Figure 11-20.—Table of computations of elevations on an unsymmetrical vertical curve.In this example, then, the middle vertical offset at thePVI is calculated in the following manner:e = [(4 x 2)/2(4 + 2)] x [(+6) - (–4)] = 6.67 feet.Second, you are cautioned that the check on yourcomputations by the use of second difference doesNOT work out the same way for unsymmetrical curvesas for a symmetrical curve. The second difference willnot check for the differences that span the PVI. Thereason is that an unsymmetrical curve is really twoparabolas, one on each side of the PVI, having acommon POVC opposite the PVI; however, thesecond difference will check out back, and ahead, ofthe first station on each side of the PVI.Third, the turning point is not necessarily aboveor below the tangent with the lesser slope. Thehorizontal location is found by the use of one of twoformulas as follows:from the PVCor from the PVTThe procedure is to estimate on which side of the PVIthe turning point is located and then use the properformula to find its location. If the formula indicates thatthe turning point is on the opposite side of the PVI, youmust use the other formula to determine the correctlocation; for example, you estimate that the turningpoint is between the PVC and PVI for the curve in figure11-19. Solving the formula:x_{t}= (l_{1})^{2}(g_{1})/2ex_{t}= [(4)^{2}(4)]/(2 x 6.67) = 4.80, or Station 42 + 80.However, Station 42 + 80 is between the PVI and PVT;therefore, use the formula:x_{t}= (l_{2})^{2}(g_{2})//2ex_{t}= [(2)^{2}(6)]/(2 x 6.67) = 1.80, or station 42 + 20.Station 42 + 20 is the correct location of the turningpoint. The elevation of the POVT, the amount of theoffset, and the elevation on the curve is determined aspreviously explained.CHECKING THE COMPUTATIONBY PLOTTINGAlways check your work by plotting the gradetangents and the curve in profile on an exaggerated11-19