It is with utmost pleasure that I present you this token of our unabated admiration for your tireless work to promote and profligate the Metrum Asinorum (ma). 

As it is our charter to aid and abet U.S. industry, it goes without saying that your commitment to disseminating the technical advantages inherent in  the ma as the standard by which American commercial transport is conducted remains strangely unheralded. Or should I not say that?

Abmho P. Barye, 
Undersecretary, 
Locomotive Equine Standards

• collections of funny headlines and bumper stickers;
• ten-item lists of satirical observations about topical events;
• reasons why God never got a PhD;
• how you can tell if you are a geek or a nerd, a redneck or a liberal.

It's an exponential phenomenon: Every modem on earth will receive at least x copies of each message after m forwardings to the nth power. That doesn't happen, presumably, because some sizable fraction f of the recipients have not yet become habituated by their respective icons for re-transmissions (the mathematical expression for which is left as an exercise for the reader).

With scarcely a moment's thought, I clicked "Send," after first scarfing up a few nicknames from my address book and pasting them in the "TO" field. One of them was for Tom Bray, renown sculptor and didgeradoo prodigy. That was a mistake. Tom's immediate reply plunged an elderly compulsive into frantic private researches...

"Okay, Mr. Smartypants, what is the ideal track gauge?"

 

Did the wheel separation on the  6th Century BC Etruscan Chariot determine the track gauge for the  21st Century AD Railway Truck?

Apparently not.

Track Gauges for Railways of the World This tabulation affords to sophisticated readers a decided advantage for competing in a game of some unimaginably advanced edition of Trivial Pursuit. Format: country | year | ownership | gauge | length in miles Algeria | 1862 | 4 ft 81/2 in  | 3,071 Argentina | 1857 | state | 5 ft 6 in. | 15,462 | metre | 10,715 4 ft 81/2 in | 2,210  Australia | 1854 | state | 4 ft 81/2 | 8,302 | 5 ft 3 in.  Austria | 4 ft 81/2 | 6,998  Bangladesh | 1861 | state | metre | 2,517  Belgium | 1835 | state | 4 ft 81/2 | 7,754 Brazil | 1854 | state | metre | 14,553  Bulgaria | 1866 | state | 4 ft 81/2 | 3,584 Burma | 1877 | state | metre | 2,400  Canada | 1836 | state | 4 ft 81/2 | 35,147 | private | 4 ft 81/2 | 29,321  Ceylon (Sri Lanka) | 1865 | state | 5 ft 6 in. | 1,236  Chile | 1851 | state | metre | 3,844 | 5 ft 6 in. | 2,349  China | 1881 | state | 4 ft 81/2 | 23,900 Czechoslovakia | 1839 | state | 4 ft | 81/2 | 13,226 Denmark | 1847 | state | 4 ft 81/2 | 3,395 East Africa (Kenya, Uganda. Tanzania) | 1897 | state | metre | 4,370  Egypt | 1854 | state | 4 ft 81/2 | 4,149  Finland | 1862 | state | 5 ft | 5,462  France | 1828 | state | 4 ft 81/2 | 49,028 Germany (East) | 1835 | state | 4 ft 81/2 | 18,179 Germany (West) | 1835 | state | 4 ft 81/2 | 44,999 Greece | 1869 | state | 4 ft 81/2 | 2,002 Hungary | 1846 | state | 4 ft 81/2 | 8,442 India | 1853 | state | 5 ft 6 in. | 36,353 | metre | 21,770 | 2 ft 6 in. | 3,513  Indonesia | 1864 | state | 3 ft 6 in. | 4,852  Iran | 1917 | state | 4 ft 81/2 | 2,5 81 Ireland | 1834 | state | 5 ft 3 in. | 2,282  Italy | 1839 | state | 4 ft 81/2 | 20,649 Japan | 1872 | state | 3 ft 6 in. | 25,426 | private | 3 ft 6 in. | 5,733  Korea (South) | 1899 | state | 4 ft 81/2 | 3,378 Malaysia | 1885 | state | metre | 1,428  Mexico | 1850 | state | 4 ft 81/2 | 30,613 Morocco | 1911 | state | 4 ft 81/2 | 1,632 Mozambique | 1886 | state | 3 ft 6 in. | 2,551  The Netherlands | 1839 | state | 4 ft 81/2 | 4,568 New Zealand | 1863 | state | 3 ft 6 in. | 4,499  Nigeria | 1901 | state | 3 ft 6 in. | 2,680  Norway | 1854 | state | 4 ft 81/2 | 3,452 Pakistan | 1861 | state | 5 ft 6 in. | 7,664  Poland | 1845 | state | 4 ft 81/2 | 16,540 Portugal | 1856 | state | 5 ft 6 in. | 2,944  Rhodesia | 1897 | state | 3 ft 6 in.|  2,040  Romania | 1869 | state | 4 ft 81/2 | 6,838 South Africa | 1860 | state | 3 ft 6 in. | 19,648  Spain | 1848 | state | 5 ft 6 in. | 13,792  The Sudan | 1900 | state | 3 ft 6 in. | 3,379  Sweden | 1856 | state | 4 ft 81/2 | 11,611 Switzerland | 1844 | state | 4 ft 81/2 | 4,249 | private | 1,529 | metre  Taiwan | 1891 | state | 3 ft 6 in. | 1,061  Thailand | 1893 | state | metre | 2,733  Tunisia | 1876 | state | metre | 1,743  Turkey | 1856 | state | 4 ft 81/2 | 5,874 Soviet Union (former) | 1837 | state | 5 ft | 86,691  United Kingdom | 1825 | state | 4 ft 81/2 | 34,471 United States | 1830 | private | 4 ft 81/2 | 305,179 Yugoslavia (former) | 1846 | state | 4 ft 81/2 | 9,433 Zaire | 1911 | 3 ft 6 in. | 3,702  Zambia | 1905 | state | 3 ft 6 in. | 1,000  Predominant ownership is given; most countries have both private and state owned lines. Gauge of the principal mileage; most countries have lines of several gauges. So-called "Standard Gauge" = 4 ft 81/2 in.; "metre" = 3 ft 3 in. Data for early 1970s.  Source: Jane's World Railways 1971-1972

