Solar Cooker Performance Evaluation by Reciprocity with Photographic Analysis
A unique new method of determining the effective area of solar cookers has been developed. Initially it was developed for panel and parabolic cookers but it has been shown to work for box cookers. Results from preliminary tests on the performance of a CooKit and a Sunny Cooker are included.
A new way of determining the performance of panel and parabolic solar cookers has been developed. Some people have used the reflection of the pot on the reflectors in various ways. However, since no reference to the overall procedures has been found, the procedure is believed to be original. Digital photographic techniques are used to evaluate the effective area of the cooker. The results can be presented in terms of the effective area of the cooker or the effective area can be multiplied by solar intensity (in Watts per unit area) to determine the power impinging on the cooking pot (in Watts).
The new procedure is based upon reciprocity and is referred to as the Reciprocal Method of Solar Cooker Performance Evaluation. In the normal operation of a panel or parabolic solar cooker, parallel rays from the sun enter the mouth of the cooker and some of them are focused onto the cooking pot. In this new procedure, the process is reversed. The pot becomes the source of light. Rays from the pot travel in all directions. However, the effective rays are the ones that travel toward the spot where the sun would be if the cooker was operating normally. A photograph of the cooker is taken with a digital camera that is placed in front of the cooker on a line toward the spot where the sun would be if the cooker was operating normally. Figure 1 is a typical photograph of the CooKit set for a sun elevation angle of 45 degrees with the front flap in the upper position. The effective area of the cooker is the illuminated area in the photograph. Photo analysis software is used to determine the number of illuminated pixels in the photograph. This result and the pixel density which is determined from a calibration photograph such as Figure 2 are used in the calculation of the the effective area of the cooker.
 In radio antenna design, a somewhat similar principle is called the reciprocity theorem. The reciprocity theorem states that the performance of an antenna is identical whether the antenna is used for transmitting or receiving.
 The effective area of a parabolic or panel cooker is a cross section perpendicular to the sun’s rays at the mouth of the cooker for which the sun’s rays hit the pot. It is proportional to the power impinging upon the pot.
Figure 1: Cookit at 45 Degree Sun Elevation Angle
Figure 2: Calibration Photograph
Description and Procedure
This section includes a more detailed description of the new method of determining the effective area of a cooker.
Light Source- Pot Substitute
Since in this reciprocal test the cooking pot becomes the light source, one challenge was to find a glowing pot. A compact florescent light was placed inside the bottom part an orange plastic pail. The pail is 5⅛ inches diameter at the bottom, 7⅛ inches at the top and 6 inches high. The top of the pail was cut from a green plastic wastebasket. The top was made a different color in an effort to make it possible to identify what portion of the incoming power hits the top of the pot. The size and shape of the pot may affect the performance of the cooker, but this pot appeared to be a reasonable compromise for the initial tests. Figure 3 shows the pail mounted in a CooKit tilted at 45o, with the light in the pail off and the room lights on. Figure 1 is a similar set up with the light in the pail on and the room lights off.
Figure 3: CooKit with Pail Light off and Room Lights on
Description of Test Set up and Procedure
When testing cookers, the basic test set up consists of the cooker under test with pail (the light source) mounted where the pot would normally be in the cooker. A digital camera is placed on a tripod in front of the cooker. The camera is placed as far from the cooker as possible to minimize parallax effects (parallax effects are explained later in this paper). For most of the preliminary tests, the camera was about 26 feet from the cooker. The height of the camera is set at the same height as the center of the pail. The height of the camera remains constant for all sun elevation angles and the cooker is tipped forward at an angle corresponding to the sun elevation angle.
The tilter shown in Figure 4 was constructed to aid in tilting the cooker. The tilter is made from two pieces of wood attached at one end by a hinge. The resulting tilter is essentially a large hinge. Three triangles (a 15o-75o triangle, a 30o-60o triangle and a 45o triangle) were cut from wood and are used for adjusting the tilt angle. In Figure 4, the 45o triangle is holding the CooKit at 45o tilt and the other two triangles can be seen in the background. These triangles make it possible to set the tilt angle from 15 degrees to 90 degrees in 15 degree increments. Since the cooker is tipped forward by as much as 90 degrees, it is necessary to attach the pail and the cooker to the tilter. This was done by drilling a small hole through the bottom of the pail, the bottom of the cooker and the tilter and installing a bolt through the hole.
