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Metros and pure commuter railways often also allow steeper gradients, over 4%, for the same reason. High-speed railways commonly allow 2.5% to 4% because the trains must be strong and have many wheels with power to reach very high speeds. For freight trains, gradients should be as gentle as possible, preferably below 1.5%.
The allowable gradients may be based on the ruling gradient which is the maximum gradient over which a tonnage train can be hauled with one locomotive. In some countries, momentum gradient which is a steeper but shorter gradient may be allowed. This is usually when a track gradient connects to a leveled tangent track long enough and with no ...
To compensate for this, the gradient should be a little less steep the sharper the curve is; the necessary grade reduction is assumed to be given by a simple formula such as 0.04 per cent per "degree of curve", the latter being a measure of curve sharpness used in the United States. On a 10-degree curve (radius 573.7 feet) the grade would thus ...
Extremely steep gradients require the use of cables (such as 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 [15]) or some kind of rack railway (such as the Pilatus railway in Switzerland, with a maximum grade of 48% (26°), claimed to ...
A now little used alternative to the rack and pinion railway is the Fell system, in which traction and/or braking wheel are applied to a central rail under pressure. Rack and pinion animation Another alternative is a cable car in which the car runs on rails, but grasps a continuously moving cable underneath the rails for propulsion, releasing ...
The minimum railway curve radius is the shortest allowable design radius for the centerline of railway tracks under a particular set of conditions. It has an important bearing on construction costs and operating costs and, in combination with superelevation (difference in elevation of the two rails) in the case of train tracks , determines the ...
The Pilatus Railway is the steepest rack railway in the world, with a maximum gradient of 48% and an average gradient of 35%. Functioning of the rack and pinion on the Strub system. 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 the running rails.
The maximum gradient between Paddington and Didcot is 1 in 1320 (0.75 ‰ or 0.075%); between Didcot and Swindon it is 1 in 660 (1.5 ‰ or 0.15%) but west of Swindon, gradients as steep as 1 in 100 (10 ‰ or 1%) are found in places, such as Box Tunnel and to the east of Dauntsey.