I came across this article in MR http://trains.com/mrr/default.aspx?c=a&id=290 and am wondering if anyone would be able to find the time to answer some questions I have about laying out easement curves.
For example in Part B (d ) Points M and A directly in line with P. Where are points M and A located ?
I have some other questions but was hoping one of you who might be familiar with this article, or have a better understanding than I do, would be willing to assist.
With all due respect to Linn Westcott, who was a true model railroading pioneer as well as a long-time employee of Kalpubco, unless you are laying out full-scale curves to be used by Acela, TGV or the Shinkansen the techniques and templates in that article are a gross overkill!
Simple, straightforward way to lay out easements (John Armstrong approved, have used it for decades and I know it works.)
Draw the centerline of your tangent (straight track) to a point at right angles to the center of the curve. This is the theoretical point of tangency.
Measure back the length of your longest car (in HO, an 89 foot humongubox is about 12.5" long.) You have just found the actual point of tangency.
Locate the center of the curve, at right angles to the tangent line, and measure radius plus approximately 1/24 the length found in 2 above (for this example, 1/2" is close enough.) The offset point should be marked and labeled theroretical point of curvature. Swing the centerline of the curve.
From the radius line found in 3, strike a chord the length found in 2. The point where that chord intersects the curve centerline is the theoretical point of curvature.
Find a point half way between the theoretical point of tangency (1 above) and the theoretical point of curvature (3 above.) That point, with the actual point of tangency (2 above) and the actual point of curvature (4 above) gives you the three points needed to establish the spiral easement. This can be drawn using a bent batten (John Armstrong’s method of choice) or a limber piece of flex track (Atlas code 100 in HO works for me.)
If you are trying to spread track centerlines going into a multi-track curve, you can simply use a longer spiral easement into the inside track, more offset, and 24X offset for chord length and tangent setback. (Example - tangents 2" apart, curve radii 24" an
On my last layout, I pasted one of the easement templates available on poster board and then carefully cut out the edge with the track center line.
I then used a a compass based on a retractible tape measure with a centering pin and a pencil at the outer end. I set the point for the radius center at 90 degrees from the tangent with a 1/2 inch offset and drew the curve.
Then, I slide the template along the tangent until the curve of the easement intersects the curve. Draw the easement.
I’m trying to get my head around this, so please bear with me.
I assume the template you mention is from the link I posted originally ?
When you say you cut out the edge with the track center line, is that the line marked “center line of track on spiral” on template C ?
If I understand correctly, you draw your tangent on the sub-roadbed and then the intended radius curve that will join the tangent plus 1/2" offset. e.g. with a 30" radius curve, the point for the curve is actually 30 1/2" from tangent track ?
Again, using template C as an example, you then line up the tangent line from the template with the tangent drawn on the sub-roadbed and slide the template until the “center line of track on spiral” curve on the template meets the 30" radius curve you have drawn on the sub-roadbed ? You then draw a curve from that point back to the tangent and you have your easment curve ??
Appreciate your patience in explaining how this works. I really would like to get a better understanding. I have the John Armstrong publication, but still can’t quite grasp the concept.
I, likewise, set my curves 1/2" inside my tangents and then eyeball a a smooth curve between them. Unless you take a set of calipers to them they will be visually and operationally indistinguishable from the mathmatically calculated ones.
This is really hard to grasp without a diagram, so I will give you a diagram.
I agree with Dave. I use a piece of flextrack to form the shape of the curve between the point on the tangent track and the point on the curve. I use the “midpoint” (on my diagram) as a guide to make sure the easement doesn’t stray too far.
I start and end the easement 12 inches from where the curved track would meet the tangent track if there were no easement (original tangent).
The offset is the distance the new tangent track is from where the original tangent track would be, measured outward. I use an offset of one inch, mostly because it looks good to me. You may want to use 1/2 inch.
Then I put the piece of flextrack down so that it is even with (parallel to) the tangent track and the curve at the start and end points, and adjust until it looks like a smooth transition. The midpoint should be about halfway between the rails, but this isn’t critical. What’s important is that it looks smooth.
Finally, I mark where the flextrack is located so I can lay permanent track in the right place.
It’s really very easy. None of the measurements is critical. I often use “one track width” instead of measuring one inch for the offset.
