Math Is Fun Forum

irefay

Member

Registered: 2005-05-04

Posts: 2

Solar Water Boiler

Hello
I am creating a solar water boiler. The max dimensions are 1meter diameter. What I would like to do is create a giant parabola with water can at its focus point. Unfortunately, I need to brush up on my parabolic knowledge. The parabola should be as wide as possible in order to capture the maximum amount of sunlight but the focus must stay within 1 meter of the origin of the parabola. Anyone want to run me through first few steps?
Thanks a bunch

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Solar Water Boiler

The parabola will focus the rays on to ONE spot (ouch! that'll be hot!)

The equation is: y = x² / 4p, where p is the height of the focal point

Have a look at the graph x² on our little graph applet

So, for example, if you want the focal point to be 1 meter above the parabola's base you would use:

y = x² / 4

So, Width (either right or left of center) vs Height would be

W  ... H 
0.3 ... 0.02
0.6 ... 0.09
0.9 ... 0.2
1.2 ... 0.36
1.5 ... 0.56
1.8 ... 0.81

I found a really great way for you to lay out the parabola at this website: http://www.gizmology.net/parabola.htm, and after sketching using their technique, you can take a few measurements and confirm that the relationship y = x² / 4p still works.

---

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman