1. This document provides information about combined curves, which are a combination of circular curves and transition curves used in railways and highways. It defines the key elements of a combined curve and provides the notation and formulas for calculating elements like spiral angle, shift, tangent length, and chainages of points. 2. Steps for setting out a combined curve are outlined, requiring data like deflection angle, radius, and transition curve length. Formulas are given for computing elements like spiral angle, shift, and length of the circular curve. 3. Types of vertical curves are defined as summit/convex and valley/concave curves, with examples given of where each would be used. The formula for calculating the length of

2. Faculty:- Prof. RUCHI GUPTA
SUBJECT:- SURVEYING
GROUP NO:-M9
ENROLLMENT NO. NAME
130450106043 Rashidbhai Badare Munir
130450106044 Shah Ishani Milankumar
130450106045 Shah Richaben Umeshbhai
130450106046 Shrimali Pritesh Bharatbhai
130450106047 Taira Naznin Iqbal

3. CURVES

4. COMBIEND CURVES
 Combined curves are a combination of simple
circuler curve and transition curves.
 These types of curves are preferred in
railways and highways.
 When transition curves are introduced at a
both ends of a circular curve, the resulting
curve is known as a combined curve or
composite curve.

5. B
T1
F
E
∆
∆
∆-2∆s
O
D1 F1
R R
D
T1′
T2′
T
2
A
C
SHIFT

6. NOTATIONS
 AB = Back tangent
 BC = Forward tangent
 2T1 = Point of curve
 T2 = Point of tangency
 ∆ = Deflection angle
 ∆s = Spiral angle
 T1D or T2F =Length of the
transition curve

7.  DEF = Length of circular curve
 T1ʹ D1 or T2ʹF1 = Shift of the curve
 T1DEFT2 = Length of the combined
curve
 ∆ -2∆s = Central angle

8. COMPUTATIONS FOR A
COMBINED CURVE
 For setting out a combined curve,the
following data are required.
 The data given are:
1) Deflection angle (∆)
2) Radius of curve (R)
3) Length of transition curve(L)
4) Chainage of point of intersection B.

9. 1) Spiral angle (∆s)
 ∆s = L
2r radians
= L X 180 Degrees
2r π
2) Shift (s)
S = L2
24R

10. 3) Tangent length
 TT = BT1 =(R+S) TAN ∆ + L
 2 2
4) Length of circular curve
Lc = πR (∆ - 2∆S)
180
5) Chainages of various points
Chainage of T1 = Chainage of B –BT1
Chainage of D =Chainage of T1+ L
Chainage of T2 = Chainage of F + L

11. 6) Length of the normal chords
Generally,10 m for the transition curve and 20 m for
the circuler curve are used.
7)Length of sub chords=
It is calculated after knowing the chainages of
salient points .
8) Deflection Angles=
a) For transition curve
α =18002 minutes
πRL

12.  L is measured from the tangent point T1.
 The deflection angle at the junction of transition
curve and circular curve for l=L is
αn =1800L
πR
b) For circular curve
δ =1718.9 C minutes
R
c = length of the chord
δ =tangential angles from tangent at D.

13.  The total deflection angles are=
 ∆ 1 =δ 1
 ∆ 2 = ∆ 1 + δ 2
 ∆ 3 = ∆ 2 + δ 3
 ∆ n = ∆n-1 + δn
 ∆ n should be equal to 1 (∆ -2 ∆ s)
2

14. TYPES OF VERTICAL
CURVES
There are two types of vertical curves.
1) Summit curve or convex curve
2) valley curve or concave curve
1) summit curve or convex
curve
Summit curve is provided in following situations.
An a upgrade (+g1) followed by a down grade(-g2).

15. A
T1
T2
F
E=-g1=+
g2=-

16.  An upgrade (+g1) followed by another upgrade
(+g2) g1 >g2.
 A down grade (-g1) followed by another down
grade(-g2). g2> g1.
 A plane surface followed by down grade(-g1).

17. 2) Valley curve or concave curve
 Valley curve is provided in following situations.
 A down grade (-g1) followed by a upgrade.(+g2).
 A down grade (-g1) followed by another down
grade(-g2). g1 > g2.
 An upgrade(+g1) followed by another upgrade
(+g2). g2 > g1.
 A plane surface followed by upgrade (+g1).

18. T1 T2
A
F
g1=- g2=+
E=+

19. Length of a vertical curve
 The length of vertical curve can be obtained by
dividing the algebric difference of the two grades
by the rate of change of grade
 Length of curve(L)= total change of grade
 rate of change of grade
 = g2 – g1
 r
 Where, g1,g2 = grades in %
 r=rate of change of grade (%)

20. 1) in respect to calculation for
setting out of combined curve if ∆
=34⁰30′, radius of circular curve is
400m,length of transition curve
60m. calculate shifts, tangent
length and spiral angle.
solution
L =60 m
∆= 34⁰30′
R=400m

21. 1) shift (s)
S = L2 = 602 = 0.375m
24R 24x400
2) Tangent length
T = (R+S) tan ∆ + L
2 2
= (400+0.375)tan 34⁰30′ + 60
2 2
= 124.32+30
=154.32 m

22. 3) Spiral angle (∆s)
∆s = L
2R
= 60
2x400
= 0.075 radian
=0.075 x 180
π
= 4⁰17′50″

23. 2) Calculate length of parabolic
curve joining curve two uniform
grades of +1.2% per 100m.
solution
g1=+1.2%
g2= -0.8%
r =0.15% (rate of change of grade)
Length of curve = L = (g1- g2 ) x 100
r
= (-0.8-.1.2) x 100
0.15
= 1333.33m

24. 3) A parabolic vertical curve is to be
set out connecting two uniform
grades of +1.25 and 0.8%. The Rate
of change of grade is 0.05% per 20
m chain. The R.L of point of
intersection is 120 m ,calcuate R.L
of beginning and end of
Curve.
g1 =1.2%
g2 =-0.8%
r= 0.05% (for 20 m)

25. Length of curve = L = g2 –g1 x 20
r
= -0.8-1.2 x20
0.05
=800m
R.L of beginning point of curve =120- 1.2x800
100 2
=120 – 4.80
= 115.20 m

26. R.L. of end point of curve = 120 – 0.8 x 800
100 2
= 120 – 3.2
= 116.8m

27.  An upgrade of 3% followed by down grade 5%
are connected by a vertical parabolic curve of
500m length. If R.L. of point of intersection is
400m, calculate the R.L. of beginning point, end
point and the mid point of curve.
 Solution
g1= +3%
g2= -5%
Length of curve =L= 500m
R.L. of beginning point of curve = 400- 3 x500
100 2
= 392.5m

28. R.L. of end point of curve = 400 - 5 x 500
100 2
= 387.5m
R.L. of mid point of long chord = 392.5 + 387.5
2
=390m
R.L. of mid point of curve =
R.L. of point of intersection+ R.L. of mid point of
long chord
2
400+390
2
=395m