As built geography, track plan, and route map

One design principle that I try to adhere to is to think about the routes that can be travelled through the layout's space so people can get to the various areas. It's related to using sight lines as a design principle that I discussed earlier this year.

I like to have the roads, tracks, sidewalks, trails, and so on mapped out and understood how they connect up the layout's areas. As I'm working on that I try to make sure these things have fairly realistic dimensions as they're being laid out. The roads can't be too narrow, the walking gradients can't be too steep, and so on. Thinking about these things helps me keep the scenes within the realm of possibility. I often think getting the routes through the space physically right is more important than detailing, well, at least as important. 

Shown above is one such route map. It isn't the only one of course, but thinking about it helped me a lot in developing scenic possibilities.

The Trefoil Transform

In issue #119 of Voie Libre there's a story about a fascinating O-14 layout called The Boidon-Cuncou Wire Drawing Mill. When I saw its trackplan it seemed like a trefoil to me even though it's more like a triangle with rounded corners - it's likely another case of me seeing trefoils in everything :-) So somewhat tongue-in-cheek I applied The Trefoil Transform to trefoilize it. Well, the trefoilization was not that effective as I think the trackplan would require further modification if it were to be used on a trefoil layout board. But, that inner trackage provides an interesting starting point for a trefoil based layout that is something other than a simple tour around the perimeter. 

6 views, not 3

Ok, I've finally finished the first round of mountain surfacing.

I've decided the next step should be priming the surface with gesso to even out the colour to look for areas needing improvement. 

When I sat back to look at the thing I realized the trefoil planform offers 6 basic views, not 3. I was fixated on the lobes, of which there are 3, but completely ignored the negative spaces, of which there are also 3.

Well, look, even 6 views isn't the limit. There are an infinite number of views, but there are 6 basic viewpoints.

Negative space. It's easy to overlook.

Well, I need to head back to the grotto to see if there are any more spaces that need looking into. I'll leave you with The Belle Stars:

A sign from above?

While out on today's walk I saw this licence plate. It stopped me in my tracks. A sign from the Mt. Lowe model railroading universe? If I see one tomorrow that says Mt. Lowe I'll be looking over my shoulder for Rod Serling :-)

How I built the Mt. Lowe layout's trefoil base

Trefoil layout base made from styrofoam. Area is 4 sq. ft..

Last fall I wrote about some notes Bill Schopp published on trefoil planform layouts. I've been intrigued with the shape since then, especially for micro-layouts, and I spent many evenings last winter making drawings in my sketchbook of possible layouts. The shape seems to offer a way to build small layouts with good scene separation since each lobe could host its own scene with vertical elements providing a degree of visual separation in accordance with the design philosophy advocated by Olson and Furlow.

The glued up base is a 2-1/4" thick, 3-layer foam sandwich.

I like to use foam sheets for my layout bases because the results are lightweight as well as quite rigid and strong. Foam sheets are also easy to work with. 

I made the base for the Mt. Lowe micro from 3/4" thick sheets of styrofoam measuring 14-1/2" wide by 4' long that came in a 6-pack from a big box home renovation store. I think the price was around $17 CDN. This isn't the only material you could use to build a base. It just happened to be convenient, and I also had some scraps in the workshop, so that was what I used. 

Paper template; 4 sq. ft., maximum micro-layout size.

You may recall that last fall I also drew a full size template of a 4 sq. ft. trefoil shape so I could physically compare it to a square of the same area. I made use of that template to trace the lobes onto the styrofoam sheets. 

Once again, I'd like to make it clear that you don't have to build up the base in pieces as I'm showing here. If you have a large, thick sheet of foam you can cut the entire shape in one piece from it. In fact, that would be the best way to go, but if all you've got are small pieces, you aren't prevented from making a base, you just have to be a bit more cunning.

Lobe template detail showing interior edge lines.

Do you see those lines radiating from the centre of the template marked by the red arrows in the photo above? Those are the interior edges of the three lobes we're going to cut out. I laid the lobe template on a foam sheet and with a Sharpie pen traced around the lobe's perimeter to where it intersected both those interior edge lines. Then I marked the trefoil's centre with a dot - I had previously punched a small hole in the centre with a compass. After I lifted the template from the sheet I used the Sharpie and a ruler to join the centre dot with the ends of the lobe's perimeter. 

