90-473: The Arth–Rigi railway line is a Swiss standard gauge rack railway that runs from Arth-Goldau RB to Rigi . It was built by the eponymous Arth-Rigi-Bahn ( lit. ' Arth-Rigi Railways ' ) between 1873–1875 and operated by that company until its merger with the Vitznau-Rigi-Bahn in 1992 to form Rigi Railways . When the people of Art , canton of Schwyz , heard that a railway to Rigi
180-472: A x = μ W , {\displaystyle F_{\mathrm {max} }=\mu W,} where μ {\displaystyle \mu } is the coefficient of friction and W {\displaystyle W} is the weight on the wheel. Usually the force needed to start sliding is greater than that needed to continue sliding. The former is concerned with static friction (also known as " stiction " ) or "limiting friction", whilst
270-401: A diesel locomotive or electric locomotive , the steam locomotive only works when its powerplant (the boiler, in this case) is fairly level. The locomotive boiler requires water to cover the boiler tubes and firebox sheets at all times, particularly the crown sheet , the metal top of the firebox. If this is not covered with water, the heat of the fire will soften it enough to give way under
360-477: A 20- tooth , 3-foot (914 mm) diameter cog wheel (pinion) on the left side that engaged in rack teeth (two teeth per foot) on the outer side of the rail, the metal "fishbelly" edge rail with its side rack being cast all in one piece, in 3-foot (1 yd; 914 mm) lengths. Blenkinsop's system remained in use for 25 years on the Middleton Railway, but it became a curiosity because simple friction
450-440: A continuous rack. So long as the breaks in the rack were shorter than the distance between the drive pinions on the locomotive, the rack rail could be interrupted wherever there was need to cross over a running rail. Turnouts are far more complex when the rack is at or below the level of the running rails. Marsh's first rack patent shows such an arrangement, and the original Mount Washington Cog Railway he built had no turnouts. It
540-575: A few are transit railways or tramways built to overcome a steep gradient in an urban environment. The first cog railway was the Middleton Railway between Middleton and Leeds in West Yorkshire , England, United Kingdom , where the first commercially successful steam locomotive , Salamanca , ran in 1812. This used a rack and pinion system designed and patented in 1811 by John Blenkinsop . The first mountain cog railway
630-443: A flange on the track dissipates large amounts of energy, mainly as heat but also including noise and, if sustained, would lead to excessive wheel wear. Centering is actually accomplished through shaping of the wheel. The tread of the wheel is slightly tapered. When the train is in the centre of the track, the region of the wheels in contact with the rail traces out a circle which has the same diameter for both wheels. The velocities of
720-445: A gradient. This is one of the reasons why rack railways were among the first to be electrified and most of today's rack railways are electrically powered. In some cases, a vertical boiler can be used that is less sensitive for the track gradient. On a rack-only railroad, locomotives are always downward of their passenger cars for safety reasons: the locomotive is fitted with powerful brakes, often including hooks or clamps that grip
810-466: A hard slippery lignin coating. Leaf contamination can be removed by applying " Sandite " (a gel–sand mix) from maintenance trains, using scrubbers and water jets, and can be reduced with long-term management of railside vegetation. Locomotives and trams use sand to improve traction when driving wheels start to slip. Adhesion is caused by friction , with maximum tangential force produced by a driving wheel before slipping given by: F m
900-404: A heavy train slowly. Slip is the additional speed that the wheel has and creep is the slip level divided by the locomotive speed. These parameters are those that are measured and which go into the creep controller. On an adhesion railway, most locomotives will have a sand containment vessel. Properly dried sand can be dropped onto the rail to improve traction under slippery conditions. The sand
990-495: A ladder between two L-shaped wrought-iron rails. The first public trial of the Marsh rack on Mount Washington was made on August 29, 1866, when only one quarter of a mile (402 meters) of track had been completed. The Mount Washington railway opened to the public on August 14, 1868. The pinion wheels on the locomotives have deep teeth that ensure that at least two teeth are engaged with the rack at all times; this measure helps reduce
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#17327907055891080-436: A region of slippage. The net result is that, during traction, the wheel does not advance as far as would be expected from rolling contact but, during braking, it advances further. This mix of elastic distortion and local slipping is known as "creep" (not to be confused with the creep of materials under constant load). The definition of creep in this context is: In analysing the dynamics of wheelsets and complete rail vehicles,
