Ruling Gradient
   HOME

TheInfoList



OR:

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 motive power (or how light the train) must be in order for the run to be made without assistance. Even if 99% of the line could be run with a low-powered (and inexpensive) locomotive, if at some point on the line there is a steeper gradient than such train would be able to climb, this gradient "rules" that a more powerful 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. 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 (to help justify the fixed daily cost of the helper operation). 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 An axle or axletree is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the wheels rotating around the axle. In the former case, beari ...
) 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.


Compensation for gradients in tunnels

Tunnels on steep gradients can present problems for air-breathing locomotives, such as
steam locomotive A steam locomotive is a locomotive that provides the force to move itself and other vehicles by means of the expansion of steam. It is fuelled by burning combustible material (usually coal, oil or, rarely, wood) to heat water in the loco ...
s and
diesel locomotive A diesel locomotive is a type of railway locomotive in which the prime mover is a diesel engine. Several types of diesel locomotives have been developed, differing mainly in the means by which mechanical power is conveyed to the driving whe ...
s. 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. 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 North America

In steam days Southern Pacific trains eastward across
Nevada Nevada ( ; ) is a state in the Western region of the 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, ...
and
Utah Utah ( , ) is a state in the Mountain West subregion of the Western United States. Utah is a landlocked U.S. state bordered to its east by Colorado, to its northeast by Wyoming, to its north by Idaho, to its south by Arizona, and to its ...
faced nothing steeper than 0.43% in the 531 miles from
Sparks Sparks may refer to: Places *Sparks, Georgia * Sparks, Kansas *Sparks, Kentucky *Sparks, Maryland * Sparks, Nebraska *Sparks, Nevada *Sparks, Oklahoma *Sparks, Texas * Sparks, Bell County, Texas * Sparks, West Virginia Books * ''Sparks'' (Raffi ...
to Ogden—except for a few miles of 1.4% east of
Wells Wells most commonly refers to: * Wells, Somerset, a cathedral city in Somerset, England * Well, an excavation or structure created in the ground * Wells (name) Wells may also refer to: Places Canada * Wells, British Columbia England * Wel ...
. Trains would leave Sparks with enough engine to manage the 0.43% grade (e.g. a
2-10-2 Under the Whyte notation for the classification of steam locomotives, represents the wheel arrangement of two leading wheels, ten powered and coupled driving wheels, and two trailing wheels. In the United States of America and elsewhere the is ...
with a 5500-ton train) 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 at Wells so trains must leave Sparks with enough power to climb the 1.4%, making that the division's ruling grade. 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 ) , image_map = Sacramento County California Incorporated and Unincorporated areas Sacramento Highlighted.svg , mapsize = 250x200px , map_caption = Location within Sacramento C ...
to Oakland face nothing steeper than 0.5% on Track 1, the traditional westward track, but nowadays they might need to approach the Benicia bridge on Track 2, which includes 0.7 miles at about 1.9% on otherwise 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. In the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., federal district, five ma ...
, 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 (2.2%). Later when charters were drawn up for the Canadian Pacific Railway in Canada and for the Union Pacific Railroad, the national governments imposed the Standard Ruling Grade on the two lines because each received federal assistance and regulation. (Vance, JE Jr.,1995)


Summits

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 Ardglen is a village on the Main North railway line and close to the New England Highway on the North West Slopes region of New South Wales, Australia. History A railway station was opened there on 13 August 1877 as Doughboy Hollow, which was l ...
.


Curve and Gradient Books

*
Australian Rail Track Corporation The Australian Rail Track Corporation (ARTC) is an Australian Government-owned statutory corporation. It operates one of the largest rail networks in the nation spanning 8,500km across five states, 39 worksites and more than 50 First Nations. ...

– excludes Transport Asset Holding Entity lines, and non-operational country lines.


Other tunnels

* (in order of steepness) * Otira Tunnel 1 in 33 – 3% * Swan View Tunnel 1 in 49 – 2.04% - asphyxiation death in 1942 *
Devonshire Tunnel Devonshire Tunnel is on the closed Somerset & Dorset Joint Railway main line, between Midford and Bath Green Park railway stations, below high ground and the southern suburbs of Bath, England, emerging below the northern slopes of Combe Down v ...
1 in 50 – 2.00% - on other side of summit to Combe Down Tunnel * Dove Holes Tunnel 1 in 90 – 1.11% - 1865 * Box Tunnel 1 in 100 – 1.00% - 1839 – double track * Combe Down Tunnel 1 in 100 – 1.00% ; (1 in 131 average) – 1874 – fume problems * Connaught Tunnel 1 in 105 – 0.95% - 1916 – double track when built – ventilation problems * Woodhead Tunnel 1 in 201 – 0.50% - 1845 – twin bores


See also

*
Grade (slope) The grade (also called slope, incline, gradient, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero ind ...
* Hillclimbing (railway) *
List of steepest gradients on adhesion railways The inclusion of steep gradients on railways avoids the expensive engineering works required to produce more gentle gradients. However the maximum feasible gradient is limited by how much of a load the locomotive(s) can haul upwards. Braking when ...
* Mountain railway * Old Main Line (Baltimore and Ohio Railroad) * Rack railway


References

{{Railway track layouts Track geometry