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'[EE] Solar Array Tracking'
2006\08\21@103656 by Bob Axtell

face picon face
To my delight, I have been given a shot at designing a solar tracking
system,
the arrays running at 24V. The arrays are very large, 14' sq and 18' sq. The
user is UNCONNECTED from the AC mains, running his entire business
from inverters attached to the system.

Anybody have ideas? I know about (1) not allowing the moon to be tracked,
(2) end the day by moving the array to immediately catch the dawn sun
when it comes up, to minimize movement, and (3) the funny 4-diode array
to determine where the sun is..

--Bob

2006\08\21@105701 by Thomas C. Sefranek

face picon face
I started that project years ago.
The existing discrete electronics were always failing.
I just reverse engineered the existing electronics, and cast it into a PIC.
Sorry, I can't supply the details.
This array was for focused mirror solar heat.

Tom

 *
 |  __O    Thomas C. Sefranek  spam_OUTWA1RHPTakeThisOuTspamARRL.NET
 |_-\<,_   Amateur Radio Operator: WA1RHP
 (*)/ (*)  Bicycle mobile on 145.41MHz PL74.4

ARRL Instructor, Technical Specialist, VE Contact.
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http://www.harvardrepeater.org

{Original Message removed}

2006\08\21@113939 by M. Adam Davis

face picon face
There's lots of ways to do this.  Assuming you want full tracking
(azimuth, elevation), and assuming the location is fixed, then I'd use
a simple RTC and sun camera.  The sun camera would be attached to the
solar array iteself (moves with the array so you don't have to
calibrate the motors).

Since you know the time and location, you can point to the sun.  The
elevation only needs to be adjusted perhaps once a week if you want
nearly perfect tracking, but even once a month or four times a year is
about as good.  Most trackers only do azimuth (horizon to horizon) and
are user adjustable for elevation since 4 times a year is within a few
percent of total energy output.

The sun camera is used to determine the location of the sun on clear
days, and can be used to set the RTC as well as the array.  It's not
needed if the motors are calibrated (ie, a known home position, like a
printer does) and you know the time is exact (GPS receiver).

You could use the phototransistors instead of a sun cam, and probably
get pretty good resolution.  It would certainly take less processing
if you went digital, and going digital gives you an easy way to reset
the array at the end of the day.

If you used a GPS receiver, a magnetic field detector, and had good
motors you could conceivably correctly track the sun on a moving
platform.

-Adam

On 8/21/06, Bob Axtell <.....engineerKILLspamspam@spam@neomailbox.com> wrote:
{Quote hidden}

> -

2006\08\21@125050 by Bob Axtell

face picon face
Good info, thanks!

Probably more money than  he'd want to spend. However, we will allow an
RS232 connection
to sync the internal PIC time-of-day, and to determine when to move to
the dawn position.

Yes, the horizon to horizon could be automatic, then simply advise the
user than there is an error
in direction, so he can press buttons to move it manually.

--Bob

M. Adam Davis wrote:
{Quote hidden}

>> --

2006\08\21@134009 by James Newtons Massmind

face picon face
Sadly, many years of attempts have shown that the best solar tracking is...
No tracking at all. Mechanical systems fail and so require maintenance. In
every case, the cost of maintenance exceeds the increase in power.

I would focus on the careful placement of FIXED mirrors to increase the dawn
and dusk sunlight striking the solar panels.

---
James.



> {Original Message removed}

2006\08\21@135337 by Xiaofan Chen

face picon face
On 8/21/06, Bob Axtell <.....engineerKILLspamspam.....neomailbox.com> wrote:
> To my delight, I have been given a shot at designing a solar tracking
> system,
> the arrays running at 24V. The arrays are very large, 14' sq and 18' sq. The
> user is UNCONNECTED from the AC mains, running his entire business
> from inverters attached to the system.
>
> Anybody have ideas? I know about (1) not allowing the moon to be tracked,
> (2) end the day by moving the array to immediately catch the dawn sun
> when it comes up, to minimize movement, and (3) the funny 4-diode array
> to determine where the sun is..
>

Search for MPPT (maximum power point tracker ) and Photovoltaic and you
might get some interesting results.

http://www.fsec.ucf.edu/pvt/pvbasics/

Regards,
Xiaofan

2006\08\21@140032 by James Newtons Massmind

face picon face
> I started that project years ago.
> The existing discrete electronics were always failing.
> I just reverse engineered the existing electronics, and cast
> it into a PIC.
> Sorry, I can't supply the details.
> This array was for focused mirror solar heat.
>
> Tom

Solar HEAT is the only area where tracking makes any sense. And even then,
reliability is such an issue that I would strongly suggest using a FIXED
concave mirror placed vertically with the pipe or other elongated heat
exchanger placed below and in front of the mirror. Given the correct
orientation, the sun will always be concentrated on some point along the
length of the pipe. This was suggested by Peter some time ago:

techref.massmind.org/images/member/jmn-efp-786/sun/verticalcollector.
gif

---
James Newton, massmind.org Knowledge Archiver
EraseMEjamesspam_OUTspamTakeThisOuTmassmind.org 1-619-652-0593 fax:1-208-279-8767
http://www.massmind.org Saving what YOU know.

2006\08\21@143122 by M. Adam Davis

face picon face
True.  And the cost of solar continues to be larger than the cost of
petroleum.

The issue with most solar trackers is --> Is the additional cost of
tracking lower than the gain in energy.  If this is the only question,
then the answer is almost always no - tracking is never worth it.

There are situations where that is not the best equation.  If you are
limited in panel size, and cost is not an issue (homeowner
associations, zoning, etc) then a tracker is worthwhile.

If you have an old satellite dish on the property (very rugged, very
reliable mechanics) then the tracker is practically free.

If you want to spend a ton of money on very expensive panels and make
a very large array, you may be able to reduce the number of panels
needed if you use cheaper trackers to make the remainder more
efficient.  If your customers are willing to pay an extra 5% for
"green energy" then the maintenance is covered.

So in general consumer installations one could always say "The cost is
never recovered" but that isn't always the correct criteria in the
decision.

-Adam

On 8/21/06, James Newtons Massmind <jamesnewtonspamspam_OUTmassmind.org> wrote:
{Quote hidden}

> > {Original Message removed}

2006\08\21@145613 by Bob Axtell

face picon face
James Newtons Massmind wrote:
> Sadly, many years of attempts have shown that the best solar tracking is...
> No tracking at all. Mechanical systems fail and so require maintenance. In
> every case, the cost of maintenance exceeds the increase in power.
>
>  
Well, he made the array and the mechanics. He said that tracking doubled
the power out of the array.

--Bob
> I would focus on the careful placement of FIXED mirrors to increase the dawn
> and dusk sunlight striking the solar panels.
>
> ---
> James.
>  
>  
>
>  
>> {Original Message removed}

2006\08\21@152852 by David VanHorn

picon face
I've seen this done with a four-quadrant photodiode and an aperture plate,
and with four solar cells and a cruciform center baffle.  The idea was to
drive the motors such that the outputs of the X and Y pairs were equal,
within the pair. That is to say that left and right are equal, and up and
down are equal, but up does not necessarily equal right.

But factoring in the cost and complexity, it does seem to bear minimal
return.

2006\08\21@154219 by Marcel duchamp

picon face
James Newtons Massmind wrote:
> Sadly, many years of attempts have shown that the best solar tracking is...
> No tracking at all. Mechanical systems fail and so require maintenance. In
> every case, the cost of maintenance exceeds the increase in power.

A friend of mine has a system that tracks the sun but has no motors or
electrical control system.

His setup has a differential set of pipes with a working fluid that
evaporates when in the sun.  The fluid condenses on the side in the
shade and creates a weight imbalance which makes the panels rotate until
there is equal weight on both sides.



2006\08\21@161622 by Brooke Clarke

flavicon
face
Hi Bob:

You might want to look at back issues of Home Power magazine.  A problem
with a system that aligns the array toward the Sun's image is that when
it's cloudy they get lost.  The type that depends on a clock will be
pointing at the Sun when it pops out of the clouds.  But an advantage of
the alignment type is that when it's cloudy the array is not moved
saving energy whereas the clock type wastes energy pointing at the sun
when it's cloudy.

It's interesting that the south facing 132 kw array at Realgoods in
Hopland, California (15 minutes south of me) is fixed.  They have a
number of smaller tracking systems, maybe 4x4 panels that often are
pointing straight up or not at the sun.  The elevation angle is
optimized for the weather at it's location.  
http://www.eere.energy.gov/greenpower/markets/pr/newsola_999_pr.html

I was recently there and took a look at the Fuel Cell demo.  It has a
small solar panel driving a 4" square flat plate electrolyzer that
outputs hydrogen and oxygen into seperate water filled tubes.  The
hydrogen powers a small Fuel Cell and in turn is supposed to turn a
small propeller via a small DC motor.  During the tens of minutes that I
was around it I never saw the propeller turn.  But it sure would have if
the solar panel was connected directly.  Like Don Lancaster says
hydrogen is just an energy storage medium, not a source of power.

Have Fun,

Brooke Clarke

--
w/Java http://www.PRC68.com
w/o Java www.pacificsites.com/~brooke/PRC68COM.shtml
http://www.precisionclock.com

2006\08\21@162023 by Brian Riley

picon face
I have lived off-grid for almost 20 years. I designed and installed  
my own system (<http://www.wulfden.org/Wulfden017.jpg>) and have been  
involved to various extents with a dozen other systems and have  
visited literally dozens of sites of all sorts of configurations.

