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Clive wrote, about bearings when passing a headland or landmark-

"There is a description of these bearings in Bowditch Vol 1 (my copy is 
1984)
in the Piloting section para 1012 (circa page 301) and a more detailed
example in Vol 2 Chap 5 Distance \calculations,in my copy (1981)this is on
page 472.
I can send copies if you are interested."

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.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 


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