LESSON NOTE ON TWO THEODOLITE METHOD FOR SETTING OUT A CURVE

TWO THEODOLITE METHOD FOR SETTING OUT A CURVE

RANKINE'S METHOD In this method, curves are staked out by use of deflection angles turned at the point of curvature from the tangent to points along the curve.

This method is based on the following geometry:

 Let AB & BC be two tangent intersecting

at B, the deflection angle be (shown infig.)

 the tangent length is calculated &

tangent pt. are marked.

 Let,

= first pt. on the curve.

= length of cord.

= deflection angle for first chord.

R = radius of curve

= total deflection for the chord.

 Procedure:-

i. Set the instrument up at the tangent point, sight along the tangent and turn off the first deflection angle ( Φ =Ө/2 ).

ii. Fix one end of tape at A, measure off 'c' meters, and swing tape until it aligns with the line of sight. Put in peg B.

iii. Turn theodolite a further Φ°. Fix one end of tape at B, measure off 'c' meters, and swing tape until that point on the tape crosses the line of sight. Put in peg C. iv. Repeat step (iii) until you peg the curve. If the line of sight becomes obstructed, then simply set up on any peg on the curve, sight back along the chord to the previous peg and continue to establish the deflection angles.

 Precautions to take:

Calculate the angle Φ to seconds, or errors will be considerable if many pegs must beplaced.

The final reading, to the other tangent point, should equal L.

Aim: To set out the simple curve by two theodolite method.

Instruments Required : Two Theodolites and Ranging rods.

Principle: The angle between the target and the chord is equal to the angle which that chord subtends in opposite segment.

Given : Chainage of the curve , angle of intersection and Radius of curve (R).

Procedure :

1. Prepare a table of deflection angle for the first sub chord, Normal chord and last sub chord .

2. Set up one theodolite over T1 and another over T2 .

3. Direct the instrument at T1 to the ranging rod at the point of intersection B and bisect it.

4. Direct the instrument at T2 to the first target point T1 and bisect it.

5. Set the verniers of both the theodolites to read zero.

6. Set the first deflection angle (D1) on both theodolites so that the telescopes are in the direction of T1D and T2D respectively.

7. Move the ranging rod until it is bisected by the cross hairs of both the theodolites to locate the point D on the curve .

8. Set the second value of deflection angle on both the theodolites and repeat the step 7 above to get the location of E.

9. Continue the process for obtaining the locations of other points in a similar manner.