What is a common application of the middle ordinate and external distance formulas in highway construction?

Answer: B — Designing circular curves

The use of the middle ordinate and external distance formulas is integral to designing circular curves in highway construction. Circular curves are essential when aligning roads to transition smoothly around bends, and these formulas help in determining various geometric characteristics of the curve. The middle ordinate is the perpendicular distance from the midpoint of the chord connecting the endpoints of a circular arc to the arc itself. This measurement is crucial for creating accurate curve layouts and ensuring that the transition from a straight path to a curved one is smooth and safe for vehicles. The external distance, on the other hand, is the distance from the center of the circle to the midpoint of the tangent line extended from each end of the curve. This information is vital for determining how far the curve sits away from the original roadway line, which directly influences road safety and aesthetics. By utilizing these formulas, engineers can design curves that accommodate vehicle dynamics, ensure proper drainage, and maintain safety standards, making them a common and fundamental aspect of highway design.