Designing a Cardboard Canoe
Every year, my high school holds a canoe race, where students from the Engineering, Physics, and Calculus classes compete to design, build and race a canoe over the span of two weeks.
The standard way to do this was to first create the keel, then create ribs at regular intervals. From that, you can add a cardboard “skin” and then coat the whole thing in duct-tape.
The only real limit is that the canoe’s contours must be defined by an equation (thus relating it back to the class content). Most teams created two equations - one for the profile view, and one for each of the ribs.
I though we could take that further, and make a parametric function to define the entire surface of the boat. From there, one can plug in rib locations and automatically generate a table telling us what shapes to cut out. Turns out I already made a tool to make the process of creating the contour a visual one.
Using the Math4D system, I started out with three separate contours, then actually created the 2-variable parametric. It turns out the ability to render the boat shape was very useful, as the team suggested many modifications - both aesthetic and practical.
However, an equation is not a boat, and we still had to build the thing. The fact that we could so quickly generate the table certainly helped, as we could get a bit of a head-start.
We ended up winning two of the four heats, as well as taking the first prize overall. In the end though, the equations only helped us so much - many teams had really good designs. What set our boat apart was exceptionally sturdy build quality, as well as quality rowers.
