# Elliptical paraboloid surface in matlab using F/D = 0.3

1. Jul 1, 2017

### Monsterboy

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. Jul 3, 2017

I got it.