Description of the Problem
The solar box cooker presently in use by the members of Las Mujeres Solares de Totogalpa was developed over several years in order to avoid cooking on a wood burning stove. This cooker relies on the absorption of sunlight by a black body and conversion of the light energy to heat air, cooking food primarily via convective heat transfer. Though this is attractively simple in design and highly effective for many cooking needs, it is not suitable for applications that depend on conductive heat transfer (contact with a hot surface). This includes making fried foods and cooking tortillas, a staple of the Nicaraguan diet.
A sub group of the solar oven project this semester decided to expand the range of food which can be cooked by the sun in order to further eliminate the use of a wood burning stove. The team decided to devise a concentrating solar cooker to satisfy those cooking functions that are not compatible with a box oven design.
Research and Comparison of Existing Concentrated Cookers
Parabolic Dishes
The team initially examined design options that rely on a reflective parabolic dish. The geometry of a parabola takes incoming light that is parallel to its own line of symmetry and reflects the rays such that they converge on a single point in space called the focus. This focusing of sunlight can result in very high temperatures in a dark object placed at the focus. However, there were a number of issues with using a parabolic dish. In a review of existing parabolic cookers, none of the designs reviewed could be used to fry foods, as they relied on enclosed pots and/or clear plastic bags as the cooking vessel. This is related to the fact that the cooking vessel must intercept rays from many angles, unlike a flat cooking griddle that is heated from below by a wood fire. Likewise, a parabolic dish is somewhat awkward to use, as energy is aimed at a point hovering in space, requiring the cook to reach across the dish to reach the cooking vessel, which can create performance problems when the cook's shadow falls on the dish and blocks the sun. There are also safety concerns that users could easily burn themselves by accident if a hand strayed too close to the focus, the location of which is not visually obvious.
Non-Dish Concepts
Through further searching, however, the team uncovered three designs that did not rely on a parabolic dish as the reflector. Professor Bowman's FIT Concept 3, Professor Bernard's independently-developed NELPA cooker, and the Xavier Devos open focused cooker pictured below:
Left to Right: Bowman FIT Concept 3, Bernard's NELPA Solar Cooker, Devos Cooker
All three designs share several characteristics that make them very interesting as inspiration for this team's concentrating cooker. The user-interface is very similar to stove-top cooking, as the cook can stand behind a table with solar energy being directed onto pots and pans from below. This allows the cook to access the pot while cooking, so adjustments to the food such as patting of a tortilla can be done easily. Additionally, the cook's position behind the table also means that no shadow interferes with the reflector array, and the table top protects the user from being burned.
The Bernard and Bowman cookers rely on a linear array of flat panel reflectors rather than a 3-dimensional parabolic dish. This simplifies construction and is more intuitive in its design, since the modular reflectors can be thought of as individually angling to reflect sunlight onto the cooking element. The two designs also differ in a number ways, which the team will carefully consider in formulating its own Nicaraguan design. Bowman's FIT Concept 3 uses mirrors set in a straight line, in which each mirror flips up to an angle appropriate for reflecting solar radiation toward the cooking element. By contrast, Bernard's NELPA cooker appears to use an array of mirrors set into an approximately parabolic configuration. Although Bowman's linear array appears easier to design, the curved shape of the NELPA array saves space and allows the cooker to be folded into a convenient "packet" when not in use.
The Devos cooker utilizes a different design which is wider, increasing the collector area. The Devos concentrator is asymmetrical, with a complicated shape, close to a truncated paraboloid which is composed of piecewise mirrors. This design has a focus which is thrown off center and is located out of the sunlit zone that gets to the concentrator. Therefore, all the solar incident rays can be collected. Another special component of the Devos cooker is a device which can regulate the heat under the pot. A shutter and an indicator allow the cook to reduce or increase the heat under the pot based on the intensity of the sun at a given time. This adjustment can be paralleled to turning up or down the gas or electric on a basic stove and can certainly be easier than adjusting the heat on a wood burning stove.
The Devos shape and fabrication of the piecewise mirrors can be difficult to replicate and therefore the team has chosen a design which combines aspects of all three prototypes. The team has selected to develop a tabletop frame and two parabolic shapes which can move simultaneously in a swing component to focus the light onto a 10 inch diameter. The selected design also utilized the concepts of adjusting the heat as proposed by the Devos cooker.
Development of the Design
Design Criteria
In developing our concentrating solar cooker, our team sought to honor the following criteria:
1. Safety - The design should minimize the danger of burns and dazzling associated with using the cooker.
2. Power - The design should reliably yield enough heating power to cook common Nicaraguan foods, particularly tortillas. It should also be possible to modulate the power output to suit the cooking application.
