# Speed Reduction Capabilities of Two-Geometry Roundabouts
## 2 Experiment Design and Methodology  
The investigation presented in this paper was conducted on 40 single-lane roundabout schemes designed in the Autodesk AutoCAD 2021 software. A total of 32 initial schemes (Figure 1a) were constructed by varying the major axis of the elliptical outer edge of a two-geometry roundabout (a) from 18 to 25 m, with a 1 m increment. According to previous research given in [19], these outer radii are commonly used for single-lane roundabouts worldwide. An increment of 1 m was chosen to capture the dispersity of the results and to create a sample that is representative, manageable, and easy to present at the same time. Figure 1: Roundabout design procedure. (**a**) Initial scheme; (**b**) Front axe 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. According to [22], the minor axis of the elliptical outer edge of a two-geometry roundabout (b) is determined using the following equation:  
\[0.75<b/a<0.90. \tag{1}\]  
In this investigation, for each major axis (a), four two-way geometry roundabouts were designed by varying the minor axis of the elliptical outer edge of a two-geometry roundabout (b), as shown in Table 1. Eight initial schemes were created to represent a standard modern roundabout with an outer radius (R = a) between 18 and 25 m, designed with a 1 m increment. Roundabout approach leg axes in all schemes intersect in the center of the roundabout's outer edge, as shown in Figure 1a. Approach legs are radial to the outer edge, and their axes intersect in the center of the roundabout. A triangular splitter island, 15 m long, 3 m wide, and placed 0.5 m from the roundabout outer edge, was selected for this investigation. Carriageway widths and carriageway edge design elements were determined using computer simulations of the design vehicle movement and the resulting swept paths generated by the Autodesk Vehicle Tracking 2020 software. Vehicle Tracking is a third-party computer-aided design (CAD) software released for AUTODESK. It can track the swept paths of selected design vehicles with the help of its algorithm and automate the entire design process. The design vehicle used in this investigation was a tractor with a semi-trailer based upon a Scania R500 LA6x2/4 MNA (Sodertalje, Sweden) tractor with a generic 13.6 m long and 2.55 m wide trailer (Figure 2), which is defined as a standard European long vehicle in the Vehicle Tracking 2020 database. The input parameter necessary for defining the swept path at roundabouts is the design vehicle steering path, i.e., the front axle center point path. For this investigation, the front axle center point paths for the circular movement around the central island (shown in blue in Figure 1b) were constructed with a circular arc with a radius that is offset by 2 m from the roundabout's minor axis (R\({}^{\prime}\) = b \(-\) 2). Paths for the right turn (shown in pink in Figure 1b) were constructed with an entry line that was offset by 1.75 m from the splitter island on the roundabout entry, an exit line that was offset by 2.0 m from the splitter island on the roundabout exit, and a circular arc (R\({}^{\prime\prime}\)) tangential to these lines. Paths for straight \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**a** & **b/a = 0.75** & **b/a = 0.80** & **b/a = 0.85** & **b/a = 0.90** \\ \hline
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 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Major (a) and minor (b) two-geometry roundabout axes.