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re: thermostat for winter
19 feb 2000
diane diberardino wrote:
>actually, 73 is *very* comfortable.......
>
>..... for sitting around in shorts and a tank top :)
sounds fetching :-)
>it's one of my favorite sunbathing temps; you are warm in the sun but
>not too warm that you sweat.
you might be comfy in colder air luxuriating on the bench of your very
own tanning cabana (tm). an ashrae-standard 106 pound naked human with
20 ft^2 of surface and a still air-film conductance of 1.5 btu/h-f-ft^2
(with no regulatory sweating) has a total conductance of 30 btu/h-f-ft^2.
tanned, with 50% reflectance and 10ft^2 exposed to 6 suns, she'd receive
about 0.5x6sunsx10ft^2x250btu/h-ft^2 = 7,500 btu/h (2.2 kw) of sun power,
enjoying 100 f skin until the air temp drops to 100f-7500btu/h/(30btu/h-f)
= - 150 f, ie 150 below...
wrote
> i have a little external pool and i want to heat the water.
> can anybody know how can i buil a solar collector.
> i need plans, instructions or something.
how about a nearby concentrating cabana? something 11' tall and
10' deep and 12' long in the ew (z) direction?
. ---11'
.
. [in courier font]
. y
<-- south .
. ^ z * is a small
*| / automatic winch
. /
<-- x f.....cw ---2' cw is a counterweight
. .
..................................................
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10' 2' 0'
the south side would be open, like the 2' of north wall above the bench.
the north roof would be nielsen's reflective mylar ($0.09/ft^2 in 4' wide
rolls from http://www.snomo.com/mylar.html) greased onto thin 4'x8' sheet
metal (painted on the outside) screwed to 16' kerfed 2x4s on 4' centers
bent into a 6:1 concentrating shape (y^2=4fx), directed at the horizon
and focused at f = 2'.
duane johnson (redrok@redrok.com) and his friends have tested nielsen's
film with laser pointers and found it sufficiently specular (mirrorlike)
for concentration up to 100:1, on a smooth substrate. longer foci increase
heat loss and captured sun, but make the structure taller and shallower
and less useful for people. all this could also be built into an attic
or 3-sided lean-to city park homeless or trail shelter with hot rainwater
for showers...
the bench on the north side would be 2'x2'x12' long, with a water-filled
polyethylene duct liner and an insulating top that's reflective underneath
that automatically raises up on a north hinge to collect sun during the
day, using a photocell and something like an auto windshield wiper motor
or a garage door opener.
say the pool has a movable 8' diameter cover, and all materials
(except the water :-) cost $1/ft^2...
10 tout=30'outdoor temp (f)
20 tpool=72'pool temp (f)
30 dpool=8'pool diameter (feet)
40 hpool=4'pool height (feet)
50 rtop=15'r-value of cover (us)
60 rside=10'r-value of sidewall (us)
70 atop=3.14*dpool^2/4'pool top area (ft^2)
80 wtop=0.5*atop'cover weight (pounds)
90 cost=atop'materials cost ($)
100 aside=3.14*dpool*hpool'pool sidewall area (ft^2)
110 cost=cost+aside'materials cost ($)
120 conpool=atop/rtop+aside/rside'thermal conductance of pool (btu/h-f)
130 epool=24*(tpool-tout)*conpool'daily pool heat requirement (btu)
140 print "daily pool heat (btu):",epool
150 print"cover weight (pounds):",wtop
160 print
170 hstore=2'heat store height (feet)
180 rstore=15'r-value of heat store surfaces (us)
190 tauwind=.81'transmittance of heat store window
200 f=2'focus (feet)
210 x=10'reflector depth (feet)
220 y=sqr(4*f*x)'height of reflector above focus (feet)
230 hmirror=hstore+y'max mirror height above ground (feet)
240 print"max mirror height (feet):",hmirror
250 t=sqr(4*x^2+4*f*x)'mirror length term
260 s=(t+2*f*log((2*x+t)/y))/2'parabola curve length (feet)
270 print"mirror curve length (feet):",s-f
280 l=12'ew reflector length (feet)
290 amirror=(s-f)*l'mirror area (ft^2)
300 print "mirror area (ft^2):",amirror
310 cost=cost+amirror'materials cost ($)
320 ref=.9'reflectance of mirror
330 beamax=729'max beam sun (btu/ft^2-day)
340 ein=beamax*y*l*ref*tauwind'daily beam sun input (btu)
350 print "daily beam sun (btu):",ein
360 astore=2*((hstore+f)*l+hstore*f)'heat storage surface (ft^2)
370 cost=cost+astore'materials cost ($)
380 constore=astore/rstore'heat store conductance (btu/h-f)
390 rwind=1'r-value of heat store window (us)
400 conwind=l*f/rwind'heat store window conductance (btu/h-f)
410 tstore=tout+(ein-epool)/(6*conwind+18*constore)'avg day heatstore temp (f)
420 print
430 print"avg day heatstore temp (f):",tstore
440 tcloud=(tstore+tpool+10)/2'avg cloudy day store temp (f)
450 ecloud=24*(tcloud-tout)*constore+epool'avg cloudy day heat loss (btu)
460 gal=8*l*f*hstore'heat store volume (gal)
470 print"heat store volume (gal):",gal
480 estored=8*gal*(tstore-tpool-10)'useful stored heat (btu)
490 dcloud=estored/ecloud'cloudy storage time (days)
500 print"cloudy storage time (days):",dcloud
510 print
520 print"materials cost ($):",cost
run
daily pool heat (btu): 13504.51
cover weight (pounds): 25.12
max mirror height (feet): 10.94427
mirror curve length (feet): 12.04342
mirror area (ft^2): 144.5211
daily beam sun (btu): 57040.23
avg day heatstore temp (f): 191.9632
heat store volume (gal): 384 [anyone know if nielsen's film
cloudy storage time (days): 10.7904 can be tack-welded to greenhouse
polyethylene with an iron to
materials cost ($): 399.2411 avoid the sheet metal cost?]
