Catenary Curves
Functions & Equations
A hanging rope is not a parabola but how different is it?
Introduction
Explore catenary curves and determine an equation of a landmark near you. Use Google Earth to locate the perfect spot to take a photo of powerlines.
Guiding Questions
- Hang a chain or rope and photograph it. Is it a parabola? Fit one and look at the residuals.
- The true shape is a catenary (built from exponentials). Fit that too — how much better is it?
- For what spans and sags is the parabola a good enough approximation?
- Where do engineers rely on the difference — and can you measure a real example like a power line?