- #1

Monsterboy

- 303

- 96

## Homework Statement

To generate a elliptical paraboloid antenna surface in MATLAB using the given F/D ratio (= 0.3)

F- focal length

D- Diameter = 50 m

## Homework 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

## 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

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)

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##.