# Short Cyclic Algorithm for Turbo Block Construction
## 2 Known Issues and Dilemmas  
Traditional turbo block construction principles are demonstrated in Figure 5. For clarity reasons, only _Rc_ radii are labeled. There is a single continuous spiral lane colored in gray. It starts with the first segment, having inner radius _Rc1_. After passing translation axis _Ta3_, the second segment follows with inner radius _Rc3_. Beyond translation axis _Ta4_ (third segment), the radius switches to _Rc5_. Figure 5: Spiraling lane segments with variations in pavement width along the spiral lane—turbo-rotor type from Dutch policies. In the central part of the turbo block, the centers of the four groups of arcs are labeled, each group representing the centers of arcs belonging to a specific sector (enclosed between a particular pair of translation axes). Currently, comprehensive research of vehicle trajectories within the turbo roundabout is underway at the Faculty of Civil Engineering, University of Belgrade (not published yet). It appears that substantial uncertainties in vehicle positioning are expected right in the first segment. It is logical, even at first glance, that the critical vehicle enters the first segment with maximum off-tracking to the right and then proceeds into the left curve of minimal curvature (based on _Rc1_). Simulation tests show that it is best to keep the first segment in constant (the largest) width _Wi_, as shown in Figure 3. It should be noted that any design methodology of a turbo roundabout should include an analysis of swept paths [16]. The width of a driving lane always depends on its inner radius. Traditionally, the width of the last (third) segment is kept at the constant width. Hence, with the driving lane width at the end of the middle segment being sufficient, the lane width along the entire last segment is wider than necessary. Apart from being unnecessarily wide, the third segment stops well before reaching its geometrical end, at the point where the vehicle leaves the roundabout. Definitely, there are two reasons for keeping the first segment at a constant width rather than the last one. For the first one, there is substantial uncertainty in predicting the exact vehicle position (trajectory) in the first segment. Second, it is better to have surplus pavement area in the first segment than along the last segment (if the last segment, by tradition, is constructed in constant width). Depending on national standards [9; 10; 11; 12; 17], the innermost and/or the outermost edge lane could be wider. In cases like these, the question arises whether to match marking lines (Figure 6) or curb lines (Figure 7) [18]. Namely, with a wider innermost edge lane, when transitioning from the first to the second part of the spiral, it is possible to connect the innermost marking line with the consecutive outer marking line along the first divider. But in that case, the innermost curb line (along the central island) would not match the outer curb line of the first divider. Actually, the divider in question is some distance away and there is no physical connection to the central island of the roundabout. From the perspective of drivers, it would be more suitable to provide geometrical continuity between the marking lines, although they are not physically connected as well. Figure 6: Connecting the radii—matching marking lines. Similarly, when the outermost edge lane is wider, the same question arises at the start of the last segment: whether to match curb lines or mark lines. And again, it seems more logical to provide geometrical continuity between consecutive marking lines. Relevant national policies [9; 10; 11] are vague about this. Perhaps they do not give much importance to the problem in question, but the geometrical construction of a turbo block, especially when it comes to computer programming, must be absolutely clear. The algorithm presented herein supports both matching the marking lines and matching the curb lines.