A Degree in Curves

What has to be out of scale in even the most spacious layouts? The
curves! – John Armstrong, The Classic Layout Designs of John Armstrong, p. 74.

On my post on my 4th, experimental layout I mentioned that I ran into an issue with curve radii. In this post I’ll describe the results of the subsequent research I undertook on curves.

First, of all there are two types of limitations for model railroad curve radii: operational and aesthetic. Our model trains are designed to be able to negotiate much, much tighter curves than prototype trains, so there has been a lot of published work addressing operational limitations. I’ll cite some of that work here, but my main concern is the aesthetic side.

Operational radii limitations

In his terrific book, Track Planning for Realistic Operation, John Armstrong discusses radii limits on pages 73-77 and provides this table:


Armstrong goes on to define each type of curve by the type of equipment you can reliably run on it. (A much more detailed table is provided by the NMRA, standard RP-11, for those trying to find the absolute minimum curves for their situation.)

In his book John Armstrong also provided a great suggestion for pushing these operational limits, demonstrating 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. Armstrong called that the “coefficient of lurch”, and showed how spiral easements – a section of track that transitions from curve to tangent – can reduce the coefficient of lurch and allow a tighter radius than would otherwise be possible. On page 75 he shows 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.

I highly recommend this section of Armstrong’s book for anyone who is trying to squeeze tight, but operationally sound, curves into a layout. Actually, I highly recommend the whole book for anyone interested in getting serious about layout design.

Aesthetic radii limitations

When you are building layouts with curves that test the limits of how tight curves can go you don’t worry about the aesthetics of how trains look going around the curves. I mean, it’s pretty obvious that an HO train going around a 15” curve or an N scale train around a 9” curve don’t look anything like the prototype, with the trucks turned at extreme angles and the ends of the cars hanging far over the sides of the track. You know it looks wrong, but due to space limitations that’s just something you deal with. That’s the situation I was in with my first 3 HO layouts.

At some point you may decide that for your NEXT layout things will be different. That’s how I was with my 4th layout, my first N scale experiment. I was still dealing with a 4x8 space, but now in N scale. A 17” radius curve in HO scale is very sharp, per the Armstrong table above, but in N scale it’s a broad curve. So I built a bunch of 17” curves, and even built one curve to 20” radius just to see how a “very broad radius” curve looked. But as I watched the trains go around it something slowly dawned on me. Yes, the trains did not look as ridiculously toy-like as they did on very sharp curves, but even the 20” curve was still obviously way too tight.

Fortunately, John Armstrong also wrote a lot about the aesthetics of railroad curves (the quote at the start of this post was how he began one article) and that gave me some good information to start my research. First, the conventional measure of how sharp a curve is, at least in the U.S., is degrees of curve, which is how far a curve would go around a circle in a 100 foot arc. For example, suppose you had a circle with a 400 foot circumference. Then 100 feet of arc would cover 1/4th of the circle, or 90˚ (since a full circle is comprised of 360˚).

Prototype railroads naturally try very hard to limit curves – both the frequency of them and the sharpness – because curves add drag to the locomotive pulling a train much the same way that upward slopes do. Many mainlines get by with curves no sharper than 2˚ and in flat country a 5˚ curve may be unusual. The famed horseshoe curve on the Pennsylvania Railroad came in at 9.25˚, which Armstrong saw as the standard for comparing mainline curve sharpness. Finding curves sharper than that on standard gauge mainlines is hard – up to 12˚ can be found in a few areas with difficult topology and/or congested urban areas, and anything above that is rare. Narrow gauge commonly went much tighter – the Rio Grande lines typically had 24˚ as their maximum curve sharpness, and one famous narrow gauge curve in Utah was an incredible 60˚. But narrow gauge trains also typically ran at very slow speeds with very short cars

So how does this compare to our model empires? Well, a 5˚ curve in HO requires an astounding 158” radius—that’s over 13 feet. 10˚ is a little better at 79”, but that’s still over 6.5’ – and if you tried a U-shaped curve with that you’d need a diameter of over 13’. N scale is much better, but 10˚ is still about 43” radius – over 3.5’.

To better understand how model railroad radii compare to the prototype you can construct a simple spreadsheet table. Here is a small sample of a table I created in Excel:


In order to create this yourself, put the radii in the left column (A), then put the following formulae in columns B and C:

=((1200/160)*180)/(3.1416*A[row#])
=((1200/87)*180)/(3.1416*A[row#])

To explain each element in the formula:

1. “1200” is the number of inches in 100 feet. 100 feet is the length of the arc that we use as the basis for the degree measurement. When measuring for large scale you’ll want to use feet as the measurement, so change this to 100.


