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Design, construction, analysis and promotion of solar cookers

Reciprocal Optical Test for Measuring solar Cooker Performance

Abstract

The Reciprocal Optical Test is a unique new way of measuring the performance of solar cookers.  Until now, there has not been an effective way of measuring the performance of a solar cooker over the full range of sun elevation angles and for a range of rotation angles between the sun and the axis of the cooker.  Since this is an optical rather than thermal test, data can be collected without waiting for the temperature to change.  The Reciprocal Optical Test is based upon reciprocity.  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 test, the process is reversed.  The illuminated pot becomes the source of light.  Some of the rays from the pot are reflected 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 in front of the cooker where the sun would normally be.  To minimize parallax, the camera should be a long distance (preferably 50 ft (15.2m) or more) from the cooker.  The room lights are turned off when the photo is taken.  The illuminated area in the photograph corresponds to the effective area of the cooker.  An experimental 25 ft (7.6m) test range was set up and, while the procedure was being perfected, preliminary tests on a CooKit and a Sunny Cooker were conducted.  The experimental test range was replaced with an improved 50 ft (15.2m) test range and rotational capability was added.  Then successful tests were performed on a Lightoven I, a Lightoven III, and a CooKit.  Tests on other cookers are continuing.





Introduction

A new way of determining the performance of solar cookers has been developed.  Previously, some people had observed the reflection of the pot on the reflectors and used it in various ways.  Brian White used both physical models and computer simulations to observe the reflection as the sun moved.  Several examples of his work can be seen on You Tube and Instructables using the user name Gaiatechnician.  The Reciprocal Optical Test uses full size cookers and measures the effective area of the cooker using digital photographic techniques.  No references have been found to other tests that actually measure the performance of the cooker in this way.  The test results can be presented in terms of the effective area of the cooker or can be converted to power impinging upon the cooking pot by using some reasonable assumptions about the solar intensity and reflectivity of the reflective material.  So far, this new test has been applied to panel and parabolic cookers, and a preliminary investigation indicated that it can have some applications to box cookers.

The new test procedure is based upon reciprocity and is referred to as the reciprocal optical test[1].  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 illuminated pot becomes the source of light.  Rays from the pot travel in all directions.  However, the effective rays are the ones that either travel directly or are reflected 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.  If the cooker was operating normally, sun hitting the illuminated area in the photograph would hit the pot.  Therefore, the illuminated area in the photograph is the effective area[2] of the cooker.  Photo analysis software is used to determine the number of illuminated pixels in the photograph.  This result is divided by the pixel density to determine the illuminated area which is the effective area of the cooker.  The pixel density that is used in the calculation of the effective area of the cooker is determined using a calibration photograph such as Figure 2.  Photo analysis software is used to determine the number of pixels in the rectangle.  The pixel density is obtained by dividing the number of pixels in the rectangle by the area of the rectangle.


[1] 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.

[2] 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 of Test Setup

When testing cookers, the basic test set up consists of the cooker under test mounted on a test stand and a digital camera.  The light source (initially a plastic pail) is 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 the preliminary tests, the camera was about 25 ft (7.6m) from the cooker.  After the preliminary tests, an analysis of parallax effects showed that the camera should be further away.  Therefore, a new 50 ft (15.2m) test range (the longest possible in the available space) replaced the 25 ft (7.2m)range.  The height of the camera is adjusted to be the same height as the center of the pail.  The height of the camera remains constant for all sun elevation angles.  The cooker is tipped forward at an angle corresponding to the sun elevation angle. 