1170-431: A second-order effect on the critical speed. The true situation is much more complicated, as the response of the vehicle suspension must be taken into account. Restraining springs, opposing the yaw motion of the wheelset, and similar restraints on bogies , may be used to raise the critical speed further. However, in order to achieve the highest speeds without encountering instability, a significant reduction in wheel taper
1260-468: A simplified but compatible rack, where the teeth on the engine pinions engaged square holes punched in a bar-shaped center rail. J. H. Morgan patented several alternative turnout designs for use with this rack system. Curiously, Morgan recommended an off-center rack in order to allow clear passage for pedestrians and animals walking along the tracks. Some photos of early Morgan installations show this. A simplified rack mounting system could be used when
1350-495: Is compressed to a film on the track where the wheels make contact. Together with some moisture on the track, which acts as a light adhesive and keeps the applied sand on the track, the wheels "bake" the crushed sand into a more solid layer of sand. Because the sand is applied to the first wheels on the locomotive, the following wheels may run, at least partially and for a limited time, on a layer of sand (sandfilm). While traveling this means that electric locomotives may lose contact with
1440-406: Is determined by the forces arising between two surfaces in contact. This may appear trivially simple from a superficial glance but it becomes extremely complex when studied to the depth necessary to predict useful results. The first error to address is the assumption that wheels are round. A glance at the tyres of a parked car will immediately show that this is not true: the region in contact with
1530-416: Is lowered with contamination, the maximum obtainable under those conditions occurs at greater values of creep. The controllers must respond to different friction conditions along the track. Some of the starting requirements were a challenge for steam locomotive designers – "sanding systems that did not work, controls that were inconvenient to operate, lubrication that spewed oil everywhere, drains that wetted
1620-421: Is most often applied using compressed air via tower, crane, silo or train. When an engine slips, particularly when starting a heavy train, sand applied at the front of the driving wheels greatly aids in tractive effort causing the train to "lift", or to commence the motion intended by the engine driver. Sanding however also has some negative effects. It can cause a "sandfilm", which consists of crushed sand, that
1710-520: Is necessary. For example, taper on Shinkansen wheel treads was reduced to 1:40 (when the Shinkansen first ran) for both stability at high speeds and performance on curves. That said, from the 1980s onwards, the Shinkansen engineers developed an effective taper of 1:16 by tapering the wheel with multiple arcs, so that the wheel could work effectively both at high speed as well as at sharper curves. The behaviour of vehicles moving on adhesion railways
1800-435: Is possible only with wheelsets where each can have some free motion about its vertical axis. If wheelsets are rigidly coupled together, this motion is restricted, so that coupling the wheels would be expected to introduce sliding, resulting in increased rolling losses. This problem was alleviated to a great extent by ensuring that the diameters of all coupled wheels were very closely matched. With perfect rolling contact between
1890-410: Is the moment of inertia of the wheelset perpendicular to the axle, m is the wheelset mass. The result is consistent with the kinematic result in that the critical speed depends inversely on the taper. It also implies that the weight of the rotating mass should be minimised compared with the weight of the vehicle. The wheel gauge appears in both the numerator and denominator, implying that it has only
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#17327907055891980-577: Is very low, generally from 9 to 25 kilometres per hour (5.6 to 15.5 mph) depending on gradient and propulsion method. Because the Skitube has gentler gradients than typical, its speeds are higher than typical. The Culdee Fell Railway is a fictional cog railway on the Island of Sodor in The Railway Series by Rev. W. Awdry . Its operation, locomotives and history are based on those of
2070-540: The Nilgiri Mountain Railway . The Agudio rack system was invented by Tommaso Agudio. Its only long-lived application was on the Sassi–Superga tramway which opened in 1884. It used a vertical rack with cog wheels on each side of the central rack. Its unique feature, however, was that the 'locomotive' was propelled by means of an endless cable driven from an engine house at the foot of the incline. It
