | 26.95 | 43.57 | 15.30 | 61.64 | |||||

18.00 | 28.65 | 46.57 | 16.06 | 60.67 | 27.48 | 43.50 | 14.08 | 59.41 | |||||

21 | 15.75 | 34.16 | 58.60 | 20.64 | 86.78 | 25.79 | 39.63 | 15.64 | 66.74 | 30.06 | 43.56 | 16.10 | 62.28 |

16.80 | 29.60 | 50.39 | 17.94 | 61.17 | 26.44 | 38.09 | 13.26 | 51.27 | |||||

17.85 | 29.41 | 44.78 | 16.07 | 56.19 | 26.70 | 37.56 | 12.79 | 53.00 | |||||

18.90 | 25.72 | 45.40 | 16.21 | 51.73 | 25.94 | 39.03 | 15.80 | 63.38 | |||||

22 | 16.50 | 31.89 | 58.24 | 19.01 | 63.03 | 27.90 | 39.92 | 13.52 | 52.34 | 30.76 | 46.94 | 14.26 | 58.82 |

17.60 | 30.34 | 49.85 | 18.40 | 62.14 | 27.71 | 40.91 | 13.34 | 51.08 | |||||

18.70 | 30.21 | 49.03 | 16.28 | 56.96 | 27.83 | 42.36 | 13.32 | 52.85 | |||||

19.80 | 31.50 | 48.47 | 16.01 | 59.88 | 29.22 | 43.24 | 14.61 | 53.39 | |||||

23 | 17.25 | 30.51 | 52.63 | 20.04 | 58.67 | 27.01 | 46.24 | 13.83 | 55.59 | 31.82 | 50.04 | 14.20 | 85.30 |

18.40 | 30.77 | 51.44 | 18.71 | 60.75 | 27.49 | 40.04 | 13.42 | 55.18 | |||||

19.55 | 29.93 | 47.06 | 16.78 | 57.51 | 27.78 | 40.01 | 13.09 | 51.75 | |||||

20.70 | 30.33 | 46.19 | 15.48 | 58.97 | 29.12 | 41.00 | 13.36 | 55.16 | |||||

24 | 18.00 | 31.69 | 50.62 | 19.48 | 64.34 | 27.12 | 41.84 | 13.30 | 48.86 | 32.91 | 52.95 | 14.69 | 65.82 |

19.20 | 31.26 | 52.26 | 17.77 | 58.47 | 28.99 | 38.88 | 13.38 | 50.55 | |||||

20.40 | 31.31 | 47.51 | 16.88 | 56.57 | 29.00 | 46.14 | 13.81 | 52.81 | |||||

21.60 | 31.50 | 44.54 | 16.14 | 59.31 | 32.20 | 47.47 | 14.75 | 61.02 | |||||

25 | 18.75 | 32.67 | 52.84 | 18.92 | 60.86 | 26.97 | 38.92 | 13.34 | 49.11 | 33.96 | 52.93 | 14.70 | 68.15 |

20.00 | 31.67 | 49.85 | 17.86 | 61.17 | 27.65 | 44.51 | 13.84 | 50.82 | |||||

21.25 | 31.20 | 45.76 | 16.86 | 58.12 | 30.48 | 46.37 | 14.15 | 56.48 | |||||

22.50 | 32.33 | 48.26 | 15.11 | 58.62 | 31.44 | 44.28 | 14.45 | 55.48 |

**Table A4.**Investigation results for Condition 3 (D > 7 m), Condition 5 (V > 35 km/h, V

_{2}> 35 km/h), and Condition 6 (V

_{1}–V

_{2}< 25 km/h) for the fixed circulatory roadway width along the minor axis (y).

