Title:    Some geometric remarks concerning the overthrow of 
          the different types of railway vehicles when sitting 
          on curved track

Authors:  Eugenio Roanes-Lozano
          (Univ. Complutense de Madrid, Madrid, Spain)

Extended Abstract:

Many railway passenger coaches in Continental Europe, like 
German "m wagen" or French "Corail" coach are 26.40 m long 
and 2.825 m wide.

The reason is that there are size standards in order to allow 
trains to pass from one railway network to another (that is, 
to be interoperable). The maximum size and shape of the 
rolling stock is denoted "gauge". More precisely, the 
following definitions: 

  << - Gauge: A document or drawing describing how big a train 
       may be, or how small a structure may be. It may include 
       a gauge line.  

     - Gauge Line: A notional line, usually described by 
       points, illustrating the limits of a gauge. The gauge 
       line may require adjustments according to gauge rules.

     - Gauge rules: A series of standard conditions under 
       which the vehicle or strucutre must comply with when 
       evaluating against the gauge line

     - Static Gauge: A gauge line and set of rules to be 
       applied when the vehicle is stationary on curved or 
       straight track. In the former case, it is usually 
       necessary to apply overthrow adjustment.

     - Dynamic (or kinematic) Gauge: A static gauge further 
       adjusted to account for suspension movements associated 
       with motion. >>

can be found in the document "Gauging. The V/S SIC Guide to 
British gauging practice", published by the British RSSB (Rail 
Safety and Standards Board). 

Sometimes further distinctions are made, like in Chapter 7 
"Gauging Issues" of S. Iwnicki's  "Handbook of Railway 
Vehicle Dynamics", where a (static) "swept gauge" is 
distinguished: 

  << On curves, vehicles sweep a larger path than on straight 
     track, a phenomenon known as "overthrow". >> 

The standard gauges are defined by the UIC (Union 
Internationale des Chemins de Fer --International Union of 
Railways) in its "505" series of leaflets.

Calculating the dynamic gauge is far more complex than 
calculating the static gauge, as different possible 
deviations have to be taken into account (displacements due 
to the suspension movements, superelevation of the track, 
tolerances, tilting bodies...). There are two well-known 
packages for computing dynamic gauges: VAMPIRE(R) and 
ClearRoute(TM).

Nevertheless, from the geometrical point of view, analyzing 
the influence of the different types of railway vehicles in 
the overthrow when sitting on curved track is very 
interesting, and can be easily performed using a computer 
algebra system such as Maple.

We shall distinguish the following types of coaches: 

- two-axle coaches 
  (obsolete, like Renfe's 7000 or the DR/DB "Donnerb??chsen" 
  --Thunder Boxes), 

- bogie coaches (2-axles bogies) 
  (a "bogie" (UK) or "truck" (US) is a structure underneath a 
  railway vehicle, that can turn w.r.t. the vehicle's body, 
  and to which axles are attached through bearings)
  (this is the most common kind of coaches nowadays), 

- coaches sharing bogies (Jakob-type bogies), 
  (like DB's ICE, SNCF's TGV and AGV, Renfe's AVE series 100 
  and 103 and Civia commuter trains,...),

- Talgo coaches (with independent wheels situated between 
  coaches);

and the parameters considered are: 

- the radius of the curve (only constant radius curves will 
  be considered), 

- the total length of the body of the vehicle, 

- the width of the body of the vehicle, 

- the bogie pivot distance (or wheelbase if the vehicle has 
  no bogies), 

- the bogie wheelbase (distance between the two axles of the
  bogie --if applies),

- ...

Some curious results are obtained, and even a surprise (one 
negative value is obtained for Talgo coaches).

Let us finally emphasize that Talgo company has recently 
released the new train "Avril", of which a high-density 
widebody version will be offered. Regarding gauge, this 
version benefits from the advantages of using "short" coaches 
and situating the wheels at the end of the coaches (the width 
is 3.00 m for the standard version and 3.45 m (!) for the 
widebody one). Other passenger trains, such as Bombardier's 
"Zefiro 380" are also offered in widebody versions (3.4 m
for the "380 Zefiro").