What’s Happening

EmetteJep:

Thanks for your comment. I hope to post more but I am not sure when that will be. I have more insect photos waiting in the wings.

Lately I have been experimenting with efficient twig-fueled cooking stoves. I am very pleased with the results. Anyone interested can find what I did by doing a search on “rocket stoves”.

I have also been experimenting with regenerative radios, trying to find the one that uses the least power and fewest number of active devices (read: “transistors”) yet performs with sensitivity, selectivity, stability and covering a wide tuning range that includes short wave as well as AM broadcast. Someday I may publish my results. So far, it seems to me that three transistors are the minimum needed for a practical radio. I have been able to get one to run a long time on the power left in a battery that, for other purposes, is essentially dead.

From my organic garden I have been eating strawberries. Also: peppermint, curly dock, dandelion leaves, wild grape twigs and leaves, lambsquarters, winter savory, sorrel, garlic chives, common chives, wild lettuce and green onions. I typically collect a bowl full of an assortment of the above, wash it, chop it up fine, mix it with a bit of mayo, and eat it with biscuits, along with a tea from roasted dandelion roots.

I also love poke. It is very tender and has a delicate flavor. I do not include it in the above mix because it needs to be boiled twice before eating (or so I have heard; being one never to doubt authority, I always boil my poke twice).

I have a potato plant I transplanted when it volunteered in an inconvenient spot. Sweet potato slips are sprouting in the kitchen window. I also have carrots raising their heads in the garden. Carrots are all I deliberately started from seed this year (so far). They are slow growers, but I am faithfully keeping them watered and weeded.

I recently dumped a good bit of compost on the raised bed garden. The compost came from worm bins kept in the basement and an outside compost pile.

I still collect rainwater and filter it with a slow sand filter. I use the filtered water to hydrate the basement worm bins. I use unfiltered water to hydrate the outside bins and keep the seedlings from wilting.

I am still eating last years’ sour kraut from a jar in the refrigerator. It has been several months since I checked what is growing in the crocks kept in the basement. Reluctance to look comes from a little fear about what I might find.

I have not baked sour-dough bread for a while but I know how easy it is to create another starter from whole wheat flower should I ever need to.

I recently learned that the secret to soft biscuits is adding sugar to the dough.

I have not used the solar oven yet this year, mostly due to a sparsity of sunny days. It looks like summer is about to put an end to our rainy season soon, though.

It has been a good spring for wild mushrooms, but I have not found any that I could identify well enough to eat.

I am still convinced we need to take a serious look at true socialism. Obamanomics, the hysteria of media lick-spittles aside, is not socialism.

I might take up oil painting again soon. I did that a bit a very long time ago but have some new ideas about mixing paint that I want to try.

As you see, I keep very busy. Blogging frequently sits on the back burner. Thanks, again, for your interest.

Curlydock

Taboo Socialism

by Curlydock

In 1949, Albert Einstein published an essay in the May issue of Monthly Review entitled “Why Socialism?”. The following is my take on what he said. His essay can be found on the Web at “http://www.monthlyreview.org/598einst.htm”. I strongly recommend you read it. Your take might not be exactly the same as mine.

Now, as then, the terrible and subversive topic of socialism is “under a powerful taboo”. I agree with Einstein; we need to break this taboo.

He said it is important we express our views even if we are not experts in economics, science, philosophy, etc. I am taking him to heart here and now.

Economics, he said, is such a messy topic that it cannot be studied with rigor like other fields of science. Socialism is more an end than a means. While engineering, math and science might help us find a better way to an end, there is nothing they can really say about whether socialism should be our goal. We each will have to study, think, discuss with each other and come to our conclusions as best we can. As for myself, I have decided to abandon capitalism for socialism and to promote this decision. It is gratifying to know that a mind the caliber of Einstein’s would concur.

Einstein believed we are in a cultural crisis that is ultimately rooted in a self-contradiction in what it means to be a human being. Within each individual are conflicting needs. We need to both stand apart and stand together with others.

Our sense of freedom demands we go our own way. But the reality is that we cannot do without others. Somehow we came to see our individual interests as in conflict with the interests of society. Calm reflection tells us we are all in the same boat, but we still seem to need to assert ourselves over everyone else. How does this come about?

Is this internal conflict natural, from the time of birth, or is it something we learn from growing up in a culture devoted to greed and competition?

Einstein said there are no easy answers but for the sake of inner equilibrium we must try to orchestrate the demands of our contradictory nature. Unless a solution is found, a person cannot contribute significantly to society’s well-being.

In the development of solutions, we must hold faith that “nurture” can trump “nature”. We have memory and communication abilities that allow us to take charge of our development.

Anthropology has shown that cultural patterns are not fixed. We can choose our culture if we only will. Thinking and wanting can help determine what we will become, unlike ants and bees which are fixed in their cultures. This is a job for our imagination.

However, he said, while we may adjust some things to enhance life, some things that used to be possible will never be possible again. Man will never again be able to choose self-sufficiency as an individual or small group. To sustain the population level, we must continue to use the technologies that allowed the population to grow this large. We must continue to use extreme division of labor and large scale production if we are to satisfy our material needs. This must be done even in a socialist culture. Whatever else is possible, a global network of production and consumption must continue.

