English

Pronunciation

Noun

slopes

1. Plural of slope

Verb

slopes

1. third-person singular of slope

A grade (or gradient) is the pitch of a slope, and is often expressed as a percent tangent, or "rise over run". It is used to express the steepness of slope on a hill, stream, roof, railroad, or road, where zero indicates level (with respect to gravity) and increasing numbers correlate to more vertical inclinations.

Expression

There are three common numbering systems:

• the angle from horizontal in degrees,
• as a percentage: the tangent of the angle of inclination: the ratio of the altitude change to the horizontal distance (this is the more common percentage type), or
• an alternative definition as a percentage: the sine of the angle: the ratio of the altitude change to the surface length between any two points on the grade—also known as rise to run (not to be confused with the "rise over run" taught in grade-school geometry).

The difference between the latter two is small for gentle slopes (see small-angle formula). The ambiguities and the small differences that result may permit these two inconsistent approaches to coexist unrecognised, especially where grades considered are 15% or less.

Many of the mathematical principles of slope, that follow from the definition, are applicable in topographic practice. Grade is usually expressed as a percentage. Expressing it as the angle from horizontal carries the same information, but may lead to confusion for readers who are not proficient in trigonometry: they may confuse degree with percent, and/or not know how to do the conversion. In the UK, for road signs, maps and construction work, the gradient is often expressed as a ratio such as 1 in 12, or as a percentage http://www.highwaycode.gov.uk/signs05.htm.

Road

In vehicular engineering, various land-based designs (cars, SUVs, trucks, trains, etc.) are rated for their ability to ascend terrain. (Trains typically rate much lower than cars.) The highest grade a vehicle can ascend while maintaining a particular speed is sometimes termed that vehicle's "gradeability" (or, less often, "grade ability"). The lateral slopes of a highway geometry are sometimes called fill or cuts.

Railways

Steep gradients limit the size of load that a locomotive can haul, including the weight of the locomotive itself. A 1% gradient (1 in 100) halves the load. Early railways in the United Kingdom were laid out with very gentle gradients, such as 0.05% (1 in 2000), because the early locomotives (and their brakes) were so feeble. Steep gradients were concentrated in short sections of lines where it was convenient to employ assistant engines or cable haulage, such as from Euston to Camden Town, about 8 km. Extremely steep gradients need the help of cables, or some kind of rack railway.

The steepest non-rack railway lines include:

• 13.5 % - Lissabon tram, Portugal
• 11.6 % - Pöstlingbergbahn, Linz, Austria
• 9.0 % - Ligne de Saint Gervais - Vallorcine, France
• 7% - Bernina Railway, Switzerland
• 5.6% (1 in 18) - Flåm, Norway.
• 4.0% - Cologne-Frankfurt high-speed rail line
• 4.0% (1 in 25) - Tarana - Oberon, New South Wales.

It is customary for civil engineers to refer to the steepest grade on a section of rail line as the ruling grade for that section. Civil engineering works such as cuttings, embankments and tunnels are employed to achieve this.

Effects of grade

The greater a grade, the more energy an animal or a machine spends climbing it; therefore routes with lower grades are preferred, so long as they do not have other disadvantages, such as causing significantly increased overall travel distance.

Vehicles proceeding upgrade demand more fuel consumption with typically increased air pollution generation. Sound level increases are also produced by motor vehicles travelling upgrade.

See also

• Grade separation
• Slope

References

External links

• A Simple Explanation and Example of Grade Calculation