All three lobes laid out on the styrofoam sheets.

I repeated the process two more times to produce three lobes. It was then on to cutting them out.

Checking the fit of the interior edges.

I cut the interior edge lines first so I could check the alignment of the pieces before trimming the lobes' perimeters. I used a razor saw and a metal ruler to make the cuts.

After trimming the lobe perimeters to shape.

The lobe perimeters were then cut to shape freehand with the razor saw. Once the cutting was done, the edges were lightly sanded to smooth them a bit.

Gluing the lobes together. A weight holds the pieces down while drying.

The next thing to do was glue the lobes together. Start by spreading a generous amount of white glue over all the internal edges, then press them together. That metal box in the photo is full of nuts and bolts and is a good weight for holding the lobes in place while the glue dries. The box is an item from the workshop stuff I inherited from my father. I think he made it in high school shop class in the '40s. It's still full of the nuts and bolts it has always contained. That stash comes in handy now and then, not to mention its weight :-)

Filling layer for the styrofoam sandwich that will be the base

Here it is a few hours later after the glue has dried. The pieces fit together quite well. 

At this point the base is quite flimsy and needs careful handling, so be gentle moving it around. What we're going to do next is make a styrofoam sandwich with the above layer as the filling.

Applying the first piece of a 'bread' layer to the centre section.

The top and bottom bread layers of the sandwich are pieces of sheet foam glued to the filling layer we just made. At this stage, the bread pieces don't need to be cut to any particular shape. We'll trim them up once they're glued in place. 

Start by taking a long sheet of foam and laying it on the filling layer so that all three of its edge joints are covered. The sheet can extend well beyond the top and bottom of the filling layer - we'll trim it later. Now apply a generous amount of glue to the area on the filling layer where the bread sheet will go. Place the bread on top and hold it in place with some weights and clamps. Yeah, I've got a second collection of inherited nuts and bolts I keep in a plastic bin, and along with the metal box inside, it makes for a nice weight to hold this half sandwich together while the glue dries. 

Applying a bread layer to a lobe.

When the glue has dried, trim the bread piece's edges so they match those of the filling layer. The next steps are just a repetition of that first application of a piece to the bread layer. You keep gluing on pieces until both sides of the filling layer have bread sheets glued to it. There's nothing special to know other than these two points to keep in mind: 1) make sure you apply a large slab over the centre edges that covers them and as much of the filling layer as possible, and 2) make sure the joints of all the other bread pieces applied to the lobes have the joints staggered with respect to the top and bottom layers. Point 2) helps make the base is as strong as possible. If the joints on the upper and lower bread surfaces line up it makes for a weaker final structure.

Almost done adding pieces of bread :-)

The above photo shows the base when the sandwich is almost done. Over on the left side of the photo you can see the perimeter is rough cut at this stage. Once all the pieces of the bread layers had been glued together and cut to match the filling layer, some final shaping  was done with a rasp and sanding block to smooth out the contours.

All the trimming of the bread layers creates a lot of styrofoam odd cuts. I saved most of them for use when building the mountain scenery.

And here it is. The sandwich is done and awaiting perimeter smoothing.

This way of making the base is fairly easy, although it does take a bit of time. So, if you've got a few pieces of sheet foam lying around, this method allows a layout board to be built up from those scraps.

Before I go for coffee I should mention that when I built this base I wasn't sure if the layout would work, that is, I didn't know if could I successfully install the multilevel track plan with its complex - well, complex for me - grades, easements, and curves. Now that track work is behind me, and the layout appears viable, I think I might add some extra foam layers to the bottom so I can cut in some deep valleys to make the track seem even higher. Well, that's for the future, now is for coffee :-)

Trefoil knot as trackplan?

Since writing about Bill Schopp's investigation into trefoil layout boards I've been looking online now-and-then for information about trefoils.