The root of our problems today, the source of evil, is the economic anarchy of capitalism. Workers are not paid based on the value of what they produce. They are paid only enough to keep them engaged to the process. The difference in value is taken by the owners of the means of production. This makes a parasite of the owner and a slave of the worker. Wealth accumulates to the few and the many are impoverished.

The intense concentration of wealth in a few hands nullifies democracy by corrupting the government, the press and the educational system. Competition, profit motive, and technological advancement keeps too many people unemployed. Selfish use of capital for the short term causes instability in the system which then cycles through periods of overproduction and underproduction; boom and bust.

Einstein said the worst evil of capitalism is the crippling of individuals. This comes early in life by an educational system geared to stress greed and competition above all else.

The only cure Einstein could see is a planned socialist economy and an educational system emphasizing social skills.

He cautioned, however, that a planned economy is not the same as socialism. True socialism is achieved only through the liberation of the individual. He said we must carefully avoid the centralization of power, whether it is based on government or business.

That is my take on Einstein’s essay.

I agree with most of it, but I wonder about the need to keep extreme division of labor, the current level of technology and a world-scale productive network. Our population, even larger now than when Einstein wrote, may already have passed a level that can be sustained even with the continued use of big and complicated production. These techniques have only worked in the short run by cheating in the accounting of all the costs to the environment and non-renewable resources. We may be on the verge of a very hard limit. On this I certainly hope I am wrong.

Dear reader, can you convince me otherwise? Did I make a mistake on my take of Einstein’s essay? Please feel very welcome to comment.

Somewhere in Time and Kentucky

Somewhere in time and Kentucky,
‘tween furnace fire and frigid flurries,
beats the heart and warms the blood
and finds the brain
bittersweet in joy and pain.

By cast iron stove the scuttle sits,
full of coal and snowy bits
melting, glistening, into drips
that rust the metal bucket’s pit
and reinforced wire upper lip.

Though the scuttle’s galvanized,
acidic anthracite denies
longevity; yet, for today,
keeps my heart alive
and ice and cold at bay.

Quiet rooms; silent home;
floor of wood on cornerstone;
Bible fast by telephone;
I do not feel alone
for I know and I am known.

Good of Service: A Poem

So, here I am. Again:
back in my chair
with my pen in my hand,
determined to drag it out,
kicking and screaming,
by the hair if I have to:
the TRUTH.

Here I am, in pain again,
consorting with anger.
The muscles in my jaw contract;
the tips of my incisors ache
to rip and tear apart
the curtain between me
and TRUTH.

But is there a need to bleed?
I hope not.
I should rest, cool my engines, then
explain.

-…-

Ok; I’m chilled out now.
Where to begin?

I cannot begin at the beginning;
I lost that long ago.
So, I begin at the end:
I am full of rage.

Rage I need, I believe, to save me
from depression’s dark paralysis.
Before the rage, there was depression,
I recall.
I remember how
the pain bound me in a straight-jacket
while the world yet waited
for me to tie my shoes and begin
another day. No
way.

They wanted me to leave my home and,
in some strange land, take a stand,
weapon in hand and
kill or be killed.

It was very clear: no thought was required.
I was not to think it through first. No, I
was just expected to
do it. I
refused.

They then rejected me,
for the good of their service, and I
was supposed to believe:
there was something wrong with me;
not with them.

For a long time now, still I know
not what to believe. But, then as now,
one thing was, and is, certain: I
will not allow myself to kill
another being, be it human or not,
unless I know, beyond a doubt,
that it is right
to do so.

Of that I was and am still sure.
But they were not prepared
to let me think it through. No, I
was just expected to
do it.
No. Way.
I refused.

-…-

Before that, there was school;
a place where I was trained
and strained past the breaking points
clicking like prayer beads, one
against the other,
along the thread of time.

School, a place
before time, out of time, where I
was expected
to dance to their tunes,
sing their songs,
crack their books,
and flee from shame as bugs might from the light
finding the over-turned playground rock,
only to be crushed
under the feet of young bullies.

School, a place
where discipline is by disgrace
and you are to learn your place.
A place where there is no place
to hide when they laugh in your face.

School is for my own good,
they said.
Looking back now, I think: not.
I think:
school is only for the good
of their service.

First Multi-Mirror Solar Oven Simulations

by Curlydock
Nov 27, 2007

Results published in previous posts increased confidence in my solar oven simulation program. Those tests were confined to the single-mirror configuration. By keeping things simple, results were intuitively judged. Now it gets more interesting as we encounter kaleidoscopic multi-mirror configurations with results that may challenge intuition but that are, nevertheless, we hope, still accurate.

The number of variables that define the problem make closed form expression prohibitive, at least for me. Thus, my use of simulation.

HERE IS A LIST OF THOSE VARIABLES:

The oven seems simple enough in that it is composed of two sets of hinged mirrors and a sphere called a “bounding sphere” that stands for the oven cavity. The oven cavity is the part of the oven that gets hot enough to cook food. It is constructed like a small green house, but we need not concern ourself with those details.

The bounding sphere is all we need to know about the oven cavity. The center of the sphere gives the CAVITY LOCATION in EXTENSION and ELEVATION from the “origin”, the lowest point on the vertical R1-R2 hinge. The cavity location is always in the bisecting plane of the oven’s bilateral symmetry.

The radius of that sphere gives the SIZE OF THE CAVITY. Now, to make results easier to compare across simulations, I have normalized all units of distance to the diameter of the oven cavity. So, instead of inches, feet, meters, etc, all lengths are in units of cavity diameters.