Major Axis | Minor Axis | Major Axis Direction (Axis a) | Minor Axis Direction (Axis b) | Standard Geometry (b = a) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a (m) | b (m) | D (m) | V (km/h) | V_{2} (km/h) | V_{1}–V_{2} (km/h) | V_{3}–V_{2} (km/h) | D′ (m) | V′ (km/h) | V′_{2} (km/h) | V′_{1}–V′_{2} (km/h) | V′_{3}–V′_{2} (km/h) | D (m) | V (km/h) | V_{2} (km/h) | V_{1}–V_{2} (km/h) | V_{3}–V_{2} (km/h) |

18 | 13.50 | 6.5 | 44 | 35 | 24 | 37 | 6.5 | 41 | 34 | 18 | 40 | 11.4 | 39 | 27 | 20 | 30 |

14.40 | 7.4 | 41 | 33 | 22 | 37 | 7.4 | 38 | 31 | 17 | 36 | ||||||

15.30 | 8.3 | 41 | 31 | 23 | 30 | 8.3 | 39 | 28 | 21 | 31 | ||||||

16.20 | 9.2 | 41 | 30 | 22 | 32 | 9.2 | 39 | 28 | 19 | 34 | ||||||

19 | 14.25 | 7.3 | 42 | 34 | 24 | 33 | 7.3 | 39 | 31 | 18 | 36 | 12.0 | 40 | 28 | 22 | 30 |

15.20 | 8.2 | 41 | 32 | 24 | 27 | 8.2 | 38 | 28 | 18 | 34 | ||||||

16.15 | 9.2 | 40 | 30 | 23 | 24 | 9.2 | 38 | 27 | 21 | 34 | ||||||

17.10 | 10.1 | 40 | 30 | 23 | 29 | 10.1 | 40 | 28 | 21 | 28 | ||||||

20 | 15.00 | 8.0 | 41 | 33 | 23 | 30 | 8.0 | 38 | 27 | 21 | 29 | 13.0 | 40 | 28 | 20 | 29 |

16.00 | 9.0 | 40 | 31 | 21 | 26 | 9.0 | 40 | 28 | 20 | 27 | ||||||

17.00 | 10.0 | 40 | 30 | 22 | 26 | 10.0 | 38 | 29 | 20 | 29 | ||||||

18.00 | 11.0 | 40 | 30 | 21 | 28 | 11.0 | 39 | 28 | 21 | 29 | ||||||

21 | 15.75 | 8.8 | 43 | 34 | 23 | 35 | 8.8 | 38 | 29 | 17 | 31 | 14.0 | 41 | 30 | 19 | 29 |

16.80 | 9.8 | 40 | 31 | 21 | 27 | 9.8 | 38 | 27 | 19 | 26 | ||||||

17.85 | 10.9 | 40 | 30 | 20 | 26 | 10.9 | 38 | 26 | 19 | 27 | ||||||

18.90 | 11.9 | 38 | 30 | 20 | 23 | 11.9 | 38 | 29 | 17 | 29 | ||||||

22 | 16.50 | 9.5 | 42 | 32 | 24 | 26 | 9.5 | 39 | 27 | 20 | 26 | 15.0 | 41 | 28 | 23 | 29 |

17.60 | 10.6 | 41 | 32 | 21 | 27 | 10.6 | 39 | 27 | 20 | 26 | ||||||

18.70 | 11.7 | 41 | 30 | 22 | 26 | 11.7 | 39 | 27 | 21 | 27 | ||||||

19.80 | 12.8 | 42 | 30 | 22 | 28 | 12.8 | 40 | 28 | 20 | 26 | ||||||

23 | 17.25 | 10.3 | 41 | 33 | 21 | 24 | 10.3 | 38 | 28 | 23 | 28 | 16.1 | 42 | 28 | 24 | 40 |

18.40 | 11.4 | 41 | 32 | 21 | 26 | 11.4 | 39 | 27 | 20 | 28 | ||||||

19.55 | 12.6 | 40 | 30 | 20 | 26 | 12.6 | 39 | 27 | 20 | 26 | ||||||

20.70 | 13.7 | 41 | 29 | 21 | 28 | 13.7 | 40 | 27 | 20 | 28 | ||||||

24 | 18.00 | 11.0 | 42 | 33 | 20 | 27 | 11.0 | 39 | 27 | 21 | 25 | 17.1 | 42 | 28 | 25 | 32 |

