Elliptical paraboloid surface in matlab using F/D = 0.3

In summary, the conversation discusses how to generate an elliptical paraboloid antenna surface in MATLAB using a given F/D ratio and focal length and diameter values. The equation for an elliptical paraboloid is given and the angle ##\theta## is determined using the given data. The code used to generate the paraboloid is also provided. However, when using the equations from a source, the resulting paraboloid does not have the desired shape.
  • #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


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##.
 
Physics news on Phys.org
  • #2
I got it.
 

FAQ: Elliptical paraboloid surface in matlab using F/D = 0.3

1. What is an elliptical paraboloid surface?

An elliptical paraboloid surface is a three-dimensional shape that resembles a shallow dish or bowl. It is formed by rotating an ellipse around its minor axis, creating a curved surface with an elliptical cross-section.

2. What is the significance of F/D = 0.3 in the context of an elliptical paraboloid surface?

F/D = 0.3 refers to the ratio of the focal length (F) to the diameter (D) of the paraboloid. This ratio is often used in optics to describe the shape of a parabolic mirror or lens, with a lower F/D value indicating a deeper and more curved surface.

3. How can I create an elliptical paraboloid surface in MATLAB?

To create an elliptical paraboloid surface in MATLAB, you can use the "peaks" function to generate a grid of points on the surface, and then use the "surfc" function to plot the surface in three dimensions. Alternatively, you can use the "meshgrid" function to create a grid of points and then use the "surf" function to plot the surface.

4. What are some practical applications of an elliptical paraboloid surface?

An elliptical paraboloid surface has many practical applications, including in optics, where it can be used to create parabolic mirrors and lenses for focusing and collimating light. It is also commonly used in the design of satellite dishes, radio telescopes, and other reflective surfaces.

5. How can I manipulate an elliptical paraboloid surface in MATLAB?

In MATLAB, you can manipulate an elliptical paraboloid surface by changing the values of the parameters used to define the surface, such as the focal length, diameter, and position. You can also apply transformations, such as rotation and translation, to the surface to change its orientation and position in space.

Similar threads

Back
Top