Design, construction, analysis and promotion of solar cookers
Reciprocal Optical Test for Measuring solar Cooker Performance
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.
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. 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
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.
 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 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.
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
Figure 5: Rear View of Test Stand That Can be Rotated
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.
Procedure for a Typical Reciprocal Test of a Panel or Parabolic Cooker:
The cooker to be tested is mounted on the test
stand with the pail (light source) mounted where the cooking pot normally would
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.
The light in the pail is turned on.
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.)
The tilt angle (sun elevation angle) is set at 15
degrees. The digital camera is turned on
and adjusted and a photograph is taken.
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.
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
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
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
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
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
8: Power Impinging on Cooking Pot in
Sunny Cooker vs. Sun Elevation Angle
Figure 9: Maximum CooKit and Sunny Cooker Power
on Cooking Pot
From Tests Using Rotatable Test Stand on 50 foot Test Range
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.
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.
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
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
Figure 13: Lightoven III: Power Hitting Pot vs.
Sun Elevation Angle
III: Power Hitting Pot vs. Cooker Rotation Angle
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
16: CooKit Rotation Test on 50 Foot Test
Range Using Rotatable Test Stand.
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
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 18: CooKit With and Without Secondary Reflections
Direct, Primary Reflection, and Secondary Reflection Components of
Reciprocal Optical Test of Hypar 42 and Parvati 32 Cookers
The Reciprocal Optical Test that I
developed for evaluatingSolar 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
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
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.
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
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.
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).
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:
More panel cookers
Hypar and other parabolic and parabolic approximation cooker