2160-588: The Snowdon Mountain Railway . It is featured in the book Mountain Engines . The Štrbské Pleso rack railway in Slovakia is featured in "The Bounty" by Janet Evanovich and Steve Hamilton . Adhesion railway An adhesion railway relies on adhesion traction to move the train, and is the most widespread and common type of railway in the world. Adhesion traction is the friction between
2250-404: The "vehicle velocity". When a wheel rolls freely along the rail the contact patch is in what is known as a "stick" condition. If the wheel is driven or braked the proportion of the contact patch with the "stick" condition gets smaller and a gradually increasing proportion is in what is known as a "slip condition". This diminishing "stick" area and increasing "slip" area supports a gradual increase in
2340-476: The 1920s, and measures to eliminate it were not taken until the late 1960s. The maximum speed was limited not by raw power but by a possible instability in the motion. The kinematic description of the motion of tapered treads on the two rails is insufficient to describe hunting well enough to predict the critical speed. It is necessary to deal with the forces involved. There are two features which must be taken into account: The kinematic approximation corresponds to
2430-722: The Abt system was on the Harzbahn in Germany, which opened in 1885. The Abt system was also used for the construction of the Snowdon Mountain Railway in Wales from 1894 to 1896. The pinion wheels can be mounted on the same axle as the rail wheels, or driven separately. The steam locomotives on the West Coast Wilderness Railway have separate cylinders driving the pinion wheel, as do the "X"-class locomotives on
2520-646: The Abt system, but typically wider than a single Abt bar. The Lamella rack can be used by locomotives designed for use on the Riggenbach or the Strub systems, so long as the safety-jaws that were a feature of the original Strub system are not used. Some railways use racks from multiple systems; for example, the St. Gallen Gais Appenzell Railway in Switzerland has sections of Riggenbach, Strub, and Lamella rack. Most of
2610-668: The Art-Ober Art-Goldau section started in 1874. On 4 June 1875, the Art-Rigi Railway ( Art-Rigi-Bahn ) was able to commence operations along the whole line. Although it had lost the race against the Vitznau–Rigi Railway, the line had glorious views and more luxurious coaches. The mountain railway started operating in winter between Goldau and Rigi-Kulm in 1928. Originally, the standard gauge line began in Art on
2700-875: The British market. Between 1903 and 1909, the McKell Coal and Coke company in Raleigh County, West Virginia, installed 35,000 feet (10,700 m) of Morgan rack/third-rail track in its mines. Between 1905 and 1906, the Mammoth Vein Coal Company installed 8,200 feet (2,500 m) of powered rack in two of its mines in Everist, Iowa , with a maximum grade of 16%. The Donohoe Coke Co. of Greenwald, Pennsylvania had 10,000 feet (3,050 m) of Goodman rack in its mine in 1906. The Morgan system saw limited use on one common carrier railroad in
2790-535: The Morgan rack was not used for third-rail power and the Morgan rack offered interesting possibilities for street railways. The Morgan rack was good for grades of up to 16 percent . The Goodman Equipment Company began marketing the Morgan system for mine railways , and it saw widespread use, particularly where steep grades were encountered underground. By 1907, Goodman had offices in Cardiff, Wales , to serve
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2880-547: The Strub system is on the Jungfraubahn in Switzerland. Strub is the simplest rack system to maintain and has become increasingly popular. In 1900, E. C. Morgan of Chicago received a patent on a rack railway system that was mechanically similar to the Riggenbach rack, but where the rack was also used as a third rail to power the electric locomotive. Morgan went on to develop heavier locomotives and with J. H. Morgan, turnouts for this system. In 1904, he patented
2970-617: The Swiss government. Eager to boost tourism in Switzerland, the government commissioned Riggenbach to build a rack railway up Mount Rigi . Following the construction of a prototype locomotive and test track in a quarry near Bern , the Vitznau–Rigi railway opened on 22 May 1871. The Riggenbach system is similar in design to the Marsh system. It uses a ladder rack, formed of steel plates or channels connected by round or square rods at regular intervals. The Riggenbach system suffers from
3060-716: The United States, the Chicago Tunnel Company , a narrow gauge freight carrier that had one steep grade in the line up to their surface disposal station on the Chicago lakefront. The Lamella system (also known as the Von Roll system) was developed by the Von Roll company after the rolled steel rails used in the Strub system became unavailable. It is formed from a single blade cut in a similar shape to
