Tom the Toy Man discusses scales and gauges for model railroading.
Here’s the Proto 48 layout that he is talking about.
The problem for railroad modeling is that the scales that models are built are based on gauges that were made to come out even in dimensions in inches based on a rail gauge that is no way even to anything. That’s why model railroaders have always either compromised gauge, scale or both. There’s also the problem that many of the standards were promulgated when the access to tools was limited and the materials were not likely to hold up it the dimensions were correct in scale. So wheel treads in standard HO, are in the National Model Railroad Association much wider than real railroad wheel. The Proto gauges are an attempt by some modelers to correct those deficiencies.
The rail modelers in Japan have it even more interesting as the standard gauge in Japan for most trains is Cape Gauge at 3’6″ because of the big push for narrow gauge in the late 19th Century. Followed in the mid 20th Century the Shinkansen in standard gauges. So Japanese modelers have had to compromise on either scale or gauge to fit on the manufactured track that follows NMRA standards. Which has led to some three HO scales or gauges, and at least two N scales.