19.20 | 12.2 | 41 | 31 | 22 | 25 | 12.2 | 40 | 27 | 19 | 26 | ||||||

20.40 | 13.4 | 41 | 30 | 21 | 25 | 13.4 | 40 | 27 | 23 | 26 | ||||||

21.60 | 14.6 | 42 | 30 | 20 | 27 | 14.6 | 42 | 28 | 23 | 29 | ||||||

25 | 18.75 | 11.8 | 42 | 32 | 22 | 26 | 12.0 | 38 | 27 | 19 | 25 | 18.2 | 43 | 28 | 25 | 33 |

20.00 | 13.0 | 42 | 31 | 21 | 27 | 13.0 | 39 | 28 | 22 | 25 | ||||||

21.25 | 14.3 | 41 | 30 | 20 | 26 | 14.3 | 41 | 28 | 23 | 28 | ||||||

22.50 | 15.6 | 42 | 29 | 23 | 28 | 15.6 | 41 | 28 | 21 | 27 |

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**Figure 1.**Roundabout design procedure. (

**a**) Initial scheme; (

**b**) Front axle center point path parameters and elements (path for the circular movement around the central island is shown in blue, path for the right turn is shown in pink, path for straight passage in major axis direction is shown in orange, path for straight passage in major axis direction is shown in green); (

**c**) Final roundabout design elements.

**Figure 2.**Design vehicle (Scania R500 LA6x2/4MNA tractor with a generic 13.6 m long and 2.55 m wide trailer).

**Figure 3.**Roundabout performance checks. (

**a**) Deflection around the central island (measured between the edge of the central island and the line connecting the right edges of the opposite splitter islands shown in red dashed line), according to [10]; (

**b**) Parameters for the determination of the expected driving speed through the roundabout according to [14] (fastest path is represented by the red solid line, while the distances between the tangent of the entry radius and the tangent of the exit radius are represented by the red dash line); (

**c**) Parameters for the fastest path (represented by the red solid line) analyses according to [16].

**Figure 4.**The linear dependency of the distance between the tangent of the entry radius and the tangent of the exit radius (L and L′) and the major axis length (a) for roundabout schemes with variable (y).

**Figure 5.**The linear dependency of the deflection (U and U′) and the major axis length (a) for roundabout schemes with variable (y).

**Figure 6.**The linear dependency of the entry path radii (R

_{1}and R′

_{1}) and the major axis length (a) for roundabout schemes with variable (y).

**Figure 7.**The linear dependency of the circulating path radii (R

_{2}and R′

_{2}) and the major axis length (a) for roundabout schemes with variable (y).

**Figure 8.**The linear dependency of the exit path radii (R

_{3}and R′

_{3}) and the major axis length (a) for roundabout schemes with variable (y).

**Figure 9.**The linear dependency of the distance between the tangent of the entry radius and the tangent of the exit radius (L and L′) and the major axis length (a) for roundabout schemes with fixed (y).

**Figure 10.**The linear dependency of the deflection (U and U′) and the major axis length (a) for roundabout schemes with fixed (y).

**Figure 11.**The linear dependency of the entry path radii (R

_{1}and R′

_{1}) and the major axis length (a) for roundabout schemes with fixed (y).

**Figure 12.**The linear dependency of the circulating path radii (R

_{2}and R′

_{2}) and the major axis length (a) for roundabout schemes with fixed (y).

