Subject:  Solar Funnel Cooker / solar cooking research at BYU
  
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   THE SOLAR FUNNEL
   Steven E. Jones
   Department of Physics and Astronomy
   Brigham Young University
   Provo, UT 84602 USA
   
   A funnel-shaped solar cooker has been developed to concentrate the
   energy brought by sunlight into a cooking pot or jar, then trap the
   heat using the greenhouse effect. A simple system allows
   pressure-cooking to increase the cooking rate while releasing steam.
   In this way, solar fusion energy can be used for cooking and
   pasteurizing water. The Solar Funnel will be particularly useful in
   sunshine-rich countries where the vast resource of the sun's fusion
   energy is appreciated.
   
   HISTORY
   
   The Parabolic Concentrator
   An early type of solar cooker uses a parabolic reflector as shown in
   Figure 1 to concentrate sunlight to a point. This parabolic
   concentrator was first tried in the 1860's but is difficult and
   expensive to build and can only cook small quantities of food. There
   is also a significant safety problem associated with concentrating
   sunlight to a point, where damage to eyesight can occur quickly. In
   Bolivia, fires have accidentally been started when such parabolas have
   been stored near wooden structures.
   
   ---->fig 1
   At BYU, we have built an inflatable parabolic cooker about 1.2 meters
   in diameter in order to make an inexpensive cooker of this type. We
   using aluminized plastic sheeting on one side and clear plastic
   sheeting on the other, sandwiched between two pieces of plywood with a
   1.2-m circular hole cut into each. A tube was inserted between the
   plastic sheets to permit inflation. When inflated, a reasonably good
   and inexpensive parabolic reflector is formed. Sunlight on January 11,
   1996 in Provo, Utah was focussed to a spot about 6 cm in diameter at a
   focal length of about 2 m. The concentrated sunlight ignited paper
   after a few seconds in the spot. Durability, portability and safety
   remain as deterrents to widespread use of this type of cooker.
   
   I have also conceived of replacing the curved parabolic reflecting
   mirror with a grooved but flat Fresnel parabolic reflector, as shown
   in Figure 2. This reflector is effectively a series of concentric
   reflecting conical sections of short-height, nested on a plastic
   plate. The resulting reflector is a flat reflector that is designed to
   concentrate sunlight to a diameter of about 10 cm rather than a point
   for safety reasons (and to avoid the likelihood of burning food). A
   wire mesh is mounted above the reflector so as to identify the
   location of the hot- spot, and a frying pan or cooking pot would be
   placed on this mesh-grill. A 1.1-meter diameter Fresnel reflector of
   this type would deliver about 500 Watts on a frying pan, at mid-day
   near the equator. The Fresnel Fryer is under development at BYU.
   
   --> fig 2
   The Solar Box Cooker
   
   The solar box cooker uses a glass plate to admit sunlight while
   keeping infrared radiation ("heat") effectively trapped inside the
   box. A pot or jar is placed inside the box, preferrably a dark color
   to absorb the sunlight. The cooking pot radiates heat mostly as
   infrared radiation while the glass or plastic plate on top of the box
   inhibits cooling by the outside air. The solar box oven thus formed
   dates from the 1760's, but most designs have been slow-cooking and
   expensive.
   
   In the mid-1970's, Barbara Kerr in the U.S. developed a solar oven
   that can be made from cardboard and aluminum foil along with a glass
   or plastic window. An adjustable reflecting plate above the glass
   plate concentrates additional sunlight into the oven (see Figure 3a).
   This type of box oven is promoted by "Solar Cookers International" (
   SCI, formerly Solar Box Cookers International), a nonprofit
   organization with headquarters in Sacramento, California. It has found
   acceptance in third-world countries throughout the world. A portable
   SCI solar box cooker is being sent to Bolivia in May 1996 for
   field-tests on the Altiplano, where sunlight is abundant but fuel wood
   is extremely scarce. A modification shown in Figure 3b permits
   additional concentration of sunlight by adding three more reflecting
   panels.
   
   -->figs 3a, 3b
   Reflective Cookers/ The Solar Funnel
   
   A weakness of the solar box cooker is that sunlight is admitted only
   through the top window, while heat escapes from all sides of the box.
   Good insulation is therefore required along the sides and bottom of
   the box, and typically two or three nested boxes (often with crumpled
   paper stuffed between boxes) are used to improve the insulation.
   Cooking is also slow, typically requiring rotation of the box to
   follow the sun over a 1 - 3 hour period.
   
   While studying the solar box cookers in Figure 3, I realized that one
   could place a clear glass jar (or oven-safe plastic bag) at the bottom
   of the reflectors, which would substitute for the box altogether, and
   allow sunlight to enter from all sides except just the bottom, which
   is insulated. A black pot or jar inside the clear jar or plastic bag
   would serve as the cooking vessel.
   
   By using a 60-degree cone-shaped reflecting funnel, sunlight would be
   concentrated along the axis of the funnel at the bottom, where the
   cooking pot or jar would be placed, as shown in Figure 4. Sticks or
   rope or cloth should be placed under the cooking jar (inside the
   plastic bag) to provide insulation. Safety comes from the fact that
   the sunlight is concentrated along a line deep inside the funnel where
   the eyes cannot go without blocking the sun. If you put your arm up
   the bottom of the funnel, it feels warm in a hurry; but it won't burn
   you. This is much safer than concentrating sunlight to a point above a
   parabolic collector, for example. The Solar Funnel was born.
   

