Hi all,
Many posts mentioning curves especially for minimum radius. I understand 18" radius. What is implied with, say, 18 degree curves? 360 degrees in a circle no matter the radius, so obviously I am missing a concept.
Thank you in advance for the education.
Pete
http://mysite.du.edu/~jcalvert/railway/degcurv.htm
Basically, they place a chain at one point along a surveyed path, measure out another chainlength, and then take the angle needed to maintain their centerline as the surveyed path suggests it should.
-Crandell
http://mysite.du.edu/~jcalvert/railway/degcurv.htm
Smile,
Stein
Thank you!
The chord is the missing (chain) link. Interesting and educational - unlike radius, the larger the degrees, the tighter the curve.
Not exactly, when degrees are measured, what is taking place place is the measurement of a angle at three points. Radius measurement is measuring the distance from a fixed point to a circle’s edge (or 1/2 the diameter of a complete circle).
This is how I measure radius relating to MRRing. Let’s say we want an 18" radius. Take a string and tie it to a fixed point around a nail afixed into a sheet of plywood. Then measure the distance along the string out to 18". Now wrap a pencil around the string at the 18" point and then pull the string tight and pencil in the curved line onto the plywood letting the string be your guide from the center point (the nail.) . That is the 18" radius that is drawn onto the plywood. … I believe what you meant to say is the tighter the degrees the tighter the circle which is true…chuck
Chuck, I believe he has it correctly. Small radius number means higher degree number curvature. Smaller radius number means tighter curve with that higher degree of curvature.
A curve of only 6 deg is relatively mild, but not exactly high speed. We would all love such curves on your layouts. With as few as 6 deg of curvature, the radius would be prohibitively large on all but monster layouts.
-Crandell
Railroad surveying uses a 100 ft chord, highway surveying uses a 100 ft arc.
Here is another website that explains things a little bit differently, and also has a table which shows degrees of curvature converted to HO and N scale radii: http://www.steamlocomotive.com/model/curve.shtml
The simple way I think of it is (simple is the best I can usually do), a circle is 360 degrees. If it takes 4 pieces of track to make a circle, each piece is 90 degrees, 8 - 45 degrees, 12 - 30 degrees, etc. It is a portion of a circle at that curvature.
Hope this helps.
Good luck,
As was stated, the curvature in degrees is determined by trigonometry, and requires that you can determine TWO of the following:
In the field, it is frequently impossible to put a theodolite at the center of the curve and measure the angle directly. However, it is usually possible to determine the angle between two adjacent 100 foot chord lines - which is the complement of the desired angle.
An extreme example - a curve with a 100 foot radius would form an equilateral triangle. The adjacent chord lines would meet at an angle of 120 degrees. Ergo, that’s a 60 degree curve.
Too tight? On the Uintah the tightest curve was 68 degrees. In Japan, two of my prototype favorites (one standard gauge, one 2.5 foot gauge) had 30 meter radius curves - close enough to 100 feet for most purposes.
Chuck [Modeling Central Japan in September, 1964 - with some 28 (scale) meter radius curves]
Every thing you say is true, BUT that is not the “degrees” that is being talked about here. This is exactly the difference the original poster was asking about. Degrees in this case is not how much of a circle is complete but another measure of the tightness of the curve. In HO scale 18" radius = 45 degrees of curvature 80" radius = 10 degrees of curvature.
As the others have said, the measure of degree of curvature of a track is the amount of curvature it makes given a 100 foot cord. One can figure it out with algebra/geometry (angle bisection, opposite interior angles, and all that 10th grade proof stuff) but it is a whole lot easier using trigonometry (arctan). A 10 degree curve is considered tight.
My brain hurts…
Here is a link to a chart comparing Degree of Curve to Radius.
http://www.trainweb.org/freemoslo/Modules/Tips-and-Techniques/degrees_of_curve_to_radius.htm
For the overall picture that would be correct but the curve angle is much smaller and depends on the radius in your example. A 90 degree turn would be an L shape. Most loco’s cannot negotiate such an angle. [:-^]
The link posted above is a good quick guide. In a nut shell a curve is basically numerous straight sections with each section building on the other with slight angles. Depending on the application there are standards on how long those straight sections are before making another bend.
If you think about it, if railroads in the past didn’t use a bunch of straight sections with small angles at each link, they would have taken forever to attempt to heat and bend the rails.
A 90 degree curve would have a (prototype) radius of 70.7 feet - generous by streetcar standards and well within the capability of ‘critters’ and steeplecabs.
Rail bends much more easily than the above would indicate. Just watch a string of cars loaded with 20 strings of Continuously Welded Rail squirm around the curves of a mountain grade. The rollers complain, but the rail bends - and that’s modern heavy rail, not the lighter sections used in years gone by.
Chuck (Modeling Central Japan in September, 1964 - on the verge of laying CWR)
Keep in mind on the prototype, the rail doesn’t have to curve very much since prototype curves are generally much more gradual than we can do on a model railroad. High speed mainline curves are generally kept to low single-digit degrees of curvature. If you look at the trainweb link from above, a 2-degree curve works out to over a 394" radius curve in HO. The curvature on a single piece of flextrack would be almost indistinguishable from a straight track.
I was just reading a book on “The Dinky”, C&NW’s narrow gauge line in SW Wisconsin. It’s equipment was severely limited due to a couple of 250’ radius curves - only the smallest engines could get around them, and “half size” narrow gauge cars.
In HO, that curve would be 34"R - what we consider “broad” curves suitable for large engines and 80’ passenger cars with body mounted couplers.