Ruling gradient
Encyclopedia
The term "ruling grade" is usually used as a synonym for "steepest climb" between two points on a railroad. But if the steepest climb is, say, a quarter-mile of 2% upgrade preceded and followed by 1.5% grade the "ruling grade" can only be defined arbitrarily.
In the 1953 edition of Railway Engineering 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. In steam days Southern Pacific trains running east across Nevada 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.
So the term is always ambiguous, and is more ambiguous still if the ruling grade is 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%. How to define "ruling grade" there? Should we assume a running start? How much of one? If we don't assume a running start, what train length should we assume, many freight trains being longer than the hill?
(And if we do assume a running start at some arbitrary speed, the calculated "ruling grade" will be different for locomotives having different power-vs-speed characteristics.)
In addition, the friction of the wheels against the curved rails increases the pull needed from the locomotive.
s and diesel locomotive
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.
, too little compensation for tunnel gradient was made. It is worthwhile even in hindsight to consider how else the problem might have been tackled.
The tunnel should have a slight gradient to facilitate drainage of water.
Should the new steep approaches ever become operationally inconvenient, then it might be replaced by say, a spiral tunnel. Unlike the main 2.6 mile tunnel, which can only be replaced on an all or nothing basis, an inadequate approach can be replaced in dribs and drabs.
A level main tunnel would have avoided the need for electrification of the main tunnel to eliminate the smoke problem, and perhaps even eliminated the need for a second longer tunnel later on.
near Sydney was built in 1869 to avoid having to build a long tunnel.
The zig zag
became a bottleneck because amongst other reasons the length of the top and bottom roads restricted train lengths. A single track tunnel was built in 1892 to replace the Lapstone Zig Zag
. Unfortunately, this tunnel was on a steep gradient, indeed the ruling grade of 1 in 33, which caused problems with the smoke from hard working locomotives.
By 1908, the situation had become unbearable, and with the need to duplicate the line, the old single track tunnel was replaced by an almost tunnel-free alignment at a reduced ruling grade on 1 in 60.
These problems predated the fume problems with the first Cascade Tunnel
at the opposite side of the world.
was built in 1869, when the colony of New South Wales
had limited tunnel building resources, and the Zig Zag became something of a wonder of the world.
By the 1900s, the single track Zig Zag had become a bottleneck, and duplication of the line became essential. By careful alignment of the new line to exploit a large number of clefts in the terrain, a double track
deviation with 10 short tunnels was possible rather than one long one. These tunnels have a relatively gentle gradient of 1 in 90 (1.11%). However, the frequent gaps between the tunnels provide good natural ventilation. In the latter days of steam, a train with 4 locomotives might haul a train to the entrance of the ten tunnels, with only 2 locomotives having to proceed through the tunnels themselves. Thus the fume problems in these tunnels was moderate.
was summit tunnel of 3 miles (4.8 km) length and suffered from poor working conditions as the gradient of 1 in 200 (0.5%
) in the tunnel was not sufficiently reduced compared to the 1 in 100 (1%) ruling grade of the approaches as a whole. The tunnel actually consisted of two separate bores, of minimum cross-section
.
is approximately 2000 m long. It is straight and level, and double track. The tunnel is near sea-level, which partly explains why it is near level. There are no intermediate ventilation shafts. There are short rising grades of 1 in 40 and 1 in 80 on either side of the tunnel. The ruling grade of the line is 1 in 40, and taking all these factors into account, the tunnel has never suffered heavily from smoke. In all, a reasonably well designed tunnel. The line was electrified in 1961, but since the 1990s freight trains have reverted to diesel haulage.
is a 500 m (1,640 ft) long tunnel at the summit located at a low point at top of the Great Dividing Range
. It is approached by steep 1 in 40 gradients (2.5%
) in both directions. Heavy traffic predominates in the south bound direction. The tunnel is sloped so as to favour loaded southbound trains.
This tunnel is located at the Great Dividing Range
. It is not known how winds would affect the fume issue.
In the 1953 edition of Railway Engineering 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. In steam days Southern Pacific trains running east across Nevada 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.
So the term is always ambiguous, and is more ambiguous still if the ruling grade is 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%. How to define "ruling grade" there? Should we assume a running start? How much of one? If we don't assume a running start, what train length should we assume, many freight trains being longer than the hill?
