A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 Feb 15, 18:54 -0800
Alex, you said that you're looking for tidal harmonics for "British harbors. US (N America colonies) harbors."
For locations in Britain, you may have to dig around a bit because these data are still protected by copyright. For US locations, it's easier. Go to the NOAA tides and currents harmonic constituents page here: https://tidesandcurrents.noaa.gov/stations.html?type=Harmonic+Constituents. Select a location. For example, you could select "The Battery" at the southern tip of Manhattan. That links to this page: https://tidesandcurrents.noaa.gov/harcon.html?id=8518750. You'll find a list there:
N: name amp phase
1: M2 2.188 234.0°
2: S2 0.42 253.3°
3: N2 0.509 217.8°
4: K1 0.331 104.3°
5: M4 0.082 328.3°
6: O1 0.171 106.5°
The amplitudes are in feet and the phases in degrees. There are other components, but they are smaller and could be counted as noise especially since weather-driven variations in water level could easily exceed those smaller components. The amplitudes each multiply a sinusoidal term with a unique frequency related to astronomical factors. The phases are key for timing, of course. Some of the names on the terms have obvious meanings. The M2 tidal component is the semi-diurnal lunar term ("M" for Moon, "2" for twice daily). The S2 component is the semi-diurnal solar term. N2 depends on the lunar perigee, and K1 and O1 are the principal daily factors which are driven by the Moon's altitude in the sky at upper and lower transit and therefore basically declination-dependent.
There are some fixed properties of the tides that you can derive from the harmonics. For example, there is the so-called establishment of the tide. That's the number of hours after meridian passage of the Moon before the next high tide. Similar rules work for low tides. In Mystic, Connecticut, for example, low tide occurs about three hours after the Moon's meridian passage. Similarly the phase difference between M2 and S2 (when properly related to their rates, etc.) will tell us how much the Sun tides lead or lag the Moon tides, and that helps to determine the date of Spring tides. Along the New England coast, in defiance of common knowledge, the maximum monthly tides (Spring tides) occur about a day after New Moon and Full Moon, for example.
Note that these dependable properties are not present, or they are much more difficult to define, in areas with mixed tides (which alternate between semi-diurnal and diurnal over the course of a month) as on the US west coast. Out there, you basically have to run the numbers. Fortunately for your book (I'm imagining you writing a novel about British-American naval affairs in the late 18th century...), the tides on both sides of the North Atlantic are safely semi-diurnal almost everywhere.
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA