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    Re: Regarding fix bearings
    From: NavList
    Date: 2008 Dec 21, 15:06 -0800

    I think George's acceptance of my formula is what I hoped for-just another, 
    more universal (I hope) method, one of dozen others.  Please see below, 
    especially the second paragraph.
    Thank you
    Response from George-
    The description on para 1012 of Bowditch vol 1 refers to a slightly 
    different problem than the one that A-08  (inuik-AT-yahoo.com ) was 
    tackling. (It would be nice if he offered us a better name to call him by, 
    by the way). He was deriving an expression for the beam distance at which a 
    headland or landmark would be passed, as equal to the difference travelled 
    between two observations with specified relative bearing. Bowditch para 1012 
    was offering a table (table 7) in which you provided the two angles on the 
    bow, and it returned, not the beam distance-off, but the distance to the 
    headland at the time of the second bearing. It would only be beam 
    distance-off when the second angle happened to be 90�.
    However, as Clive points out, para 505 in Bowditch Vol 2, "Special 
    Calculations" in the chapter "Distance calculations", does deal with the 
    same situation as does "A-08", providing pairs of angles on the bow at which 
    the run between them will be equal to the distance at which the object will 
    be passed abeam.. Table 505 is provided, giving values of such second-angles 
    when the first angle varies between 20� and 45�. Beyond that point, you 
    don't find the distance-off until after the headland has been passed, by 
    which time it may be rather too late. Table 505 is just a table of angle 
    pairs for which A-08 provided a formula: that formula applies even to 
    angle-pairs greater than 45� / 90� . It could just as well have been plotted 
    as a simple graph.
    As Bowditch states, the rule is simply finding pairs of angles in which 
    their cotangents differ by one, and inspection of the formula was given in 
    A-08's posting will confirm that this is the case. He has provided a 
    different way of looking at an old technique.
    By the way, when applying these techniques in practice a navigator should 
    take great care to correct his observed speed for the effects of tide and 
    current, to obtain ground track, particularly as such currents are usually 
    enhanced at headlands.
    [Sent from archive by: inuik-AT-yahoo.com]
    Navigation List archive: www.fer3.com/arc
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