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Offline Alsterstreek  
#1 Posted : 03 December 2014 15:34:53(UTC)
Alsterstreek

Germany   
Joined: 16/11/2011(UTC)
Posts: 5,336
Location: Hybrid Home
Hi,

My name is Ak and I have a "spleen": For aesthetic reasons, I aspire to have easements at the beginning of curves or adjacent to switches. Why? Because close-coupled passenger cars look odd and not very realistic when re-entering straight track after a "normal" curve without easement. At least three forum members encouraged me recently to have my coming-out. Now:

Definition & motivation
A track transition curve, or spiral easement, is a mathematically calculated curve on a section of railroad track, where a straight section changes into a curve; the outside of the curve is gradually raised until the correct degree of bank is reached. While used for the prototype to prevent sudden changes in lateral acceleration, it is of interest for the model railroader for cosmetic reasons: The changeover between a rather tight curve and straight track results in a unattractive misalignment between the locomotive and a coach on two trucks.

More theory
In his terrific book, "Track Planning for Realistic Operation", the late John Armstrong discussed radii limits on pages 73-77. Pushing these operational limits, he demonstrated that the main issue with tight radii occurs when transitioning from tangent (straight) track to curved track. That is the point where the curve places the most strain on couplers and axles and is most likely to cause derailments or decoupling, dubbed by him “coefficient of lurch”. A spiral easement – a section of track that transitions from curve to tangent – reduces the coefficient of lurch and allows a tighter radius than otherwise possible. On page 75 he showed an example where an 18” radius HO curve with spiral easement creates less stress on the train than a 24” radius curve without the easement.

C-track and you
One of the niceties of C track geometry is the presence of many different curve radii. If one had sufficient space and planned to employ C track, I would advise to use easements - i.e., a single piece of larger radius curve - where the beginnings of curves are visible. E.g., incorporate one piece of R3 curve between a straight stretch and a curve "ruled" by R2 radius. The larger the better. Inserting only a short straight track (either 24064 of 24077) or by "counterbalancing" a R1 with a very wide radius track, as R4 or R5, instead, nicely defuses (even R1-based) S-curves. On my layout(s) this works fine for all kind of motive power and rolling stocks, European and US, coaches and freight cars, both pulling and pushing.

Photographic evidence
Below - see attached photo - is an illustration of the positive effect of easements - in this case a piece of curved R9 track, respectively - at the beginning at all types of M* C-track radii (R1/R2/R3/R4/R5): All 27 cm coaches glide smoothly into the curves, whether the R9 is followed by R1 in the front or R5 in the back.

Previous forum discussions
First serious mentioning of this topic:
https://www.marklin-user...3----why.aspx#post205146
Most recent discussion on this topic:
https://www.marklin-user...f-layout.aspx#post474629

Tip of the day
Forum member Kimballthurlow pointed out that the R9 piece of track - being a 12.1° curve - is difficult to combine with the M* 30° standard curve segment. Indeed, "taming" the 24912 is a challenge (as long as one does not resort to a saw). Hint: Combining 24912 (12.1°) + 24206 (5.7°) + 24912 (12.1°) leads to 29.9° which is close enough to obtain a 30° curve; e.g. one of the visible 180° "turns" on my former layout "Slumburg" consisted of 1 x 24912 (12.1°) + 5 x 24230 (150°) + 1 x 24206 (5.7°) + 1 x 24912 (12.1°).

To be continued?
Alsterstreek attached the following image(s):
cle2.png
thanks 7 users liked this useful post by Alsterstreek
Offline Irish Rail  
#2 Posted : 03 December 2014 18:50:41(UTC)
Irish Rail

Ireland   
Joined: 04/03/2014(UTC)
Posts: 123
Location: West Cork
Am I reading this correctly? There are two types of easement - horizontal easement by introducing wider radius curves at the beginning and end; and vertical easement that involves banking the outside of the curve (like on a racetrack).

The first seems easy enough to achieve (even with M track). But how to achieve vertical easement with relatively rigid track sections....??
thanks 1 user liked this useful post by Irish Rail
Offline Alsterstreek  
#3 Posted : 03 December 2014 21:48:03(UTC)
Alsterstreek

Germany   
Joined: 16/11/2011(UTC)
Posts: 5,336
Location: Hybrid Home
Okayokayokay, then we extend the scope of this topic to include:

Superelevation of tracks which is meant to compensate for the centripetal acceleration when moving along a curved path to minimize the lateral acceleration experienced by passengers or cargo load. Not of importance for sturdy MRR trains, but of cosmetic interest by creating a dynamic impression. Yes, you might have guessed it, I model(led) that, too. When still working with wood, I used open-grid benchwork which allowed me to tilt the supports of the thin plywood roadbed supporting C-track. Now, in the world of foam, I cut ramp supports with a "lateral tilt" to achieve the same effect - see pic of the result in one of the curves.
Alsterstreek attached the following image(s):
s-el.png
thanks 6 users liked this useful post by Alsterstreek
Offline Alsterstreek  
#4 Posted : 03 December 2014 22:12:20(UTC)
Alsterstreek