Figure 4: Tilter at 45 Degrees
Test Procedure for a Typical Reciprocal Test of a Panel or Parabolic Cooker:
1. The cooker to be tested is mounted on the tilter with the pail (light source) mounted where the cooking pot normally would be located.
2. The digital camera is set up on a tripod in front of the cooker at the height of the center of the pail. The camera should be as far from the cooker as possible to minimize the effect of parallax. The zoom on the camera should be adjusted such that cooker is included in the photograph with minimal border. Once set, it is important that the zoom and the position of the camera remain constant throughout the test.
3. The light in the pail is turned on.
4. The room lights are turned off.
5. The tilt angle (sun elevation angle) is set at 15 degrees. The digital camera is turned on and adjusted and a photograph is taken.
6. Repeat step 5 for tilt angles of 30, 45, 60, 75, and 90 degrees. Figure 5 is a collage of the six photos that were taken during one test of the CooKit with the front flap on the upper line.
7. To obtain a calibration photograph such as figure 2, turn the room lights on and replace the cooker with a large piece of board type material with a rectangle of known size and contrasting color attached to the board. When taking the photograph, it is important that the zoom setting and position of the camera be unchanged from steps 5 and 6.
8. Process each of the photographs from steps 5, 6, and 7. There are several computer programs that could be used for obtaining the desired results from the photographs. However, GIMP (http://www.gimp.org/) was used for the initial tests. GIMP has the functions needed for this analysis and is unrestricted freeware that anyone can download and use.
a. The goal of analyzing the photographs from steps 5 and 6 is to determine the number of illuminated pixels in the photograph. This can be done by using the threshold function in GIMP. After some experimentation, it was found that the best results were obtained by opening two copies of the photograph in GIMP. The GIMP threshold function is used on one of the copies and the threshold level is adjusted until the area above the threshold matches the illuminated area in the other copy. The threshold adjustment must be done with care but with a little practice it is possible to obtain consistent results that are believed to be quite accurate. Since the threshold function in GIMP does not give the number of pixels above the threshold, it is also necessary to open the histogram function which can be adjusted to give the number of pixels above the threshold.
b. The goal of analyzing the calibration photograph from step 7 (Figure 2 is a typical calibration photograph) is to determine the number of pixels in the rectangle of known size. The threshold function in GIMP is used. However, since in this initial test setup, the rectangle was black on a white background, the black pixels were the ones below the threshold.
c. Using the results from step 9(b) divide the number of pixels in the rectangle by the area of the rectangle. The result will be pixels per unit area. Divide the number of illuminated pixels from each of the photographs analyzed in step 9(a) by the pixels per unit area to obtain the effective area of the cooker.
d. The results of the test could be left in terms of the effective area of the cooker, but the effective area is usually multiplied by a typical solar intensity to obtain the power in Watts. For the initial tests, the incoming solar intensity was assumed to be 1000 Watts/m2. It was assumed that 10% of the solar radiation is diffuse and does not contribute to the reflected power and that the reflectivity of the reflective material is 80%. Therefore the resulting solar intensity is reduced to 720 watts/m2.
e. As the photographs are analyzed, the results are entered into an Excel spreadsheet where the calculations are done and the results are plotted.
 While developing the procedure, several room lighting schemes were tried but the best contrast between the illuminated and non illuminated portions of the photographs was obtained with the room lights off.
 For the initial tests, a 9 inch by 12 inch sheet of black construction paper was attached to a sheet of Coroplast.
Figure 5: Collage of Photographs from One Test of CooKit Performance
Test procedure for a typical test of a box cooker:
The procedure for testing a box cooker is similar, but slightly modified from that used for testing a panel or parabolic cooker. There are two cases to consider when testing box cookers.
1. For box cookers such as the Global Sun Oven, where the interior surface of the box is black, the reciprocal method can determine the solar power that is hitting the window of the box. A light source is placed inside the box and the window is covered with a translucent material. For this preliminary test, three layers of a plastic tablecloth were used as the translucent material. Except for the change of light source, the cooker test follows essentially the same procedure outlined in steps 1-8 for a panel or parabolic cooker. Figure 6 is a preliminary photograph that shows a Global Sun Oven tilted so that the window is vertical (perpendicular to the sun’s rays). This test was very preliminary and the only conclusion that should be drawn from it is that the reciprocal method may have potential for evaluating the performance of box cookers.
