Large Radius Easements - Yes or NO?

As I have the luxury of large radius (30in) mainline curves in my still in design HO layout, I have been considering the inclusion of easements for those curves. Most of the traffic will be contemporary freight and diesel, with some passenger service (including a Pioneer Zephyr tourist train).
The easements do add to the space requirements (equivalent to 32in radius curves), so are there compelling advantages to using them?
Thanks
Alan

In John Armstrong’s book Track Planning for Realistic Operation he says:

“The improvement is so great that operation is better with the sharp but eased curve than with a more gentle (and much more space-consuming) curve which springs directly from the straight track.”

Later in the same book he recommends a 1/2" offset for 30" curves and the length of the easement is 18", half of which is applied to the tangent track.

I have used them and not used them, operationally the trains run fine if they are appropriate to the curve and run at realistic speeds, but they do look better with easements and seem to run a little smoother. But I don’t run long cars or have diaphragms. Because the offsets are so small I use them for permanent layouts where I am laying flex track.

You could always mock up some curves both ways and see which you like best.

Good luck

Paul

Easements - YES!

Even with 30 inch radius curves in N scale, appropriate easements add to that well-engineered railroad look - especially when used with appropriate superelevation.

In my own work I offset the tangent 10mm at a 90 degree angle to the curve radius, measure 250mm (approximate length of my longest car) back on the tangent and strike a 250mm arc along the curve. That gives me my two end points. The third point is 1/2 way from the curve line to the offset tangent line. Bending a flexible batten (or using Atlas flex track and letting it find its own curve) establishes the easement - without resort to esoteric engineering math.

Superelevation starts from zero at the point where the rails begin to deviate from tangent, reaches half-height at the point where the radius is 90 degrees to the tangent and full height at the point where the rails begin the uneased part of the curve. It should not be overdone, unless you intend to run your Acela, TGV or Shinkansen at prototypical speed. Four (scale) inches of height difference between the rails is plenty.

Try laying a test curve, with easement and without, on a sheet of ply or foam. You’ll be amazed at the difference.

Chuck (Modeling Central Japan in September, 1964 - with spiral easements and superelevation)

Hi Doc,

you still have the wrong conception about easements.

The drawing above shows clearly it is all about offset and required extra length, not about a substitution radius.

John Armstrong too said you could have a smaller radius when applying easements. Keep in mind not the radius it-self is often the critical issue, the sudden change of direction might be the cause off derailments. A to small radius can cause binding problems and even derailments, no doubt about it. The sudden change of direction however causes e.g. a momentarily huge coupler mismatch. Lower speeds will be sufficient to tackle his problem.

An easement is an awesome addition when looking at trains gradually leaning into a curve. The required extra length will often be hard to find when a station is envisioned just beyond the curve; train-length versus great looking curves. In contrary with the required extra length the offset is usually to small to influence trackplans, when laying them out on a subroadbed you have to allow for extra width.

For a 30" radius, with 12" long passenger coaches, the extra required length (see the words of Chuck too) is 12". The total length of the easement will be 24", the offset = (24x24) / (24x30) = 5/6 inch.

When you apply a shorter easement of 18" (the required extra length then is 9") the offset will be:

Offset = (18x18) / (24x30) = 9/20 inch, almost half an inch.

Smile

Paul

Always, yes. The graphic representation of what Armstrong called the “Coefficient of Lurch” in Track Planning for Realistic Operation is invaluable in understanding the benefits of easements. The key is how the illustration shows a sharper radius with easement is smoother than a wider radius without.

Granted, as the actual radius increases, this difference shoud drop. SO maybe if there is room for 60" or larger radius, it becomes less important. 30" is generous but not exceptionally so. It seems that way coming from a history that regarded 15" radius Snap-Track as quite an acceptable solution, and not just for trolley lines, but in the grand scheme of things, an HO 30" radius is still quite a tight curve.

–Randy

Easements my or may not help depending on what you run, if you run small stuff like me, most of the layout rules like easements and s curves mean nothing. If you are running longer car (which you seem to want), then you will have it work better without the s curves and with easements and if you have cars with diaphram’s, then those become almost mandatory!

Paul

I wasn’t referring to a substitution radius, rather the physical space an eased curve takes up in the layout design. ( I let WinRail do the calculation; the result is essentially the same as Armstrong’s calculation diagram).

Hi!

My answer to your question is a resounding “Yes”! Thirty inch curves are certainly not sharp, but they will definitely benefit from an easement. In fact, I believe that any radius curve deserves an easement.

The easement is a help to “train flow”, and also athesthically pleasing to the eye - whether it be the train itself or the bare trackage.

ENJOY!

