Searching the beginning of the climb to get the most reliable difficulty index

The climb is the steep fragment of the road. In road cycling, climbs should be categorized by the effort necessary to overcome it. Two values have the greatest influence on a difficulty of the climb: its average slope (rise/run ratio) and length. A simple approach to describing a climb's difficulty is multiplication slope squared and run. In this paper, the beginning of the climb is mathematically established to get the most reliable difficulty index. Moreover, it is presented a special case where the value of difficulty index does not depend on the location of the beginning point.