Ruling gradient

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The term ruling grade is usually used as a synonym for "steepest climb" between two points on a railroad. More simply, the steepest grade to be climbed dictates how powerful the locomotive must be (or how light the train) in order to complete the run without assistance. Even if 99% of the line could be run with a light (and inexpensive) locomotive, if at some point on the line there is a steeper gradient that a light engine would be unable to climb, this gradient "rules" that a more powerful (and expensive) locomotive must be used, in spite of it being far too powerful for the rest of the line. This is why special "helper engines" (also dubbed "Bankers") are often stationed near steep grades on otherwise mild tracks, because it is cheaper than running a too-powerful locomotive over the entire track mileage just in order to make the grade, especially when multiple trains run over the line each day.

Locomotive Railway vehicle

A locomotive or engine is a rail transport vehicle that provides the motive power for a train. If a locomotive is capable of carrying a payload, it is usually rather referred to as multiple units, motor coaches, railcars or power cars; the use of these self-propelled vehicles is increasingly common for passenger trains, but rare for freight.


In the 1953 edition of Railway Engineering William H. Hay says "The ruling grade may be defined as the maximum gradient over which a tonnage train can be hauled with one locomotive....The ruling grade does not necessarily have the maximum gradient on the division. Momentum grades, pusher grades, or those that must regularly be doubled by tonnage trains may be heavier." This means the "ruling grade" may change if the management chooses to operate the railroad differently.

Compensation for curvature

Other things being equal, a train is harder to pull around a curve than it is on straight track because the wagons – especially bogie (2 axle) wagons – try to follow the chord of the curve and not the arc. To compensate for this, the gradient should be a little less steep the sharper the curve is; the necessary grade reduction is assumed to be given by a simple formula such as 0.04 per cent per "degree of curve", the latter being a measure of curve sharpness used in the United States. On a 10-degree curve (radius 573.7 feet) the grade would thus need to be 0.4% less than the grade on straight track.

Wheelset (rail transport) wheel-axle assembly of a railroad car

A wheelset is the wheel–axle assembly of a railroad car. The frame assembly beneath each end of a car, railcar or locomotive that holds the wheelsets is called the bogie. Most North American freight cars have two bogies with two or three wheelsets, depending on the type of car; short freight cars generally have no bogies but instead have two wheelsets.

Compensation for gradients in tunnels

Tunnels on steep gradients can present problems for air-breathing locomotives, such as steam locomotives and diesel locomotives. Poor ventilation in long or narrow tunnels can starve the locomotive of power. The solution is analogous to compensation for curvature and requires the gradient in the tunnel and for some distance on either side to be greatly reduced compared to the ruling grade. Unfortunately, the necessary compensation for gradient is not a simple equation, but is rather a trial and error process. Since one cannot build several tunnels to find out which one is best, it is useful to study existing tunnels with steep gradients.

Steam locomotive Railway locomotive that produces its pulling power through a steam engine

A steam locomotive is a type of railway locomotive that produces its pulling power through a steam engine. These locomotives are fueled by burning combustible material – usually coal, wood, or oil – to produce steam in a boiler. The steam moves reciprocating pistons which are mechanically connected to the locomotive's main wheels (drivers). Both fuel and water supplies are carried with the locomotive, either on the locomotive itself or in wagons (tenders) pulled behind.

Diesel locomotive locomotive powered by a diesel engine

A diesel locomotive is a type of railway locomotive in which the prime mover is a diesel engine. Several types of diesel locomotive have been developed, differing mainly in the means by which mechanical power is conveyed to the driving wheels.

Moisture from exhausts and springs can also make the rails slippery, and allowance may need to be taken for that as well.

General situation in the United States

In steam days Southern Pacific trains eastward across Nevada and Utah faced nothing steeper than 0.43% in the 531 miles from Sparks to Ogden—except for a few miles of 1.4% east of Wells. Trains would leave Sparks with enough engine to manage the 0.43% grade (e.g. a 2-10-2 with 5500 tons) and would get helper engines at Wells; the "ruling grade" from Sparks to Ogden could be considered 0.43%. But nowadays the railroad doesn't base helper engines and crews at Wells so trains must leave Sparks with enough power to climb the 1.4%, making that the division's ruling grade.