(And if we do assume a running start at some arbitrary speed, the calculated "ruling grade" will be different for locomotives having different power-vs-speed characteristics.)
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 - follow the chord of the curve and not the arc of the curve. 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.In addition, the friction of the wheels against the curved rails increases the pull needed from the locomotive.
Compensation for gradients in tunnels
Tunnels on steep gradients can present problems for air-breathing locomotives, such as steam locomotiveSteam locomotive
A steam locomotive is a railway locomotive that produces its power through a steam engine. These locomotives are fueled by burning some combustible material, usually coal, wood or oil, to produce steam in a boiler, which drives the steam engine...
s and diesel locomotive
Diesel locomotive
A diesel locomotive is a type of railroad locomotive in which the prime mover is a diesel engine, a reciprocating engine operating on the Diesel cycle as invented by Dr. Rudolf Diesel...
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.
Case Study - Cascade Tunnel, Washington, US
As happened on the first Cascade TunnelCascade Tunnel
The Cascade Tunnel refers to two tunnels at Stevens Pass through the Cascade Mountains, approximately to the east of Everett, Washington. The first Cascade Tunnel was a 2.63-mile long single track railroad, built by the Great Northern Railway in 1900 to avoid problems caused by heavy winter...
, too little compensation for tunnel gradient was made. It is worthwhile even in hindsight to consider how else the problem might have been tackled.
Tunnel 1 as built
The lines approaching the first cascade tunnel had a ruling gradient of 2.2% (1 in 45.5), while the tunnel itself had a gradient of 1.7% (1 in 58.8) facing eastbound trains. This gradient appears to be chosen by the expedient of building the shortest possible tunnel that connected with the original switchback route connecting Tye (Wellington) (West) at 955 m and Cascade Tunnel Station (East) at 1031 m. The higher portal of the 13,873 feet long (4228 m) tunnel was 305 feet (93 m) higher than the lower portal. Even though the ruling gradient in the tunnel was (slightly) less than that on the tracks on either side, the first Cascade tunnel soon proved to have problems with fumes, which was later tackled by electrification.Tunnel 1 as might have been
The gradient problem in the first tunnel is the result of the western portal being 100 metres lower than the eastern end, assuming that the tunnel joins the switchback route at the first available opportunity. If the 4% gradients at the western end had started several kilometres earlier, then the western portal could have been 100 m higher, making the first tunnel practically level and free of smoke problems. Strictly speaking, the level gradient should continue for a suitable distance beyond the portal, so that eastbound trains crawling up the hill can accelerate to line speed by the time that they enter the tunnel, so that the passage through whole of the tunnel uses the minimum throttle and generates minimum smoke.The tunnel should have a slight gradient to facilitate drainage of water.
Open air grade
Since in the open air, as many engines as needed can be added to a train to overcome a steep gradient, a better solution would have been to have a level tunnel from "New Tye" (West) to Cascade Tunnel Station (West) , with a 2.6 mile stretch of say 4% gradient ( 1 in 25 ) on the western approaches from say Windy Point Tunnel. The New Tye would have been about 250 feet higher in elevation. Levelling the main tunnel at the Cascade Tunnel Station is likely to require extra tunnel because the elevation of the valleys are higher.Should the new steep approaches ever become operationally inconvenient, then it might be replaced by say, a spiral tunnel. Unlike the main 2.6 mile tunnel, which can only be replaced on an all or nothing basis, an inadequate approach can be replaced in dribs and drabs.
A level main tunnel would have avoided the need for electrification of the main tunnel to eliminate the smoke problem, and perhaps even eliminated the need for a second longer tunnel later on.
Lapstone Zig Zag deviation tunnel, NSW, Australia
The original zig zag at LapstoneLapstone, New South Wales
Lapstone is a small village on the eastern escarpment of the Blue Mountains in New South Wales, Australia. Lapstone is located 62 kilometres west of Sydney in the local government area of the City of Blue Mountains and is part of the federal electorate of Macquarie. The village consists mostly of...
near Sydney was built in 1869 to avoid having to build a long tunnel.
