DELIVERABLE 2.8 - urban track

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.