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26-667: Beartrap Hollow begins on South White Deer Ridge in Washington Township. It flows north down the ridge for several tenths of a mile before turning north-northwest. After several tenths of a mile, the stream reaches the bottom of the ridge and receives an unnamed tributary from the left . It then turns northeast for a short distance before reaching its confluence with White Deer Hole Creek. Beartrap Hollow joins White Deer Hole Creek 10.84 miles (17.45 km) upstream of its mouth. Beartrap Hollow has no named tributaries. However, it does have one unnamed tributary. This tributary

52-409: A 71 percent grade instead of a 100 percent. But in practice the usual way to calculate slope is to measure the distance along the slope and the vertical rise, and calculate the horizontal run from that, in order to calculate the grade (100% × rise/run) or standard slope (rise/run). When the angle of inclination is small, using the slope length rather than the horizontal displacement (i.e., using

78-415: 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 indicates horizontality . A larger number indicates higher or steeper degree of "tilt". Often slope is calculated as a ratio of "rise" to "run", or as a fraction ("rise over run") in which run is the horizontal distance (not the distance along

104-687: 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 fills or cuts where these techniques have been used to create them. In the United States, the maximum grade for federally funded highways is specified in a design table based on terrain and design speeds, with up to 6% generally allowed in mountainous areas and hilly urban areas with exceptions for up to 7% grades on mountainous roads with speed limits below 60 mph (95 km/h). The steepest roads in

130-427: A well-known example of this being the southern left bank and the northern right bank of the river Seine defining parts of Paris . The shoreline of ponds , swamps , estuaries , reservoirs , or lakes are also of interest in limnology and are sometimes referred to as banks. The grade of all these banks or shorelines can vary from vertical to a shallow slope. In freshwater ecology , banks are of interest as

156-475: Is 1168978. The stream does not have a name of its own, but instead takes its name from the valley through which it flows. It is also known as Bear Trap Hollow. Beartrap Hollow was surveyed by the Pennsylvania Fish and Boat Commission on June 14, 2013. It was listed on the Pennsylvania Fish and Boat Commission website as being considered for wild trout designation on January 20, 2015. Beartrap Hollow

182-739: Is 23.1% by the 67-Bernal Heights on Alabama Street between Ripley and Esmeralda Streets. Likewise, the Pittsburgh Department of Engineering and Construction recorded a grade of 37% (20°) for Canton Avenue. The street has formed part of a bicycle race since 1983. Grade, pitch, and slope are important components in landscape design , garden design , landscape architecture , and architecture ; for engineering and aesthetic design factors. Drainage, slope stability, circulation of people and vehicles, complying with building codes, and design integration are all aspects of slope considerations in environmental design . Ruling gradients limit

208-455: Is a long narrow island composed of sand and forming a barrier between an island lagoon or sound and the ocean. A submerged plateau is a relatively flat topped elevation of the sea floor at shallow depth — generally less than 200 metres (660 ft) — typically on the continental shelf or near an island . Grade (slope) The grade (US) or gradient (UK) (also called stepth , slope , incline , mainfall , pitch or rise ) of

234-437: Is approximately 0.6 miles (0.97 km) long and starts lower on South White Deer Ridge than the main stem . It joins Beartrap Hollow in its lower reaches. The elevation near the mouth of Beartrap Hollow is 553 feet (169 m) above sea level . The elevation near the stream's source is 1,536 feet (468 m) above sea level. The headwaters of Beartrap Hollow are on a ridge known as South White Deer Ridge . The ridge

260-744: Is entirely within the United States Geological Survey quadrangle of Williamsport SE. Its mouth is located near Elmsport. Beartrap Hollow is being considered by the Pennsylvania Fish and Boat Commission for wild trout designation. The valley of Beartrap Hollow was entered into the Geographic Names Information System on August 2, 1979. Its identifier in the Geographic Names Information System

286-654: Is expressed as a percentage, the angle can be determined as: If the angle is expressed as a ratio (1 in n) then: For degrees, percentage (%) and per-mille (‰) notations, larger numbers are steeper slopes. For ratios, larger numbers n of 1 in n are shallower, easier slopes. The examples show round numbers in one or more of the notations and some documented and reasonably well known instances. In vehicular engineering , various land -based designs ( automobiles , sport utility vehicles , trucks , trains , etc.) are rated for their ability to ascend terrain . Trains typically rate much lower than automobiles. The highest grade

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312-407: Is located near Tiadaghton State Forest . left bank In geography , a bank is the land alongside a body of water . Different structures are referred to as banks in different fields of geography, as follows. In limnology (the study of inland waters), a stream bank or river bank is the terrain alongside the bed of a river , creek, or stream . The bank consists of the sides of

338-452: Is relatively steep in the stream's upper reaches, but becomes less steep towards the lower reaches of the stream. It flows down into the broad valley of White Deer Hole Creek. Beartrap Hollow is in the Ridge and Valley Freestone region. Beartrap Hollow is not designated as an impaired waterbody. The watershed of Beartrap Hollow has an area of 0.42 square miles (1.1 km). The stream

