OK,I’ll likely look a bit ignorant to some,but there’s a data I read about frequently on this forum and others that I don’t really understand.To me,curves have a radius that sets the sharpness of said curves and then they have durations that are part of circles expressed in degrees.Put simply,to me a 90 degree curve should be a quarter turn and a 180 degree one is a half turn.
However,what puzzles me is that I read all the time about X or Y degrees turns that don’t specify any radius,so how can one draw such a curve on paper?Is this a standard geometrical curve meaning,for example,that an X degree curve will be the same in N scale as in HO?Is this a specific railroad design term?I’m not too bad with geometry,but this I’ve never learned.To me,regular curves have two datas.Thanks.
I’ll give this a try as I understand it. I was a bit confused when I first encountered some track with degrees on it,thought I had some wider radius track than it was. I THINK I have the idea, but may be wrong.
Radius is half the diameter of the circle that the curved track will make.
Degree is how much of that circle is in one piece of track, regardless of the radius. For example if it takes 4 pieces of track to make a circle, you have a 90 degree section. If it takes 8 pieces to complete the circle it is a 45 degree section. I have seen some HO track marked with some really strange degree markings and I am not sure if it takes a certain number of full pieces to make a complete circle or if some require partial (1/2 or 1/3) sections to complete the circle.
A curve is determined by either the radius or by the degree of curvature. The degree of curvature is, IIRC, calculated by a cord of 100ft. and the angle which is derived from the corresponding triangle. The higher number, the smaller the radius.
Get out your old high school geometry set and get some graph paper. A 90 degree curve is always 90 degrees. What changes is the distance traveled to make the turn. The larger the radius the longer the distance traveled to make the turn.
I bought this big pad of graph paper at staples for $8.00. The squares are 1 inch across. 1 inch equals 1 foot. Take the compass out of your high school geometry set and use the squares as a guide to set your radius. I made a radius legend in the corner of the paper using a ruler with millimetres on it. I then would set my compass using the legend. It’s not perfect, but got me close enough.
On the actual layout I made some cardboard templates to make sure I did not go under my minimum radius as I went. I like the look of a curve where the radius changes through the curve. As long as you don’t go under your minimum a changing radius looks more natural.
Cardboard templates to make sure I meet radius minimums.
Brent, everything you said is exactly right if one is talking about degrees of a circle. But I do not think that is what the OP is asking about. He wants to know what is meant when a prototype railroad states something like " the main line had 10 degree curves". As Sir Maddog said this measure of degree of curvature is based on a 100 foot cord. A 10 degree curve is considered very tight on a prototype railroad.
Starting in reverse order,
Yes regular curves have two datas. Actually there are many more than just two ways to describe a curve mathematically for engineering.
To deal with curves measured in degrees using geometry one would have to look up the formulas related to cords. An easier way is to break out the trigonometry.
Yes, This is a standard geometrical curve definition that is the same in all scales especially the 1:1 prototype. The prototype railroads almost never measure curves in radius.
To draw a curve measured in degrees on paper is not hard but a bit hard to explain. Here is a page posted by DSchmitt back in 2003:
Sectional track is sometimes described in how many degrees of the circle the track is. For example, for sectional track that is 12 sections to a circle each section would be 30 degrees (360/12). This is not the same as the railroad degrees and is not sharpness of the curve. It is how much of the circle the track piece covers.
Thanks gentlemen for your great answers.In the end,it is somewhat what I thought it was…a standard curvature that will look the same on any plan,whatever the scale.What I didn’t know was how to achieve it on a drawing as I didn’t know what were the basic parameters.However,it isn’t a better way to design a curve on a layout plan so I’ll stick with using the radius to draw.But still,I’ll go to bed tonight feeling a little smarter.Thanks again.
Well keep in mind turnouts (switches) are measured by degree in a sense, the “number” of the turnout indicates the degree that the track diverges from the straightaway. The larger the switch no., the more gradual (and lower degree) of the switch.
Think of it this way…in the early days they used a chain to plan where tracks would go. If you were adding a turnout to a straight track, if you measured 10 chain lengths on the straightaway for every one chain length you diverged to the right or left for the switch, it would be a No.10 turnout. If it only took six chain lengths measured along the straight away for one chain length of divergence, it would be a No.6 turnout.
It really worked the same measuring curves on the prototype…if you measured 100 chains straight and a curve was three chains off center to the right or left, it would be a 3 degree curve.
In the US, curves are described in degrees because it is easy to set up a theodolite on the right of way centerline and measure the angular offset between adjacent 100 foot chords (Yup, that’s where the measurement in degrees comes from!)
Interestingly enough, my own prototype, while undoubtedly doing the survey work in the same way, describes curves by radius (in meters) on little markers affixed to ties at the entrance to each curve.
Chuck (Modeling Central Japan in September, 1964 - with curves defined by radius)
