(or how to make your layout more appealing)
Transition curve laid out as in Fig.3. The minimum radius of 1 metre occurs above the furthest arch of the bridge.
(Photo by Alan Hackett)
Traditional layout planning has often largely consisted of straight lines and arcs of circles. Armed with ruler and compass both are easily drawn unless the arc has a larger radius than the compass can handle and having as much straight track as possible allows the maximum amount of trackwork in a given space and space is, of course, always at a premium.
A new layout plan tends to start with a maximum length of straight track down the longest walls of the room, with curves at each end which are a compromise between the desirability of large radius curves which take up a lot of room and the practicality of tighter radius curves which allow us to fit in the station and point work. Large sweeping curves would be nice, but "none of us have the room".
If that is as far as the layout design goes the result will appear somewhat stilted and unprototypical as it does not reflect the way the prototype is laid out. Railway track is rarely straight for long except in flat country as it seeks a compromise between following the contours, which is cheaper in requiring less earthworks and easing gradients, and keeping to a straight line or large radius curves which allow higher speeds and require less land by ensuring a shorter route.
What then needs to be done is to introduce some large radius curves (with a radius of 20' or more) into the layout design, not as replacements for the curves already drawn but as replacements for some or all of the straight track. Every layout can fit in some of these - they may not be very long but they will look good. Consider Figure 1. Does the dotted line or the straight line joining the curves at each end appeal to you more? There is an added bonus that the dotted line actually offers a greater length into which pointwork can be fitted. Try pinning down a couple of yards of track using a very gentle curve laid by eye and see for yourself. Actually it is easier in practice to lay track to a gentle curve than to lay perfectly straight track.
Taking the process one stage farther look at figure 2. The large radius curve used here offers even greater length for the station and takes away the rectangular look. Because the curve at the right hand end no longer has to turn through almost a right angle it can be a larger radius without taking up too much extra space. Of course, this arrangement takes up more space on the right hand wall but one can't have everything.
We will turn later to how a curve of such a large radius can be drawn conveniently on the drawing board and more importantly when building the layout itself.
At this point you are possibly wondering where transition curves come into all of this and of what relevance they are to layout planning. First let me define a transition curve as a curve of constantly and smoothly changing radius. A circle, of course, is not a transition curve, being a curve of constant radius while an ellipse and a parabola are both examples of transition curves.
"All very exciting" I hear you saying, "But why the geometry lesson?". Consider a car driving along a straight road and coming to a corner. The driver does not suddenly jerk the steering wheel round, hold it there to turn the corner and then jerk the car straight again. To do so would at best be uncomfortable and hard on the car, and at worst would cause a skid. The driver will gradually wind the steering wheel into the tightest part of the corner and then unwind it to straighten up. The result is easier on car, tyres, occupants and the road itself. The path taken by the car is a transition curve. Railway engineers similarly and for the same reasons use transition curves as a matter of course (no pun intended, but it’s not a bad one) in laying out the track alignment.
There is no reason why our model layouts should not also use them. They not only look better and improve running but they are actually easier to lay out than fixed radius curves. By easing the sudden change from straight to the inevitably too sharp curve on the model they lead both the eye and the train gently from one to the other. The sharpness of the minimum radius in such a curve is not so apparent because the eye cannot readily detect a gradual change of radius when looking along a curve. The running is better because, like the prototype, the model is not subjected to violent changes of motion. Buffer lock, by the way, is not caused by sharp radius curves but by a sudden change of radius.
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37ft radius curve leading into transition curve in the foreground |
56ft radius curve laid out as in Fig.6 |
I do not know the specific type of transition curve used on the prototype but that need not concern us as there a simple form of transition curve which is easy to use and gives good results. Look at Figure 3. BC and DE are two tracks approaching at right angles. We could join them by a quarter circle of radius BO. Instead, divide AB into a number of equal parts (say 20). The number is not critical, but should not be too small. Number the segments Bl, B2, etc. starting from A. Similarly divide AD into the same number of equal parts and number them Dl, D2, etc., but starting from D. With a truly straight edge join Bl and Dl, B2 and D2, etc. The envelope of all these lines (the heavy line) forms a transition curve. It has a radius at entry B of twice BO. This radius tightens until at G it reaches a minimum of radius of BO divided by the square root of 2 (ie. 0.707*BO, which is the same distance as FO), after which it eases until by D, it once again has a radius of twice BO. For example, if AB is 3 feet, the minimum radius will be 25.5 inches and the radius at B will be 6 feet. Note that this curve has been drawn with the aid of a straight edge only, of length BO, despite part of the curve having a radius of twice that distance. Exactly the same method of drawing the curve is used for both planning the layout and laying it out on the baseboards prior to laying track.
