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>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
>>doesn't.
>>
>>George.

===============

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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