If a crest vertical curve has a K value of 250 and an algebraic difference in grades of 5.0%, what is the length of the vertical curve?

To determine the length of a crest vertical curve, you can use the formula that relates the length of the curve (L) to the K value (which represents the rate of change of grade in feet per percent of grade change) and the algebraic difference in grades (A). The formula is given as:

L = K * |A|

Where:

• L is the length of the vertical curve in feet,

• K is the K value,

• A is the algebraic difference in grades expressed as a percentage.

In this question, the K value is 250, and the algebraic difference in grades is given as 5.0%. First, it is essential to convert the percentage into its decimal form, which is 0.05.

Now, plugging the values into the formula:

L = 250 * |5.0|

L = 250 * 5

L = 1250 feet

Thus, the length of the crest vertical curve is calculated to be 1250 feet. This calculation shows why this value is the correct answer—it accurately reflects the relationship between the K value and the algebraic change in grades according to the formula for vertical curves in roadway design. Understanding this principle is crucial for traffic operations engineers in