he premise of the historical review set forth above is that 4 feet, 8.5 inches is "an exceedingly odd number," by which, no doubt, is meant, "not an integral number." To be sure, 4 feet, 8.5 inches amounts to 4.70833 feet.

• A track gauge of, say, 5 feet 'even' would probably not be regarded by most people as an exceedingly odd number.
• Likewise, lopping off a half-inch gives you 56 inches, which might not be considered 'odd' in any sense of the word.

 

Now, 4 feet, 8.5 inches happens to be exactly 113 on the 'plug-tine separation scale.'  If you have any doubt of that, pull an electrical plug out of the wall and take it to the nearest railroad track.    Thing is, railroads came first.

So, let us not sneer at an emergent standard based on...

• the war horse's ***,
• the wheel spacing for chariots,
• the ruts in roads, and
• the jigs for wagons that were used in the construction of early railway rolling stock.

s a new international unit, Metrum Asinorum will unabashedly honor its equine origin along with the wisdom of our progenitors in the field of transportation technology. Thus, the gauge of railroad tracks will be forever known to measure exactly 1 metrum asinorum. Who will deny that as being preferable to 4 feet, 8.5 inches? {Satirical Comment}

Application of this new unit outside railroading, though, will call for some adjustments.

• Doorways in our homes will be 1.381 by 0.531 metra asinora.
• What we know as a mile will become 1,121.416 metra asinora (1.121 kma, perhaps).
• The length of a football field is 63.717 metra asinora.

Metrum asinorum will never enjoy an official sanction without an Act of Congress, by one of which in July 1, 1901 was set up the National Bureau of Standards (since 1988 the National Institute of Standards and Technology -- hmm, it must have been a matter of morale: Anybody would rather work for an institute than a bureau).

Some, no doubt, will protest that the modern 'meter,' which is based on physical phenomenon ought to take precedence over the metrum asinomum. Indeed, the metric system has been modernized to take into account 20th-century technological advances. But, hey, that was in 1960, long after railroads had reached their zenith. And talk about "exceedingly odd numbers"! You will see the reason for that exclamation point in the next sentence, which also ends with an exclamation point:

The meter is now defined as 1,650,763.73 wavelengths in vacuum of the orange-red line in the spectrum of krypton-86!

What we call a "second" is now defined as the duration of 9,192,631,770 cycles of the radiation associated with a specified transition, or change in energy level, of the cesium atom.

he lampoon of military specifications demonstrated an exceedingly Anglo-centric view of railroading ("that's the way they built them in England, and the US railroads were built by English expatriates"). It turns out that only about 60% of the track-miles of the world have gauges measured at unity metrum asinorum. Take a look at the adjacent graph.

Now, based on economic factors, it will be easily argued that, if one were to select a different gauge, narrower is better (shorter ties and less ballast, smaller tunnels and bridges). On the other hand, higher speeds might justify a wider gauge. {Mathematical Analysis}

As indicated, there are three ranges of track gauges that have been adopted by the dominant railroads (usually state owned) in various countries around the world. In addition to 1.0 ma, adopted by 29 railroads, there are 19 countries that have tracks separated by about 0.7 ma and 9 railroads built with approximately 1.15 ma between rails.

• The wider gauges are curiously close to what Europeans have adopted as a standard for their building trades ("one meter eighty") -- possibly a mere coincidence.
• In round numbers, the narrow gauges are clustered at about 1 meter (1,650,763.73 wavelengths in vacuum of the orange-red line of the spectrum of krypton-86) -- definitely not a mere coincidence.

...from which it is possible to discern four eras characterized solely by the selection of track gauges...

Enough said.   Well, almost enough said...