**Figure 13.**The linear dependency of the exit path radii (R

_{3}and R′

_{3}) and the major axis length (a) for roundabout schemes with fixed (y).

a | b/a = 0.75 | b/a = 0.80 | b/a = 0.85 | b/a = 0.90 |
---|---|---|---|---|

18 | 13.50 | 14.40 | 15.30 | 16.20 |

19 | 14.25 | 15.20 | 16.15 | 17.10 |

20 | 15.00 | 16.00 | 17.00 | 18.00 |

21 | 15.75 | 16.80 | 17.85 | 18.90 |

22 | 16.50 | 17.60 | 18.70 | 19.80 |

23 | 17.25 | 18.40 | 19.55 | 20.70 |

24 | 18.00 | 19.20 | 20.40 | 21.60 |

25 | 18.75 | 20.00 | 21.25 | 22.50 |

**Table 2.**Circulatory roadway widths along the major axis (x) and the minor axis (y) for roundabout schemes with variable (y).

a (m) | b/a = 0.75 | b/a = 0.80 | b/a = 0.85 | b/a = 0.90 | b/a = 1.00 | ||||
---|---|---|---|---|---|---|---|---|---|

x (m) | y (m) | x (m) | y (m) | x (m) | y (m) | x (m) | y (m) | x = y (m) | |

18 | 11.85 | 7.35 | 10.60 | 7.00 | 9.35 | 6.65 | 8.20 | 6.40 | 6.05 |

19 | 11.75 | 7.00 | 10.50 | 6.70 | 9.30 | 6.45 | 8.10 | 6.20 | 5.95 |

20 | 11.75 | 6.75 | 10.45 | 6.45 | 9.25 | 6.25 | 8.05 | 6.05 | 5.80 |

21 | 11.85 | 6.60 | 10.45 | 6.25 | 9.20 | 6.05 | 8.10 | 6.00 | 5.75 |

22 | 11.85 | 6.35 | 10.55 | 6.15 | 9.25 | 5.95 | 7.95 | 5.75 | 5.60 |

23 | 11.95 | 6.20 | 10.55 | 5.95 | 9.25 | 5.80 | 7.95 | 5.65 | 5.45 |

24 | 12.05 | 6.05 | 10.65 | 5.85 | 9.25 | 5.65 | 7.95 | 5.55 | 5.45 |

25 | 12.25 | 6.00 | 10.75 | 5.75 | 9.35 | 5.60 | 7.95 | 5.45 | 5.35 |

**Table 3.**Distances between the tangent of the entry radius and the tangent of the exit radius along the major axis (L) and deflections along the major axis (U) for roundabout schemes with variable (y).

a (m) | b/a = 0.75 | b/a = 0.80 | b/a = 0.85 | b/a = 0.90 | b/a = 1.00 | |||||
---|---|---|---|---|---|---|---|---|---|---|

L (m) | U (m) | L (m) | U (m) | L (m) | U (m) | L (m) | U (m) | L (m) | U (m) | |

18 | 54.06 | 1.88 | 53.51 | 2.77 | 57.17 | 4.09 | 61.20 | 5.37 | 64.63 | 7.65 |

19 | 54.52 | 2.52 | 57.26 | 3.87 | 58.47 | 5.09 | 62.76 | 6.46 | 69.66 | 8.85 |

20 | 56.09 | 3.51 | 59.26 | 4.92 | 62.76 | 6.24 | 64.89 | 7.52 | 71.44 | 10.14 |

21 | 62.98 | 4.59 | 61.75 | 5.94 | 65.20 | 7.31 | 62.37 | 8.03 | 75.60 | 11.12 |

22 | 63.13 | 5.51 | 65.32 | 6.89 | 68.83 | 8.31 | 74.11 | 9.80 | 79.15 | 12.32 |

23 | 64.02 | 6.37 | 68.38 | 7.92 | 70.85 | 9.31 | 74.80 | 10.75 | 83.36 | 13.55 |

24 | 67.99 | 7.34 | 71.44 | 8.86 | 75.21 | 10.40 | 78.90 | 11.83 | 87.44 | 14.62 |

25 | 71.66 | 8.20 | 74.33 | 9.80 | 77.27 | 11.30 | 82.53 | 12.88 | 91.66 | 15.79 |