3. Ease of use - The design should be comfortable and convenient to cook on. It should be compatible with current cooking implements and cooking habits. Ideally, it should be easy and intuitive to adjust for varying solar conditions.
4. Durability - Both the frame and the reflectors should be sturdy and hard-wearing.
5. Ease of storage - The design should be easy to transport and store.
6. Ease of repair and maintenance - The design should enable repair and maintenance using household tools and few specialized skills. Parts used should be replaceable and/or repairable and should be modular where possible.
7. Ease of construction - The construction of the design should be within the scope of readily available materials, tools, and skills. The cost of materials and construction should be minimized.
In particular, the team chose to emphasize safety and power when constructing the prototype, to help ensure a robust, useful, and compelling proof-of-concept.
Core Concept
The design devised by this year's team represents a novel contribution to the pursuit of simple, low-cost, yet robust solar cooking. Although it shares several defining characteristics with previous designs, the core design concept is unique within the context of this application.
A survey of existing literature reveals an apparent conundrum between simplicity and power. Concentrating cookers must gather solar radiation from a relatively large area and direct it onto a relatively small area. A simple 2-dimensional parabola shape is able to focus radiation in one dimension only - e.g. a parabolic trough can reflect light onto a line, but not onto a point. This limits their focusing power; however, 2D parabolas are simple to make, as one can simply bend a piece of sheet metal or other flexible material. By contrast, a 3-dimensional paraboloid is able to focus radiation in 2 dimensions---e.g. a mirrored satellite dish can reflect light onto a single point. However, 3D paraboloids are very difficult to build by hand and impossible to construct continuously from flat elements, relying instead on piecewise approximation of the appropriate geometry.
This conundrum is exemplified by a comparison between Bernard's NELPA cooker and the Devos cooker. In the aerial-view schematic shown infigure 1, the simple shape of the NELPA's concentrator is only able to focus light in the Y dimension, whereas the complicated shape of the Devos' concentrator is able to focus light in both the X and Y dimensions. The NELPA is much simpler to construct, but the Devos is significantly more robust, using its wide design to intercept a larger area and yield higher power.
Figure 1 - Simplicity vs. Power in the Bernard (left) and Devos (right) cookers
The design created by our team, however, combines the simple geometries of the Bernard cooker with the power of the Devos cooker using a simple yet powerful concept. It features inverted, secondary reflectors that reflect sunlight after it has struck the primary reflector. The wide primary reflector focuses radiation in the Y dimension (much like the Bernard cooker), whereas the inverted secondary reflectors focus radiation in the X direction. The use of two separate concentrator geometries rather than one allows the design to simplify each reflector component, which greatly reduces the cost and complexity of construction without sacrificing the area of solar radiation that can be captured.Figure 2depicts our own design alongside graphs of the parabolic geometries at play, depicted in green. The reflectors form a single assembly that pivots like a swing to accommodate varying solar elevations.
Primary Reflector Parabola (Side View)
Secondary Reflector Parabola (Front View)
Figure 2 - Combining simple geometry with wide area using the secondary-reflector concept
Determination of Targets and Parameters
Upon arriving at our core design concept, the team had to identify our design constraints and boundary conditions in order to arrive at appropriate dimensions and specifications. The team began by determining what power output would be necessary in order to achieve the desired performance. To this end, research was conducted on Nicaraguan cooking needs and habits. Advisor Tim Bond knew from previous trips that the women of this village cook tortillas in aluminum pans, the largest being perhaps 12" in diameter. The team thus decided that a round cooking hole 10" in diameter should suffice and sought information on what wattage would be sufficient for heating a surface of this size.
Nicaraguan tortilla recipes found online indicated that tortillas could be cooked on a modern electric kitchen griddle set to 400-450 degrees Fahrenheit. Since electricity converts to heat with nearly 100% efficiency, the wattage of various electric griddles served as an excellent reference for the solar power needed. The team discovered one model whose small size was comparable with the 10" cooking hole. The Presto "Liddle Griddle" measured 8.5"x10.5" -only slightly larger in area---and drew 1000W of electrical power. For the concentrating solar cooker, the team assumed a 10% loss in power due to the known properties of the aluminum that would be used as reflective material in Nicaragua. Thus, it was determined, that the cooker should intercept 1111 W of solar power.
The standard assumption of solar insolation used for the box ovens was 1000 W per square meter (as measured perpendicular to the sun rays), a figure that was corroborated by online research. This meant that our design's reflector assembly needed to be large enough to intercept sunlight falling on an area 1.111 m2 in size.
