In this Article we will deal with the design of transition curves types, need and uses.
It ensures a smooth change from straight road to circular curves.
A transition curve differs from a circular curve in that its radius is always changing. As one would expect, such curves involve more complex formulae than the curves with a constant radius and their design is more complex.
The Need For Transition Curves
Circular curves limited in road designs due to the forces which act on a vehicle as they travel around a bend. They are used to introduce those forces gradually and uniformly thus ensuring the safety of passenger.
Transition curves have much more complex formulae and are more difficult to set out on site than circular curves as a result of the varying radius.
- To Introduce gradually the centrifugal force between the tangent point and the beginning of the circular curve, avoiding sudden jerk on the vehicle.This increases the comfort of passengers.
- Enable the driver turn the steering gradually for his own comfort and security,
- To provide gradual introduction of super elevation, and
- Provide gradual introduction of extra widening.
- To enhance the aesthetic appearance of the road.
The Use Of Transition Curves
Transition curves can be used to join to straights in one of two ways:
- Composite curves
- Wholly transitional curves
Types of Transition Curve
There two types of curved used to form the transitional section of a composite or wholly transitional curve, These are:
- The clothoid
- The cubic parabola.
This is a curve at which radius of the curve is inversely proportional to its length.
Therefore, ρ α (1/s)
Or, ρ = c/s
Where, c is known as the constant of the spiral, ρ is the radius of curvature and s is the length of the curve.
At the end of spiral, ρ = Rc and s = l
Therefore, c = L*Rc
This is a curve at which the radius of the curve varies inversely as its abscissa (X).
Therefore, ρ α (1/X)
Or, c = ρ * X
Therefore, c = Rc * X
Length of Transition Curve
The length of the transition curve should be determined as the maximum of the following three criteria: rate of change of centrifugal acceleration, rate of change of superelevation, and an empirical formula given by IRC.
- Rate of change of centrifugal acceleration
- Rate of introduction of super-elevation
- By empirical formula
Due to the application of transition curve on both sides of the circular curve, the circular curve gets shifted towards inner side and this shift is called lateral shift and is given by:
S = Ls2 / (24*R)
Where, R is the radius of the circular curve and Ls is the designed length of the transition curve
Tangent length (T) = (R + S) tan α/2 + Ls / 2
Apex distance (E) = (R + S) (sec α/2 -1)
Spiral angle (φs) = [Ls / (2*R)] c = (Ls*180) / (2*π*R)
Length of the circular curve (Lc) = (π*R*Δs) / 180
Where, Δs = Angle of circular curve = α – 2*φs
Where, α is the total deflection angle
IRC suggest the length of the transition curve is minimum for plain and rolling terrain,
Ls = 2.7v2 / R
For steep and hilly terrain,
Ls = v2 / R
Where, v is the design speed in kmph and R is the radius of the curve in meters.
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