x
y
The
Horizontal distance from the PVC to any
POVC or POVTback of the PVI, or the distance
from the PVT to any POVC or POVT ahead of
the PW, measured in feet.
Vertical distance (offset) from any POVT to
the corresponding POVC, measured in feet;
which is the fundamental relationship of the
parabola that permits convenient calculation
of the vertical offsets.
vertical curve computation takes place after
the grades have been set and the curve designed.
Therefore, at the beginning of the detailed computa-
tions, the following are known: g1, g2, l1, l2, L, and the
elevation of the PVI. The general procedure is to
compute the elevations of certain POVTs and then to
use the foregoing formulas to compute G, then e, and
then the Ys that correspond to the selected POVTs.
When the y is added or subtracted from the elevation
of the POVT, the result is the elevation of the POVC.
The POVC is the finished elevation on the road, which
is the end result being sought. In figure 11-15, the y is
subtracted from the elevation of the POVT to get the
elevation of the curve; but in the case of a sag curve,
the y is added to the POVT elevation to obtain the
POVC elevation.
The computation of G requires careful attention to
the signs of g1 and g2. Vertical curves are used at
changes of grade other than at the top or bottom of a
hill; for example, an uphill grade that intersects an
even steeper uphill grade will be eased by a vertical
curve. The six possible combinations of plus and
minus grades, together with sample computations of
G, are shown in figure 11-16. Note that the algebraic
sign for G indicates whether to add or subtract y from
a POVT.
The selection of the points at which to compute
the y and the elevations of the POVT and POVC
is generally based on the stationing. The horizontal
alignment of a road is often staked out on 50-foot or
100-foot stations. Customarily, the elevations are
computed at these same points so that both horizontal
and vertical information for construction will be pro-
vided at the same point. The PVC, PVI, and PVT are
usually set at full stations or half stations. In urban
work, elevations are sometimes computed and staked
every 25 feet on vertical curves. The same, or even
closer, intervals may be used on complex ramps and
interchanges. The application of the foregoing funda-
mentals will be presented in the next two sections
under symmetrical and unsymmetrical curves.
Symmetrical Vertical Curves
A symmetrical vertical curve is one in which the
horizontal distance from the PVI to the PVC is equal
to the horizontal distance from the PW to the PVT. In
other words, l1 equals l2.
The solution of a typical problem dealing with a
symmetrical vertical curve will be presented step by
step. Assume that you know the following data:
g1
= +97%
g2=
–7%
L = 400.00´, or 4 stations
The station of the PVI = 30 + 00
The elevation of the PVI = 239.12 feet
The problem is to compute the grade elevation of the
curve to the nearest hundredth of a foot at each 50-foot
station. Figure 11-17 shows the vertical curve to be
solved.
Figure 11-17.—Symmetrical vertical curve.
11-15