3150-401: The boiler pressure, leading to a catastrophic failure. On rack systems with extreme gradients, the boiler, cab, and general superstructure of the locomotive are tilted forward relative to the wheels so that they are more or less horizontal when on the steeply graded track. These locomotives often cannot function on level track, and so the entire line, including maintenance shops, must be laid on
3240-469: The braking forces and the centering forces all contribute to stable running. However, running friction increases costs, due to higher fuel consumption and increased maintenance needed to address fatigue damage and wear on rail heads and on the wheel rims and rail movement from traction and braking forces. Traction or friction is reduced when the top of the rail is wet or frosty or contaminated with grease, oil or decomposing leaves which compact into
3330-433: The case which is dominated by contact forces. An analysis of the kinematics of the coning action yields an estimate of the wavelength of the lateral oscillation: where d is the wheel gauge, r is the nominal wheel radius and k is the taper of the treads. For a given speed, the longer the wavelength and the lower the inertial forces will be, so the more likely it is that the oscillation will be damped out. Since
3420-418: The centre of mass of the units, the wheel gauge and whether the track is superelevated , or canted . Toppling will occur when the overturning moment due to the side force ( centrifugal acceleration) is sufficient to cause the inner wheel to begin to lift off the rail. This may result in loss of adhesion – causing the train to slow, preventing toppling. Alternatively, the inertia may be sufficient to cause
3510-595: The centre rail, as well as by means of the normal running wheels. The first successful rack railway in the United States was the Mount Washington Cog Railway, developed by Sylvester Marsh . Marsh was issued a U.S. patent for the general idea of a rack railway in September 1861, and in January 1867 for a practical rack where the rack teeth take the form of rollers arranged like the rungs of
3600-403: The construction of turnouts. If the rack is elevated above the running rails, there is no need to interrupt the running rails to allow passage of the driving pinions of the engines. Strub explicitly documented this in his U.S. patent. Strub used a complex set of bell-cranks and push-rods linking the throw-rod for the points to the two throw-rods for the moving rack sections. One break in the rack
3690-488: The contact forces can be treated as linearly dependent on the creep ( Joost Jacques Kalker 's linear theory, valid for small creepage) or more advanced theories can be used from frictional contact mechanics . The forces which result in directional stability, propulsion and braking may all be traced to creep. It is present in a single wheelset and will accommodate the slight kinematic incompatibility introduced by coupling wheelsets together, without causing gross slippage, as
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3780-459: The drive wheels and the steel rail. Since the vast majority of railways are adhesion railways, the term adhesion railway is used only when it is necessary to distinguish adhesion railways from railways moved by other means, such as by a stationary engine pulling on a cable attached to the cars or by a pinion meshing with a rack . The friction between the wheels and rails occurs in the wheel–rail interface or contact patch. The traction force,
3870-403: The early 1880s, Abt worked to devise an improved rack system that overcame the limitations of the Riggenbach system. In particular, the Riggenbach rack was expensive to manufacture and maintain and the switches were complex. In 1882, Abt designed a new rack using solid bars with vertical teeth machined into them. Two or three of these bars are mounted centrally between the rails, with the teeth of
3960-405: The engine), falling to 50 kilonewtons under the worst conditions. Steam locomotives suffer particularly badly from adhesion issues because the traction force at the wheel rim fluctuates (especially in 2- or most 4-cylinder engines) and, on large locomotives, not all wheels are driven. The "factor of adhesion", being the weight on the driven wheels divided by the theoretical starting tractive effort,
4050-407: The highest friction and the heaviest locomotive. The friction can vary a great deal, but it was known on early railways that sand helped, and it is still used today, even on locomotives with modern traction controls. To start the heaviest trains, the locomotive must be as heavy as can be tolerated by the bridges along the route and the track itself. The weight of the locomotive must be shared equally by
