There is a short and a long answer about the Roman origin of 4'8.5".
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The short answer: it is quite easy to trace the standard gauge from Ancient Rome (& especially Ancient Greece) to today's railroads; 4'8.5" is not a bad choice; and there is no such thing as an "unusual" number (but that is another joke for another time). Numbers are odd, even, integral, prime, etc., but not unusual.
That said, I'll give you my longer, and probably just as winded, but more easily verifiable story about the gauges: By the 1880s, the dominant (by mileage) common carrier gauge in North America & Europe was 4 foot 8-1/2 inches. There indeed were other gauges for steam common carriers -- wider and narrower -- but all of them came AFTER 4'- 8.5" had been adopted by the first steam roads in the U.S. and England.
How did this not unusual measure of 4'8.5" come about? The Roman cart grooves (and they were indeed Roman -- I'll get to that later) in stone village pathways all over Europe were roughly 5 feet apart measured from the OUTSIDE edges of the grooves or ruts. The ruts themselves (some of which still exist to be examined) were each about 4" to 6" in width. (Note: being grooves in stone to carry off mud, excrement, & etc. they weren't exactly calibrated in micrometers.) Rough widths were good enough for cartwheels to transverse the towns without breaking their axles on the "crosswalks." Indeed, a wide width for the grooves was necessary since the wheels were NOT guided with flanges -- the next key engineering point.
Hence, comes the second, and most interesting part of re-engineering Julius Caesar's mandated gauge for carts (Yes, he did mandate this -- I'm getting to that). Lo & behold, some genius in the 16th Century noticed that if a flange was applied to a guideway mechanism, an animal-pulled cart could be run on a wooden rail higher than the ground, instead of being guided by the rutted and uneven grooves in the dirt or wooden plank road. (Guidance plus a smoother surface lowered rolling friction so the animal would eat less and pull more.)
Now, flanges can be inside or outside of a wheel, but the flanges also could be part of the RAIL. Without access to a major government R&D program to judge the most effective architecture for infrastructure-reducing friction, the first-generation railroads ("tramroads") picked the flanged or "edge" RAIL for their first systems, instead of today's common flanged WHEEL. Like I always say, little things can make a big difference. But first the gauge width:
The conventional carts (trams) of the day had their wheels about 5 feet apart -- stemming from the Roman cart gauge (don't worry, I'm getting to the Romans), and measured from their OUTSIDE wheel edges, with tolerances noted above for rut widths. In 1789, one William Jessop of the Butterley Iron Works in Derby, England laid a new colliery tramroad on a heavily used conventional roadway between Loughborough and Nanpantan with a novel, L-shaped iron "edge" rail. The rail had its riser on the inside of the track, but the "track" had to be depressed so the top of the riser was flush with the surface of a conventional roadway permitting other vehicles to continue to use the right-of-way. Since the guidance part of the L was below the roadway surface, two sets of wheels on each axle were used: one set riding on the top of the iron L-beam bearing most of the weight of the cart, and another set riding on the bottom of the L to guide the cart and keep the other wheel on the top of the L-beam.
The track had its iron L-beams depressed in the roadway like this: _| |_
Hence the flanged wheel was born -- but the guiding mechanism (which became a flange when the wheel was cast as one piece of iron) was on the OUTSIDE of the supporting wheel, not the inside as on today's integral flanged railroad wheel.
Jessop found that the outside, double-wheel, flanged system was unsatisfactory. Therefore, Jessop rearranged the double, now integral iron wheels so their flanges were on the INSIDE, but initially kept the L-shaped rail track architecture as above (the flanges running in the mud -- I didn't say the roadway was paved). It was reasoned that with this arrangement the L-shaped "edge" rails would better keep the wheels in position on the AXLES and solve other problems which I will not get into here. This twist was the HTML of railroading -- little details can make a BIG difference.
Now let's do the numbers: Since the L-beams were about 1.5" wide in total (the L-beam was formed from a 3/4" plate bent 90 degrees), plus a 1/2" clearance for mud & dirt, the so-called standard gauge of the world became: 60" - (2 x 1.5") - 0.5" = 56.5" = 4' 8.5". Not an unusual number at all. This took place in 1800.
The first steam roads in England, the U.S., Germany, France and Belgium all followed Jessop's 4'-8.5" template. Since the first roads also got their steam engines from England (or tried to), and since they all used conventional coal carts and stagecoaches for their first rail vehicles, following the 5' (minus rutted width) was not really a major paradigm shift.
And there is no mystery of how 5' was derived from the Roman rutted path width. Back to Julius Caesar. Shortly before he was stabbed by Brutus et others in 44 B.C., the General visited his new possessions in Greece, in particular the military base at the Isthmus of Corinth. He observed the stone rutted cartway in operation there to transfer specially-built, mostly military, w[hee]led boats from the Gulf of Corinth to the Saronikos Kolpos (gulf in Greek), avoiding some 400 miles of sailing in dangerous waters roundabout the Peloponnisos. The cartway had been built with carved stones roughly 5 feet apart, with each stone having a Greek letter carved on it for some mysterious reason. This was a fairly meticulous-built guideway, carts and all, though very little is known of who designed it & when, though it is pretty clear why. Jules, saw that the key was that all the cart/boats which used it were STANDARDIZED by the Hellenic military for wheel and axle dimensions. He applied this version of HTML to a growing
problem in the Empire -- chariots that had to slow in towns because the ruts were all over the place. His edict for standardized rut widths lasted a long time, and it is hard to argue with the dimensions.
I was in Corinth 2 years ago and of course I visited the excavated guideway. It apparently was in use into the early Middle Ages and then was forgotten and got filled with debris and dirt. When the famous Corinthian canal was built in the 19th Century the guideway was re-discovered (it was thought to be a myth) and a few yards not demolished by the canal have been restored, mysterious Greek letters and all. I measured the ruts (actually they are quite neatly laid and cut stones). 4'-8.5". You betcha.
1. The Loughborough Nunpanton railway was in fact a rutway, development of a long line of such routes. The following extract is from an early Encyclopaedia Britannica, cited as a source by Prof Solomons: