hi,
The prototype uses curvature degrees in stead of a radius. The NMRA, e.g. has a table, but I would like to know the math behind it. I remember having seen it somewhere long time ago.
Must be comparable with switchnumbers I guess.
I can imagine the “100 feet chaingang” could easily measure the angle between the tangent(AB) and the cord(AC, AC = 100 feet). If that’s the angle, the math is straight forward.
If otherwise, please explain or tell me were I can find the answer.
Paul
Hi Paul,
here is the explanation!
hi Uhlrich,
you are my hero. I added a drawing in my original posting. Your info made it clear. What a difference with all the stuff I found in threads dating 2 years back.
a very simple formula: for HO Radius in feet = 5700 / ( angle x 87) or even more simple:
Radius in inches (rounded) = 790 / angle of curv. and the angle of curv. = 790 / radius
And the angle used by the “100 feet chaingang” is half the angle of curvature of course.
You provided me with a great site, and a little bit of math (radians) did the trick.
BTW, I had send you a private mail, but all are lost? Just to wish you and Petra (no kids?) a happy New Year and above all a good health.
Are you sure about your “new” house now? I hope and pray you will be able to recover, so you and your family can start looking forward again in 2010.
Paul
This link on degree of curvature includes a table and is very easy to understand. It has been posted multiple times on this forum in the last couple of years, at least.
Degree of curvature has nothing to do with switch number.
hi alco fan,
i am rude tonight, but it would help if you would have read my first posting.
this was the very first thing I said, but I wanted to know the math behind it and the definition.
Ulrich presented me a proper site. I confused the angle of curvature with the angle of the “chaingang”. The beauty of math is: it comes all down, sometimes, to a pretty simple formula. (C x R = 790 in HO; with C = curvature in degrees and R = radius in inches)
To me just as easy to understand, and I don’t need a table nor a calculator to get a result. BTW I am and was always curious about the why.
If in a switch, the part from the points to the frog could be seen as a curve with a fixed radius, the angle of the frog would be the very same as the curvature. Both angles are twice the angle of the “chaingang”.
Railroad workers carried a 100 feet long chain with them. The chain was fixed at a point on the line, and the foreman directed them to the next point of the line. The angle between the tangent and the chain could be measured. By using the proper chaingang-angle (0.5 C) the appropriate radius could be kept. In real life the formule was C x R = 5700. The 100 feet chain is shorter in HO (devide by 87 first) and the radius is given in inches, not in feet; so multiply with 12 and you get the formula above.
Real railroads measured the length of their lines by counting the number of chains. Because in curves the arc is a bit longer then the cord the real length was a bit larger too.
Paul