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    Re: tidal heights calculations...
    From: Brent Ferrantelli
    Date: 1999 Jul 08, 2:47 PM

    This is cool!  The coast guard doesn't teach simple effective things like
    the rule of twelths.  I am currently a great lakes sailor (lake superior)
    with little more than one or two inches of water level change either way,
    but I am soon bound for Newport, RI and would greatly appreciate further
    discussion of methods of East Coast tides/currents prediction.  Also, as a
    coast guard quartermaster speciallizing in aids to navigation positioning I
    would be intereseted in comments (on or off list) relating to buoys, fixed
    aids, GPS, DGPS, LORAN -- what's good, what's bad--- etc.
    Brent Ferrantelli, QM1, USCG
    CGC SUNDEW (WLB-404)
    >From- Lu Abel 
    >Subject: Re: tidal heights calculations...
    >Date: Thu, Jul 8, 1999, 3:19 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
    > 1,2,3,3,2,1.
    > 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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