4140-436: The latter is dynamic friction, also called "sliding friction". For steel on steel, the coefficient of friction can be as high as 0.78, under laboratory conditions, but typically on railways it is between 0.35 and 0.5, whilst under extreme conditions it can fall to as low as 0.05. Thus a 100-tonne locomotive could have a tractive effort of 350 kilonewtons, under the ideal conditions (assuming sufficient force can be produced by
4230-512: The latter, however, claimed more and more space for its rail tracks, the ARB built its notable wrought iron high-level platform over the Gotthard Railway’s tracks in 1897. Now, the majority of the ARB's passengers arrived by train. From 2011 to 2013, a new, two-track station layout was built before the high-level platform and the heritage-listed platform was rebuilt as an entrance hall. Originally,
4320-461: The likelihood of wheelslip include wheel size, the sensitivity of the regulator and the skill of the driver. The term all-weather adhesion is usually used in North America , and refers to the adhesion available during traction mode with 99% reliability in all weather conditions. The maximum speed at which a train can proceed around a turn is limited by the radius of turn, the position of
4410-508: The line from Staffelhöhe to Rigi Kulm (1752 m above sea level). The Vitznau–Rigi Railway company line connected its line with this line in the summer of 1873 and it had to pay fees for the use of the Staffelhöhe–Rigi Kulm section until the merger of the two companies in 1992. Construction of the line from Goldau (518 m asl) – those days not more than a hamlet – to Staffel via Kräbel and Klösterli (1315 m asl) started in 1873 and work on
4500-400: The locomotive is moving (known as creep control) to generate the maximum coefficient of friction, and the axles must be driven independently with their own controller because different axles will see different conditions. The maximum available friction occurs when the wheels are slipping/creeping. If contamination is unavoidable the wheels must be driven with more creep because, although friction
4590-489: The minimum radius of curvature is closer to 7 km (4.3 mi). During the 19th century, it was widely believed that coupling the drive wheels would compromise performance, and this was avoided on engines intended for express passenger service. With a single drive wheelset, the Hertzian contact stress between the wheel and rail necessitated the largest-diameter wheels that could be accommodated. The weight of locomotives
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#17327907055894680-460: The minimum radius would be about 2.5 km (1.6 mi). In practice, the minimum radius of turn is much greater than this, as contact between the wheel flanges and rail at high speed could cause significant damage to both. For very high speeds, the minimum adhesion limit again appears appropriate, implying a radius of turn of about 13 km (8.1 mi). In practice, curved tracks used for high speed travel are superelevated or canted , so that
4770-472: The most common rack system in Switzerland at the time – was limited to a maximum gradient of 1 in 4 (25%). Locher showed that on steeper grade, the Abt system was prone to the driving pinion over-riding the rack, causing potentially catastrophic derailments, as predicted by Dr. Abt. To overcome this problem and allow a rack line up the steep sides of Mt. Pilatus , Locher developed a rack system where
4860-552: The mountain had also been connected by the metre-gauge Rigi–Scheidegg Railway ( Rigi-Kaltbad-Scheidegg-Bahn , RSB), but this was dismantled in 1942. On 3 June 2000, the Arth–Rigi Railway celebrated its 125th anniversary with a steam festival. During the night of 19–20 January 2014, the high-level platform in Arth-Goldau station was raised by two metres so that it could be reconstructed on site. After this renovation, it
4950-586: The opening of a new station parallel to the SBB route had been considered, but this had to be discarded because the SBB needed more space in this area due to the building of the Gotthard Base Tunnel . On 1 May 1907, the ARB was the first standard-gauge rack railway in the world converted to electric traction. The bottom station of the cable car to Rigi Scheidegg (1568 above sea level) is in Kräbel. Earlier
5040-419: The order of 15 mm across. The distortion in the wheel and rail is small and localised but the forces which arise from it are large. In addition to the distortion due to the weight, both wheel and rail distort when braking and accelerating forces are applied and when the vehicle is subjected to side forces. These tangential forces cause distortion in the region where they first come into contact, followed by