I will comment on this from two standpoints ...

 - engineering - so far every electric/electronic system I have seen  
has fallen short, they all screw up, usually sooner than later.  
Reasons - poorly designed electronics, that inadequately do the job,  
poorly produced (they  work, sort of, but either fry in inadequately  
insulated enclosures, or lose their minds at -40F in a Vermont  
winter), poor mechanicals, and every combination thereof. Now the  
passive units that uses the gas tubes  (<http://www.zomeworks.com/
solar/trackrack/trackwork.html>) that sense temperature differentials  
that slowly rotate using pneumatic hydraulics to follow the daytime  
sun the reset themselves to the East at the start of the day, they do  
seem to work. I know of several units well into their second decade  
and still in service ... and I know several that didn't make it out  
of their first decade.

 - cost analysis - the rule of thumb is that a tracker will produce  
a gain of 9-10% output by maximizing the sun on the array. Now, if  
you consider a manual array mounting rack (manual meaning, you go out  
at some regular interval, say once a month, and adjust its elevation  
angle and it more or less stays fixed pointing South), the additional  
cost of a rack with automated tracking mechanisms above the cost of a  
manual, will, depending on which unit you get be the equivalent of  
one to two additional solar panels. Even adjusting in an increase  
cost for a manual rack that can accommodate two additional panels,  
you will still be expending a given amount of money to get 10% more  
power via 'geekness' when  the the same amount of money could be  
spent to reap 15-25% more power via brute force.

In other words .... why bother!

---
cheers ... 73 de brian  riley,  n1bq , underhill center, vermont
  <http://web.mac.com/brianbr/>  Tech Blog
  <http://www.wulfden.org/DiskShop.shtml>
   Home of the
      K107 Serial LCD Controller Kit   FT817 Power Conditioner Kit
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On Aug 21, 2006, at 10:54 AM, Thomas C. Sefranek wrote:

{Quote hidden}

> {Original Message removed}

2006\08\21@162356 by James Newtons Massmind

face picon face
> A friend of mine has a system that tracks the sun but has no
> motors or electrical control system.
>
> His setup has a differential set of pipes with a working
> fluid that evaporates when in the sun.  The fluid condenses
> on the side in the shade and creates a weight imbalance which
> makes the panels rotate until there is equal weight on both sides.

I would love to document that! The closest I've seen was black rubber bags
that expanded or contracted with heat. Any chance he could send some pic's
or tell us what the working fluid is?

---
James.


2006\08\21@170756 by Brian Riley

picon face
Sadly not even close to true.  The accepted figure for tracker gain  
is 10% tops.

---
cheers ... 73 de brian  riley,  n1bq , underhill center, vermont
  <http://web.mac.com/brianbr/>  Tech Blog
  <http://www.wulfden.org/DiskShop.shtml>
   Home of the
      K107 Serial LCD Controller Kit   FT817 Power Conditioner Kit
      Tab Robot Laser Tag Kit            MSP430 Chips and Connectors
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On Aug 21, 2006, at 2:05 PM, Bob Axtell wrote:

{Quote hidden}

2006\08\21@173525 by Marcel duchamp

picon face
James Newtons Massmind wrote:
>> A friend of mine has a system that tracks the sun but has no
>> motors or electrical control system.
>>
>> His setup has a differential set of pipes with a working
>> fluid that evaporates when in the sun.  The fluid condenses
>> on the side in the shade and creates a weight imbalance which
>> makes the panels rotate until there is equal weight on both sides.
>
> I would love to document that! The closest I've seen was black rubber bags
> that expanded or contracted with heat. Any chance he could send some pic's
> or tell us what the working fluid is?
>
> ---
> James.
>  
>
After reading the posting of Brian Riley, I believe it worked as he
described rather than the way I put it. His description jogged my memory
of what the owner had originally explained to me some years past.

So perhaps Zomeworks is where to start?
http://www.zomeworks.com/solar/trackrack/trackspecs.html

Before I would pay for one, I would do the math on roi.  You might be
better off with fixed arrays and put the money into more of them rather
than into fewer arrays that move.

2006\08\21@175135 by Gerhard Fiedler

picon face
Bob Axtell wrote:

> To my delight, I have been given a shot at designing a solar tracking
> system, [...] Anybody have ideas?

Move the array in steps (to conserve power). Use a real-time clock (with
some tables or a formula) as sanity check for the position.

Gerhard

2006\08\21@175738 by Jinx

face picon face

> I would love to document that! The closest I've seen was black
> rubber bags that expanded or contracted with heat. Any chance
> he could send some pic's or tell us what the working fluid is?

A fluid that would probably do is methylene chloride. It's used
in those "nodding bird" things that forever tip and drink out of a
glass

http://sci-toys.com/scitoys/scitoys/thermo/solar_bird/bird.html

2006\08\21@181113 by Jinx

face picon face
> it's cloudy they get lost.  The type that depends on a clock will
> be pointing at the Sun when it pops out of the clouds.  But an
> advantage of the alignment type is that when it's cloudy the array
> is not moved saving energy whereas the clock type wastes
> energy pointing at the sun when it's cloudy

You can calculate whether there will be a nett gain if the array is
moved. The sky ahead of the array's travel can be monitored with
a line of sensors. There is no reason why both a clock/calendar and
light tracking system (plus perhaps even an historical record) can't
be used together to determine how much potential energy is left in
the day

2006\08\21@181831 by Marcel duchamp

picon face
Jinx wrote:
>> I would love to document that! The closest I've seen was black
>> rubber bags that expanded or contracted with heat. Any chance
>> he could send some pic's or tell us what the working fluid is?
>
> A fluid that would probably do is methylene chloride. It's used
> in those "nodding bird" things that forever tip and drink out of a
> glass

I've found that beer works well for me.

2006\08\21@182102 by S Bakaletz

flavicon
face
This seems too be a trivial problem.  Since there are programs to
compute the position of the Sun in the sky verses date and time.
One could either:  A). Program a PIC to do the calculations on the fly.
                           B). Put a pre-calculated table on an EEPROM.
This would simplify the design by eliminating the sensor array, its wiring,
and maintenance (cleaning).

2006\08\21@182107 by olin piclist

face picon face
David VanHorn wrote:
> I've seen this done with a four-quadrant photodiode and an aperture
> plate, and with four solar cells and a cruciform center baffle.  The
> idea was to drive the motors such that the outputs of the X and Y
> pairs were equal, within the pair. That is to say that left and right
> are equal, and up and down are equal, but up does not necessarily
> equal right.

You should only need three sensors.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products

2006\08\21@182642 by olin piclist

face picon face
Brian Riley wrote:
> Sadly not even close to true.  The accepted figure for tracker gain
> is 10% tops.

That doesn't add up mathematically.  Unless I've really screwed up the
integrals (quite possible since I'm supposed to be getting home and am
rushed), it seems up to 57% gain is possible.  That assumes that sunlight is
the same strength and available for a whole 180 degrees and the tracker is
kept flat on to the sun as apposed to a fixed midday orientation.  I know
the effective sunlight will be less in the morning and evening as it passes
thru more atmosphere, but still optimum daily tracking versus fixed midday
but at proper height should be better than 10%.

I'm always immediately skeptical when someone quotes "accepted figures" or
"everyone knows" without justification or the test conditions carefully
spelled out.  Often these general wisdoms are true for a certain set of
conditions lost in time, and then get applied lots of places where the
assumptions aren't valid.


******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products

2006\08\21@190834 by olin piclist

face picon face
Brian Riley wrote:
> Now, if
> you consider a manual array mounting rack (manual meaning, you go out
> at some regular interval, say once a month,

This part seems like the "why bother".  If I remember right, the earth tilts
+-22.5 degrees over a year.  So if you point a collector at the equanox sun
height, you're never off by more than 22.5deg, and less than half that on
average.  Cos(22.5deg) = .924, which means you have 7.6% loss worst case.
Cos(11.25deg) = .981, so you lose less than 2% averaged over a whole year
with no vertical (seasonal) adjustment at all.  The daily sun travel angle
is much more, so tracking horizontally would be a bigger bang, although also
more complicated and expensive.


******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products

2006\08\21@193811 by Brian Riley

picon face
I have lived off-grid for almost 20 years. I designed and installed  
my own system (<http://www.wulfden.org/Wulfden017.jpg>) and have been  
involved to various extents with a dozen other systems and have  
visited literally dozens of sites of all sorts of configurations.

I will comment on this from two standpoints ...

 - engineering - so far every electric/electronic system I have seen  
has fallen short, they all screw up, usually sooner than later.  
Reasons - poorly designed electronics, that inadequately do the job,  
poorly produced (they  work, sort of, but either fry in inadequately  
insulated enclosures, or lose their minds at -40F in a Vermont  
winter), poor mechanicals, and every combination thereof. Now the  
passive units that uses the gas tubes  (<http://www.zomeworks.com/
solar/trackrack/trackwork.html>) that sense temperature differentials  
that slowly rotate using pneumatic hydraulics to follow the daytime  
sun the reset themselves to the East at the start of the day, they do  
seem to work. I know of several units well into their second decade  
and still in service ... and I know several that didn't make it out  
of their first decade.