As mentioned above, there are economic benefits to be derived from building tracks with gauges smaller than 1 ma; nevertheless, the Bay Area Rapid Transit (BART) system, which was put into service in 1972, has a track gauge of 1.189 ma (oh all right, 5 feet, 6 inches). Ever curious, I asked a BART engineer why they chose that track gauge.

"To fit the cars," he answered, wiping a smirk from his face.

Stand and Deliver

The tone of this analysis reminds me of an anecdote told by Antony Jay in Management and Machiavelli.  Following a routine exercise of a British artillary unit during WWII, Antony Jay inquired of the field commander why one of the soldiers stood at attention throughout the maneuver.

"He's number six," replied the General.

"I can count, sir. But what is number six supposed to do?"

"That's his assignment. Number six stands at attention."

"While all the others run around positioning the cannon, loading, and firing?"

"Yes, of course," grunted the General. "It's always been that way."

Royal Cubit

The royal cubit was developed about 3000 BC based on the length of the arm from the elbow to the extended fingertips. Not precise enough for you? The ancient Egyptian standardized the measurement by a royal master cubit of black granite, against which all the cubit sticks were measured at regular intervals. Some will complain that the royal cubit (524 millimetres or 20.62 inches) was subdivided in an complicated way...

The basic subunit was the digit (width of a finger, don't you suppose?). There were 28 digits in the royal cubit. Naturally, four digits equaled a palm, five a hand. Twelve digits, or three palms, equaled a small span. Fourteen digits, or one-half a cubit, equaled a large span. Sixteen digits, or four palms, made one t'ser. Twenty-four digits, or six palms, were a small cubit. Tell your friends.

The digit was in turn subdivided. The 14th digit on a cubit stick was marked off into 16 equal parts. The next digit was divided into 15 parts, and so on, to the 28th digit, which was divided into 2 equal parts. Thus, measurement could be made to digit fractions with any denominator from 2 through 16. The smallest division, 1/16th of a digit, was equal to 1/448th part of a royal cubit.

One cannot talk about civilized history without mentioning the Magna Carta (1215), which contains a clause to correct measurements applicable to grain and, most importantly, wine. A standard yard, "the Iron Yard of our Lord the King," was prescribed for the realm, divided into the traditional 3 feet, each of 12 inches, "neither more nor less." The perch (later the rod) was defined as 5.5 yards, or 16.5 feet. The inch was subdivided into 3 barley corns, which means that the so-called standard railroad gauge of today can really be explained by its equivalance in barley corns (168). {Return}

Show Respect

In olden times, people snickered at one definition of a "horse show"...

A bunch of horses showing their ***es to a bunch of horse's ***es showing their horses.

Track Gauge and Train Speed

Trains are typically much wider than the tracks on which they run, so volumetric efficiency must play a minor role in the decision process. Stability, though, is another matter.

The wider the track gauge, the faster a train can operate without falling over when going around a curve. The maximum speed can be increased for any given track gauge, of course, by elevating the outside rail relative to the inside rail ('super-elevation' is the term of art). The limiting factor is center of gravity. Generally speaking, the greater the payload, the higher the center of gravity. For every vehicle in the 'consist,' the location of the center of gravity above the rails must be taken into consideration in two ways...

1. At high speed a high center of gravity subjects the vehicle to an outward roll-over for a given super elevation.
2. At low speed -- hey, like stopped -- a high center of gravity subjects the vehicle to an inward roll-over for a given super elevation.

For sophisticated readers who are inclined to recreational calculations, it is possible to estimate the effect of track gauge on maximum allowable train speed, ceteris paribus. You will observe that in the vicinity of G = 1.0 metrum asinorum, a change in track gauge of as much as 30% will produce a change in maximum train speed of only 10%. This assumes a level track and all other variables held constant. The following expressions were derived using First Principles, assuming an exact balance between weight and centrifugal moments:
 

 

VMAX = sqrt ((R * g * (H * sin (B) + (G / 2) * cos (B)) / (H * cos (B) + (G / 2) * sin (B))); Eo = G * sin (arc tan (((Vo ^ 2) - G / (2 * H)) / (1 - ((Vo ^ 2) * G /(2 * H)))) where... VMAX = maximum train speed (fps) Vo = VMAX @ G = Go G = track gauge (ft) Go = 1 metrum asinorum (4 ft, 8.5 in) E = super elevation of outside rail (ft) Eo = super elevation to achieve Vo g = gravitational acceleration (fpsp) R = radius of track curvature (ft) H = height of center of gravity (ft) B = bank angle (rad); B = arc sin (E / G), where... F = centrifugal force (lb);  F = (W / g) * (VMAX ^ 2)) / R, where... W = vehicle weight (lb)

Consider a segment of level track with a gauge of 1 metrum asinorum has a radius of curvature of 1,250 feet. A vehicle with its center of gravity located 15 feet above the track, would be able to operate on that curve at up to 54 mph without tipping over. If the track gauge were cut in half, the maximum speed would be reduced by approximately 30% to 37.8 mph. Now, by elevating the outside rail only 2.25 inches, the train could operate again at 54 mph.