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    Re: Double Altitude - Sensitivity to Time Interval
    From: Tom Sult
    Date: 2016 Dec 05, 09:26 -0600
    First it appears you were standing in the back yard of your red roofed house. Too bad the google image did not catch you in the act. 

    Second, I have proven many times in this forum that I am NO math wiz. But isn't one of the issue the vary small angle you are using between fixes? A small error in a small angle is still a big error.  

    What am I missing?

    Tom Sult, MD
    Author: JUST BE WELL

    On Dec 5, 2016, at 01:58, David C <NoReply_DavidC@fer3.com> wrote:

    Whle mowing the lawns this afternoon I noticed that the sun was visible more often than it was hidden by cloud. I checked a phone app and at my location the sun would be on the prime vertical at 1716 NZDST (-13). I looked at my watch and it was 1645. Clearly a double altitude sight was in order.

    I took three pairs of sights. Unfortunately about 10 min before the sun was due west the sun disappeared behind a cloud. The cloud cover was such that I decided to put my sextant away. Then I noticed a blunder in the first pair of sights so I was left with two pairs of sights.

    When I analysed the sights I discovered that the approximate formula cos lat = a/15/t is so sensitive to errors in time as to make it  useless. It is possible that I have made an arithmetical error but I found that a four second error in three minutes gives an change in lat of nearly 1 °. It is many many years since I studied differential calculus so I doubt I could work out d lat/d t for the above formula.

    Here is what I did:

    I observed the sun in an AH. I noted the times when the bottom and top limbs touched and then when the top and bottom limbs touched. That is a change of two diameters but I am using an AH so the actual change is one diameter or 32.4'.

    To check the accuracy of the sights I worked the first sight of each pair as an intercept and then as a time sight (with gps lat). I then used the formula cos lat = a/15/t to determine the lat by double altitudes. The intercept was worked with the cos formula, a calculator and the ABC tables. The time sight was worked by calculator.

    Base data

    GPS  position  S41° 06.5'  E175° 05.2'

    Zone -13  (NZDST)

    Zone date 2016/12/5  (what is preferred time format for this forum?)

    Sight 1

    Ho  39°  39.4'

    Time 1  165504

    Time 2 165754

    Intercept  0.2' A

    Az  N 85.7 W

    Long by Chron 175 5.0'

     

    Sight 2

    Ho  38°  35.9'

    Time 1  170037

    Time 2  170331

    Intercept  0.7' A

    Azimuth  N 86.5 W

    Long by Chron  175° 6.1'

    Double Altitudes

    The change in altitude is 32.4 * 60 arc seconds

    The time interval is 170 secs for the first pair and 174 sec for the second pair.

    These numbers give 40° 19' and 41° 51' for the lat. What I find interesting is not the error in lat but just how sensitive lat is to the time interval.

    Have I made a blunder?

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