I have named the four mirrors of concern: R1, R2, R3 and R4. Hinged on a vertical axis are R1 and R2. R3 and R4 are hinged horizontally. So, we have the two angles: R1–R2 ANGLE and R3–R4 ANGLE.

We will also be concerned with where the sun is in respect to our oven, so we have: SOLAR ALTITUDE ANGLE or elevation; zero degrees on horizon and 90.0 degrees at zenith, and SOLAR AZIMUTH ANGLE. In all runs I presently contemplate, the azimuth will not change, confining the sun to the plane that bisects the symmetry of the oven.

We also have to be concerned with R1 WIDTH and R1 HEIGHT. R2 is always identical to R1 in width and height.

Since R3 and R4 are hinged horizontally, it is confusing to speak of their width and height, so I define the dimension R4 RATIO, the length of the horizontal hinge, as a portion of the opening of R1-R2.

R3 is always parallel to, or in the plane of, the horizon. R1-R2 sits on R3 like an open book with the bottom two corners on the axis of the R3-R4 hinge. Because of this configuration, the reflective part of R3 will always be a triangle with size and shape determined by the width of R1, R2 and the R1-R2 angle. The other mirrors are always square or rectangular.

R4 EXTENSION is how far R4 extends from the horizontal hinge.

Also an input variable is the QUANTITY OF REFLECTIVE PLANES. I can consider four possibilities: R3 only; R1 and R2; R1, R2 and R3; as well as all four mirrors.

I think that about covers the input variables. So far I have not concerned myself with losses based on reflective angles, surface imperfections, convection, conduction, mass, re-radiation, transmission distances, imperfect insulation, etc.

OUTPUT

What we get for output is the amount of idealized SOLAR FLUX GAIN on the oven cavity over what the cavity would have gotten directly from the sun without any concentration. This is not a temperature; it is a ratio. The minimum value will always be 1.0 unless the cavity is in shadow or blocked from direct rays, where the value could fall to zero. The maximum value depends on all the inputs.

Because of the large quantity of possible combinations of input variables, I must find a way to lock some of them down so they can be temporarily ignored. That will simplify the problem and help us make sense of where we are in our journey to the “perfect” design. I do not know if there can ever be a proof that a particular design is the best possible one. There might always be a combination of inputs hitherto unconsidered that will yield a greater flux gain than what we thought was the best. If there is such a proof, a bigger brain than my own will need to find it.

That is why I am willing to share my program listing with anyone who is interested and who agrees to keep my program or any derived from it in the public domain, not for profit.

I am also willing to do runs for others who would like to see particular results of inputs meaningful to them. Perhaps they have built an oven or two and want to see what the simulation says about comparative performance. If you are interested, just leave your request in the comments section and I may publish my response or run results in a future post.

Next, some multi-mirror runs:

For the time being I will keep R1-R2 angle at 60.0 degrees. The decision is arbitrarily based on the fact that an oven I built uses that angle. In the long run, there may be a better angle.

Also, for now I keep the width of R1 at 4.0 cavity diameters. I do that because prior runs with R3-only seemed to result in 4.0 as the optimum size for the side of R3, given the R1-R2 angle = 60.0 degrees. The length of a side of R3 is the same as the width of R1 (and R2). Lastly, to start, I make the height of R1 equal to its width.

Chart “nov1029a” shows the effect of cavity extension on flux gain where only R1 and R2 are in play. For these inputs, the best value seems to be 1.4, but it depends on the angle of the sun. By this chart, for sun angles higher than about 40.0 degrees we might want to make the cavity extension less than 1.4 cavity diameters.

Next, keeping cavity extension at 1.4 and everything else the same, we do four runs, one for each of four different heights of R1-R2. That results in chart “nov1030” where
red (1) = 4.0
green (2) = 6.0
blue (3) = 8.0
black (4) = 10.0
cavity diameters.

We see gains increasing at higher sun angles as the height of R1-R2 increases. The gain increment decreases so returns are diminishing. At this point I will make the compromise of R1-R2 height = 6.0 and keep that for the next set of runs.

I cannot resist the temptation to add more mirrors at this point. Chart “nov1032” run (1) is a repeat of “nov1030” run (2), for reference. It looks different because the vertical axis of the chart is re-calibrated to cover higher gains.

Note the gain still peaks at about 6.0. That gain makes sense when you consider that two mirrors at a 60.0 degree angle would allow the sun to see six images of the cavity. Run (1) is only with R1 and R2 in play.

For run (2) I merely add reflector R3 to the play, and the results show a significant increase in gain. If we consider that R3 would double 6 images to 12, the gain seen of about 9.0 makes sense, considering some of the images will be partially obscured.

Now we take a lesson from a prior post when we were testing with only R3 and learned that it is best to elevate the cavity somewhat over R3. We do just that in run (3) and see that the gain is even closer to 12.0. Supposedly, the reason is that the images are less obscured when the cavity is elevated.

In run (4) I put R4 in play and made R4 the same size and shape of R1 and R2. It is a handy size if the oven is collapsible and you stack the reflectors for storage. The solar flux gain reached 14.0. One might worry that the simulation is malfunctioning because the flux gain is below 1.0 for very low angles of the sun. More thought reveals that at these low solar angles the cavity and lower part of the oven are in the shadow of R4, so one’s confidence in the program rebounds.

