Transition Curve

Transition curve is provided to change horizontal alignment from straight to circular curve gradually. Transition curve has a infinite radius at straight road and gradually changes to designated radius at circular curve. As the length of transition curve increases radius decreases,  i.e.

 

from straight to circular curve centrifugal force introduce gradually. i.e. 

Objectives or Necessity of transition curve:

• To gradually introduce the centrifugal force in between straight and circular curve.
• To avoid sudden jerk.
• Transition curve will insure easy to follow path for drivers.
• To gradually introduction of super elevation. 
• To introduce extra widening gradually.
• Improve aesthetic appearance of the road.  

Ideal shape of transition curve or Requirement of ideal transition curve:

• Rate of introduction of centrifugal force or rate of change of centrifugal acceleration should be constant or uniform. 
• Length of transition curve is inversely proportional to radius of curve.
• Spiral type of curve or clothoid type of transition curve fulfil the conditions of ideal transition curve as per IRC.      

Length of transition curve:

As per the IRC minimum length of transition curve should be determined as maximum of the following three criteria's,

1. As per rate of change of centrifugal acceleration. 
2. As per rate of change of super-elevation.
3. Minimum length of transition curve by empirical relation.  

1. As per rate of change of centrifugal acceleration :

2. As per rate of change of super elevation: 

• 1 in 150 for plain and rolling terrain
• 1 in 60 for mountainous and steep terrain 

where, 

1 in N means, 

1 = rise height of outer edge which is achieved at N length of transition curve.

therefore, 

length of transition curve can be written as,

Lt = 150. x            for plain and rolling terrain 

Lt = 60. x              for steep and mountainous terrain              

Calculation of x :

1. Rotation about inner edge: 

2. Rotation about central axis:

3. Minimum length of transition curve as per empirical relation:

for plain and rolling terrain, 

for steep and mountainous terrain,

Where, 

V in kmph

R in meter

Lt in meter

Design of Horizontal Alignment Super Elevation

In order to resist the centrifugal force, it is usual practice to super elevated the roadway cross section. The horizontal alignment design elements include,

• Super Elevation 
• Transition Curve
• Extra-widening 
• Set Back Distance

Super Elevation : 

When a vehicle moves on a horizontal curve then it is subjected to an outward force, commonly known as centrifugal force acting in outward direction which causes discomfort to the passenger and increases the possibility of accidents. So, design of horizontal alignment is an important feature which influence the efficiency and safety of highway. The design speed is the single most important factor which governs the design of horizontal alignment. 

We know,

Presence of horizontal curve in horizontal alignment introduces centrifugal force in outward direction of curve,

So the effect of centrifugal force on the vehicle are:

1. Overturning of Vehicle
2. Lateral Skidding
3. Combination of Overturning and Lateral Skidding 

From the above figure,

Overturning Moment is, Mo = P x h

and

Resisting Moment is, Mr = W x (b/2)

Conditions :

1.  When the moment of resistant (Mr) is greeter than moment of overturning  (Mo) then it is safe or stable condition for overturning, or if we put the values in condition we can say that in safe condition impact factor (I) is less than (b/2h). 
2.  When the impact factor (I) is less than lateral friction (F) the it is safe condition for lateral skidding.

Rising of outer edge wit respect to inner edge to counter balance the centrifugal factor and to reduce tendency of vehicle to overturn is called Super elevation.

where, 

W = wight of vehicle

F  = Friction force between wheels and pavements

θ = Transverse slope due to super-elevation 

Super-elevation by IRC recommendation,

Sr No	Terrain	Max Super elevation
1	Urban Area	4 % or 0.04
2	Plain & Rolling Terrain	7 % or 0.07
3	Steep & Mountainous Terrain	10 % or 0.10