Had a visit yesterday to a new - for me - model shop on Carnforth Station, of Brief Encounter fame with Trevor Howard and Celia Johnson (1946). Marvellous shop with lots of goodies, the reason for the vist was afore mentioned switches, never seen one before, and I have to say, WOW!! They look fantastic, but what a size, they will eat up a lot of room on my set up. Are they as good as I have been told? They look like they should be with the proper rail built frog. I didn’t buy one but I came away with a Piko ready built water tower for £29, bargain!
Kim, one must bear in mind that they are NOT radius switches, they are #6 divergent switches! They diverge from the straight at a 9.5 degree angle. Unlike LGBs they cannot replace a curve section in a circle!
They use a 100ft “cord” as the standard, lay that cord inside the radius of a curve. Run two tangents from where the end points of the cord are on the radius to the center point of the radius. The included angle between the tangents is the degree of curvature for that radius.
Another way of looking at the railroad’s ‘degree of curvature’ and how it’s defined.
In Geometry, a chord is a straight line connecting two points on a circle. A chord that passes through the center of a circle is the diameter.
The degree of curvature on the railroad is the answer to the question. ‘How many degrees does a 100 foot chord subtend?'. In layman’s talk, if you extend lines from the ends of the chord to the center of the circle, what is the angle between the two lines. (In geometry talk, these extended lines are perpendicular to lines of tangency to the arc at the ends of the chord.)
Example 1: the degree of curvature is 1 degree. The track therefore curved but one degree during the approximately 100 foot length of track. It would take 360 sections of track, then, to complete a circle because there are 360 degrees in a circle. The length of track for that circle would be 360 times 100 feet or 36,000 feet. Dividing 36,000 feet by pi (3.14159) gives the diameter or 11,443 feet. Half the diameter is the radius: 5,722 feet(all numbers rounded to the nearest foot).
Example 2: the degree of curvature is 3 degrees. The track has curved 3 degrees during the approximately 100 foot length of track. Again, it would take 120 sections of track to complete a circle as 360 degrees divided by 3 equals 120. A circle with a circumference of 12,000 feet has a diameter of 3,814 feet and a radius of 1,907 feet.
Note that these calculations are approximations as a chord is always slightly shorter than the arc it subtends. But for angles less than 5 degrees, the two lengths are equal for all practical purposes. As an example of how great the difference can get, a 60 degree curve would have a radius of 100 feet but the circumference of that circle iwould be 629 feet, the chord is still 100 feet, but the arc it subtends is 629 feet divided by 6 or 105 feet rounded to the nearest foot
Looking at the drawing data it would appear that using a 100ft Cord and the resulting calculated angle is somewhat more complicated than stating the radius - be it in Imperial or Metric measures.
Railroads cannot use a trammel and circle center to lay out an arc or a curved section of track. Rivers, mountains, hills prevent this. But a table can be prepared to use a simple method of using a straight line and measuring offsets from this straight line. The table has offsets for the various curvatures that are required.
Some 60 years ago while in high school, I came across a book that described this method.
At the start of the curve, Point A, extend a line 100 feet to Point B.
Consult the table for the offset needed for the desired curvature; at Point B, measure the offset at right angles from the line and establish Point C.
Sight a straight line from Point A to Point C and extend the line 100 feet to Point D.
At Point D, using the same offset from step 2, establish Point E.
As in step 3, sight a straight line from Point C to Point E and extend the line another 100 feet to establish another point.
This process is continued until the straight line is headed in the proper direction (called a tangent) that can be extended to the start of the next curve.
Flags are positioned at points, A, C, E, etc., and the track crew grades the right-of-way accordingly.
The table that I found had offsets specified for the mid points of the extended lines but I doubt that they were really necessary although they would define the curve more accurately.
ER, it’s not surprising that degrees of curvature are not mentioned in an European book as it’s strictly American, based on that 100 foot chord. Doesn’t translate well into metric.
Don’t know about Canada, but a cord in my dictionary is something flexible like a cable or a heavy string, and a chord is a straight line between points on a circle or three or more musical tones, triads, dominant sevenths. etc.
Your drawing of degree of curvature was neat! Wish I could master posting pictures, etc.
