xyTheHorizontal distance from the PVC to anyPOVC or POVTback of the PVI, or the distancefrom the PVT to any POVC or POVT ahead ofthe PW, measured in feet.Vertical distance (offset) from any POVT tothe corresponding POVC, measured in feet;which is the fundamental relationship of theparabola that permits convenient calculationof the vertical offsets.vertical curve computation takes place afterthe grades have been set and the curve designed.Therefore, at the beginning of the detailed computa-tions, the following are known: g_{1}, g_{2}, l_{1}, l_{2}, L, and theelevation of the PVI. The general procedure is tocompute the elevations of certain POVTs and then touse the foregoing formulas to compute G, then e, andthen the Ys that correspond to the selected POVTs.When the y is added or subtracted from the elevationof the POVT, the result is the elevation of the POVC.The POVC is the finished elevation on the road, whichis the end result being sought. In figure 11-15, the y issubtracted from the elevation of the POVT to get theelevation of the curve; but in the case of a sag curve,the y is added to the POVT elevation to obtain thePOVC elevation.The computation of G requires careful attention tothe signs of g_{1 }and g_{2}. Vertical curves are used atchanges of grade other than at the top or bottom of ahill; for example, an uphill grade that intersects aneven steeper uphill grade will be eased by a verticalcurve. The six possible combinations of plus andminus grades, together with sample computations ofG, are shown in figure 11-16.Note that the algebraicsign for G indicates whether to add or subtract y froma POVT.The selection of the points at which to computethe y and the elevations of the POVT and POVCis generally based on the stationing. The horizontalalignment of a road is often staked out on 50-foot or100-foot stations. Customarily, the elevations arecomputed at these same points so that both horizontaland vertical information for construction will be pro-vided at the same point. The PVC, PVI, and PVT areusually set at full stations or half stations. In urbanwork, elevations are sometimes computed and stakedevery 25 feet on vertical curves. The same, or evencloser, intervals may be used on complex ramps andinterchanges. The application of the foregoing funda-mentals will be presented in the next two sectionsunder symmetrical and unsymmetrical curves.Symmetrical Vertical CurvesA symmetrical vertical curve is one in which thehorizontal distance from the PVI to the PVC is equalto the horizontal distance from the PW to the PVT. Inother words, l_{1 }equals l_{2}.The solution of a typical problem dealing with asymmetrical vertical curve will be presented step bystep. Assume that you know the following data:g_{1}= +97%g_{2}=–7%L = 400.00´, or 4 stationsThe station of the PVI = 30 + 00The elevation of the PVI = 239.12 feetThe problem is to compute the grade elevation of thecurve to the nearest hundredth of a foot at each 50-footstation. Figure 11-17 shows the vertical curve to besolved.Figure 11-17.—Symmetrical vertical curve.11-15