# Parabolic shape configuration's effect on photon volume?

My understanding is that the amount of heat energy a parabolic reflective surface generates is not the volume of surface area of the mirror, but essentially the volume of surface exposed perpendicular to the suns rays. This effective surface can be also described as the area of shadow that is cast by the mirror. Example: A very deep conical parabolic mirror has a linear surface area of 1000 but casts a shadow of 500, while a flatter parabolic mirror has a linear surface of 700, but casts a shadow of 600 . The smaller parabolic mirror gathers more photons with the larger "shadow".
I've attached an example of two configurations with equal linear amounts, but with unequal exposure.
Can someone comment on this? Is my above assumption correct? and a second question .... can photons be compressed?

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.Scott
Homework Helper
You are right. It's called the aperture. And, assuming the parabolic mirror is doing its thing, the size of that aperture determines the amount of light that is collected and focused.

As for "compressing photons": except in very extreme conditions, photons do not interact with each other - so the limit to how many you can have in a specified volume is generally limited to how many you can get in there at the same time without frying something.

Depending on the circumstances, there are limits to how precisely you can focus photons to a small area.

Can you speak to the possible difference between "focus" and "compression" of photons?
I think the sunlight has 1 kw of energy per sq meter. I am working on trough type parabolic systems.
Obviously when you combine the total photon energy source onto a Receiver Tube (target) of the system, onto a smaller area... the total area of the source being a greater area than the total area of the target there is a a multiplication of energy produced. So....
1) If you focus 10 times the surface area of light onto your target, is the energy created ten times greater?
2) Can a group of photons be compressed, or is that the same thing as being focused?
thanks!
Steven

jbriggs444
Homework Helper
2) Can a group of photons be compressed, or is that the same thing as being focused?
You are the one using the words. How about you tell us what they mean?

heh. Ok. To the best of my ability .... because I am trying to understand the distinction between some definitions too.
For a parabolic mirror to create heat it needs sunlight (source)and a curve that "concentrates" (here's one word when used with photons I want learn more about)... the light onto an object (target).
My systems are "trough systems" so they are not a hemisphere shaped mirror they are a half a tube shape mirror, with a copper tube (target) that absorbs the concentrated light from the sun (source).
Scott points out that photons do not interact, so in that respect I understand that they probably do not physically "compress"
But I can get my target tube up to almost 500F in 15 minutes on a clear day and an 85F ambient temperature.
So whether the term is focus, compress, or concentrate, ... there is a cumulative affect.
And I assume there is a definitive principle as to what a photon is, and what it does when a bunch of them reflect onto one small spot. In terms of calculating an expectation of heat generated from a parabolic surface, atmosphere, reflective quality, accuracy of the geometry are all variables.
I play with these things, but I am a moron about photons, and why they can be organized to accumulate heat energy on the surface of something.
But not only do I not know the answers, I don't even know the questions!

jbriggs444
Homework Helper
I don't even know the questions!
Fair enough. I do not know the answers.

What I do know is that photons are not relevant to it. Those are used for a quantum mechanical description of light. This is an engineering problem. A classical picture of light with ray optics is plenty good enough.

As a first approximation, conservation of energy will tell you that a trough width of sunlight reflected onto a tube width of tube will give you the full energy times the reflector efficiency times the tubes absorbance efficiency. I would expect the reflector efficiency to be a large fraction of 100% and the absorbance to be a somewhat smaller fraction of 100%.

Then you start dealing with how absorbance depends on angle of incidence and tube temperature and how much heat is wasted in radiation, convection and conduction.

A graph of temperature versus time and knowledge of the thermal mass of the tube might let you determine some of the parameters pretty well.

sophiecentaur
Thanks!, as a "Prototyper" I unfortunately, more often than not cheat or b.s. my way through a build, by building the model first with a best guess, and observe/measure results second, then selectively pick the more obvious variables to decide what factors are important to consider, and modify the next version based on that. But I guess listening to you guys I can <almost> form a better question........ I'll ask these then leave it alone, as I know I'm beating it to death.
1) Do photons travel in a straight line?
2) Do they respond when they strike a surface on an angle "bouncing off" at the compliment angle to the surface?
3) Do photons lose energy over distance?