notes:
1. sunlight from the horizon is focused at f=2' at dawn, and closer to
the north wall as the sun rises. this should work well at noon on 12/21
in philadelphia (40 n. latitude), when the sun elevation is 90-40-23.5
= 26.5 degrees above the horizon. the bench is completely shaded by the
parabola's upper south edge at (10,8.84) when tan(alpha) = 8.84/(10-2),
ie above a sun elevation alpha = 47.9 degrees here, which happens at noon
on march 27. phila's max sun elevation angle is 90-40+26.5 = 73.5 degrees,
which happens at noon on june 21.
2. this structure needs reflective endwalls to contain morning and
afternoon sun, since it is almost square. more rectangular versions
would not need reflective endwalls. the cabana might be fully enclosed
(at greater expense) and insulated to make it warmer in winter. and
the pool might be inside the enclosure. south glazing would lower
the solar input by about 10%, but the warm air inside might also heat
lower temperature water via a fan-coil unit.
3. nrel's red book ("solar radiation data manual for flat-plate and
concentrating collectors") says an single east-west horizontal axis
tracker can collect at most 2.3 kwh/m^2 of solar heat on an average
january day, ie 729 btu/ft^2. i assume this one-axis trough can do
almost as well in january, over an average 6 hour day, which makes
for a conservative heat loss, since it only takes about 3 hours to
collect 729 btu/ft^2 of beam radiation at 250 btu/ft^2-h.
4. duane and i worked out where the 23 kerfs (sawcuts) go:
10 f=2'focus (feet)
20 w=.125'kerf width (in)
30 d=2.5'kerf depth (in)
40 a=atn(w/d)'kerf angle (radians)
50 yk=.2'initial kerf height (feet)
60 xk=yk^2/8'initial kerf x-coordinate (feet)
70 dk=w/24+sqr(xk^2+yk^2)'kerf distance along beam (feet)
80 ah=a/2'half-angle (radians)
90 for k=1 to 23'number of kerfs
100 xr=int(1000*xk+.5)/1000'round
110 yr=int(1000*yk+.5)/1000'round
120 dr=int(1000*dk+.5)/1000'round
130 drm=int(dk*30.48*100+.5)/100'kerf distance along beam (cm)
140 print 500+k;"'";k,xr,yr,dr,drm
150 xl=xk:yl=yk:dl=dk'last kerf coordinates (feet)
160 theta=ah+k*a'chord angle (radians)
170 b=-4*f*tan(theta)'quadratic term
180 c=4*f*(yl*tan(theta)-xl)'quadratic term
190 yk=(-b+sqr(b^2-4*c))/2'next kerf y-coordinate
200 xk=yk^2/(4*f)'next kerf x-coordinate (feet)
210 dk=dl+w/12+sqr((xk-xl)^2+(yk-yl)^2)'kerf distance along beam (feet)
230 next k
^
run x y feet | centimeters
1 .005 .2 .205 6.26
2 .02 .401 .417 12.71
3 .046 .604 .632 19.26
4 .082 .809 .851 25.95
5 .13 1.02 1.078 32.85
6 .191 1.235 1.312 39.98
7 .266 1.458 1.557 47.46
8 .356 1.688 1.815 55.32
9 .465 1.929 2.09 63.69
10 .595 2.181 2.384 72.65
11 .749 2.448 2.702 82.36
12 .932 2.731 3.05 92.96
13 1.151 3.035 3.434 104.68
14 1.412 3.361 3.863 117.76
15 1.728 3.718 4.349 132.57
16 2.109 4.108 4.905 149.52
17 2.577 4.541 5.553 169.26
18 3.156 5.025 6.318 192.59
19 3.884 5.574 7.241 220.7
20 4.813 6.205 8.374 255.24
21 6.024 6.942 9.802 298.78
22 7.64 7.818 11.651 355.11
23 9.863' 8.883' 14.126' 430.55 cm
nick
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