DELIVERABLE 2.8 - urban track

3. THE VIENNESE CURVE
3.1. INTRODUCTION
D0208_STIB_M24.doc
TIP5-CT-2006-031312 Page 23 of 44
URBAN TRACK Issued: August 13, 2008
Quality checked and approved by project co-ordinator André Van Leuven
From the very beginning of railway engineering the design of the ideal track geometry layout was a key
problem. Two hundred years ago, with the debut of the steam engine simple geometric and kinematic
basics were developed which are still valid today. From then to now engineers were busy to develop a
track alignment that reduces forces in the wheel – rail contact point, minimizes wear of the tracks and the
wheels and that advances the safety of the passengers.
A reduction of discontinuities (reduction in the mathematical order) was first proposed by F.R. Helmert
in 1872 and G. Schramm in 1934, who replaced the straight course of the cant gradient and curvature by
two curves, thus dividing the element into two. In 1936, A.E. Bloss proposed the simplest possible
polynomial for a simple part element, which is now increasingly used. As early as 1907, K. Watdrex
achieved a further reduction of discontinuities with a sinus-shaped curse. These two curves solve the
problem of discontinuities at the joints in the first.
Really fundamental investigations were done by Dr. Walter Heindl for the Österreichische Bundesbahnen
(ÖBB) since 1988. He developed the first homogeneous systems of methods and rules based one pure
geometry (strip theory), kinematics and physics. The method was mathematically perfect, but seems to
be unacceptable for use by the railway organisations.
Hence, a new start was made by Austrian Railways, the Wiener Linien and Dipl.-Ing.Dr.techn. Herbert
L. Hasslinger a civil and mechanical engineer from Vienna in 1995. A homogeneous system of rules
covering conventional and modern track alignment designs was created. A new simple method and new
curves just fulfilling the basic demands were developed. The result is the “Viennese transition curve and
cant gradient” type HHMP7. It shows the typical “out-swinging” as an effect of “track alignment design
for the centre of gravity” that was already known by the other researchers, but never constructed in such
an easy manner. This design feature is protected by international patents, which are jointly owned by
Wiener Linien and by ÖBB, the Austrian Federal Railways.
The Wiener Linien operates and enlarges its net already in this modern manner and ÖBB has used the
transition curve many times in its network.
A comparative measurement investigation was performed for the verification purposes and for gaining
practical experience. The conventional geometry of clothoid and constant cant gradient was perfectly
executed and tested by a measurement train. Afterwards the modern geometry was tamped and tested
following the same procedure. The first inspection already shows that typical peaks at the connecting
areas vanished with the new geometry. The comprehensive deterministic and statistic evaluation clearly
proofs the advantages of centre of gravity alignment design through better running characteristics.
Therefore, a better track stability can be expected.
A carriage's centre of gravity is not at the same height as the track alignment, yet contemporary transition
curves (clothoid, Bloss-curve, Schramm-parabola, co sinusoidal curve, and sinusoidal curve) ignore this
fact. This explains why additional forces are needed to move the centre of gravity on elevated tracks.