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The Hallade method, devised by Frenchman Emile Hallade, is a method used in track geometry for surveying, designing and setting out curves in railway track. [ 1 ] It involves measuring the offset of a string line from the outside of a curve at the central point of a chord .
Rankine's method or tangential angle method is an angular technique for laying out circular curves by a combination of chaining and angles at circumference, fully exploiting the theodolite and making a substantial improvement in accuracy and productivity over existing methods. This method requires access to only one road/path of communication ...
Other lengths may be used—such as 100 metres (330 ft) where SI is favoured or a shorter length for sharper curves. Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is Dr = 18000/π ≈ 5729.57795, where D is degree and r is radius.
The length of the curve is given by the formula = | ′ | where | ′ | is the Euclidean norm of the tangent vector ′ to the curve. To justify this formula, define the arc length as limit of the sum of linear segment lengths for a regular partition of [ a , b ] {\displaystyle [a,b]} as the number of segments approaches infinity.
The safety of a horizontal curve is affected by the length of the curve, the curve radius, whether spiral transition curves are used, and the superelevation of the roadway. For a given curve deflection, crashes are more likely on curves with a smaller radius. Spiral transitions decrease crashes, and insufficient superelevation increases crashes.
This means that the tape changes length by 1.16 mm per 10 m tape per 10 °C change from the standard temperature of the tape. For a 30 meter long tape with standard temperature of 20 °C used at 40 °C, the change in length is 7 mm over the length of the tape.
With being the distance between A and B gives: = + Using the trigonometric identities tan α = sin α / cos α and sin(α + β) = sin α cos β + cos α sin β, this is equivalent to:
Although link chains were later superseded by the steel ribbon tape (a form of tape measure), its legacy was a new statutory unit of length called the chain, equal to 22 yards (66 feet) of 100 links. [8] This unit still exists as a location identifier on British railways, as well as all across America in what is called the public land survey ...
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