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 in (13 cm) diameter at the bottom, 7⅛ in (18 cm) at the top and 6 in (15.2 cm) 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 can affect the performance of the cooker, but this pot appeared to be a reasonable compromise.  This light source has been used if all panel cooker tests so far, except for the test on the Lightoven I where a taller thinner pot structure was used.  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 the Light in Pail Turned Off and Room Lights On

Test Stands for Holding Cooker During Test

Two test stands have been used.  For the preliminary tests, the tilter shown in Figure 4 was used to support the cooker.  The tilter is made from two pieces of wood attached at one end by hinges.  The resulting tilter is essentially a large hinge.  Three triangles (a 15-degree by 75 degree triangle, a 30 degree by 60 degree triangle and a 45 degree triangle) were cut from wood and are used for adjusting the tilt angle.  In Figure 4, the 45 triangle is holding the CooKit at 45 degree tilt.  Two other triangles can be seen in the background. These triangles are used for adjusting the tilt angle from 0 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.  Then lamp parts were used to run the power cord for the light through the hole up into the pot.

Figure 4:  Tilter at 45 Degrees

After the preliminary tests, the tilter was replaced with a new test stand that could be rotated as well as tilted.  Figure 5 is a rear view of the rotatable test stand.  It rotates on a lazy Susan  bearing.  The radius of the rear arc was adjusted to make one degree of rotation correspond to one centimeter.  A printable cm scale was glued to the arc.  The tilting function operates the same on the new test stand as on the tilter.

Figure 5:  Rear View of Test Stand That Can be Rotated and Tilted

Cameras Used for the Test

Two different cameras have been used for the tests.  For the preliminary tests, a pocket camera with limited manual control and zoom was used.  However, on the 50 foot test range, the camera needs a long zoom lens and should have full manual control.  A DSLR could meet the requirement, but would require a minimum zoom lens of about 480 mm which would be large and expensive.  Very few non-DSLR cameras have both a long zoom and full manual control.  A Panasonic FZ150 which has 24X zoom, full manual control and raw capability was used for the later tests.  Most photos on the 50 foot test range were taken using manual camera settings and about 22X zoom.

Test Procedure for a Typical Reciprocal Test of a Panel or Parabolic Cooker:

  1. The cooker to be tested is mounted on the test stand 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 the 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.  (While developing the procedure, several room lighting schemes were tried, but the best contrast between the illuminated  and non-illuminated portions of the photograph was obtained with the room lights 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 6 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 place a piece of board type material with a rectangle of known size and contrasting color attached to the board the same distance from the camera as the center of the pot.  (For the initial tests, a 9 in (22.9cm) by 12 in (30.5 cm) sheet of black construction paper was attached to a sheet of white plastic fluteboard.  Later tests used a 9 by 12 in sheet of white construction paper on a piece of black foamboard.)  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 processing 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 to determine the number of pixels in the rectangle.  Then, the number of pixels in the rectangle is divided by the area of the rectangle.  The result will be pixels per unit area.  Then divide the number of illuminated pixels from each of the photographs analyzed in step 8(a) by the pixels per unit area to obtain the effective area of the cooker.

c.  The results of the test can be left in terms of the effective area of the cooker, but the effective area is often 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. 

d.  As the photographs are analyzed, the results are entered into an Excel spreadsheet where the calculations are done and the results are plotted.

Figure 6:  Collage of Photographs from One Sun Elevation Test of CooKit Performance.

The procedure is written for an Elevation Test.  However, the procedure for a Rotation Test is essentially the same except that the cooker is rotated rather than elevated for each photograph.

Preliminary Test Results for a CooKit and a Sunny Cooker

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 will be refined and repeated later.  The preliminary results illustrate the power of the procedure, but one should use the results with caution until further tests are completed. 

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 flap (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.

The Sunny cooker that was tested 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.

The CooKit and the Sunny Cooker performance are compared by plotting the CooKit Maximum and the Sunny Cooker Maximum on Figure 9.

Figure 7:  Power Impinging on Cooking Pot in CooKit vs. Sun Elevation Angle

Figure 8:  Power Impinging on Cooking Pot in Sunny Cooker vs. Sun Elevation Angle
Figure 9: Maximum CooKit and Sunny Cooker Power on Cooking Pot

Results From Tests Using Rotatable Test Stand on 50 foot Test Range

Lightoven Tests

The first cookers to be tested using both rotation and sun elevation tests were the Lightoven I and Lightoven III cookers.  These cookers were designed by Dr. Hartmut Ehmler in Germany.  As can be seen from the photos and descriptions on the Lightoven website, The Lightoven I and Lightoven III are very different cookers.  The test results shown in figures 10, 11,13, and 14 clearly illustrate the advantages and disadvantages of each design.

