Logarithm Tables and Astronavigation Option: proposing an alternative approach to calculate your position at sea without the use of a scientific calculator, based on logarithm and azimuth tables
This page is important, as it forms the basis of the “Logarithmic” menu with the links below.
ALL THE PAGES IN RELATION TO THE LOGARITHM TABLES
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EXPLANATION OF THE LOGARITHM TABLES
EXAMPLE OF HOW TO CALCULATE THE ALTITUDE OF THE SUN (Hc) WITH THE TABLES
TWO EXERCISES TO CALCULATE THE ALTITUDE OF THE SUN (Hc)
ADDITIONAL
LOGARITHMS OF WHOLE NUMBERS(Table 4) (Explanation of how this table works — not very intuitive — specifically adapted for use as an anti-log in our particular applications.)
SAME NAME / NOT SAME NAME Method used in our spreadsheet for logarithms calculation .
ANCESTRAL CELESTIAL DOUWES FORMULA (Theoretical explanation of the formulas used, particularly suited to logarithm tables — included not because this knowledge is essential, but to satisfy deeper curiosity.)
The five tables required for the logarithmic method:
Logarithm Tables and Astronavigation Option: Introduction
Logarithm tables and celestial navigation: these five tables, should be used in chronological order to gradually fill in the spreadsheet and obtain the calculated altitude of the sun.
NOTE:
Common logarithm tables used in the U.S.
Common logarithms (base 10) use bar notation to simplify negative values. For example, log(cos(16°)) ≈ −0.017158. You will find 9.982842 in the American tables (they added 10). This method presents the logarithm in a more user-friendly way.
I meticulously composed this chapter for individuals interested in alternative or 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.
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.
Course Method:
In fact, as a marine student, I learned to calculate the height of the sun without a calculator.
Also, I use logarithm tables to calculate the sun’s height, mainly using Douwes’ formulas.
As a matter of fact, this method follows the same principle as using a calculator. ( see worksheet for manual completing )
Specifically, you should start the LaRochelle exercise.
The logarithm tables: Table 1 to 5
In fact, the dedicated tables require downloading approximately 190 pages for five different tables, and the tables must be used in chronological order.
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
exercises
To sum up, there are four exercises using logarithm tables, all fully solved and freely accessible. (See the links at the top of this page: one example, two exercises, and the fourth — the La Rochelle exercise, available in the calculator or tables option.)
Also 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.
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Course Suitability for Marine Students
However, this course, based on the alternative approach using logarithm tables, is less useful 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.
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 with the Douwes formula 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 (see below).
HAVE FUN !
**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.
