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    Re: short horizon Hs correction
    From: Thomas Schmidt
    Date: 2000 May 23, 8:04 AM

    Frank Dinkelaar wrote:
    
    > In regards to the attachment (navigation formulas) send by Ed Kitchin
    > the formula in #1 of the great circle course
    > it seems to me it looks like this
    > cos D =  abs(sinL1 - sinL2) - abs(cosL1 x cosL2 x cos Dlo)
    > it would save me many hours of experimenting if somebody
    > could confirm or send me the formula in a clearer form.
    > thanks
    
    According to my textbook on spherical geometry, the distance D
    along a great circle between two points at latitudes L1 and L2
    and with the difference in longitude DLo between them is
    
    cos(D) = sin(L1)*sin(L2) + cos(L1)*cos(L2)*cos(DLo)
    
    We may test this with the example given for mid-latitude sailing,
    where it's stated that the great-circle distance between
    
      L1 = 41 deg 26 min N   Lo1 = 71 deg 23 min W
      and
      L2 = 32 deg 22 min N   Lo2 = 64 deg 39 min W
                             DLo =  6 deg 44 min
    is 632.2 miles:
    
    
    cos(D) = 0.66175 * 0.53534 + 0.74973 * 0.84464 * 0.99310
           = 0.98314
    
    D = arccos(0.98314) = 10.536 deg = 632.2 nm, as expected.
    
    
    (Note that since D is relatively small, cos(D) is close to 1
    and therefore it may be more practical to apply Formula #11
    in this case, especially if you use tables or a slide rule.
    The above formula is still valid, though).
    
    
    --
      -------------------------------------------------------------------
      Thomas Schmidt                  e-mail:     schmidt{at}hoki.ibp.fhg.de
    

       
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