Radius? Diameter? How wide is that curve?
Measuring model railroad layout curves
There often seems to be confusion in model railroading over radius, diameter, and the width of benchwork needed for a "turnback" curve (the 180-degree turn at the end of a peninsula of benchwork or at the ends of an oval).
For those for whom High School Geometry was a long time ago, here's a simple visual refresher.
Scale model railroad curves are measured in radius to the centerline of the track*. To figure the benchwork width needed, one must add the curve diameter (2 times the radius), the track width, and 2 times the safety margin to the edge of the benchwork. The nominal minimum safety margin is determined by the minimum clearance so that trains won't derail, but obviously it’s much safer if we provide at least 3-4" outside the track so that derailed trains don't fall to the floor.
Note also that model railroaders find that they cannot reach more than about 30" over a scenicked layout. For that reason, typical turnback curves in HO scale, and nearly all turnback curves in larger scales, will require access all around or an access hatch in the middle.
Because of the space required, turnback curves are often the tightest curves on the layout and thus usually determine the minimum radius. The Layout Design SIG has published a handy Curve Radius Rule-of-Thumb to help you choose an appropriate minimum radius in any scale.
Real-life (prototype) curves are measured in degrees, not radius or diameter, because of the tools needed to lay out real curves in the world. (In short, it's Trigonometry). Prototype curves are almost always much broader than model railroad curves. Here's a link to a handy cross-reference.
An additional confusion is that sectional model railroad track is often sold as a certain "degree" curve. This is a completely different measurement than the prototype, however, and simply relates to how much of a complete 360-degree circle that piece would be. Thus, it would take sixteen 22.5-degree sectional track pieces (regardless of radius) to complete a full circle of track (16X22.5=360). But again, these sectional track degree descriptions bear no relation to the prototype degree measurements.
* O Gauge ("Tinplate" – like Lionel) curves are measured in diameter, thus O-36 curved track makes a turnback curve 36" across.