CIVIL ENGINEERING FORMULAS

278 CHAPTER ELEVEN

PVTpoint of vertical tangency, end of curve

G 1 grade at beginning of curve, ft/ft (m/m)

G 2 grade at end of curve, ft/ft (m/m)

Llength of curve, ft (m)

Rrate of change of grade, ft/ft^2 (m/m^2 )

Velevation of PVI, ft (m)

E 0 elevation of PVC, ft (m)

Etelevation of PVT, ft (m)

xdistance of any point on the curve from the PVC, ft (m)

Exelevation of point xdistant from PVC, ft (m)

xsdistance from PVC to lowest point on a sag curve or highest point

on a summit curve, ft (m)

Eselevation of lowest point on a sag curve or highest point on a summit

curve, ft (m)

Equations of Parabolic Curves

In the parabolic-curve equations given next, algebraic quantities should always
be used. Upward grades are positive and downward grades are negative.

(11.13)

(11.14)

(11.15)

(11.16)

(11.17)

Note: Ifxsis negative or if xs L, the curve does not have a high point or
a low point.

HIGHWAY CURVES AND DRIVER SAFETY

For the safety and comfort of drivers, provision usually is made for gradual
change from a tangent to the start of a circular curve.
As indicated in Fig. 11.4, typically the outer edge is raised first until the outer
half of the cross section is levelled with the crown (point B). Then, the outer edge
is raised farther until the cross section is straight (point C). From there on, the
entire cross section is rotated until the full superelevation is attained (point E).

EsE 0 

G^21

2 R

xs

G 1

R

ExE 0 G 1 x^1  2 Rx^2

E 0 V^1  2 LG 1

R

G 2 G 1

L