Making a Parabolic Reflector Out of a Flat Sheet

The unattended parabolic solar cooker [1] requires an imprecise parabolic reflector. Such a reflector can be molded or stamped in quantities, much like a salad bowl or a baby wading pool. However before it is commercially available, you can make one at home. The easiest way is to cut and fold a flat sheet into a parabolic dish. Then glue a layer of aluminum foil on its inner surface, for reflectivity. The flat sheet can be as cheap as cardboard. However water resistant material, such as plastic or metal, will last longer.

The reader should practice with a scaled-down (for example 1:4 or 1:5) model, using a piece of paper. If you find a parabolic reflector too difficult, a funnel shaped reflector will be a good alternative. Detailed instructions are given in [2]. However you will need a bigger hole at the bottom of the funnel [1].

As a concrete example, I shall describe the layout of a reflector with 130 mm focal length (f), and 800 mm diameter (D). All dimensions can be scaled to make reflectors of other sizes. A square sheet approximately 1000×1000 mm is needed. It may consist of one, two, or four pieces (fig. 1). There should be no overlap between adjacent pieces.

Draw four concentric circles, with radii shown in Table 1. It is OK if the largest circle is not completely contained in the sheet. If the sheet consists of multiple pieces, the center of circles must be located on the border of all pieces.

Divide the circles by 8 uniformly spaced diameters (22.5° apart). Each circle should consist of 16 identical sectors. If the sheet consists of multiple pieces, each border between the pieces must coincide with one of the divisions (fig. 2).

On each circle, and symmetric to each division, mark an arc whose length is shown in table 1 below. The values tabulated are the total arc lengths, including both sides of the division. Since each arc spans over a very small angle (less than 5°), it is practically indistinguishable from its corresponding cord.

Connect, approximately along the radial direction, end points of arcs just marked. Cut off area outside of the largest circle. The wedges outlined by the connections (fig. 3) will not collect sunlight. They will be either removed, or used as margins to connect adjacent paddles. Do not cut along the radial connections as yet, instruction will be given later.

The paddles will be bent over the circles drawn earlier, to create facets. The circles are shown in dashed lines in fig. 3. Bending over an arc is not easy, unless the sheet material is very thin and elastic. With a cardboard the bends will be over the corresponding cord instead.

If the sheet consists of multiple pieces, they should be jointed now at the inner circle. The best way is to duplicate the inner circle on a single piece. Then attach each piece of the reflector on top of this duplicate.

After bending and folding, the paddles should overlap in such a manner that a paddle is above (or below) both of its neighbors. Therefore a paddle should have either no margin, or two margins (one on each side). Paddles with and without margins alternate circumferentially (fig. 4). Normally, paddles with margins will be below paddles without margins.

Since the paddles are planar at and near the inner circle, there is a transition between planar and overlapping regions. To avoid interference in the transition zone, some clearance should be provided between adjacent paddles near the inner circle. Extra width can be shaved off paddles with and/or without the margins near the inner circle (fig. 4).

A hole approximately 5 mm in diameter should be drilled at the tip of each wedge. These holes are too small to be shown on fig. 4. They will make cutting easier.

The paddles can be jointed together by staples, nails, adhesive, sewing, or other means. The optimal solution depends on the sheet material, and availability/cost of the fasteners.

In a rare case where the flat sheet is very thick, the paddles should abut with each other. No margin should be provided in this case. Some clearance should be provided for the adhesive. In addition to adhesive applied in the gap, adhesive tapes can also be applied on the inner and outer surfaces to hold the paddles together. Of course, tapes applied on the inner surface should be very thin so as not distort the reflecting surface.

It is generally advisable to attach one paddle at a time, either clockwise or counter-clockwise. Attach each paddle from the outer section first. Then proceed inward. Attach all sections of a paddle before working on another paddle.

Unless your sheet is already reflective, a reflective foil should be applied after the parabolic reflector takes shape. Aluminum foil for ordinary kitchen use is ideal. A thicker (heavier gage) foil will be more durable. Aluminized plastic film such as shiny food and beverage bags, or gift-wrap, is acceptable but slightly less efficient and noticeably less durable than aluminum foil.

Usually the foil is glued to the reflector. Most water-based glue will do. This includes glue made of flour, rice, or starch. To avoid wrinkles on the foil, the glue must be thin enough that it flows easily.

It is easier to glue the foil on a flat sheet than on a parabolic dish. However unless the sheet is very thin, the process of bending the sheet will create wrinkles on the foil. Therefore it is best to apply the foil after the dish is formed. By the way, sheet material that expands and contracts significantly with humidity and temperature also tends to create wrinkles on the foil. This is why cardboard is not an ideal sheet material. The wrinkles reduce the efficiency. They also shorten the life of the foil.

The foil should be cut into trapezoids first. Two identical trapezoids can be cut from a rectangle with very little waste (fig. 5). Try with used newspaper first to determine the optimal width, length, and slope, as it depends on the shape and size of your foil supply. Short slots may be cut along edges of the trapezoid, so that the foil can overlap instead of wrinkle. The trapezoids should cover all facets completely, except that the inner circle will be covered by a circular foil at the end.

Coat the inner surface of a paddle thoroughly with glue. However do not overuse glue if the sheet material (such as cardboard) may swell when wet. Apply the foil, with the shinny side facing up. To avoid bubbles, it is best to engage a small portion of the foil on the paddle at first. Keep most of the foil in the air, free of glue. Then slowly extending the engaged area by pushing over the foil. It is best to attach foil near its center line (along its length) first. So that it will be obvious how much the foil should bend and overlap near its edges. It is OK if excess glue smears over the reflecting surface. The glue can be wiped off later.

It is best to overlap the foil slightly, so that no direct sunlight will strike the sheet material. For the same reason, it is best to have a little extra length so that the foil can fold over the rim of the dish. This prevents ultraviolet in the sunlight from damaging the reflector.

When the entire reflecting surface is covered by aluminum foil, wipe the reflective surface gently with damp, clean cloth. Wash the cloth frequently as needed. The wiping removes excess glue, flattens the foil, and improves adhesion. Allow the glue to dry, which may take a few days if the sheet material is permeable to water. Then wipe again with damp, clean cloth to remove the remaining glue smear and smudge.

Caution:

Do not work with reflective material in direct sunlight, as it may cause eye injury. Keep your reflector indoors until it is completely assembled onto a solar cooker.