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    Re: Graphical solution
    From: Thomas Alley
    Date: 1997 Feb 14, 20:57 -0500

    >Given a polar plot of the expected performance of a sailboat, given your
    >present position, and given the place you want to get to, is there a simple,
    >graphical plotting method one canue to determine the optimal course?
    
    Without going into a great amount of detail to check this, I would think
    the following would hold true:
    
    Given a chart on which your desired course is plotted, superimpose the
    polar plot over your current position on the chart and align it with the
    current wind direction. Using a set of parallel rules (or equivalent
    "rolling" ruler), align it to be perpendicular to the desired course such
    that the ruler is between your boat and its destination. Bring the ruler
    closer to your current position until it just touches the polar diagram.
    Draw a line from your current position to the point of tangency. This line
    represents the course that will give you the maximum rate of progress
    towards your intended destination.
    
    The second step will be to determine a limit for cross track error from the
    desired course and to tack back and forth when this limit is achieved. This
    effectively keeps the desired track centered on each leg of every tack.
    
    This approach is strictly theoretical and will be compromised by practical
    considerations.  Examples include, but are not limited to:
    
    o  Sea state may limit pointing ability or be too hard on the crew for
       extended beats. Easing off a bit will make for a much more comfortable
       ride but at the expense of a sub-optimal course.
    
    o  Prudent seamanship may suggest deviations from the optimal course to
       avoid charted hazards or to minimize the time one is in an area with
       heavy shipping traffic.
    
    o  As the wind direction and sea state change, the "optimum" course will change
       along with it and needs to be recomputed.
    
    o  Following the "optimal" course for each individual wind shift may result in
       a course that is less than optimal when considered over the entire voyage.
       (Consider the racing tactic of anchoring in light winds when caught in a
       foul tidal current.)
    
    Hope this helps. Anybody have any other ideas?
    
    							Tom
    
    ------------------------------------------------------------------------
    Thomas Alley                                               alley{at}acm.org
    KD2VH, Youngstown, New York                      Alberg 35, "Tomfoolery"
    
    
    
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    Date: 15 Feb 97 08:32:13 EST
    From: Bob.Trenkamp{at}gw.pps.com (Bob Trenkamp)
    Subject: Re: Graphical solution
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    --- Thomas Alley wrote:
    Given a chart on which your desired course is plotted, superimpose the
    polar plot over your current position on the chart and align it with the
    current wind direction. Using a set of parallel rules (or equivalent
    "rolling" ruler), align it to be perpendicular to the desired course such
    that the ruler is between your boat and its destination. Bring the ruler
    closer to your current position until it just touches the polar diagram.
    Draw a line from your current position to the point of tangency. This line
    represents the course that will give you the maximum rate of progress
    towards your intended destination.
    --- end of quoted material ---
    
    Tom,
    
    It's elegant - thanks. You're resolving any course into components parallel and
    perpendicular to the desired track and selecting the course based upon maximum
    component in the desired track direction. Neat. Thanks.
    
    bob
    
    

       
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