Formulation of shift of a circular curve with unequal transition length September 22, 2013 Formulation of co-ordinates for circular curve. Normally rail or road alignment moves through different curvatures. It may consists of straight lines, circular curves and compound curves. This paper presents the generation of co-ordinates or the alignment having straight lines and circular curves. First of all the relations will be drawn in local co-ordinate system which can be very easily converted into WGS-84 or any other type of global co-ordinate system. Global co-ordinate does not mean only standard co-ordinates system like WGS-84 but a co-ordinate system adopted for a project. Straight Line For given two number of points other points between them can easily be find out as the relationship between them will remain linear. Circular Curve Let us consider a circular curve of radius ’R’ between the tangents T1 O and T2 O . The deviation angle between the tangents are δ. The center of the circular curve is c1 . The circular curve touches the left and right hand tangents at A and B respectively. Take a case when the circular curve is shifted in such a way that the center of the curve assigns a new position c2 from its old position c1 . Absolute distance between c1 and c2 is s. c2 M and c2 N are perpendicular to the tangents from c2 . Refer figure 1 on page no. 4 Transition curve starts from T1 and T2 . Transition curves are widely accepted in the form of cubical parabola. Let us take a cubical parabola as
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