Hi Doc,

it was you who was talking about a 32" radius as some kind of a replacement for a 30 inch radius with easement. The needed extra length is not 2", but somewhere between 6" and 12", while the extra required width or offset is less then 1". Both numbers have nothing to do with the 2" difference between your minimum radius and the 32" you mentioned above.

You can NOT replace a curve by an eased curve with a slightly larger radius, while maintaining the originally required radius. Hence i used the word substitution. Just like Chuck Tomikawa said: " allow extra length and width to the curve" and you are done.

Since you have the 3’rd edition of Track Planning For Realistic Operation you’ll find exactly the very same information as I gave you on page 116. Though John Armstrong proposed an 18" long easement (so the extra required length is 9" with a 1/2 " offset.)

Not smiling
Paul

For looks, especially ground level photography, yes, absolutely, every time…broad or tight curves, it doesn’t matter.

For function, only in certain conditions. Generally, with modest lengths in frames and with broad curves, they will serve no purpose with our models if photography and looks are not so important. There are no humans or livestock to protect from the lurch imparted when tangent tracks are met with curves at speed. When coupler geometry becomes a problem, obviously easements will help a great deal.

This is all a matter of semantics, guys. I think we all know what an easement is, and how it is applied, no matter how we refer to it.

In all fairness to the OP, he merely indicated that an easement adds to the space requirement on a layout, and that the extra space requirement is equivalent to a larger radius curve.

Rich

hi Rich,

You are making the same mistake, the extra space requirement is not equivalent to a larger radius.

For drawing trackplans just allowing an extra straight at the end of the curve is enough. Opinions might differ about the needed length, for HO values between 6" and 12" are not uncommon, depending on the length of your equipment.

When a 90 degree turn is involved you could replace the 30" radius by one between 36" and 42". You could then talk about a substitution radius; however not the 32" Doc mentioned.

If however a 180 degree turn is involved, your blob does not become significantly wider, maybe one inch. The extra length required remains 6" to 12"; in this situation it is completely impossible and unnecessary to talk about a substitution radius. Adding an extra straight at the ends of a curve is all that is required.

Paul

Paul,

With all due respect, I don’t think anyone is making a mistake here.

Using your term of a “substitution radius”, you would only create a larger radius curve without an easement. What the OP is doing is correctly applying an easement and adding to the space requirement, albeit a small one.

As I see it

[:)]

Rich,

a last try

I used the word substition radius, made it very clear however it meant NOT just a wee bit larger radius. That was done by Doc, when he talked about a 32" radius for an eased 30" radius.

I am/was concerned about the needed extra space, hence the content of my remarks. Just adding 2" to a radius as Doc did, is, is way apart from what is needed. John Armstrong is talking about 9" extra length and 1/2 " offset.

Paul,

Plus ca change, plus c’est la meme chose.

When all is said and done, the OP will have created an easement.

[;)]

Rich

Just curious here. Using the bent stick method will provide a constant radius easement rather than a gradually decreasing radius? Or does having the stick following the curve radius at one end and the tangent at the other provide something more like a true easement?

Bill

That’s a good question.

When laying track, how do others decide where and how to place the easement?

Rich

[quote user=“richhotrain” That’s a good question.When laying track, how do others decide where and how to place the easement? Rich
[/quote]

I just use the build-in tool that WinRail provides (also in Atlas RTS). Allows setting radius, length of easement (in degrees) and whether the curve is just a single easement into a curve or a complete curves (easement to constant to easement). The result is a very good approximation to the manual method illustrated in John Armstrong’s book.
Using the tool, one can create a 90 degree curve that is nothing but easement, no constant radius section).

Alan

I just use the build-in tool that WinRail provides (also in Atlas RTS). Allows setting radius, length of easement (in degrees) and whether the curve is just a single easement into a curve or a complete curves (easement to constant to easement). The result is a very good approximation to the manual method illustrated in John Armstrong’s book.
Using the tool, one can create a 90 degree curve that is nothing but easement, no constant radius section).

Alan
[/quote]

Rich, given the parameters I stated above, the easements pretty much place themselves once the curve center has been established. You just offset the tangent 1/12 the length of the longest car likely to use that curve and use the diagram Paulus Jas provided to establisn the points of true tangency and true curvature.

Alan, that nothing but easement' curve is a parabola. The tangents can be at any angle, but when they go under 90 degrees the legs’ start reaching for infinity (they get there at zero, when the tangents are parallel.) My as-yet-unbuilt `dance down the canyon’ will be several connected parabolic reverse curves - no true curves except at the ends, no tangents. Speed limit, 40KPH (close enough to 25MPH not to make a difference.)

Chuck (Modeling Central Japan in September, 1964)