The zig zag
Zig Zag (railway)
A railway zig zag, also called a switchback, is a way of climbing hills in difficult country with a minimal need for tunnels and heavy earthworks. For a short distance , the direction of travel is reversed, before the original direction is resumed.A location on railways constructed e.g...
became a bottleneck because amongst other reasons the length of the top and bottom roads restricted train lengths. A single track tunnel was built in 1892 to replace the Lapstone Zig Zag
Lapstone Zig Zag
The Lapstone Zig Zag was a ##Zig Zag #railway#|zig zag railway## built near ##Lapstone, New South Wales|Lapstone## on the ##Main Western railway line, New South Wales|Great Western Railway## of ##New South Wales## in ##Australia## between 1863 and 1865, to overcome an otherwise insurmountable climb...
. Unfortunately, this tunnel was on a steep gradient, indeed the ruling grade of 1 in 33, which caused problems with the smoke from hard working locomotives.
By 1908, the situation had become unbearable, and with the need to duplicate the line, the old single track tunnel was replaced by an almost tunnel-free alignment at a reduced ruling grade on 1 in 60.
These problems predated the fume problems with the first Cascade Tunnel
Cascade Tunnel
The Cascade Tunnel refers to two tunnels at Stevens Pass through the Cascade Mountains, approximately to the east of Everett, Washington. The first Cascade Tunnel was a 2.63-mile long single track railroad, built by the Great Northern Railway in 1900 to avoid problems caused by heavy winter...
at the opposite side of the world.
Lithgow Zig Zag deviation tunnels (1910), NSW, Australia
The original Lithgow Zig ZagZig Zag Railway
The Zig Zag Railway is a heritage railway at Lithgow in New South Wales, Australia on the site of the famous Great or Lithgow Zig Zag which operated between 1869 and 1910. As built, the line formed part of the Main West line from Sydney across the Blue Mountains and served to lower the line from...
was built in 1869, when the colony of New South Wales
New South Wales
New South Wales is a state of :Australia, located in the east of the country. It is bordered by Queensland, Victoria and South Australia to the north, south and west respectively. To the east, the state is bordered by the Tasman Sea, which forms part of the Pacific Ocean. New South Wales...
had limited tunnel building resources, and the Zig Zag became something of a wonder of the world.
By the 1900s, the single track Zig Zag had become a bottleneck, and duplication of the line became essential. By careful alignment of the new line to exploit a large number of clefts in the terrain, a double track
Double track
A double track railway usually involves running one track in each direction, compared to a single track railway where trains in both directions share the same track.- Overview :...
deviation with 10 short tunnels was possible rather than one long one. These tunnels have a relatively gentle gradient of 1 in 90 (1.11%). However, the frequent gaps between the tunnels provide good natural ventilation. In the latter days of steam, a train with 4 locomotives might haul a train to the entrance of the ten tunnels, with only 2 locomotives having to proceed through the tunnels themselves. Thus the fume problems in these tunnels was moderate.
Woodhead tunnel (1845), England, UK
The Woodhead TunnelWoodhead Tunnel
The Woodhead Tunnels are three parallel trans-Pennine 3-mile long railway tunnels on the Woodhead Line, a former major rail link from Manchester to Sheffield in northern England...
was summit tunnel of 3 miles (4.8 km) length and suffered from poor working conditions as the gradient of 1 in 200 (0.5%
Percent sign
The percent sign is the symbol used to indicate a percentage .Related signs include the permille sign ‰ and the permyriad sign , which indicate that a number is divided by one thousand or ten thousand respectively...
) in the tunnel was not sufficiently reduced compared to the 1 in 100 (1%) ruling grade of the approaches as a whole. The tunnel actually consisted of two separate bores, of minimum cross-section
Structure gauge
The structure gauge, also called the minimum clearance outline, is the minimum height and width of tunnels and bridges as well as the minimum height and width of the doors that allow a rail siding access into a warehouse...
.
