What does the variable 'r' represent in the formula L = (g2-g1)/r?

In the formula L = (g2 - g1)/r, 'r' represents the radius of the circular curve. This relationship is commonly used in surveying and civil engineering to analyze various aspects of circular paths or arcs.

The formula itself is used to determine the length of a tangent line based on the difference in grades (g2 - g1) over the radius of the curve. In this context, 'r' is crucial because it influences how sharp the curve is and subsequently how the roadway or pathway transitions from one grade to another.

Understanding that 'r' is the radius helps clarify how the curve's geometry directly affects the design and safety of the roadway. For example, a smaller radius indicates a sharper turn, which can have implications for vehicle dynamics and engineering design requirements, including superelevation and sight distance.

The other choices do not align with the formula's context: the length of the tangent is not represented by 'r', and the maximum allowable rate of change or the diameter of the curve are separate concepts that do not fit within that specific relationship.