Astronavigation and Logarithm tables Option

Astronavigation and Logarithm tables Option: proposing an alternative approach to calculate your position at sea without the use of a scientific calculator, based on logarithm and azimuth tables

Astronavigation and Logarithm Option, image of a page of the table logarithms  whole numbers
example of page 4200 to 4600 from the Logarithms of whole numbers tables (23 pages)

The classic table ‘Logarithms of whole numbers’ is utilized for calculating a line of position without a calculator.

Zaliznyy Port, Kherson region, (Ukraine). Author image: Грибюк Руслан Володимирович

I meticulously composed this chapter for individuals displaying erratic behavior and those drawn to ancestral methods. However, when I start sailing again, these tables arranged in chronological order would have the best place on my sailing boat, and I would never use a calculator again.

alternative approach based on  tables image logarithm table
Astronavigation and Logarithm tables Option. Tapley aboard the bark Saint James
Mrs. Tapley sailed with her husband aboard the bark Saint James during the late 19th century.source National Parks
Logarithm table method

Logarithms are a powerful mathematical tool that allows for simplifying calculations by transforming multiplications into additions and divisions into subtractions.

This can be particularly useful when you have to perform complex calculations without the help of a calculator.

This course does not require an understanding of logarithms, but rather the use of logarithm tables.

autumnal equinox sunrise at North Palm Beach, Florida. Author image: Bob Peterson

Astronavigation and Logarithm tables Option:

Course Method:

As a marine student, I learned to calculate the height of the sun without a calculator.

I use logarithm tables to calculate the sun’s height, mainly using Douwes’ formulas. This method follows the same principle as using a calculator. ( see worksheet for manual completing )

Naturally, you are accompanied by the interactive worksheet for these logarithm tables.

Specifically, you should start the LaRochelle exercise. At the bottom of this page, you will find the button that will take you to the interactive worksheet page for tables.

Rocky beach south of the dunes near Bamburgh Castle Image Author: pam fray

The logarithm tables: Table 1 to 5

In fact, the dedicated tables requires downloading approximately 190 pages for five different tables, and the tables must be used in chronological order.

Astronavigation and Logarithm tables Option, 1 to 5 logarithm closed
The author developed these tables with the help of Google Sheets.
The five tables

The five tables necessary to obtain the calculated height (Hc)

  • Table 1: log cosine
  • Table 2: log versine
  • Table 3: natural cosine
  • Table 4: logarithms of whole numbers
  • Table 5: natural sine

The logarithm tables open and closed

Astronavigation and Logarithm tables Option, 1 to 5 logarithm open
The author developed these tables with the help of Google Sheets.
Astronavigation and Logarithm , image of the 5 tables foe logarithm solution

Astronavigation and Logarithm Option

The azimuth table

In addition, to determine the direction of the sun’s azimuth, you can download the azimuth tables in the store consisting of 47 pages.

Furthermore, the author developed the azimuth tables using Google Sheets.

Shot at Sagar Nagar Beach Visakhapatnam. Author image: Kalidhar P


To sum up, In the interactive worksheet page (Hc section) there are four exercises utilizing logarithm tables, fully solved and are freely accessible.

Also in the interactive worksheet page (Zv section) there are five exercises utilizing azimuth tables that have been fully solved and are freely accessible.

After completing the ‘La Rochelle’ exercise, however, for the remaining seven exercises in the exercise section, you will need to purchase the solution worksheets from the store.

Also, they will come with the fully extended tables.


The Scavaig River meets the sea .[Yorkshire Dales] . Author image: Gordon Hatton

Astronavigation and Logarithm Option

Course Suitability for Marine Students

However, this course which is based on the alternative approach based on logarithm tables is less enriching for students in merchant marine schools. France formalized the use of calculators around 1980.

Undoubtedly, This course primarily caters to sailors who navigate ocean passages around the world.

Certainly, also intended for both professional mariners who operate trans ocean conveying vessels and mariners who participate in offshore races without electronic instruments.

Astronavigation and Logarithm Option, voyage planning
Classic volume on ocean voyage planning

alternative approach based on tables

In fact, with some practice, one can become faster with tables than with a calculator.

During my time as a trainee, I completed more than 300 sight calculations with the officers on board.

I almost always used my calculator, while they always used logarithm tables. However, I never beat them in terms of speed.

For instance, this method was used in the Dutch merchant navy.

From the end of the 18th century until the end of the 20th century

And its worksheet is printed in the Dutch navigation tables “Zeevaartkundige Tafels,” edition 1976.


Between the River and the Deep Blue Sea The estuary at Lossiemouth. Author image: Ann Harrison

**I found the name Douwes thanks to M Paul Bedel

He wrote an incredible book “navigation tables 1840-1980” Collection of the Bureau des longitudes.

The author, M Paul Bedel, is a professor and inspector general of maritime education in France.