The Lightoven I is basically a parabolic trough with a tall thin pot located at the focal point of the parabola.  As figures 10 and 11 show, the peak power is high when the parabola is in focus (The measured peak power is the highest the author has seen in any panel cooker).  Apparently one of the design goals was to maximize the cooking power from the low sun in northern Europe.  The test results show that this design goal was met.  However, the downside of the high peak power is relatively critical focusing.  This effect can be observed in Elevation on figure 10 and in Rotation on figure 11[1]

The Light source (pot substitute) that was used for the Lightoven I test was constructed starting with parts from the pot structure that is supplied with the Lightoven I.  A compact florescent light was placed inside the polycarbonate tube that normally surrounds the cooking pot, and the inside of the polycarbonate tube was lined with lampshade material.


[1] The Sun Elevation Test on the Lightoven I was Performed with the cooker on the old tilter test stand.  The cooker was then removed from the test stand and the new rotatable test stand was constructed.  The cooker was then mounted on the new test stand and the Rotation test was performed.

Figure 10: Lightoven I: Power Hitting Pot vs. Sun Elevation Angle

Figure 11: Lightoven I: Power Hitting Pot vs. Sun Elevation Angle

Figure 12:  Pictures from Lightoven III Elevation Tests

Figure 12,which was prepared by Dr. Hartmut Ehmler, is a matrix of the 21 photographs from three sun elevation tests on the Lightoven III.  The illuminated area in each photograph is the effective area of the cooker and is proportional to the power hitting the pot.  The pictures show how the effective area changes with sun elevation angle.  Each photograph, when analyzed corresponds to one labeled point on one of the three traces on figure 13.  The results from two rotation tests on the Lightoven III.


The Lightoven III was designed as a portable general purpose cooker.  As can be seen from figures 13 and 14, the peak power is a bit less than in the Lightoven I, but it can be used over a much wider range of sun elevation and rotation angles.  It is a good general purpose cooker that requires only minimal adjustment while cooking.

The light source (pot substitute) that was used for the Elevation and Rotation tests on the Lightoven III is the same one that was used earlier for the tests on the CooKit and the Sunny  Cooker.

Figure 13: Lightoven III: Power Hitting Pot vs. Sun Elevation Angle

Figure14: Lightoven III: Power Hitting Pot vs. Cooker Rotation Angle

CooKit Results

The CooKit that had been tested on the 25 foot test range during the preliminary tests was retested using the rotatable test stand on the 50 foot test range.  The test results are shown on figures 15 and 16.  The author plans to obtain a new CooKit and repeat the test, because the CooKit is old, has been patched, and the shape may be distorted.

Figure 15:  Sun Elevation Test on the CooKit on the 50 Foot Test Range

Figure 16:  CooKit Rotation Test on 50 Foot Test Range Using Rotatable Test Stand.

Resolving Transmission Path of Sun's Rays

While not normally a part of the Reciprocal Optical Test, it is somewhat important to determine the path that various sun rays travel before hitting the pot.  There are three types of paths.  They are: Direct rays that hit the pot with no reflection, Primary reflection where the rays are reflected once before hitting the pot, and Secondary reflection where the rays are reflected two or occasionally more times before hitting the pot.  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: 1000 W/m2 for direct rays, 1000(0.9)(0.8)=720 W/m2 for primary reflection, and 1000(0.9)(0.8)2=576 W/m2 for double secondary reflection.

In the tests reported earlier in this paper, 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 preliminary 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 17 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 then carefully placed on the cooker where it would eliminate the secondary reflections without affecting 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 18 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.  The lower portion has the black paper removed.

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 19 shows the results of these tests.