sophiecentaur
Gold Member
2020 Award
Scott points out that photons do not interact, so in that respect I understand that they probably do not physically "compress"
This (using photons) is not a fruitful way to approach the situation. In free space, you can 'concentrate' a light beam as much as you like. (Remember, it will always spread out again past this focus). That is because space can be looked upon as linear and electromagnetic fields in space do not interact. If you focus light in any medium (even air) the EM radiation will interact with the medium and there is a limit to the Power Density in a region, after which the air will ionise and form a spark (plasma).

jbriggs444
wow. Thank You! (et al).
I love this forum.

s.

sophiecentaur
Gold Member
2020 Award
wow. Thank You! (et al).
I love this forum.

s.
No prob!
One thing i should point out. If you are using a 'concentrator' for sunlight then your optics need not be particularly good unless you really want a tiny volume heated up. Your tubes will, I assume, carry water in them, to be heated so they will probably be at least 15mm diameter. There is no advantage in focussing the light on a very narrow strip down the tube - in fact any local areas that are very high temperature will be more likely to re-radiate significant heat.
I once looked into solar heating for the house and came across a number of different systems. One of them used half round concentrators and they have a big advantage in that the water temperature is actually much higher (and hence more useful) than what you get with simple blackened tubes on a black backing. You can pump the water slowly through the tubes and get pretty hot water directly, even soon after sun-up.
Good luck with the project.

jbriggs444
Homework Helper
1) Do photons travel in a straight line?
2) Do they respond when they strike a surface on an angle "bouncing off" at the compliment angle to the surface?
3) Do photons lose energy over distance?
Light rays travel in straight lines general speaking. Though refraction (lenses and prisms), diffraction (slits and corners) and reflection (mirrors) change that.

Light bounces off smooth surfaces at the same angle away from the vertical as it arrived. It bounces off rough surfaces in a diffuse fashion, spreading out in all directions - not always equally in all directions.

Light does not generally lose energy over distance. Though smoke and such can absorb and scatter it it so that little comes out the other side.

Light can lose density over distance. A beam that is tightly concentrated at the source can spread with distance. Its brightness (illumination per unit area or "flux density") will diminish, but the total illumination across the entire beam width (total "radiant flux") remains constant.

reference first jbriggs, then sophiecentaur.
"light can lose density" (!!!!!!!) ok, that is really interesting. I'm going to need to read up on that (suggested links?).
Interestingly when I built wind turbines and studied the core principle similar to my studying this, it appeared it was not solely wind velocity, but wind density that was a factor.

My parabolic heat generators: I'll send photos if requested .... but the target tubes are 1/2" copper painted black, centered inside a clear poly-carbonate tube (with .065" air space between), in order to minimize radiant and ambient heat loss, and maximize the amount of heat transfer into the tube's water system. The water is circulated at a rate, to maintain a certain temperature based on the type of heat release system I hook up to it.
The reflective material is mirror grade stainless steel. Aluminum is actually the highest reflective material, typically coated for weather resistance, and much more expensive than stainless.
The frame used to secure and form the stainless steel reflector, is a 3d Printed assembly made of PETg plastic. One of my 3d printed frame systems is 48" long and 24" wide. The pattern for the parabolic curve is generated from an algorithm to a DXF file (AutoCad), so its accuracy is damn near absolute. Its not the linear curve that creates issues in the integrity of the reflective geometry, its the TWIST in the frame that may occur. So for that I have micro cables with turnbuckles, I adjust to correct that. And that's easy as all you do is observe the area that starts to brightly glow on the target tube, and adjust until it covers the entire length of the tube.
The frame and curve is pretty easy for me. I was 3d modeling with some of the very first structural simulators in 1986. The key is building an efficient target system, that minimizes ambient heat loss.
My machinist/fabricator reproduced one of my designs, but forgot to paint the copper black, used too big a poly-carbonate tube so there was about a 1/4" space between, ... and tube was old and not clear, foggy and scratched.
We fired it up anyway, and in about 10 minutes the poly-carbonate tube was melting quickly, dripping big "clobs"of plastic on to the driveway!
Peace,
Steven

jbriggs444
Homework Helper
"light can lose density" (!!!!!!!) ok, that is really interesting
I hope you did not read that as meaning something like "it can float higher in water".

I simply meant that if you try to read a newspaper in the light of a flashlight, it's easier to do when the flashlight is in close than when it is 50 miles away. The "flux density" of the light on the page is higher in the one case than the other.

