Catenary equation

A catenary equation describes the shape a flexible, uniform chain or cable takes when hung freely under its own weight between two supports. Due to gravity, the cable forms a smooth curve called a catenary, which isn’t a parabola but is mathematically defined by a hyperbolic cosine function. The equation relates the cable's shape to factors like its weight per unit length, the horizontal distance between supports, and the tension in the cable. This understanding is important in engineering for designing bridges, power lines, and suspension structures to ensure they can support loads safely and efficiently.