One interesting page I found was this one on trefoil knots. It got me thinking that trefoil layout boards are all well and good, but the important thing is having an interesting track plan running on them. I started wondering if any of those knots could be the basis of a trackplan. Clearly they  would need to be adjusted to account for the physical realities of track. They also might have a bit of the 'rabbit warren' about them, but for something like a Mt. Lowe inspired layout, that might be a good feature to have. 

Anyway, I parked those thoughts until last week when Voie Libre #115 dropped in my mailbox. Inside there's a gorgeous HO-9 circular layout - size unspecified, but it might have the same diameter as an extra-large pizza - by Frédéric Blandel whose trackplan seemed to me like a variation on one of those trefoil knots. Here's a side-by-side comparison of the layout's trackplan against one example knot:

Left: One possible trefoil knot | Right: M. Blandel's trackplan

M. Blandel's trackplan is not a pure trefoil knot, but it certainly appears to be in the spirit of one. It's ingenious and allows for both continuous scenic running as well as a little switching fun for when the mood strikes. And there doesn't appear to be a need for overly complex wiring as there are no reversing loops. This layout might be thought of as a trefoil knot trackplan on a circular board. It might be interesting to see what a trefoil knot based trackplan on a trefoil board would look like.

Bill Schopp, Trefoil Micro-Layouts, and Me in 2023*

Trefoil planform (according to Bill Schopp) shown in blue outline

There’s a brief note by Bill Schopp in the Trouble Shooting column of the May ’68 issue of Railroad Model Craftsman about a new idea for a layout table’s planform: the trefoil**. The idea was brought to Mr. Schopp’s attention by an enthusiastic reader identified only as ‘R.W.D.’. It seems Mr. Schopp was both intrigued and dismissive about the practically of the idea even though the reader said he was well into construction of a trefoil shaped layout. On the one hand Mr. Schopp notes his conflicting views:

“This idea held me enthralled for 3 days now trying to draw interesting layouts for it in N, HOn3, and HO traction with little success. I discarded at once the idea of ‘scenery first, track afterwards,’ as suitable for prototype but not model railroads: it’s the kind of idea an armchair expert could convince himself was the ‘only way’. I’ve drawn and redrawn the trefoil design with variations and have come to the conclusion that as a site for a layout, the trefoil table has little or no merit. But, I am constantly gnawed by the suspicion that I may be putting down one of the greatest ideas to hit model railroading since…well, since 2-rail.”

But then he firmly concludes that the trefoil planform probably is “not a good model railroad table” and goes on to list 3 issues he has with it:

1. “…it would restrict the design of a pike either to just following the curves, or making a 3-lobed version of a figure-8.”

2. “…takes up a terrible lot of space.”

3. Requires advanced carpentry skills to build.

In the Sept. ’68 issue a R. W. Bide of Lethbridge, Alberta wrote in to comment on Bill Schopp’s assessment,

“Thanks for not squashing the Trefoil. It’s the first sensible island design I’ve seen and I’m an around the walls layout fan. Two very good treatments for a start. Very high center of the lobe for scenery and a central valley full of action or very high ridges along the center lines giving three lovely scenes. Treatment could be a gorge or canyon, Lake Superior Shore or other Canadian Shield stuff. Or even a horseshoe curve. Walk around control with complete success. One lobe might be enlarged to the width of the others. The biggest problem I can see is radii but horrible curves can be hidden.”

When I read that letter I wondered if R. W. Bide was actually the mysterious ‘R. W. D.’ who alerted Bill Schopp to the trefoil planform. RMC didn’t have the most stringent copy editing in those days, so I wouldn’t be surprised if R. W. B. of Lethbridge was ‘R. W. D.’. I’ve looked in later issues for any mention of Bide’s trefoil layout, but I haven’t found any, so I don’t know how his worked out. If I find a story I’ll post an update.

Then in the Oct. ’68 issue a David Zavadi of State College, Pennsylvania wrote in to say that he derived the area of the trefoil plan and gave this equation***:

A = R² (6 √3 + π)

A is the area of the trefoil, and R is the radius of the circle upon which it is based.