2. 160” or “87” is the scale you are using, in this case N and HO respectively. Substitute 48 for O scale, 220 for Z, etc.


3. 180 is the number of degrees in a semi-circle. You might think we’d use 360 for a full circle, but because we are basing this formula on radius, which is half a diameter, we cut the number of degrees in half as well.


4. 3.1416 is an approximation for π.


5. The “A[row#]” is the number of inches in the radius. When measuring for large scale change this quantity to feet – and do the same for (1) above.

It helps to create such a table yourself because it gives you a chance to play with the numbers and see the possibilities for your situation. But no matter how you slice the numbers you’ll see why John Armstrong made the statement which started this post – with curve radii the difference between the model and the prototype is just huge.

Out of doors the situation isn’t quite so bad, although it is still challenging. With large scale minimum radii are measured in feet, not inches. If you model the narrow gauge Rio Grande, as I am doing, the 24˚ minimum translates to a bit under 12’ radius in 1:20.3 F scale, which means a half-circle turnaround requires a diameter of about 23.5’. That’s still a lot of space, but doable on many outdoor lots.

For indoor layouts John Armstrong recommended that model railroaders set a minimum radius based primarily on operational requirements, but that they made sure to include one curve of realistic gentleness – 10˚ or less – for aesthetics. This is a good recommendation, but there are also other things you can do with regard to curve radii, and I cover those in the next section.

Dealing with unrealistically tight curves

Here is a short catalog of things people have done, or can do, in response to the realization that model railroad curves look unrealistically tight. These are not independent solutions, as it is possible to use a combination of any or all of these solutions on a given layout for different situations.

1. Ignore the problem
   
   Seriously, if it doesn’t bother you don’t worry about it. We have to make a lot of other compromises in our make-believe empires. Alas, for me this doesn’t work … for me many a picture of an otherwise terrific model railroad has had the illusion spoiled by an curve that is obviously too sharp. This depends entirely on your personal preference.



2. Hide the problem
   
   This is probably the most common solution, other than #1. Put the curve under a tunnel or behind a viewblock. I did this with my second and third layouts (well, that is I would have if I’d completed the scenery) and if done well it can also hide the overly short consists we tend to run on our smaller layouts.
   
   However, this is not perfect. Except for switches, curves are where most derailments occur, so you have to arrange some kind of access to those tracks. Depending on your chosen model theme the viewblocks and tunnels may seem out-of-place (the original Rio Grande was positively allergic to tunnels, for example), so you may be introducing an element that doesn’t look appropriate for the scene. And finally, for smaller layouts, like my third one, hiding all the curve track ends up hiding the majority of track, which may not be as pleasing as you thought it would be when you started.



3. Disguise the problem
   
   This is different than hiding the problem in that you leave the curves out in the open but control the optical viewing angles to make the curve sharpness less obvious.
   
   The most common way to do this is to move the layout to eye level or near eye level, and the second most common is to arrange the track so that viewers can see the train only from the inside of the curve, not the outside. When used together this makes it almost impossible to assess just how sharp the curve is.
   
   The eye level trick, by itself, certainly helps because the viewer can’t look down on an empty track and see how obviously sharp it is. In fact, this also helps disguise unrealistic “spaghetti track” formations because the viewer only sees the side of the nearest track. However, eye level doesn’t help quite so much when the viewer is on the outside of a tight curve, as the angle between cars tends to be a visual giveaway.
   
   Also, eye level layouts are the subject of one of the hobby’s great debates. Proponents love them because “you see trains just as you do in real life”. Critics (and I am one) argue that in “real life” we often seek out platforms from which we can look down on trains and get a better view, so a view from above is actually a good thing. Furthermore, we argue, if you want the eye level view you can still get it with a lower layout by bending or sitting down. Lastly, not everyone has the same eye level, and shorter people and children tend to get short changed with layouts set at 66” or so above the floor. I’ve noticed in recent years a trend away from the eye-level traveling layouts that were prevalent 10 or so years ago.
   
   The view-from-inside-the-curve trick is useful anytime, even from higher levels, although it’s most effective at eye-level. Unfortunately you can’t always limit your layout to only inside-the-curve views – and in many cases you can only build outside-the-curve views, such as with a rectangular-shaped show layout. However, if you have an inside-the-curve view you can take advantage of that to use a smaller aesthetic radius than you use elsewhere.



