Highway Geometric Design (Vertical Curves)

Vertical Curves: Provided in elevation at change of gradients. These curves are convex when two grades meet at a ‘summit’ and concave when they meet at a ‘sag’.

Summit Curves are provided when

(a) ‘Positive Grade’ meets ‘Negative Grade’.

(b) ‘Positive Grade’ meets another ‘Milder Positive Grade’.

(c)’Positive Grade’ meets ‘Level Stretch’.

(d) ‘Negative Grade’ meets ‘Steeper Grade’.

>>  Assumptions in the design of vertical curves:

(a) The curve is so flat that the length of curve is equal to the length of chord.

(b) The portions of the curve along tangents on either side of the intersection and equal.

(c) The angle subtended by the tangents horizontal are so small that the tangents of these angles are equal to the angles in radius themselves.  

>> Length of vertical curves:Square parabolic curves are generally adopted due to best riding qualities, simplicity of calculation work and having uniform rate of change of grade throughout the parabola.

L = Total change of grade / Rate of change grade

(g₁— g₂) Algebraic difference of grade

Equation of parabola is: y = N/2L x²

>>  Design of summit curves:

Criteria: Sight distance

Length of summit curve for SSD:

>> Minimum radius of parabolic summit curve R=L/N

>> On humps, where the sight distance s not a problem simple transition curve is more appropriate