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Math Help - Calculating skip distance

  1. #1
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    Feb 2013
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    Guernsey, CI
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    Calculating skip distance

    Hi there,

    I am struggling a great deal with this problem, the main issue being where/how to start.


    For failsafe long distance communications, the military still uses short-wave radio signals. Thesesignals are bounced off the atmosphere and can skip even the distance between continents.


    For a given inclination α and for a givenatmospheric setting (specified below),your task is to find the the skip distance.





    1. Physics Department: The radio signal propagates along a curve C that minimises thetime of flight for fixed start and end points (Fermat’s principle).The speed of the signal is given by c = c0/n(x, y), where c0 = 3 × 108 m/s is the vacuumspeed of light and n(x, y) is the position dependent refractive index.


    1. Met Department: The refractive index can be modeled by n(x, y) = 1 + ∆n exp{−y/h}with ∆n = 0.0027 and h = 25km.


    I had an idea that if c = c0/ 1 + ∆n exp{−y/h} was used as Lagrange function I could then use the Beltrami Identity. However, this is where I'm stuck, I'm not sure how to get it in that form. Any advice would be much appreciated.
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  2. #2
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    Feb 2013
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    Guernsey, CI
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    Re: Calculating skip distance

    Solved this!
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  3. #3
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    Joined
    Oct 2013
    From
    Devon
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    Re: Calculating skip distance

    Heya i have pretty much the same problem and i am also stuck could you give me a push in the right direction
    Thanks
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