How to handlay a 2-rail curve?

I'll be interested in hearing other practices.  It sounds like what you're really asking is "how do I construct an easement" whereby a straight track gently eases into a full curve.    Here's an example I found by Googling "model railroad easement" link.

 

 

Thanks Gregg.  That link is a good resource.

 

I'd like to hear how 2-rail o scale guys approach this problem, if possible.

I use a spline or long,flexible straightedge and bend it to the required radius.  Doing it this way also "adds" the easement right into the curve from the tangent.

I like the flexible "spline" method, too. One recommendation (which I followed with both

hand-laid and flexible track) was to decide upon an "offset" between the centerline of the

tangent track and the centerline of the curve.

 

In other words, draw your 54" curve centerline all the war around to the point of tangency, then establish the centerline of the tangent track around 1" (or more, if you like) to the outside of the centerline of the circle. Then measure 18-20" along the curve and 18-20' along the tangent from this point and use a flexible spline to "ease" the curve into the tangent over the total distance between these two points. Some articles suggest using a total easement length greater than the wheelbase of the longest car that will run over the layout.

 

This free-hand easement system works very well, and is much easier than calculating and plotting an actual spiral easement, which is over-kill for a model railroad in any case. The end result is a very nice transition from straight to fixed-radius curve.

You can play with "offset" and length of the transition to get the effect you like that still fits available space.

When laying out the easements for my 3RS layout, I used the spline method with [IIRC] a 3/4" offset.  I remember at the time wondering how does one choose the offset size - I used 3/4" because my straight track had already been laid and all the room I had for the O72 curve was for a small offset.  Is there a formula one is supposed to use, or do you just select an offset arbitrarily??

Gregg, that Link is very useful. I used some very wide curves on my 2-rail layout (as wide

as 100") bit even so the addition of an easement greatly improved the look of a large steam engine and train entering the curve. I may have used a 5/8" offset because of the large radius, but now i can't remember exactly. I extended the easement about 18" into

both curve and tangent (what's shown as L-1 and L-2 on the drawing in your link).

Pretty much all you need to know about trackwork:

 

Main link, scroll down to Trackwork

http://nmra.org/members/data-sheets

 

 

Page 2 of this document shows how to do the "bent stick" method.

Bent stick is probably the easiest (most popular too) method of creating easements on your layout.

http://nmra.org/sites/default/files/d3b3.pdf

 

More technical stuff

http://nmra.org/index-nmra-sta...ecommended-practices

 

 

Description of Bent Stick:

 The stick is usually of wood. smooth and straight grained,
of uniform cross-section and free from
cracks or knots which cause it to bend more easily
in one place than another. A piece of un-kinked
rail. if long enough, could also be used. The stick
should be flexible enough to bend to the sharpest
curve radius used and still spring back when
released.

1. The tangent or straight section is laid out first.
2. The curve radius is laid out next offset from the
tangent section laid out in Step 1. The offset is
called 'X'. 'X' is a function of the curve radius(R)
and length(L) of spiral easement. Once the size
of 'X' is determined the curve radius can be
drawn offset from the tangent section at the
tangent point by 'X'.
3. Measure and mark ½ L from the tangent point
along the tangent and along the curve.
4. Drive a double row of brads or nails along the
tangent and curve lines away from the junction
starting at the 2 marks made in Step 3. 0ne row
of brads or nails should be on the curve and
tangent lines. The other row of brads or nails
should be the thickness of your stick along the
first set of brads or nails.
5. The stick is placed inside the two rows or brads
or nails. The stick should be held firmly so that
it conforms to the tangent and circular curves
and forms a smooth curve between them.
6. The line of the track may then be drawn along
the stick to transition from the tangent section to
the circular curved section.

 

For high resolution version of illustration - clink link below

http://www.ncecorporation.com/...ogress/bentstick.jpg

 

It works out well if L is equal to one half the radius.

