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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 .
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 larger the degree of curvature, the sharper the curve is. Expressing the curve in this way allows surveyors to use estimation and simpler tools in curve measurement. This can be done by using a 62-foot (18.90 m) string line to be a chord to connect the arc at the gauge side of the reference rail.
A double-end Euler spiral. The curve continues to converge to the points marked, as t tends to positive or negative infinity. An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
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 ...
Although link chains were later superseded by the steel ribbon tape (a form of tape measure), its legacy was a new statutory unit of length called the chain, equal to 22 yards (66 feet) of 100 links.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 ...
The Abney level is an easy to use, relatively inexpensive, and, when used correctly, an accurate surveying tool. Abney levels typically include scales graduated in measure degrees of arc, percent grade, and in topographic Abney levels, grade in feet per surveyor's chain, and chainage correction.