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    The mathematics of tacking downwind
    From: Bob Goethe
    Date: 2016 Jul 28, 10:37 -0700

    We have had discussion this last week on tacking into the wind.  And you are right indeed, Graham, that the ability of a sailboat to use momentum to gain distance to windward during the tack can depend on the mass and design of the boat...and also on wind conditions.  Sometimes, in a given vessel, the wind is such that you lose so much way on the boat as you come about that you have to dip down to a beam reach to accelerate after the tack, and then gradually edge back up to close hauled.  In this case, you have definitely lost distance to windward, over the short haul, with your tack.

    I lived in Japan for a while, where I owned a Yamaha 13 foot dinghy that sported a mainsail into which I had installed reef points.  Sometimes when I was out sailing, and the wind was too strong for me even with a reefed mainsail, I would sail under jib alone.  I could sail into the wind with just that jib, but lost significant distance to windward whenever I came about.  So of course, in that situation, the longer the tacks I could sail before having to come about, the better off I was.

    Tacking downwind has also been mentioned in our discussion, and the issues are a bit different here.  I have done some research into mathematically optimizing the angle at which one tacks downwind.  This is summarized in the attached PDF file, which is itself an extract from a user manual I have written to accompany the Mark 1 Navigator's Slide Rule.

    This slide rule does not exist yet except in my head.  But I decided to do something I have WANTED to do in software development, but never had the freedom to try, which is to write the documentation for a product first...and then, after I have sorted out usability/design features in the course of creating that documentation, actually build the product itself.

    There is a saying in life that if you don't know where you are going, any road will do.  But if you have a particular end in mind, some roads are better than others.  So knowing in advance just what problems you want to solve with a slide rule can help you sort out which scales you need, and how they should be arranged.

    I have created the full user manual now, and did indeed make several changes in the design of the slide rule in the course of creating the manual.  My next step is to 3-D print a prototype of this slide rule, to see if the 3-D process is, in year 2016, up to the level of precision required for a slide rule.

    Although this excerpt is written with a slide rule in mind, the math and the concepts naturally work just fine with a pocket calculator.

    Bob



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