Our next step was to decide upon a goal for what solar elevations our solar cooker should accommodate. Solar elevation is one of two angles that characterize the sun's movement over the course of a day. The solar azimuth is the angle between the sun and due north, and the solar elevation is the angle between the sun and the horizon. A cooker can be adjusted for solar azimuth by simply turning the entire cooker around a vertical axis to face the sun at all times. However, an angular adjustment to the swinging reflector assembly is necessary to adapt to changing solar elevation.
The team decided that a useful cooker should be operable for a minimum of 2 hours per day on the shortest day of the year. Tim Bond gave us an approximate Nicaragua latitude, from which we calculated that solar elevations ranging from 52o to 90oshould provide just under 2 hours of cooking on the shortest day of the year and 6 - 8 hours during the summer. The section titled Solar Elevation Calculations for Concentrated Cooker, found on the following page, provides complete calculations. Having determined the desired area and range of movement for the reflector assembly, the team was equipped to seek appropriate dimensions and focal lengths for the primary and secondary reflectors. To this end, the team created models of the reflectors in an excel spreadsheet to allow us to experiment with various parameters and observe the effects. This excel file, named Concentrating_solar_cooker_VISUALIZER.xlsis on the CD and should also be available on the website.
The "primary reflector" tab graphs a parabolic shape relative to the ground, incoming sun beams, and the tabletop (i.e. the focus of the parabola). The user is able to adjust the inputs for focal length, tabletop height, and solar elevation. The allowable tabletop height was constrained by human comfort, as it needed to be low enough for comfortable cooking. This, combined with the desired range of solar elevations, placed a constraint on how long the reflector assembly could extend in the Y direction. If the assembly was too long, we could see that the reflector would run into the ground before it could swing low enough to reach the position for 52o solar elevation. Alternatively, it could extend above the edge of the tabletop as it is swung high to accommodate 90o, creating a safety hazard as the tabletop would no longer be between the reflector and the cook. Experimenting with various focal lengths allowed us to optimize the shape of the parabola to avoid these tendencies. We found that the maximum length that could be achieved in the Y-direction, given the constraints, was about 1.0 m as measured perpendicular to the sun's rays (or 1.2 m as measured parallel to the ground when positioned for 52o solar elevation). This occurred with a primary reflector focal length of 0.7 m.
Knowing this, we knew that the secondary reflectors needed at least 1.1m of "useful width" in order to provide the power necessary. The "secondary reflector" tab in the excel modeler graphs a parabolic shape relative to the tabletop and to the lower bound of how far the reflectors may extend. The allowable height of the secondary reflectors was found by subtracting the tallest point of the primary reflector from the total tabletop height. With this number in place, the user is allowed to experiment with the "intersect width" (which is a function of focal length). The modeler then calculates the resultant width of the X-dimension, given the height constraint. It also gives a corrected, "true width" to account for energy "wasted" from sunlight that lands on the flat space between the edge of the cooking hole and the beginning of the secondary reflector. From this model, we were able to determine that an intersect width of 0.75m gave a total width of 1.613m and a "true width" of 1.117m. Thus, we were able to achieve the collector surface area required and could feel confident about anticipated performance as we began construction. The section entitled Concentrated Cooker Technical Specifications, found on the following page, provides a summary of the concentrating cooker's dimensions and technical specifications.
Solar Elevation Calculations for Concentrated Cooker
The solar elevation angle is the angle formed between the sun and the horizon. Thus, the solar elevation is 0o at sunrise or sunset and 90owhen the sun is directly overhead such that objects do not cast a shadow. It is often denoted as ΘS and can be calculated using Equation 1:
The hour angle h is an expression of solar time for a given point on earth. It is the angle through which the earth must turn in order to bring the meridian of that point directly under the sun. Thus, the hour angle is 0o at solar noon and changes by 15owith each hour of the day. The hour angle is considered negative in the AM and positive in the PM.
h = [(Current Solar Time) - (Solar Noon)] * (15° / Hour) (2)
The sun declination d is the angle between the sun's rays and the plane of the earth's equator; it can be found using Equation 3: 
Thus, the solar elevation at any given time and place can be calculated based on 3 inputs: local latitude, current hour, and current date.
