Grade (slope)
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The grade (US) or gradient (UK) of 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 in which run is the horizontal distance and rise is the vertical distance.
25% ascent warning sign, Wales
30% descent warning sign, over 1500 m. La Route des Crêtes, Cassis, France
A trolleybus climbing an 18% grade in Seattle
Ascent of German Bundesstraße 10
Bank engine
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A bank engine, banking engine, helper engine or pusher engine is a railway locomotive that temporarily assists a train that requires additional power or traction to climb a gradient. Helpers/bankers are most commonly found in mountain divisions, where the ruling grade may demand the use of substantially greater motive power than that required for other grades within the division.
SZ Taurus pushing a freight train on the grade between Koper and Hrpelje-Kozina in Slovenia. An SZ class 363 is leading the train. July 2007.
1915 photo of a quadruple header (four front locomotives) train with a rear helper, climbing the Denver & Rio Grande Western's grade up Soldier Summit
1949 photo of a Black Five climbing the Lickey Incline in Worcestershire with MR 0-10-0 Lickey Banker 'Big Bertha' providing banking at the rear of the train. In the present day, almost all trains can climb the incline unassisted, though heavier freight trains still require bankers.
Uncoupled banking service: BDe 4/4 multiple unit separating from the Voralpenexpress after assisting on the 5 percent grade