E4004 Survey Computations A

1. E4004 Survey Computations A Reverse Circular Curves

2. Compound Circular Curves • Combination of two or more simple circular curves of different radius having their curvature in the same direction R2 O2 R1 O1

3. Compound Circular Curves • A common tangent point exists at the junction of the curves • ABC is a straight line C TP2 B A TP3 TP1 R2 O2 R1 O1

4. Compound Circular Curves • Both circle centres lie along the line BO1 being at right angles to AC C TP2 B A TP3 TP1 R2 O2 R1 O1

5. 3 Compound Circular Curves • The deflection angles formed at the intersection of the straights are called 1 and  2 • The deflection angles formed at the intersection of TP1A and TP3C (3 ) equals 1 and  2 C TP2 1 2 B A TP3 2 TP1 R2 1 O2 R1 O1

6. Compound Circular Curves • The line AC is equal to the sum of the tangent lengths; AB and BC C TP2 1 2 B A TP3 2 TP1 R2 1 O2 R1 O1

7. Reversed Circular Curve • It may join with a second circular curve of opposite curvature • Consider a simple circular curve

8. Reversed Circular Curve • Line ABC is the common tangent and is a straight line • Construct the tangent lines for each curve B A C

9. Reversed Circular Curve • Construct the curve centres and associated radii O2 TP3 R2 B A C TP2 R1 TP1 O1

10. Reversed Circular Curve • O2BO1 is a straight line perpendicular to ABC and equal to, R1+R2 O2 TP3 R2 B A C TP2 R1 TP1 O1

11. Reversed Circular Curve • Each curve has a deflection and included angle, 1 and  2 O2 TP3 2 R2 2 1 B A C TP2 R1 1 TP1 O1

12. Reversed Circular Curve • The line AC is equal to the sum of the tangent lengths; AB and BC O2 TP3 R2 B A C TP2 R1 TP1 O1