Precise railway alignment measurements of the horizontal circular curves and the vertical parabolic curves using the chord method

Abstract

The chord method is generally used for the horizontal and vertical versine measurements of rails in order to maintain their alignment. In this study, the horizontal versines of the left and right rails were precisely calculated, and the vertical versine functions were exactly derived. According to the inferences, the line charts used for determining the vertical versine were created to demonstrate the proportional relationship with the grade difference and the curve length. The equations for proximate vertical versine calculations were therefore derived. The asymmetrical chord measurements were introduced as well. The results indicated that the versine difference between the inner and outer rails should be considered when measuring the horizontal circular curve with a radius less than 300 m using a 10-m chord. According to the design criteria, a maximum vertical versine of 30 mm formed by the parabolic curves could be measured using a 10 -m chord, or a maximum versine of 7.5 mm could be measured using a 5 -m chord, which should be considered as the essential versines. The deviation tolerance should be based on these values for accurate rail inspections.