 - cost analysis - the rule of thumb is that a tracker will produce  
a gain of 9-10% output by maximizing the sun on the array. Now, if  
you consider a manual array mounting rack (manual meaning, you go out  
at some regular interval, say once a month, and adjust its elevation  
angle and it more or less stays fixed pointing South), the additional  
cost of a rack with automated tracking mechanisms above the cost of a  
manual, will, depending on which unit you get be the equivalent of  
one to two additional solar panels. Even adjusting in an increase  
cost for a manual rack that can accommodate two additional panels,  
you will still be expending a given amount of money to get 10% more  
power via 'geekness' when  the the same amount of money could be  
spent to reap 15-25% more power via brute force.

In other words .... why bother!

---
cheers ... 73 de brian  riley,  n1bq , underhill center, vermont
  <http://web.mac.com/brianbr/>  Tech Blog
  <http://www.wulfden.org/DiskShop.shtml>
   Home of the
      K107 Serial LCD Controller Kit   FT817 Power Conditioner Kit
      Tab Robot Laser Tag Kit            MSP430 Chips and Connectors
      Propeller Robot Controller         SX48 "Tech Board" Kit



On Aug 21, 2006, at 10:54 AM, Thomas C. Sefranek wrote:

{Quote hidden}

> {Original Message removed}

2006\08\21@195631 by David VanHorn

picon face
>
>
> You can calculate whether there will be a nett gain if the array is
> moved. The sky ahead of the array's travel can be monitored with
> a line of sensors. There is no reason why both a clock/calendar and
> light tracking system (plus perhaps even an historical record) can't
> be used together to determine how much potential energy is left in
> the day


That's what I would suggest.
The clock also acts as a sanity check, in case there's a bird sitting on
your tracking optics.
(Or bird poop!)

You know where the sun ought to be, and if the tracker says you're a little
off, then you go there, and see if output power rises or falls. If the
tracker says you're way off, then you know you have a tracking system
problem, and just use the clock positioning. Even then, if the array isn't
outputting much, and the position error should be small, then don't bother
moving it, the gain won't be worth it.


--
> Feel the power of the dark side!  Atmel AVR

2006\08\21@195643 by David VanHorn

picon face
>
>
> You should only need three sensors.


True, but I haven't run into a three section photodiode.
Just reporting what I've seen.

2006\08\21@200009 by David VanHorn

picon face
On 8/21/06, Olin Lathrop <RemoveMEolin_piclistTakeThisOuTspamembedinc.com> wrote:
>
> Brian Riley wrote:
> > Sadly not even close to true.  The accepted figure for tracker gain
> > is 10% tops.
>
> That doesn't add up mathematically.  Unless I've really screwed up the
> integrals (quite possible since I'm supposed to be getting home and am
> rushed), it seems up to 57% gain is possible.  That assumes that sunlight
> is
> the same strength and available for a whole 180 degrees and the tracker is
> kept flat on to the sun as apposed to a fixed midday orientation.



The curve of power available vs time of day ought to be gaussian or
sinusoidal (can't remember which offhand), so those early and late hours
don't actually add up to much in terms of joules in the can.

2006\08\21@201245 by Jinx

face picon face
> > the same strength and available for a whole 180 degrees and the
> > tracker is kept flat on to the sun as apposed to a fixed midday
> > orientation.
>
> The curve of power available vs time of day ought to be gaussian
> or sinusoidal (can't remember which offhand), so those early and late
> hours don't actually add up to much in terms of joules in the can.

I did some measurements a couple of years ago with a small cell I
wanted to use as a battery float source. For some time after dawn
and before sunset you could see quite easily the voltage just falling
on a meter and there's no current behind it either. I'd hazard a guess
at maybe 30 degrees off the horizon and downward

2006\08\21@201425 by James Newtons Massmind

face picon face
> That doesn't add up mathematically.  Unless I've really
> screwed up the integrals (quite possible since I'm supposed
> to be getting home and am rushed), it seems up to 57% gain is
> possible.  That assumes that sunlight is the same strength
> and available for a whole 180 degrees and the tracker is kept
> flat on to the sun as apposed to a fixed midday orientation.  
> I know the effective sunlight will be less in the morning and
> evening as it passes thru more atmosphere, but still optimum
> daily tracking versus fixed midday but at proper height
> should be better than 10%.

There are several reasons why it isn't as much of a gain as you might
expect:

1. The covering over the solar panels is designed to collect the energy from
a wide range of angles. E.g. you don't see any real increase just from the
light striking head on rather than at an angle. The area being collected
does change of course.

2. The morning and evening sun are MUCH less powerful due to the increased
mass of air (and pollution, etc...) through which the light passes. There is
a lensing effect that accounts for the apparent increase of the diameter of
the sun or moon, and you feel the heat since the low frequency IR bends
nicely, but the high energy UV is just not there and that is what solar
panels (primarily) collect.

3. The actual range of angles is usually less than 180 due to surrounding
obstacles like hills, trees, buildings the slant of the roof, and so on.

4. In many areas, during at least part of the year, morning dew or fog must
burn off before anything at all gets in from the sun.

It might double the power during the early morning or evening, but that time
isn't much of the total day. The over all result is unlikely to be more than
10%. And very unlikely to be more than the cost of the tracker.

I would be happy to see figured to the contrary.

---
James.


2006\08\21@201654 by Brian Riley

picon face
Well, I have done absolutely no theoretical computations. I just know  
what  computed during a week of working outdoors here building that  
garden for my wife. I loosened bolts of the mounts and tracked one by  
moving it every 15 minutes or sooo. I also draw on the real life  
experiences of other off-gridders with whom I have associated.  The  
best figures I have seen show 12% increase. When I first got into  
this none of them promised better than 10%.

I did some looking around in the last few and now I am seeing a  
number of different sources quoting 25-40% increase. I don't know  
what these new trackers are promising and what they are actual  
delivering. I really haven't paid much attention to it in the last  
three four years. Zomeworks references an article by Dick Perez from  
Home Power magazine (<http://www.zomeworks.com/solar/trackrack/
Homepower_june2004.pdf>). Richard is pretty good and he usually has  
his ducks all in a row before he opens his mouth so I would think  
there's some good info there.

I still feel that the application of money to solar PV should go into  
more panels rather than tracking technology except in the most  
moderate of climates in the high sun regions. Murphy just loves  
adverse weather conditions. I am a 1600 feet on the western slope of  
Mount Mansfield where it can get as cold as -45F, November and  
December brings windstorms that gust 80 mph ( every year we see gusts  
over 100 mph anywhere from two to a dozen times ) if someone can find  
me an automatic tracker that will stand up to all that, I will give  
it a whirl.


On Aug 21, 2006, at 6:25 PM, Olin Lathrop wrote:

{Quote hidden}

2006\08\21@202711 by Jinx

face picon face
I wrote -

> For some time after dawn and before sunset you could see quite
> easily the voltage just falling on a meter

Obviously V doesn't fall when the sun is rising, I meant useable
current isn't available as soon as the sun appears

2006\08\21@204041 by olin piclist

face picon face
David VanHorn wrote:
>> That doesn't add up mathematically.  Unless I've really screwed up the
>> integrals (quite possible since I'm supposed to be getting home and am
>> rushed), it seems up to 57% gain is possible.  That assumes that
>> sunlight is
>> the same strength and available for a whole 180 degrees and the
>> tracker is kept flat on to the sun as apposed to a fixed midday
>> orientation.
>
> The curve of power available vs time of day ought to be gaussian or
> sinusoidal (can't remember which offhand), so those early and late hours
> don't actually add up to much in terms of joules in the can.

Which I pointed out in the part you snipped.  However, there is still a big
difference between 57% and 10%.  It's not obvious to me that all of that can
be accounted for by reduced incident power due to atmospheric obsorption.


******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products

2006\08\21@204837 by David VanHorn

picon face
what DO you do about hail?

2006\08\21@205024 by James Newtons Massmind

face picon face
> I still feel that the application of money to solar PV should
> go into more panels rather than tracking technology except in
> the most moderate of climates in the high sun regions.

I agree. The only area I can see that is possibly worth looking into is the
/careful/ placement of mirrors to reflect additional light onto the panels
during the early morning and evening and during the winter; all the times
when the panels are not getting the maximum they can use.

The cost of the mirrors and mounts should be (?) low, and if they are placed
correctly, they will not cause the panels to exceed their maximum ratings.

My guess is that this would make more of a difference for the winter months.
My panels drop back a lot due in part to shorter days, but also the sun is
low and doesn't seem as strong even at noon. Perhaps, with effort, some
arrangement could be found that causes the mirrors to reflect light on the
panels only when the sun is low in the sky.

---
James.


2006\08\21@205718 by Brian Riley

picon face
I go out on the 20th of each month (except June and December, the  
solstices) and set the array to the optimum angle for one month  
hence  (<http://www.wulfden.org/pvangles.pdf>). It takes a 3/4" open  
end wrench and an inclinometer ($10 at Home Depot) and about 5  
minutes on each of my two racks. The above referenced article has the  
charts and some explanatory text is also by Richard Perez from a 1993  
article.


the costs is nothing to speak of, requires a basic rack , as opposed  
to azimuthal tracking which in your own words

>  so tracking horizontally would be a bigger bang, although also
> more complicated and expensive.


