# Speed Reduction Capabilities of Two-Geometry Roundabouts
## 1 Introduction  
Modern roundabouts are intersections with a raised central island and a circulatory roadway at which the yield-at-entry rule is applied. At these types of intersections, the traffic is continuous and circulates at low speed in one direction on a circulatory roadway toward the exits at the intersection legs [1]. When adequately designed, modern roundabouts provide numerous benefits compared to conventional intersections, such as improved intersection safety and capacity, better vehicle speed management, reduced maintenance costs, and reduced pollution generated by road traffic [2; 3; 4; 5; 6; 7]. The benefits of modern roundabouts result from the fact that they are designed to control traffic speeds [8; 9]. This control is achieved through the selection of appropriate design elements that result in adequate vehicle path curvature upon entry, around the central island, and upon exit. It is considered that the driving speed through the roundabout is mostly influenced by the deflection of the vehicle path, which is caused by the roundabout's central island. The influence of deflection on roundabout performance is evaluated either by measuring the deflection provided by roundabouts' design elements (for example, using the procedure given in [10]) or by defining the radius (or radii) of the centerline of a vehicle traveling along the so-called fastest path through the roundabout and then calculating the vehicle speed [11]. This theoretical fastest path is representative of the most used trajectory by drivers under free flow conditions when minimizing their driving discomfort [12]. In the latter approach, speed prediction models that are based on fundamental functions of vehicle dynamics are used. For example, the FHWA model, described in [13], predicts the speed for five locations on the fastest paths (right-turn, left-turn, through circulating, exit, or entry movements) based on the vehicle path radii, side friction factor, and superelevation on these locations. On the other hand, the CROW model, described in [14], gives a single value of vehicle speed for all specific locations onthe through path: the entry, around the central island, and the exit. It predicts the expected driving speed through the roundabout based on the vehicle path radius. This radius is calculated using measured roundabout design elements and it is assumed to be constant along the vehicle through path. There are also empirically derived speed prediction models, such as a multiple linear regression model developed for Italian roundabouts (described in [15]) or a model for speed prediction that includes the central island diameter and the average of entry, circulating, and exit widths as derived variables (described in [8]). The investigations that led to the development of these models showed that the FHWA model overestimates entry and exit speed values. At the same time, investigation results given in [16] showed that the CROW model results in an even larger estimated speed compared to the FHWA model and that these differences are proportional to the path radius. As described in detail in [1], roundabout design, i.e., the selection of roundabouts' design elements, is an iterative process that is comprised of the following steps. The first step is the selection of the roundabout size, considering the spatial limitations and the number and alignment of the legs. The second step is the selection of the circulatory roadway width. The third step is the selection of the splitter island shape, which is conditioned by the required level of traffic flow channeling, as well as the design of the right carriageway edge. The fourth step is the control of the selected geometry, i.e., the swept path analysis for a design vehicle (a vehicle identified as the least maneuverable vehicle expected to use the intersection), the fastest path analysis for personal cars, and visibility checks. When design elements meet the conditions of these performance checks, a detailed roundabout design is conducted.