Is this the best design? I doubt it. Only more testing can tell, I guess. At least, it is a benchmark for measuring more attempts.

In a future post I can make the input variables conform to the oven I have actually constructed and see what the simulation says. I will be able to compare a real oven with this benchmark and tell what changes might make it better or worse without getting my hands dirty (not meaning to disparage getting one’s hands dirty).

Last Single-Mirror Solar Oven Simulation Test

by Curlydock
Nov 24, 2007

In my previous couple of posts I showed some of the results of tests of a program I wrote to simulate what I call a “kaleidoscopic” type solar oven. In earlier posts I detail the actual oven I use to bake bread. I wanted to see how to build a better oven of this type, so I wrote the simulation for ray-tracing various reflector sizes, shapes, quantities and configurations.

This post will cover what I hope is the last of the one-reflector tests. I wish to begin tests of two-mirror simulations in the next post.

Graph “nov1026a” shows the results of five runs with a single equilateral triangular reflector in the plane of the horizon. That reflector I frequently refer to as “R3”. Five sweeps of the sun from zero degrees (horizon) to 90 degrees (zenith) are shown, one sweep for each size of R3. The sides are all equal and are measured in cavity diameters. The smallest R3 is 2.0 and the largest is 8.0 cavity diameters on a side. The cavity bounding sphere is represented by the ball that is aways in the corner farthest from the sun when the sun is on the horizon.

Observe that the gain never exceeds 2.0 and never falls below 1.0. This is consistent with my expectations of what happens with only one mirror and increases my confidence in the simulator.

Rule 1026a

Also observe that the increment of improvement in gain decreases as R3 gets larger. Large mirrors increase the gain when the sun is at lower angles but the reflector has to get perhaps impractically large to produce these gains. At solar angles above about 20.0 degrees, it hardly seems worth having a floor reflector larger than 4.0 cavity diameters on a side. This is more than my prejudice up until now, which was that 3.0 cavity diameters on a side was the practical limit. The actual oven I made has only 3.0. So, the next time I build one of these ovens I will probably go with 4.0. It depends on what else we learn when more reflectors are in play.

“Rule 1026a” is, then: the triangular reflector always parallel with the plane of the horizon, that is the one the cavity is above, should be sized to about 4.0 cavity diameters on a side, physical practicality permitting, and probably not less than 3.0.

Now I combine this rule with rule 1010a from the previous post, which said the cavity should be elevated. That results in chart “1027a”:

For this run I kept the mirror sized to 8.0 cavity diameters on a side and elevated the bottom of the cavity from just touching R3 to where the bottom of the cavity is 0.5 cavity diameters over R3. Otherwise the run and chart calibration are the same.

Again, the gain never exceeds 2.0 and never falls below 1.0, which is good.

Also note that elevating the cavity improves gain when the sun is at higher angles. This is consistent with what we learned in the prior post and was to be expected. The simulation still seems to work. For this configuration, with the cavity elevated, the range of sun angles with the maximum gain of 2.0 is much larger.

In a prior post I expressed some doubt about whether the simulation was following the ray trace through an arbitrary number of reflections or breaking off too soon. I later discovered that was indeed a problem. But it only affected simulations of more than one mirror, none of which I had published yet. I fixed the bug and am now confident that I am ready to do multi-mirror tests. In the next post we will see some results using two reflectors. Those reflectors are the ones I have named “R1” and “R2” in prior posts. They are linked by a vertical hinge and open like a book over the plane of R3. R3 will be put aside while we consider only R1 and R2 and will return probably much later when three-mirror tests begin.

More Elementary Tests of a Solar Oven Simulation

by Curlydock

Nov 16, 2007

In the prior post I introduced a test of the simulation using only one plane of the “kaleidoscopic” type solar oven. So far, we have seen the bounding sphere of the oven cavity positioned over one triangular concentrator. That concentrator corresponds to the R3 reflector mentioned in other posts describing an actual oven that I have been using. The R3 reflector is in the plane that appears to be parallel with the earth’s surface and the cavity assembly rests on R3. In later posts we will be considering the effect of the other reflectors: R1, R2 and R4. This post is confined to more implications of the R3 reflector.

Diagrams “nov1007” and “nov1008” illustrate the oven cavity bounding sphere positioned at two different levels over the triangular reflector.

The red dots represent the absorption of a light ray on the surface of the bounding sphere. The blue dots represent rays reflected from the surface of the mirror that do not intercept the cavity. The shadow of the cavity can be seen on the mirror. The other dark spot on the mirror is that portion of the mirror where rays are reflected that do intercept the cavity.

This Test

The present question is how the height above the mirror affects the amount of solar flux gain the cavity will receive as the sun sweeps over an altitude angle from zero degrees on the horizon to 90 degrees at the zenith.

Diagram “nov1010” shows the result of four simulated solar sweeps, one for each of four different heights of the oven cavity above mirror R3.

On Units

Unless otherwise noted in these posts, the units of distance measurement will be cavity diameters. I think that is more interesting and informative than using yards or meters, etc. So, no matter what the radius of the cavity is in feet, centimeters, inches or any other unit, it is always 0.5 in cavity diameters. When the cavity rests on the mirror the center of the cavity will be 0.5 cavity diameters from the surface. The lowest point on the cavity, in that case, will be zero cavity diameters from the mirror.