Now, from Backwoods Solar (Sandpoint, ID) (I have dealt with them for  
16 years) on the web page <http://www.backwoodssolar.com/
Catalogpages2/pvmount2.htm#SUN%20TRACKER%20MOUNTS> they say the  
following;

"ZOMEWORKS UNIVERSAL TRACK RACKS follow the sun through the day for  
more hours of full power generation. Solar heated freon moves the  
tracker with no motors or mechanism. Effectively boosts summer power  
for water pumping & refrigeration. Power is increased 35% to 50% in  
summer, but only 0% to 9% in winter. Lower % numbers apply to  
northern U.S.  For improved winter power in the north where winter  
sun moves little and overcast prevails, use more modules instead."



From this same page quoted and referenced above, I find that a  
tracking rack for my two racks of panels would cost me $1470 each  
plus about $210 freight charges. That is a combine price of $3360 ...  
for that price I could purchase 8 more Seimens SP75's, a two seas  
universal rack (manual), a ten foot length of 6" Schedule 40 pipe,  
and an SB50 MPPT Controller and increase my PV capacity by a hard 50%  
year around.



On Aug 21, 2006, at 6:11 PM, Olin Lathrop wrote:

{Quote hidden}

2006\08\21@214456 by James Newtons Massmind

face picon face
>
> what DO you do about hail?


Live in southern California.

---
James.


2006\08\21@220031 by Bob Axtell

face picon face
Jinx wrote:
>> it's cloudy they get lost.  The type that depends on a clock will
>> be pointing at the Sun when it pops out of the clouds.  But an
>> advantage of the alignment type is that when it's cloudy the array
>> is not moved saving energy whereas the clock type wastes
>> energy pointing at the sun when it's cloudy
>>    
>
> You can calculate whether there will be a nett gain if the array is
> moved. The sky ahead of the array's travel can be monitored with
> a line of sensors. There is no reason why both a clock/calendar and
> light tracking system (plus perhaps even an historical record) can't
> be used together to determine how much potential energy is left in
> the day
>
>  
Jinx, that's very intuitive. I now know why you get paid the big bucks.
Thanks!

--Bob

2006\08\21@220257 by Bob Axtell

face picon face
Olin Lathrop wrote:
> Brian Riley wrote:
>  
>> Sadly not even close to true.  The accepted figure for tracker gain
>> is 10% tops.
>>    
>
> That doesn't add up mathematically.  Unless I've really screwed up the
> integrals (quite possible since I'm supposed to be getting home and am
> rushed), it seems up to 57% gain is possible.  That assumes that sunlight is
> the same strength and available for a whole 180 degrees and the tracker is
> kept flat on to the sun as apposed to a fixed midday orientation.  I know
> the effective sunlight will be less in the morning and evening as it passes
> thru more atmosphere, but still optimum daily tracking versus fixed midday
> but at proper height should be better than 10%.
>  
I think so, too, Olin. He said if it is tracking, his batteries are
topped by the time he gets to the office
at 9:30AM (we get early sun out here, about 6:15 AM now).

--Bob
{Quote hidden}

2006\08\21@220704 by cdb

flavicon
face
This topic seems to have gone off at a tangent or cosine or two  :-) in relation to the OP's question.

What interests me (also off at a cosine or two) is what about the figures for tracking in a hot country that has more or less guaranteed sunshine all year - here I'm talking South East Queensland Australia. Would the 10% RoT still apply?


Colin

--
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Web presence: http://www.btech-online.co.uk  

Hosted by:  http://www.1and1.co.uk/?k_id=7988359

Do No Harm.

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.



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2006\08\21@221644 by Bob Axtell

face picon face
Thanks, folks, for all the suggestions. I never realized that so many
PIClisters were involved in solar power.

Things are looking up! The future looks pretty good.

--Bob

2006\08\21@222516 by Jinx

face picon face
 
> Jinx, that's very intuitive. I now know why you get paid the big
> bucks.

Ha ! Say what ? ;-)

Yeah, multi-hundredaire, that's me

But y'know, I'd trade it all in for just a little more

<rationalising> Still, job satisfaction counts too eh ? </rationalising>

Seriously, this forum of peers has been exceptionally useful and
appreciated over the years for many business and personal reasons.
I'm so glad I'm here, and thanks to all who contribute

2006\08\21@222703 by Jinx

face picon face
> Things are looking up!

groan ;-)

2006\08\21@222832 by Bob Axtell

face picon face
Brian Riley wrote:
> I have lived off-grid for almost 20 years. I designed and installed  
> my own system (<http://www.wulfden.org/Wulfden017.jpg>) and have been  
> involved to various extents with a dozen other systems and have  
> visited literally dozens of sites of all sorts of configurations.
>
> I will comment on this from two standpoints ...
>
>  
Your house and arrays are beautiful.

I have a lot of questions...can you answer a few?

1. Do you heat water for cooking and cleaning with a solar water heater?

2. Do you supplement solar with a generator in the winter?

3. How much insulation is in your log house?

--Bob

2006\08\21@223052 by Brian Riley

picon face
My first panels were Solarex, one of the reasons I selected the  
Solarex MSX-0 panels was they were the designated panel the US Forest  
Service used for remote sites. At that time they were warranteed  
withstand 125 mph quartering winds (think  'pressure differentials'!)  
AND could with stand direct impact of 1" hail.

The good panels have a tempered glass thats pretty rugged.


---
cheers ... 73 de brian  riley,  n1bq , underhill center, vermont
  <http://web.mac.com/brianbr/>  Tech Blog
  <http://www.wulfden.org/DiskShop.shtml>
   Home of the
      K107 Serial LCD Controller Kit   FT817 Power Conditioner Kit
      Tab Robot Laser Tag Kit            MSP430 Chips and Connectors
      Propeller Robot Controller         SX48 "Tech Board" Kit



On Aug 21, 2006, at 9:41 PM, James Newtons Massmind wrote:

>>
>> what DO you do about hail?
>
>
> Live in southern California.
>
> ---
> James.
>
>
> --

2006\08\21@223758 by William Chops Westfield

face picon face

On Aug 21, 2006, at 2:45 PM, Gerhard Fiedler wrote:

> Use a real-time clock (with some tables or a formula)
> as sanity check for the position.
>
(uninformed opinions follow)

Use a real-time clock to determine position, and forget the
fancy and presumably (from what others are saying) error and
failure prone tracking sensors.  I'll bet you can find an
algorithm for determining sunrise and sunset time based on
date, and that should be all you need to get real close to
as good as you can get with actual tracking.  If you're doing
2-axis tracking, you can base the other axis on month.

BillW

2006\08\21@235818 by Russell McMahon

face
flavicon
face
> To my delight, I have been given a shot at designing a solar
> tracking
> system,
> the arrays running at 24V. The arrays are very large, 14' sq and 18'
> sq. The
> user is UNCONNECTED from the AC mains, running his entire business
> from inverters attached to the system.
>
> Anybody have ideas? I know about (1) not allowing the moon to be
> tracked,
> (2) end the day by moving the array to immediately catch the dawn
> sun
> when it comes up, to minimize movement, and (3) the funny 4-diode
> array
> to determine where the sun is..

Do some calculations to convince yourself how much insolation varies
with off-optimum angle. You'll find that for small angle errors the
drop in output is minimal. Concentrating on other loss areas is liable
to produce more output gains than getting tracking exactly right.
Sin(90) = 1 . This reduces by only about 1.5% for variations of +/- 10
degrees. Its only 6% down at +/- 20 degrees ! Clean glass is liable to
be far more important that a 10 degree variation. Power cable losses
and joint losses etc are liable to be significant compared to this.

If your tracking is done using input maximisation the Moon is not
liable to be a major issue. If the Moon ever happens to be the highest
energy source available at the time by all means track it :-).

There is vast amounts of information available on this with many
groups and papers. Google knows much.

Consider a slave tracking array which intelligently works out where
best energy is coming from and then moves the main array after it has
made sure of best position. Fun to watch and not hard.

Most of the time tracking the easily enough calculated sun position is
going to be entirely adequate. Only under conditions of partial
shading is it likely to be worthwhile pointing off the known true sun
position. Whether this is energy efficient may be debateable.

For a big/high power array if you want to track highest energy point
then you probably can justify something better than a simple sensor
like the 4 sensor array you mention. These (if you mean what I think
you mean) simply use 4 sensors in a quad which has shields so the
sensors are equally illuminated when the sensor is pointed fully at
the sun and has reduced output on some sensors when the array is off
alignment in X or Y directions. As any such sensor relies on error
signal to work it arguably will always point you very very slightly
off optimum. (Not much though). A scanning system using a sub array
looks around the expected best position and drives the main array to
the best point found. It would be unusual to need this level of
complexity.

An idea which is sometimes used is a rolling eyeball in a water tank
which thermally points a point on the ball at the sun. Off axis energy
results in differential heating which reorients the ball. Such a
device could be used as a tracker whose position is sensed and used to
locate a large electrical array. It has the advantage of no
electronics at all for its basic action.

As noted already, second axis tracking is very slow as it varies with
season. If it is used at all it can be calculated rather than
measured.


       Russell




2006\08\22@001946 by William Chops Westfield

face picon face
On Aug 21, 2006, at 7:02 PM, Bob Axtell wrote:

> He said if it is tracking, his batteries are topped by the
> time he gets to the office at 9:30AM

Ah.  I don't have any problem believing that the gain from
tracking is substantial during the "early morning" or "late
afternoon" phases of things.  But I think the claims is that
for the whole day the difference is smaller because most of
the energy is going to show up in that 9am-3pm timeframe where
tracking is less critical.

If his batteries are topped off by 0930, I think he could
have gotten by with smaller panels (or he needs a bigger
battery.)

