# How to construct a compact linear Fresnel reflector

I have recently come across the concept of CLFRs, and I want to build one myself, as a private experiment.

I have a rudimentary knowledge of optics (which I'm sure I'll have to refresh on) - any useful links would be appreciated on bringing me up to speed.

My understanding of the technology is as follows (I stand to be corrected if this knowledge is incorrect).

1. A linear Fresnel reflector is constructed by taking equal width "strips" out of a parabolic mirror and "translating" the "strips" on to a horizontal surface in such a way that all the strips have bases with the same Y coordinate.

2. A compact linear fresnel reflector superimposes two parabolic mirrors (facing oposing directions) and decomposes them into two sets of alternating, equal width "strips" lying on the same horizontal line.

Is my understanding of the construction of CLFR correct? If yes, is there an algorithm I can use to "slice" a parabola into slices of width w, whilst preserving the reflecting angle of each "slice"?

I can think of a way of generating an algorithm, using geometry and elementary calculus - BUT, I don't profess to be an expert in this area, so I want to know what specialists in this field suggest.

A schematic of a CLFR is shown below:

In summary, how may I build a CLFR by "decomposing" two parabolas into two alternating rows of strips of width w ?

• Toolbars not appearing in my browser (FF 59.0.2 (64-bit)). Could someone please edit this so that the image shows? – Homunculus Reticulli Apr 27 '18 at 10:08
• The markdown required for adding images without the toolbar is: '[![enter image description here][1]][1] followed by [1]: https://i.stack.imgur.com/GEWN2.jpg somewhere, so the system knows where [1] should link to. You can add an "l", "m", or "s" before the ".jpg" in the URL to link to a pre-shrunk image to improve loading times and formatting in some situations – Jonathan R Swift Apr 27 '18 at 15:50

Nope, it's not that simple. You are forgetting that as you move each section back that its focal point will move with it.

Figure 1. If you move a section of the parabola back to the base line the focus will move with it.

I've never seen one but a Fresnel parabolic mirror would have to be made of strips of different parabolas.

To answer @fred_dot_u the angle for a flat section at radius r with a focal point at h above the mirror plane is given by the equation $\frac{1}{2}tan^{-1} \frac{r}{h}$.

Figure 2. Calculating the angle for a flat spiral strip Fresnel parabolic mirror.

• "You are forgetting that as you move each section back that its focal point will move with it." I thought there was more to it than met the eye! ... I think you're onto something here. I'll wait a little longer to see if this answer can be improved upon before making a final decision. – Homunculus Reticulli Apr 28 '18 at 9:42

If the idea of a flat surface cut into a spiral qualifies for your objective, you may be able to make something work based on Rick Steenblik's design.

From the 1982 Popular Science magazine, the article described how he cut the shape and aligned marks placed on the spiral to attach the reflective material to the cross members. As each segment was "pushed" into position, the outside edge lifted at the angle necessary to provide a common focus.

Allowing for some error, the continuous strip of reflective foil bent progressively greater as the spiral reached the edge.

I was a young adult when I purchased the template for this item and did not have the resources to build it. I've long since given up on trying to find the template, although if I did, I'd be building one in a flash. I also recall attempting to contact Mr. Steekblik a number of years ago and having the envelope returned to me, probably using the address shown in the article.

Another "dead-end" link can be found at a solar cooking wiki page. One of the photographs on that site shows clearly the spiral as well as the pairs of mounting holes necessary to accomplish the bend.

It would be great if someone could perform the analysis and create a parametric file for creating this reflector in varying sizes and widths.

• See my update. I think Mr. Steekblik may not have needed to be a genius to work this out. – Transistor Apr 27 '18 at 21:36