CIVIL ENGINEERING FORMULAS

HIGHWAY AND ROAD FORMULAS 277

(11.5)

(11.6)

(11.7)

(11.8)

(11.9)

(11.10)

(11.11)

(11.12)

PARABOLIC CURVES

Parabolic curves are used to connect sections of highways or railroads of differ-
ing gradient. The use of a parabolic curve provides a gradual change in direction
along the curve. The terms and symbols generally used in reference to parabolic
curves are listed next and are shown in Fig. 11.3.

PVCpoint of vertical curvature, beginning of curve

PVIpoint of vertical intersection of grades on either side of curve

b

c^2

R

approximate

a

c^2

2 R

approximate

sin

d

z



c

2 R

exact for chord definition



Dc

100

approximate for chord definition

d

Dl

100

exact for arc definition

LC

L^3

24 R^2



C^3

24 R^2

approximate

L

100 I

D

exact

C 2 R sin^1  2 I exact

L

2

PVI

(elev. V)

PVC (elev. E 0 ) PVT (elev. Et)

Elev. Ex

L

X

G 2

G 1

L

2

FIGURE 11.3 Vertical parabolic curve (summit curve).