The cant of a
railway
Rail transport (also known as train transport) is a means of transport that transfers passengers and goods on wheeled vehicles running on rails, which are incorporated in tracks. In contrast to road transport, where the vehicles run on a pre ...
track or
camber
Camber may refer to a variety of curvatures and angles:
* Camber angle, the angle made by the wheels of a vehicle
* Camber beam, an upward curvature of a joist to compensate for load deflection due in buildings
* Camber thrust in bike technology
* ...
of a road (also referred to as superelevation,
cross slope
Cross slope, cross fall or camber is a geometric feature of pavement surfaces: the transverse slope with respect to the horizon. It is a very important safety factor. Cross slope is provided to provide a drainage gradient so that water will run o ...
or cross fall) is the rate of change in elevation (height) between the two rails or edges. This is normally greater where the railway or road is curved; raising the outer rail or the outer edge of the road creates a
banked turn
A banked turn (or banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the ...
, thus allowing vehicles to maneuver through the curve at higher speeds than would otherwise be possible were the surface flat or level.
Rail
On railways, cant helps a train steer around a curve, keeping the wheel flanges from touching the rails, minimizing friction, wear and
rail squeal.
The main functions of cant are the following:
* Improve distribution of the load across both rails
* Reduce wear on rails and wheels
* Neutralize the effect of lateral forces
* Improve passenger comfort
![Series-E257-M103](https://upload.wikimedia.org/wikipedia/commons/d/d7/Series-E257-M103.jpg)
The necessary cant in a curve depends on the expected speed of the trains and the
radius
In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
. However, it may be necessary to select a compromise value at design time, for example if slow-moving trains may occasionally use tracks intended for
high-speed trains
High-speed rail (HSR) is a type of rail system that runs significantly faster than traditional rail, using an integrated system of specialised rolling stock and dedicated tracks. While there is no single standard that applies worldwide, lines ...
.
Generally the aim is for trains to run without
flange
A flange is a protruded ridge, lip or rim (wheel), rim, either external or internal, that serves to increase shear strength, strength (as the flange of an iron beam (structure), beam such as an I-beam or a T-beam); for easy attachment/transfer of ...
contact, which also depends on the
tire profile
A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide traction on the surface over which t ...
of the wheels. Allowance has to be made for the different speeds of trains. Slower trains will tend to make flange contact with the inner rail on curves, while faster trains will tend to ride outwards and make contact with the outer rail. Either contact causes
wear and tear
Wear and tear is damage that naturally and inevitably occurs as a result of normal wear or aging. It is used in a legal context for such areas as warranty contracts from manufacturers, which usually stipulate that damage from ''wear and tear'' w ...
and may lead to
derailment
In rail transport, a derailment occurs when a rail vehicle such as a train comes off its rails. Although many derailments are minor, all result in temporary disruption of the proper operation of the railway system and they are a potentially ...
. Many high-speed lines do not permit slower freight trains, particularly with heavier
axle load
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, bearing ...
s. In some cases, the impact is reduced by the use of flange
lubrication
Lubrication is the process or technique of using a lubricant to reduce friction and wear and tear in a contact between two surfaces. The study of lubrication is a discipline in the field of tribology.
Lubrication mechanisms such as fluid-lubric ...
.
Ideally, the track should have sleepers (
railroad tie
A railroad tie, crosstie (American English), railway tie (Canadian English) or railway sleeper (Australian and British English) is a rectangular support for the rails in railroad tracks. Generally laid perpendicular to the rails, ties transfer ...
s) at a closer spacing and a greater depth of
ballast
Ballast is material that is used to provide stability to a vehicle or structure. Ballast, other than cargo, may be placed in a vehicle, often a ship or the gondola of a balloon or airship, to provide stability. A compartment within a boat, ship, ...
to accommodate the increased forces exerted in the curve.
At the ends of a curve, the amount of cant cannot change from zero to its maximum immediately. It must change (
ramp
An inclined plane, also known as a ramp, is a flat supporting surface tilted at an angle from the vertical direction, with one end higher than the other, used as an aid for raising or lowering a load. The inclined plane is one of the six clas ...
