The rule of twelfths is a rough guide to how the tide rises or falls: one twelfth of the range in the first hour, two twelfths in the second, three in the third and fourth, two in the fifth and one in the sixth.
The tide does not rise or fall at a steady rate. It starts slowly after low or high water, is fastest in the middle of the rise or fall, and slows again near the end. The rule of twelfths turns this into easy arithmetic, assuming about six hours between low and high water:
- first hour: 1/12 of the range;
- second hour: 2/12;
- third hour: 3/12;
- fourth hour: 3/12;
- fifth hour: 2/12;
- sixth hour: 1/12.
So by three hours after low water the tide has made half its rise (1 + 2 + 3 = 6 twelfths), and half the whole rise happens in the middle two hours.
Example. Low water is 0.5 metres at 0900, and high water is 3.5 metres at about 1500, so the range is 3 metres and one twelfth is 0.25 metres. By 1100, two hours after low water, the tide has risen 1/12 + 2/12 = 3/12, which is 0.75 metres, so the height of tide is about 1.25 metres. If the chart shows a bank drying 0.5 metres and your boat draws 1.5 metres, you need a height of tide of at least 2 metres plus a safety margin before you cross. That is reached at about 1200, three hours after low water, so with a margin of half a metre you would wait until about 1300.
The same works on a falling tide, counting from high water.
Limits of the rule:
- it is only an approximation, and many places have tides that do not follow the even curve it assumes;
- the time between low and high water is rarely exactly six hours, so divide the actual interval into six;
- it gives no allowance for weather, which can raise or lower the tide.
Use it for planning and for a quick check, and always leave a margin of extra water under the keel.
More in the book: Chapter 14, Buoys, charts and tides