Any chart of curve track #'s?

[ebtnut]

My memory was a bit faulty.  The correct formula is 5,730/degrees of curve = radius.  Therefore, that 36" radius curve is almost a 23 degree curve. 

[Len]

There's an explanation with pictures over on Wikipedia:
https://en.wikipedia.org/wiki/Degree_of_curvature

Len

[jward]

I've always wondered why model railroad curves aren't measured in degrees like the prototype.

The two methods are apples and oranges.It would be impossible to measure curves by degrees the way the civil engineers do. In their measurement, the degree of curvature has nothing to do with the total arc of the curve. In model railroading, the arc is much more important.

[bbmiroku]

ebtnut, that's the formula for finding the curvature of an arc.  But the sectional track Bachmann produces is set at standard arcs and standard degrees.  The only difference is the radius of the circle formed.

[jward]

bb don't pretend to understand what you don't.

What ebt posted is the formula for finding the "Degree of curvature" which is a civil engineering way of expressing the sharpness of a curve. It is roughly equivalent of what we call radius. In engineering, when laying out a curve, it is far easier to mark the curve in 100 foot segments than to find the center point of the arc and measure from there. The center point of a curve may be a mile or more away from where the actual curve is. "Degrees of curvature" as expressed by civil engineers has nothing to do with the total degrees in the curve itself.

As an example, the sharpness of Horseshoe Curve in Altoona, PA is 9 degree 30 minutes. But the total curvature of the arc is 225 degrees. When you look at the curve from the air, you see the 225 degree arc. When you are at ground level, in the park at the center of the curve, it wraps around you on three sides. But if you looked at the track charts (Engineering diagrams) for the curve, all you'd see are notations of the start and end points of the curve, and the figure 9degrees 30 minutes.


Degrees of curvature as expressed by the real railroads and by model railroaders are two completely different things.

[Trainman203]

Man. Too much math 😱😂.  I gotta go lay down.😂😂

[jward]

Man. Too much math 😱😂.  I gotta go lay down.😂😂

Not me. I am fascinated by the engineering process.

[J3a-614]

Here's a table that might help those who aren't into the mathematics.

http://www.trainweb.org/freemoslo/Modules/Tips-and-Techniques/degrees_of_curve_to_radius.htm

For some perspective, a 5 degree curve is considered moderately sharp; it limits train speeds to about 60 mph or sometimes less.  It scales out to just under 158 inches radius, or more than 13 feet!!

A 20 degree curve is very tight; large engines such as 4-8-4s and E-unit diesels can negotiate them at a walking pace to get to or from an engine terminal, and do so with flanges howling.  But even that scales out at almost 40 inches!

The B&O didn't run passenger service on curves sharper than 16 degrees (49.5 inches).

Cass Scenic, a former logging railroad  that operates exclusively with geared steam engines, has curves as sharp as 40 degrees.  That scales out to something we use, at just over 20 inches!

Obviously we have to compromise considerably in our curves!

On thing that would help, both in operation and appearance, is to work in a graduated or easemented curve.  This is a curve of constantly changing radius, typically a cubic parabola, and provides a gradual change from straight to curved track.  The real roads calculate these with great precision in the field, but we can take shortcuts, such as using a flexible stick between the tangent or straight track and the actual curved radius.  It's not the cubic parabola, but it does give a smooth, flowing transition from the tangent to the curve.

This not only makes the appearance better (trains flow into the curve instead of jumping around like, like Lionel toys on sectional track do), and you get less couple swing at the entrance of the curve.  The latter can actually let you get away with a tighter radius than a curve without such a transition.  

Even a larger section of sectional track (say 22 inch radius leading into 18 inch radius) can help.  

The only thing to keep in mind is that this does cut your straight track lengths down a little.  

Your minimum easement length should be about as long as the longest car that will be negotiating the curve.  

It's worthwhile to use easements even if you're modeling a prototype with almost streetcar like curves, such as some industrial roads, and for the reasons mentioned.  Arguably, they are even more important on such a minimum radius railroad than on one with more generous curvature. 

It may not look like it, but trolley lines, with street corner curves as sharp as 35 feet, had graduated curves. 

In some cases, using a switch at the start of the curve can give you an easement effect if you are using the curved or angled leg as the curve approach--and you get a location for an industrial spur, too.

[Trainman203]

Man.  I have to think too hard at work all day long.  When I first started work a million years ago I was fascinated by all kinds of work generating stuff too. 

But I'm at retirement age!  Weeks away!  Full time model railroading is imminent!