) gradually in a
track transition curve
A track transition curve, or spiral easement, is a mathematically-calculated curve on a section of highway, or railroad track, in which a straight section changes into a curve. It is designed to prevent sudden changes in lateral (or centripetal ...
. The length of the transition depends on the maximum allowable speed; the higher the speed, the greater length is required.
For the United States, with a standard maximum unbalanced superelevation of , the formula is this:
:
where
is the superelevation in inches,
is the curvature of the track in degrees per 100 feet, and
the maximum speed in MPH.
The maximum value of cant (the height of the outer rail above the inner rail) for a
standard gauge
A standard-gauge railway is a railway with a track gauge of . The standard gauge is also called Stephenson gauge (after George Stephenson), International gauge, UIC gauge, uniform gauge, normal gauge and European gauge in Europe, and SGR in Ea ...
railway is approximately . For high-speed railways in Europe, maximum cant is when slow freight trains are not allowed.
Track unbalanced superelevation (
cant deficiency
The term "cant deficiency" is defined in the context of travel of a rail transport, rail vehicle at constant speed on a constant radius curve. Cant (road/rail), Cant itself is a British synonym for the superelevation of the curve, that is, the elev ...
) in the United States is restricted to , though is permissible by waiver. The maximum value for European railways varies by country, some of which have curves with over of unbalanced superelevation to permit high-speed transportation. The highest values are only for
tilting train
A tilting train is a train that has a mechanism enabling increased speed on regular rail tracks. As a train (or other vehicle) rounds a curve at speed, objects inside the train experience centrifugal force. This can cause packages to slide abo ...
s, because it would be too uncomfortable for passengers in conventional train cars.
Physics of track cant
Ideally, the amount of cant
, given the speed
of a train, the radius of curvature
and the gauge
of the track, the relation
:
must be fulfilled, with
the gravitational acceleration. This follows simply from a balance between weight, centrifugal force, and normal force. In the approximation it is assumed that the cant is small compared to the gauge of the track. It is often convenient to define the ''unbalanced cant''
as the maximum allowed additional amount of cant that would be required by a train moving faster than the speed for which the cant was designed, setting the maximum allowed speed
. In a formula this becomes
:
with
the curvature of the track, which is also the turn in radians per unit length of track.
In the United States, maximum speed is subject to specific rules. When filling in
,
and the conversion factors for US customary units, the maximum speed of a train on curved track for a given cant deficiency or unbalanced superelevation is determined by the following formula:
:
with
and
in inches,
the
degree of curvature
Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying.
Definition
The degree of curvature is defined as the central angle to the ends of an agreed length ...
in degrees per 100 feet and
in MPH.
Examples
In Australia, the
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.
...
is increasing speed around curves sharper than an radius by replacing wooden sleepers with concrete ones so that the cant can be increased.
Rail cant
The rails themselves are now usually canted inwards by about 5 to 10 percent.
In 1925 about 15 of 36 major American railways had adopted this practice.
Roads
![Ellerker Ave, Doncaster - from the ground](https://upload.wikimedia.org/wikipedia/commons/a/a9/Ellerker_Ave%2C_Doncaster_-_from_the_ground.jpg)
In
civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage ...
, cant is often referred to as
cross slope
Cross slope, cross fall or camber is a geometric feature of pavement surfaces: the transverse slope with respect to the horizon. It is a very important safety factor. Cross slope is provided to provide a drainage gradient so that water will run o ...
or camber. It helps rainwater drain from the road surface. Along straight or gently curved sections, the middle of the road is normally higher than the edges. This is called "normal crown" and helps shed
rainwater
Rain is water droplets that have condensed from atmospheric water vapor and then fall under gravity. Rain is a major component of the water cycle and is responsible for depositing most of the fresh water on the Earth. It provides water fo ...
off the sides of the road. During road works that involve lengths of temporary carriageway, the slope may be the opposite to normal – for example, with the outer edge higher – which causes vehicles to lean towards oncoming traffic. In the UK, this is indicated on warning signs as "adverse camber".
