Highway Engineering

When x =L:

(6.39)

(q being the slope of the second straight line gradient)
Therefore:

q =kL+C =kL+p (6.40)

Rearranging Equation 6.40:

k =(q -p) ∏ L (6.41)

Substituting Equations 6.38 and 6.41 into Equation 6.36:

(6.42)

Integrating Equation 6.42:

(6.43)

From Fig. 6.18:

p =(y +Y) ∏ x (6.44)

Substituting Equation 6.44 into Equation 6.43:

(6.45)

Rearranging Equation 6.45:

y

qp

2

=- x^2

Ê -

Ë

ˆ

L ̄

Y

qpx

2

yY

2

=

Ê -

Ë

ˆ

L ̄ ++()

Y

qpx

2

px

2

=

Ê -

Ë

ˆ

L ̄ +

dY

dx

qp

= xp

Ê -

Ë

ˆ

L ̄ +

dY

dx

=q

Geometric Alignment and Design 181

Y

x

PI

T1

T2

L

L/2 L/2

e

e

y

Figure 6.18Basic parabolic curve.