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High Speed 1 (section 2) in the UK has a minimum vertical curve radius of 10,000 m (32,808 ft) [6] and High Speed 2, with the higher speed of 400 km/h (250 mph), stipulates much larger 56,000 m (183,727 ft) radii. [7] In both these cases the experienced change in weight is less than 7%.
The design of a horizontal curve entails the determination of a minimum radius (based on speed limit), curve length, and objects obstructing the view of the driver. [ 4 ] Using AASHTO standards, an engineer works to design a road that is safe and comfortable.
For example, given a road segment with a 60 miles per hour (97 km/h) design speed except for a curve with a 45 miles per hour (72 km/h) design speed, the entire segment would have a 45 miles per hour (72 km/h) design speed. The road may have a 45 miles per hour (72 km/h) advisory speed on the curve and higher safe operating speeds elsewhere.
Some countries do not have specification on the exact geometry of vertical curves beyond general specification on vertical alignment. Australia has specification that the shape of vertical curves should be based on quadratic parabola but the length of a given vertical curve is calculated based on circular curve. [5]
Road curves are irregular bends in roads to bring a gradual change of direction. Similar curves are on railways and canals. Curves provided in the horizontal plane are known as horizontal curves and are generally circular or parabolic. Curves provided in the vertical plane are known as vertical curve.
Vertical clearance: The minimum vertical clearance under overhead structures, such as bridges, is 16 feet (4.9 m), including both paved shoulders and an allowance for extra layers of pavement. Through urban areas, at least one routing is to have 16-foot (4.9 m) clearances, but others may have a lesser clearance of 14 feet (4.3 m).
The distance from (x 0, y 0) to this line is measured along a vertical line segment of length |y 0 - (-c/b)| = |by 0 + c| / |b| in accordance with the formula. Similarly, for vertical lines (b = 0) the distance between the same point and the line is |ax 0 + c| / |a|, as measured along a horizontal line segment.
For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. [1] [2] [3]