Civil Engineering Reference
In-Depth Information
in situations where only one arc segment is used to connect two tangents,
the arc radius cannot be too small as the curvature change is from zero to
the arc's curvature.
A spiral can be a perfect fit for a transition from one curvature to another
as it is so defined that the curvature change is proportional to the curve
distance. As shown in Figure 18.4, a spiral is used to connect two segments
that have different radius. In addition to the requirements of maximal cur-
vatures at two end segments, the spiral length, which controls the rate of
the curvature change, cannot be too short.
Parabolic curve, which is exclusively used for vertical and transverse curves,
fails to possess the advantages of arcs or spirals as horizontal curve transitions
(Hickerson 1959). In most horizontal transition situations, tangents (straight
lines), arcs, spirals, and their combinations are commonly used.
18.2.2 types of vertical curves
Vertical curves are used to make a transition from one slope to another.
Parabolic curve is the only type of curve used in vertical curves. As shown
in Figure 18.5, the parabolic segment is called sag vertical curve when the
transition of slopes is from negative to positive and crest vertical curve vice
versa.
18.2.3 types of transverse curves
A roadway is usually required to have certain crowns in the middle and
cross slopes on sides to help water draining from roadway laterally. Thus,
the cross section or profile at any station of a roadway contains two tan-
gents and one transition curve. As shown in Figures 18.6 and 18.7, the
parabolic curve is widely used in transverse curves.
18.2.4 superelevation and superwidening
When traveling along curve transition segment, vehicles will overcome
centrifugal forces by mainly lateral tire friction to maintain movement in
circular. In cases where either roadway curvature is big or design speed is
high, the transverse slope on the outer side of a roadway should be raised
up to flat or even positive toward inner side so that extra horizontal forces
+ Elevation
Parabola
Straight line
Connecting
point
End point
Connecting
point
Connecting
point
Straight line
Start
point
Straight line
Parabola
Straight line
Connecting
point
Parabola
Connecting
point
Connecting
point
+ Station
Figure 18.5
An example of a vertical curve—components of a vertical curve.
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