Concentrated Cooker Final Report
Description of the Problem
The Solar Oven team here at Cornell has continuously collaborated with organizations in Nicaragua to improve upon the implemented solar box cooker design. The box cookers currently used by the women in Nicaragua reach temperatures up to 180 degrees Centigrade (350 Fahrenheit), which is high enough to cook food, but falls short of the temperatures required to fry food. This becomes a relevant issue when considering the typical Nicaraguan meal, which incorporates tortillas as a staple food. Tortillas must be fried, and this requires a cooking surface that reaches temperatures of at least 250 Centigrade.
Because the solar box ovens cannot fry these tortillas, they are presently being cooked on wood-burning stoves indoors. Typical Nicaraguan housing does not provide proper ventilation for such methods. This causes harmful particles and toxins (including carbon monoxide) to be dispersed into the air within housing units. If inhaled, these toxins can trigger asthma attacks and in some cases, cause cancer from long-term exposure. According to the Minnesota Pollution Control Agency, breathing air containing wood smoke can also "irritate eyes, lungs, throat and sinuses, reduce lung function (especially in young children), increase severity of existing lung diseases such as asthma, emphysema, pneumonia and bronchitis, increase risks of heart attacks, and trigger headaches and allergies." 1
Additionally, the manual labor required to gather and cut wood to fuel the stoves is a large time commitment. The surrounding environment consists mainly of forested areas, which means the Nicaraguans are both depleting their dwindling natural resources and further enabling soil erosion. Since the year 1990, Nicaragua has lost 20.6 percent of its forests. Currently, deforestation is occurring at rate of 1.3 percent annually 2. The primary threat to Nicaragua's forests is illegal logging; this is in part contributed to by wood demand for fueling stoves.
With this cultural context, the Solar Oven team started pursuing the concept of a concentrated parabolic cooker. The goal is to create a design that works well enough to be a possible alternative to wood-burning stoves. The concentrated cooker utilizes the geometry of the parabola in the reflector to focus sunrays at a single focal point; this gathers heat more rapidly and efficiently than a solar box cooker, and can reach the frying temperatures of 250 Centigrade. In consideration of its potential use in Nicaragua, the cooker design must be conscientious of the building materials available in the area and take into account the windy conditions outdoors.
The Solar Oven teams from previous years have made several attempts at achieving an effective concentrated cooker design. One team made a shallow, modular three-dimensional parabolic reflector, which was too small and inexactly executed to achieve any results. The most recent team built a large two-dimensional parabolic trough reflector, which failed to effectively focus the light at a single point. (See Appendix A for images of past projects.) After careful consideration, we decided to pursue a new three-dimensional (3D) parabolic design, which will conserve material and allow for a more compact, efficient concentrated cooker. Our main goal was constructing a functioning reflector that focuses light at a single focal point and heats the point up to 250 Centigrade.
Methods
In order to make informed design decisions, we needed to thoroughly research 3D parabolic cookers and their construction processes. We split up the concentrated cooker design-build process into two stages: (1) the parabolic reflector and (2) the framework for the reflector/cooking surface. After testing the reflector and confirming that it indeed had a single focal point and was able to rapidly gather heat, we went on to building its framework.
The Parabolic Reflector
Design:
Our research found that many of the existing 3D parabolic cookers are not parabolic, but in fact spherical. A spherical reflector is much easier to construct, but is not as effective as a parabolic reflector due to a phenomenon called spherical aberration. The diagram below (Figure 1) demonstrates the effects of spherical aberration in part (a) and its elimination with the parabolic reflector geometry in part (b), when considering light rays of parallel incidence.
Figure 1: Spherical Reflector and Parabolic Reflector 3
The spherical reflector is unable to focus light at a single focal point; rays that hit the surface further from the optical axis (the horizontal centerline) focus in tighter, and vice versa. The parabolic reflector remedies this problem by focusing all rays to a single focal point (as long as there is parallel incidence). We therefore decided to construct a true parabolic reflector, not a spherical one.
We also needed to determine whether to construct a shallow or deep paraboloid. Most 3D parabolic cookers utilize shallow parabola geometry. Shallow reflectors are more mobile and easily manipulated to the angles needed to receive direct sunlight. This also leaves more flexibility for the design of the cooking surface in relation to the reflector.
Lastly, we needed the dimensions of the shallow parabolic reflector we wanted to construct. Many of the reflectors we researched had a diameter of approximately one meter. We consulted with Tim Bond (the Manager of Civil Infrastructure Complex, including Winter Lab), and he said he had 3' by 4' aluminum sheeting, which was close to this dimension.
Construction
The construction of a 3D parabolic shape is not trivial. We quickly realized the impracticalities of molding sheet metal to the desired shape, and researched methods to build the paraboloid from petals. Figure 2 details how the flat sheet would look with the appropriate partitions, before assembly.
Figure 2: Sketch of Metal Flat Sheet with Partitions
Because Tim provided us with a thin 3' by 4' aluminum sheet, we decided not to cut out a circle and retain as much reflective surface area as possible. We first cut the sheet into 16 sections as shown, and then plotted the paraboloid points needed for a shape with a focal length of 25 cm. A center circle of diameter 3 cm was left uncut to preserve structural stability. Instead of cutting along the paraboloid petals and adhering them edge-to-edge, we folded the slices up and overlapped them to give us room for error. We used reflective tape to keep the petals in place and complete our 3D parabolic reflector. Below is the finished product in Figure 3. Appendix B Table 1 contains the points we used to create these petals, all dimensions in cm. Appendix B Figure 1 details how to plot the points in Table 1.
Figure 3: Finished 3D Parabolic Reflector
The Framework for the Reflector / Cooking Surface
Design:
The framework of the reflector has a cross-shaped support system, with measured parabolic geometry to properly maintain the reflector's shape. It also accommodates the tilting of the reflector to receive sunlight at different angles corresponding to its position in the sky due to time of day. Bolts and nuts tightened appropriately prevent the reflector from further rotating when the desired angle is achieved. The entire system is on wheels for greater mobility and braced for structural stability. Unfortunately, we were unable to start the design and construction of the cooking surface.
Construction:
Refer to our finished results shown in Figures 4 and 5.