 

To help maintain consistency of the easement consider positioning the bent stick at the midpoint of the offset at the completion point of the fixed radius sweep.  Otherwise the evenness of the easement may be somewhat of a caricature.

 

i.e. if your offset between the 54" circle and the tangent is 7/8" then when you position the bent stick make sure that at  the junction of L1/L2  the sticks c/l marking edge is 7/16" from the fixed circle or tangent.

 

However, do not let the exactness of the formula get you all bent.  Sometimes there just simply is not enough room to fully develop a proper easement.  IMO, any eased attempt is better than a tangent hitting a fixed radius curve.

 

I find taking time to make some easement templates is of great help in laying out the right of way.  This 12' X 29' staging track photo shows easements of a 1/2 radius L for each successive curvature on 4 1/2" centerline.  '

 

 

The tighter the curve the more important the easememnt.

I also use the bent stick method to lay out easements.   On a 62" radius curve I use 3/4" offsets with a 30" long easement between the point of curvature and the point of tangency.  On wider curves I use longer easements.  John Armstrong's Track Planning for Realistic Operation provides useful guidelines and methods for laying out easements.  My mainline curves are super-elevated with the transition made in the length of the easement.

 

Ed Rappe

I am planning to hand lay code 125 rail with easements and super elevation. Does Armstrong's book describe method for super elevation? Thx.

Not to be the odd guy out, but I think you would be better off going to a slightly larger radius.  Spiral easements take up room that could be used to make the circle bigger - stated another way, with a given space, an easement will force the final curve to be tighter.

 

For realism, just give it a slight superelevation. 1/16" at the outer edge of the ties is enough.

On the other hand, an offset of only 3/4" or so really improves the transition from tangent-to-curve both aesthetically and operationally, while effectively adding no more than 1-1/2" to the width required for installation. I think you would have to increase the diameter of a fixed-radius curve significantly more than that to achieve the same operational result, and would still miss the improved appearance of an eased transition.

 

Martin,

Just because you go to 60" R does not mean that you should not ease the 60" R curve.  I ease 90" R curves and they look spectacular.

Ed

I know the focus of this thread has been on hand-laid track, but the discussion of easements and superelevation applies equally to flexible track. In other words, you

don't have to hand lay the track in order to incorporate these elements.

 

I hand laid all the track on my first layout (a rite of passage?) but the second time around I used Micro Engineering code 148 flexible track and I'm very happy with the results (the track has tie plates and very small spikes molded in). I glued the track down with a product called Weld Bond and, once ballasted, it became very solid: absolutely no movement of the track in 10 years. 

Don't worry Ed!  I plan to ease into the 60", should I choose to install that radius.

Not to back track too much here but I am a big fan of using a long flexible straightedge as others have stated.  After having handlayed what seems like miles of track that is what works the best for me...I have 66" min radius on my curves and the easements make a huge difference in the approach and departure of longer rolling stock...and I like the final look as well. 

All,

In the May/June, 2004, O Scale Trains on pages 48 and 49, there is a discussion and table for determining the offset, length of easement and the radius.  These three dimensions are interdependent.  

Ed

My point was, if you only have room for a 60" curve without easements or a 54" curve with easements you are better off with 60".  If you have unlimited room, by all means use spiral easements and stick to 72" minimum radius in the actual curve.

According to the chart I referred to above, you can use a 59.5" radius curve with a 0.5" offset and a 26"easement and have one of the best of all combinations.

Ed

 

If the trains will operate reliably on 54" radius, then there is no particular reason to use a larger radius, other than the improvement of appearance. But because easements improve appearance (in my opinion) by reducing the offset between the ends of long cars entering a curve and by allowing a nicer "flow" of the whole train, they are worth the small sacrifice.

 

If 54" radius provides operational reliability for the equipment you are using, then a wider radius (such as 60" if the space is available) in fact offers has only an aesthetic improvement, which can be greatly enhanced by reducing the 60" maximum a little bit and building in easements at each end of the curve. 

