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    Cross-tide strategy (was: DR plotting techniques)
    From: George Huxtable
    Date: 2003 Oct 25, 21:06 +0100

    I've renamed this thread to suit the topic better.
    
    Rodney Myrvaagnes and I have been indulging in a friendly argument about
    the best strategy to adopt when making a passage across a tidal stream.
    Sorry about the delay in responding, to his last message, but I've been
    away in Cornwall for a few days.
    
    I did my best to summarise the position, comparing my strategy with his
    strategy, as copied below-
    
    >>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.
    
    Rodney then countered (my responses are interpolated)-
    >If you know what the ideal heading should be, they are indeed
    >equivalent.
    
    No, not equivalent at all. What I said in an earlier message was-
    
    "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 situation in which the two strategies are equivalent.
    
    Rodney continues-
    
    >But a wrong constant heading in the steady cross-current
    >case can be costly. For example, if the set is half the boat speed,
    >heading straight across will take twice as long as with no current,
    >counting the upstream slog at the end. A correctly calculated course
    >will take only 11% longer than it would without current, as would the
    >continuously corrected course.
    
    Here, he has set up an Aunt Sally to shy at, which is quite irrelevant to
    the argument, Neither of our strategies would head straight across in such
    an absurd way. His numbers, by the way, appear correct. With such a
    constant current, both strategies would be the same, requiring 11% more
    distance than if there were no current.
    
    >I don't think the 11% would be exceeded at any time if the set didn't
    >exceed half boat speed, even in the periodic case.
    
    Well, I agree, in that special case where the speed of the tide was never
    more than half the boat-speed. If he always sails in such an environment,
    and with such boat speed under his belt, Rodney is privileged in a way that
    those of us who sail slow craft in strong tides are not. For small
    sailboats in English Channel waters at spring tides, it's common to find
    the tide running every bit as fast as the boat can travel. How would
    Rodney's strategy of brute-force bucking of the tide, to maintain a
    straight ground-track, cope then? He would find himself expending all his
    boat's way in fighting the tide, making no headway at all toward his goal.
    No, it's necessary then to be more subtle, to coexist with the tide rather
    than oppose it.
    
    Mariners, especially fishermen under sail, in strongly tidal waters, have
    for many generations been making such allowances, in their heads, after
    holding up a wet finger. Unlettered, few would understand a vector diagram.
    Not having GPS, they wouldn't know, or care, if they were following a
    straight ground-track.
    
    My sailing area includes the Alderney Race, with tidal currents of up to 9
    knots in places, maybe more, locally, at perigee springs. One can only
    transit that race, in a 4-knot craft, by timing the passage right. One can
    only cross it, to reach or leave Alderney, by even more careful timing.
    Fortunately, it's only a short passage (IF you get that timing right!). By
    the way, the French give this the evocative name of the "Raz Blanchard",
    the washerwoman's race, which describes it well. When you pop out the other
    end, it can feel like having been through the laundry. Once you're in the
    tidal stream, there's definitely No Turning Back. You are in it for the
    full cycle; wash, rinse, and spin. Occasionally, though, it can be quite
    benign.
    
    Apologies for that diversion about the Alderney race, which was completely
    beside the point.
    
    >For periodic tides
    >one could calculate the error at the end from missing the cancellation
    >by 90 degrees. It would not be insignificant for the 12-hour trip, but
    >surely would be for anything over a couple of days.
    
    >In my wanderings, the Gulf of Maine crossing is long enough so that
    >tides do cancel out, about 30 to 40 hours.
    
    I don't see the logic in that statement above. In semidiurnal tide areas, a
    "tide", between reversals, takes a bit over 6 hours, so 38 hours would be
    about 6 such tides and should indeed cancel out. But, by that same
    reasoning, a passage time of 32 hours would be 5 whole tides, and
    (depending on the phase at departure) you easily could end up displaced
    sideways from your goal by one whole tide's-worth, to port or to starboard.
    If the passage time is as loosely specified as "30 to 40 hours", then
    cancellation can not be relied on.
    
    >The tides are not charted in
    >detail there, but the Bay of Fundy has significant effects for some
    >distance. There are circulating tides, so they will have different
    >effects depending on the exact track across.
    
    Yes, the tides can be more complex than a simple linear to-and-fro motion,
    and any such complexity needs to be taken into account, but that doesn't
    invalidate the principle of allowing for the complete predicted tidal set
    over the whole passage, from departure.
    
    >In Long Island Sound and the area adjoining the Elizabeth Islands
    >(Buzzards Bay and Vineyard Sound) the current is more bucking or aiding
    >than setting sideways.
    
    In that case there's no call for altering the heading to be anything other
    than the direct A to B course, with either strategy.
    
    >The Long Island Sound currents are altered from
    >the charted values by rainfall and often are weaker or stronger than
    >the predictions.
    
    Just from looking at the topography on my atlas, it seems unlikely that
    currents in the Sound from river systems are going to be comparable with
    the tidal streams. But no doubt Rodney knows those waters well, and I don't
    know them at all. In areas where the currents really are unpredictable,
    then the strategy must be modified accordingly.
    
    >In all these circumstances I think constant ground track is a good way
    >to compensate for unknown set.
    
    It's true that my tidal strategy requires some sort of prediction of what
    the tidal streams are going to be, where Rodney's strategy needs only a
    knowledge of what the tide happens to be at that moment. If the tide is
    unpredictable, or if the navigator has no means of making tidal-stream
    predictions, there may be no alternative to adopting Rodney's
    less-efficient strategy. As a general rule, however, tides, where
    important, are usually predictable; much more so than winds are.
    
    >I'll gladly risk 11% to avoid 100%
    >possible penalty.
    
    That "100% penalty" was a fiction invented by Rodney for the occasion (see
    "Aunt Sally", above). It has no relevance.
    
    >Of course most unknown sets will be much less than 3
    >kt, so both penalties will also be smaller.
    
    >So I ask George. Can you predict just how long your crossing will take
    >within an hour or so?
    
    A sensible question. Answer: Under sail, no, probably not, even for a
    12-hour passage. Within two hours, perhaps yes, most times. The tidal
    displacement over a known time will usually be predictable to within a
    couple of miles, but progress along the intended track depends on the
    fickle wind. Sometimes, it will become more favourable, resulting in better
    progress than expected. But for some reason, vice versa is more common!
    
    >If you are not coming in where you want to, when
    >do you decide to take corrective action?
    
    A very sensible question. Answer: Throughout the passage, and indeed right
    from the start, if progress is different from expected, the
    direction-to-steer can be reassessed, using the same criteria as at
    departure. That is; where are we now, how much longer is it likely to take
    to reach our destination, how much net tidal offset to allow for over that
    period? And then a new course-to-steer is set, intended to drop us right at
    the harbour entrance without further changes of course. But keeping in mind
    the possibility that further modiification may be called for. It's
    necessary to be flexible, to adapt as circumstances change.
    
    I will concede, however, that I hate to find myself downtide of my
    destination, so as journey's end approaches I will make a reassessment that
    will ensure being uptide to some extent. There's no point in making such
    fine-adjustments until late in the proceedings, when few unknown factors
    remain.
    
    ==================
    
    In this discussion, so far, we have considered only variation of tidal
    current with time, avoiding any extra complexity resulting from the common
    situation where tides run more powerfully in one area of a passage than in
    another. And we have assumed that we can always head in the desired
    direction, although the wind may force us to tack, and add some delicious
    little complexities of its own. How do we relate what tack to take, to the
    tide direction, to best advantage? Any offers?
    
    George.
    
    
    ================================================================
    contact George Huxtable by email at george---.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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