5130-405: The outer wheel tread speeds up linearly, and the inner wheel tread slows down, causing the train to turn the corner. Some railway systems employ a flat wheel and track profile, relying on cant alone to reduce or eliminate flange contact. Understanding how the train stays on the track, it becomes evident why Victorian locomotive engineers were averse to coupling wheelsets. This simple coning action
5220-414: The pinions rotationally offset from each other to match. The use of multiple bars with offset teeth ensures that the pinions on the locomotive driving wheels are constantly engaged with the rack. The Abt system is cheaper to build than the Riggenbach because it requires a lower weight of rack over a given length. However the Riggenbach system exhibits greater wear resistance than the Abt. The first use of
5310-515: The possibility of the pinions riding up and out of the rack. The Riggenbach rack system was invented by Niklaus Riggenbach working at about the same time as, but independently from Marsh. Riggenbach was granted a French patent in 1863 based on a working model which he used to interest potential Swiss backers. During this time, the Swiss Consul to the United States visited Marsh's Mount Washington Cog Railway and reported back with enthusiasm to
5400-724: The problem that its fixed ladder rack is more complex and expensive to build than the other systems. Following the success of the Vitznau–Rigi railway, Riggenbach established the Maschinenfabrik der Internationalen Gesellschaft für Bergbahnen (IGB) – a company that produced rack locomotives to his design. The Abt system was devised by Carl Roman Abt , a Swiss locomotive engineer. Abt worked for Riggenbach at his works in Olten and later at his IGB rack locomotive company. In 1885, he founded his own civil engineering company. During
5490-573: The rack for driving (with the conventional rail wheels undriven) such as the Dolderbahn in Zürich , Štrbské Pleso in Slovakia and the Schynige Platte rack railway instead must switch the rack rail. The Dolderbahn switch works by bending all three rails, an operation that is performed every trip as the two trains pass in the middle. The geometry of the rack system has a large impact on
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#17327907055895580-470: The rack is a flat bar with symmetrical, horizontal teeth. Horizontal pinions with flanges below the rack engage the centrally-mounted bar, both driving the locomotive and keeping it centered on the track. This system provides very stable attachment to the track, also protecting the car from toppling over even under the most severe crosswinds. Such gears are also capable of leading the car, so even flanges on running wheels are optional. The biggest shortcoming of
5670-418: The rack rail is continuous or not. Lines where the rack rail is continuous, and the cog-drive is used throughout, are described as pure-rack lines. Other lines, which use the cog drive only on the steepest sections and elsewhere operate as a regular railway, are described as rack-and-adhesion lines. On rack-and-adhesion lines, trains are equipped with propulsion and braking systems capable of acting both through
5760-401: The rack rail solidly. Some locomotives are fitted with automatic brakes that apply if the speed gets too high, preventing runaways. Often there is no coupler between locomotive and train since gravity will always push the passenger car down against the locomotive. Electrically powered vehicles often have electromagnetic track brakes as well. The maximum speed of trains operating on a cog railway
5850-581: The rack railways built from the late 20th century onwards have used the Lamella system. Rack railway switches are as varied as rack railway technologies, for optional rack lines such as the Zentralbahn in Switzerland and the West Coast Wilderness Railway in Tasmania it is convenient to only use switches on sections flat enough for adhesion (for example, on a pass summit). Other systems which rely on
5940-429: The rails, and so on.." Others had to wait for modern electric transmissions on diesel and electric locomotives. The frictional force on the rails and the amount of wheel slip drops steadily as the train picks up speed. A driven wheel does not roll freely but turns faster than the corresponding locomotive velocity. The difference between the two is known as the "slip velocity". "Slip" is the "slip velocity" compared to
6030-411: The road is noticeably flattened, so that the wheel and road conform to each other over a region of contact. If this were not the case, the contact stress of a load being transferred through a line contact would be infinite. Rails and railway wheels are much stiffer than pneumatic tyres and tarmac but the same distortion takes place at the region of contact. Typically, the area of contact is elliptical, of
6120-433: The running rails . The trains are fitted with one or more cog wheels or pinions that mesh with this rack rail. This allows the trains to operate on steep gradients of 100% (45 degrees) or more, well above the 10% maximum for friction-based rail . The rack and pinion mechanism also provides more controlled braking and reduces the effects of snow or ice on the rails. Most rack railways are mountain railways , although
