There are many examples of streams, arroyos, and gullies that must be bridged on a curve by railroads. It would not be a very smooth ride on a train if every time a curving rail line had to cross something with a bridge, the track straightened out. Yet, the physics of building materials requires that straight pieces are used for construction. Whether it is a wooden pile bridge or a steel bridge, the stringers are usually straight - even if only from pier to pier.
So, railroads overlay their curving line above the straight stringers. These photographs show how this works. In the top of the photograph is the HOn3 Micro-Engineering 30 foot open deck girder bridge. Below that is a scratch built low pile bridge. Actually, the lower bridge has only the wooden stringers. The piles and sway braces will be built later.
Even though the Micro-Engineering bridge has a piece of HOn3 bridge flex track that come with it, I wanted to use wooden ties to give a varied appearance. I stained Campbell Scale Models Profile Ties with Builders in Scale Silverwood, Brownwood Stain and Redwood Stain. Unfortunately, the Campbell Scale Models website said that these ties are sold out. There is an unwritten rule in model railroading - "Get 'em while you can". So many offerings in the hobby are limited run and once they are gone, you have to search for them in various hobby shops. That's why they call them "collectors' items".
Curve to the Outside
One of the subtle things that you notice is that the ties should be laid with a little more tie to the outside of the curve - past the supporting beams underneath. You can see how this works in the photos.
There are a couple of reasons for this. In order for a very heavy weight, like a train, to balance, it needs to remain over the beams as much as possible. Imagine the rails going from the inside of the beam to the outside of the beam. The ties need to follow this path. Outside of the swing of the rails, there is also some extra space for someone to walk across the bridge - or seek limited refuge if a train comes along.
Some railroads make this part of their engineering and might even include a walkway for safety. Also, think of a open passenger car platform. On a curve the outside end steps will be sticking farther out than the center of a car. In case of needing to get off of a passenger car in the middle of the bridge, there needs to be longer ties on the outside of the curve.
In the case of a derailment, the trucks would tend to move toward the outside of a curve. The net effect of all of this is that ties should be longer on the outside of the curve.
Keeping the Ties In Line
There are a lot of forces associated with the movement of a train over a bridge. The "dynamics" of force is a complicated subject, (see Railroad Construction by Walter Loring Webb for a detailed discussion) but consider a locomotive wheel exerting force upon the rail as it pulls a train. There is a tendency for the rail to be pushed backwards. This is the "opposite reaction" to the forward movement of a train. When the rail is fastened to a supporting structure, it does not go backwards. The train goes forwards because the rail is stationary.
So, the more things that hold the rail (and ties) in place, the better. On ground, the earth itself can work to keep the rails stationary. Ballast surrounds ties. Spikes hold rails onto the ties. It is usually a pretty solid system as long as the track gang performs its maintenance functions.
On a bridge, the earth is remotely connected to the supporting structure. On an open trestle or open girder bridge, there is no ballast. So, guard rails or wooden beams are necessary to help hold the ties in place. This is critical in the case of a derailment, when the train would tend to separate the ties.
Wooden Guard Rails
In the early twentieth century, these guard rails on the edge of the ties were wooden and bolted to the ties. They were straight. The length of these beams was limited by the curve and fitted in place. For Colorado narrow gauge, ten feet long is reasonable.
For a thirty foot long bridge, there should be three guard beams on each side. For each bridge, I needed to cut six beams. The ends of the straight beams have a slight angle to allow for the curvature of the bridge. In the color photos that I have seen, the Denver and Rio Grande Western would sometimes color these guard rail with a mineral red color. So, I used the Builders in Scale Redwood Stain for them. It provides a nice contrast to the ties. Weathering will later homogenize the colors a little.
I use Elmer's Glue-all on the tip of a toothpick to apply a tiny amount of white glue to every third tie or so. This will do a good job of holding it in place, yet give you a little time to adjust the final location of each beam.
This view of the open deck girder bridge show all six pieces of wood in place. It also shows how the curve is followed by the straight pieces. By the way, that plastic cutting board under the bridge is a good moveable work surface. Not only is it good for cutting, but it protects the desk, workbench or table from excess paint and glue.