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_s2/24R_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