364-441: The channel , between which the flow is confined. Stream banks are of particular interest in fluvial geography, which studies the processes associated with rivers and streams and the deposits and landforms created by them. Bankfull discharge is a discharge great enough to fill the channel and overtop the banks. The descriptive terms left bank and right bank refer to the perspective of an observer looking downstream ;

390-424: The perpendicular cross slope . There are several ways to express slope: Any of these may be used. Grade is usually expressed as a percentage, but this is easily converted to the angle α by taking the inverse tangent of the standard mathematical slope, which is rise / run or the grade / 100. If one looks at red numbers on the chart specifying grade, one can see the quirkiness of using the grade to specify slope;

416-466: The Great Western main line, nicknamed Brunel's Billiard Table, because the early locomotives (and their brakes) were feeble. Steep gradients were concentrated in short sections of lines where it was convenient to employ assistant engines or cable haulage , such as the 1.2 kilometres (0.75 miles) section from Euston to Camden Town . Extremely steep gradients require the use of cables (such as

442-639: The Guinness Book. Drawing on the U.S. National Elevation Dataset, 7x7 (magazine) identified ten blocks of public streets in San Francisco open to vehicular traffic in the city with grades over 30 percent. The steepest at 41 percent is the block of Bradford Street above Tompkins Avenue in the Bernal Heights neighborhood. The San Francisco Municipal Railway operates bus service among the city's hills . The steepest grade for bus operations

468-684: The Scenic Railway at Katoomba Scenic World , Australia, with a maximum grade of 122% (52°), claimed to be the world's steepest passenger-carrying funicular ) or some kind of rack railway (such as the Pilatus railway in Switzerland, with a maximum grade of 48% (26°), claimed to be the world's steepest rack railway ) to help the train ascend or descend. Gradients can be expressed as an angle, as feet per mile, feet per chain, 1 in n , x % or y per mille. Since designers like round figures,

494-463: The horizontal run by using the Pythagorean theorem, after which it is trivial to calculate the (standard math) slope or the grade (percentage). In Europe, road gradients are signed as a percentage. Grades are related using the following equations with symbols from the figure at top. The slope expressed as a percentage can similarly be determined from the tangent of the angle: If the tangent

520-546: The load that a locomotive can haul, including the weight of the locomotive itself. On a 1% gradient (1 in 100) a locomotive can pull half (or less) of the load that it can pull on level track. (A heavily loaded train rolling at 20 km/h on heavy rail may require ten times the pull on a 1% upgrade that it does on the level at that speed.) Early railways in the United Kingdom were laid out with very gentle gradients, such as 0.07575% (1 in 1320) and 0.1515% (1 in 660) on

546-426: The location of riparian habitats . Riparian zones occur along upland and lowland river and stream beds. The ecology around and depending on a marsh , swamp , slough , or estuary , sometimes called a bank, is likewise studied in freshwater ecology. Banks are also of interest in navigation , where the term can refer either to a barrier island or a submerged plateau , such as an ocean bank . A barrier island

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572-753: The method of expression can affect the gradients selected. The steepest railway lines that do not use a rack system include: Gradients on sharp curves are effectively a bit steeper than the same gradient on straight track, so to compensate for this and make the ruling grade uniform throughout, the gradient on those sharp curves should be reduced slightly. In the era before they were provided with continuous brakes , whether air brakes or vacuum brakes , steep gradients made it extremely difficult for trains to stop safely. In those days, for example, an inspector insisted that Rudgwick railway station in West Sussex be regraded. He would not allow it to open until

598-400: The numbers go from 0 for flat, to 100% at 45 degrees, to infinity as it approaches vertical. Slope may still be expressed when the horizontal run is not known: the rise can be divided by the hypotenuse (the slope length). This is not the usual way to specify slope; this nonstandard expression follows the sine function rather than the tangent function, so it calls a 45 degree slope

624-736: The sine of the angle rather than the tangent) makes only an insignificant difference and can then be used as an approximation. Railway gradients are often expressed in terms of the rise in relation to the distance along the track as a practical measure. In cases where the difference between sin and tan is significant, the tangent is used. In either case, the following identity holds for all inclinations up to 90 degrees: tan ⁡ α = sin ⁡ α 1 − sin 2 ⁡ α {\displaystyle \tan {\alpha }={\frac {\sin {\alpha }}{\sqrt {1-\sin ^{2}{\alpha }}}}} . Or more simply, one can calculate

650-413: The slope) and rise is the vertical distance. Slopes of existing physical features such as canyons and hillsides, stream and river banks , and beds are often described as grades, but typically the word "grade" is used for human-made surfaces such as roads, landscape grading, roof pitches , railroads , aqueducts , and pedestrian or bicycle routes. The grade may refer to the longitudinal slope or

676-715: The world according to the Guinness Book of World Records are Baldwin Street in Dunedin, New Zealand, Ffordd Pen Llech in Harlech, Wales and Canton Avenue in Pittsburgh, Pennsylvania. The Guinness World Record once again lists Baldwin Street as the steepest street in the world, with a 34.8% grade (1 in 2.87) after a successful appeal against the ruling that handed the title, briefly, to Ffordd Pen Llech . A number of streets elsewhere have steeper grades than those listed in

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