Handbook of Civil Engineering Calculations

FIGURE 21

LOCATION OFA SUMMIT

An approach grade of+1.5 percent intersects a grade of-2.5 percent at station 29 + OO of
elevation 226.30 ft (68.976 m). The connecting parabolic curve is to be 800 ft (243.8 m)
long. Locate the summit.

Calculation Procedure:

1. Locate the PC
   Draw a freehand sketch of the curve, and record all values in the sketch as they are ob-
   tained. Thus, station of PC = station of PI - L/2 = 25 + 00; elevation of PC = 226.30 -
   400(0.015) = 220.30 ft (67.147 m).


2. Calculate the rate of change in grade; locate the summit
   Apply the average-grade method to locate the summit. Thus, r = (-2.5 - 1.5)7800 =
   -0.005 percent per foot.
   Place the origin of coordinates at the PC. By Eq. 42, xs = -GJr = 1.5/0.005 = 300 ft
   (91.44 m). From the PC to the summit, Gav =^1 AG 0 = 0.75 percent. Then ys = 300(0.0075)
   = 2.25 ft (0.686 m); station of summit = (25 + 00) + (3 + 00) = 28 + 00; elevation of sum-
   mit = 220.30 + 2.25 = 222.55 ft (67.833 m). The summit can also be located by the tan-
   gent-offset method.

PARABOLIC CURVE TO CONTAIN

A GIVEN POINT

A grade of-1.6 percent is followed by a grade of+3.8 percent, the grades intersecting at
station 42 + OO of elevation 210.00 ft (64.008 m). The parabolic curve connecting these