What is the primary application of the degree of curvature in surveying?

The degree of curvature is a crucial element in horizontal curve geometry in surveying and is primarily used to determine the angle subtended by an arc. It offers a clear measurement of how sharply a road or path curves by relating the curve's radius to the angle that the arc subtends at the center of the circular path. This helps surveyors plan and design roads, railways, and other infrastructure with appropriate curvature for safety and efficiency.

Establishing the angle subtended by the arc enables civil engineers and surveyors to ensure that vehicles can safely navigate the curve without risk of tipping over or losing control, as well as to provide adequate sight distances and transitions between straight segments and curves. This application is foundational in the layout and design of transportation routes, where understanding the behavior of the curve in relation to the vehicle dynamics is essential.

In contrast, the other choices relate to different aspects of curvature and design. While defining the length of a vertical curve is important in grading and drainage considerations (not directly tied to the degree of curvature), calculating maximum slope pertains to the steepness of a section, which does not directly involve horizontal curvature. Establishing the straightness of a road is not related to curvature but rather to alignment and geometric layout.