parabola is used primarily because its shape providesa transition and, also, lends itself to the computationalmethods described in the next section of this chapter.Designing a vertical curve consists principally ofdeciding on the proper length of the curve. Asindicated in figure 11-13, the length of a vertical curveis the horizontal distance from the beginning to theend of the curve; the length of the curve is NOT thedistance along the parabola itself. The longer a curveis, the more gradual the transition will be from onegrade to the next; the shorter the curve, the moreabrupt the change. The change must be gradualenough to provide the required sight distance (fig.11- 14). The sight distance requirement will depend onthe speed for which the road is designed; whetherpassing or nonpassing distance is required; and otherassumptions, such as one’s reaction time, brakingtime, stopping distance, height of one’s eyes, andheight of objects. A typical eye level used for designsis 4.5 feet or, more recently, 3.75 feet; typical objectheights are 4 inches to 1.5 feet. For a sag curve, thesight distance will usually not be significant duringdaylight; but the nighttime sight distance must beconsidered when the reach of headlights may belimited by the abruptness of the curve.ELEMENTS OF VERTICAL CURVESFigure 11-15 shows the elements of a verticalcurve. The meaning of the symbols and the units ofmeasurement usually assigned to them follow:PVCPoint of vertical curvature; the place where thecurve begins.PVIPVTPOVCPOVTgIg2Figure 11-15.—Elements of a vertical curve.Point of vertical intersection; where the gradetangents intersect.Point of vertical tangency; where the curveends.Point on vertical curve; applies to any point onthe parabola.Point on vertical tangent; applies to any pointon either tangent.Grade of the tangent on which the PVC islocated; measured in percent of slope.Grade of the tangent on which the PVT islocated; measured in percent of slope.Figure 11-14.—Sight distance.11-13
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