BillW

2006\08\22@010326 by Also-Antal Csaba

flavicon
face

> To my delight, I have been given a shot at designing a solar tracking
> system,
> the arrays running at 24V. The arrays are very large, 14' sq and 18' sq. The
> user is UNCONNECTED from the AC mains, running his entire business
> from inverters attached to the system.
>
> Anybody have ideas? I know about (1) not allowing the moon to be tracked,
> (2) end the day by moving the array to immediately catch the dawn sun
> when it comes up, to minimize movement, and (3) the funny 4-diode array
> to determine where the sun is..

use a heat pipe solar collector, with rear relfector. you dont need any
sun following electonics.

udv
Csaba

2006\08\22@023927 by Tony Smith

picon face
> > A friend of mine has a system that tracks the sun but has
> no motors or
> > electrical control system.
> >
> > His setup has a differential set of pipes with a working fluid that
> > evaporates when in the sun.  The fluid condenses on the side in the
> > shade and creates a weight imbalance which makes the panels rotate
> > until there is equal weight on both sides.
>
> I would love to document that! The closest I've seen was
> black rubber bags that expanded or contracted with heat. Any
> chance he could send some pic's or tell us what the working fluid is?
>
> ---
> James.


There's a similar item used in greenhouses.  Some sort of hydraulic actuator
that open panels when it gets too hot.

Works at low temperatures, around 35-40C.  Maintenance free.

Tony

2006\08\22@030325 by Sebastien Bailard

flavicon
face
On Tuesday 22 August 2006 02:39, Tony Smith wrote:
{Quote hidden}

(Beating the kibbitzing dogpile, I hope.)

I think you mean Nitinol, shape memory alloy.   (If you have a spring of the
stuff, you can stretch it, and it will stay stretched, only to regain its
shape once you heat it.)
www.robotstore.com/site/shapememoryalloys.asp?afid=home
http://en.wikipedia.org/wiki/Nitinol

Regards,

-Sebastien Bailard
reprap.org - self-reproducing 3D printer project

2006\08\22@031515 by Luis.Moreira

picon face
A few years back there was an article in the Portuguese Elector magazine
where they described a system for tracking the Sun by using 3 LDRs each
one inside a pipe which served to limit the sun incidence to right above
the LDR. The LDRs and pipes were attached to the array and moved with
it. The principle was that you want the Sun to be always more on the
middle LDR, if one of the others was getting more sun then you move the
array in that direction. Never tried it but it seemed feasible at the
time... Now I think that first you have to find the Sun and you probably
need 5 LDR's to do the two axis, you will have to find the right length
of pipe to use and you probably need to determine end stops for the
travel of the arrays.  
Is cheap so it's probably worth a try.
Best regards
               Luis



{Original Message removed}

2006\08\22@033418 by Tony Smith

picon face
> >
> >
> > You should only need three sensors.
>
>
> True, but I haven't run into a three section photodiode.
> Just reporting what I've seen.


4 sensors means you can be lazy with with math.  Much easier to figure out X
& Y motions.

I like the ones where they use LEDs as the photodiodes.

Tony

2006\08\22@044716 by Tony Smith

picon face
{Quote hidden}

Wasn't Nitinol.  From memory, it said it used some sort of wax, but probably
a liquid with a low boiling point as someone else mentioned.  The main point
was there was no power needed.

I didn't think Nitinol would work at that low a temperature.  I guess if you
put it in a black pipe it might.  The ones I've seen had current run thru
them to produce the heating.

Tony

2006\08\22@050402 by Bob Axtell

face picon face
Russell McMahon wrote:
{Quote hidden}

I too am beginning to think calculating will work better than anything,
especially if time corrections
can be made by RS232 serial once a day or so.

--Bob

2006\08\22@064007 by Brian Harris

flavicon
face
Silicon Chip did this a few years back.
Analogue IIRC, LDR's, windscreen wiper motors,
but able to reset itself for the next day.

Brian Harris

2006\08\22@075537 by olin piclist

face picon face
James Newtons Massmind wrote:
> There are several reasons why it isn't as much of a gain as you might
> expect:
>
> 1. The covering over the solar panels is designed to collect the energy
> from a wide range of angles. E.g. you don't see any real increase just
> from the light striking head on rather than at an angle. The area being
> collected does change of course.

I wasn't even taking into account the fact that the panels will reflect more
light at shallow angles, although they will.  I was using the cosine of the
incident angle which only models the smaller area intercepted.  That's basic
physics that a flat panel can't do anything about.

However your other points are well taken.  My first reaction was that it was
a stretch to have them account for the difference between 57% and 10%, but
apparently not.


******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products

2006\08\22@093736 by Russell McMahon

face
flavicon
face
> A fluid that would probably do is methylene chloride. It's used
> in those "nodding bird" things that forever tip and drink out of a
> glass

Very carcinogenic, fwiw.
Use, if at all,  with suitable care


       RM

2006\08\22@093737 by Russell McMahon

face
flavicon
face
Save this email somewhere special.
I agree with Olin :-)


       Russell

{Quote hidden}

2006\08\22@093737 by Russell McMahon

face
flavicon
face
>> I've seen this done with a four-quadrant photodiode and an aperture
>> plate, and with four solar cells and a cruciform center baffle.

> You should only need three sensors.

Three may be conceptually OK if you are prepared to do calculations
(digital or analog summing). But the simplest 4 sensor systems just do
gross on/off control when cell pair exceed a certain level.

With a single axis tracker (or a 2 axis one with occasional manual
control of the second axis) you need only two sensors with a dividing
baffle.

You could use one sensor (tm) if you placed it on a vibrating/moving
arm :-). Oscillate it either side of the array's pointing vector and
note whether the energy insolation peak occurs when the arm is normal
(ie at right angles) to the array's face. If not, adjust the array
accordingly. The oscillatory movement COULD be arranged to be
activated resonantly by wind and 90 degree position switching could
use eg a reed switch or hall cell or a photo diode. It would be worth
doing for the confusion and wonderment that it would cause informed
observers :-). It would fail in absolutely windless conditions but
could be designed to need only the merest smidgeon of breeze. In a
complete calm you could "kick" it into motion with a slight burst of
the panel motors - highly undesirable way to design a system but great
fun.


       RM

2006\08\22@093739 by Russell McMahon

face
flavicon
face
> Well, I have done absolutely no theoretical computations. I just
> know
> what  computed during a week of working outdoors here building that
> garden for my wife. I loosened bolts of the mounts and tracked one
> by
> moving it every 15 minutes or sooo. I also draw on the real life
> experiences of other off-gridders with whom I have associated.  The
> best figures I have seen show 12% increase. When I first got into
> this none of them promised better than 10%.

Just did a rough theoretical calculation.
Some assumptions are definitely shonky

ASSUME sun intensity varies by sine of angle across day.
ie 100% at noon, 70.71% (sine of 45 degrees at 9am and 3pm) no sun at
6am or 6pm

Pointing error for a noon facing fixed panel is Cosine(90-angle).

SO:
SA = sun angle

Etp = Output of tracking panel = summation(sine(SA)) across the day

Efp = Output of fixed panel = summation [ sine(SA) x cos(90-SA)]

Summing over 180 1 degree increments gives Etp/Efp ~= 1.27
ie a 27% increase for the above assumptions.
Integration would have produced a similar result but excel helps you
to check that things are as expected along the way.

Less than I would have expected.
More than people are reporting here.

If sun output tends to peak more towards noon and drop off more
towards dawn and dusk (as I would intuitively expect) then tracking
gain would be even lower.



       R "all models are wrong, some models are useful" M










2006\08\22@093740 by Russell McMahon

face
flavicon
face
>> what DO you do about hail?

> Live in southern California.

What DO you do about earthquakes :-) ?


       R

2006\08\22@093743 by Russell McMahon

face
flavicon
face
> Ah.  I don't have any problem believing that the gain from
> tracking is substantial during the "early morning" or "late
> afternoon" phases of things.  But I think the claims is that
> for the whole day the difference is smaller because most of
> the energy is going to show up in that 9am-3pm timeframe where
> tracking is less critical.

Applying my assumptions from prior post to 9am - 3pm gives a tracking
gain of only ~10%.

So. most of the gains are, as expected at the ends of the day.
Checks ...
Yes, the 6am - 9am tracking gain is 2.07:1

ie 1Q & 4Qgain is 2:1
2Q & 3Q gain is 10%
Overall gain is 27%
Those figures can't be linearly added as both raw insolation and
tracking gain vary with angle.


       Russell




2006\08\22@095414 by Jinx

face picon face
> > methylene chloride
>
> Very carcinogenic, fwiw

Very ? Sure ?

http://www.hsia.org/white_papers/dcm%20wp.htm

"potentially" - whatever that means

http://www.osha.gov/SLTC/methylenechloride/

Take reasonable precautions I think, but not give the
sphincter a work-out

2006\08\22@110625 by David VanHorn

picon face
On 8/22/06, Russell McMahon <TakeThisOuTapptechEraseMEspamspam_OUTparadise.net.nz> wrote:
>
> >> what DO you do about hail?
>
> > Live in southern California.
>
> What DO you do about earthquakes :-) ?


Watch em on CNN.  :)

2006\08\22@140805 by James Newtons Massmind

face picon face
> >> what DO you do about hail?
>
> > Live in southern California.
>
> What DO you do about earthquakes :-) ?
>

Stand near a lady with large breasts.




Earthquakes are very overrated as a danger.
http://www.nsc.org/lrs/statinfo/odds_dying.jpg You have a better chance of
being struck by lightning, getting the electric chair, fatal bee sting,
dying of heat stroke, drinking yourself to death, being electrocuted, shot
(accidentally), plane crash, bicycle, fire, motorcycle, drowning, being run
over while walking, shot (on purpose), falling, suicide, car crash, stroke,
cancer or heart disease. In fact, floods and fireworks are safer than
earthquakes.

Truth is, out here in the west, the gun slingers are more likely to get you,
ma'am. Or you might die from complications after plastic surgery... You DO
know that all Californians are required to have plastic surgery right?

Food poisoning from the pink tofu is another possibility...

Any other myths about SoCal I need to comment on?

---
James.


2006\08\22@142957 by Alex Harford

face picon face
On 8/22/06, James Newtons Massmind <RemoveMEjamesnewtonspamTakeThisOuTmassmind.org> wrote:
>
> Stand near a lady with large breasts.
>

That will be hard to find in Cali. :-D

>
>
> Earthquakes are very overrated as a danger.
> http://www.nsc.org/lrs/statinfo/odds_dying.jpg

Since I live in a country that doesn't have legal executions, does
that increase my risk of dying in an earthquake?  *hides under my
desk*

Alex

2006\08\22@150420 by David VanHorn

picon face
Before this gets into a descussion of damped oscillations in mamilliary
tissues, What I was really wondering about, is how those who use solar cells
deal with hail threats.

I've seen what hail can do up close and personal, with 3-4 inch hail balls
at 100 miles/hr.
The storm we had in oakville would have made very short work of any solar
array.
I know you could put a lexan overlay on, but that of course will cost output
all the time, and scratch/haze etc over time.

2006\08\22@153154 by Brian Riley

picon face
Solarex MSX series panels are warranted to withstand direct impact of  
1" hail and pressure differentials of 125 mph quartering winds


---
cheers ... 73 de brian  riley,  n1bq , underhill center, vermont
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On Aug 22, 2006, at 3:04 PM, David VanHorn wrote:

{Quote hidden}

> --

2006\08\22@154705 by William Chops Westfield

face picon face

On Aug 22, 2006, at 6:11 AM, Russell McMahon wrote:

> ASSUME sun intensity varies by sine of angle across day.
>
Additional item: the sky is pretty bright.  You can point your
solar cell at right angles to "direct" sunlight and still pick
up some power...

BillW

2006\08\22@155225 by David VanHorn

picon face
On 8/22/06, Brian Riley <brianbrEraseMEspam.....mac.com> wrote:
>
> Solarex MSX series panels are warranted to withstand direct impact of
> 1" hail and pressure differentials of 125 mph quartering winds


Hmm.. That would make me a bit nervous.
Not too uncommon around here to have severe thunderstorms with downbursts in
the 100+ mph area (estimated by damage) and 1" hail is also not rare.

My old explorer has dents all over the body, but most tellingly in the roof
support columns on either side of the windshield.

2006\08\22@160810 by Paul Hutchinson

picon face
> -----Original Message-----
> From: EraseMEpiclist-bouncesspammit.edu On Behalf Of David VanHorn
> Sent: Tuesday, August 22, 2006 3:04 PM
>
> Before this gets into a descussion of damped oscillations in
> mamilliary tissues, What I was really wondering about, is how those who
> use solar cells deal with hail threats.
>
> I've seen what hail can do up close and personal, with 3-4
> inch hail balls at 100 miles/hr.
> The storm we had in oakville would have made very short work
> of any solar array.
> I know you could put a lexan overlay on, but that of course
> will cost output all the time, and scratch/haze etc over time.

Not sure how they do it on large arrays but, for small arrays like on small
instruments the best material I've found is a special polyurethane resin
from Development Associates, Inc. http://www.daius.com/.

It is used on the mini-panels manufactured by Sol-Lite Manufacturing Company
Ltd. http://www.sol-lite.com/

Paul  

2006\08\22@164458 by Bob Blick

face picon face
> Before this gets into a descussion of damped oscillations in mamilliary
> tissues, What I was really wondering about, is how those who use solar
> cells
> deal with hail threats.

Move someplace without hail? Get insurance? Temporary covers?



2006\08\22@170028 by Robert Rolf

picon face

Bob Blick wrote:

>>Before this gets into a descussion of damped oscillations in mamilliary
>>tissues, What I was really wondering about, is how those who use solar
>>cells
>>deal with hail threats.
>
>
> Move someplace without hail? Get insurance? Temporary covers?

Raise the panels to vertical automatically to avoid direct hail impact?

Put heavy wire grid mesh above the panel to turn large hail into
french fries if it doesn't just bounce off? Would cost a few percent
in shading losses but would be inexpensive to do.

R

2006\08\22@174315 by David VanHorn

picon face
>
>
> Raise the panels to vertical automatically to avoid direct hail impact?


Wouldn't really help. I have pictures of holes in vertical walls punched by
3"-4" hail balls.
They don't just fall from above, they are often blown by a downburst.

Put heavy wire grid mesh above the panel to turn large hail into
> french fries if it doesn't just bounce off? Would cost a few percent
> in shading losses but would be inexpensive to do.


I thought about this, but in terms of a kevlar web.
You wouldn't turn hail into french fries, but hail might batter it's
way through wire.


--
Feel the power of the dark side!  Atmel AVR

2006\08\22@180929 by Robert Rolf

picon face


David VanHorn wrote:

>>
>>Raise the panels to vertical automatically to avoid direct hail impact?
>
>
>
> Wouldn't really help. I have pictures of holes in vertical walls punched by
> 3"-4" hail balls.
> They don't just fall from above, they are often blown by a downburst.

You mean like this?
http://lab.chill.colostate.edu/cases/20JUNE2001/Hail02.gif

{Quote hidden}

Good point.
And the Kevlar would have some recoil, bouncing the hail off, particularly
if it was parallel to the panels, giving them glancing blows.

We don't get 4" hail up here, and the large stuff tends to be quite mushy.

Robert

2006\08\22@182441 by David VanHorn

picon face
>
>
> You mean like this?
> http://lab.chill.colostate.edu/cases/20JUNE2001/Hail02.gif


Yes!

Good point.
> And the Kevlar would have some recoil, bouncing the hail off, particularly
> if it was parallel to the panels, giving them glancing blows.
>
> We don't get 4" hail up here, and the large stuff tends to be quite mushy.


I've seen 2-3" stuff that was very hard.
Dented the support columns on my explorer it did!

2006\08\22@184404 by Bob Blick

face picon face

> I've seen 2-3" stuff that was very hard.
> Dented the support columns on my explorer it did!

Are people killed by hail on a regular basis? I think I'm happier with the
occasional earthquake.

Cheerful regards,

Bob


2006\08\22@191940 by Jinx

face picon face
> Are people killed by hail on a regular basis ?

Just the once Bob, just the once

(no Hindi correspondence entered into)

2006\08\22@202750 by David VanHorn

picon face
On 8/22/06, Bob Blick <RemoveMEbblickEraseMEspamEraseMEsonic.net> wrote:
>
>
> > I've seen 2-3" stuff that was very hard.
> > Dented the support columns on my explorer it did!
>
> Are people killed by hail on a regular basis? I think I'm happier with the
> occasional earthquake.


It happens, but it's the large fragile mostly horizontal glass panels that
worry me.

2006\08\22@214246 by John Scott

flavicon
face
What bout using that 1" bullet proof glass. A hail stone has a much
larger surface area than a bullet, so it shouldnt even crack. It would
most likely break the hail stone before it breaks the glass.

David VanHorn wrote:
{Quote hidden}

2006\08\22@225913 by Tony Smith

picon face
> >
> > Stand near a lady with large breasts.
> >
>
> That will be hard to find in Cali. :-D
>
> > Earthquakes are very overrated as a danger.
> > http://www.nsc.org/lrs/statinfo/odds_dying.jpg
>
> Since I live in a country that doesn't have legal executions,
> does that increase my risk of dying in an earthquake?  *hides under my
> desk*
>
> Alex


Ha, love that it points out that the odd of dying from any cause is 1:1.

The odd of dying from ladies with large breasts, or the odds of dying if you
are a lady with large breasts is unfortunately absent.  Immediate studies
are required, I feel.  No, wait, I think, I think!  What would Freud say?

Tony

2006\08\22@235217 by William Chops Westfield

face picon face

On Aug 22, 2006, at 2:43 PM, David VanHorn wrote:

> I have pictures of holes in vertical walls punched by 3"-4" hail
> balls. They don't just fall from above, they are often blown
> by a downburst.
>
You mentioned dents in the roof supports around your car windows.
Do the car windows break in each hailstorm?

BillW

2006\08\23@004723 by David VanHorn

picon face
>
>
> You mentioned dents in the roof supports around your car windows.
> Do the car windows break in each hailstorm?



They can, sometimes you get lucky.

2006\08\23@010529 by Tony Smith

picon face
> > Move someplace without hail? Get insurance? Temporary covers?
>
> Raise the panels to vertical automatically to avoid direct
> hail impact?
>
> Put heavy wire grid mesh above the panel to turn large hail
> into french fries if it doesn't just bounce off? Would cost a
> few percent in shading losses but would be inexpensive to do.


