Maths and Sailing: the Day I Discovered “Tacking” Is Basically Algebra With Wet Shoes

There are two kinds of people in the world: those who think maths is thrilling, and those who think it’s something that happens to other people in exam halls. Then there are sailors… who accidentally do maths all the time, usually while holding a rope and trying not to look panicked.

When you sail on a river (hello, Thames), you quickly realise you can’t just point at where you want to go and go there. The wind has other plans, the stream has very other plans, and the boat has the personality of a stubborn shopping trolley. So you tack — zig-zagging upwind — which is basically a real-life lesson in angles, vectors, and “Why isn’t this working the way it did on the whiteboard?”

1) Angles: “Close-hauled” is a geometry problem

Upwind sailing is all about the angle between the boat and the wind. Too close and the sail flaps like a sad flag. Too far off and you lose ground. That sweet spot? It’s the practical version of “find the optimal angle” — except your calculator is a tell-tale and your teacher is the wind shouting “NO.”

Classroom link: get students drawing angle diagrams with wind direction as a reference line, then ask: Which heading gives the fastest progress toward the buoy? It’s bearings and geometry with purpose.

2) Speed and distance: the river won’t wait for your calculations

Want to know if you’ll reach the mooring before the tide pins you sideways? That’s speed = distance ÷ time — but with a moving conveyor belt underneath you. On the Thames, “I’ll just glide in” turns into “Why am I drifting into Berkshire?”

Classroom link: real data problems: boat speed through water vs speed over ground. Give students two speeds and ask them to work out drift, time to a marker, or whether the boat arrives upstream or embarrassingly downstream.

3) Ratios and forces: the sail is a giant triangular maths lesson

Sail shape (and how tight you pull everything) affects speed. A flatter sail is different to a fuller one — and suddenly you’re in ratios, proportional reasoning, and “adjust this by a bit and the whole system changes.”

Classroom link: show a simple sail triangle and explore how changing one side (sheet tension, boom position) changes the “shape” and performance. You don’t need to go full physics — just proportional thinking and graphs.

4) Turning circles and pivot points: maths you can feel

Powerboaters learn that boats pivot in different places depending on forward or reverse. Dinghies do their own version when tacking and gybing — turn too fast and you stall; too slow and you drift. It’s all about rates of change in the real world.

Classroom link: graph “heading vs time” during a tack and discuss steep vs gentle slopes. Suddenly gradients mean something other than “that line goes up.”

5) Probability: will this tack work… or will I be doing an accidental three-point turn?

Every tack is a mini gamble: wind shift, gust, lull, other boats, and the dreaded “in irons.” That’s probability, decision-making, and risk — plus a splash of psychology.

Classroom link: simple tree diagrams: if wind shifts left/right, what’s the best choice? Add constraints like river width. This becomes a genuine “thinking problem” rather than a worksheet.

Making maths more interesting (without pretending it’s all fun)

The trick isn’t to say “maths is amazing!” while students stare back like you’ve suggested revising for fun. The trick is to give maths a job to do.

Sailing gives you a ready-made world where numbers matter:

• If you get the angle wrong, you don’t reach the buoy.

• If you misjudge time and drift, you miss the mooring (and your dignity).

• If you don’t estimate properly, the river teaches you… repeatedly.

And the best part? Students who think they “aren’t maths people” often are — they just haven’t met maths in a form that moves, splashes, and occasionally shouts “LEEWARD!”

If you want to make maths more interesting, don’t add more gimmicks. Add more reasons. Ideally ones involving boats.