Highway Engineering

should therefore normally be designed to the absolute minimum K value

detailed in Table 6.12. For both crest and sag curves, relaxations below the

desired minimum values may be made at the discretion of the designer, though

the number of design steps permitted below the desirable minimum value will

vary depending on the curve and road type, as shown in Table 6.13.

180 Highway Engineering

Road type Crest curve Sag curve

Motorway 1 or 2 steps 0 steps

All-purpose 2 or 3 steps 1 or 2 steps

Table 6.13Permitted

relaxations for different

road and vertical curve

types (below desired

min. for crest curves

and below absolute min.

for sag curves)

6.6.4 Parabolic formula

Referring to Fig. 6.18, the formula for determining the co-ordinates of points

along a typical vertical curve is:

(6.34)

where

p and q are the gradients of the two straights being joined by the vertical curve

in question.

Lis the vertical curve length

x and y are the relevant co-ordinates in space

Proof

If Y is taken as the elevation of the curve at a point x along the parabola, then:

(6.35)

Integrating Equation 6.35:

(6.36)

Examining the boundary conditions:

When x =0:

(6.37)

(p being the slope of the first straight line gradient)

Therefore:

p =C (6.38)

dY

dx

=p

dY

dx

=+kx C

dY

dx

ka constant

2

2 = ()

y

qp

2

= x^2

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