Easy and reliable transition curves...

The easiest trick I have learned is to use an electrician's conduit fish tape to lay out curves.  Fasten the end of the fish tape with pins so it is straight for about the last 4 inches before your intended curve, then stretch it out until you can fasten the last four inches straight at the other end of the radius.  You can then adjust the tape until the center of the curve is in the desired location, and the two ends will automatically adjust into a perfect transition.

 

I would get a 1" strip of countertop surfacing, and place it on its side, pinned as cacole suggests...if you don't happen to have the fish tape.  I'm talking about arborite, although masonite would be fine...whatever will take a fairly stiff curvature without integrity failure.  I would start the strip on the entering tangent, then lay the curve just 1/8" outside its intended path near and at the apex, so it would slightly curve outward from the pins before it began to conform to the path that you intend.  At the far end, it should be pinned along the tangent for several inches.  Then, simply press the apex of the curve so that it is 1/8" inside the line you have drawn for the simple curve.  See if that works.  You can adjust the place where you put the apex to suit your eye and preference, but you should get a decent approximation of the easement.  It won't be mathematical, but it will be functional.

-Crandell

Two ways to form transitions, both of which work for me:

Make a template, on a piece of card stock or thin hardboard:

1. Establish the "theoretical point of curvature (TPC)."  This is the point where an un-easemented tangent would meet a circular curve - the sort of thing you get with sectional toy train track.
2. Offset the tangent outward, dimension variable.  I personally use 10mm, but 1/2 inch is also valid.  Mark a point 1/2 way from the tangent line to the curve line.
3. Measure 24 or 25 times the offset down the tangent from the TPC and mark the "actual point of tangency."
4. Measure the same distance as an arc of the curve from the TPC and mark the "actual point of curvature."
5. Bend anything that is uniformly flexible to connect the "dots" marked in 2, 3 and 4, and draw the curve.

The resulting curve can be cut out and used wherever a transition is desired as long as the curve radius and the tangent offset are the same.

Mark the points on the subgrade as above, draw the line, install roadbed material of choice (split cork, for example, with the split line exactly on the transition line) and lay track.  An alternate method would mark the transition on top of pre-installed roadbed material which could then be carved to final shape.  This has the advantage of being useable on any curve radius, since it's done in place.

In my own flex track laying, I usually establish the actual points of curvature and tangency and let the natural springiness of Atlas flex track set the easement.

Hope this helps

Chuck

Two things I can bring to this table: I use the spring batten method, too, but I use a 1/4 or 3/8 square strip of wood. If you look it up in John Armstrong's book "Track Planning for Operation" The first time is the hardest. It does get easier and faster with practice.

 For a given radius there is an optimum offset and half-lengthof transition, such as : for 18" radius O= 1/2", L/2= 9 inches, for 24" r. I use O= 5/8", L/2= 10", for 48" I use O=3/4", L/2=12", for 72"r. I use O=1", L/2=18". And I start pinning 6" at each end of the transition instead of 4".

Also a suggestion, If you are going to do a lot of them, get a piece of 1/8" door skin at Home Depot or Lowes type of store. Sometimes you can get damaged or half skins cheap! Using the 6" along the straight edge lay out your transition , and go 6" or more past the point where you are on the actual radius.  Now mark all the above mentioned points, Offset, and Length/2 and radius. Mark your transition with the batten. Now use a small saber saw and cut just to the outside of the line. Finish to the line with sandpaper. Cut your template 6 to 8" wide at the tangent (straight track) end and let it taper to the radius curve perpendicular to the butt end. Mark the points mentioned on both sides so you can just flop the template over. I make a template for each size radius I intend to use and they are a lot of work, but once you have them, done you are set up to lay it on the benchwork and mark a transition curve anywhere on the layout. A real time saver! Happy railroading! jc5729

Here's how I eased my curves:

1.  Draw out the straight sections of track, extending the line past the start of the curve.

2.  Draw your centerline of your curve 1" to 1 1/2" inside the straight sections of track.  For instance, if you're drawing a 24" radius curve, the center will be 25" to 25 1/2" inside the straight sections.

3.  Draw a curve TWICE the radius of your curve that's tangential to both the straight line and the cruve.  In this case a 48" radius.  This will make the "eased" curve about 12 to 18" long, long enough for the rail car to enjoy the transition.

When you lay out your flex track it will naturally buffer the two transitions and you'll be hard pressed to actually see precisely where the curve starts.

