Almanacs and many other nautical publications contain predictions of the times of high and low tides at many major standard ports
. Also listed are differences in times of tides from these ports
for additional secondary ports. To work with this succinct data we need two extra tools:
Rule of Twelve
To interpolate between high and low water heights we use the Rule of Twelve. We assume the tidal curve to be a perfect sinusoid with a period of 12 hours*. The height changes over the full range in the six hoursP between HW and LW.
* During first hour after HW the water drops 1/12th of the full range.
* During the second hour an additional 2/12th.
* During the third hour an additional 3/12th.
* During the fourth hour an additional 3/12th.
* During the fifth hour an additional 2/12th.
* During the sixth hour an additional 1/12th.
Hence, two hours after the HW the water has fallen 3/12 (1/4) of the full range.
Corrolorary - Rule of Thirds:
It’s readily apparent that the (2) 6 hour* half-cycles (during which the tide either rises or falls) can each be broken down into thirds.
□ During the first third (2 Hrs) the water level changes 1/4 of full Range.
□ During the middle third (2 Hrs) the water level changes ½ of full Range.
□ During the last third (2 Hrs) the water level changes 1/4 of full Range.
Rule of Seven:
To interpolate between spring and neap tides. Since the change from spring range to neap range can be assumed linear (instead of sinusoid), each day the range changes with 1/7th of difference between the spring and neap ranges.
Hence, the daily change in range is (spring range - neap range) ÷ 7.
* Actually, there are about 12 Hours, 25 minutes between high tides, so tidal flow reverses every 6 Hours 12 ½ Minutes.