If I remember correctly, John Armstrong defined "broad curves" as 60" in radius, which he believed  sufficient to accommodate almost all 0-scale equipment with a minimum of tinkering and adjustment. So, the only reason to exceed that radius is to make the trains look better, which is something that an easement helps with. Even on his own layout, Armstrong had one exceedingly wide radius curve just because it looked good.

True, but what if he suddenly wanted to run a Northern, or some scale passenger cars?  With an 0-4-0, you can probably drag freight cars around 36" radius if you give the couplers a little extra swing.

I feel strongly that 54" is the sweet spot for me.  I think 21+ inch cars look sufficiently good for me on that radius.

 

36" is completely unacceptable to me.  I can't even stand seeing it with 3-rail stuff.

 

Just a note in passing here...  Some have asked whether the length of a spiral easement for a curve of a given radius has an effect on the offset.  The answer to that is yes, it does.  And conversely, if for some reason the offset is wanted to be fixed, that will determine the length.  Usually you will want to leave your radius unchanged.

Most of the referenced methods did not recognize this interrelationship.  One did, but the table of values for H0 track did not seem to be internally consistent-- that is to say that all of the values should have scaled up in approximate ratios determined by the percentage change to each value (well, it's a bit complex & not always obvious).

What is needed is a way to estimate the offset for a desired length of spiral (which offset will vary with any particular curve radius).  Then a way is needed to adapt it to the flexible spline method (seems to be the favorite here).  I believe I can devise both in a way that will make the results more satisfactory without involving too much trouble.  By more satisfactory, I mean that while a particular length or offset may not effect the running quality, a mismatch between the two will.  And large mismatches could occur with some of the approaches referenced.

Would explain more, but it is late now.  Tomorrow, more likely Wednesday.   --Frank

 

Edited for clarity.

As a follow on to my post of yesterday, I'll describe an approximate method to construct a spiral.  Then one only has to use geometry to determine what the offset is.  Having the offset, one then needs only a method of using a spline in such a way that the length of spiral produced will match that offset.  [I will describe a method for that tomorrow.  BTW, a spline is the engineering office name for a small, flexible plastic strip.  They come in a polished walnut case, with their 5 whales... like fine whiskey. ]

For an approximation to a spiral, we could use for example. a piece of 0-144 as a spiral for an 0-72 curve.  This would be super easy in the calculations, as the spiral would begin and end with the 0-144 section, assuming both were 1/16 of a circle.  This would be called a one-segment approximation.  But there is a better approximation, which I devised, in a desperate effort to improve our draftsperson's speed and polish on the drawing with these spirals, when encountered.

This would be the two-segment approximation, my term.  [In our office calculations, we used the three-segment approximation, which was said be truly marvelous in its closeness to the real thing.  It had a tangent segment and two curved segments, identified by our IBM 650-- literally an electronic Frieden.  The program was written by an insane professor-- we called it the research program.]  So don't sneeze at a mere two-segment approximation, even with only one curve.

Let's say 0-72 is a curve of 40 degrees-- that is, it turns through an angle of 40 deg in a distance of 100 scale feet (about 25" in 1:48, along the arc of its center rail).  Now let's take a curve of 0-54.  Notice that 54/72 is 3/4.  Or in degrees of curvature, 0-72 is 3/4 as sharp as an 0-54 central curve.  Both track have 16 sections per circle.  Suppose we ease a central curve of 0-54 using a section of 0-72.  And further suppose we say that the 0-72 segment is 2/3 the length of the two-segment spiral we are creating.  What do we then have?

Well, 4/3rds the original tinplate track-section length with 3/4ths the degree of original 0-54 curvature will give [4/3 x 3/4] the same total curvature.  So we don't need more curvature, but we do need more spiral "approximation" length, which will be a segment of tangent (ie, straight) track.  Suppose we make that tangent half as long as the piece of 0-72, which is the curved segment.