The triangular mirror, R3, seen in the above illustrations and used in this particular post, is equilateral and 3.0 cavity diameters on a side. The cavity CENTER heights used to generate the data for the chart “nov1010” are 0.5 (red), 1.5 (green), 2.5 (blue) and 3.5 (black) cavity diameters. There is one color coded sun altitude sweep for each cavity placement.

The Solar Sweeps

These “altitude sweeps” are not the natural movements of the sun, so don’t be confused. The sweeps begin at the lowest point on the horizon and end at the highest point in the sky, or the zenith, at 90 degrees. The point on the horizon, zero degrees, where the sweep begins, is always in a vertical plane that bisects an angle of the triangular reflector.

The reason for this type of sweep is to see how the more complicated mirror arrangements respond to different solar angles, all of which keep the sun in the plane that bisects the symmetry of the concentrator arrangement. The purpose was to have a standardized sweep with which to compare different arrangements under any solar angle that might happen no matter what the season, location on the earth, or time of day, given that one could always adjust the oven so the sun is in that bisecting plane. Such an adjustment would not change the fact that R3 is in the plane of the horizon; it would merely rotate R3 in that plane. The tests to see how the simulated oven responds to a natural solar transit will probably be some of the last tests.

Rule 1010a

Now back to chart “nov1010”.

Note that when cavity height is lowest, 0.5, which corresponds to touching the mirror, the gain never reaches the greater levels it does when the cavity is elevated from the mirror. This is the reason for placing the inverted glass bowl underneath the oven cavity assembly, as seen in my prior posts detailing an actual solar oven. The lower bowl elevates the whole assembly a bit. I was never quite sure just how much it should be elevated but now it seems my simulations may help to determine this.

So, Rule 1010a for building kaleidoscopic solar ovens is: elevate the cavity over the mirror that is parallel to the plane of the horizon instead of letting it rest on it.

Next, we see just how much elevation is best. The above graphs suggest that the best cavity elevation will depend on the solar altitude. The angle of the sun is constantly changing; so, if we can figure out a way to easily adjust the cavity elevation about every twenty minutes, that would optimize flux gain at all times. Such a rig might be more complicated than the extra flux gain is worth, however.

Diagram “rule1010a”, seen below, might be used in the design and operation of a one-triangular reflector solar oven with an equilateral shaped mirror three cavity diameters on a side. It probably would not work for baking because the flux gain would never exceed 2.0. It might be useful for proofing bread dough or keeping a plate warm. It might also apply to ovens with more reflectors, but we have to wait to see what more tests produce to be sure.

This diagram allows us to determine the best cavity height above the reflecting plane for any given altitude angle of the sun. I gathered the data for the diagram from repeated runs with the simulation program. That these curves seem to make sense to me reinforces my confidence in the accuracy of the program so far (no guarantee, of course).

The runs show rather broad peaks. That suggests that a particular cavity elevation would work well for a wide range of solar angles without need to re-adjust the height. For that reason, the diagram “rule1010a” shows a region instead of a line. The acceptable region is in yellow-green between two limiting lines. The limiting lines represent the points where the solar flux gain has dropped to 0.9 times the peak value seen in the sweep. The graph seems to indicate that for solar angles below about 25 degrees there is no need to elevate the cavity at all. The flux gain might be very low, but elevating the cavity will not help.

How to Apply Rule 1010a

Here is an example of the use of diagram “rule1010a”:

Suppose the sun is at 70.0 degrees above the horizon. Find 70.0 degrees on the horizontal axis of the chart. Follow the vertical from 70 degrees up until it just reaches the green region (the first limiting line). Follow the horizontal from that point to read the cavity height. That yields about 0.70 cavity diameters.

Continue on the 70.0 degree vertical until the green region just ends (on the other limiting line). Following the horizontal from that point yields about 2.9 cavity diameters.

Therefore, the maximum gain will be when the BOTTOM (not the center) of the cavity is between 0.70 and 2.9 cavity diameters from the surface of mirror R3.

If the cavity is 12.0 inches in diameter then 0.70 cavity diameters represents 0.70 X 12.0 = 8.4 inches. Likewise, 2.9 cavity diameters X 12.0 inches per cavity diameter = 34.8 inches. At these points the gain will be about 9/10 what it would be at the peak.

To find the height corresponding to the actual peak, you can use the average. In this case, the average cavity height is (0.70 + 2.9) / 2.0 = 1.8 cavity diameters, and 1.8 X 12.0 = 21.6 inches.

In the morning and evening hours the sun is not so high and the cavity will not need so much elevation. Even if the cavity elevation is not optimum, the losses will not make the oven useless, it will probably just take a little longer to cook something. Also, when we start adding the other reflectors R1, R2 and R4, the gain will be considerably beyond 2.0, so some small maladjustments will be even less of a problem.

Initial Test of Solar Oven Simulation

by Curlydock
Nov 15, 2007

The diagram labeled “nov1002” displays a rudimentary test of my solar oven simulator. From this I hope to begin to see if the program is behaving correctly.

The oven cavity is seen as a ball above a triangular mirror.

A cross section of the solar flux is seen in yellow above right.

Any ray absorbed by the cavity is drawn in red. This could be either a ray directly from the sun or a ray reflected from the triangular mirror.

