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7. Compound Curves

a. Geometry

Sometimes a simple equal tangent vertical curve cannot be fit to a particular design condition. For example, the vertical curve in Figure B-24 must start at an existing intersection at sta 20+00 elev 845.25 ft and end at a second intersection at sta 28+00 elev 847.75 ft. To minimize earthwork an incoming grade of +2.50% is followed by an outgoing grade of -1.00%. This places the PVI at sta 23+00 elev 852.75 ft.

Figure B-24
Fitting a Curve


This combination results in a PVI that is not midway between the BVC and EVC. If a 600.00 ft equal tangent curve were used, it would begin at 20+00 and end at 26+00, 200.00 ft back along the -1.00% grade from the specified EVC.

This situation requires an unequal tangent vertical curve. While a mathematical curve other than a parabolic arc could be used, the traditional method is to use two back-to-back equal tangent curves. This is referred to as a compound curve, Figure B-25.

Figure B-25
Compound Curve


A compound curve isn't as complex as it looks: the key is to break it into two successive equal tangent veritical curves.

PVIs are created for each curve at midpoint on the grade lines. A new grade, g3, is created by connecting the new PVIs. This is the outgoing grade for the first curve and the incoming grade for the second.

The CVC is the Curve to Vertical Curve point which is the EVC of the first curve and the BVC of the second; its station is the same as the overall PVI station. Once we have sufficient information for each curve to set up its Curve Equation, we can compute each curve independently.

The closer the individual curve's k values, the smoother the transition between them, particularly when there is a large grade change over a short distance.