This interactive worksheet is designed to help learners understand how to calculate a simple Sun Line of Position (LOP) using logarithm and azimuth tables.
The “Celestial Course” page includes eight fully worked exercises, allowing you to train step by step and gain a complete understanding of the method.
From personal experience, I have worked with marine officers who were significantly faster using tables than I was with a calculator—proof that, in skilled hands, this “ancient” technique can still be remarkably effective.
It also provides feedback on the correctness of answers or solutions.
This page presents only the solution to the La Rochelle exercise. I recommend fully mastering it before moving on to the remaining seven.
Apart from the “La Rochelle” exercise, the remaining exercises and their corrected answers are available on the Celestial Course page.
Furthermore, this immediate feedback allows learners to assess their understanding and progress in real time, enabling them to identify areas that need improvement.
The six sections
Ho = observed altitude
P = polar angle
D = sun’s declination
Hc = calculated altitude
Zv = true azimuth
Intercept = difference between Ho and Hc
see: blank worksheet (spreadsheets) PDF file for the tables
see symbols and abbreviations of the worksheet
Our observations on the La Rochelle exercise page
Now that you were supposed to find these red entries from our observations on the La Rochelle exercise page, we can proceed with the calculations.
INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES
Section 1
-Ho- (observed altitude)
We will calculate and explain Ho in two steps:
Step 1: Blue section
Apparent altitude of the sun (theory Ha)
Step 2: Red section
Observed altitude of the sun (theory Ho)
Final result for this part of the worksheet: Hs → Ho.
INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES
Section 2
Local Hour Angle (LHA) and (Polar Angle) P
GHA = _ _ ° _ _ ‘, _
+pp = _ _° _ _ ‘, _
GHA = _ _° _ _’, _
___________________
*G = _ _ ° _ _ ‘, _
_____________________
LHA = _ _ ° _ _ ‘, _
In fact *G add if East / subtract if West
Sun in the East !
How to calculate GHA + pp ( increment)
dead reckoning position L and G
After finding LHA, how to deduce P ?
ロ LHA < 180°
sun in the West P = LHA
ロ LHA > 180°
sun in the East P = 360- LHA
P = _ _ ° _ _ ‘, _
NE / NW / SE / SW
(To clarify, for example P = _ _ ° _ _ ‘, _ SE , We are situated in the Southern Hemisphere, and the sun is in the East at the time of our observation.
Section 3
-D- (Declination of the sun)
D = _ _ ° _ _ ‘, _
correc. d = _ _ ° _ _ ‘, _
___________________
D = _ _ ° _ _ ‘, _
Section 4
Calculating the Computed Height (Hc) of the Sun with the EasySextant Tables
L…………..= _ _ ° _ _ ‘, _
D………….= _ _ ° _ _ ‘, _
__________
(L +/- D)….= _ _ ° _ _ ‘, _
1T 1………….LOG COS L =
2T 1………….LOG COS D =
3T 2….LOG VERSINE P =
_______________________________+
………………LOG 2e Term =
T 3………..COS (L +/- D) =
T4………………..NAT 2eT =
____________________________-
………………………..SIN Hc =
T 5………………………….Hc =
1) Explanation of the logarithms tables.
2) example Hc with the logarithm tables
Once we have examined the preceding examples and exercises, we will complete the La Rochelle (Hc) exercise!
Entries:
L = 46°12′ N
D = 18°39,7′ S
P = 27°33,4′ NE
Section 5
INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES: Zv (true azimuth)
Firstly , Explanation and example Zv calculation with the azimuth tables
Once we have examined the preceding examples and exercises, we will complete the La Rochelle Zv exercise.
Entries:
L = 46°12′ N
D = 18°39,7′ S
P = 27°33,4′ NE
Section 6
Intercept
Ho………….= _ _ ° _ _ ‘, _
Hc…………. = _ _ ° _ _ ‘, _
Intercept…= _ _ ° _ _ ‘, _
intercept = Ho – Hc
Then + Intercept towards the sun / – away from the sun
Seven fully worked examples for practice and revision
After completing the La Rochelle exercise, you can continue practising with seven other fully worked examples. They can also serve later, after a long period without using the tables, as a revision or refresher.
INTERACTIVE CELESTIAL WORKSHEET LOGARITHM/AZIMUTH TABLES: Additional Knowledge
Concerning the time interval between two Lines of Position (LOPs), the process of transferring a LOP, and understanding the uncertainty area associated with a LOP
Sun’s LOP running fix and the uncertainty zone.
Day planning with the two sun LOP’s
Using the local apparent noon sight latitude with the sun is a widely adopted technique in maritime navigation.
It offers a straightforward and swift approach for determining latitude.
Local apparent noon sight latitude
Calculate Local Apparent Noon Time
INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables:
I recommend fully mastering the free La Rochelle exercise on this page. This way, testing your skills on the remaining exercises will be enjoyable. Remember that it is also the groundwork for the stars, moon, and planets.
INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables, The Importance of Persistence and Effort in Achieving Progress
In fact, it’s essential to set realistic expectations and understand that working through the worksheet will take effort and time on your part. However, with dedication and persistence, you will eventually see progress.
Certainly, as you work through the exercises, you may encounter challenges or feel frustrated at times.
Therefore, don’t be discouraged if you don’t see progress right away; it’s all part of the process.
In summary
In summary, remember that progress takes time, effort. If you find yourself feeling overwhelmed or frustrated, however, step away from the worksheet for a little while.
Furthermore, for individuals who are fluent in French, there exists a French rendition of this website that goes by the name www.ladroitedehauteur.com