Syzygy Sailing

Almost every day, I tell my students, “Trust me, you’ll need to use this math someday.” When they’re learning about arcs of a circle, and how two rays of an exterior angle cut through the circle can be subtracted and that the result equals half the exterior angle, their eyes glaze over and I wonder how better to convince them. “Well, I know it’s slightly boring, and maybe you don’t see the relevance now,” I say, “but trust me!”

Well, kids, take a look at this: Eight pages of mathematics, all done for the practical, real-world purpose of making new water tanks.

Jonny mentioned that before we hacked up that port watertank, Matt and I measured it, because our plan all along has been to build new similarly-shaped tanks out of epoxy-coated plywood. But he failed to mention some complications. (It’s a sailboat; of course there were complications, right?) The complications: the tank was shaped funny. It wasn’t a nice boxy shape, like a coffin, but rather one side was more like a torqued trapezoid. The first problem was that trapezoids are kinda looked down on in the shapes world as a named-yet-odd shape. More importantly, the torqued trapezoid was like a piece of paper with the top edge twisted one way and the bottom edge the other, ie. not a flat plane.

This nefarious, twisting face of the tank was a dilemma, because 1/2″ marine-grade plywood cannot be curved in the same way that stainless-steel can. What really vexed us, though, was the way that the face was just barely curved — not enough to measure easily, but enough to make it very difficult to reproduce in wood. In a way, it’s like it was just daring us to try.

Matt, the ex-physicist and I, the ex-math teacher, attacked the problem of determining the shape with a vengeance, each with our own methods, furiously battling to see who could come up with an answer that would best satisfy the other and thus win the king for the day. Diagonals were measured, plumb-lines were drawn, angles were estimated, cosines were determined, arc-tangents were employed, lengths were re-measured, and spreadsheets created. Around and around we went. Jonny, the ex-english-writer-something-or-other-that-required-little-to-no-mathematics person, behooved us to consider his idea for determining the shape. “Just trace it,” he said. “Nonsense!” Matt and I exclaimed. “Your assumptions are invalid!” And off again to our calculations we went. I found errors in Matt’s work; he found errors in my work. Jonny’s suggestion was ignored.

A new day arose, and with it, the need to begin cutting the plywood. Before making those first cuts, we invoked that old saying, “measure twice, cut once,” and double-checked our measurements. What should have been a simple operation became a 20-minute math discussion, with errors discovered left and right. Once again, Jonny once implored us to consider his suggestion, but he was overruled by us math crazies. More measurements were made, more calculations completed, and then, finally, all three of us settled on a solution.

In the workyard, I picked up the jig-saw for the second time, determined to cut perfectly. (You’ll recall that the first time I used the jig saw, I essentially cut a hole in the hull of our boat.) Matt and Jonny were impressed as I cut away, but we still weren’t 100% sure if I was cutting the right shapes.

After I’d cut the six pieces, we assembled the wooden tank with screws, to make sure it’d fit. Voila! Fit it did! It was 1/4″ off on one end, but that was easily remedied. After days of work, our tank-to-be sat there in the workyard, a thing of beauty. Granted, we still had hours of fiberglassing and epoxying ahead of us, but we felt we’d taken a great leap forward. So we sat around and drank canned beers with the yard manager, Miguel, satisfied at having accomplished something, even if we weren’t done yet.

Oh yes, whose method did we use? Not the ex-physicist’s, nor the ex-math teacher’s. We used Jonny’s method. King’s to you, Jonny.