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re: composite solar system question
25 apr 2001
anthony matonak wrote:
>> we might trickle some water over the faces of 3-sun panels with mirrors.
>> put a gutter below with a sump and a float valve to keep it full and a
>> bilge pump like attwood's v625 (650 gph, 12v 1a, $19.99 from boatus...)
>and instantly void the warranty on most panels.
my understanding is that this would have little effect on their lifetime...
>how much do mirrors that will last as long as the panels cost?
$1 for 1 ft^2 glass mirrors or 10 cents for mylar which might need
replacing every 5 years. duane glues it to plywood with a thin layer
of axle grease to make this easy. i've greased it to 24' wide 4-year
5 cents/ft^2 greenhouse poly film, for stretching over parabolically-
bent 2x4 bows.
>i'm assuming some kind of front surface polished aluminum with some
>kind of poly film over it to seal it from the weather as glass might
>be too heavy for this.
glass might weigh less than pv panels...
>then you'll need a tracker of some kind which is only going to hold 1/3
>of the panels it would normally be rated for since the other space will
>go to mirrors.
nrel's pv panel test tracker makes 3 suns with 4 flat outboard mirrors...
>since a tracker is going to be constantly pointing the panels in a
>different direction this is going to pose a challenge as to how to
>trickle water over the face of the panels in such a way as to
>guarantee 100% coverage.
a garden hose might connect to a sprinkler pipe mounted over the panels.
>you may also need to make sure the water you are using is fairly mineral
>free as hard water could leave mineral residue on the glass over time.
we might clean them every few weeks. a little crud or a plastic scrim
might be helpful in making the water sheet vs trickle.
>> phila is 76.7 f in july on average, with a humidity ratio w = 0.0133, ie
>> a vapor pressure pa = 0.65 "hg... 140 f water is roughly... 6.2 "hg.
>> ashrae says a square foot loses about 100(pw-pa) = 555 btu/h... so we
>> need 457/1000 = 0.457 pounds per hour per square foot, ie it looks like
>> that $20 12w pump can cool 650x8/0.457 = 11,379 ft^2 (1057 m^2) of 3-sun
>> panels, producing an additional 254 kw of electrical output at $0.00008
>> per peak watt...
those extra peak watts could be $4/$0.00008 = 50,000 times cheaper :-)
>as i understand it you are suggesting essentially a swamp cooler for the
>panels with the panels themselves acting as the evaporator. wouldn't the
>relative humidity change the performance of this kind of evaporator?
sure. i used averages for phila in july. you might use other numbers.
>...would there be ordinary conditions which would cause overheating?
>say 100% relative humidity on a hot august day with 100 f air temp,
i wouldn't want to live in a place like that. maybe the tracker should
turn the panels out of the sun if they overheat for any reason. a fixed
concentrator might have a roll of shadecloth at the top of the panels,
with a solenoid to release it if they overheat...
>so then, let's look at the costs again. that $20 12w bilge pump is only
>rated at 650 gph at zero head. at 3.3 feet it's rated at 425 gph...
so it could only cool 425/650x11379 = 7440 ft^2 of panels? :-)
>ok then, the other parts, a $1200 tracker has some 120 sq feet for stuff.
and maybe more outboard stuff.
>let's call the mirrors $1 a sq foot lacking better information. since we're
>talking three suns concentration only a third of a 120 sq foot tracker will
>have pv (40 sq feet) while the other two thirds have mirrors (80 sq feet).
>a typical pv panel would run about 12 or so watts per sq foot at one sun
>and they cost at best some $4 a watt for $48 per sq foot and $1920 for this
>tracker...
gee, the tracker got more expensive. rich komp describes a winston
concentrator on page 60 of his 1995 book, practical photovoltaics:
its great advantage for smaller concentration ratios is that it does
not have to track the sun daily... table 3.1 gives the acceptance angle
and frequency of adjustment for different concentration ratios... the
axis of the trough collector is horizontal and pointing east and west.
table 3.1 acceptance angle and adjustments needed per year for
different concentration ratios for a winston concentrator
acceptance number of shortest period
concentration angle theta adjustments between adjustments
ratio c (degrees) per year (days)
2 30 0 --
3 20 2 180
4 14.5 4 35...