Car yards sometimes have "hail proof" meshing.  They usually install it
after their stock gets wiped out, and Sod's Law says it'll wear out just
before the next big storm.

Tony

2006\08\23@020215 by David VanHorn

picon face
>
>
> Car yards sometimes have "hail proof" meshing.  They usually install it
> after their stock gets wiped out, and Sod's Law says it'll wear out just
> before the next big storm.


I've seen those.

2006\08\23@065253 by Alan B. Pearce

face picon face
>To my delight, I have been given a shot at designing a solar
>tracking system, the arrays running at 24V. The arrays are very
>large, 14' sq and 18' sq. The user is UNCONNECTED from the AC
>mains, running his entire business from inverters attached to
>the system.
>
>Anybody have ideas? I know about
>(1) not allowing the moon to be tracked,
>(2) end the day by moving the array to immediately catch
>the dawn sun when it comes up, to minimize movement, and
>(3) the funny 4-diode array to determine where the sun is..

Hmm, many years ago Mother Earth News published a 1 or 2 page article about
a guy who used a hydraulic method to do something similar. The array was
mounted on a vertical pole so it could swivel, and used a double acting
piston to move it. Then down each side of the array he had a pipe filled
with liquid which was warmed by the sun. Each of these pipes was "wired" to
the piston so that as the sun warmed the liquid, that side was moved to face
the sun until the pipe on the other side of the array was equally warmed and
could balance the pressure in the piston. It may have had a limitation on
the angle of swing from the piston, but I would have thought you could get
120 degrees readily.

I always thought it was an impressive solution to the problem.

If your array is that large that you have to use a motor to move it, I can
see no reason why you couldn't use a suitable heat sensor pair with a micro
to do the same balancing trick. Sensing heat is probably the way to get
around the moon tracking, and using a micro could give the "move back at
night ready for morning" action, although I wonder if that really is
necessary.

2006\08\23@073433 by olin piclist

face picon face
Russell McMahon wrote:
>> You should only need three sensors.
>
> Three may be conceptually OK if you are prepared to do calculations

Which even a PIC 10F could handle easily.  This is a perfect example of how
a little bit of firmware cleverness can save real hardware cost and
complexity.


******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products

2006\08\23@113536 by Bob Axtell

face picon face
Olin Lathrop wrote:
> Russell McMahon wrote:
>  
>>> You should only need three sensors.
>>>      
>> Three may be conceptually OK if you are prepared to do calculations
>>    
>
> Which even a PIC 10F could handle easily.  This is a perfect example of how
> a little bit of firmware cleverness can save real hardware cost and
> complexity.
>
>
>  
Exactly. Good application. And I could send the info down a single wire
as manchester coding,
like I did my water fountain.

--Bob

> ******************************************************************
> Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
> consultant in 2004 program year.  http://www.embedinc.com/products
>  

2006\08\23@124801 by Russell McMahon

face
flavicon
face
>>> You should only need three sensors.
>>
>> Three may be conceptually OK if you are prepared to do calculations
>
> Which even a PIC 10F could handle easily.  This is a perfect example
> of how
> a little bit of firmware cleverness can save real hardware cost and
> complexity.

I agree completely. And that's fine for you and me, or for that matter
many people on this list, but there are still many people who are very
capable indeed in their chosen fields who would consider rising to the
challenge of a bit of analog electronics but who would never
realistically venture into the " ... even a PIC10F ..." realm. Maybe
"even a BASIC Stamp" would be acceptable to some such.



       Russell

2006\08\23@131940 by Nate Duehr

face
flavicon
face

On Aug 22, 2006, at 2:44 PM, Bob Blick wrote:

>> Before this gets into a descussion of damped oscillations in  
>> mamilliary
>> tissues, What I was really wondering about, is how those who use  
>> solar
>> cells
>> deal with hail threats.
>
> Move someplace without hail? Get insurance? Temporary covers?

Covers don't work unless you have some way to know it's hailing and  
by then it's too late to install them without serious risk of head  
trauma.  :-)

--
Nate Duehr - WY0X
RemoveMEnateTakeThisOuTspamspamnatetech.com



2006\08\23@132136 by Nate Duehr

face
flavicon
face

On Aug 22, 2006, at 3:00 PM, Robert Rolf wrote:

>
> Bob Blick wrote:
>
>>> Before this gets into a descussion of damped oscillations in  
>>> mamilliary
>>> tissues, What I was really wondering about, is how those who use  
>>> solar
>>> cells
>>> deal with hail threats.
>>
>>
>> Move someplace without hail? Get insurance? Temporary covers?
>
> Raise the panels to vertical automatically to avoid direct hail  
> impact?
>
> Put heavy wire grid mesh above the panel to turn large hail into
> french fries if it doesn't just bounce off? Would cost a few percent
> in shading losses but would be inexpensive to do.

Large hail is usually very very tough stuff.  It doesn't break easily.

--
Nate Duehr
EraseMEnatespamspamspamBeGonenatetech.com



2006\08\23@132341 by Nate Duehr

face
flavicon
face

On Aug 22, 2006, at 4:09 PM, Robert Rolf wrote:

>> Wouldn't really help. I have pictures of holes in vertical walls  
>> punched by
>> 3"-4" hail balls.
>> They don't just fall from above, they are often blown by a downburst.
>
> You mean like this?
> http://lab.chill.colostate.edu/cases/20JUNE2001/Hail02.gif

Welcome to Colorado!  ;-)

--
Nate Duehr - WY0X
RemoveMEnateKILLspamspamnatetech.com



2006\08\23@133003 by Nate Duehr

face
flavicon
face

On Aug 22, 2006, at 4:24 PM, David VanHorn wrote:

>> We don't get 4" hail up here, and the large stuff tends to be  
>> quite mushy.
>
>
> I've seen 2-3" stuff that was very hard.
> Dented the support columns on my explorer it did!

You haven't lived until you've been out stormchasing and realize (too  
late) you let yourself get on the "backside" (typically southwest  
side around here) of the thunderstorm and the hailshaft either just  
caught up to you, or you just drove into it.

:-)

Training people to LOOK around is one of the key concepts, yet even  
those of us experienced enough to "know better" sometimes do it...  
with varying levels of damage to our vehicles.  Probably 80% of the  
time, you figure it out while you're still in the SMALL stuff, and  
you get the flock outta there... but once in a great while (or more  
often if you're downright careless) an icy ball cracks your windshield.

Stay out from under the rain-free bases and if a rain shaft looks  
"extra pretty" because it's LIGHTER than the other ones... almost  
white in certain lighting conditions depending on overall cloud cover  
and the location of the Sun in the sky... you're looking at the hail  
coming to get you.  Go and get out of the way and find somewhere else  
to spot from.  :-)

--
Nate Duehr
nateSTOPspamspamspam_OUTnatetech.com



2006\08\23@133033 by Nate Duehr

face
flavicon
face

On Aug 22, 2006, at 4:44 PM, Bob Blick wrote:

>
>> I've seen 2-3" stuff that was very hard.
>> Dented the support columns on my explorer it did!
>
> Are people killed by hail on a regular basis? I think I'm happier  
> with the
> occasional earthquake.

No, usually the lightning gets them first.  :-)

But when earthquakes do kill, they kill a LOT more people in one  
sitting.

--
Nate Duehr
spamBeGonenateSTOPspamspamEraseMEnatetech.com



2006\08\23@133146 by Nate Duehr

face
flavicon
face

On Aug 22, 2006, at 7:42 PM, John Scott wrote:

> What bout using that 1" bullet proof glass. A hail stone has a much
> larger surface area than a bullet, so it shouldnt even crack. It would
> most likely break the hail stone before it breaks the glass.

Wonder how much light they block/diffuse/refract/reflect.

--
Nate Duehr
KILLspamnatespamBeGonespamnatetech.com



2006\08\23@133253 by Nate Duehr

face
flavicon
face

On Aug 22, 2006, at 11:05 PM, Tony Smith wrote:

>>> Move someplace without hail? Get insurance? Temporary covers?
>>
>> Raise the panels to vertical automatically to avoid direct
>> hail impact?
>>
>> Put heavy wire grid mesh above the panel to turn large hail
>> into french fries if it doesn't just bounce off? Would cost a
>> few percent in shading losses but would be inexpensive to do.
>
>
> Car yards sometimes have "hail proof" meshing.  They usually  
> install it
> after their stock gets wiped out, and Sod's Law says it'll wear out  
> just
> before the next big storm.

Or the weight of light hail in quantity collapses the meshing and  
supports onto the cars.  :-)

--
Nate Duehr
EraseMEnatespamEraseMEnatetech.com



2006\08\23@142924 by David VanHorn

picon face
>
>
> You haven't lived until you've been out stormchasing and realize (too
> late) you let yourself get on the "backside" (typically southwest
> side around here) of the thunderstorm and the hailshaft either just
> caught up to you, or you just drove into it.


Yup, I've lived.. :)

Didn't know you were a spotter too!

2006\08\23@174601 by Gus S Calabrese

face picon face
put a net above panels with enough bounce to decelerate the big boys  
and bounce them away

On 2006-Aug 23, at 11:21hrs AM, Nate Duehr wrote:


On Aug 22, 2006, at 3:00 PM, Robert Rolf wrote:

{Quote hidden}

Large hail is usually very very tough stuff.  It doesn't break easily.