4. Build layouts that require minimal curves
   
   Tight curves are only a problem if you need curves. A long industrial, point-to-point shelf layout doesn’t need them, for example, except for very short lengths. Or if your layout requires only one or two U-turn curves you can hide those (per point 2 above) and emphasize the rest, including building straight track over the hidden curves.



5. Choose curvy prototypes
   
   Kind of the opposite of (4). Instead of choosing a layout theme that requires no curves, choose a prototype that had lots of very tight curves that you can either match exactly, or perhaps model just a little bit tighter.
   
   Two very obvious examples of this are narrow gauge railroads, which as mentioned above commonly had curves of 24˚ or tighter, and trolley systems, which were made to negotiate curves around street corners. Also popular for modelers are the common industrial short lines of the last century, run by very short steam, diesel or even electrical locomotives, that moved shortish (50’ in length or less) cars amidst very congested commercial districts.
   
   These types of prototypes are popular for many reasons, but certainly one key reason is that they fit into our layout rooms without having to compromise the curves.
   
   The only problem with this solution – as with solution (4) – is that it only applies to certain layout themes. If you want a layout featuring heavy mainline traffic these solutions don’t apply.



6. Convert to a smaller scale
   
   Admittedly this is not a viable option in most situations, since most people have a strong reason for choosing a given scale and often already have a sizable stock of items in that scale. But this can be a really useful design trick when viable. Alternatively, you can use this same trick by forcing yourself to design a layout for your space in a larger scale, then switch to your own scale.
   
   You see, most people try to cram as much layout as they can into a given space (count me as one of those guilty of that sin). Double the space available and few of us will simply expand the same basic concept to the new space, but instead most of us will try to add more towns, yards, and industries. But what if you struggled through a given layout design for a limited space, making the normal sorts of compromises before finally getting a design that you think you could live with, and suddenly someone offered you 3.5 times the space – or even 7 times the space? What if instead of trying to cram more into that space, you decided to keep your previous design but simply apply it to the larger space, using longer trains, more space between towns, and larger radii?
   
   To see what this might look like, consider John Armstrong’s famous personal layout, the Canandaigua Southern. He chose O scale, which was still very common in the 1940s when he started the layout. Here is a map of that layout taken from the March 1971 Model Railroader:
   
   
   John spent a lot of time designing this, a process he described in an article which can be found today starting on page 46 of The Classic Layout Designs of John Armstrong book mentioned earlier. Like all of us, he had to make compromises to fit everything in. He settled on a minimum radius of 48”, which is about 30˚ in O scale, and of course accepted shorter consists and a smaller yard than he probably would have liked. The fact that all track was handlaid meant it still took him decades to complete the line, with only partial scenery, but nevertheless the layout gave over 50 years of enjoyment to Armstrong and the large number of his friends who helped him build and operate it.
   
   Now imagine you had exactly the same room, with exactly the same layout, with curves and towns at exactly the same location, but this time you worked in N scale. That 48” minimum radius now gets you curves of slightly under 9˚! You can triple – or more – the number of tracks in the yard and the length of your trains. Or, if you don’t want to add that much length to your trains, you can increase the apparent distance between towns.
   
   Consider that Armstrong’s personal layout is universally considered a great success. Not just because it was so innovative (which it was – no other layout has pioneered so many influential design concepts as this one did) but because it was FUN for all involved. An N scale layout, in the same space with the same essential design, would generate just as much fun, but the trains would look much more realistic.
   
   So, apply that example to another layout. Let’s suppose you’ve designed an HO layout for your available space but you’ve got some nagging concerns. Now try doing the exact same layout in exactly the same space, but in N scale. Wow. You’ll have the same schematic but with a lot more room. Or, suppose you can’t change scale. Instead force yourself to design a layout for a space of about ½ of what you actually have, then after you polish it, convert to the space you actually have.



7. Set very high minimum radii during the design phase
   
   So, you’ve tried everything else, but you still don’t have a solution that works for you. You care about getting realistic curves (otherwise #1 would work for you) but for various reasons none of the suggestions given above work: you can’t hide/disguise the curves, the prototype you want won’t permit you to use tight curves realistically, you can’t move to a smaller scale, and the trick of pretending to have a smaller space than you really do doesn’t work for you.
   
   If this is your situation, then you are where I was in 2003 and 2004. So I tried something else. Most layout design books will recommend that as an early design step you set some standards, such as “minimum switch size”, “track spacing”, “maximum train length”, and of course “minimum radius”. These standards may vary depending on situation – such as separate standards for mainline, branches, yards, and staging— but within a given category they are the basis for your design.
   
