Unit – 2
Curves
Q1) What is transition curve?
A1)
- It is a curve introduced between a simple circular curve industry tour between two simple circular curves.
- Also known as easement curve.
- Its videos, gradually changing from a finite to infinite value or vice versa.
- It is generally used in highway and Railway.
Q2) Explain the methods of setting out the curve?
A2)
(a) Linear method
(i) Offset from long chord
Where 
offset at some point P at distance x from midpoint D.
(ii) Perpendicular offset from tangent
(iii) Radial offset from tangent:
(iv) Successive Bisection of Arc or chord
(v) By offset from chord produced
last sub chord
b) Angular method
i) Rankine's method of deflection angle
- It is generally used for setting out a circular curve of long length and large radius.
- It gives good result except then chords are long as compared to radius, so that variation between length of an Arc and its cord becomes considerable.
- It is used in highway and Railway
= Tangential angle
C = chord length
(ii) Tacheometric method
-It is similar to Rankine’s method of deflection angle.
- The theodolite at 
may be used as Tacheometric and Tacheometric observation are made.
- Less accurate as compared to Rankins.
- Chaining is completely dispersed in this method.
(For Incline and line of sight)
(For horizontal line of sight)
ii) Two theodolite method
- Convenient than any of to our method when ground is undulating rough and not suitable for Linear measurements.
- Two theodolites are used and linear measurement are completely eliminated.
- Hence, most accurate method.
- It is based on principle that angle between the tangent and chord is equal to angle subtended by chord in opposite segment.
- Time consuming method
- Most accurate method
- Highly expensive.
Q3) Explain length of transition curves?
A3)
a) Method of arbitrary gradient:
e = total super elevation provided at junction of transition curve with circular curve
L = ne
Where rate of super elevation is ∆ in n
(b) Method of Time rate:
time rate of super elevation
Method of rate of change of radial acceleration
Rate of change of radial acceleration
t is the time attained by radial acceleration (a)
a = 
Q4) Describe the elements of transition curve?
A4) (a)Total Tangent Length
Tangent length 
(b) Length of long chord
(c) Total length of curve
Total length of curve
=Total length (3)
(d) Apex distance E
Q5) What do you mean by reverse curve and its use?
A5) When to normal circular curves of different or equal radii, have opposite in direction of curvature join together, the formed or resultant curve is known as reverse curve.
Uses:
a) When angle between two straight line is very small.
b) When two straight lines are parallel to each other.
Q6) What are element of reverse curve?
A6) Element of reverse curve
- VA and uc include deviation angle of
.
- 
centres of two curve.
- 
are radii of two curve.
- 
common tangent which is perpendicular to 
- Join 
and draw 
In ∆BVE,
In 
From (1) and (2)
In, 
In,
Also,
From (3) and (4)
Q7) What is the relation between the radius of curve and degree of curve?
A7) If R = radius of curve
D = degree of curve as per arc definition for 30m arc length.
D° = 
Q (radians) = 
For 20 mm length
(2)
Q8) What is super elevation?
A8) It is defined as the raising of outer end of a road or outer rail over inner one.
h = super elevation = e
w = weight of vehicle
P = centrifugal force
g = acceleration due to gravity
R = radius of curve
G = gauge distance between rails
u = speed of vehicle
B = width of pavement
= Angle of super elevation
h = super elevation = e
w = weight of vehicle
P = centrifugal force
g = acceleration due to gravity
R = radius of curve
G = gauge distance between rails
u = speed of vehicle
B = width of pavement
= Angle of super elevation
Centrifugal ratio
Q9) Explain vertical curves?
A9) These are curves in a vertical plane, used to join two intersecting grade lines.
A vertical summit curve is provided when a rising grade join a falling grade and a vertical curve is provided when a falling grade joins a rising grade.
Q10) What are the types of vertical curves?
A10) Types of vertical curves
i) Upgrade followed by a downgrade
ii) Upgrade followed by another upgrade
iii) A downgrade followed by an upgrade
iv) A downgrade followed by another downgrade
