# Short Cyclic Algorithm for Turbo Block Construction
## 4 Turbo Block Construction--New Algorithm  
The method of turbo block construction proposed herein relies on the first segment being of constant width, with the width of the second and third segments gradually decreasing. Geometrical construction based on the third segment being of constant width, with the first and second segments of variable width, is also possible [9; 10; 11; 12; 17; 23], as shown in Figure 5. According to some national policies [20; 21; 22], even the construction of all segments with constant width is proposed. With the first segment having constant width, depending on the type of the turbo block (two, three, or four translation axes), the innermost part of the turbo block is assembled as shown in Figure 10. The starting segments are to be cut out from the circular ring of width  
Figure 9: Turbo-star construction with three and two spiraling lanes. equal to Wi (upper part of Figure 10) and then reassembled in a staggered form, as shown in the lower part of Figure 10.  
With the first segment being of constant width (construction method presented herein), variations in pavement width, segment by segment, are given in Figure 11. Throughout the entire first segment, the pavement width stays constant at 5.00 m. This equals the width _Wi_ from Figure 3. At the end of the second segment, pavement width drops down from _Wi_ to _Wm_. Along the third segment, pavement width drops even further, below 4.50 m, which is the nominal width _Wo_ of the third segment. Nevertheless, the usable part of the third segment stops well before the leg axis (centerline) _C1I_, as the vehicle leaves circulatory roadway. Figure 11: Variations in pavement width along the spiral lane—proposed algorithm. Figure 10: Assembling the staggered starting segments of constant width. The construction of a turbo block can be carried out spiral by spiral or segment by segment. Spiral by spiral construction is demonstrated in Figure 12. This is supposed to be the turbo block serving the creation of a turbo-rotor. The first spiral is the red one. It starts in the sector enclosed within the translation axes _Ta1_ and _Ta2_. In this sector, there are only two concentric arcs, _Rc1_ and _Rm1_, with the red center in point _C1_. At translation axis _Ta2_, radii _Rc1_ and _Rm1_ connect to radii _Rc3_ and _Rm3_. Radii _Rm2_ and _Rc2_ are introduced in the sector enclosed by translation axes _Ta2_ and _Ta3_ as well. Red arcs with radii _Rm2_, _Rc2_, _Rc3_, and _Rm3_ are concentric to each other, with the red  
Figure 12: Construction of the spiral lane—new algorithm. center in point C23. To smoothly match with _Rc1_ and _Rm1_, the _Rc3_ and _Rm3_ centers (red center _C23_) must be moved for _Rm3-Rm1_ along the _Ta2_ axis, from red center _C1_. After passing translation axis _Ta3_, the set of four red arcs with radii _Rm4_, _Rc4_, _Rc5_, and _Rm5_ must connect to the four red arcs from the previous sector (_Rm2_, _Rc2_, _Rc3_, and _Rm3_). To provide for smooth connection, the center of these new red radii (red _C45_) is to be moved for _Rm4-Rm2_ along the translation axis _Ta3_, from red center _C23_. Finally, the fourth part of the red spiral, consisting of two arcs with radii _Rm6_ and _Rc6_, is added. These two arcs are concentric to each other, with the red center _C6_ moved for _Rm6-Rm4_ along translation axis _Ta4_, from red center _C45_. The second spiral, the blue one, starts at translation axis _Ta2_. The first part of this spiral (blue radii _Rc1_ and _Rm1_), in order to provide constant pavement width _Wi_ in the first segment, must be concentric to the red arcs with radii _Rm2_, _Rc2_, _Rc3_, and _Rm3_. Consequently, blue center _C1_ of the first part of blue spiral is collocated with the red center _C23_. Further, the second part of the blue spiral (_Rm2_, _Rc2_, _Rc3_, and _Rm3_) must smoothly connect to its first part. Therefore, blue center _C23_ is moved for _Rm3-Rm1_ along translation axis _Ta3_, from blue center _C1_.