A ray reflected from the mirror that is not absorbed by the cavity is drawn as a short light blue vector. Any time a vector is drawn, the direction is indicated by the small ball at the end, which could be interpreted as an arrow head.

To reduce clutter in the diagram, the rays reflected and lost to space are drawn very short. They appear as a sort of light blue haze over the triangular reflector. You can see the “shadow” of the cavity on the mirror. Rays that neither hit the cavity nor the reflector are not drawn at all.

The program calculated the solar flux gain in this case to be 1.974359. This means that the cavity received almost twice as much solar radiation as it would have without any reflector at all. This is precisely what I would expect. The flux received by the cavity directly is doubled by the presence and proper placement of the mirror. The cavity would “see” two suns: one directly and the other reflected. Reciprocally, the sun would “see” two cavities, also one direct and one reflected. The analytical solar flux gain is two.

The theoretical flux gain without any reflector would be exactly one. That would be the minimum ever seen. Any properly directed reflections will increase that. The flux gain is calculated by dividing the quantity of rays absorbed with mirror concentrators in place by the quantity that would be absorbed directly from the sun when there are no mirrors. The simulation counts the rays and calculates the gain.
To see the importance of mirror orientation, we next consider what happens when the sun is at different angles, everything else remaining the same.

Diagram nov1003 shows how the flux gain drops to nearly unity when the sun is at a very low angle. The reason is that the triangular mirror is not of infinite extent. If it could be made large enough, we could get our gain back up to two. Thus the physical trade-off for the solar concentrator with the sun at small angles to the surface.

Diagram nov1004 shows the other extreme. Here, the sun is nearly at the zenith, but again the gain has dropped to nearly unity. This time the reason is that the cavity obscures the sun’s reflection. Where the cavity would “see” the sun it now only sees itself. The sun can only see the direct image of the cavity. The reflected image of the cavity is mostly hidden from the sun by the cavity itself.

These preliminary results continue to indicate that the simulation is correct.

Next, we can have the simulation sweep the solar altitude angle from zero degrees (on the horizon) to 90 degrees (at the zenith) and graph the flux gain against the solar angle. The triangular reflector is in the horizontal plane and therefore parallel with the horizon.

Diagram nov1005 shows the results of just such a sweep. We see the flux gain peaks at 2.0 broadly when the sun is around a 50.0 degree angle and falls to unity when the angle of the sun is either much more or much less than that.

In conclusion, the program I wrote to simulate some types of solar ovens seems to be working so far. I do still have reservations. There is more testing to do.

In future posts I hope to show the results of adding more reflecting flux concentrators. The flux gain will go up much more quickly with each added reflective plane as each added reflector exponentially increases the number of images (as in a kaleidoscope) while the increase in the number of mirrors is only linear. But limitations due to image obscuration, as we have already seen here, will subtract from the advantage of adding more reflectors, producing diminishing returns.

Some factors that affect real physics of multiple reflections I am going to ignore. I feel they would add a great deal of complexity without proportionally increasing the accuracy, at least for my purposes.

One of these factors is that every time a light beam is reflected, there is some loss. The amount of loss depends upon the angle of incidence. In my program, so far, this type of loss is not deliberately encoded. I assume no such losses.

Another factor is that no real reflector is perfect. Imperfect reflective surfaces will throw the light ray off at a non-ideal angle. Nor do I try to account for this effect.

Another factor is that I have some doubt about whether my program, as it is currently written, will ray-trace beyond about 4 or 5 reflections. I am not sure if this is true or why it happens if it does occur. I am keeping a look out for the effect but am not letting this doubt stop me from reaching for some results.

There may be other factors that have escaped my wildest dreams; who knows?

This work I put in the public domain for purposes of information and I do not claim it is perfect and suitable for just any application. If you are interested in seeing the listing, I am willing to share it. I can post it later.

Kaleidoscopic Solar Oven Temperature vs Time

by Curlydock
Nov. 13, 2007

In my previous post, on September 27, 2007, I went into detail describing the “Kaleidoscopic” type of solar oven that I have been using to bake bread.

Now I post the time versus temperature for an actual bread baking episode. The episode occurred in Jefferson County, Kentucky, USA, on a day in October, 2007. There had been a recent rain and the cloudless sky was unusually clear and free of haze. Starting at 10:55 AM EST, the bread baked to completion in about an hour. The maximum temperature recorded, between the black lid and top glass bowl, was 320 F (160 C). Just as I removed the bread, I saw the temperature was 325 F and probably still climbing. The ambient temperature was 64 F at the beginning and 70 F at the end.

The results are tabulated and graphed in the next image:

__Time____Ambient______Oven________Note___________

10:55 AM ___ 64 F ___ not recorded ___ start baking

11:05 AM ___ 64 F ___ 240 F (116 C)

11:15 AM ___ 64 F ___ 275 F

11:20 AM ___ 66 F ___ 280 F (138 C)

11:30 AM ___ 68 F ___ 290 F

11:34 AM ___ 68 F ___ 300 F (140 C)

11:44 AM ___ 69 F ___ 308 F

11:56 AM ___ 70 F ___ 320 F (160 C) ___ condensation seen

12:06 AM ___ 70 F ___ 320 F ___ good odor, end baking

The optimum design for this type of oven is a fascinating problem. I wonder if 60 degrees is the best angle for the vertical axis and what the best sizes and proportions are for the reflecting panels. I am pretty sure it would be pointless to have the width of the vertically hinged panels be either more or less than three times the diameter of the oven cavity, for example. But I would like to have some way to test these personal prejudices.

