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Convergency and conversion angle. Need help

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  • Convergency and conversion angle. Need help

    Hi Guys!
    I have a question and I dont know how to solve this questions. Would appricate if someone could tell me how do solve it.

    Question:
    The great circle bearing of position B in latitude 30.00 S from position A (30.00S, 165E) is 100 T.
    What is the great circle track from A to B?
    The lonitude position at B?

    How do I solve these? Im stuck and cant find it in the book.


  • #2
    To find an unknown longitude from a known longitude you need to calculate the 'change of longitude'.

    There are two tracks between two positions A and B; a great circle (straight line) track and a rhumb line (constant bearing) track.
    The rhumb line track between two positions A and B on the same parallel of latitude will be 090T (to the east) or 270T (to the west).

    Positions A and B are on the same parallel of latitude. The great circle track at A = 100T, therefore, this is an easterly track. As such, the rhumb line track will be 090T.

    The difference between the great circle and the rhumb line at any point is 'CONVERSION ANGLE', which is equal to 1/2 x Change of Longitude (degrees) x Sine Mean Latitude.

    GCT = 100T, RLT = 90T; therefore, Conversion Angle = 100 - 90 = 10

    Substitute known values into the equation to solve the change of longitude

    CONVERSION ANGLE = 1/2 x Change of Longitude (degrees) x Sine Mean Latitude
    10 = 1/2 x Change of Longitude (degrees) x Sine30
    10 = 1/2 x Change of Longitude (degrees) x 0.5

    Transpose the formula to solve 'change of longitude'

    Change of Longitude (degrees) = 10 / (0.5 x 0.5)
    Change of Longitude (degrees) = 10 / 0.25
    Change of Longitude (degrees) = 40

    Longitude = E165 + 40 = E205
    This exceeds the maximum longitude of 180

    To resolve, subtract 205 from 360 and change hemisphere

    Longitude E 205 = 360 - 205 = W155

    Hope that helps.

    Tony

    www.cat3c.com
    ​​​​​​​

    Last edited by Tony Pike; 12-10-2017, 09:37.
    Best Regards,

    Tony Pike

    Give Sergei back his dignity......Simples!

    Comment


    • #3
      Best Regards,

      Tony Pike

      Give Sergei back his dignity......Simples!

      Comment


      • #4
        Tony, stop advertising or you will be banned.

        Comment

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