Planning for Tides & the Rule of Twelfths

Tides are the vertical rise and fall of sea level caused by the combined effects of the gravitational forces exerted by the Moon and the Sun, and the rotation of the Earth
Tidal terms. Diagram by Ulamn/Wikipedia

Very simply stated, tides are the vertical rise and fall of sea level caused by the combined effects of the gravitational forces exerted by the Moon and the Sun, and the rotation of the Earth. Depending on the size of body of water and its location on Earth, tides can be very significant or practically nil.  Predict with the Rule of Twelfths

According to the National Atmospheric and Oceans Administration, if the Earth were a perfect sphere without large continents, all areas on the planet would experience two equally proportioned high and low tides every lunar day. The large continents on the planet, however, block the westward passage of the tidal bulges as the Earth rotates. Unable to move freely around the globe, these tides establish complex patterns within each ocean basin.

Predicting tides combines an adequate sample of local tidal observations with astronomical theory. In the past, these predictions were printed in books known as tide tables, and it was necessary to have the yearly volume for finding the height of tide for ports in a particular cruising area. Depending on the design of the tide table mathematical formulas, such as the Rule of Twelfths, were used by boaters to determine the height of tide at a boat’s location for a given time of day. Today, chart plotters and smartphone apps contain up to the minute tidal height predictions for the closest tidal station to a vessel’s location, worldwide, at the tap of a button or soft key. 

Having the knowledge of how to use the height of tide at anytime, anywhere a yacht cruises, is central to the safety of the vessel. When cruising in tidal areas, whether the range of tide on a given day is two feet or 12 feet, the ability to determine clearances under the keel will determine whether a vessel can safely anchor without running aground during the fall of the tide overnight.

 

A simple diagram showing chart datum

TIDAL HEIGHT DEFINITIONS
Chart datum is the level of water from which charted depths displayed on a chart are measured. Charts issued by the United Kingdom use Lowest Astronomical Tide (LAT) as chart datum, while charts produced by U.S. government agencies use Mean Lower Low Water (MLLW) as chart datum. Lowest astronomical tide is the height of sea level at the lowest possible theoretical tide which can be predicted to occur using gravitational effects of the Sun and Moon only, under average meteorological conditions. Mean lower low water is the average height of the lowest tide recorded at a tide station during each day of the sampling period.

Charted depth is the depth of the water, below chart datum, displayed as soundings on a chart in feet, meters or fathoms.

Height of tide is the height of sea level above chart datum at any given time. The height of tide peaks at the moment of high water or low water, and then falls or rises in between the daily patterns of highs and lows.

Neap tides occur when the Sun and the Moon appear at right angles to each other in the sky. This occurs at the First Quarter and Last Quarter moons. Neap tides are not as high and not as low as spring tides.

Spring tides occur when the Sun and the Moon appear next to each other or opposite each other in the sky. This occurs at the New Moon and Full Moon. Spring tides have higher high tides and lower low tides than neap tides.

SOLVING TIDAL HEIGHT CALCULATIONS
When anchoring overnight, using some basic formulas (such as the rule of 12ths), a depth sounder and that evening’s tidal predications give a captain the tools needed to help locate that perfect spot within an anchorage. 

The depth finder’s readings adjusted to the waterline can be written as:

Depth of water = Charted depth plus the height of tide

The depth finder’s readings adjusted to the bottom of the keel can be expressed as:

Clearance below the keel = Depth of water minus the vessel’s draft 

The crux of the situation, whether the boat will be sitting in the mud, on some rocks or floating when low tide occurs during the night can be calculated with this formula:

Clearance below keel after a predicted fall of tide = Depth of water minus the fall of tide minus the draft 

Every captain has their own minimum clearance below the keel at which they can sleep comfortably while at anchor. Knowledge of local weather conditions, such as a strong offshore breeze, which can push water out of an anchorage and cause lower tides than those predicted, require increasing that margin of safety.

RULE OF TWELFTHS

The rule of twelfths is an approximation to a sine curve. It can be used as a rule of thumb for estimating a changing quantity where both the quantity and the steps are easily divisible by 12. Typical uses are predicting the height of the tide.

Graph showing relationships between the rule of twelfths (colored bars), a sine wave (dashed blue curve) and a clockface if high tide occurs at 12:00. Diagram by CMG Lee/Wikipedia
Graph showing relationships between the rule of twelfths (colored bars), a sine wave (dashed blue curve) and a clockface if high tide occurs at 12:00. Diagram by CMG Lee/Wikipedia

Example:
If a tide table gives the information that tomorrow’s low water would be at noon and that the water level at this time would be two meters above chart datum, and that at the following high tide the water level would be 14 meters, then the height of water at 3:00pm can be calculated as follows:

  • The total increase in water level between low and high tide would be: 14 – 2 = 12 meters.
  • In the first hour the water level would rise by 1 twelfth of the total (12 m) or: 1 m
  • In the second hour the water level would rise by another 2 twelfths of the total (12 m) or: 2 m
  • In the third hour the water level would rise by another 3 twelfths of the total (12 m) or: 3 m
  • This gives the increase in the water level by 3:00 p.m. as 6 meters.

This represents only the increase – the total depth of the water (relative to chart datum) will include the 2 m depth at low tide: 6 m + 2 m = 8 meters.

The calculation can be simplified by adding twelfths together and reducing the fraction beforehand:

Rise of tide in three hours 

The rule is a rough approximation only and should be applied with great caution when used for navigational purposes. Officially produced tide tables should be used in preference whenever possible. The rule assumes that all tides behave in a regular manner, this is not true of some geographical locations, the rule also assumes that the period between high and low tides is six hours but this is an underestimate and can vary. (Source: Wikipedia.) 

Capt. Jeff Werner
Capt. Jeff Werner is a Senior Instructor with International Crew Training in Ft. Lauderdale, and is a 22 year veteran of the yachting industry. www.yachtmaster.com