1. TOPIC 4
CURVES

2. CURVES
At the end of the unit you should be able to : Explain the basic concept of curves.
 To identify the terminologies of curves.
 To differentiate between circular curves,
transition curves and vertical curves.
 Explain the methods of setting out circular
curves.
 Calculate setting out of circular curves, transition
curves and vertical curves.
 Apply the method of setting out of a circular
curves and transition curve.

3. ROAD CONSTRUCTION
RAILWAY
CONSTRUCTION
RESERVOIR
CONSTRUCTION
BUILDING
CONSTRUCTION
RAILWAY
CONSTRUCTION
DAM CONSTRUCTION

4. INTRODUCTION
is a continuation of the straight lines
and curves with a radius of a fixed or
variable.
PURPOSE
to connect a straight line through the
point of intersection (θ) which lies
between two straight lines to allow the
movement to reverse slowly in the
horizontal and vertical directions.

5. Reasons for curves
construction:
Physical state of hilly land, swampy.
•Connecting the exit or entrance as the exit roads
'toll‘,
•Avoiding the position of the details remain, such
as building mosques, cemeteries.
•Safety of road users in order to travel more
comfortable and secure.
•

6. Differentiate Between Circular Curves,
Transition Curves and Vertical Curves.
Definition
Purpose
Types
Geometry
Setting out
method

7. CURVES DEFINITON
Horizontal curves
Curves of
constant
radius
required to
connect two
straights set
out on the
ground.
Vertical curves
The curves
are designed
and built to
connect the
straight lines
with circular
curves
Transition curves
The curves
are designed
and made to
join two
different
straight slope.

8. CURVES PURPOSE
Horizontal curves
Vertical curves
Transition curves
For the
convenience of
road users
To connect the
straight lines with
a horizontal curve
To avoid the
situation where a
sudden change in
the vehicle
entering the curve
from a straight
round
To avoid the
situation where a
sudden change in
the vehicle when it
starts down the
road after
climbing a hill or
otherwise.

9. CURVES TYPES
Horizontal curves
-Circular curves
-Transition curves
-Compound curves
-Reverse curves
Vertical curves
None
Transition curves
Crest curves
Sag curves

10. CURVES GEOMETRY
Horizontal curves
δ
Vertical curves
I
θ
P
T1
T2
R
O
Transition curves
The parabola has the desirable
characteristics of
(1)a constant rate of change of
slope, which contributes to
smooth alignment transition,
(2)ease of computation of
vertical offsets, which permits
easily computed curve
elevations
T1
T1
Crest curves
Sag curves
T2
T2

11. CURVES – SETTING OUT
METHOD
Horizontal curves
Offset From The
Tangent line
Offset From The
Long chords line
Deflection angle
method
Sub chords line
method
Vertical curves
Wacky turn
Setting out the
transition curves
from T1 to T2
Setting out the
transition curves
from T4 to T3
Setting out the
circular curves
from T2 to T3
Transition curves
None

12. Circular curves - types
R
R
R2
R1
R1
R2
R2
R1

13. End of sub -topic
• Continued….