Page 304 - 360.revista de Alta Velocidad - Nº 5

Balmaseda, Lucía. Gallego, Inmaculada. Sánchez-Cambronero, Santos. Rivas, Ana.

1. Background

The calculation of the vertical forces on rail tracks is traditionally determined from a static
analysis. However, experimental measurements confirmed that the loads that are transmitted
to the rail track increased with speed. This finding prompted research in the railway field that
proposed the use of a dynamic amplification coefficient .

The expressions of Whinkler and Pihera in 1915, Driessen in 1936 and Schramm in 1955 are the
most notable expressions among the first empirical expressions that were proposed to quantify
the magnitude of this coefficient.

During an extensive test campaign by Deutsche Bahn (DB) in the 1960s in Germany, the test
results indicated that the dispersion of the dynamic loads increased with speed compared with
their average. The magnitude of these dispersions was directly related to the quality of the rail
track and the vehicle. These results caused Birmann to propose the following formula to the
Committee D-71 of the ORE in 1966:

In 1969, Eisenmann proved that these dispersions follow a normal distribution, as shown in
figure 1.

Figure 1: Dynamic oscillation of the load per wheel. Source: Teixeira, 2003

Based on the experimental results, Eisenmann proposed an empirical formula to determine
C :
d
= 1 + ∗ ∗ (2)

where
is the factor of probabilistic certainty such that

=1 68.3% of the values,
= 2 95.5% of the values,
= 3 99.7% of the values;

is a factor that is dependent on the condition of the rail track,
= 0.1 very good condition,
= 0.2 good condition,

= 0.3 poor condition,
is a factor that is dependent on the running speed,

302 360.revista de alta velocidad