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    Re: DR plotting techniques
    From: George Huxtable
    Date: 2003 Oct 18, 21:24 +0100

    >On Sat, 18 Oct 2003 00:13:24 +0100, George Huxtable wrote:
    >>Rodney Myrvaagnes wrote-
    >>>I can't see how an uptide or downtide arc could be more efficient than
    >>>a continuously-corrected rhumbline. Could you explain which is more
    >>>efficient, and why?
    >>Rodney, I'm glad someone asked that question. I can explain it best by an
    >>example, which not by chance happens to correspond rather closely with the
    >>passage between my own home port of Poole and its opposite number on the
    >>French coast, Cherbourg.
    >>Consider a passage from port A to port B, which is due South of A, across a
    >>channel which runs East-West, and is subject to a strong tide, running 6
    >>hours each way. Say the distance A to B is such that in smooth water and at
    >>the vessel's cruising speed, the passage would take just 12 hours. And say
    >>the vessel departs from A, just when the East-going tide commences.
    >Come on, George. That is an extremely special case.
    >I am leaving to catch a tide in the East River, but I will try to
    >pursue this further next week.
    >>If the vessel just steers a Southerly course throughout, the tide will take
    >>her, say 15 miles to the East of the direct straight A to B track, over the
    >>first 6 hours. Then, the tide will turn Westerly, and over the next 6 hours
    >>it will bring her back West by that same 15 miles, to deposit her right at
    >>the doorstep of port B.
    >>If the vessel was following a ground-track using GPS, waypoints would be
    >>set at A and B, and a straight-line ground track drawn between them. The
    >>helmsman would be commanded to steer West of South during the first 6 hours
    >>to keep to that track and counteract the tide, and then, later, East of
    >>South, to do the same. In the case of a slow vessel, and a hot tide, the
    >>attempt to keep to the straight track may even become impossible. But in
    >>any case, those Eastings and Westings are quite counterproductive,
    >>cancelling each other out, and are made at the expense of the Southing,
    >>which in this case is all that matters. Sceptics may find that a simple
    >>vector diagram will convince them, but are welcome to argue back if it
    George counters-
    No, it isn't a "special case", at all, as Rodney claims. Certainly, I chose
    the simplest, and most obvious example, to show it up.
    It's true that over ANY cross-current passage, when that cross-current
    varies significantly with time, then trying to counter that cross-current
    at every moment, by varying the heading to hold to a short and straight
    ground-track, will not be the best way to go. It will always be more
    efficient to stick to a constant heading, which is calculated to compensate
    for the total net tidal displacement over the duration of the passage,
    whatever that happens to be.
    Following a straight ground-track will turn out to be the same as the
    procedure above if, and only if, the cross-current stays constant with
    time. This may be the case when crossing an ocean current, or a river flow,
    or making a short cross-tide passage which only takes an hour or so, a
    small fraction of a tidal cycle (such as when crossing the Solent). In
    those cases, following a straight ground-track will be just as good. That's
    the special case.
    But in general, the tidal cross-currents will vary appreciably with time
    over the duration of a passage, and then it will always be advantageous to
    adopt a constant-heading strategy, and ignore any specified straight-line
    track. That's the general case.
    Things get rather more complex when a cross-current varies with POSITION
    across the passage, and I haven't attempted to tackle that problem!
    Please argue back, anyone, if you're unconvinced.
    And Rodney, enjoy your trip, and take care when crossing a tideway.
    Yours, George.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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