Fig. 1 shows a parabolic reflector. Light rays parallel to the axis are reflected at the central point called focus (F). They can be of dish type (one focal point) or though type (parabolic cross-section; light focused along a line). Using parabolic reflector instead of hemispherical avoids spherical aberration.
Fig. 2 shows a crude model of parabolic water pasteurizer constructed in Rwanda entirely from the locally available metal sheet roofing material. The two supports and the trough are pre-cut for easy assembly.
There are at least two issues with this design:
1) There is no way of knowing if the bottle is placed along the focal line.
2) There is no way of knowing whether the trough is of parabolic shape.
The objective is to design a solar trough for water pasteurization that
1) has a clearly identified focus
2) retains the shape of a parabola
3) the trough is easy to build for someone with limited knowledge of mathematics.
If the parabola is given by an equation:
y = a x2
Then the focal length is given by:
F = 1 / 4a
The focal point has the (x, y) coordinates of (0, F).
Fig. 3 shows a parabola of the equation (1) where a = 1.
As two points define a straight line, three points uniquely define a parabola. In addition, parabola has to be symmetrical. The above parabola is defined by points (0, 0), (1/2, 1/4), and (1, 1). The focal point has coordinates (0, 1/4).
Fig. 4 shows a cross section of the parabolic shape of a solar collector with sun rays converging at the focal point F. A small lens or concave mirror (L/M) can be used to orient the trough toward the sun by focusing light on the tangent parallel surface.
The drawing to the right shows a view of the parabolic trough. Between x = 0 and x = 1, the length of a parabola given by equation (1), where a = 1, is 1.479. Between x = 0 and x = 0.5, the length is 0.574. That way one can determine the exact location to attach supports L and S.
If one connects points (½, ¼) and (-½, ¼) and points (1, 1) and (-1, 1) at the two ends of the trough, it will assume close-to-parabolic shape at the cross section with the focal axis clearly defined.
One can use four supports connecting those points: two long (L) and two short (S). The line connecting the centers of the short supports is the focal axis (A). If one cuts notches in the supports and the trough, they can be installed without any additional parts. A bottle (B) (dark for pasteurization or even boiling liquid; transparent for improved solar disinfection aka SODIS (Solar disinfection)–type UV treatment of water on a partially cloudy day or with one side painted to enable both uses) is placed along the focal axis.
Long and short supports L and S have a dual role: they provide structural integrity, and they assure close-to-parabolic shape of the trough. In addition, short supports S have a third role: they pinpoint the focal axis A. The device can be used for (a) pasteurization of all liquids, (b) boiling water, (c) cooking, and (d) improved above-mentioned SODIS-like treatment. Multiple bottles can be placed in a long trough.
Fig. 5 shows a photo of an improved working prototype with a brown beer bottle in the trough. The trough is made from two layers: cardboard for structural integrity and a thin reflective surface, both cheaply obtained from arts supply stores. The four supports are wooden. Both supports and cardboard/sheet metal are precut log cabin style (notched) for easy assembly without tools. Additional supports can be used to place the bottle exactly along the focal axis, but, because of the short focal length, the bottle can simply be laid inside. The device can be propped to face the sun.
I ran the experiment using the setup shown on Fig. 5 on April 5, 2009. The ambient temperature was only 13 oC (55 oF) on a sunny day.
I placed a brown beer bottle in the trough. Since the focal axis is close to the apex, most of the time, depending on the position of the sun, one doesn’t need a special support as the sun rays are focused somewhere on the bottle’s surface.
I filled the bottle with water and placed a WAPI (water pasteurization indicator) inside. Water is pasteurized at 65 oC (149 oF). Milk and food are pasteurized at 71 oC (160 of). WAPI (obtained from Solar Cookers International) contains wax that melts at 71 oC.
Fig. 6 shows the use of reflective mirror (Solar Spark obtained from Sundance Solar) to orient the parabolic trough so that faces the sun (as shown on Fig. 6). One can see the smoke coming from the piece of cork at the focal point. The use of such device is not necessary but it helps.
Success! Fig. 7 shows that the WAPI had melted. Within an hour the bottle was so hot I couldn’t touch it. The water seemed to be close to boiling. One could use long troughs to pasteurize several bottles at the same time.
I later used the setup shown on Fig. 5 to boil water for coffee after we lost electricity due to snowstorm.