## 2 Materials and Methods  
Vehicle swept paths can be defined at the test site, by driving a real vehicle in a real traffic situation, but also by applying simulation methods that try to show the movement of the vehicle as close to the real world as possible. The advantages of the computer simulation of design vehicle movement are a simple and fast way of defining different types of vehicles of arbitrary dimensions, setting different vehicle paths, varying turning angles, as well as a fast drawing of the required swept paths [17; 18]. In this investigation, the method of the computer simulation of vehicle movement using the Autodesk Vehicle Tracking 2020 software was used to define the swept paths. 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 applicability of approach A-2 was tested on 25 single-lane roundabout schemes designed in the Autodesk AutoCAD software. These schemes were constructed by varying the outer radius of roundabouts (R) from 13 to 25 m, with a 0.5 m increment. According to previous research given in [9], these outer radii are commonly used for single-lane roundabouts worldwide. An increment of 0.5 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. Roundabout approach leg axes on these schemes intersect in the center of the roundabout's outer radius, as shown in Figure 1. A triangular splitter island, 15 m long and 3 m wide, placed 0.5 m from the roundabout outer radius (R), was selected for this investigation. Tested FACPPs (shown in Figures 2 and 3) were constructed for straight passage through the intersection by applying the following design boundary conditions:  
* The entry and exit branches on the paths are parallel to the edge of the splitter island and offset by 2 m;
* The positions of points A, B, and C on the paths constructed by the A-1 and A-2 approaches are the same for each outer radius, R;
* Point B is offset by 2.5 m from the outer radius, R;
* Radius R1 is larger or equal to R2 and smaller than R3;
* Radius R2 is smaller than R3 by at least 2 m;
* Radius R2 on FACPP constructed by A-2 is concentric to outer radius R;
* For every FACPP, the lengths of short straight lines (I\({}_{81}\) and I\({}_{82}\)) are between 5.0 and 5.5 m.  
The type and dimensions of the design vehicle can be determined in the following ways [9]:  
1. Based on a statistical analysis of data on the presence of vehicles of certain dimensions (wheelbase, overhang length) on the observed section of the road, where the criterion for selecting the design vehicle is the frequency of the occurrence of a certain type of vehicle;
2. By adopting the design vehicle defined by the appropriate guidelines for the intersection design according to the criterion of the largest turning envelope;
3. Based on data from the catalog of the most represented vehicle manufacturers on the market, whereby the criterion for selecting the design vehicle is the frequency of the appearance of a certain type and the dimensions of the vehicle. For the simulations conducted in this investigation, a custom design vehicle was created based on the dimensions given in German guidelines [19]. German guidelines for the design vehicle lengths were selected for this analysis based on the results of the investigation conducted in [9]. This investigation included the comparison of turning envelope requirements for the design vehicles given in Austrian, German, and Serbian guidelines and Swiss norms, as well as vehicles whose dimensions were collected from the catalogs of the most represented manufacturers on the European market. The investigation results showed that the vehicle defined in German guidelines has the widest swept path when negotiating a roundabout for a tractor with a semi-trailer.