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Spreadsheets for track laying

PostPosted: Wed May 07, 2014 6:15 pm
by AndiS
This will become a small series of useful spreadsheets that give you more control over the track laying details while saving you from doing the maths yourself.

I will cut out as much of the maths behind as possible.

I am well aware that they all serve special needs in special situations, so I published little of this through all the years. But Ruth sending me to the dark domain of track geometry and Jim enabling Excelsheets as attachments brought the whole lot to the light of day.

Shallow S-Curves
Sometimes, you want to offset track by a foot or two, e.g., to change from spacing 3.5 to 4.0 m.

The enclosed spreadsheet takes you through the process - there is much more text in it than figures.
Basically, you play with the overall length of the S-curve and the radius until you like the trade-off between the nearly invisible curve and a length of the S-curve that is limited by your needs.

Re: Spreadsheets for track laying

PostPosted: Thu May 08, 2014 9:51 am
by hertsbob
Excellent. I shall be using that this evening! :D

Thanks, Andi.

Continental Switches

PostPosted: Fri May 16, 2014 11:50 pm
by AndiS
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.
  1. 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.
  2. The speed limit for the diverging branch is given in km/h or mph.
  3. The angle in radians is of cursory interest to the reader, but necessary for further calculations.
  4. 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.
  5. 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.
  6. To bend a switch, enter the radius of the straighter in the blue cell of the line for the chosen switch.
  7. 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 (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.