To that end, I have given in to the temptation to do a detailed theoretical analysis. My way of doing this is to write a computer program that uses something like “ray tracing” to simulate the oven, allowing me to more easily see how different configurations affect the solar flux concentration. That program is pretty much finished and I hope to post some of the results in the near future.

Kaleidoscopic Solar Oven / Cooker

by Curlydock

One of my earliest installments dealt with the theory of the best angle to use with the reflecting planes of the solar concentrators of the Box-type solar oven. Since then, I have come to prefer what I call a “Kaleidoscopic” type solar oven.

I feel I have many reasons for this preference, but the most important is simplicity or ease of construction. Roughly speaking, the 3-D description of a Box-type oven takes about 20 vertexes and 32 lines. For the Kaleidoscopic type, it is 8 vertexes and 11 lines. So the Box type is about three times more complicated than the Kaleidoscopic type.

Image 92 shows the Kaleidoscopic oven I used to bake many loaves of genuine sourdough bread over this past summer.

Image 91 shows a not-fully-risen loaf before baking. I consider it fully risen when the top of the loaf reaches the top of the bowl. The bread bakes in the oven-proof glass bowl which sits in the oven cavity. The cavity is detailed later.

Images 82 and 83 show a finished loaf.

Image 89 looks into the front of my Kaleidoscopic oven. Most of the essential parts are seen. Missing is the glass bowl that would sit inverted over the top of the black lid. The oven cavity is shown in position and ready to receive the bowl of dough.

The reflective concentrators are in four planes. Two that I will call R1 and R2 form a vertically hinged unit that opens like a book and sits at a 60 degree angle. The hinge for R1 and R2 is made with strapping tape. The oven cavity just touches R1 and R2 and sits on R3, which is a separate unit the shape of a triangle.

The R3 angles are all 60 degrees and the length of each side is three times the diameter of the oven cavity. R1 and R2 are as wide as the sides of R3 and considerably taller than that.

R4 is also a separate piece and extends from the open edge of R3 as if it were hinged horizontally to R3. It could be permanently hinged but I feel there is no need for it. A pole pivots from the outer edge of R4 and fixes on the ground. It is used to set the angle of R4 so that the oven cavity is the brightest you can make it. If the wind is not blowing, gravity and the angle adjustment pole will keep R4 in place.

If there is wind, then I fasten all the sail-away reflective panels to the table with shoestrings. The cardboard from which R1, R2 and R4 are made is reinforced along bottom edges with narrow wood strips and package sealing tape. The shoestrings go through holes punched in the cardboard, around the wood strips, and through the mesh of the table top.

The weight of the oven cavity keeps R3 in place.

When the wind is very strong I use sandbags to hold down the table legs.

Here is a diagram comparing the Box and Kaleidoscopic type solar cooker / ovens and labeling of the concentrator panels I have been describing:

The Box type has only one side glazed. That is the side where the solar flux enters the box. The other five sides have to be well insulated to keep the heat in. The maximum reachable temperature will depend a lot on the effectiveness of this insulation and the quality of box construction.

The Kaleidoscopic type does away with this particular need altogether by making all sides glazed. So, solar flux would enter all around the oven cavity, in theory. In actuality, this will not be perfect. The reasons have to do with the positioning of the oven cavity among the reflecting walls. Some positions are better than others.

Here is a detailed semi-exploded diagram of the oven cavity:

The oven cavity works like a green house to trap the heat from the focused solar flux. The ideal would be a series of concentric spheres. The outermost sphere is transparent glazing that passes light. The next sphere is an insulating jacket to keep the heat, for which a vacuum would be best but air is easier. The next inner sphere is flat black metal which absorbs light and converts it to heat. This heat ideally accumulates in the central sphere where the food cooks in its container.

The ideal is approximated here by the use of oven proof glass bowls and a stainless steel metal mixing bowl.

The outermost sphere consists of two glass bowls: (1) is inverted on top and (4) completes the bottom half.

The insulating air jacket is made by suspending the metal radiation absorber bowl (6) on a ring (7) cut from a double layer of heavy corrugated cardboard. The ring rests on the lip of outer glass bowl (4). The lip of the metal bowl (6) makes a snug fit in the ring (7) so that the metal bowl will not fall through. The metal absorber does not touch the outer bowls anywhere. It only touches the cardboard ring. The ring and air jacket are poor conductors of heat. They confine most of the heat to the cooking area.

The metal radiation absorber bowl is a stainless steel mixing bowl painted flat black on the outside with the kind of paint that withstands heat, or the paint you would use on a charcoal grill. Let the paint dry, cure under heat and air out for several days before using it for cooking. You probably would not like paint flavored bread.

I was lucky in finding a black metal cooking pot lid (2) that just fits over the lip of (6) and rests on ring (7). There are cake or pie tins that might also work if painted black on the outside.

Bowl (3) holds the food or bread dough. It does not have to be transparent. I have been using oven proof glass but recently found a ceramic bowl that should also work. Another metal pot identical to (6) would fit snugly and maximize cooking space and thermal conduction to the food, but I have not tried that yet. In fact, I suppose you could do without (3) altogether by putting the food in the radiation absorber bowl (6). But, since (6) is not easy to get on and off ring (7) and the cardboard of (7) should not be washed or get wet, I decided to use another bowl to hold the food.