Woy Woy tunnel (1888), NSW, Australia
The Woy Woy tunnel in New South WalesNew South Wales
New South Wales is a state of :Australia, located in the east of the country. It is bordered by Queensland, Victoria and South Australia to the north, south and west respectively. To the east, the state is bordered by the Tasman Sea, which forms part of the Pacific Ocean. New South Wales...
is approximately 2000 m long. It is straight and level, and double track. The tunnel is near sea-level, which partly explains why it is near level. There are no intermediate ventilation shafts. There are short rising grades of 1 in 40 and 1 in 80 on either side of the tunnel. The ruling grade of the line is 1 in 40, and taking all these factors into account, the tunnel has never suffered heavily from smoke. In all, a reasonably well designed tunnel. The line was electrified in 1961, but since the 1990s freight trains have reverted to diesel haulage.
Ardglen Tunnel, NSW, Australia
Ardglen TunnelArdglen Tunnel
The Ardglen Tunnel is a summit tunnel on the Main North railway in New South Wales, Australia, between Newcastle and Werris Creek. It crosses under the Liverpool Range near its east end below Nowlands Gap , the crossing used by the New England Highway.It is approximately 500 metres long, and...
is a 500 m (1,640 ft) long tunnel at the summit located at a low point at top of the Great Dividing Range
Great Dividing Range
The Great Dividing Range, or the Eastern Highlands, is Australia's most substantial mountain range and the third longest in the world. The range stretches more than 3,500 km from Dauan Island off the northeastern tip of Queensland, running the entire length of the eastern coastline through...
. It is approached by steep 1 in 40 gradients (2.5%
Percent sign
The percent sign is the symbol used to indicate a percentage .Related signs include the permille sign ‰ and the permyriad sign , which indicate that a number is divided by one thousand or ten thousand respectively...
) in both directions. Heavy traffic predominates in the south bound direction. The tunnel is sloped so as to favour loaded southbound trains.
This tunnel is located at the Great Dividing Range
Great Dividing Range
The Great Dividing Range, or the Eastern Highlands, is Australia's most substantial mountain range and the third longest in the world. The range stretches more than 3,500 km from Dauan Island off the northeastern tip of Queensland, running the entire length of the eastern coastline through...
. It is not known how winds would affect the fume issue.
Other tunnels
- ( in order of steepness)
- Dove Holes TunnelDove Holes TunnelDove Holes Tunnel is a tunnel built by the Midland Railway between Peak Forest Signal Box and Chapel-en-le-Frith in Derbyshire.In the mid-nineteenth century, the Manchester, Buxton, Matlock and Midlands Junction Railway was jointly leased by the LNWR and Midland Railway, and ran as far as Rowsley...
1 in 90 - 1.11% - 1865 - Connaught TunnelConnaught TunnelConnaught Tunnel, in the Selkirk Mountains under Rogers Pass on the Canadian Pacific Railway main line between Calgary, Alberta, and Revelstoke, British Columbia, at long was, at the time it was built, the longest railway tunnel in North America. Dug under Mount Macdonald to ease growing traffic...
1 in 105 - 0.95% - 1916 - double trackDouble trackA double track railway usually involves running one track in each direction, compared to a single track railway where trains in both directions share the same track.- Overview :... - Woodhead TunnelWoodhead TunnelThe Woodhead Tunnels are three parallel trans-Pennine 3-mile long railway tunnels on the Woodhead Line, a former major rail link from Manchester to Sheffield in northern England...
1 in 201 - 0.50% - 1845 - Combe Down TunnelCombe Down TunnelCombe Down Tunnel is on the now-closed Somerset and Dorset Joint Railway main line, between Midford and Bath Queen Square, below high ground and the southern suburbs of Bath, England, emerging below the southern slopes of Combe Down village....
- - - - - 1874 - fume problems
See also
- Hillclimbing (railway)Hillclimbing (railway)While railways have a great ability to haul very heavy loads, this advantage only really applies when the tracks are fairly level. As soon as the gradients stiffen, the tonnage that can be hauled is greatly diminished.- Techniques to overcome steep hills :...
- Mountain railwayMountain railwayA mountain railway is a railway that ascends and descends a mountain slope that has a steep grade. Such railways can use a number of different technologies to overcome the steepness of the grade...
- Old Main Line (Baltimore and Ohio Railroad)
- Rack railwayRack railwayA rack-and-pinion railway is a railway with a toothed rack rail, usually between the running rails. The trains are fitted with one or more cog wheels or pinions that mesh with this rack rail...