Transition Curves:
If a vehicle travelling on a straight enters a horizontal curve abruptly, it will cause shock and sway. To avoid this, it is customary to provide a transition curve (Figure). Incidentally, the transition curve is also used to provide gradual application of super- elevation and widening of the curve. A spiral is the most commonly used transition curve.
Figure: Main Elements of a Circular Curve Provided with Transitions
Some of the important properties of the spirals are given below :
(a) Ls R_{c} = LR = constant
(b) L = M√ θ , where M is a constant
M = √2RL
Also, L = 2 Rθ
(c) θ= (L/L_{s})^{2} θs
(d) θs = Ls/2R_{c } radians = 28.65 L_{s}/R_{s} degrees
(e) Ts = Ls/2 +(Rc+s)tan(Δ/2)
(f) s= L_{s}2/24R_{c}
(g) E_{s}= (Rc+s)sec Δ/2-R_{c}
The following nomenclature may be noted:
θ_{s} : Spiral angle
Δ_{c} : Angle of the circular curve
Δ : External angle
L_{s} : Spiral Length
R_{c} : Radius of circular curve
L : Length of spiral from starting point to any point
R : Radius of curvature of the spiral at the point distant L from starting point
θ : Deflection angle at any point of the spiral distant L from the starting point
Ts : Tangent distance
Es : Apex distance
s : Shift
HIP : Horizontal Intersection Point
BS : Beginning of spiral
BC : Beginning of circular curve
EC : End of circular curve
ES : End of spiral