   So, set your “minimum radius” standard to a very high number and see what kind of layout you can design. For me I chose 48” as an N scale minimum and started trying to design layouts using that as a rule. It was enlightening in a way that can only be understood when you actually try to do it – as opposed to reading about it. Consider, for example, an around-the-walls kind of layout. A 48” minimum can easily be used in curves in the corners, but this means that the tangent track between two corners will be a full 4’ shorter than if you use a 24” minimum curve and 5’ shorter than using an 18” minimum. Let’s suppose you have a 12’x12’ room and that you generally keep track at least 6” from the walls. This means that if you use an 18” minimum radius the longest tangent track you can have between two corners is 10’ but that for a 48” minimum radius the longest tangent track is only half of that.
   
   That example describes only one of the early discoveries you’ll have. As you work more with the layout design you’ll discover ways to work with the larger radius curves, such as working switches into the 48” curves. Since 48” is a very gentle radius in model railroading terms transitions from curves to switches flow better, especially with spiral easements. And if you use a switch like the Peco code 55 “long”, which uses a 36” constant radius on the diverging route, or the Peco code 55 curved switch, which has 36” for the outside curve, the flow is even better.
   
   Eventually you may find that your ultra-wide radius is workable AND that the resulting track will flow much more easily. Of course, there will be sacrifices in terms of what you can include – there have to be – and only you can determine if the trade-off is worth it.

My personal solution

That concludes my discussion of options for modeling realistic curves. So what did I end up doing for my layouts?

For the iNdoor layout, after working with 48” for a while I tried 44” and 36” to see the difference in terms of layout planning. I then set up a number of curves with temporary track to view the appearance of trains on the various radii. What I discovered wasn’t surprising. While a difference of 5” makes a huge different in appearance for trains on small radii, such as going from 10” to 15” – it makes only an almost imperceptible difference in appearance in large radii, such as going from 43” to 48”. Once I recognized this I really had to question whether the benefit of going the extra effort for 40+” radii was worth the cost in terms of design trade-offs.

Eventually I settled on 36” as the absolute minimum for the mainline, with the understanding that I’d go above this as much as possible with each curve. This is about 12˚, which is still very good for a model railroad, and in a congested city setting is reasonable. Plus the fact that most curves are wider than that, with probably half at 40” or more, helps the appearance even more.

One other point is that in the prototype there are tight curves in special situations, such as congested yards and industries, and in those cases very slow speeds (10 mph) are required. One of my favorites is the curve leading from the Burlington race track line to Chicago’s Union station that I rode on as a youngster. I remember vividly how the coach trucks would squeal loudly going around that curve. For those situations I set a 24” minimum radius (18˚) and use it only in the approach to Union Station and in two local switching areas. I hope to one day include a sound system that duplicates the squeals of the wheels around those curves.

As you read this keep in mind that my personal minimums are on the extreme end for this hobby. In years of reading about layouts in magazines I’ve never seen any other layout with minimums this high. (One N scale layout in an oval-shaped dining room employed a lot of 48” curves along the curved walls, but also used 12” curves at a wall with a right angle.) Usually featured HO layouts have smaller minimum radii than I have for my N scale layout.

I do have smaller minimums in the hidden track, such as staging, since aesthetics are of no value there. However, I still stick to an 18” minimum in staging to aide in smooth operations to assure that I’ll always be able to run any equipment that I might acquire. (Note that the NMRA standard mentioned above states that 21.5” may be required for steam locomotives with a rigid scale 28’ wheel base. However, that standard is now over 20 years old. I know of no mass-produced N scale equipment built in the last 20 years that can’t run on a radius of 17” or less, so any exceptions are likely to be expensive custom-made brass imports, which I don’t bother with due to cost and difficulty running under DCC.)

For the outdoor layout the situation is different. There will be no staging, no hiding and no disguising. For the outdoor layout, what you see is what you get. Fortunately as I noted earlier my prototype, the narrow gauge Rio Grande, had a standard of 24˚ curves on the mainline so I should be able to duplicate that with an 11.75’ radius minimum. If I have to compromise in one or two spots in the freight yard to an 11’ or even 10’ radius I’ll still be within 28˚, which is also realistic for Rio Grande narrow gauge slow-speed operations. The key factor is that I’ll be running prototype narrow gauge cars from the 1880s, which were very short and thus looked appropriate around curves such as those.