DELIVERABLE 2.8 - urban track

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D0208_STIB_M24.doc TIP5-CT-2006-031312 Page 30 of 44 URBAN TRACK Issued: August 13, 2008 Quality checked and approved by project co-ordinator André Van Leuven Either huge force amplitudes or long areas with geometry other than the prescribed one are obtained. Especially, for constant cant gradients the following results are estimated: Sharp kinks at the ends of constant cant gradients are impossible for continuous welded rails. There are always rounded connections, which elongate the constant cant gradient. Steep constant cant gradients have either a great length of the rounded connections (>> 10 m) or high stress in the railroad track. Therefore, rapid decay of the track alignment geometry starting from the kinks of the straight ramp. Steep and short constant cant gradients are never straight but everywhere bended. Curvature and cant in the rounded connections are no longer proportional. The Viennese Curve: The Viennese transition curve and cant gradient and its similar products have a very smooth connection to the neighbouring elements and are based on a high order function. They all fulfil the following requirements: Acceleration and jerk are continuous and smooth, not only in the track centre line, but also everywhere within the guided vehicle. In the cant gradient, the continuous welded rails are not forced to yield the prescribed geometry. The shape is kept with minimal forces obeying bending theory. Track alignment design is performed for a certain height (the medium height of centres of mass of the vehicles), not for the singular track centre line. Therefore, guiding forces are kept small. The Viennese curve has the simplest mathematical description for the fulfilment of all these demands: Low forces (external from the vehicle and internal from the track). Less maintenance (high potential for durability). The following graphs show the basic functions and their derivates in comparison with the well-known transition curves presently used.
Figure 3.6 Figure 3.7 Bezogene Überhöhung 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 D0208_STIB_M24.doc TIP5-CT-2006-031312 Page 31 of 44 URBAN TRACK Issued: August 13, 2008 Quality checked and approved by project co-ordinator André Van Leuven Alle Überhöhungsrampen - Lage 0 0,2 0,4 0,6 0,8 1 All cant gradients - position Bezogene Winkel 2,5 2 1,5 1 0,5 0 -0,5 Bezogener Weg Alle Überhöhungsrampen - W inkel 0 0,2 0,4 0,6 0,8 1 All cant gradients – angles Be zoge ne r W e g Linear ramp Bloss ramp COS (Japanese) ramp Helmert (Schramm) ramp Watorek ramp SIN ramp Herbert's HT ramp Viennese type HHMP7 © Hasslinger Linear ramp Helm ert (S chramm ) ramp Blos s ram p COS (Japanes e) ram p W atorek ram p SIN ram p Herbert's HT ram p Viennes e type HHM P7 © H asslinger
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Page 3 and 4: D0208_STIB_M24.doc TIP5-CT-2006-031
Page 5 and 6: 0.6. CONCLUSIONS D0208_STIB_M24.doc
Page 11 and 12: Figure 2.3 Figure 2.4 Lateral widen
Page 13 and 14: 2.3. BREMEN (BSAG) D0208_STIB_M24.d
Page 15 and 16: 2.4. SAARBAHN Figure 2.7 Rail profi
Page 17 and 18: 2.6. KARLSRUHE (VBK) Figure 2.9 Rai
Page 19 and 20: Figure 2.11 Figure 2.12 Test of dif
Page 21 and 22: 2.9. NEW DEVELOPMENTS D0208_STIB_M2
Page 23 and 24: 3. THE VIENNESE CURVE 3.1. INTRODUC
Page 27 and 28: Figure 3.3 D0208_STIB_M24.doc TIP5-
Page 29: Figure 3.5 D0208_STIB_M24.doc TIP5-
Page 33 and 34: 3.3. IMPLEMENTATION Figure 3.9 Figu
Page 35 and 36: Figure 3.14 Figure 3.15 D0208_STIB_
Page 37 and 38: Figure 3.16 D0208_STIB_M24.doc TIP5
Page 41 and 42: Figure 3.19 D0208_STIB_M24.doc TIP5

DELIVERABLE 2.8 - urban track

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