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elliptical paraboloid surface in matlab using F/D = 0.3

  1. Jul 1, 2017 #1
    1. The problem statement, all variables and given/known data
    To generate a elliptical paraboloid antenna surface in MATLAB using the given F/D ratio (= 0.3)
    F- focal length
    D- Diameter = 50 m
    2. Relevant equations
    ## \frac {F}{D} =\frac {1}{4tan(\theta/2)} ##

    ## F = \frac {D^2}{16H} ##

    H = height of the paraboloid

    Equation of a elliptical paraboloid

    ## z = \frac{x^2}{a^2} + \frac{y^2}{b^2} ##

    https://i.stack.imgur.com/sDgkP.png

    In the example above H =10 and D appears to be -1 to +1 so D = 2

    3. The attempt at a solution
    The elliptical paraboloid has a diameter of say 50 metres.
    The F/D ratio is 0.3
    then F = 15 m, H = 10.416 m
    I am taking a circular paraboloid so a = b in the equation, so

    ##z = \frac{x^2 + y^2}{a^2} ##


    http://image.mathcaptain.com/cms/images/113/image-of-parabola.png

    The angle between the line passing through the axis through the focal point and another line joining the focal point and the rim of the paraboloid is the angle ## \theta ##.

    Using the given data i got ## \theta = 79.611^{\circ} ##

    I am able to get a paraboloid but not of the shape i want, i am not getting the required ##\theta ## i am getting a surface similar to the one in the first link i have provided where ##\theta## is much smaller than 79.611.

    [x y] = meshgrid( -25:1:25);

    for z = 0:10.416
    z = (x.^2 + y.^2);
    figure
    surf(x,y,z)
    end


    using the equations, i get ## \theta = \frac {\theta}{2}arctan(\frac{D}{4F}) ## i don't know how include ##theta## into the equation.

    http://mathworld.wolfram.com/Paraboloid.html

    I tried to use the equations in the above link in the code instead.

    [u v] = meshgrid([0:1:25], [0:pi/10:2*pi]);

    x = u.*sqrt(u/h).*cos(v);
    y = v.*sqrt(u/h).*sin(v);

    z = x.^2 +y.^2;
    figure
    surf(x,y,z)


    the value of h is declared earlier = 10.416 , but still i am getting a paraboloid with very small ##\theta##.









     
  2. jcsd
  3. Jul 3, 2017 #2
    I got it.
     
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