2. Solution

1.1 Chainage of Apex V

This section details the calculations necessary for determining chainage and related measurements in road alignment, specifically focusing on the apex of a circular curve.

1.2 Deflection Angle D

This section explains the concept of the deflection angle in road design, detailing how to calculate various key parameters such as tangent lengths, the length of curves, and chainages.

1.3 Radius R

This section provides fundamental calculations related to circular curves in surveying, including the methods to determine the radius, lengths of tangents, and other crucial parameters.

1.4 Peg Interval

This section discusses the calculation of peg intervals in survey measurements, particularly in relation to setting out circular curves.

2.1 Tabulate the data needed

2.2 Chainage of PI

This section covers the calculations and methodologies used to determine the chainage of points of intersection (PI) in circular curves.

3.1 Tabulate the necessary data

4.1 Two tangents intersect

This section focuses on the calculations and principles related to the intersection of two tangents and the layout of circular curves.

5.1 Two straights intersect

This section covers the principles of calculating intersections between two straight lines and the design of curves connecting them.

6.1 A right hand compound curve

This section details the calculations and methods for setting out right-hand compound curves in highway engineering.

7.1 Two straights AC and BC

This section focuses on calculating parameters for setting up circular curves that connect two straight paths, emphasizing concepts like chainage, deflection angles, and tangential lengths.

8.1 Two straights BA and AC

This section covers the calculation of various parameters for connecting two straight lines using circular curves.

9.1 Two straights AC and CB

This section delves into the calculations and processes involved in setting out circular curves between two straights, focusing on determining chainages, tangent lengths, and curve lengths.

10.1 Two parallel railway lines

This section focuses on calculating parameters for setting circular curves between two parallel railway lines.

11.1 Two parallel lines

This section discusses the calculations involved in setting out circular curves connecting two parallel lines, emphasizing tangent lengths, chainages, and deflection angles.

12.1 A reverse curve ACB

This section covers the calculations and principles involved in setting out a reverse curve in road design, including tangent lengths, chainages, and curve lengths.

13.1 A reverse curve

This section discusses reverse curves in road and railway design, focusing on the calculations needed to set out curves accurately.

14.1 A transition curve of the cubic parabola type

This section covers the mathematical principles and applications of cubic parabola transition curves in road and railway construction, emphasizing their importance in managing changes in curvature.

15.1 A compound curve AB and BC

This section explains the principles of calculating and setting out compound curves in surveying, detailing examples and formulas for practical application.

16.1 Length of vertical curve

This section explores the calculations and methodologies involved in determining the length of vertical curves, crucial for effective road design.

17.1 Length of vertical curve

This section delves into the calculations and concepts essential for determining the length of vertical curves in roadway design.

18.1 Calculate the RL of various stations

This section outlines the methodology for calculating the Reduced Level (RL) at various stations by employing geometric principles involved in road design and surveying.

19.1 A 1% grade meets a +2.0% grade

This section covers the calculations and methodology involved in designing curves in highway engineering, focusing on vertical and horizontal alignment transitioning between different gradients.

20.1 Two straights AB and BC

This section discusses the calculation and setting out of circular curves connecting two straight lines, with practical examples illustrating the concepts.