Note that access to the centre of any part of the curve is not necessary. Those who have tried will know that even where the centre of a circle is accessible and pillars or whatever do not intervene, accurately drawing a circle of even 3 foot radius on a baseboard is not a simple exercise to execute with accuracy.
While the minimum radius of the curve is less than the equivalent circle, provided your stock will negotiate that minimum radius, that is not a problem. Visually it is not apparent and because there are no dramatic changes of radius, running will be improved rather than be poorer and there is the added benefit that due to the larger radius on entry, it is possible to place pointwork on the curve, even where the additional track has to come inside the curve.
Of course, once we move away from "rectangular planning" as discussed earlier, tracks will not necessarily approach each other at right angles and a means of drawing transition curves in a more generalised case is needed. Actually the "rectangular" model in Figure 3 is simply a special case of the more general situation which is shown in Figure 4. As before, the two approach tracks are BC and DE. AB = AD. AH is parallel to DB. Using exactly the same procedure as in the above case, divide AB and AD into an equal number of equal parts and join the corresponding points. The resulting curve has a minimum radius equal to FO and a maximum radius equal to HO. Were an arc of circle drawn instead, it would be of radius DO. Note that as the angle between the two approach tracks grows smaller, the difference between the maximum and minimum radii reduces. Conversely, where the angle between the approach tracks is greater than a right angle, (see Figure 5), the minimum radius becomes very tight and in such situations the use of a transition curve may not be advisable.
For those of you who still speak trigonometry, in the general case in Figure 4:
There is another method of drawing the same transition curve which is more convenient when the angle between the two approach tracks BC and DE is small and the length of AB suggests a large radius curve. Since the angle is small, the difference between the minimum and maximum radii will also be small and the benefits of using a transition curve instead of a circular arc are less pronounced. In this case the main benefit of using the transition curve is being able to easily and accurately draw a large radius curve, which as was discussed above is very difficult using the traditional beam compass or trammel method. In Figure 6, we once again have BC and DE as approach tracks. Mark the mid-points of AB and AD, F and G respectively. Join FG and mark the mid point, H, of FG. Mark and join the mid-point of FH and FB and the mid-point of GH and GD. Repeat the above process as shown by the additional lines in Figure 6. Repeat until further repetition will not be distinguishable. The envelope of these straight lines will give the same transition curve as the method illustrated in figure 4.
In this general case of large radius curves, it is no longer necessary for AB and AD to be equal, within reasonable limits. See Figure 7. In this case the calculation of the minimum radius is very complicated and I will not attempt to explain it. Provided this asymmetrical scheme is only used when the minimum radius is clearly adequate, there is no need to know precisely what it is.
In practice, layout planning is best initially carried out in broad terms using straight lines and arcs of circles rather than immediately trying to lay out large radius and transition curves. Once the broad plan has been worked out, where appropriate, straights can be replaced by large radius curves joined again by arcs of circles. If the circle radii are chosen with the minimum radius of the associated transition curve in mind, then when the plan is substantially complete, the arcs of circles can be replaced by the equivalent transition curve.
The transition curves are best drawn on separate sheets of paper and then traced onto the plan. Alternatively they can be cut along the line of the curve and used as a template. These separately drawn curves can be retained for future use. Each should be annotated with the relevant minimum, nominal and maximum radii for easy reference.
Using used fanfold stationery or a roll of wallpaper or similar, it is possible to make full size templates on the floor, bench or wherever, by the same methods. These templates can then be used for cutting out baseboards, trackboards etc. and for joining pre-cut sections so as to accurately maintain the chosen curve.
All this may sound fairly complicated at first, but it is in reality quite straightforward. Those of you who find the above too simplistic, should try reading the Scalefour Society thesis on the subject which has been known to reduce strong men to gibbering strangely at passing modellers on club nights. There is only one test of whether it is for you - try it, even if you only pin down a couple of yards of Streamline temporarily on a sheet of Caneite. Pin down a quarter circle of track and next to it a transition curve of the same nominal radius and see which you prefer.
Ó Alan Hackett 1998
