TwoPi and I, still traveling around visiting family, were just on the Oregon coast for a few days. While we were there, my brother-in-law Ken took us out crabbing. The crabbing turned out to be a wash dinner-wise since they were too small, but the day was beautiful, the beaches calm, and as a bonus there was some cool math.
It seems that the best time to go crabbing is when the currents are weakest. To find out those times, Ken used a Tide Predictor:
The weakest tides are right at High Tide and at Low Tide. Why? That’s when the change in sea level — the derivative, in other words, is close to zero. Calculus in action! (Indeed, I imagine that current could be viewed as a kind of derivative of the sea height, since it is strongest when the slope of the water levels is changing the fastest.) As an aside, high tide is apparently better for catching crabs than low tide, but that has less to do with calculus and more to do with crustaceous personalities.
Edited 7/2 to add: I just realized that the second derivative also plays a role! If the second derivative is closer to zero as well, it means that the current isn’t changing as quickly (in addition to not being very strong) so that gives a longer time period to check the traps and put them out again before the current gets strong enough that the crabs run back to the river sides or ocean.
If we hadn’t had the tide charts, we could have used this fancy Tide Clock on the wall:
Except it wasn’t working.
The tide itself leads to all sorts of other math problems. One of the neatest has to do with the cycles of the tides. The high tide peaks changed by almost 25 hours each day, not 24, so high and low tide cycle through different times of the year. It turns out that it takes 18.6 years for the pattern of high/low tide times to repeat itself. Apparently people used to be hired to take careful measurements of the tide and once the record stretched back 18.6 years, it was considered complete for that particular area. Not the most exciting job I suspect, but certainly important.