Back in secondary school and during university, there were always jokes about how some complex math equations we'd learned would never be useful outside the classroom. I still see those jokes floating around on social media, and they never quite sit right with me. So, I’m here to bore you with a real-life example of one such equation—the Quadratic Equation (QE)—that we encounter in our daily lives. Let’s dive into how quadratic equations are actually used in road design.
Whether you're driving, walking, or cycling up a hilly road, you look forward to the ride downhill. If you're like me, that feeling of coasting with minimal effort gives you extra comfort. If you were to trace the path of your steering wheel or handlebars going uphill and downhill, you'd draw a series of parabolas. Each time you go up and down a hill, you're essentially following a parabolic curve.
Roads are designed this way for several reasons. The original surface might have had a similar shape, making it more cost-effective to design safe hills rather than flatten the terrain. Additionally, subsurface conditions might influence the surface design. Whatever the reason, engineers must determine the appropriate elevations to ensure a safe and comfortable ride for everyone using the road.
Cue in the QE. This mathematical tool becomes crucial in road design. With the help of QEs, engineers can calculate the precise elevation changes needed for a road's surface when going uphill and downhill. By using quadratic equations, they can ensure that the road provides a smooth and safe experience for all travelers. Here's how it works:
Knowing the profile of the road approaching the bottom of the proposed hill, the required height of the hill, and the horizontal distance between the two lowest points of the valleys that flank the hill, engineers can use quadratic equations to calculate the surface elevations needed. These calculations help design and build a road that follows a smooth and predictable path, ensuring safer and more comfortable travel.
So, the next time you’re on a hill, give a shout-out to quadratic equations and parabolas. They play a crucial role in making our daily commutes smoother and safer.