2. For box cookers where the interior of the box is reflective material and the goal is to reflect as much as possible of the incoming solar energy onto the pot, it may be useful to use the same sight source as for panel and parabolic cookers and put it inside the box where the cooking pot would normally be. Then follow the same procedure as for panel and parabolic cookers.
Figure 6: Preliminary Photograph of a Global Sun Oven Under Test
Preliminary Test Results for a CooKit
and a Suncooker
Preliminary tests of the performance of a CooKit and a Sunny Cooker were done while perfecting the reciprocal method of testing solar cooker performance. These tests probably will be refined and repeated later, but the preliminary results illustrate the power of the procedure.
The CooKit that was tested was purchased from Solar Cookers International. The CooKit was mounted on the tilter and the complete procedure outlined in steps 1-8 of the “Test Procedure for a Typical Reciprocal Test of a Panel or Parabolic Cooker” was done for each of the two marked positions of the front panel (about 13 and 35 degrees from horizontal). The results of these two tests are plotted on figure 7 along with a CooKit Maximum curve which is the maximum of the two tests for each sun elevation angle.
Figure 7: Power Impinging on Cooking Pot in CooKit vs. Sun Elevation Angle
A Sunny cooker was constructed from cardboard with a Mylar reflective surface using the plan on the Sunny Cooker website. The Sunny Cooker was tested in each of the four positions described on the Sunny Cooker website. The results of these four tests along with a maximum curve are plotted on Figure 8
Figure 8: Power Impinging on Cooking Pot in Sunny Cooker vs. Sun Elevation Angle
The CooKit and the Sunny Cooker performance are compared by plotting the CooKit Maximum and the Sunny Cooker Maximum on Figure 9.
Figure 9: Maximum CooKit Power and Maximum Sunny Cooker Power
Resolving Transmission Path of Rays
from Pot to Camera
In normal operation of a solar cooker, the sun’s rays hit the pot (or window for a box cooker) in one of three ways. They can:
1. Direct rays that hit the pot with no reflection.
2. Primary reflection where the rays are reflected once before hitting the pot.
3. Secondary reflection where the rays are reflected two or occasionally more times before hitting the pot.
It is important to know which type of path the rays follow because the intensity of the rays hitting the pot will vary with the path. For example, if the solar intensity is 1000 W/m2, the diffuse component is 10% (which does not contribute to useful reflection), and the reflectivity of the reflective surface is 80%, the corresponding intensities will be:
1. 1000 W/m2 for direct rays.
2. 1000(0.9)(0.8)=720 W/m2 for primary reflection.
3. 1000(0.9)(0.8)2=576 W/m2 for secondary reflection with two reflections.
When testing cookers using the reciprocal method, the path of the light rays is reversed. Light rays are emitted from the light source (the pail) and the effective rays are the ones that travel toward the camera that is located where the sun would have been if the cooker was operating in normal mode.
1. Direct rays travel directly from the pot toward the camera.
2. For primary reflection, rays from the pot are reflected once before traveling toward the camera.
3. For secondary reflection, rays from the pot are reflected two or more times before traveling toward the camera. More than two reflections are unusual and unless otherwise indicated secondary reflection refers to rays that are reflected twice.
In the preliminary tests reported in the previous section, all of the effective area was treated as primary reflection. This underweighted the direct rays from the pot, but it was thought that this might not be too important when comparing cookers using the same pot. However, the test of the CooKit yielded some unexpected results. For example, Figure 9 shows 213 watt peak power for a sun elevation angle of 60 degrees with the front reflector at about 35 degrees. This peak was not present in a previous computer simulation of the CooKit performance. It was believed that this unexpected peak was primarily due to secondary reflection that had not been included in the computer simulation. Therefore, an investigation was conducted to determine the contribution from each of the three paths.
