A "true" easement is a variable-radius curve that gradually transitions between the overall curve's radius, and tangent (straight) track. With sectional track, we only have discrete radii of trackage with which to work. But we can assemble a curve from pieces with different radii, to approximate easements, while still fitting in the space allotted. Below is a Unitrack doubletrack oval; the outer track radius is 12-3/8". Shown are two 180 degree eased curves (on the right) and one pair (on the left) of eased 90 degree curves, all using standard Unitrack sectional track pieces. If necessary, the straightaways of the eased ovals can be shortened to fit the same space. I didn't show that because the tracks would overlap too much and be difficult to distinguish. Note that all easements that will fit in the same space, will necessarily contain tighter radius sections than the uneased curve contains. But since these minimum radii are bounded by broader radius curves, the reliability (and appearance) of the entire curve is improved. Stated another way, transitions between tangent and minimum radius trackage is operationally more severe than the same (or even a bit tighter) minimum radius curves embedded in the middle of a broader radius curve.
Oops, I forgot, the left hand side is actually two different 90 degree eased curves, not two identical 90 degree eased curves. The two different eased curves have the same relative endpoints as each other and the original uneased 12.375" radius curve.
It was advice just like this I received when starting my Unitrack layout that helped me to plan for a smoother running layout. Make a Sticky out of this!
this is whats needed more ways to setup unitrack. when i built mine i didn't even think about this easements stuff. Dang now i have to go back and replan my future layout....Thank you Andy
Interesting... (for math nerds, anyway) Apparently the definition of curvature as the inverse, or reciprocal, of radius, goes back quite a while... According to a recent article in Quanta Magazine, "Two Students Unravel a Widely Believed Math Conjecture" (https://www.quantamagazine.org/two-students-unravel-a-widely-believed-math-conjecture-20230810/), "About 2,200 years ago, the Greek geometer Apollonius of Perga inquired about how circles would fit together if they all touched each other at a single point." Apollonius used the reciprocal of radius (e.g. 1/R) to define curvature. It turns out, that if you start with three arbitrary circles with integer curvatures (in any unit), touching each other at single points (not overlapping, but touching), then inscribe a circle around them, touching each circle only once, then you can continue to pack the outer circle with smaller circles, they will always have an integer curvature (1/R=N). Well it turns out these two students disproved the 2200 year old conjecture... but the definition* of curvature as the reciprocal (1/r) of the radius goes back at least 2200 years. I knew it wasn't new, but wow! *Railroads define curvature of trackage as the angle of track deflection from straight (tangent), in 100 feet of survey chain. This definition made surveying the track route much easier than locating and using the center of radius for the curve, especially in difficult terrain, where the center may be inaccessible, whether buried in a mountainside, or floating out in the air. Okay... back to your regularly scheduled railroading.
If I had to figure all that math cr*p out when I laid my track 12 years ago...I would still be at it !!!! Straight into a 15 radius curve all the way around works for me. No derailments in 12 years and I don't give a hoot if the N Scale engineer gets whiplash when the train goes into those curves !
This right here! I had some pretty tight corners when I first started, redesigned everything for much wider radius. I have a couple of 13.75" corners through town, but other than that everything opened up to 15" or+. No sense having Shinkansen "bullet trains" if you have to run them at 1/4 throttle. 15-17" corners all around, plan to set them puppies free
And here I am trying to get my Ntrak club to change from three-foot corners to four footers. A three-foot corner has max radii of 28, 26. 5 and 25 inches. Add a one-inch deflection for a real easement and the three track radii are reduced to 27, 25.5 and 24 inches. A four-foot corner would have max radii 12 inches larger than the three-footer. With a 39-inch radius that curve only scales out to a prototypical 520-foot curve, still a sharp curve for mainline railroads. Horseshoe curve on the old PRR mainline had 11-degree curves, the smallest of which was about 610 feet in radius. An N scale 15-inch radius would scale out to a 29-degree curve while a 9.75-inch radius would equal a 45-degree curve.
I have minimum 24" curves on my layout and I don't need easements. I can see them being necessary for tighter radius curves, but not for 24". As someone mentioned earlier, there's no point in running your Shinkansen at 1/4 throttle!
Although I appreciate the math and geometery that goes into most layouts. I don't always rely on it. I agree with Traindork and Big Jake. The thing is once you get out to 15" radius curves an easement isn't all that necessary. It's the tighter radius curves that demand such attention. I built in my own version of easements and ignored the math. Looking for the results I wanted and usually got. Once again I didn't use sectional track with built in easements. Flex track to the rescue. Later!!
Note, the Unitrack Double Track Easement Curves are not radius easements at all. They only provide the transition into super-elevation, and have the same radius choices as the non-easement double track sections. They do have less angular span (22.5 degrees each) than standard super-elevated curves. Of course, if you are using the shorter radius super-elevated doubletrack curves, you can "ease" radius transitions into them by substituting longer radius super-elevated easement sections.
Okay, I took mechanical engineering in high-school. Later Architectural drafting. There are elevations, easements and they aren't just focused on one thing. With regard to elevations I once again built into my layout the super elevations I wanted. My problem was and still is I have some stoves that need to run flat. Otherwise they jump the track. So super elevations were minimized. I'm happy with the results. More on this later if you want ideas. Isn't this fun??
Fun?! That's why I enjoy this board! What; I might learn (or teach) something new?! That's the frosting on the cake.
Yes, but only in spans of 45 degrees. The easement sections span 22.5 degrees each, for a total of 45 degrees (ease-on and ease-off of super-elevation). So all super-elevated curves' total spans, including both easements, are limited to increments of 45 degrees.
What I should have said was does Kato make double-track curve sections that are BOTH non-easement AND non-super-elevated?
