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.
The primary focus of our website is to offer guidance on the precise calculation of the Line of Position (LOP).
On this page, 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°.
Azimuth Zv: counted from the north cardinal point, from 0° to 360° (clockwise)
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: Part I and Part II, A Quick Overview
Part I
INPUT:
P and L → lc
P and D → dc
OUTPUT:
lc and dc → zc
Z = acute or obtuse
Part II (two volumes: acute and obtuse)
INPUT:
L et zc. (From Part I)
pages 0° to 90° acute or
pages 90° to 180° obtuse (From Part I)
OUTPUT:
Z
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:
explanation through an example.
Azimuth tables: part 1
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°)
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
We no longer use the rule of signs but same name or 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.
( 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
obtuse
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
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.