**Table 4.**Distances between the tangent of the entry radius and the tangent of the exit radius along the minor axis (L′) and deflections along the minor axis (U′) for roundabout schemes with variable (y).

a (m) | b/a = 0.75 | b/a = 0.80 | b/a = 0.85 | b/a = 0.90 | b/a = 1.00 | |||||
---|---|---|---|---|---|---|---|---|---|---|

L′ (m) | U′ (m) | L′ (m) | U′ (m) | L′ (m) | U′ (m) | L′ (m) | U′ (m) | L′ (m) | U′ (m) | |

18 | 51.48 | 1.70 | 50.41 | 2.86 | 55.53 | 4.43 | 57.74 | 5.39 | 64.63 | 7.65 |

19 | 51.92 | 2.77 | 52.98 | 3.99 | 56.66 | 5.25 | 63.51 | 6.62 | 69.66 | 8.85 |

20 | 53.21 | 3.76 | 58.71 | 5.18 | 59.97 | 6.36 | 63.70 | 7.62 | 71.44 | 10.14 |

21 | 54.93 | 4.67 | 58.66 | 6.13 | 62.14 | 7.42 | 63.86 | 8.49 | 75.60 | 11.12 |

22 | 59.62 | 5.78 | 62.82 | 7.11 | 66.17 | 8.45 | 71.22 | 9.85 | 79.15 | 12.32 |

23 | 59.92 | 6.37 | 64.85 | 8.13 | 68.39 | 9.47 | 73.38 | 10.86 | 83.36 | 13.55 |

24 | 63.19 | 7.60 | 69.24 | 9.12 | 72.44 | 10.55 | 80.40 | 12.04 | 87.44 | 14.62 |

25 | 65.05 | 8.41 | 69.34 | 9.97 | 76.86 | 11.54 | 81.57 | 13.02 | 91.66 | 15.79 |

**Table 5.**Circulatory roadway widths along the major axis (x) and the minor axis (y) for roundabout schemes with fixed (y).

a (m) | b/a = 0.75 | b/a = 0.80 | b/a = 0.85 | b/a = 0.90 | b/a = 1.00 | ||||
---|---|---|---|---|---|---|---|---|---|

x (m) | y (m) | x (m) | y (m) | x (m) | y (m) | x (m) | y (m) | x = y (m) | |

18 | 10.00 | 5.50 | 9.10 | 5.50 | 8.20 | 5.50 | 7.30 | 5.50 | 5.50 |

19 | 10.25 | 5.50 | 9.30 | 5.50 | 8.35 | 5.50 | 7.40 | 5.50 | 5.50 |

20 | 10.50 | 5.50 | 9.50 | 5.50 | 8.50 | 5.50 | 7.50 | 5.50 | 5.50 |

21 | 10.75 | 5.50 | 9.70 | 5.50 | 8.65 | 5.50 | 7.60 | 5.50 | 5.50 |

22 | 11.00 | 5.50 | 9.90 | 5.50 | 8.80 | 5.50 | 7.70 | 5.50 | 5.50 |

23 | 11.25 | 5.50 | 10.10 | 5.50 | 8.95 | 5.50 | 7.80 | 5.50 | 5.50 |

24 | 11.50 | 5.50 | 10.30 | 5.50 | 9.10 | 5.50 | 7.90 | 5.50 | 5.50 |

25 | 11.75 | 5.50 | 10.50 | 5.50 | 9.25 | 5.50 | 8.00 | 5.50 | 5.50 |

**Table 6.**Distances between the tangent of the entry radius and the tangent of the exit radius along the major axis (L) and deflections along the major axis (U) for roundabout schemes with fixed (y).

a (m) | b/a = 0.75 | b/a = 0.80 | b/a = 0.85 | b/a = 0.90 | b/a = 1.00 | |||||
---|---|---|---|---|---|---|---|---|---|---|

L (m) | U (m) | L (m) | U (m) | L (m) | U (m) | L (m) | U (m) | L (m) | U (m) | |

