The length of your equipment, even more than the scale of the model, is the most important factor in setting a minimum radius. The list below includes conventionally accepted minimums for each of the major scales. Note that there does not appear to be much difference between them. The reason; large scale models often have compromises built-in to allow operation on some very tight curves. The trade-off is that they don't always look very good while doing it.
In general, large models like scale-length passenger cars, autoracks, intermodal equipment and large steam locomotives will require a larger radius than short rollingstock like switch engines and "shorty" freight cars. You can decrease the minimum radius by increasing the distance between cars, but this compromises the train's appearance.
- Z Scale: 195 mm
- N Scale: 9 3/4 inches
- HO Scale: 15-22 inches
- HOn3 Scale: 15 inches (narrow gauge)
- S Scale: 20 - 30 inches
- O Scale ("Toy"): 13.5 inches
- O Scale ("Scale"): 72 inches
- On3 Scale: 36 inches
- G Scale: 24-44 inches
A note about O scale: O scale trains really come in two forms. Traditional 3-rail toy trains often feature major compromises in body length, articulation, couplers, etc. that allow them to make incredibly sharp turns. More to-scale models better replicate the prototype, including a more demanding turn radius. Of course, there are small "scale" prototypes and large "toy" models meaning there is still no definitive minimum radius.
Minimum Radius and Multiple Tracks
If you have parallel tracks in a curve, the spacing between tracks is important. The sharper the radii, the greater the distance between rails will need to be. Depending on the model, trains may overhang the track on both the inside and outside of a curve. Space tracks too close and they could sideswipe.
Minimum Radius and Easements
Easements are a gradual transition in radius. Used at the entrance / exit of curves, an easement can make even a tight minimum radius operate more effectively. Easements can be easily added using either flexible or sectional track.
Minimum Radius and "S" Curves
"S" or reverse curves look amazing when done correctly. When the radii are tight however, they can pose problems. Adding easements and a short section of tangent (straight) track between the curves can reduce operating problems.
Minimum Radius and Appearance
Just because a model train can negotiate a minimum radius doesn't mean it has to. Most layout curves are already tighter than the prototype could manage. Larger curves prevent unrealistic overhang, allow close-coupling multiple unit locomotives and passenger cars, and are usually less prone to derailments.
In addition to easements, super-elevation, or banked curves also help make a curve look more realistic. There is nothing like watching a long model train lean into a broad sweeping super-elevated curve.
Ultimately, the minimum radius for your railroad is up to you.