Welcome to the NavList Message Boards.

NavList:

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

Compose Your Message

Message:αβγ
Message:abc
Add Images & Files
    Name or NavList Code:
    Email:
       
    Reply
    Re: 1984 Bowditch question
    From: Robin Stuart
    Date: 2016 Jul 27, 10:13 -0700

    Stan,

            While I now appreciate that the accuracy of the “exact” form of the dip short formula is not your focus the claim that it is "exact" for thr refraction model adopted might be a bit of a stretch. The derivation of the Distance by Vertical Angle Measured Between Sea Horizon and Top of Object Beyond Sea Horizon formula was discussed here previously see

    https://NavList.net/m2.aspx/dip-dip-short-distance-off-with-buildings-FrankReed-jan-2006-w27040

    https://NavList.net/m2.aspx/dip-dip-short-distance-off-with-buildings-FrankReed-jan-2006-w27094

    Refraction is introduced by increasing the Earth’s radius everywhere by a factor 1/(1- β) where β=0.1684. This is a surprising good approximation but an approximation to real refraction models nevertheless. For arguments sake let’s call it the “refraction model”. The derivation of the Distance by Vertical Angle Measured Between Sea Horizon and Top of Object Beyond Sea Horizon uses a series expansion of sine and cosine and so is not exact in that respect.

    It is of course possible to calculate the dip short exactly within the “refraction model” by simple trigonometry and I’ve added the result to the bottom of the pdf file. From it we see a further inconsistency in the “exact” result. tan Ds differs from Ds by cubic terms in Ds however cubic terms in ds/r are dropped from the right hand side. However in your case of extremely close short dip Ds is large compared to ds/r the use of tan Ds would appear to be justified. Whether the formulas are accurate enough in practice to justify the use of tan Ds over Ds is another question.

    In the case you cite of height of eye of 7ft and 50 yards give

    “approximate”                      2°40.43’

    “exact”                                 2°40.32’

    "refraction model" exact      2°40.32’

    It would be pretty straightforward for someone with a theodolite to actually check how well the formulas do for a dip short at 50 yards. I understand that it standard practice in surveying to account for refraction by adjusting the Earth’s radius.

    Regards,

    Robin Stuart



    File:

      

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    NavList is a community devoted to the preservation and practice of celestial navigation and other methods of traditional position-finding. We're a group of navigators, navigation enthusiasts and hobbyists, mathematicians and physicists, and historians interested in all aspects of navigation but primarily those techniques which are non-electronic.

    To post a message, if you are already signed up as a NavList member, start a new discussion or reply to any posted message and use your posting code (this is a simple low-security password assigned when you join). You may also join by posting. Your first on-topic messsage automatically makes you a member, and a posting code will be assigned and emailed to you for future posts.

    Uniquely, the NavList message boards also permit full interaction entirely by email. You can optionally receive individual posts or daily digests by email, and any member can post messages by email (bypassing the web site) by sending to our posting address which is "NavList@NavList.net". This functionality is similar to a traditional Internet mailing list: post by email, read by email, reply by email. Most members will prefer the web interface here for posting and replying to messages.

    NavList is more than an online community... more about that another day.

    © Copyright notice: please note that the rights to all messages and posts in this discussion group are held by their respective authors. No messages or text or images extracted from messages may be reproduced without the explicit consent of the message author. Email me, Frank Reed, if you have any questions.

    Join / Get NavList ID Code

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

    A NavList ID Code guarantees your identity in NavList posts and allows faster posting of messages.

    Retrieve a NavList ID Code

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

    Email Settings

    NavList ID Code:

    Custom Index

    Subject:
    Author:
    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