Figure 17:  Laser Level Showing Secondary Reflection

Figure 18:  CooKit With and Without Secondary Reflections

Figure 19:  Direct, Primary Reflection, and Secondary Reflection Components of CooKit Power

Reciprocal Optical Test of Hypar 42 and Parvati 32 Cookers

Introduction

The Reciprocal Optical Test that I developed for evaluating Solar Cooker Performance has been used to test a Hypar 42 Cooker and a 32 inch diameter Parvati Cooker (Parvati 32) These tests were the first time that the Reciprocal Optical Test had been used to evaluate the performance of parabolic type cookers. The mechanics of the test setup work best when the cooker stand is in its normal vertical position. Also, if these cookers are aimed directly at the sun, the only variation for different sun altitudes is the aspect of the cooking pot. Therefore, the tests on parabolic style cookers were done for sun altitude of 0 degrees above horizontal.

Test Results

Figure 20 shows data that was obtained from Reciprocal Optical Tests that were performed on a Hypar 42 and a Parvati 32 solar cooker during April 2017. The results from a previously reported reciprocal optical test that was performed May14, 2014 on a CooKit were added to Figure 1 for comparison purposes. The CooKit data was from a rotational test, for a sun altitude angle of 45 degrees, with the front flap in the low sun position. (To be fair to the CooKit, it should be noted that the power reached 196 watts at a sun altitude angle of 60 degrees with the front flap in the high sun position.)


Figure 20: Optical Test Results for a Hypar 42, Parvati 32 and a CooKit


Figure 21 is a collage of all the pictures from the Hypar 42 test. Each picture is analyzed to determine one data point on the red Hypar 42 curve on Figure 1. As previously explained in more detail, the illuminated area in each photograph represents the effective area of the cooker under test. The number of illuminated pixels in the photograph is measured using photographic software. The effective area of the cooker is then found by dividing the number of illuminated pixels in the photograph by the pixel density. The pixel density in the photograph is determined by finding the number of pixels in a known size rectangle in a calibration photograph and dividing the number of pixels in the rectangle by the area of the rectangle.

The Reciprocal Optical Test measures the effective area of the cooker, and the results sometimes are presented directly in term of effective area of the cooker under test. However, we usually express the answer as power impinging upon the pot structure by multiplying the effective area by 720 watts per square meter resulting in power in watts. (The 720 w/m2 assumes that solar intensity on a surface perpendicular to the sun is 1000 w/m2, 10% is diffuse and will not be reflected toward the pot, and the reflectivity of the reflecting surface is 80%.)


Figure 21: Pictures from Hypar 42 Test


Figure 22 is a collage of the pictures from the Parvati 32 test.  Each picture was analyzed to determine one data point on the Parvati 32 curve on Figure 20.

Figure 22: Pictures from Parvati 32 Test

Parallax Effects

When using the Reciprocal Optical Test to measure 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. 

Parallax Effect 1

Objects in the photograph will appear closer to the center than they really are.  This effect is illustrated in Figure 23.  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.  However, if the observation point (digital camera) is at point C, the ray will follow the blue line.  Thus, 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.  It  also computes the percentage error between the distance from Point A to the centerline and the apparent distance that point B is moved toward the centerline.  The case shown in Appendix A is the same as the one shown in Figure 20.  For this case, parallax causes the reflection from point A which is 16 inches from the centerline to appear 12.52 inches from the centerline 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 25 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 angle at the outer edge of a funnel or Parvati cooker and is thought to be one of the worst cases for parallax.  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 23:  Illustration of Parallax Effect 1

Parallax Effect 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).   

Future Plans

  • Develop a more uniform light source.  This should make it possible to more accurately determine which pixels are illuminated.
  • 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.  Initial attempts to identify areas by color were not successful.  This probably was due to non uniform color from the light source and/or a poor choice of colors.  It is thought that it would be easier to distinguish pure colors such as pure red and pure green than the pastel orange and green which has been used in the tests so far.
  • Test a variety of cookers including:
  1. More panel cookers
  2. Hypar and other parabolic and parabolic approximation cooker


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