Nevada U.S. state in the United States

Nevada is a state in the Western United States. It is bordered by Oregon to the northwest, Idaho to the northeast, California to the west, Arizona to the southeast, and Utah to the east. Nevada is the 7th most extensive, the 32nd most populous, but the 9th least densely populated of the U.S. states. Nearly three-quarters of Nevada's people live in Clark County, which contains the Las Vegas–Paradise metropolitan area where three of the state's four largest incorporated cities are located. Nevada's capital is Carson City.

Utah U.S. state in the United States

Utah is a state in the western United States. It became the 45th state admitted to the U.S. on January 4, 1896. Utah is the 13th-largest by area, 30th-most-populous, and 11th-least-densely populated of the 50 United States. Utah has a population of more than 3 million according to the Census estimate for July 1, 2016. Urban development is mostly concentrated in two areas: the Wasatch Front in the north-central part of the state, which contains approximately 2.5 million people; and Washington County in Southern Utah, with over 160,000 residents. Utah is bordered by Colorado to the east, Wyoming to the northeast, Idaho to the north, Arizona to the south, and Nevada to the west. It also touches a corner of New Mexico in the southeast.

Sparks, Nevada City in Nevada, United States

Sparks is a city in Washoe County, Nevada, United States. It was founded in 1904, incorporated on March 15, 1905, and is located just east of Reno. The 2010 U.S. Census Bureau population count was 90,264. It is the fifth most populous city in Nevada. It is named after the late Nevada Governor John Sparks, a member of the Silver Party.

As such, the term can be ambiguous; and is even more ambiguous if the ruling grade is impacted by the effect of a momentum grade. Overland Route trains from Sacramento, California to Oakland face nothing steeper than 0.5% on Track 1, the traditional westward track, but nowadays they might need to climb to the Benicia bridge on Track 2 which includes 0.7 mile at about 1.9%, preceded and followed by near-level track. Using this as an example, several issues arise on defining "ruling grade". One issue is whether a running start should be assumed and, if yes, the speed to assume. Another issue is the train length to assume, given that certain lengths exceed the length of the hill in question. And if a running start at some arbitrary speed is assumed, the calculated "ruling grade" will be different for locomotives having different power-vs-speed characteristics.

Sacramento, California State capital and city of California, United States

Sacramento is the capital city of the U.S. state of California and the seat of Sacramento County. Located at the confluence of the Sacramento River and the American River in Northern California's Sacramento Valley, Sacramento's estimated 2018 population of 501,334 makes it the sixth-largest city in California and the ninth largest capital in the United States. Sacramento is the seat of the California Legislature and the Governor of California, making it the state's political center and a hub for lobbying and think tanks. Sacramento is also the cultural and economic core of the Sacramento metropolitan area, which had a 2010 population of 2,414,783, making it the fifth largest in California.

Oakland, California City in California, United States

Oakland is the largest city and the county seat of Alameda County, California, United States. A major West Coast port city, Oakland is the largest city in the East Bay region of the San Francisco Bay Area, the third largest city overall in the San Francisco Bay Area, the eighth most populated city in California, and the 45th largest city in the United States. With a population of 432,897 as of 2019, it serves as a trade center for the San Francisco Bay Area; its Port of Oakland is the busiest port in the San Francisco Bay, the entirety of Northern California, and the fifth busiest in the United States of America. An act to incorporate the city was passed on May 4, 1852, and incorporation was later approved on March 25, 1854, which officially made Oakland a city. Oakland is a charter city.

In North America, Congress set the Standard Grade for railroads eligible for subsidies and grants in the 1850s. They took as that standard the one adopted by the Cumberland – Wheeling Railway, that grade being 116 feet per mile. Later when charters were drawn up for the Union Pacific Railroad and the Canadian Pacific Railway in Canada, the national governments imposed the Standard Ruling Grade on the two lines because both received federal assistance and regulation. (Vance, JE Jr.,1995)

North America Continent entirely within the Northern Hemisphere and almost all within the Western Hemisphere

North America is a continent entirely within the Northern Hemisphere and almost all within the Western Hemisphere. It is also considered by some to be a northern subcontinent of the Americas. It is bordered to the north by the Arctic Ocean, to the east by the Atlantic Ocean, to the west and south by the Pacific Ocean, and to the southeast by South America and the Caribbean Sea.


A ruling grade is often found at a long climb up to a summit. Ideally, the cutting at the summit should be as deep as possible, such as at Shap, as this helps reduce the amount of climb and the steepness of the gradient. Alternately, a summit tunnel should be provided, such as at Ardglen.

Curve and Gradient Books

Other tunnels

See also

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