# Tide calculation

Tide calculation is a term used in nautical navigation . With the help of tide calculations, attempts are made to make predictions about water levels in tidal waters . Typical calculations provide the high and low tide times and heights of a given location. Further calculations determine the water levels at times between high and low water. The calculations usually use tide tables. In Germany, tide tables are published annually by the Federal Maritime and Hydrographic Agency (BSH). The British United Kingdom Hydrographic Office publishes the Admiralty Tide Tables . These contain tide tables for a large number of locations around the world. When calculating tides using tide tables, only the known gravitational influences of the moon and sun can be taken into account. Other influences such as the effect of the wind must be estimated using other calculation models.

In exams for certain sailing licenses such as the Sportküsten- or the Sportseeschifferschein , tasks on calculating tides have to be solved. For example, the water depth is to be determined for a given location at a specific date and time. Another type of task asks for the earliest possible time at which a shoal can be crossed when the water is flowing. This requires knowledge of the depth of the chart and the draft of the vessel.

## Definitions of terms

Illustration of some terms.
Illustration of terms related to the course of the water level over time.

The two pictures illustrate some abbreviations and terms that are common in tidal science. The sinusoidal curve describes the course of the water level over time. The following table explains the abbreviations used.

abbreviation term
FD Case duration
H Height of the tide, i.e. the water level at a given point in time
HW Flood
HWH High water level
HWZ Flood time, i.e. the time at which the flood occurs
KT Chart depth, i.e. the depth indicated on the nautical chart .
MW Mean water
NW Low tide
NWH Low water level
NWZ Low water time
SD Climb time
SKN Nautical chart zero
TF Tide fall
TG Draft
TS Tide rise
WT Water depth
WuK Water under the keel

The German tide tables use Lowest Astronomical Tide (LAT) as sea chart zero (SKN). Other terms are related to the 'age of the tide'. The age of the tide determines whether a certain date is spring , midday or sipping time . The following table summarizes some of the abbreviations and terms used.

abbreviation term
MNpD Average Nippsteig or Nippfall duration
MNpHW Medium nip flood
MNpNW Medium nipp low water
MSpD Medium jumping climb or jumping fall duration
MSpHW Medium spring flood
MSpNW Medium spring low water
NpHW Nip flood
NpNW Nipp low water
NpTH Nipptidenhub
SpHW Spring flood
SpNW Jumping low water
SpTH Spring tide range

For example, MSpHW is the height of the flood averaged over many periods at spring time.

## German tide tables

The tide tables published by the BSH differentiate between reference locations and connection locations. The high and low water data for the reference locations can be read directly from the tables. A reference point is assigned to each connection point. The tabulated sizes are only listed as differences for connection locations, which must then be added to the values ​​of the respective reference location. The tide tables consist of four parts: Part 1 contains detailed projections for the European reference points, while Part 2 lists tidal differences for the European connection points; Parts 3 and 4 contain auxiliary tables and tide maps.

### Reference locations

Part 1 of the tide tables contains the geographic coordinates of the reference locations for each reference location and a small map showing the location of the location. In tabular form, it is then indicated for each day at what time high or low tide occurs and at what height. In these tables you can also find information about the respective moon phase . Furthermore, under the tables you can find the time zone to which the specified values ​​refer. Finally, at each reference point there is a diagram that describes the mean temporal course of the water level for jumping time and sipping time. From these diagrams, water levels can be determined graphically at times between high and low tide. The latter applies to both reference and connection locations with an accuracy that is sufficient in practice.

Example: The following table shows an excerpt from Part 1 of the 2010 tide tables for the reference location Wilhelmshaven .

July
time height
27 1 44 4.6
7 45 0.7
Tuesday 13 53 4.9
20 11 0.6
UTC + 1h00min (CET)

Accordingly, the afternoon flood occurs on Tuesday, July 27, 2010, at 1.53 p.m. with a height of 4.90 m. The time zone must be taken into account. Since the table values ​​(in the Wilhelmshaven case) are given in Central European Time (CET), the flood occurs at 2:53 p.m. Central European Summer Time . The specified water levels refer to LAT . The map depth ( KT ) has to be added to these in order to get the water depth (WT).

### Connection locations

The following table shows an entry from Part 2 of the 2010 tide tables.

 No. place Geographical location mean time differences medium height differences width length HW NW HW NW ° ' ° ' h min Tf.5 h min Tf.5 m m m m Reference location: SpHW NpHW SpNW NpNW 512 Wilhelmshaven 53 ° 31'N 8 ° 09'E 4.8 4.3 0.6 1.1 754 Wangerooge, Long Reef 53 48 7 56 −1 07 −0 38 −1.2 −1.0 −0.1 −0.2

Information on the respective reference location is printed in bold. The geographical coordinates are first given for each connection point. The entry times of high and low water are listed as differences to the respective times of the reference point. Finally, the table shows the height differences between high and low water. These differences to the heights of the reference point depend on the age of the tide. At midday the respective mean values ​​are to be used, formed from the values ​​of the jumping and sipping times.

For individual connection locations, additional corrections to the HWZ and NWZ must be taken into account. In such cases there is an abbreviation in the column labeled 'Tf.5' in the table above. The additional corrections depend on the HWZ or NWZ of the reference location and are determined using a table in Part 3 of the tide tables.

Example: Using the example above, we calculate the afternoon high tide and the subsequent low tide on July 27, 2010 for Wangerooge , Long Reef. First, the age of the tide must be determined. Table 2 from Part 3 of the tide tables serves for this purpose. The jumping delay is already taken into account in this table, so that the jumping time for the specified date results. The following table illustrates the calculation to be carried out.

place HWZ HWH NWZ NWH
Projections Wilhelmshaven 13 53 4.9 20 11 0.6
differences Wangerooge, Long Reef −1 07 −1.2 −0 38 −0.1
Result Wangerooge, Long Reef 12 46 3.7 19 33 0.5

Here, too, the time zone must be taken into account, and here too the heights relate to LAT.

## Twelfth rule

Illustration of the rule of twelfth. The dashed line compares the approximate values ​​with the course of a sinusoid.

The twelfth rule offers a simple procedure to estimate water levels at points in time between high and low tide or between low and high tide. It can only be used with sufficient accuracy if the tide is sinusoidal . The twelfth rule assumes that the water level changes by 1/12 of the tidal range in the first hour after low or high tide . In the second, third, ..., sixth hour the change is 2/12, 3/12, 3/12, 2/12 or 1/12 of the tidal range.

Example: At one location the low water occurs at 6.25 a.m. with a height of 1.20 m. The subsequent flood has a height of 3.20 m. The tidal range is therefore 3.20 m − 1.20 m = 2 m. What is the tide at 8.25 a.m.? Since the mentioned point in time is two hours after the low tide, a height difference of 1/12 + 2/12 = 1/4 of the tidal range, i.e. (1/4) · 2 m = 0.5 m, can be expected. This height difference must be added to the low water height, so that the tide height is 1.20 m + 0.50 m = 1.70 m at 8.25 a.m.