# Speed Reduction Capabilities of Two-Geometry Roundabouts
## 2 Experiment Design and Methodology
Finally, a calculation of the expected driving speed through the roundabout for the major and minor axis directions of each roundabout scheme was conducted using the CROW model, where the relation between speed (\(V\)) and the vehicle path radius (\(R\)) was as follows [14]:  
\[V=7.4\times\sqrt{R}. \tag{3}\]  
The second approach included the estimation of vehicle speed based on the fastest through paths constructed on final roundabout schemes. The fastest path is the smoothest, flattest path possible for a single vehicle in the absence of other traffic and ignoring all lane markings, traversing through the entry, around the central island, and out the relevant exit [16]. The fastest paths were constructed in Autodesk AutoCAD 2021 software using cubic splines, piecewise polynomials of the third degree with function values, and second derivatives that agree at the points (nodes) where they join. Nodes were defined in such a way that they result in a spline curve tangent with the following minimum clearances: 1 m from the painted edge line of the splitter island and 1.5 m from the right carriageway edge and the central island (Figure 3c). Following the construction of the fastest through paths, the critical radii along these paths were determined:  
* the entry path radii (R1 and R1), which are the minimum radii on the fastest through paths before the entrance line;
* the circulating path radii (R2 and R2), which are the minimum radii on the fastest through paths around the central island; and
* the exit path radii (R3 and R3), which are the minimum radii on the fastest through paths into the exit. 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 V1 along R1, Figure 3c), the circulating speed (V2 along R2 and V1 along R2, Figure 3c), and the exit speed (V3 along R3 and V1 along R3, Figure 3c). The resulting relative speed between the consecutive fastest path elements on the entrance path, the path around the central island (V1-V2), and elements on the path around the central island exit path (V3-V2) was also investigated. Six conditions were investigated for all designed roundabout schemes in the first part of the investigation:  
* **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 4:** the deflected vehicle path radius (R1) should not exceed 80-100 m [22]. * **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 (V1-V2 and V3-V2) should not exceed 25 km/h [16]. To meet the requirements of Condition 1 and Condition 2, the second part of the investigation was conducted on 40 modified roundabout schemes. The modification included the definition of the fixed circulatory roadway width along minor axes (y) of 5.5 m. Conditions 3-5 were investigated for these modified roundabout schemes. 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'), the deflection along the major and minor axis (U and U'), personal vehicles' fastest path radii along the major and minor axis (R1 and R1, where i = 1-3), and the axis length, these values along both the major and minor axis were plotted for all analyzed roundabout schemes.