Outside UK, switches are made from prefabricated parts that are available in a number of shapes. Most notably, the frog angle is fixed and generally linked to a certain maximum speed and a certain radius (or two).
There is always a "straight" track, and a diverging one. (The French have symmetric Y switches but I cut them out for now.) If both branches are curved, then a straight track is taken and bent, leading to a "straighter" track and a diverging one, either to the inner or outer side of the curve. The frog angle is retained in this process. There are limits to the amount of bending, but for the purpose of RW we can skip the research of the prototype in this regard. It is easy to see when the minimum radius is reached.
I restricted myself to Germany, North America and France mostly because I have data for those. But also because they show different approaches to switch definitions that will be found in other countries, too.
The enclosed spreadsheet offers a few things.
- It gives an impression of the popular designs in terms of angle and radius. The angle is specified as 1:x in Germany and US, and as tangent in France.
- The speed limit for the diverging branch is given in km/h or mph.
- The angle in radians is of cursory interest to the reader, but necessary for further calculations.
- The curve length is of critical importance in combination with the radius. Draw the arc of a switch at the given radius and length (+/- 10%) and you got the listed frog angle spot-on enough.
- For the purpose of cross-overs, the length of a straight track between two switches of the given type is shown - for various track distances. Add a straight of the given length to a curve as specified above and snap-to-track should complete the cross-over by a curve that is more or less identical.
Standard distances in Germany are 3.5 m (mainline old), 4.0 m (mainline newer), and 4.5 m (yards and high-speed mainline). North American mainlines are 13 ft (almost 4 m) apart, otherwise 14 ft is the minimum and yard tracks (ladder tracks) are 15, 18 or 20 ft apart. The minimum six-foot in France measures 2 m leading to track spacing 3.57 centre to centre. 4.4 m is also often seen in switch arrangements. I stuck in 4.0 for lack of alternatives.
Note that a few cells are empty, showing that you cannot have a cross-over using this switch with this track spacing. - To bend a switch, enter the radius of the straighter in the blue cell of the line for the chosen switch.
- The next two columns show the radius for a diverging branch towards the inner side of the curve formed by the "straighter track", and to the outside. A negative radius means that the curve is turned to the opposite side, forming an asymmetric Y-switch.
Notes on the sources:
German track geometry is described under heading
Oberbauvorschriften at
epoche2.de. (The site sometimes prohibits deep linking but currently it seems to work.)
North American speed limits were taken from
Wikipedia.
North American track spacing was taken from random rule collections for
Nevada and
Canada.
Radius and length of the North American switches are calculated based on the
writings of J Calvert aiming at start of the straight section just before the frog, which is estimated as 15 cm inside the rail.
Loads of scanned French prototype diagrams including trackwork are found
here and in other posts in the same forum.
I lifted the French speed limits and the geometry of the high-speed switches from
some forum post.