Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve.

May 9, 2016 · One of the historical methods to survey a track alignment is to measure the offsets from a chord to the running edge of the rail at the centres of successive overlapping chords, laid out along the outer or high rail of the surveyed track …

The following formula applies to the measurement of the versine hf at any point of the chord is with the distances a and b of the chord endpoints. Versine at any given point.

Mar 5, 2025 · The versine, also known as the "versed sine," is a little-used trigonometric function defined by versin(z) = 2sin^2(1/2z) (1) = 1-cosz, (2) where sinz is the sine and cosz is the cosine. The versine can be extended to the complex plane as illustrated above.

Dec 8, 2016 · There are three types of versines used for the track realignment and rectification methods (Radu, 2003): Measured (existing) versine – the versine measured with a real chord on the outer rail of the real existing track.

The versine function (commonly written as versin (θ)) is a historical trigonometric function that represents the complementary value of the cosine function. The formula for the versine function is: versin (θ) = 1 − cos. (θ) This means the versine measures the …

The Versine Calculator is a handy tool designed to simplify the process of calculating the versine of any given angle. It eliminates the need for manual calculations, making it a time-saving and accurate solution for trigonometric computations.

Determination of Radius - (1) The radius of a curve is determined by measuring the versine on a chord of known length, from the equation, (2) Curves can be designated by the radius in metres or by its degree. The angle subtended at the center by a …

The versine is the perpendicular distance of the midpoint of a chord from the arc of a circle. The relationship between the radius and versine of a curve can be established as shown in Fig. 13.1. Let R be the radius of the curve, C be the length of the …

The versine or versed sine, versin(θ), is a trigonometric function equal to 1 − cos(θ) and 2sin2(½θ). It appeared in some of the earliest trigonometric tables and was once widespread, but it is now little used.