               \         /
                 \     /
--> fig 4          \o/

   --> Start by cutting a 1-m diameter half-circle from cardboard (or
   thick plastic). Cut a concentric half-circle about 1-ft in diameter
   inside this. Glue (white glue + water 1:1 works well, just as Joseph
   Radabaugh said) Al-foil or emergency blanket to inside of cardboard.
   Then bring the two sides together to form a cone; hold with tape or 3
   nuts and bolts. The cone does not get hot. Back to text.
   
   The first Solar Funnels were made (at my home) cheaply from cardboard
   cut into a half-circle then covered with aluminum foil. The opening
   angle PHI of the funnel is related to the fraction F of a flat circle
   from which the cone is later formed as follows: sin (PHI/2) = F. White
   glue diluted about 1:1 with water was used to apply the aluminum foil
   to the cardboard.
   
   --> For a half-circle, F = 1/2, so the opening angle of the funnel =
   60 degrees. Our experiments show this is about right; 45 degrees is
   better if you want to keep moving the funnel to follow the sun. 60
   degrees works for about 1.5 hrs, just point the funnel a little ahead
   along the sun's path.
   
   We are exploring ways to make the solar funnel using aluminized mylar,
   laminated to another piece of mylar if necessary to make a
   self-supporting funnel. High-reflectivity is of course crucial to
   accelerate the cooking process. The funnel can be placed in a shallow
   hole in the ground to prevent winds from upsetting the cooker.
   
   -->We have made a few of these mylar-funnels, and they are neat, I
   think-- light, roll-able, easy to form into a funnel. I plan to make a
   bunch from Al-ized mylar, soon. Costed these at about $2.50 each when
   made in large quantities. Cheap enough?
   
   I have learned that SCI now sells a "Solar CooKit" which is somewhat
   similar in concept to the solar funnel described above. Figure 5 shows
   the geometry of this cooker, with five straight sides, which while
   clearly not as optimal as the funnel shape for concentrating sunlight
   will nevertheless be very useful. Two of these CooKits will also be
   taken to Bolivia in May for testing along with Solar Funnels and a
   solar box cooker.
   
   -->These are now on their way to the Altiplano for field testing by
   the Benson Institute of BYU, along with a solar box cooker, and 2
   solar funnels.
   
   ANALYSIS OF THE FUNNEL COOKER
   
   In sun-rich tropical countries like Bolivia, the sun's intensity on
   the ground is approximately 500 watts/m2 at noon. (In southwestern
   U.S., the figure is about 300 W/m2 at noon.) By assembling a funnel
   with a 60-degree opening angle to collect sunlight along an axis near
   the bottom of the cone, with a 0.5- meter opening at the top (chosen
   for ease of use and portability), we estimate heating of about 300
   watts even after accounting for reflection and insulation losses. This
   should permit cooking in an hour or two, with perhaps one re-alignment
   of the funnel to follow the sun.
   
   -->Check my numbers? Thanks.
   
   In Provo, Utah, on January 11, 1996, the outdoor temperature was 7.6 C
   (46 F) at 12:30 p.m. The angle of the sun above the horizon was about
   30 degrees (measured using a ruler casting a minimum shadow on the
   ground). Conditions were mostly sunny, with high clouds. A small can
   of baked beans (label was red and black mostly) was placed on
   cardboard (insulator) inside an oven- safe plastic bag and this was
   placed at the bottom of a solar funnel (laid on one side due to the
   very low angle of the sun) for 1.25 hours. A platinum-resistance
   thermometer was used to measure temperatures. At 13:45, the
   temperature on the can top was 97.1 C (207 F), to my surprise. The can
   was opened (with release of some steam) and the temperature at the top
   of the beans was 68.9 C. The beans were then stirred thoroughly, and
   the temperature in the beans was 61 C, showing that the beans had been
   warmed through rather evenly. I enjoyed a hot can of beans for lunch,
   heated using the sun's fusion energy. -->This was my first effort with
   the solar funnel.
   
   On January 12, water was heated in a jar which had been painted black
   on the outside then placed inside a larger clear jar. The water
   reached boiling temperature in about one hour despite winter
   conditions in Utah. The metal lid on top of the tightly- closed
   blackened jar reached 109.2 C. Subsequent experiments in Utah
   demonstrated that the solar funnel always heated water significantly
   faster than either the "solar cookit" or the solar box cooker. Tests
   in Bolivia will follow.
   
   We found that steam often builds up on the inside of the plastic bag
   or clear jar which is used to provide a "greenhouse effect" for the
   inner blackened jar. This steam tends to reduce the heating by the
   sun. So we developed a simple tube-on-disc that replaces the jar lid
   and allows steam to be carried out of the clear housing (Figure 6). In
   addition, we designed a simple cap to fit on top of this tube with a
   rim to permit circular weights to be added to the cap. This simple
   system allows pressure to build up in the jar to increase cooking
   rates. Every 10 C rise in temperature doubles the cooking speed. This
   pressure-cooking scheme should be particularly useful at high
   altitudes, such as the Altiplano in Bolivia, where cooking by boiling
   is retarded by the lower boiling temperature due to lower atmospheric
   pressure at the high altitude.

          _
        / | \  = metal cap fits over tube; has rim to hold
          |       heavy washers to allow pressure build-up
          |
          |  -- plastic bag tied here; steam escapes tube
          |
          |
 _________|___________ = disc, replaces lid in Mason / Kerr jar
 --                 -- = rubber ring goes under disc; seals

   Jar, painted black on outside, goes here, inside plastic bag.
   
   In conclusion, it is possible that the people in sun-rich countries
   such as Bolivia may be the first to tap into useful fusion energy
   (from the sun) on a broad scale, effectively leap- frogging past other
   nations.
   
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