So then the total spiral becomes 4/3rds curved plus 2/3rds tangent, with a length of 6/3rds, or twice, the length of the original curved 0-54 track section replaced.  That the spiral be twice the length of the amount of constant curvature central curve replaced is one of the conditions imposed upon spirals for railroad use.  I will explain why in future post, perhaps after I explain the use of the spline (and its whales...) to substitute a smooth spiral "approximation" for the two-curve approximation [tomorrow].

But first, to conclude the issue of use of an approximate spiral to obtain approximate offsets, note that: The offset for 0-54 eased by a section of 0-72 is very close to 5/8".  (I mean that working to 32nds, it would be 20/32nds or 5/8".)  The length of the two-segment spiral approximation is the length of the 0-72 curve (14-3/8" IIRC) plus a tangent of half that (7-3/16"), total 21-9/16", which is 86'-6", and conveniently as long as a 21+ inch car.

Second, there is another pair of radii with readily available tinplate (or other prefab arrangements) in 0 scale:  I refer to the 0-72" eased by an 0-96 section.  These are sections available in 16 per circle also.  Thus the various lengths will be proportionate; in particular the offset will be 5/6" (4/3 x 5/8 = 20/24ths = 5/6").  The triangular engineer's and architect's scales will be useful in laying centerlines to such dimensions-- available in stationery stores; in plastic fairly inexpensive.

The scale person will of course be interested in the 48" curve, if not also the 60 (0-96 and 0-120).  Following the principles of the first two examples, suitable offsets can be worked out, on paper without need for sectional track.  Nor need they need to be proportional to the examples.  Railroads almost invariably used a 200-foot spiral (altho sharp curves could require more).  Somewhere around a 100-foot spiral seems an acceptable compression in the model.

Just remember the rule is, for the two-segment approximation, for the curve segment:  Use three-fourths the (degree of) curvature for two-thirds of the spiral length; tangent for the remaining one-third length.  Calculate the offset at the two-thirds point.

I'm sure I don't have to explain how to figure the outward offset when only a  single compound to a 2nd radius is involved, so this essentially concludes the determination of offset procedure.  Smoothing with spline covered Wednesday.

--Frank

Frank,  The verbose merging of earlier NMRA easement standards  may be more helpful to traditional high rail folks building with sectional 0-something or other track. 

 

IMO the same effect on the 2-rail SCALE forum would not be realized.  None of the track pieces or nomenclature mentioned would normally be used in 2-rail SCALE.

 

 

 

 

 

Sounds a bit like you slightly confused Tom.  You totally lost me.  As I understand it, a spiral easement is a gradual change from tangent to desired curve, not an abrupt change from one radius to another.

 

I am not sure I understand the realism attained by using a spiral easement into an unrealistic curve - but then I have never even attempted a spiral easement.  If I had the room, it would surely make my superelevation more coherent.

 

My locomotives need every inch of that 74" radius curve, and my articulated coach actually had to have an extra 1/16" spacing to safely make it around that same curve.  Giving up the room for a spiral easement into a 70" radius curve would mean even more space between passenger cars, but it would also mean that my Northerns and Decks would have no place to run.

This little beauty needs 74" radius, because cylinders and tail beam are close to scale.  The tailbeam has a taper, unlike the real thing, to enable the very sharp 74" radius.

 

This one did not cost $8 grand - I think I have maybe $125 in materials in the body and another fifty in motor and gearbox.  My 21" cars need the radii above 70" to avoid body contact on the curves.  There is a slight jerk when the locomotives hit the abrupt 64" radius on the inner loop, but I was unwilling to go below that radius even for the smaller Pacifics and freight cars that populate that loop.

I'll never be able to run passenger cars.  All I have is cheap stuff from the modern era that will easily run even on 36" radius.

 

I saw somebody running an $8000 Kohs last weekend and I realized I'm playing in a totally different ballpark.

While it's true that most model railroad curves are unrealistic (Horseshoe Curve would require a diameter of around 27 feet in O scale), the abrupt change from tangent to fixed-radius curve can be softened a little by using an easement, at relatively little cost in

real estate. I'm very pleased with the way the easements on my layout allow trains to

enter the fixed curves a little more gracefully.