Germany   
Joined: 16/11/2011(UTC)
Posts: 5,336
Location: Hybrid Home
Horizontal easement examples from my layout.
Alsterstreek attached the following image(s):
c ex.png
thanks 4 users liked this useful post by Alsterstreek
Offline Alsterstreek  
#5 Posted : 03 December 2014 22:57:30(UTC)
Alsterstreek

Germany   
Joined: 16/11/2011(UTC)
Posts: 5,336
Location: Hybrid Home
"Classical Curve" starting an ending with R9, respectively, and an uncoordinated mix of R3/R2/R1 in the middle.
Alsterstreek attached the following image(s):
HC.png
thanks 5 users liked this useful post by Alsterstreek
Offline Alsterstreek  
#6 Posted : 03 December 2014 23:11:03(UTC)
Alsterstreek

Germany   
Joined: 16/11/2011(UTC)
Posts: 5,336
Location: Hybrid Home
And finally, the central gentle S-curve.
Alsterstreek attached the following image(s):
scdl.png
thanks 3 users liked this useful post by Alsterstreek
Offline kimballthurlow  
#7 Posted : 04 December 2014 05:56:24(UTC)
kimballthurlow

Australia   
Joined: 18/03/2007(UTC)
Posts: 6,368
Location: Brisbane, Australia
Originally Posted by: Alsterstreek Go to Quoted Post
"Classical Curve" starting an ending with R9, respectively, and an uncoordinated mix of R3/R2/R1 in the middle.


https://www.marklin-users.net/forum/resource.ashx?p=25722

Hi Ak,
What a great illustration of how an easement looks, using C track.
Progress of trains entering curves is dynamically more effortless.

With the addition of raising the outer rail (super elevation), it also looks impressive for a a bystander.

regards
Kimball
HO Scale - Märklin (ep II-III and VI, C Track, digital) - 2 rail HO (Queensland Australia, UK, USA) - 3 rail OO (English Hornby Dublo) - old clockwork O gauge - Live Steam 90mm (3.1/2 inch) gauge.
thanks 3 users liked this useful post by kimballthurlow
Offline perz  
#8 Posted : 04 December 2014 21:42:48(UTC)
perz

Sweden   
Joined: 12/01/2002(UTC)
Posts: 2,577
Location: Sweden
Originally Posted by: Alsterstreek Go to Quoted Post

Previous forum discussions
First serious mentioning of this topic:
https://www.marklin-user...3----why.aspx#post205146



This is even earlier. Isn't it "serious"?

https://www.marklin-users.net/forum/yaf_postst9281_Transitation-curves--or-How-to-fit-R9-on-75-cm.aspx#post9281
thanks 1 user liked this useful post by perz
Offline kimballthurlow  
#9 Posted : 05 December 2014 00:06:50(UTC)
kimballthurlow

Australia   
Joined: 18/03/2007(UTC)
Posts: 6,368
Location: Brisbane, Australia


Hi Perz,

Yes, that is serious enough. In fact it is very helpful. (originally posted by member LeoArietis in 2008)
Each square on the below diagram appears to be 250mm.

https://www.marklin-users.net/upload/Community/Layoutplans/LeoArietis/overganskurva.jpg

Because it illustrates exactly how much extra width you will need for a layout board, when using a half circle.
Each square on the above diagram appears to be 250mm.

For example:
"How to do it:
Change the last track in the curve to one with larger Radi. If you have a half-circle of R1, just changing the last curve up front at your layout from R1 to R3 only need 0.0208 m (~2.1 cm), that is less than 1 inch! (dia 720mm goes to 740.8mm)"

regards
Kimball
HO Scale - Märklin (ep II-III and VI, C Track, digital) - 2 rail HO (Queensland Australia, UK, USA) - 3 rail OO (English Hornby Dublo) - old clockwork O gauge - Live Steam 90mm (3.1/2 inch) gauge.
thanks 3 users liked this useful post by kimballthurlow
Offline Alsterstreek  
#10 Posted : 05 December 2014 11:30:32(UTC)
Alsterstreek

Germany   
Joined: 16/11/2011(UTC)
Posts: 5,336
Location: Hybrid Home


Many thanks Perz,

Yes, fulfills both criteria, "earliness" (three months older than the 2008 post I had dug out) and "seriousness" (illustrative indeed). However, my search did not detect the topic as header and narrative refer to the mysterious "transitation-curve"...

;-)
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