On more severe bends, the outside edge of the curve is raised, or ''superelevated'', to help vehicles around the curve. The amount of superelevation increases with its
design speed
The design speed is a tool used to determine geometric features of a new road or street during road design. Contrary to the word's implication, the design speed of the road or street is not necessarily its vehicle speed limit or maximum safe sp ...
and with curve sharpness.
Off-camber
![Adverse camber UK traffic sign](https://upload.wikimedia.org/wikipedia/commons/c/cb/Adverse_camber_UK_traffic_sign.jpg)
An off-camber corner is described as the opposite of a
banked turn
A banked turn (or banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the ...
, or a negative-bank turn, which is lower on the outside of a turn than on the inside.
[ Off-camber corners are both feared and celebrated by skilled drivers.][ Handling them is a major factor in skilled vehicle control, both single-track and automotive; both engine-powered and human-powered vehicles; both on and off closed courses; and both on and off paved surfaces.
On race courses, they are one of a handful of engineering factors at the disposal of a course designer in order to challenge and test drivers' skills.][ Off-camber corners were described by a training guide for prospective racers as "the hardest corners you will encounter" on the track.][ Many notable courses such as ]Riverside International Raceway
Riverside International Raceway (sometimes known as Riverside, RIR, or Riverside Raceway) was a motorsports race track and road course established in the Edgemont area of Riverside County, California, just east of the city limits of Riverside ...
combine off-camber corners with elevation and link corners for extra driver challenge.[
On the street, they are a feature of some of the world's most celebrated paved roads, such as The "Dragon" (US 129) through Deals Gap][ and the "Diamondback" (NC 226A) in North Carolina, ]Route 78
The following highways are numbered 78:
International
* AH78, Asian Highway 78
* European route E78
Australia
* Waterfall Way- New South Wales State Route B78
China
* G78 Shantou–Kunming Expressway, G78 Expressway
Iran
*Road 78 (Iran), Ro ...
in Ohio,[ Route 125 in Pennsylvania,][ Route 33 in California,][ and Betws-y-Coed Triangle at ]Snowdonia National Park
Snowdonia or Eryri (), is a mountainous region in northwestern Wales and a national park of in area. It was the first to be designated of the three national parks in Wales, in 1951.
Name and extent
It was a commonly held belief that the nam ...
in Wales.
To mountain bikers and motorcyclists on trails and dirt tracks, off-camber corners are also challenging, and can be either an engineered course feature, or a natural feature of single-track trails.[ In cyclocross, off-camber sections are very common as the courses snake around ridges, adding difficulty.
Camber in virtual race circuits is carefully controlled by ]video game
Video games, also known as computer games, are electronic games that involves interaction with a user interface or input device such as a joystick, controller, keyboard, or motion sensing device to generate visual feedback. This fee ...
race simulators to achieve the designer's desired level of difficulty.[
]
See also
* Banked turn
A banked turn (or banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the ...
* Camber angle
Camber angle is one of the angles made by the wheels of a vehicle; specifically, it is the angle between the vertical axis of a wheel and the vertical axis of the vehicle when viewed from the front or rear. It is used in the design of steering an ...
* Profilograph
Road surface textures are deviations from a planar and smooth surface, affecting the vehicle/tyre interaction. Pavement texture is divided into: microtexture with wavelengths from 0 mm to , macrotexture with wavelengths from to and megatextu ...
* Tilting train
A tilting train is a train that has a mechanism enabling increased speed on regular rail tracks. As a train (or other vehicle) rounds a curve at speed, objects inside the train experience centrifugal force. This can cause packages to slide abo ...
References
Further reading
* — includes camber in evaluating engineering of roads, one of six numerical factors modeled to determine desirability for motorcycle touring
Motorcycle touring is a format of tourism that involves a motorcycle. It has been a subject of note since at least 1915.
Motorcycle touring involves special equipment and techniques. A touring motorcycle optimized for long range travel and lugga ...
{{DEFAULTSORT:Cant (Road Rail)
Track geometry
Road infrastructure