Page 347 - Civil Engineering Formulas

278 CHAPTER ELEVEN

PVT point of vertical tangency, end of curve
G grade at beginning of curve, ft/ft (m/m)
1
G grade at end of curve, ft/ft (m/m)
2
L length of curve, ft (m)
2
2
R rate of change of grade, ft/ft (m/m )
V elevation of PVI, ft (m)
E elevation of PVC, ft (m)
0
E elevation of PVT, ft (m)
t
x distance of any point on the curve from the PVC, ft (m)
E elevation of point x distant from PVC, ft (m)
x
x distance from PVC to lowest point on a sag curve or highest point
s
on a summit curve, ft (m)
E elevation of lowest point on a sag curve or highest point on a summit
s
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.

R G 2 G 1 (11.13)
L
1
E 0 V 2 LG 1 (11.14)
1
E x E 0 G 1 x 2 Rx 2 (11.15)
x s G 1 (11.16)
R
2
G 1
E s E 0 (11.17)
2R
Note: If x is negative or if x L, the curve does not have a high point or
s s
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).