INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables

The INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables page  is designed to help learners understand how to calculate a simple Line of Position (LOP) of the sun using the tables. It also provides feedback on the correctness of answers or solutions.

INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables, image of the four tools in celestial navigation

While written for the completion of the eight exercises, the page additionally only presents the solution for the La Rochelle exercise.

Furthermore, the interactive worksheet page goes beyond this particular exercise by providing additional examples for each step throughout the entire process.

I recommend fully mastering the free La Rochelle exercise on this page before making a purchase. In addition, within the logarithm and azimuth section, you’ll find five exercises, each complemented by a fully worked-out solution.

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.


CELESTIAL SPREADSHEET logarithm and azimuth tables image logarithm table
Torrey Pines State Beach. Author image: Austin Schmidy

Furthermore, this immediate feedback allows learners to assess their understanding and progress in real time, enabling them to identify areas that need improvement.


INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables: the six sections

INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables,, image 6 sections
The six sections in the worksheet

Ho = observed height

P = polar angle

D = sun’s declination

Hc = calculated height

Zv = true azimuth

Intercept = difference between Ho and Hc

INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables, part1
INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables, part 2
The six sections in the worksheet PNG formated

see: blank worksheet (spreadsheets) PDF file for the tables

see symbols and abbreviations of the worksheet


Norway. Author image: Scott Rettberg

INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables,  red entries on worksheet

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.


let's start with sextant-sun-sight-observations and exercises

Ho (observed height)

Hs …………………. = _ _° _ _’, _

index error…….. = _ _° _ _’, _

Dip………………… = _ _° _ _’, _

 _________________________ +

Ha………………….. = _ _° _ _’, _

sun correct LL …= _ _° _ _’, _ 

__________________________ +

Ho…………………….= _ _° _ _’, _

We will calculate and explain Ho in two steps:


Blue section

CELESTIAL SPREADSHEET logarithm and azimuth tables, image sextant height
CELESTIAL SPREADSHEET logarithm and azimuth tables, blue section
Blue step
CELESTIAL SPREADSHEET logarithm and azimuth tables, blue section with the answers

Apparent height of the sun (theory Ha)

How to calculate Ha

Red section

CELESTIAL SPREADSHEET logarithm and azimuth tables, red section
Red step
CELESTIAL SPREADSHEET logarithm and azimuth tables, red section with the answers

Observed height of the sun (theory Ho)

How to calculate Ho

use of calculator

the 360° formulas

Dip and sun correction tables


John U. Lloyd Beach State Park, Florida. Author image: Georgialh

CELESTIAL SPREADSHEET logarithm and azimuth tables

Local Hour Angle (LHA) and (Polar Angle) P

GHA = _ _ ° _ _ ‘, _                                

+pp = _ _° _ _ ‘, _

GHA = _ _° _ _’, _

___________________

*G =  _ _ ° _ _ ‘, _

_____________________

LHA = _ _ ° _ _ ‘, _

*G add if East / subtract if West

CELESTIAL SPREADSHEET logarithm and azimuth tables, calcul LHA and P

theory GHA

calculate GHA + pp ( increment)

theory LHA and P

calculate LHA and P

dead reckoning position L and G

use of calculator

the 360° formulas

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.


San Diego Author image: Port of San Diego

D (declination of the sun)

D              =  _ _ ° _ _ ‘, _

correc. d = _ _ ° _ _ ‘, _

 ______________________

D           =  _ _ ° _ _ ‘, _   

CELESTIAL SPREADSHEET logarithm and azimuth tables, calcul Declination

theory D

How to calculateD

use of calculator

the 360° formulas


Bocana beach of the Nador region in Morocco. Author image: Sapha Bouamara

INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables

INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables: Hc (calculated height)

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 =

Firstly, Explanation of the logarithms tables.

Secondly, example Hc with the tables

Then, Two exercises Hc with logarithm tables and solutions

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

CELESTIAL SPREADSHEET logarithm and azimuth tables, calcul Hc

INTERACTIVE WORKSHEET (calculator) image sailing vessel under tow
Unknown sailing ship Author image: National Marine Museum U.K.

INTERACTIVE CELESTIAL SPREADSHEET for Logarithm Tables: Zv (true azimuth)

part 1 azimut table:

lc =

dc = ______________+

zc = acute ou obtuse

part 2 azimut table:

Z =

Zv =

Firstly , Explanation and example Zv calculation with the azimuth tables

Then, Four exercises 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

CELESTIAL SPREADSHEET logarithm and azimuth tables, calcul azimuth
True azimuth Zv = 152°,1

The first and third pages serve as separate reminders on how to utilize these azimuth tables, while the second and fourth pages are specifically designed for the La Rochelle exercise.


surfer Eddie Aikan (Hawaii) Author image: Anthony Quintano

Intercept

Ho………….= _ _ ° _ _ ‘, _

Hc…………. = _ _ ° _ _ ‘, _

Intercept…= _ _ ° _ _ ‘, _

CELESTIAL SPREADSHEET logarithm and azimuth tables, calcul intercept

intercept = Ho – Hc

Then + Intercept towards the sun   /  – away from the sun

theory intercept

celestial plotting sheet


INTERACTIVE CELESTIAL SPREADSHEET for Logarithm 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:

Indeed, the answers to the remaining exercises (2 madagascar/3 perth/4 san francisco/5 galapagos/6 tokyo/ 7 pointe-a-pitre/ 8 rotterdam ) can be purchased at the store. They also provide the fully extended logarithm and azimuth tables for download.

I recommend fully mastering the free La Rochelle exercise on this page before making a purchase. 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.


Cap-Pelé Westmorland County, New Brunswick.(Canada) Author: Michel Rathwell

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