theta = sin^-1(1/c) is really a half-angle. if the 3:1 version were
tilted at 40 degrees, it would accept sun at elevations from 20 to 60
degrees. the optics need not be precise. rich continues (on page 172):
the gentle parabolic curve in the metal can be approximated by bending
the sheet [of aluminum] around a round object. (we use a piece of 3-inch
plastic sewer pipe...) the wings can be fastened to the module backing
with sheet metal screws. (be careful not to drill through a solar cell.)
then make the final adjustments to the wing shape and angle. prop up
the module so you can look into it from about 15 feet away. you will
see a distorted reflection of the solar cells in each wing if you look
at the module from straight-on axis. bend and adjust the reflectors
until the blue solar cell images seem to fill the reflectors... by
moving your head to one side, you can get an idea of how much off-axis
sun angle the reflector system will accept.
if two or more modules are installed side by side, they can be mounted
so the top edges of the reflectors just touch. the reflectors can then
be fastened together, producing a very rigid support.
a standalone system sized for winter might use a simpler concentrator,
eg an 8' deep x 8' tall parabolic "solar shed" made from 12' 2x4s on 4'
centers. a 2' focal length could bounce about 3 suns down into a 2' trough
on the ground inside the reflective north wall/roof, with the pv panels
underwater, and a float valve (vs a pump) to keep the trough full. each
square foot of pvs might produce about 80 wh/day in december in phila.
with a pump, we might cover the trough with plastic film and use the
hot water for showers...
nick
10 xmax=8.15'parabola depth (feet)
20 ymax=sqr(8*xmax)'parabola height (feet)
30 n=11'number of line segments
40 w=1/4'kerf width (in)
50 f=ymax^2/(4*xmax)'focal length (feet)
60 ap=2*atn(1)-atn(2*f/ymax)'final slope (radians)
70 al=ap/n'lower kerf angle (radians)
80 au=ap/(n-1)'upper kerf angle (radians)
90 a=(al+au)/2'average kerf angle (radians)
100 xl=0:yl=0
110 ah=a/2
120 for k=0 to n-1
130 d=4*f*tan(ah+k*a)'quadratic term
140 yk=(d+sqr(d^2-4*yl*(d-yl)))/2'next kerf height (feet)
150 yl=yk'last kerf height (feet)
160 next k
170 if abs(yk-ymax)/ymax<.001 goto 200'iterate to 0.1%
180 if yk>ymax then au=a else al=a
190 goto 90
200 dl=0:yl=0
205 surd = sqr(4*xmax^2+ymax^2)
206 l=(surd+ymax^2/(2*xmax)*log((2*xmax+surd)/ymax))/2
210 print 500;"'";"kerf depth (in):";w/2/tan(ah);tab(37);"curve length (ft):";l
215 print
220 for k=0 to n-2'number of kerfs
230 d=4*f*tan(ah+k*a)'quadratic term
240 yk=(d+sqr(d^2-4*yl*(d-yl)))/2'next kerf height (feet)
250 xk=yk^2/(4*f)'next kerf x-coordinate (feet)
260 dk=dl+w/12+sqr((xk-xl)^2+(yk-yl)^2)'kerf distance along beam (feet)
270 xr$=left$(str$(int(1000*xk+.5)/1000),4)'round
280 yr$=left$(str$(int(1000*yk+.5)/1000),4)'round
290 dr=int(1000*dk+.5)/1000'round
300 drm=int(dk*30.48*1000+.5)/1000'kerf distance along beam (cm)
310 print 520+k;"'";k,xr$,yr$,dr,drm
320 xl=xk:yl=yk:dl=dk'last kerf coordinates (feet)
330 next k
kerf depth (in): 2.461909 curve length (ft): 11.99909
0 .02 .40 .428 13.032
1 .08 .82 .868 26.452
2 .19 1.2 1.335 40.697
3 .36 1.7 1.847 56.304
4 .61 2.2 2.428 73.996
5 .96 2.7 3.111 94.82
6 1.4 3.4 3.95 120.398
7 2.1 4.1 5.033 153.402
8 3.3 5.1 6.515 198.576
9 5.0 6.3 8.698 265.101
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