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    Re: Wind turbines beyond the horizon
    From: Alexandre Eremenko
    Date: 2023 Jan 7, 21:30 +0000

    The geometry of the array is what is called "hexagonal lattice": vertices of 
    equilateral triangles that tile the plane.
    I suppose this has to do with minimizing of the shading of turbines by each 
    other with various directions of
    the winds. The orientation of the lattice is probably related to the 
    prevailing wind directions in the area.
    
    When sailing in the Baltic sea, I passed through several of these huge farms. They are very common there
    near the Danish shores.
    
    Alex.  
     
    ________________________________________
    From: NavList@fer3.com [NavList@fer3.com] on behalf of Russell D. Sampson [NoReply_Sampson@fer3.com]
    Sent: Saturday, January 7, 2023 1:00 PM
    To: eremenko@math.purdue.edu
    Subject: [NavList] Re: Wind turbines beyond the horizon
    
    ---- External Email: Use caution with attachments, links, or sharing data ----
    
    Frank:
    
    Very interesting problem.  One thing to consider is the geometry of the array. 
    If the map is correct then the spacing is neither orthogonal (i.e., like 
    ordinary graph paper) nor aligned with the cardinal points.  I am guessing 
    this may have to do with meteorology (prevailing winds) and aerodynamics 
    (downwind turbulence).
    
    Russ
    
    On Fri, Jan 6, 2023 at 3:32 PM Frank Reed 
    > wrote:
    
    I spotted this random photo (from a friend of a friend) today on Facebook, and 
    I am borrowing it without credit mostly because I can't figure out where I 
    found it originally! It's a beach shot looking east-southeast from Pagham, 
    Bognor Regis on the southern coast of England. The photo captures long rows 
    of giant wind turbines, miles away, in the Rampion offshore wind 
    farm. This has relevance to navigation 
    because there are various angular piloting problems that can be puzzled out 
    here (*), and also because we have a textbook case of "masts" of fixed height 
    dropping away in apparent height beyond the horizon. Does it make sense? That 
    is, do the apparent angular heights beyond the horizon match our expectations 
    from navigational formulae? I made a map based on one at the wind farm's 
    website that may help. I haven't worked this out in detail. But it seems like 
    an interesting puzzle, and, like I say, a textbook case of beyond the horizon 
    angles.
    
    Frank Reed
    * There's a nice navigation trick here. If you look out there with your 
    binoculars and see all the turbines in one of the farm's rows all stacked up 
    on top of each other visually (like the left-hand group in the photo), then 
    you've got a line of position running right along that row. Of course you 
    have to make sure you count correctly and know just which row you're aligned 
    with!
    
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