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Easement flex angle?

Started by magnus, November 26, 2021, 09:29:28 pm

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magnus

In AnyRail, Easement Flex takes 3 inputs: Angle, Radius, Left/Right. Radius and Left/Right are straightforward, but what Angle do you guys give it? Sometimes it's given by the layout, but certainly not always. Any references?

In John Armstrong's books, he recommends the offset of the center of the Easement should be 1/2", but that is more a rule of thumb using certain assumptions of the cars (9" long) than any engineered calculation.

Also, most turnouts have a built in easement on the diverging track. For example Fleischmann HO Profi track has an 18° angle going in to a 647mm radius. If I want a 25° angle on my easement, I assume I should only enter 7° in AnyRail?

rlcross

Magnus, there are several formulas for calculating easements, plus the offset method for physically laying one out like Armstrong in his book.  None of these use the exact same inputs as AnyRail unfortunately.  Radius at the end of the easement is common to all.  When I dug into the two methods (mathematical and physical) one thing that they both produced is that the easement would go about 30 degrees into the circle from the point of tangency.  So in effect the easement replaces about the first 30 degrees of the turn.  In AnyRail terms, this would mean that a 90 degree turn would have a 30 degree easement in, a 30 degree circular curve portion, and a 30 degree easement out.  For greater curves, I use 30 degree easements, with the required circular curve between them.  For under 90 degree curves, my rule of thumb has been to use the 1/3 easement, 1/3 circular, 1/3 easement relationship.  So I use 15/15/15 for a 45 etc.  I try to not use less than 15 degree easements, just because I like to have the effect of the easement more pronounced than smaller degree easements produce.  For smaller curves, you can use just use two back to back easements.   Say 15 easement paired with a 15 easement and no circular portion for a 30 degree turn.

With regards to turnouts, I'm not familiar with the Fleischmann HO Profi track.  But on my Fast Tracks straight turnouts, the points to the frog has a curve built in.  In the case of my #6's, that's a 9.46 degree curve.  But from the frog on, the divergent rails are straight so there is no radius built into the divergent rails.  On curved turnouts they have a radius throughout, so when you exit a curved turnout you can continue the same radius without any easement.

Its all just rules of thumb to produce a pleasant looking curve so design-wise, it's up to you.  Just my two cents.

Richard

magnus

Thanks Richard, that's very helpful. The 30° rule you use seems reasonable, and I also like the 1/3 rule and the 15° min rule. Do you have any references to those rules? I looked a little bit, but could not find any definite advice. I have used 25° so far lacking anything better. (There is another thread on the forum where I'm trying to compute the input parameters for use in AnyRail.)

Attached is a pic of the Fleischmann turnout. I put the standard corresponding 18°/647mm curve section next to it. Looking closely, I'm not sure the turnout actually has an easement; the diverging turnout track looks exactly like the 18°/647mm curve both before and after the frog. The longer turnout on the left seems to have an easement though, and it's also 18°.

Interesting that the FastTrack turnout is straight after the frog. I see that Walthers and Atlas are too. But Marklin/Trix, Roco, Peco all seem to be curved after the frog. Seems like there is a US vs Euro difference here. Japanese Kato seems to be curved as well. That could be a reason why the US system of #4, #6 etc. turnouts is not used in Europe.

QuoteIts all just rules of thumb to produce a pleasant looking curve so design-wise, it's up to you.  Just my two cents.
Pleasant looking is one consideration, but I also think another consideration is how robust your trackwork will be with respect to derailments. That's what John Armstrong argues anyway, and he is usually right. :)

/Magnus

rlcross

The only basis for my 30 degree rule of thumb was a rough comparison of the results of the mathematical and physical results.  They each stipulate a resulting length of the easement, which when placed on the tangent line and the circle, yielded an end for the easement approximately 30 degrees into the circular curve.  I've been using the approximation since just for simplicity.  One of these days I should take the time to figure out the answer using the specific length results and calculating the intersection point on the circle (the angle). 

Agreed, Armstrong talks about easements reducing the risk of operational problems like derailments.  I liken it to what we experience driving a car.  Even at moderate speeds, if you crank the wheel into a turn (example hand at 12 o'clock whipped to 3 o'clock quickly and then back to 12 quickly after your turn) your turns are jerky and awkward.  Thats a straight tangent going into a circular curve (3 o'clock position).  We don't drive that way.  We ease into curves by moving from 12 to 3 more slowly (easement), holding at 3 through the curve (circular portion) and then easing it back to 12 (easement out).  I don't want my modeling to be representative of the jerky driver throwing the car back and forth.  :)