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, 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
AB & BC be two tangent intersecting
at B, the deflection
angle be (shown infig.)
angle be (shown infig.)
the
tangent length is calculated &
tangent length is calculated &
tangent pt. are
marked.
marked.
Let,
= first pt. on the
curve.
curve.
= length of cord.
= deflection angle
for first chord.
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 ).
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.
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.
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.
Φ to seconds, or errors will be considerable if many pegs must beplaced.
The final reading,
to the other tangent point, should equal L.
to the other tangent point, should equal L.
Aim: To set out the
simple curve by two theodolite method.
simple curve by two theodolite method.
Instruments Required :
Two Theodolites and Ranging rods.
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.
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).
: 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 .
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 .
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.
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.
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.
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.
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 .
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.
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.
Continue the process for obtaining the locations of other points in a similar
manner.
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