On my wish list is some kind of thin wire handle to make food bowl (3) easier to get in and out of metal bowl (6). The handle would need to quickly and easily connect and disconnect from the edge of the food bowl and not compromise the thermal seals around the edges.

The whole cavity needs to be somewhat elevated so I put it on a transparent pedestal made by inverting the smallest glass bowl (5) near a corner of the bottom reflector, R3.

Most of the glass bowls I found and purchased as a nested set. I think perhaps the largest, (4), was not part of that set and had to be separately purchased, but I am not sure.

Why Kaleidoscope

To study the effect of the focal positioning and the angle of R1 and R2, etc., I decided to research the geometrical and mathematical aspects of multiple reflections in mirrors. From that, I realized the kinship between kaleidoscopes and this type of solar cooker. The next pictures should make the relationship obvious.

Fascinating as it was, I thought it might take too long, so I did an empirical study with a scale model instead of the exacting thought experiments. I gathered some pieces salvaged from a broken mirror (never throw anything away), tape, and construction paper. Also, I borrowed a large bead from a trusting and tolerant friend.

Image 74 is an overview of the apparatus:

The bead stands for the oven cavity or focus.

The mirrors that hinge on a vertical axis stand for reflecting planes or solar concentrators R1 and R2. R3, seen here on the bottom, will be moved in and out. R4 is not shown here but will be seen later.

Images 57, 60, 61 and 62 show how the number of reflections of the bead increase as the angle between R1 and R2 decreases. This inverse relationship says to me that the narrower this angle the better as far as solar flux concentration.

Surely, the more images of the bead (oven cavity) the sun “sees” then the more solar flux will concentrate on the bead.

But there are several trade-offs.

As you can see, the ring of bead reflections gets gradually larger as the angle decreases. To compensate for this, the sizes or areas of R1 and R2 need to progressively increase. At some point R1 and R2 are too large and cumbersome.

Image 63 shows how adding one more mirror, representing R3, doubles the number of bead images. Note how one of the images is lost because it is shadowed or hidden by the actual bead.

Image 73 shows how images are partially obscured when the bead is not elevated:

This is the reason that the oven chamber is elevated a bit by bowl (6).

Image 72 shows how the bead image count can be at least doubled yet again by adding the mirror that stands for R4. But, as the count and complexity of reflections increase, more and more images are obscured. There seems to be a threshold of diminishing returns.

Image 66 shows the concentrators at work. I used flash, which, I belatedly realized, is probably not good for a digital camera in a setup like this. Fortunately, perhaps most of the energy focused and dissipated on the bead instead of getting back into the camera lens.

If bead were bread, it baked.

How I Use the Kaleidoscopic Solar Oven

I use an angle of 60 degrees between R1 and R2. There may be a better angle. I have not tried others yet. I adjust the table orientation and the angle of R4 about once every 15 or 20 minutes. This needs to be done more often when the sun is high in the sky.

I frequently measure a temperature of 280 F between the top glaze bowl (1) and the lid (2), depending on the time of day. Morning hours, with the sun at a lower angle, seem to make the oven hotter than do the noon hours, probably because of the reflection obscuring effect already mentioned. Elevating the oven cavity even more when the sun is high in the sky might make the oven even hotter, but I have not needed to try that yet.

Either time of day works fine for baking my bread. The recipe for one loaf of sourdough calls for 45 minutes at 350 F in my conventional oven. I can bake 3/4 of that recipe in the Kaleidoscope solar oven in around 90 minutes. The crust browns nicely, especially on the top.

You might be tempted to let the finished bread cool just a little bit in the oven. But don’t do that. And don’t be fooled. The oven gets very hot. Be careful not to burn yourself.

While the oven is cooking, the moisture escapes as steam. As soon as the oven starts to cool, that moisture condenses on the lids and runs down to collect on the corrugated cardboard ring. The cardboard ring may dissolve if it gets wet. But, it can withstand the highest temperatures of the oven just fine. The high temperature helps keep the ring dry. As soon as I finish baking, I dump the bread on a rack to cool.

After a bit of practice, you can tell when the bread is finished baking by how it smells around the solar oven. Also, you will begin to see condensation on the inner side of glass bowl (1) when the bread is ready.

Outside of baking sourdough and cornbread, I have not yet cooked other things in this particular oven / cooker. I wonder if the condensation will be more of a problem if, for example, I make soup. I don’t know yet.

A Note on Construction Technique

Many instruct builders of these types of ovens to glue the aluminum foil to the cardboard with diluted white glue. I no longer do this.

I believe it is sufficient to bend the foil around the edges of the corrugated cardboard and fasten it in the reflective plane about every square foot using brass plated paper fasteners. Insert the fasteners through small holes prepared with a knife blade. These fasteners can be found where you get office supplies. They look like tacks with points that can be spread apart. This is much easier than working with glue. It is easy to repair.

But the main reason I do it this way is that the foil is easily removed from the cardboard when time comes to recycle them both. My red worms can eat the cardboard but the foil might not be good for them and would not be wanted in the vermicompost.

I do use white glue or carpenter’s glue to bond cardboard to cardboard where a panel needs more strength or a flap needs to be made rigid.