A laser level was attached to a tripod and was used to check the path of the incoming sun’s rays. For example, Figure 10 shows the laser level with the beam reflecting from the front flap, then from the side reflector and then hitting the pot. This verified that the illuminated areas on the left and right ends of the front flap were from secondary reflections. Another secondary reflection was found where the beam hit the lower front portion of the side reflectors, then the bottom of the cooker and then the pot. Black construction paper was the carefully placed on the cooker where it would eliminate the secondary reflections without effecting the primary reflections. Most of the bottom of the cooker was covered as well as the left and right ends of the front flap. Figure 11 shows the CooKit tilted at 60 degrees with the front flap in the upper position. The upper portion of the figure has the black paper in place to eliminate the secondary reflections and the lower portion has the black paper removed.
Figure 10: Laser Level Showing Secondary Reflection
Figure 11: CooKit With and Without Secondary Reflection
The CooKit was tested for sun angles from 15 to 90 degrees with the black paper in place and with the black paper removed. Also, at each sun angle, the direct radiation component was determined by using GIMP to determine the number of number of pixels in the pail in each photo. Figure 12 shows the results of these tests.
Figure 12: Direct, Primary Reflection, and Secondary Reflection Components of CooKit Power
When using the reciprocal method to analyze cooker performance, ideally one would like to capture parallel light rays from the cooker. However, since a digital camera is used, it captures the rays that converge on the lens rather than the parallel rays. It is important to understand and minimize the effects of this parallax. It affects the results in two ways that will be described separately.
1. Objects in the photograph will appear closer to the center than they really are. This effect is illustrated in Figure 13. The brown line from point E to point A represents a reflective surface oriented 30 degrees from the centerline. The dashed red line represents a light ray from P to reflection point A and after reflection continuing parallel to the centerline toward an observation point an infinite distance away. However, if the observation point (digital camera) is at point C, the ray will follow the blue line and the reflection point will appear to be at point B instead of A. The MathCad program in appendix A was used to compute the location of point B and the percentage that the apparent reflection point B is moved toward the centerline. The case shown in Appendix A is the same as the one shown in Figure 13. For this case, parallax causes the reflection from point A which is 16 inches from the center to appear 12.52 inches from the center at point B. The reflection appears to be 21.7% closer to the center than is really is. Clearly 21.7% position change is unacceptable and the camera must be moved much further away to minimize this parallax effect. Most initial testing was done with the camera about 26 feet away from the center of the pot. At 26 feet the apparent position change is reduced to 5.3% and at 50 feet it is reduced to 2.9%. The 30 degree angle θ from the center line to the reflecting surface is the value at the outer edge of a funnel or Parvati cooker is thought to be one of the worst cases. For example, if θ is changed to 45 degrees as in the outer portion of most EB Cookers, the percentage position change is reduced to 20% at 4 feet, 4.7% at 26 feet and 2.5% at 50 feet.
Figure 13: Illustration of Parallax Effect 1
2. Pixels that are closer to the camera than the calibration point will be weighted more than those at the calibration point. This is because the area that is included in a photograph decreases as the distance from the camera to the surface is decreased. Since the total number of pixels in a photograph does not change with distance, the pixel density increases by the same fraction that the area decreases. It can be shown by simple geometry that the relative decrease in area as the distance from the camera is decreased from D to D-ΔD can be determined by equation (1).
∆A/(A )=(2×∆D)/D-(∆D/D)^2 (1)
If D=4’ or 48” and ΔD=6” then ∆A/A=0.234 or 23.4%
If D=25’ or 300” and ΔD=6” then ∆A/A=0.0396 or 3.96%
If D=50’ or 600” and ΔD=6” then ∆A/A=0.0199 or 1.99
1. Develop a more uniform light source. This should make it possible to more accurately determine which pixels are illuminated.
2. Develop the ability to determine what portion of the solar power hits the top of the pot, the sides of the pot, and the bottom of the pot. This probably can be done by making the top, sides, and bottom of the pot (light source) different colors and using software to measure the number of pixels in the photographs by color. However, this may be dependent upon the success of item 1 because initial attempts to identify areas by color were not successful due to non uniform color from the light source.
3. Set up a new test range where the camera will be 50 feet away from the center of the pot. Initial testing was done with the camera 25 to 26 feet away. However, analysis of parallax effects indicates that the camera should be further away. Fifty feet is the longest range that can be set up in the available space. Also, a camera with a longer optical zoom will replace the one that was used for the initial tests.