A spiral easement transition will help even more.
Curves are not difficult to calculate, but two elements must be known. For example the degree of curvature and the radius can be used to calculate all other elements (length of curve, tangent length, chord length, etc.). The easiest for the typical modelrailroader to understand, is radius because it is so commonly used to describe model curves.
The radius of a one degree curve is 5729.578 feet. So this number divided by 2 will give the radius of a two degree curve, by 10 will give the radius of a 10 degree curve, and so on. The absolute tightest curve a Union Pacific 4-8-8-4 could negotiate was 20 degrees. Any curve tighter than that would result in either a driver climbing the rail, or in the force of the driver against the gauge surface of the rail, pushing the rails out of gauge. Either way a derailment would result. So if we divide 5729.578 feet by 20, we get a radius of 286.479 feet. Converted to HO scale this is 3.290 feet or 39.475 inches. This is considered a fairly broad curve for HO scale models, but would represent the sharpest curve your Big Boy could negotiate if you intend to be prototypically accurate. Mainline curves are much broader, and subject to speed restrictions even at less than 5 degrees which would be a 157.9 inch radius in HO scale.
I should also note the 5729.578 foot radius figure I use is for a 1 degree “chord definition” roadway curve not, not an “arc definition” railroad curve. The difference is slight, but worthy of mention.
Great thread!!! One thing I see missing in the discussion is the radius in relation to the grade. We all know how that smaller radii changes the reliability with longer trains…
True.
If you do a search for “compensated grade railroad”, you’ll find a lot of discussion on the subject.
Ed
I believe Armstrong was not creating the terminology, simply reporting what the terms used regarding curves were. I suspect you can find sources before that have used the same terms; not sure who first stated them.
I wonder if Walthers saying their HO passenger cars work on 24" radius curves is related to 24"R being a “conventional curve”? Kato HO Unitrack starts at 24"R then has three sizes bigger and three smaller curves, all 2-3/8" apart.
IIRC John Allen’s first layout had some 14"R curves, and the final G&D had curves as tight as 26"R.
The B&O had at least one mainline 14 degree curve on their Pittsburgh & Western subdivision west of Pittsburgh, Pa. Trains of all kinds including Amtrak and intermodal with 89’ cars used this route. The speed was 30 mph.
The flanges definitely contacted the rail. Metal filings could be seen on the ties throughout the curve and the rail head was worn to match the wheel/flange shape.
I don’t know if they were used in regular service, but I have seen a picture of a B&O EM-1 2-8-8-4 running a fan trip on this route.
Mark Vinski
I doubt that there are many modelers of true high-speed rail; the numbers just make it impossible. High-speed lines in France and China with train speeds of around 200 mph have minimum radii of 5,000 - 7,000 meters (3 - 4.5 miles). In HO, this would translate to around 200 feet (or 2,400"). Interestingly, high-speed trains are much better equipped to deal with vertical grades, because of there very high power-to-mass ratio. The German high-speed line from Frankfurt to Cologne has 4% inclines, and there is no noticable drop-off in speed.
Traction and interurban modelers definitely have it easier in the “realistic sharp curves” departmemt, as some level of compensation for our relative lack of variety in ready-to-roll equipment! My 15" curves are very reliable (with easements and very careful work at the tracklaying stage) but sometimes spotting cars on my tightest curve, 12" radius on an industrial spur, gets a little hairy. Recently I bought an estate collection of a fellow who was into heavy steam, and I tested some of the engines on my layout; while the 2-10-4 and articulated loco didn’t clear my curves, the other steam engines did fine, including a heavy Mogul, even at relatively high speeds.
However, as scale modelers, in addition to the reduction in proportional size for the scale we operate, we often use “selective compression” to represent a larger area than the confines of garage, basement, spare room or bookshelf. Industrial buildings are shrunk from their original proportions, towns moved closer together, mainline distances and yard capacities are frequently reduced beyond their scale size, but they still look good to the viewer, because the emphasis is on the trains instead of the landscape. We use theatrical tricks to bring the eye where we want it, and away from places that break the illusion. We even use “fast clocks” to increase the illusion of greater distances traveled. In the same way, we use sharper-than-realistic curves for practical reasons, but there are many ways to disguise them and minimize their aesthetic impact. One of the most popular ways to make a sharp curve look broad is to view it from the inside; there’s a popular railroad planning idea that trains look better from inside a curve rather than outside, and monumental efforts are made to avoid “blobs” in planning both because they’re seldom found on the prototype and they draw attention to the trains’ bad side. The other method, used for blob-hiding, is to conceal the trains in a