6210-445: The running rail wheels and the cog wheels, depending on whether the rack rail is present or not. Rack-and-adhesion lines also need to use a system for smoothing the transition from friction to rack traction, with a spring-mounted rack section to bring the pinion teeth gradually into engagement. This was invented by Roman Abt, who also invented the Abt rack system. On pure-rack lines, the train's running rail wheels are only used to carry
6300-553: The shores of Lake Zug . This ran as an adhesion railway to the Goldau station. It was separated from the rack railway in 1881 and run separately as tram, but a connecting track remained. This branch was closed in 1959 and the tracks were dismantled. Initially, most passengers travelled by boat over Lake Zug. From 1882, the platforms of the ARB were placed parallel to those of the Gotthard Railway on its station forecourt. As
6390-542: The system is that the standard railway switch is not usable, and a transfer table or other complex device must be used where branching of the track is needed. Following tests, the Locher system was deployed on the Pilatus Railway, which opened in 1889. No other public railway uses the Locher system, although some European coal mines use a similar system on steeply graded underground lines. The Strub rack system
6480-420: The traction or braking torque that can be sustained as the force at the wheel rim increases until the whole area is "slip". The "slip" area provides the traction. During the transition from the "all-stick" no-torque to the "all-slip" condition the wheel has had a gradual increase in slip, also known as creep and creepage. High adhesion locomotives control wheel creep to give maximum effort when starting and pulling
6570-424: The train and do not contribute to propulsion or braking, which is exclusively done through the cog wheels. Pure-rack lines have no need of transitioning systems, as the cog wheels remain engaged with the rack rail at all times, but all track, including sidings and depots, must be equipped with rack rail irrespective of gradient. A number of different designs of rack rail and matching cog wheel have been developed over
6660-408: The train to continue to move at speed, causing carriages to topple completely. For a wheel gauge of 1.5 m (4.9 ft) with no canting, a centre of gravity height of 3 m (9.8 ft) and a speed of 30 m/s (110 km/h; 67 mph), the minimum radius of curvature is 360 m (1,180 ft). For a modern, exceptionally high-speed train at 80 m/s (290 km/h; 180 mph),
6750-408: The two wheels are equal, so the train moves in a straight line. If, however, the wheelset is displaced to one side, the diameters of the regions of contact, and hence the tangential velocities of the wheels at the running surfaces, are different and the wheelset tends to steer back towards the centre. Also, when the train encounters an unbanked turn , the wheelset displaces laterally slightly, so that
6840-421: The wavelength increases with reducing taper, increasing the critical speed requires the taper to be reduced, which implies a large minimum radius of turn. A more complete analysis, taking account of the actual forces acting, yields the following result for the critical speed of a wheelset: where W is the axle load for the wheelset, a is a shape factor related to the amount of wear on the wheel and rail, C
6930-414: The wheel and rail, this coning behaviour manifests itself as a swaying of the train from side to side. In practice, the swaying is damped out below a critical speed, but is amplified by the forward motion of the train above the critical speed. This lateral swaying is known as hunting oscillation . Hunting oscillation was known by the end of the 19th century, although the cause was not fully understood until
7020-423: The wheels that are driven, with no weight transfer as the starting force builds. The wheels must turn with a steady driving force on the very small contact area of about 1 cm between each wheel and the top of the rail. The top of the rail must be dry, with no man-made or weather-related contamination, such as oil or rain. Friction-enhancing sand or an equivalent is needed. The driving wheels must turn faster than
7110-411: The years. With the exception of some early Morgan and Blenkinsop rack installations, rack systems place the rack rail halfway between the running rails, mounted on the same sleepers or ties as the running rails. John Blenkinsop thought that the friction would be too low from metal wheels on metal rails even on level ground, so he built his steam locomotives for the Middleton Railway in 1812 with