Given the aforementioned copy editing issues I decided to see if I could still manage some high school level math and tried to derive that equation for myself. It was tough getting the brain going on these sorts of problems again after decades of neglect. I felt faint at times and had to lie down :-) but in the end I was able to confirm the equation is correct.

After getting this far I wondered what would R have to be for A = 4 sq.ft., which is the largest allowable area for a micro layout? The area equation needs to be re-arranged for R,

R = √ ( A / ( 6 √3 + π ) )

Plugging in A = 4 sq. ft. and evaluating the equation it turns out R = 6.5 inches. Ok, I should clarify the actual answer is 0.543699 ft, but I converted it to inches and rounded down a tad to get the more conservative and easily usable value of 6-1/2”.

4 sq. ft. trefoil compared to 2' x 2' foam square

I wanted to see how a 4 sq. ft. trefoil compared to a 2 ft. x 2 ft. foam square like the one I used to build the Loonar Module. So, I got out some paper, masking tape, scissors, compass, ruler, and protractor and went to work to make a paper trefoil. That's the result over on the left.

It looks like a very large fidget spinner.

4 sq. ft. trefoil overlaid on 2' x 2' foam square

Overlaying the two planforms gives a slightly better size comparison. 

Could this be the basis of a micro-layout, or do Bill Schopp's concerns squelch layouts in this category too?

I don't have a definitive answer. I think many of the points raised by Schopp and Bide still apply; however, I'll note that unlike back then we can build layouts from foam slabs, have wireless DCC control, have lots of specialized track and power trucks available, and it's not unusual for micro-layouts to be just simple track loops where scenes and scenery are the main points of interest. There need not be a concern with trying to simulate a fully operational, real railroad, or even a piece of one. So, maybe Mr. Schopp's concern with only being able to build a 3-lobed figure-8 track, or some such variation, might actually make for an interesting micro-layout. I look at the trefoil planform and think that it might be the way for me to build the Mt. Lowe layout I've wanted to do for years now. I can imagine each lobe providing a separate scene: circular bridge, granite gate, and the look out all visually separated by some suitable central rocky outcropping. 

4 sq. ft. 3-circle trefoil compared to 2'x2' foam square

If you look at this post's opening drawing with all the packed circles you can see that it's possible to slice out a three-lobed planform from the matrix based on just 3 circles instead of 4. This gives a less spindly and more compact planform.

The area for this shape is:

A = R² (4 √3 + π)

and the radius of the circle upon which it is based is:

R = √ ( A / (4 √3  +  π) )

If A = 4 sq. ft., it turns out R = 7.5" (again, I slightly rounded down R to yield a conservative and easy to use value).

4 sq. ft. 3-circle trefoil overlaid on 2' x 2' foam square

The overall shape is a bit blobbier than the 4-circle version, but it still has three distinct lobes. 

I've got to admit an advantage of the 2' x 2' x 1" pre-cut foam square is its convenience. I bought mine at Home Depot, but I should point out they are expensive for what they are: around $7 or $8 per square, which is crazy on a per sq. ft. basis compared to a 4'x8' sheet, however the pre-cut convenience can't be beat. If you're going to build either of these trefoils some cutting and gluing of foam slabs will be necessary. Or, maybe a base could be built up from corrugated plastic sheets. All this is just to say that some base construction will likely be needed, but likely no expert carpentry will be required as Mr. Schopp noted for his 1968 readers.

I haven't done a comprehensive scan of the internet, so I wouldn't be surprised if a lot has been done with trefoil planforms and their variants, so please excuse the naiveté on my part if this is obsolete news and it's just new and interesting to me.   

Digressions:

*What does this have to do with 1977? Well, nothing in the actual 1977, but in the alternate, phoney, time travelled to world of 1977 where I found this June 1977 issue of Rail Model Experimenter, a lot. Apparently that issue contained a lost article by Bill Schopp called, Advanced Trefoil Trackplans. In retrospect, I should have consulted that piece before even considering this post. If you have the issue, please let me know what's inside :-)

**The trefoil entry in Wikipedia shows shapes somewhat different than the ones in Bill Schopp's Trouble Shooting note. In this post I'm going to go with the nomenclature used in the old May '68 RMC story and leave investigating strict definitions for another time.

