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    Re: BS XM DS Daytime Venus, Redux
    From: Henry Halboth
    Date: 2011 Jan 19, 13:44 -0800

    The correction procedure for a Back Observation can become a little complicated, particularly in Solar observations. It is probably best to diagram the situation carefully, as opposed to blindly following rules, so as to understand the problem fully with respect to the necessary reversal of dip and IC signs, as well as proper handling of the SD depending on the true Limb observed, the LL becoming the apparent UL and vice verse..

    I have done only a few back sights, specifically in war time convoys, where intervening ships might obscure the horizon, or off poorly charted coastal areas, with no means of ascertaining distance off (no radar) to facilitate a short dip solution.

    Should you be interested, I have attached several pages from my notebook which rather fully detail the problem and associated corrections. The apparent contradictions between a quadrant and a sextant apparently originate in the assumption that the quadrant be fitted with a back sight mirror and peep sight while the sextant is not.




    --- On Tue, 1/18/11, Anabasis75@aol.com <Anabasis75@aol.com> wrote:

    From: Anabasis75@aol.com <Anabasis75@aol.com>
    Subject: [NavList] BS XM DS Daytime Venus, Redux
    To: NavList@fer3.com
    Date: Tuesday, January 18, 2011, 9:55 AM

    Okay, I was a bit more prepared, and had better conditions so I tried this again!
    I also did a bit more research by tapping into the 1984 Bowditch in the captain's library.  The current Bowditch tells you what a back sight is, but not how to correct it to Ho.  I was using the wrong procedure which was part of my problem.  To do this correctly, we apply negative IC and dip (in my case adding both of them) to the compliment of the Hs (180-Hs).  You must do the subtraction first, and then add the correction. 
    Then we apply the body correction and then ex-meridian correction to get what I call Ho'  Then we determine ZD and then apply to Declination to get Latitude  (in this case subtract ZD from Declination).
    I started out the math with the "easy" sight.  At due north from our anchorage I can see over the trees and use the true sea horizon.  So I took a "plain" old back sight transit shot of Venus.  I was doing this just to nail down the back sight portion of this problem.
    January 17, 2011
    GPS Lat 07-16.3' S
            Long 072-26.9' E
    HoE 106' for all sights
    Hs 101-35.1
    IE 0.8' on the arc
    Time 10h 00m 54s Local
    This gave me an error of 0.1' of latitude so I was doing the back sight correctly.
    I then moved on to the ex-meridian back sights I had taken before transit.  This had the added advantage over yesterday of a more distant shoreline that was also more perpendicular to the azimuth than the post-transit shore.  The shore varied from 2.0 to 1.9 nm away which isn't great, but less prone to error.  I also made 6 observations.  I only reduced two of them (I don't have programs to do these things, so I do it all with tables with the exception of using the dip short formula).  Both of my ex-meridians came out about 3 nm off so I suspect that the shoreline is closer than the radar indicates.  These take me 15-20 minutes each to do with tables. 
    here is the data:
    1) 09h 47m 44s
        Hs 102-21.6
        Distance 2.0nm
    2) 09h 48m 38s       I reduced this one  Lat: 07-19.6 S
        Hs 102-16.6nm
        Distance 2.0nm
    3) 09h 49m 58s
        Hs 102-12.6
        Distance 2.0nm
    4) 09h 51m 38s
        Hs 102-07.8    
        Distance 2.0nm
    5) 09h 54m 43s
        Hs 102-01.2
        Distance 2.0nm
    6) 09h 55m 52s        I reduced this one. Lat 07-19.3 S
        Hs 101-59.0
        Distance 1.9nm    
    The good thing is that the small change in declination of 0.1 during the sights doesn't seem to affect "a" to the 10ths place.  The small distance change in the shoreline does affect dip however so this is where my error is apt to be. 
    I got an "a" of 9.4' by double interpolating the table in Bowditch and my dip short for 2.0nm was 30.8' and at 1.9nm it was 32.4'
    For Kermit: I was applying my -0.3 "v" correction for GHA today.
    As a shooting note.  These are VERY difficult observations to make.  Finding Venus is difficult enough and when you are trying to shoot at over 100 degrees, any slight movement of the sextant causes to body to skate out of view, especially with the 7x scope I'm using.  I used my least dense horizon shade to provide better contrast with Venus and the shore/horizon.  The body also moves in a parabola with a positive slope (opposite of the normal sight) so you are looking for the apex of the arc as you swing.  Since the body is so high to begin with, the slope is quite small as you shift azimuths, so it is difficult to find the exact azimuth of the acme and then trying to hold the sextant perpendicular offers another challenge for the aforementioned reasons. 
    This sight is as difficult to shoot as a high-altitude circle of equal altitude observation of the moon and the math is far more intricate.  In total, this ranks as the most difficult observation I've even made in Celestial Navigation.  The ONLY thing easy about this observation is plotting the resultant LOP.

    File: 115346.back-observation.doc
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