18 | 54.06 | 3.34 | 53.51 | 4.27 | 57.17 | 5.24 | 61.20 | 6.27 | 64.63 | 8.20 |

19 | 54.52 | 4.02 | 57.26 | 5.07 | 58.47 | 6.04 | 62.76 | 7.16 | 69.66 | 9.30 |

20 | 56.09 | 4.76 | 59.26 | 5.87 | 62.76 | 6.99 | 64.89 | 8.07 | 71.44 | 10.30 |

21 | 62.98 | 5.69 | 61.75 | 6.69 | 65.20 | 7.86 | 62.37 | 8.53 | 75.60 | 11.37 |

22 | 63.13 | 6.36 | 65.32 | 7.54 | 68.83 | 8.76 | 74.11 | 10.05 | 79.15 | 12.42 |

23 | 64.02 | 7.07 | 68.38 | 8.37 | 70.85 | 9.61 | 74.80 | 10.90 | 83.36 | 13.55 |

24 | 67.99 | 7.89 | 71.44 | 9.21 | 75.21 | 10.55 | 78.90 | 11.88 | 87.44 | 14.62 |

25 | 71.66 | 8.70 | 74.33 | 10.05 | 77.27 | 11.40 | 82.53 | 12.88 | 91.66 | 15.79 |

**Table 7.**Distances between the tangent of the entry radius and the tangent of the exit radius along the minor axis (L′) and deflections along the minor axis (U′) for roundabout schemes with fixed (y).

a (m) | b/a = 0.75 | b/a = 0.80 | b/a = 0.85 | b/a = 0.90 | b/a = 1.00 | |||||
---|---|---|---|---|---|---|---|---|---|---|

L′ (m) | U′ (m) | L′ (m) | U′ (m) | L′ (m) | U′ (m) | L′ (m) | U′ (m) | L′ (m) | U′ (m) | |

18 | 51.48 | 3.55 | 50.41 | 4.36 | 55.53 | 5.37 | 57.74 | 6.29 | 64.63 | 8.20 |

19 | 51.92 | 4.27 | 52.98 | 5.19 | 56.66 | 6.20 | 63.51 | 7.32 | 69.66 | 9.30 |

20 | 53.21 | 5.01 | 58.71 | 6.13 | 59.97 | 7.11 | 63.70 | 8.17 | 71.44 | 10.30 |

21 | 54.93 | 5.92 | 58.66 | 6.88 | 62.14 | 7.97 | 63.86 | 8.99 | 75.60 | 11.37 |

22 | 59.62 | 6.63 | 62.82 | 7.76 | 66.17 | 8.90 | 71.22 | 10.10 | 79.15 | 12.42 |

23 | 59.92 | 7.07 | 64.85 | 8.58 | 68.39 | 9.77 | 73.38 | 11.01 | 83.36 | 13.55 |

24 | 63.19 | 8.15 | 69.24 | 9.47 | 72.44 | 10.70 | 80.40 | 12.09 | 87.44 | 14.62 |

25 | 65.05 | 8.91 | 69.34 | 10.22 | 76.86 | 11.64 | 81.57 | 13.02 | 91.66 | 15.79 |

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**MDPI and ACS Style**

Ahac, S.; Ahac, M.; Majstorović, I.; Bašić, S.
Speed Reduction Capabilities of Two-Geometry Roundabouts. *Appl. Sci.* **2023**, *13*, 11816.
https://doi.org/10.3390/app132111816

**AMA Style**

Ahac S, Ahac M, Majstorović I, Bašić S.
Speed Reduction Capabilities of Two-Geometry Roundabouts. *Applied Sciences*. 2023; 13(21):11816.
https://doi.org/10.3390/app132111816

**Chicago/Turabian Style**

Ahac, Saša, Maja Ahac, Igor Majstorović, and Silvio Bašić.
2023. "Speed Reduction Capabilities of Two-Geometry Roundabouts" *Applied Sciences* 13, no. 21: 11816.
https://doi.org/10.3390/app132111816