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    Re: Raw data for bubble
    From: Bill B
    Date: 2007 Mar 20, 18:41 -0400

    NOTE: This is a resend.  First try failed to appear on the list.
    Peter wrote:
    > For myself the appeal of these separate observations is that they are a
    > relatively simple and elegant means of establishing position. Another
    > advantage, for those who are worried by ambiguity, is that there is none - a
    > single line of position is derived in each case, establishing latitude and
    > longitude, leading to an unambiguous fix.
    I certainly understand you argument.  It is however a running fix, and in a
    smaller sailing vessel if you had a little compass error and a little pilot
    bias that didn't cancel out--and a good bit of leeway--being 6' off DR might
    be possible from LAN to fix, so EP would have to be used as AP for
    determining longitude.
    I am exposing my ignorance here, but it seems to me--and I hope the list
    will elucidate me--that DR is preferred for AP.  It strikes me that for a
    two-body "fix" EP would be preferred, for a three-body fix DR might be
    preferred as it will reveal a combination of leeway, set and drift.
    For the purpose of definition:
    DR = course and speed only.
    EP = course and speed corrected for leeway, set, drift, wind-induced surface
    current etc.
    Let's assume EP as AP for our discussions so latitude is less ambiguous.
    > It is interesting to look at your calculations and see how little difference
    > in azimuth results from a relatively gross (one degree) error in latitude. It
    > seems that a reasonably good idea of longitude could still be achieved with
    > such a poor idea of latitude - is that your conclusion?
    Yes, but after further examination I believe your method yields better
    results than a time sight. If one was to calculate a 90/270 time from a
    given latitude, and the latitude was off, then the Hc would not match Ho.
    The actual or reduced azimuth would not be 90/270.  A visual inspection of
    the azimuth *might* reveal immediately if you are north or south of your AP.
    It would also introduce an intercept.  That should raise a red flag about AP
    latitude, which is a plus to your method.
    Even if your latitude were off, you have a very usable longitude (much like
    longitude being off for LAN determination of latitude won't matter much).
    And you have the hopes of confirming latitude from a north/south body in a
    few hours.
    The further off 90/270 you get, the worse the current reduction methods or
    time sight or will be for determining longitude (as we saw in Sumner's
    case), but comparing Ho to Hc will get you closer than a time sight using a
    precalcuated passage IMHO.
    1 May, 2007, Sun
    AP N 40, W 60
    Az 270 (Actual transit)
    Hc 24d 00!2
    1 May, 2007, Sun
    Real position N 41, W 60
    Az 266.73
    Hc 27d 49!7
    1 May, 2007, Sun
    AP N 40, W 60
    Az 269.56
    Hc 25d 00!0
    1 May, 2007, Sun
    Real position N 41, W 60
    Az 266.20
    Hc 27d 46!0
    To review we think we are at N 40 W 60, we are actually at N 41 W 60.
    In the case of the 20:41:45 observation, the difference between Hc at N40
    and Ho at N41 is 0d 00!2, so an intercept of 0!2 from AP.
    A time sight using N40 would be 0!3 off AP.
    In the case of the 20:21:45 observation, the difference between Hc at N40
    and Ho at N41 is 0d 03!7, so an intercept 3!7 of from AP.
    A time sight using N40 would be 4!8 off AP.
    If compass or peloris observation of azimuth for the time sight closed the
    3!8 azimuth gap from 270d, it would be more accurate if latitude was way
    off.  But that is a big "IF."  On a small craft in seas compass work may be
    as much art as science, and in some waters a change of 1d latitude could
    significantly change the variation.
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