Understanding the Rule of Twelfths for Tide Prediction
The fog was rolling in quickly, and the sun would soon be setting. I was bound for Provincetown at the tip of Cape Cod, a long peninsula that extends east and loops north like the tip of an elf’s shoe. The land curls so tightly around Provincetown Harbor that it makes for an ideal anchorage. However, the bottom has a very modest slope and a large tidal range, so it can be a bit challenging.
The water was +9ft at high and -1ft at low, a tidal range of 10ft. I was hoping to anchor as close in as possible without getting in water that was too shallow. The tide was falling. As I made my way deeper into the harbor, I calculated the ideal water depth where I should set the anchor.
You don’t need to know calculus to understand tides—you only need to know the Rule of Twelfths to determine the height of the tide at any time of day. Although it’s approximate and doesn’t account for every factor that might affect the tide, the Rule of Twelfths is ideal for the sailor on-the-go. It’s especially helpful when passing over a shoal or entering a harbor at a mid-point in the tidal cycle. It’s based on the understanding that the change in depth of water is not constant, but rather increases its pace until it reaches maximum ebb or flow, then decreases until slack water. It uses a simple six-hour cycle.
Think about the tempo of the tides like the motion of a swing. As you swing toward the highest point, you slow down before changing direction. Then you accelerate as you swing down, reaching your maximum speed at the bottom. Like the tides, your fastest point is halfway through the cycle.
Most tides are semi-diurnal, meaning there are two high and two low tides a day, approximately 6 hours and 12.5 minutes apart. Between high and low tide the water accelerates to reach maximum speed (max flood or max ebb) then slows until it changes direction (slack water).
During the first hour, the water level rises by 1/12th of the total tidal range. In the second hour, it rises by an additional 2/12ths of the total. During the third and fourth hour, it rises by 3/12ths. Then the increase begins to slow down. In the fifth hour, the water only rises by 2/12ths, and in the sixth hour it rises by 1/12th. The pattern is 1,2,3,3,2,1.
I was going to drop anchor in Provincetown Harbor at 2300, 4 hours after high tide. Given a tidal range of 10 feet, at 4 hours into the cycle, approximately 9/12ths of the water had ebbed, or 7.5ft.
I expected it to drop an additional 2.5ft. My boat draws 4 feet, so I wanted at least 6.5ft of water. Remembering that the Rule of Twelfths is just a rule of thumb and does not include all the details that affect tide height, I sought out 9 feet—better safe than hard aground.
Graphic by Ben Erikson