In designing the concentrating cooker, our team sought to ensure that the cooker would be useful for a minimum of 2 hours per day in Nicaragua. The solar angle equations given above allowed us to calculate the minimum solar angle the cooker must therefore accept in order to meet this boundary condition. The local latitude in Nicaragua is about 13o N, and we use an hour angle of ±15o in order to bound one hour before and after solar noon. Since the smallest number of useful cooking hours occurs on the shortest day of the year, we calculate solar declination d using N = 355 (corresponding to the winter solstice, December 21):
Concentrating Cooker Technical Specifications
Reflector Assembly |
Tabletop |
Performance |
- Total width: 1.613 m |
- Cooking hole: 10" across |
- Minimum solar elevation: 52° |
Construction of the Concentrated Solar Cooker
Components
A - Side Panel for Secondary Reflector
B - Secondary reflector fin
C - Primary reflector
D - Secondary reflector
E - Frame
F - Cook top
Materials
¼" plywood - reflector assembly
½" plywood - cook top surface
2X4 boards
Sheet metal - reflector assembly
Mylar - reflector assembly
Various fasteners: 1", 2" screws, & wood glue
The Process
The construction of the parabolic cooker went fairly smoothly due to the careful and lengthy design process. The team began construction on the cooker Nov. 28, 2009 and attached the table top Dec. 8, 2009. Work began on the secondary reflectors first, since they required the most construction time. Side panels for the secondary reflector were cut from ¼" plywood. Next, the fins were cut from ¼" plywood. These fins would attach the sheet metal to the side panels and form the parabolic shape of the secondary reflectors. The fins were designed such that the sheet metal would slide into slots cut into the fins at the top, and strips of ¼" plywood were glued in a straight line along the base of the side panel to hold the bottom of the sheet metal. ½" plywood strips and wood glue were used to attach the fins to the side panels. Pieces of ¼" plywood were glued to the bottom curve of the side panels to fold the parabolic shape of the primary reflector. See figure 1 below for further details.
The frame of the cooker was built next. This was fairly simple as it was constructed entirely from 2X4 boards, and held together by 2" wood screws. The entire reflector assembly was attached from the side panels of the secondary reflector to the frame by two bolts. The three figures below provide additional detail.
Once the secondary reflectors were attached to the frame, the primary reflector was slid into place, and 4 struts were attached underneath the sheet metal reflector, connecting the secondary reflectors together. This completed the reflector assembly, which is able to effectively "swing" from the frame to compensate for the varying solar angles. The struts were attached to the side panels of the secondary reflector using metal L-brackets and 1" wood screws.
The basic cook top was made from ½" plywood. A 10" diameter hole is cut in the middle. A 10" hole was the design specification the team had calculated given the parabolic shapes of the reflectors. The cook top and hole have not yet been insulated to prevent the cook top from burning. See figure 5 below for further detail.
Future Testing
The concentrated solar cooker prototype has only recently been completed, so the team is looking forward to testing it as much as possible. Initially, the maximum temperature the cooker is able to reach would like to be known, simply by running tests outside in varying conditions. Also, different reflective materials could be tested, keeping in mind the materials available in Nicaragua. As the design is a prototype, testing would initially be aimed toward finding out if the cooker performs to the standards it was designed for.
Future Modifications
There are a number of future modifications possible for the concentrated solar cooker. The reflective surface of the cooker may be increased, or decreased depending on its current power output, as well as different cook top designs could be used. The team has considered a few different cook top designs to hopefully allow the cooker to have more than one cooking area. Also the team has future plans to attach to the cook top something that would effectively control the amount of light coming through the hole, and thus control the temperature. Portability and durability are other areas the team would like to improve on the cooker.
Critical Theory Issues and Challenges
With the development of this concentrated solar cooker, the experience of frying a tortilla would completely change. Currently, the women of Nicaragua use a wood burning stove to heat an aluminum frying pan early in the morning. The tortillas are all cooked before the children are sent to school and the men of the household leave for work. The sun may not be strong enough early in the morning to actually fry the tortillas effectively, so the women would have to adjust their daily schedule to accommodate for this difference.
Cooking with the team's design would require a basic knowledge of solar insolation and how it changes through the course of the day. The swing would have to be adjusted approximately every fifteen minutes to focus the sun onto the cook top. Moreover, the cooker is obviously more effective when the sun is the strongest, and on days when the sun is in the sky for the longest. Therefore on longer summer days, it may be possible to cook for eight hours, whereas on the shortest winter days, the cooker may only be effective for two hours. Additionally, safety must be addressed. It is important to instruct users on the proper procedure of frying with the cooker. For example, a pot must be in place on the tabletop or the shutter must be closed when focusing the parabolic swing in order to prevent retinal damage. Looking directly at the focus is damaging to the eye. To bridge this knowledge gap the subgroup would like to provide a brief Spanish language manual, and provide a tutorial for cooker usage and safety upon arrival in Nicaragua during spring break.