steinjr
Welcome to the forums.
From an earlier thread on the same question:
fwright
HO is "Half O", which at the time was and is exactly 7mm/foot by the definiton used at the time (at least in Great Britain).
Therefore, HO is defined as 3.5mm/foot. That is the definition used by the NMRA and Proto87. Since the 3.5mm/foot is exact, 12 inches/foot is exact, and 25.4 mm/inch is exact, the correct ratio is 1/87.08571 (according to my calculator).
This is commonly rounded off to 1/87.1 or even 1/87 on occasion.
Stein
Thanks Stein.
Before calculators (yes, there was such a day), it was much easier to work with scales expressed as "so many units on the model represent so many units on the prototype" rather than ratios. This was true across all types of modeling and all types of scale drawings in engineering. 1/4" = 1ft (North American O scale), 1/10" = 1ft (TT scale), 3/16" = 1ft (S scale) are common scales used in architecture as well as modeling.
The European toy train makers defined gauges before scales were in use. Scale wasn't important as making sure everything ran on the same track gauge. 0 gauge (later became O instead of Zero) was set at 32mm or 1.25" - I'm not sure which was the original. The Brits, in their lovable way , mixed metric and English units, and assigned 7mm/ft as the correct scale for O gauge track. Note that 7mm/ft is closer to correct scale than the more approximate North American 1/4"/ft.
As stated in my earlier post, Half O became 3.5mm/ft, and later became HO. The track gauge was corrected to 16.5mm instead of 5/8" or 16mm, which were sometimes used in the early days.
When ratios became the more favored way of expressing scales, there are actually 2 ways to run the calculation. One is taking the scale (3.5mm/ft) and computing the ratio, which gives 1/87.086. The other is to divide the track gauges to get the ratio - 1/86.976. If you divide 56.5" by 0.650" (NMRA HO track gauge minimum), you get 1/86.923. The differences show up the slight rounding errors in the original scale/gauge calculations, when current precision was not easily available.
The NMRA and Proto87 (North American) use the 3.5mm/ft as the exact definition (rounds to 1/87.1). Track gauges can and do vary and will give slightly different results when computing the ratio, which is why I prefer the scale definition.
Final note is that N and Z scales were developed after ratios had come into common use. N scale ended up being defined as 1/160 rather than as units/units.
probably way more than you wanted to know
Fred W
