Modelling a Bridge
Calculus
What is the length of the cable from which bridge is suspended?
Introduction
Think about this as an engineer would. Fit a function to the main cable of a suspension bridge, then look at the vertical hangers connecting the cable to the deck — how long is each one, and can you predict the pattern? Try it in Desmos for a few different real bridges.
Guiding Questions
- What curve does the main cable of a suspension bridge follow, and why is a quadratic a reasonable model?
- Using real dimensions of a bridge, fit a quadratic to the main cable.
- Approximate the length of the cable by breaking your curve into short straight segments and summing their lengths with Pythagoras. How does your estimate change as you use more, shorter segments?
- How do the hanger lengths vary along the deck? Predict them and check against photographs.