Parabolic Reflector Basics

March 18, 2004

Even though it doesn't look like it in Michigan's Upper Peninsula, spring is right around the corner. We still have about three feet of densely packed snow up here -- which makes this an ideal place for winter sports, but not so good for agriculture.

When the warm winds from the South begin blowing, most of this white stuff will be gone in about a week. That will be the time to open the shop doors and start "burning metal".

Last month we looked at a 10 ft. by 10 ft. flat panel reflector array. This month we'll cover the basics of parabolic reflectors, and how to set up plugs to construct a precise FRP (fiberglass reinforced plastic) 9 ft. reflecting dish.

The design and construction methods we are describing were developed by my company back in the 1980's when C-band dishes were the satellite system rage. We developed our methods to maintain a 0.015625-inch point to point accuracy over the entire face of the dish. The methods proved to work, as our dishes outperformed much larger dishes. While the application is somewhat different, the principles are the same -- whether reflecting radio waves or solar radiation.

While last month's reflector could focus down to 12 inches by 12 inches, the parabolic reflector can theoretically focus down to an infinitesimally small point with extremely high temperatures. -- In fact, a solar furnace of this type could literally melt steel at its focal point!

So where do we begin? First of all, we have to figure out how large a dish we want to construct. A good beginning point is 8-10 feet in diameter. Since we have done this once before, we'll use our 9 foot dish as an example.

Let's start by determining the overall dimensions, focal lengths, etc.

A 9 foot (108-inch) dish has an F/D (focus to diameter) ratio of 1 when the focal length is 108 inches. Therefore: 

A cross-sectional plot of the parabolic curve may be calculated in X and Y coordinates using the following equation:

The easy way to calculate the numbers is with a computer program. For those of you with Power Basic or similar programming language, here is a short program that does the job:

Chart 1: Program to calculate parabolic curve

For those of you who prefer a quick spreadsheet approach, CLICK HERE.

Once you have all of the numbers for the reflector, it's time to layout the "cookie cutter". To translate the X,Y coordinates to a sheet of plywood, use the largest X,Y coordinates as the grid area, then add another 4 inches for good measure.

For our 108" dish, with an FD of 0.357 and a radius of 54 inches, the Focal Point will be 38.51 inches, and dish depth is 18.91 inches.

To create a cross-profile we'll need a sheet of 1/4-inch plywood approximately 60 inches by 12 inches. Layout a 1" by 1" grid on the plywood, and locate points on the grid using the calculated X,Y table. 

To make it even easier, use our table below:

Chart 2: Program data, for parabolic dish diameter 108"

Using a flexible ruler or thing strip of plywood or plastic, connect the dots to form a smooth curve. Your grid and curve should look something like this:

Next, carefully cut along the curve with a sharp razor knife and sand the edge. You now have your plug shaping cutter -- all that's needed is to finish the outer edge to form a structural outer rim on the finished dish.

Next month we'll cover the basics of building the plug from common building supplies such as cement and plaster.

Until then, let's see how many of you can build your own cutter using our numbers or coming up with your own.

Ken Rieli