Mark in Utah

This site is a bit technical, but it explains how easements are calculated.  I built these formulas into my CAD software to draw my easements.
http://www.geocities.com/budb3/arts/tech/ease.html
I'm still in the finishing my basement and tweaking the track plan phase.

Back last century, October 1969 to be exact, MR published an article on simple transition curves, including templates, which I have successfully used.  The article was called "Laying out an easement with MODEL RAILROADER templates" written by Bordes, Stackhouse and Westcott. Unfortunately I don't have access to a scanner at the moment but a fellow old codger like me may be able to help you out.

tutaenui wrote:

Back last century, October 1969 to be exact, MR published an article on simple transition curves, including templates, which I have successfully used.  The article was called "Laying out an easement with MODEL RAILROADER templates" written by Bordes, Stackhouse and Westcott. Unfortunately I don't have access to a scanner at the moment but a fellow old codger like me may be able to help you out.

No need to scan.  MR has that article as an online extra on this very website:
http://www.trains.com/mrr/default.aspx?c=a&id=290

Hello Dave,

I use the bent-stick technique shown in John Armstrong's book, "Track Planning for Realistic Operation." We'll show it again in an article I've written for the November "Model Railroader." As I mention in the article, I use this method to make templates by laying out the transition curve on illustration board, then cutting out the curve so I can trace it onto my layout's plywood subgrade. That makes the curves easy to lay out, since you only have to bend and trace the stick once for each circular radius you want to use.

Whether these curves are mathematically "accurate" or not doesn't matter at all to me. They work, which means they provide improved appearance and smoother operation by minimizing the offset between cars entering and leaving the curve.

For my HO layout I use 18-inch long transitions with the tangent offset 1/2 inch from the radius of the circular curve. Within those parameters, I doubt that any observer can tell the difference between a bent-stick easement and a cubic spiral.

so long,

Andy

Wow.  Great discussion guys... I am feeling really stupid here.... I usually  use 18" in and out of curves of a radius 4" greater than then curve radius (e.g. usually 32" easement into and out of a 28" curve).  I line up the centers very close and like some noted above, I use flextrack (soldered at joints) to smooth it out.  Is this wrong?  It looks smooth to me and I have had no problems as of yet (still test running the track....).   Just wondering....

 

Brian

ShadowNix wrote:

Wow.  Great discussion guys... I am feeling really stupid here.... I usually  use 18" in and out of curves of a radius 4" greater than then curve radius (e.g. usually 32" easement into and out of a 28" curve).  I line up the centers very close and like some noted above, I use flextrack (soldered at joints) to smooth it out.  Is this wrong?  It looks smooth to me and I have had no problems as of yet (still test running the track....).   Just wondering.... Brian

Brian.  Not "wrong".  Any easement is better than nothing - key is making the easement a car length long or longer to get the full benefits of the easement.  Most turnouts provide a built-in easement with their straight sections around the frog even on the curved route.  And Plenty of mr's still lay track with no easement at all.  But an easement does make a significant difference in appearance and performance.  In the case of "springy" flex track, you normally end up with some easement naturally as it is quite difficult to make sudden changes in radius anyway - but it may not be long enough to provide all the benefits of an easement..  The bent stick approach comes quite close to a template laid from cubic spirals, so is considered "good enough" by many, if not most.  You can make a cubic spiral template if you want to follow prototype practice more closely.

my thoughts, your choices

Fred W

"True" railroad easements are an incredibly complex topic involving more math than I care to take on.   C. Frank Allen's 1931 book "Railroad Curves and Earthwork"  (McGraw-Hill) is probably the classic text on the topic but every time I open up its 290 pages of closely packed text and tables I get drowsy and before you know it I am dreaming awful dreams (e.g. that I have replaced all my Kadees with old horn hooks ......).    But in short just about all model railroad easements are the merest approximation of the prototype.  But they can look good and actually serve much of the same function -- that is avoiding that jerk into the curve that is the lovable characteristic of Lionel and other tinplate trains.

Anyway to the many good suggestions above (and clearly the easist if you normally use 18" radius curves is just to stick in a piece or two of 22" radius) I add my method.  My layout uses plywood and/or homasote subroadbed, which is cut into curves (for double track 38" and 40" radius curves) and tangents assuming 2" spacing between double track.  Where the tangents meet the curves,  I take plywood or homasote maybe 18 to 24 inches long and kurf cut it so that it is SLIGHTLY bendable.  That is my transition between tangent and curve.  This is the same principle that makes homa-bed roadbed bendable.

Am I making myself clear?   The cuts looks a little like this, so the plywood or homasote is just slightly bendable.     

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Dave Nelson