Highway Engineering

where x is the distance along the curve measured from the start of the vertical

curve and y is the vertical offset measured from the continuation of the slope

to the curve.

At the intersection point PI:

x =L/2

Therefore

(6.46)

The co-ordinates of the highest/lowest point on the parabolic curve, frequently

required for the estimation of minimum sight distance requirements, are:

(6.47)

y p (6.48)

2p q

2

=

()-

L

x p

pq

=

-

L

e

qp

2L 2

y

qp

8

2

=-

Ê -

Ë

ˆ

̄

Ê

Ë

ˆ

̄ =

=- -()

L

L

182 Highway Engineering

Example 6.7

A vertical alignment for a single carriageway road consists of a parabolic

crest curve connecting a straight-line uphill gradient of+4% with a straight-

line downhill gradient of-3%.

(1) Calculate the vertical offset at the point of intersection of the two

tangents at PI

(2) Calculate the vertical and horizontal offsets for the highest point on the

curve.

Assume a design speed of 85 km/hr and use the absolute minimum K value

for crest curves.

Solution

Referring to Table 6.12, a K value of 30 is obtained. This gives an absolute

minimum curve length of 210 m.

Vertical offset at PI:

p =+4%

q =-3%

Contd