Sun’s azimuth tables at sea

This section of our self-instruction website highlights the significance of comprehending the sun’s azimuth tables at sea, a critical element in the calculation of the Line of Position (LOP), also commonly known as the Sumner line.

Sun's azimuth tables at sea, image sun's path

The primary focus of our website is to offer guidance on the precise calculation of the Line of Position (LOP).

 Pohnpei (Federated States of Micronesia) / Author image: Patrick Nunn

Explanation and example of the sun’s azimuth with azimuth tables.

Sun’s azimuth tables at sea: AZIMUTH (Zv)

Azimuth is a mathematical concept used in navigation and surveying to describe the direction of a point relative to a reference direction, typically north.

It is usually measured in degrees, clockwise from north, and ranges from 0° to 360°.

Theory true azimuth (Zv) image different local horizons
Sun's azimuth tables at sea, image local horizon
local horizon (blue), true azimuth Zv and height (H) of the sun

Azimuth Zv: counted from the north cardinal point, from 0° to 360° (clockwise)

Sun's azimuth tables at sea, image azimuth of the sun

Sun’s azimuth tables at sea:

Introduction azimuth tables

Technique used: azimuth by time

Hence, after finding the calculated height, the azimuth Zv must be found to within half a degree.

Firstly, the tables I present are slightly larger than the classic azimuth tables, as the reading is always from top to bottom and not from top to bottom and bottom to top, a technique used to reduce the amount of sheets but which can sometimes be tedious to use.

I do not see any other simple method for explaining azimuth tables other than by example.

Furthermore, on this page, you will find an example of how to calculate the azimuth with the tables

additionally, four exercises with their answers, and a fully worked-out solution for the La Rochelle exercise as well—all for free!

The azimuth tables sheets necessary for these exercises are provided, but downloading the full set of these tables you need to buy them in the store.

Undoubtedly using the azimuth tables can be a bit laborious at first, but after completing the exercises and practicing again, you will quickly become accustomed to them.

In fact, you may find that you become more proficient with the tables than with using a scientific calculator to calculate Zv.

Moreover, the clarifications presented in the margins of every table sheet are very beneficial, particularly after an extended period of non-utilization.

On the other hand, using a calculator and working with formulas that require a lot of brackets can sometimes be a hassle.


Azimuth calculation with tables

worksheet for the tables
Sun's azimuth tables at sea, image worksheet for tables
Sun's azimuth tables at sea, image worksheet for tables part 2
Sun's azimuth  with azimuth  tables: detail of the worksheet
detail of the worksheet

Sun’s azimuth tables at sea: Part I and Part II, A Quick Overview


Part I

Sun's azimuth tables at sea, image azimuth table part I
In the right margin of each page in Part I are the two tables same or not same name

INPUT:

P and L → lc

P and D → dc

Sun's azimuth tables at sea, image table in right margin table part I

OUTPUT:

lc and dczc

Z = acute or obtuse

Sun's azimuth tables at sea, image same name/not same name

Part II (two volumes: acute and obtuse)

Sun's azimuth tables at sea, image azimuth table part II
In the right margin of each page in Part II are the two tables latitude N/S

INPUT:

L et zc. (From Part I)

pages 0° to 90° acute or

pages 90° to 180° obtuse (From Part I)

OUTPUT:

Z

Sun's azimuth tables at sea, image table in right margin table part II

Transform Z → Zv (True azimuth)


complementary information:

lc, dc and zc do not have any specific meaning in navigation but are used only for these tables.

Z is the azimuth between 0° and 180°, while Zv is the true azimuth between 0° and 360°

The tables have been calculated using the following formulas:

Sun's azimuth tables at sea, image formulas azimuth table part I
Sun's azimuth tables at sea, image formulas azimuth table part II

Sun’s azimuth tables at sea:

explanation through an example.

Azimuth tables: part 1
let's start with sextant-sun-sight-observations and exercises

explanation through an example.

(L)atitude = 12° N

(D)eclination = 17° S

(P)olar angle = 10° NW

(the Northern Hemisphere), sun in the West

(Do not confuse it with West longitude.)

Find Zv with azimuth tables

You also find this page see below

Page P = ( 8 to 14°)

image page example, azimuth table part I

P and L → lc = 1,21

P and D → dc = 1,76

In the right margin of each page in Part 1 are the two tables below

image table in right margin table part I

We no longer use the rule of signs but same name or not same name !!!

same name/not same name

all values will always be positive

In our example:

L et D NOT SAME name

(L = North et D = South)

P < 90°

Conclusion:

zc = lc + dc (1,21 + 1,76 = 2,97)

Z = obtuse (entre 90° et 180°)

Next, we go to part 2


Azimuth of the sun calculation with tables

Azimuth tables: part 2 (Two volumes)

Note that the acute section ranges from 0° to 90° degrees, while the obtuse section ranges from 90° to 180° degrees.

With latitude L = 12° N and zc = 2.97 we obtain Z.

Sun's azimuth tables at sea, image table in right margin table part II

( Z is obtuse in our example)

In both cases (acute and obtuse), the horizontal line of the latitude 12° N displays somewhere the value zc = 2.97.

Therefore, disagreeably, mixing acute and obtuse angles is where we easily make a mistake (see below)!

acute

Sun's azimuth tables at sea, image table in right margin table part II (acute)
the acute pages part 2 (0° jusqu’à 90°)

obtuse

Sun's azimuth tables at sea, image table in right margin table part II (obtuse)
the obtuse pages part 2 (90° jusqu’à 180°)

Z is therefore 161°

But we need to find Zv (modern notation of 0° – 360°)

Also, in the right margin of each page in Part 2 are the two tables below

 image table in right margin table part II

Avec Z = 161° et P = NW

Zv = 360° – Z

Zv = 360° – 161° = 199°


Sun’s azimuth tables at sea:

Once you grasp the concept of these azimuth tables, proceed to the four exercises utilizing them.