Welcome to the NavList Message Boards.


A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Add Images & Files
    Latitude from duration of day
    From: Tony Oz
    Date: 2018 Dec 17, 11:44 -0800

    [Moved from "long by chron" discussion...]

    I want to solve for Lat from known Dec, H and LHA for nothing serious. It came up in my conversation with a friend who is going to go on vacations in Spain. I asked him to measure the day time duration by noticing the Sunrise and Sunset, to halve the difference and to send me an SMS with that value. I was going to tell him his latitude. He did not believe me it was possible - especially by a sliderule alone - so demanded to give him a walk-through of supposed calculations. He looked-up the day-time duration for the place and date he was planning to visit, I bravely embarked in the calculation.

    The original formula was:

    sin(H) = sin(Lat)·sin(Dec) + cos(Lat)·cos(Dec)·cos(t)

    I transformed it to:

    cos(t) = (sin(H) - sin(Lat)·sin(Dec))/(cos(Lat)·cos(Dec))

    Then I declared that at Sunset and Sunrise the H = 0° (which is plain WRONG!) and "simplified" the formula thus:

    cos(t) = -(sin(Lat)·sin(Dec))/(cos(Lat)·cos(Dec))

    From which I could get:

    tg(Lat) = -cos(t)/tg(Dec)

    Doing that stage with the given t = daytime/2 and DecSun for the date I gave him the answewr that was ~2° off the mark. A-ha! he cried, that's more than 200km from my planned hotel!

    I did not expect that neglecting sin(H) = sin(-0°50') that actuallly is the case on sunsets/sunrises would have such an impact on accuracy of results.

    So I had to take my Casio fx-85ES+ and iteratively change the Lat in the original formula untill I got the given daytime duration. My friend insists he won the argument.

    Now I want to show him it is nevertheless possible to calculate his Lat from known Dec and t in one go.

    I think I must use Napier's analogies for that...

    So it is nothing more than a mathematical joke. :)

    Warm regards,


    60°N 30°E

    Browse Files

    Drop Files


    What is NavList?

    Join NavList

    (please, no nicknames or handles)
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.

    Email Settings

    Posting Code:

    Custom Index

    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site