2. Grade Change Rate
A vehicle enters the curve at g1 and after a distance of L it departs the curve at g2. The total grade change is (g2-g1). The grade change rate, k, is the total grade change divided by the distance, Equation B-3.
For example, a -2.00% grade into a +1.00% grade connected with a 400.00 ft curve has a k of:
This tells us that the grade changes +0.75% per each 100 ft of curve. If we go 100 ft past the BVC, the curve grade is -1.00%+0.75% = +0.25%
Increasing the curve length to 900.00 ft changes k to +0.33%/sta.
That second smaller k means the longer curve is flatter since is spreads the total grade change over a longer distance, Figure B-4.
Different Curve Lengths
Note that the example was a sag curve with a positive k: we went from a negative grade to a positive grade. A crest curve, on the other hand, would have a negative grade change rate, Figure B-5.
Crest and Sag Curves
What about curves whose grades at both ends are different but have the same mathematical sign? Figure B-6 shows four different curve situations where the incoming and outgoing grades have the same mathematical sign.
Grades with Same Mathematical Sign
The two curves on the left are both crest curves having a negative k since the outgoing grades are less than the incoming grades.
The two curves on the right are sag curves having a positive k since their outgoing grades are mathematically greater (less negative or more positive) than the incoming grades.