No. I did get that .... but only as far as the general concept. I'd love to see a link to "explanations of flux density written for the village idiot".
And the other answers were very clear and helpful. And I do know what we consider a smooth surface, light considers a ragged chaos, to send light bouncing in all directions.

jbriggs444
Homework Helper
No. I did get that .... but only as far as the general concept. I'd love to see a link to "explanations of flux density written for the village idiot".
In clear air, the total amount of light in a cross-section of a beam is the same at the source as at the destination. None is lost. If the beam spreads out to be twice as wide (four times the area) at the destination, it must be have a flux density that is 1/4 as much.

That's pretty much also an explanation of how the inverse square law works for point sources.

Generated light from a flashlight the spread of light is pretty obvious. Does sunlight spread out? (From the source to the target)?

jbriggs444
Homework Helper
Generated light from a flashlight the spread of light is pretty obvious. Does sunlight spread out? (From the source to the target)?
The sun is small. The solar system is big. Yes, it spreads out. That is one reason why Mercury is hot and Pluto is cold.

sophiecentaur
Gold Member
2020 Award
We fired it up anyway, and in about 10 minutes the poly-carbonate tube was melting quickly, dripping big "clobs"of plastic on to the driveway!
Your project sounds fun and you are clearly getting places with it. You have nearly 1kW per m2 available (as you know) and, when that is concentrated onto a much smaller area, the temperature can soar. Melting plastic is no surprise.
Good idea to vary the pump rate for your wanted temperature. As I said earlier I remember reading about a very similar idea. They sent 'raw water' through the tubes, not using antifreeze, but allowed the water to drain back into the house at night to avoid freezing. A small solar powered pump was used (only needed when there was enough sunlight to warm the water. thinking back, I remember they used thin tubing and required soft water for the system.

Yes, I did very the rate of water circulation, but actually it ended up being seeing how slow we could set circulation to maintain higher temps. Obviously faster circulation cools the "solar/optical" heated water.
Here's a video of a "toy" version I made: .
In this video's model however I used some left-over stainless and so the parabolic reflector "wings" were just a little short of enough to circulate water while maintaining 100C temps (best I could do is 98F).

The larger models we constructed grossly overestimated the target pipe size that we could get away with and maintain hot circulated water. We could heat the target up to 500F, but with circulated water we couldn't get over 170F (however that was in the winter with ambient temps of 40F).

I think this points right to the incredible value of PhysicsForum.com. The ability to predict results, and scale designs correctly depends on a collaboration between Prototypers and Formulators.
Here's another 3D Printed model (anaerobic digester) In a real scale system, Fluid and Thermodynamics is everything. I am definitely in the deep end of the pool in this environment!

Thanks so much!
Steven

sophiecentaur
Gold Member
2020 Award
Here's a video of a "toy" version I made:
The absorbing element is on a larger scale that the systems I have seen and the 'optics; need to be a bit more critical than when the tubes are relatively large compared with the paraboloid. As I remember, the cylinders are only, perhaps four or five times the width of the tubes. The whole unit ( a number of tube assemblies in parallel) could be enclosed behind a glass cover and the void filled with argon (as in double glazing) to reduce heat loss.
If you want to optimise the design there are a lot of things that need to be 'just right'.

One correction: I did get this "toy model" up to 98C (not 98F) @ about 1 liter/min circulation.
I use a white background sighting target to check alignment, and typically it is the twist of the wing not, the geometry's integrity that needs adjustment. Yo,u'll notice two lightweight cross cables I can adjust for twist.
There's a free software Parabola Calculator 2.0, that generates a DXF to Auto Cad, and from there its modeled in 3D Studio Max. But the focal line of light on the target is remarkably tight, generating it with that. Our metal "monster" my fabricator made was cut with a DXF and water jet.
If I could learn how to calculate for a trough parabolic, the length of "wings" (diameter), the length and diameter of copper, and the flow rate to maintain 200C. I'd be a happy camper!
My purpose for parabolics, is to utilize it for preheating water to be used in steam generators. (Hydrogen, and Methane boilers). My general interest is in Agricultural Enviro-Energy

PS. I have 3D Printed a Hemisphere Parabolic too (70cm diameter). But the complexity of the assembly diminishes the geometric integrity of the focused light. And besides, it's tough to imagine a studio built system accurate enough to handle any volume of heated water