Building a Parabolic Solar Hot-Water Heater using 123D

Step 2: Designing the Shape

My second step was to define the shape of my dish.  The general shape is called a parabola (or technically a parabaloid because it is a 3D surface created by rotating a parabola about its axis of symmetry).  Parabolas are shaped such that they reflect rays (in our case, sunlight) to a central focal point.  They can be described (and graphed) using a mathematical equation:  

y = x²/(4f)  Where f is the height of the focal point.  For example, I could make a parabola with a radius of 2 feet and a focal point height of 1 foot by using the equation y= x²/4 and calculating from x=-2 to 2.  

Another way of thinking about your parabola is to use the equation FD = R²/4 where D is the depth of the dish from the center to the rim and R is the radius of the rim.  

Using my equation (I used y= x²/4 and calculating from x=-2 to 2),  I calculated about 20 (x,y) points between 0 and 2.  (I didn't worry about units, because I was planning on changing the scale later.)