***The letter and the editor's associated comment mentions integration, polar coordinates, high symmetry, analytic expressions, "equasions", "plain" geometry, and so forth being deployed to find the area. For the trefoils shown in this post finding a closed form equation for the shapes' areas is not too hard, but what if you wanted to figure out if an irregular trefoil you were planning to use was less than 4 sq. ft. so it would still qualify as a micro-layout? It could be a tough go to calculate the area by developing equations for an arbitrary shape. It might be far more practical, and just as accurate, to use this method described in The Scientific American Book of Projects for the Amateur Scientist.

Layout boredom and other maladies

Current thinking on the right hand page

I’ve concluded that my layout, the Ocean Park Loop, is boring. Its got some nice points, and I’ve learned a lot during construction, but at the end of the day it’s missing something essential that my old Lost Ocean Line had. The only reason I gave up on the LOL after a couple years of fiddling and use was that I felt I had exhausted all the things I could do with it. 

Problem is the new modular layout seemed to exhaust itself far sooner than the LOL. 

One of the big issues with the current layout is it’s too big. All the modules can’t be left assembled because the layout takes up too much room, and since it’s always disassembled, I can’t run streetcars on a whim to try things. But most importantly I think the current layout is too rigid in its concept and doesn’t allow me to explore all the ideas I have. I realize that I’m not interested in rigorously replicating Toronto streets, but in capturing the essence of my experiences and thoughts.

Beginning thoughts

I’m thinking these days a variation on the LOL - adding the missing aspects the old one lacked and fixing problems - is the way to go. 

What were those LOL issues? The track plan was too complicated and unnecessarily chewed up space that I could have used for scenery and buildings - making buildings and scenery are the things I like the most. I need a simpler track plan that is more streetcar-like than train-like. It needed an urban mainstreet - long and straight, but not too long - for staging ‘typical’ Toronto streetcar scenes that allowed for buildings to be swapped in and out. It needed to be a little bigger - maybe 25% bigger - for ‘breathing room’ as well as providing space for a few more buildings and trees. It was too heavy and used too much wood - I was paranoid that it wouldn’t be strong enough so I over built. I think I could build something a little bigger than the LOL that would be significantly lighter than the original.

Next steps

Back when I was first thinking about the LOL I posted a list of things I think it needed to incorporate. Reviewing the list, I’m still more-or-less in agreement, but I’ve added a few things, so here’s an update.

1. Continuous loop

2. Flat, lots of real estate for buildings

3. Double track, switch-free, straight, downtown street

3. Buildings can be swapped in and out and re-arranged

4. Portable, easy to carry, fits in my econo-box car

5. Easy to take upstairs from the basement for showing off at Christmas and such

There's a Bill Schopp trefoil in there - more later

6. Lots and lots of trees and vegetation

7. Beachfront 

8. Ocean

9. Any and all switches at front

10. Streetcar to the beach

11. The smaller, the better, but not too small

12. Scattered Toronto and Los Angeles

13. One storey residences

14. Innocuous track

15. Lights and lighting and LEDs

16. Surfboard sized

17. Lots of pathways

18. Lightweight

19. No corners

20. Turntable

21. Retro-future, modern, re-purposed stuff

22. Eye-level views

23. DCC and DC

24. Landscape view 

25. Sydney-by-the-Sea

26. Blue, green, sunny, open

27. Percherons

29. People, figures, easy living

30. Streetcars, small diesels, trolleys, railcars and any other small rolling stock

31. Clean construction

32. Houses, cottages, and cabins

33. Streetcar-y track arrangement, not train-y track arrangement.

Most layout planners are far more rigorous than me. I don’t make formal drawings or elegant sketches or use software tools. I have some notebooks and just make rough sketches as my thoughts develop. 

With passing loops a la the Morecambe Tramway

Once I think I’ve settled on a basic plan I’ll pull out the old brass rail and make some full-size sketches in track. 

I’m not trying to be precise at this stage, I’m just playing with lines at present.