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    Re: tidal heights calculations...
    From: Lu Abel
    Date: 1999 Jul 08, 2:19 PM

    At 08:38 AM 7/8/99 +0200, Russel Sher wrote:
    >A friends of mine recently did a nav. theory course in which she said the
    >'rule of twelfths' is no longer taught for tidal calculations. Instead,
    >percentages are used. Has anybody heard of this? - Would that mean 10%, 15%,
    >25%, 25%, 25% 10% instead of 1,2, 3, 3, 2, 1 (in twelfths)?
    What course did your friend take?
    I've taught Advanced Piloting (which covers tidal calculations) for the
    Power Squadron for the past 15 years and I always teach the Rule of
    Twelfths.  It's so simple and handy it's almost a sin not to teach it --
    for the 20 years I lived and sailed in New England I found it extremely
    useful.  (I'm not 100% certain it's actually in the current USPS text and
    I've loaned out my copy so I can't check).
    For those not familiar with the Rule of Twelfths:
    If I draw a graph of the height of water vs time for waters (like New
    England) where there are two highs and two lows per day of approximately
    equal height,  it looks like a sine wave with just over six hours between
    high and low points.  The Rule of Twelfths gives a very accurate way of
    approximating that sine wave without actually using sines and cosines.  It
    says going from the time low water to high (or high to low) the tide will
    have risen (fallen)
    After one hour          by one twelfth of its range
    After two hours         by an additional two twelfths
    After three hours       by an additional three twelfths
    After four hours        by an additional three twelfths
    After five hours                by an additional two twelfths
    After six hours         by the last one twelfth
    This 1,2,3,3,2,1 pattern is trivial to remember.
    How accurate is it?  Here is a comparison of the percent of tidal rise over
    a six hour period* as predicted by a sine wave and by the Rule of Twelfths.
     Only in the first and last hours is it off, and then by only 2%!
    hours       sinusoidal   twelfths
    after low       prediction  prediction
                  (percent of range)
        1           6.70       8.33
        2          25.00      25.00
        3          50.00      50.00
        4          75.00      75.00
        5          93.30      91.67
        6         100.00     100.00
    Sounds like Russ's friend was taught a 10,15,25,25,15,10 percent rule.  It
    too will produce correct results except for the first and last hour (where
    it will be even less accurate than the Rule of Twelfths).  I guess if one
    has been sufficiently "metricated" that one can no longer divide by 12 this
    might be better but to me the pattern is a lot harder to remember than
    Lu Abel
    *  Yes, the tidal period is closer to 6h 15m, but that's only another
    percent or two of error in this prediction.  Close enough when one realizes
    how old most of bottom surveys are on our charts!

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