For the curve we are calculating, the computationswould be (7 x 4)/16 = 1.75 feet; therefore, the turningpoint is 1.75 stations, or 175 feet, from the PVT (station30 + 25).The vertical offset for the turning point is foundby the formula:For this curve, then, the computation is ( 1.75/2)^{2 }x 8 =6.12 feet.The elevation of the POVT at 30 + 25 would be 237.37,calculated as explained earlier. The elevation on thecurve would beis different from the horizontal distance between thePVI and the PVT. In other words, l_{1 }does NOT equall_{2}. Unsymmetrical curves are sometimes described ashaving unequal tangents and are referred to as doglegs. Figure 11-19 shows an unsymmetrical curve witha horizontal distance of 400 feet on the left and ahorizontal distance of 200 feet on the right of the PVI.The gradient of the tangent at the PVC is –4 percent;the gradient of the tangent at the PVT is +6 percent.Note that the curve is in a dip.As an example, let’s assume you are given thefollowing values:Elevation at the PVI is 332.68Station at the PVI is 42 + 00237.37-6.12 = 231.25.l_{1 }is 400 feetSTEP 8: Check your work.One of the characteristics of a symmetrical para-bolic curve is that the second differences betweensuccessive grade elevations at full stations are con-stant. In computing the first and second differences(columns 7 and 8), you must consider the plus orminus signs. When you round off your grade elevationfigures following the degree of precision required, youintroduce an error that will cause the second differenceto vary slightly from the first difference; however, theslight variation does not detract from the value of thesecond difference as a check on your computations.You are cautioned that the second difference will notalways come out exactly even and equal. It is merelya coincidence that the second difference has come outexactly the same in this particular problem.Unsymmetrical Vertical CurvesAn unsymmetrical vertical curve is a curve inwhich the horizontal distance from the PVI to the PVCl_{2 }is 200 feetg_{1 }is –4%g_{2 }is +6%To calculate the grade elevations on the curve to thenearest hundredth foot, use figure 11-20 as an example.Figure 11-20 shows the computations. Set four100-foot stations on the left side of the PVI (betweenthe PVI and the PVC). Set four 50-foot stations on theright side of the PVl (between the PVI and the PVT).The procedure for solving an unsymmetrical curveproblem is essentially the same as that used in solvinga symmetrical curve. There are, however, importantdifferences you should be cautioned about.First, you use a different formula for thecalculation of the middle vertical offset at the PVI. Foran unsymmetrical curve, the formula is as follows:Figure 11-19.—Unsymmetrical vertical curve.11-18

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