Islamic University of Gaza
Civil Engineering Department
Surveying II
ECIV 2332
By
Belal Almassri
Chapter 9
Route Surveying – Part 3
Linear Methods for setting out simple
circular curve.
- Method of offsets on the long chord.
- Method of offsets on tangents.
- Method of radial offsets.
- Method of deflection angles.
- Notes and Examples.
-
Setting out simple circular curve
using linear methods
These methods use the chain surveying
tools only.
 These methods are used for the short
curves which doesn’t require high degree
of accuracy.
 These methods are used for the clear
situations on the road intersections.

Types of linear method:
There are three types of the linear methods
to set out a simple circular curve.
1. By offsets from the long chord.
2. By offsets from the tangents.
3. By radial offsets.
By offsets from the long chord
Example
By offsets from the tangent
Example
Notes:
In the first method, the value of x = Lc/2
= 7.654 < 8m so we had used x = 7.654m
and y at this point equals zero.
 In the second method, the value of x =
8m < T(8.28), we had used x = 8m but we
still know that the circular curve close at
PT when T = 8.28m.

By radial offsets
Example
Notes:
In the second and the third methods the
x value will not exceed the value of T
BUT in the first method the value of x
will not exceed the value of Lc/2.
 The third method is used when the
centre of the circular curve is accessible
while the first two methods can be used
when there is an obstacle.

Underground . . .
Laying out simple circular curves by
using the deflection angles method:
Working method:
1. Fix the theodolite device to be at point
PC and directed at point PI.
2. Measure the deflection angles d and the
chords C.
3. Connect the ends of the chords to draw
the curve.
Deflection Angles: the angles between the
tangent and the ends of the chords from
point PC.
Calculations Steps:
This method is a geometric based method :
1. Calculate the values of T and L.



T = R tan (Δ/2)
L = R (Δ in radians)
2.
Calculate the chainage of point PC and
point PI.

Ch of PC = Ch of PI – T
Ch of PT = Ch of PC + L

3.
Calculate the partial chords C, C1,C2.


Choose C ≤ R/20 (then round it)
Chainage of the first station: Chainage of PC (rounded) + C
C1 = Chainage of first station – Chainage of PC (original)
C2 = L – ( C1 + n C ); n = number of intermediate chords
4.
Calculate the deflection angles d, d1, d2.


d = (28.648 C)/R
d1 = (28.648 C1)/R
d2 = (28.648 C2)/R
5.
Calculate the cumulative deflection angles.



Notes:
The total d’s will equal Δ/2.
 The chainage of the all stations on the
curve should be even number divisible of
5 or 10.
 When locating the last point before PT
we measure the distance to the PT if it
was equal C2 then it is correct or the
difference is 5- 10 cm BUT if it is more
than that we should repeat !

Example 9.2
Two tangents intersect at PI with chainage of
2140.00 m and deflection angle of 10 ͦ 35 ` 2``
Da or D˳ = 4 ͦ , Using the deflection angles
method Arrange all the information needed.
Solution !