--
Nate Duehr
@spam@nate@spam@spamspam_OUTnatetech.com



2006\08\24@074002 by Howard Winter

face
flavicon
picon face
On Tue, 22 Aug 2006 14:26:00 +1200, Jinx wrote:

> > Things are looking up!
>
> groan ;-)

"The future is looking brighter" ?  :-)

Cheers,


Howard Winter
St.Albans, England


2006\08\24@075424 by Howard Winter

face
flavicon
picon face
Bob,

On Tue, 22 Aug 2006 02:03:59 -0700, Bob Axtell wrote:

> I too am beginning to think calculating will work better than anything,
> especially if time corrections
> can be made by RS232 serial once a day or so.

I think it depends on the climate.  Where James lives it's clear skies almost every day, so time/date tracking would work fine most of the time.

But here in Blighty it's cloudy as often as it's clear, so moving the array when the whole sky is giving the same insolation is wasting energy.  In this
case you could probably optimise using a time-steered sensor which tracks the Sun, and a matching one on the array.  Then you can calculate how
much extra energy will be collected by moving the array by comparing readings from the two sensors, and only moving if it's worth it.  It's very
unlikely that an area of sky away from the Sun will produce more energy than pointing at the Sun, it's a question of whether the extra is worth the
energy to move the array from where it is, rather than where it should be for max. energy.

Cheers,


Howard Winter
St.Albans, England


2006\08\24@081102 by Howard Winter

face
flavicon
picon face
Russell,

On Wed, 23 Aug 2006 01:11:12 +1200, Russell McMahon wrote:

>...
> ASSUME sun intensity varies by sine of angle across day.
> ie 100% at noon, 70.71% (sine of 45 degrees at 9am and 3pm) no sun at
> 6am or 6pm

This only applies at Equinox, two days a year.  On the Winter side of this not only are the days shorter, so less difference between dawn/dusk and
noon, but the sunlight has to come through more depth of atmosphere, which all of your calculations ignore.

>...
> Summing over 180 1 degree increments gives Etp/Efp ~= 1.27
> ie a 27% increase for the above assumptions.

That would only apply if there was no atmosphere - the added thickness of air and pollution that the light travels through either side of noon mean
that there is much less energy available than the above calculates, due to absorbtion, diffusion, and refraction - pretty sunsets are due to the lower
frequencies being bent down towards us, whereas the higher frequencies (with their higher energy) go straight through and miss us, and our solar
panels!  :-)  

Because the level of pollution has an effect on all of this, I don't believe it's possible to calculate the differences based purely on geometry - you
need to measure it where the collector is to be installed to know how much effect there really is (and it may well vary from time to time).

All this IMHO, of course!  :-)

Cheers,


Howard Winter
St.Albans, England


2006\08\24@082400 by Howard Winter

face
flavicon
picon face
Robert,

On Tue, 22 Aug 2006 16:09:31 -0600, Robert Rolf wrote:

> David VanHorn wrote:
>...
> > Wouldn't really help. I have pictures of holes in vertical walls punched by
> > 3"-4" hail balls.
> > They don't just fall from above, they are often blown by a downburst.
>
> You mean like this?
> http://lab.chill.colostate.edu/cases/20JUNE2001/Hail02.gif

Wow, people moan about the weather in Britain, but we don't get that sort of thing!

One thing occurs to me seeing that picture - why not use whatever they use to enclose electricity meters as a top covering to the panels?  That
seems to have survived unscathed!  :-)  (OK, probably because it's cylindrical....)

{Quote hidden}

But it would lose a huge amount of its energy doing so - you may have to repair the mesh afterwards, but the solar panels would have been saved.

Cheers,


Howard Winter
St.Albans, England


2006\08\24@091701 by Gerhard Fiedler

picon face
Howard Winter wrote:

> On Wed, 23 Aug 2006 01:11:12 +1200, Russell McMahon wrote:
>
>> ASSUME sun intensity varies by sine of angle across day.

> That would only apply if there was no atmosphere - the added thickness of
> air and pollution that the light travels through either side of noon
> mean that there is much less energy available than the above calculates
> [...]

Isn't that for what Russell used the sine as approximation (differences in
intensity between horizon and noon positions)?

Gerhard

2006\08\24@103731 by Russell McMahon

face
flavicon
face
>>> ASSUME sun intensity varies by sine of angle across day.

>> That would only apply if there was no atmosphere - the added
>> thickness of
>> air and pollution that the light travels through either side of
>> noon
>> mean that there is much less energy available than the above
>> calculates
>> [...]

> Isn't that for what Russell used the sine as approximation
> (differences in
> intensity between horizon and noon positions)?

Yes.
I had a sine function in my tracking version to represent attenuation
of insolation with time of day, and a sin x cos function in my non
tracking version, the latter representing the extra degradation with
panel angle relative to the sun.


       Russell

2006\08\24@130503 by Robert Rolf

picon face


Howard Winter wrote:
> On Tue, 22 Aug 2006 14:26:00 +1200, Jinx wrote:
>
>
>>>Things are looking up!
>>
>>groan ;-)
>
>
> "The future is looking brighter" ?  :-)

Technically, if you include ultraviolet light (ozone hole)
and IR (global warming).

R

2006\08\24@155351 by Robert Ammerman

picon face
For the hail:

Don't turn the array vertical, turn it upside down!

Bob Ammerman
RAm Systems


----- Original Message -----
From: "Howard Winter" <spamBeGoneHDRWspamKILLspamH2Org.demon.co.uk>
To: "Microcontroller discussion list - Public." <.....piclistspam_OUTspammit.edu>
Sent: Thursday, August 24, 2006 7:54 AM
Subject: Re: [EE] Solar Array Tracking


{Quote hidden}

> --

2006\08\24@163418 by Gus S Calabrese

face picon face
YES !


On 2006-Aug 24, at 13:49hrs PM, Robert Ammerman wrote:

For the hail:

Don't turn the array vertical, turn it upside down!

Bob Ammerman
RAm Systems


{Original Message removed}

2006\08\24@184722 by Bob Axtell

face picon face
Gus S Calabrese wrote:
> YES !
>
>
> On 2006-Aug 24, at 13:49hrs PM, Robert Ammerman wrote:
>
> For the hail:
>
> Don't turn the array vertical, turn it upside down!
>
> Bob Ammerman
> RAm Systems
>  
His system won't do _THAT_. He wants me to to minimize it to the wind.

--Bob

2006\08\25@100726 by Howard Winter

face
flavicon
picon face
Gerhard,

On Thu, 24 Aug 2006 10:16:07 -0300, Gerhard Fiedler wrote:

{Quote hidden}

I didn't spot that!  I'm not sure why a sine would be the right shape for this, but does it account for the fact that the atmoshphere is curved?

Cheers,


Howard Winter
St.Albans, England


2006\08\25@101242 by Howard Winter

face
flavicon
picon face
Tony,

On Wed, 23 Aug 2006 12:58:48 +1000, Tony Smith wrote:

{Quote hidden}

Well Sigmund Freud wouldn't say anything because he's dead, but his Great- (-great?) granddaughter, Emma, would be very suitable to include in the
study of these phenomena!  ;-)

(She also has the extremely rare honour of having her name immortalised in rhyming slang, during her life.  That club is even more exclusive than,
say, reigning monarchs, or people who have walked on the Moon!  :-)

Cheers,


Howard Winter
St.Albans, England


2006\08\25@102945 by John Scott

flavicon
face
(She also has the extremely rare honour of having her name immortalised in rhyming slang, during her life.  That club is even more exclusive than,
say, reigning monarchs, or people who have walked on the Moon!  :-)


What is it?? haemorroid?

Regards

John

Howard Winter wrote:
{Quote hidden}

2006\08\25@104522 by Michael Rigby-Jones

picon face


>-----Original Message-----
>From: TakeThisOuTpiclist-bounces.....spamTakeThisOuTMIT.EDU [TakeThisOuTpiclist-bouncesKILLspamspamspamMIT.EDU]
>Sent: 25 August 2006 15:30
>To: Microcontroller discussion list - Public.
>Subject: Re: [EE] Solar Array Tracking
>
>
>(She also has the extremely rare honour of having her name
>immortalised in rhyming slang, during her life.  That club is
>even more exclusive than,
>say, reigning monarchs, or people who have walked on the Moon!  :-)
>
>
>What is it?? haemorroid?


Correct. Perhaps not such a great honour after all!

Regards

Mike

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2006\08\25@110913 by Tony Smith

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Dang.  I was hoping for paranoid or schizoid.

Cheers (or is that bottoms up?),

Tony

2006\08\25@113154 by Russell McMahon

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> ... I'm not sure why a sine would be the right shape for this, but
> does it account for the fact that the atmoshphere is curved?

It wouldn't :-).
But light fall off is vaguely sine shaped and it was an available and
easy function which gave some sort of half realistic feel for things.
It may even be closer to reality than one has a right to hope. And may
not.

Atmospheric path length is arguably h/cos(X) where X is angle from
vertical and h is atmospheric scale height or some other number that
works :-). So ratio of path length to noon length = 1/cos(X). This is
only truish for a flat earth but adds are it is flat enough at the
angles concerned for this expression to be useful. AFAIR above
atmosphere insolation is about 1.3 kW/m^2 whereas a figure of more
like 1 kW/m^2 is usually used at full sun terrestially. You can get
solar equivalent kWh/day tagbles for all latitudes.

Attenuation can be expected to rise faster than this as large angles
include morning  and evening mists etc. Also at low angles hills and
buildings tend to be impressively opaque :-).



       Russell


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