A very important point is how easements change your layout. If you have an oval with 24-in radius curves, then your tangent tracks will be 48 inches center-to-center without easements. With easements the distance between tangent tracks will be greater by twice your offset. In my case that is 50 inches. As an alternative, in case your tangent track alignments are fixed, you can reduce the radius of your curve by the amount of the offset. Therefore, you have to take the offsets into account in the early planning phases.
This is really hard to grasp without a diagram, so I will give you a diagram.
I agree with Dave. I use a piece of flextrack to form the shape of the curve between the point on the tangent track and the point on the curve. I use the “midpoint” (on my diagram) as a guide to make sure the easement doesn’t stray too far.
I start and end the easement 12 inches from where the curved track would meet the tangent track if there were no easement (original tangent).
The offset is the distance the new tangent track is from where the original tangent track would be, measured outward. I use an offset of one inch, mostly because it looks good to me. You may want to use 1/2 inch.
Then I put the piece of flextrack down so that it is even with (parallel to) the tangent track and the curve at the start and end points, and adjust until it looks like a smooth transition. The midpoint should be about halfway between the rails, but this isn’t critical. What’s important is that it looks smooth.
Finally, I mark where the flextrack is located so I can lay permanent track in the right place.
It’s really very easy. None of the measurements is critical. I often use “one track width” instead of measuring one inch for the offset.
A very important point is how easements change your layout. If you have an oval with 24-in radius curves, then your tangent tracks will be 48 inches center-to-center without easements. With easements the distance between tangent tracks will be greater by twice your offset. In my case that is 50 inches. As an alternative, in case your tangent track alignments are fixed, you can reduce the radius of your curve by the amount of the offset. Therefore, you have to take the offsets into account in the early planning phases.
Yes, that’s the way to do it. Just remember that the tangent must be planned all along for a position where it will lead into the easement and still afford you your desired radius at the midpoint of the curve proper. So, in real live terms, railroads are really a series of sinuous and carefully measured curves between which tangents are drawn. Neat way of looking at them after that realization.
As stated earlier, probably the least troublesome, and just as pragmatic and effective way to generate an eased curve is by pegging the first 6" of a section of flextrack to immobilize it along the tangent centreline, and then force the free end to conform to your curve near its midpoint. Your easement will appear naturally between these extremes, the fixed end and the forced end. Trust us on this one!
If you don’t draw the center line for ALL of the track you are going to lay before you do ANTHING else, you are asking for trouble. It is a lot easier to erase a pencil line than to tear up already laid track.
If you are using cork roadbed this is an absolute MUST because each half of the roadbed must be set to the centerline.
Draw the tangent. Draw the arc offset 1/2 inch. Set the tangent end of the template along the tangent already drawn. Then SLIDE it along the tangent toward the arc until the curve of the easment blends with arc.
Believe, me. This is the fastest, and most accurate way to create a spiral easement from one that has been mathematically calculated, and true to propotype.
When you say "slide template along tangent towards the arc until the curve of the easement blends with the arc, " the “curve” that your refer to is that the line marked “center line of track on spiral” on template C from the link in my original post ?
When you say "slide template along tangent towards the arc until the curve of the easement blends with the arc, " the “curve” that your refer to is that the line marked “center line of track on spiral” on template C from the link in my original post ?
Paste the template to a poster board. Carefully cut along the BLACK LINE. That is the tangent track center line followed by the easment center line. I usually extend the tangent center line a little more for acuracy.
The “curve” is the center line of the easement track which will then blend into the center line of the arc you are entering from the easement.
The beauty of this KISS method is that it only takes only a minute to draw each one. For example, if using 30 inch radius curve, measure 30 1/2 inches from the tangent 90 degrees from the center line as far along as necessary to place the curve where you want it to be. The same as if you are not using an easement. Draw as much of the curve as you want including starting at a point just before the 90 degree point of the tangent.
Place the template tangent side along the tangent line and then slide it along until the easement curve blends with the 30 inch radius curve you have already drawn.
Gotta take exception with you on this one there, tomikawaTT.
