Rule of twelfths

Rule of twelfths

The rule of twelfths^[1] is a rule of thumb for estimating the height of the tide at any time, given only the time and height of high and low water.^[2] This is important when navigating a boat or a ship in shallow water, and when launching and retrieving boats on slipways on a tidal shore.

The rule assumes that the rate of flow of a tide increases smoothly to a maximum halfway between high and low tide before smoothly decreasing to zero again and that the interval between low and high tides is approximately six hours. For the six hours, the rule says that in the first hour after low tide the water level rises by one twelfth of the range, in the second hour two twelfths, and so on according to the sequence - 1:2:3:3:2:1.^[3]

Example calculation

If a tide table gave us the information that tomorrow's low water would be at noon and that the water level at this time would be two metres above chart datum and further, that at the following high tide the water level would be 14 metres. We could work out the height of water at 3:00 p.m. as follows:

• The total increase in water level between low and high tide would be: 14 - 2 = 12 metres.
• 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 us the increase in the water level by 3:00 p.m. as 6 metres.

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 metres.

Obviously the calculation can be simplified by adding twelfths together and reducing the fraction beforehand i.e.

Rise of tide in three hours

Caveats

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, such as Poole Harbour^[4] or the Solent^[5] where there are "double" high waters or Weymouth Bay^[6] where there is a double low water.

The rule assumes that the period between high and low tides is six hours but this is an underestimate and can vary anyway.

References

1. ↑ Rule of Twelfths for quick tidal estimates
2. ↑ The Outboard Boater's Handbook: Advanced Seamanship and Practical Skills, written by David R. Getchell, published by International Marine, page 195, ISBN 978-0-07-023053-8
3. ↑ The weekend navigator: simple boat navigation with GPS and electronics, written by Robert J. Sweet, page 162, ISBN 978-0-07-143035-7
4. ↑ http://www.shrimperowners.org/sitefiles/Poole%20Tides.pdf
5. ↑ English Channel Double Tides
6. ↑ http://www.visitweymouth.co.uk/downloadForms/TideTables2010.pdf

Physical oceanography
Waves	Airy wave theory Ballantine scale Benjamin–Feir instability Boussinesq approximation Breaking wave Clapotis Cnoidal wave Cross sea Dispersion Edge wave Equatorial waves Fetch Gravity wave Green's law Infragravity wave Internal wave Kelvin wave Kinematic wave Longshore drift Luke's variational principle Mild-slope equation Radiation stress Rogue wave Rossby wave Rossby-gravity waves Sea state Seiche Significant wave height Sneaker wave Soliton Stokes boundary layer Stokes drift Stokes wave Swell Trochoidal wave Tsunami megatsunami Undertow Ursell number Wave action Wave base Wave height Wave power Wave radar Wave setup Wave shoaling Wave turbulence Wave–current interaction Waves and shallow water one-dimensional Saint-Venant equations shallow water equations Wind wave model
Circulation	Atmospheric circulation Baroclinity Boundary current Coriolis effect Downwelling Eddy Ekman layer Ekman spiral Ekman transport El Niño Southern Oscillation General Circulation Model Geostrophic current Global Ocean Data Analysis Project Gulf Stream Halothermal circulation Humboldt Current Hydrothermal circulation Langmuir circulation Longshore drift Loop Current Maelstrom Modular ocean model Ocean dynamics Ocean gyre Princeton ocean model Rip current Subsurface currents Sverdrup balance Thermohaline circulation shutdown Upwelling Whirlpool World Ocean Circulation Experiment
Tides	Amphidromic point Earth tide Head of tide Internal tide Lunitidal interval Perigean spring tide Rip tide Rule of twelfths Slack water Tidal bore Tidal force Tidal power Tidal race Tidal range Tidal resonance Tide gauge Tideline
Landforms	Abyssal fan Abyssal plain Atoll Bathymetric chart Coastal geography Cold seep Continental margin Continental rise Continental shelf Contourite Guyot Hydrography Oceanic basin Oceanic plateau Oceanic trench Passive margin Seabed Seamount Submarine canyon Submarine volcano
Plate tectonics	Convergent boundary Divergent boundary Fracture zone Hydrothermal vent Marine geology Mid-ocean ridge Mohorovičić discontinuity Vine–Matthews–Morley hypothesis Oceanic crust Outer trench swell Ridge push Seafloor spreading Slab pull Slab suction Slab window Subduction Transform fault Volcanic arc
Ocean zones	Benthic Deep ocean water Deep sea Littoral Mesopelagic Oceanic Pelagic Photic Surf Swash
Sea level	Deep-ocean Assessment and Reporting of Tsunamis Future sea level Global Sea Level Observing System North West Shelf Operational Oceanographic System Sea-level curve Sea level rise World Geodetic System
Acoustics	Deep scattering layer Hydroacoustics Ocean acoustic tomography Sofar bomb SOFAR channel Underwater acoustics
Satellites	Jason-1 Jason-2 (Ocean Surface Topography Mission) Jason-3
Related	Argo Benthic lander Color of water DSV Alvin Marginal sea Marine energy Marine pollution Mooring National Oceanographic Data Center Ocean Ocean exploration Ocean observations Ocean reanalysis Ocean surface topography Ocean thermal energy conversion Oceanography Pelagic sediment Sea surface microlayer Sea surface temperature Seawater Science On a Sphere Thermocline Underwater glider Water column World Ocean Atlas
Category Commons