Modeling Tide Heights and Kayaker's Heuristics

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2024-11-19 22:00:04

Just over a year ago, I moved to the beach, partly to be able to indulge in my passion of sea kayaking more frequently. As a result of this move, I have become much more aware of the tidal rythym of both the local Atlantic Ocean and Delaware Bay coasts.

While there are many websites that will provide detailed tide tables, and I have aqcuired a nice, decorative tide clock featuring a landscape of our local lighthouse, I found myself wanting a digital display that cycled through the tidal status at several locations.

After a bit of searching, I found the relatively inexpensive Ulanzi TC001 Smart Pixel Clock 2882 and the corresponding open source firmware AWTRIX 3. In the process of writing software to turn this device into a digital tide clock, I stumbled upon the fun little math problem that is the subject of this post.

In this post, we will derive a function that approximates the water level between low and high tides in an idealized, semi-diurnal tide region. This approximation is sufficient for my purposes, as most areas of the Atlantic ocean (including New Jersey, where I live) are subject to such a tide pattern. We will spend the rest of this post deriving the water level approximation and comparing its predictions to several heuristics frequently used by kayakers (and other boaters) to predict tide height and flow rate.

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