7200-548: Was converted to use the Strub rack system in 1934. The Locher rack system, invented by Eduard Locher , has gear teeth cut in the sides rather than the top of the rail, engaged by two cog wheels on the locomotive. This system allows use on steeper grades than the other systems, whose teeth could jump out of the rack. It is used on the Pilatus Railway . Locher set out to design a rack system that could be used on gradients as steep as 1 in 2 (50%). The Abt system –
7290-444: Was found to be sufficient for railroads operating on level ground. The Fell mountain railway system, developed in the 1860s, is not strictly speaking a rack railway, since there are no cogs with teeth. Rather, this system uses a smooth raised centre rail between the two running rails on steep sections of lines that is gripped on both sides to improve friction. Trains are propelled by wheels or braked by shoes pressed horizontally onto
7380-477: Was generally designed to have a value of 4 or slightly higher, reflecting a typical wheel–rail friction coefficient of 0.25. A locomotive with a factor of adhesion much lower than 4 would be highly prone to wheelslip, although some 3-cylinder locomotives, such as the SR V Schools class , operated with a factor of adhesion below 4 because the traction force at the wheel rim does not fluctuate as much. Other factors affecting
7470-433: Was invented by Emil Strub in 1896. It uses a rolled flat-bottom rail with rack teeth machined into the head approximately 100 mm (3.9 inches) apart. Safety jaws fitted to the locomotive engage with the underside of the head to prevent derailments and serve as a brake. Strub's U.S. patent, granted in 1898, also includes details of how the rack rail is integrated with the mechanism of a turnout . The best-known use of
7560-491: Was lowered by 1.3 m. In July 2017, the new station hall for the high-level platform went into operation and the provisional platforms were dismantled. In the same year, the rectifier in Klösterli was replaced by a more modern, higher current device. Rack railway A rack railway (also rack-and-pinion railway , cog railway , or cogwheel railway ) is a steep grade railway with a toothed rack rail , usually between
7650-742: Was not until 1941 that a turnout was constructed on this line. There were more turnouts built for the line but all were hand operated. In 2003, a new automatic hydraulic turnout was developed and built at the base as a prototype. With the success of the new turnout, more new automatic hydraulic turnouts were built to replace the hand-operated ones. The new turnouts installed on the Mount Washington line in 2007 are essentially transfer tables . The Locher rack also requires transfer tables. Originally almost all cog railways were powered by steam locomotives . The steam locomotive needs to be extensively modified to work effectively in this environment. Unlike
7740-400: Was once feared. Provided the radius of turn is sufficiently great (as should be expected for express passenger services), two or three linked wheelsets should not present a problem. However, 10 drive wheels (5 main wheelsets) are usually associated with heavy freight locomotives. The adhesion railway relies on a combination of friction and weight to start a train. The heaviest trains require
7830-466: Was required to select between the two routes, and a second break was required where the rack rails cross the running rails. Turnouts for the Morgan Rack system were similar, with the rack elevated above the running rails. Most of the Morgan turnout patents included movable rack sections to avoid breaks in the rack, but because all Morgan locomotives had two linked drive pinions, there was no need for
7920-412: Was restricted by the stress on the rail, and sandboxes were required, even under reasonable adhesion conditions. It may be thought that the wheels are kept on the tracks by the flanges. However, close examination of a typical railway wheel reveals that the tread is burnished but the flange is not—the flanges rarely make contact with the rail and, when they do, most of the contact is sliding. The rubbing of
8010-574: Was the Mount Washington Cog Railway in the U.S. state of New Hampshire , which carried its first fare-paying passengers in 1868. The track was completed to reach the summit of Mount Washington in 1869. The first mountain rack railway in continental Europe was the Vitznau-Rigi-Bahn on Mount Rigi in Switzerland , which opened in 1871. Both lines are still running. As well as the rack system used, lines using rack systems fall into one of two categories depending on whether
8100-588: Was to be built from the Lucerne side, they sought and received a concession in 1870 from the Cantonal Council of Schwyz to build lines on the Schwyz route between Staffelhöhe (Rigi Staffel) and Rigi Kulm and between Arth, Oberarth and Kulm. They commissioned the two engineers, Olivier Zschokke and Niklaus Riggenbach , to build the line. The Arter Aktiengesellschaft (Art Ltd.) immediately started building
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