I had written a script to design a concave mirror for solar cooker using Scilab. I am posting a similar but faster script using GNU Octave. In theory, a paraboloid can’t be made out of plane sheet because a paraboloid is a three dimensional shape. To fabricate a paraboloid, we use plane sheet sectors and a three-dimensional shape is assembled.
- If you look at the paraboloid from the top, you can see circles.
- This means that a paraboloid can be fabricated from concentric cylindrical rings. However this method will be very tedious for assembly. See the first figure.
- Instead, if we make many sectors, and assemble them, they can form a paraboloid. See the second figure.
- This means that if we design a shape of a sector such that each point on the sector edge will be on a circle as well as the parabola, we can assemble the shape closest to a paraboloid.
GNU Octave helps to design the sector shape
Using GNU Octave, we can design the shape of a sector. I wrote this script to find the sector dimensions if the focal length, number of sectors and number of rings is given. For the values:
- focal length=20
We have this shape for the sector. If you observe the sector shape carefully, you will see that it is not a triangle. The two sides of the shape are slightly bulged out. This helps to make the shape curved.
At various distances from the lower point of the shape, width of the sector changes. It is given in the table below:
When 36 such sectors are assembled, we can form the paraboloid which can concentrate solar rays at the focal point cooking the food for us.
Download the script
Download this script in pdf form and study it. You can design paraboloid of any size using the script.