Surveying vertical curves: When a road is being built, it usually has straight sections, all with the same grade, that must be linked to each other by curves. (By this we mean curves up and down...

Surveying vertical curves: When a road is being built, it usually has straight sections, all with the same grade, that must be linked to each other by curves. (By this we mean curves up and down rather than side to side, which would be another matter.) It’s important that as the road changes from one grade to another, the rate of change of grade between the two be constant.56 The curve linking one grade to another grade is called a vertical curve. Surveyors mark distances by means ofstations that are 100 feet apart. To link a straight grade of g1 to a straight grade of g2, the elevations of the stations are given by

Here y is the elevation of the vertical curve in feet, g1 and g2 are percents, L is the length of the vertical curve in hundreds of feet, x is the number of the station, and E is the elevation in feet of the intersection where the two grades would meet. (See Figure 5.105.) The station x = 0 is the very beginning of the vertical curve, so the station x = 0 lies where the straight section with grade g1 meets the vertical curve. The last station of the vertical curve is x = L, which lies where the vertical curve meets the straight section with grade g2.