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    Triangles and equations in navigation
    From: Andrés Ruiz
    Date: 2009 Jul 27, 14:14 +0200

    Dave Walden wrote in [NavList 9215]:

    ......

    Whoa! They should be the same!  (Note the parallelism in the equations.  Same would be seen in the Great Circle Distance equation.  All the same triangle.)

    ......

     

     

     

    The variables:

    SR

    Identificaction

    GC

    B

    B

    B1

    Dec

    Ho

    B2

    LHA

    Z

    DL

    Hc

    Dec

    90-D

    Z

    LHA

    Ri

     

    The equations:

    GC

    Cos D = sin B1 sin B2 + cos B1 cos B2 cos DL

    Cos Ri = (sin B2 - cos D sin B1)/(sin D cos B1)

    SR

    Sin Hc = sin B sin Dec + cos B cos Dec cos LHA

    Cos Z = (sin Dec - sin Hc sin B )/(cos Hc cos B)

    Body identificaction

    Sin Dec = Sin B Sin Ho + Cos B Cos Ho Cos Z

    Cos LHA = (sin Ho - sin DEC sin B )/(cos DEC cos B)

     

     

    For other treatment of this equations and LD distance see my paper “Vector equation of the circle of equal altitude” available at my Web page.

     

    Andrés Ruiz

    Navigational Algorithms

    http://sites.google.com/site/navigationalalgorithms/

     


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