I can get an N Scale 85 foot passenger car with body-mounted couplers to EASE into and out of a 9 inch radius curve - it looks like aitch on a curve of that radius but it will negotiate it - at speed and only experience an occasional trouble; if I try to LURCH an 85 foot passenger car with body-mounted couplers into or out of that 9 inch radius curve I will almost guarantee you that I am going to have troubles.
I don’t lay my curves nearly that sharp but I still use easements; I even use easements in industrial trackage because it enables me to use curves of nine and ten inches. My experience with easement curves even in the model railroad environment is that they are not only cosmetic but practical.
Methinks you misunderstood ME, pardner. I am a big advocate of easements - in fact my mountain-country railroad can be accurately described as a bunch of curves connected by easements with an occasional tangent. My point was that it doesn’t take number-crunching with an old plugboard IBM mainframe to create a visually attractive and operationally effective easement.
By using my method, I can locate a curve center without wondering what offset a template will give me. That one variable is what turned me off to templates clear back when this article was first published.
Chuck (modeling Central Japan in September, 1964 - with easements)
tomikawaTT, you are absolutely correct - I did indeed, sir, misunderstand your response and it was the fault of incautious reading on my behalf. I formed my opinion based upon that portion of your response which I cited in mine - I jumped to the conclusion that you were criticising easement curves in general whereas your criticism appears to be leveled at Linn Westcott’s techniques and the templates he designed to accompany his article published way back when Custer was a first-year cadet; you criticism is well taken because that article has, over the years, tended to cause considerable confusion. I should have realized that for you to take the time to outline your procedures for laying out easements you, in reality, do see value in them.
I have a number of radii-easement-tangent jigs cut to facilitate laying out easement curves; they are cut from 3/8 inch ply, the same thickness I use for my subroadbed, and they cover an arc of 135 degrees and provide a tangent length of 6 inches. I have about 12 of these the largest accomodating a 24 inch radius curve; since I tend to construct double track main lines every time I cut a radii-easement-tangent jig for one radii I have to cut one 1.5 inches smaller to align the inside track. The easement portion of these jigs was layed out using a spline-bow which I can adjust to varying arcs. I am hopeful of doing my next/new layout with splined roadbed and I am currently working on a spline-bow jig which will enable me to set the splined roadbed without too awfully much trouble.
Doesn’t that have something to do with volts and amperes?
“…I tend to construct double track main lines…”
I’m glad to hear that. It seems that very few layouts have double track mains, yet I view them as a “standard,” with anything less being a bad compromise. I’ve planned double track from the beginning. I also feel that trains should run on the right-hand track of the double track mains, except in very special cases. There have been several very ugly fatal crashes due to running 1:1 trains on the left-hand track.
Back to easements, my research for this thread didn’t discover any “easement sections” for sectional track. The old Lionel and American Flyer track didn’t come with easements, either. I wonder why the manufacturers don’t make them?
Here are some more links: one, two, three (included under two, in case you missed it), four.
I presume that you consider two sovereign island nations and a continent to be special cases. My double track won’t even be signaled for right-hand running.[:-,]
Lionel, American Flyer and the current sectional track is meant to be used for TOY TRAINS, not serious model railroads, the same reason that Power Wheels cars don’t have working speedometers.[;)]
Back when, a MMR who will remain nameless inserted sections of 1.5 X minimum radius and 3 X minimum radius to provide easements of a sort. It was a small improvement over nothing.[:-^]
Thanks for the data.[8D]
Chuck (modeling Central Japan in September, 1964 - to JNR standards, including left hand running)</
Here’s a good tip if you are doing a layout with a lot of curves. From your local DIY supply such as Home Depot, Lowes, etc. get a 1/8" sheet called a “door skin” for re-facing doors. Rip it up into 6" to 8" wide strips lengthwise. (it also makes great, bendable fascia boards). Now take a strip, allow 6" or so for tangent along one edge. Then do your easement and curve layout. When satisfied cut just outside the line with a saber or jig saw. Sand the edge down to the line. Now mark all the important points along both sides, the offset of true center and tangent and curve connection points. Also write on both sides with a waterproof marker the radius, L/2 (the distance on either side of the true center perpendicular, and the offset. You now have a template that you can flip over for curves in either direction for use anywhere on your layout! I love big curves and have made templates for 36", 42", 48", and 72" radii. jc5729 John Colley, Port townsend, WA