Tom--

My purpose wasn't to suggest that such pieces of prefab track be either used or copied into a 2-rail scale layout.  I meant to mention that, at the end of my post which used them as examples.  Using familiar track examples gave the simplest method of making a somewhat clear explanation.  I thought this forum would be the best place to discuss them, as clearly you people here are serious about using them, and not just in the form of any series of compound curves (just as you stated).

A very important aspect of making a proper railroad spiral is that you have a reasonably correct value of the offset associated with the desired length of spiral, and conversely.  Ed Kelly posted above: "...offset, length of easement and the radius.  These three dimensions are interdependent."  Ed is right.  Interdependent, not independent.  This means that selection of values for any two of these will absolutely determine the correct value of the third.

The problem with this is that the calculation is not a trivial matter.  I used tables (1940 and long out of print) to determine correct offsets (to the unspiraled PC).  Now there is an equation for the family of offsets starting at the TS (tangent to spiral), which includes our offset.  The solution is in the form of the sum of an infinite series of fractions alternating in sign.  Fortunately, the sum of three fractions sufficed to locate the offset to every spike in the spirals of WMATA (DC area subways) to an accuracy of 1/80th of an inch, as per contract.  (I'm not making this stuff up.)  Obviously no one here is calculating offsets every scale foot from the tangent.

What is wanted out of all this at this stage is a reasonably close estimate of the controlling offset matching the original curve and the proposed length of spiral.  There are reasons to chose a length equal to the longest passenger car; in this forum, about 21 inches as a minimum.

What I had in mind as a calculation method was three options:
1. Drop the sectional track version into a layout drawing program, letting it calculate the offset; or
2. Cobble several pieces of track into two versions of a 90-deg turn; measure the difference; or
3. Do a calculation of the difference on paper (those using 54" & 60'' *radii* have to go this route). 

Just a note:  The matching correct offset is important so that the railroad spiral will have a constant, uniform increase in the curvature of the rail.  This ensures that a constant flange force will accelerate the long and heavy boiler of a steam locomotive into a rotation about its own vertical axis.  This is roughly 48 times less of a problem in the model; in real life it was a real problem.  --Frank

PS: (1) I don't have a program: (2) measurement of track difficult to get accurate; so (3)calculation is my route by default (my preference is my mislaid tables).  Spline method adjustments tomorrow.

If anyone had taken the time to look up the reference to OST that I provided, you would have found a diagram that gives you the third value once you have chosen the first two.

The article in OST can be found at

 

http://www.oscalemag.com/docs/ost_14.pdf

 

Scroll down to page 48.

Ed

Yo Ed!  Not enough words,  you are making this way too easy.

I took the time.  Very interesting.  Am I correct in interpreting that graph to say that, for a 54" radius curve with 1/16" superelevation, x=9"?  That seems like a lot.

 

I did use run-out for my superelevation, but not  42" worth.   Next time I shall hold it down to 1/16" for better passenger car gaps.  I will most likely never have room for graceful easements.  My rolling stock needs one truck to be quite free laterally to negotiate the 1/8" superelevation, and my locomotives need special care on lead and trailing trucks, often involving huge weights and strange springing arrangements.

Bob2, with a wet thumb raised to the breeze, your 54" radius with a 27" easement would work nicely with a  9/16" "X".

 

Laterally expanding any curve a fraction of an inch for 25% (L2) of the radius beyond completion of a curve will work wonders.

 

IMO super elevation compression with our really tight curves is necessary. 

 

 

You are correct - I was reading the chart wrong.  Less than an inch for X means that a spiral easement is indeed called for.  I could probably run my stuff on 73" radius.

 

So without doing the math, can I just take a flexible stick and match the tangent to the curve, 20 some inches back from where my 74"  curve used to be tangent?

 

Should I expect noticeable improvement in appearance as the train eases in gradually?  Or am I going to lose 40" of tangent track without much advantage?