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re: solar airships
30 sep 1995
anthony kalenak  wrote:

>have you tried to make a physical model of a solar powered airship. 

not yet. altho i've thought about trying to make a higher temperature version,
an indoor floating lamp with a very lightweight bulb inside, perhaps just some
fine tungsten wire, with some fine copper wires for power transmission and
tethering. this might be an interesting toy.

physics professor paul bashus and physics student erik ferragut and i are
now putting together a fully-instrumented 2' x 4' x 8' tall solar closet
and "house", which we will reassemble and install this week next to the
astronomical observatory on top of the science building at the local college,
ursinus. it will have a microprocessor-controlled multichannel i/o electronic
data logger/controller (a lambert engineering "data trap") and a modem, with
five temperature probes and a licor pyroheliometer. (we could use some
low-speed airflow measurement equipment too.) 

the test box will contain three 36 watt fans, which we hope to seldom use.
the system is designed so that it will also operate without any fans. the
data logger will control the fans, and measure the power needed to drive
them, as well as the rest of the power used in the house, including its own,
via a current transformer and watt transducer. 

our goal is to develop and test an inexpensive system that will maintain
the house at exactly 70 f all winter, 24 hours a day, even on -10 f nights
in january, up there on the roof in the wind and the snow, while using
absolutely no backup heat at all this winter. we will put a backup heater 
in the "house," and measure the power required to run it. none, we hope. 
if you'd like to contribute to the expenses for this project, send your
tax-deductable contribution to:

physics equipment gift fund
ursinus college
collegeville, pa 19426

with an email note to me, with your postal address, and i'll send you our paper
"solar closets and sunspaces," with some illustrations and simple mathematics.
paul and i have spent about $3,000 of our own money on this so far.


below is a test box, a 2' x 4' x 8' tall "house" attached to a solar closet.

                2'             r20                      
         ---------------.---------------        30 f
        |               |               |
        |      70 f    vr      tw       |
     2' |               |               |
        |    "house"    |  solar closet |
        |               |               |
         ------vs------- ------vc-------
        |               |               | 9"
        |      ts        ggggggggggggggg
        |           sunspace            | 7"


it is built with 7 2' x 8' insulated modular panels, each made from a 1 x 3
frame with a 2 x 8 sheet of 1/4" plywood attached to the inside face and
a 2 x 8 x 2" piece of styrofoam cut to fit into the 1 x 3 frame, and
another 2" piece of styrofoam screwed to the outside of the frame.
such panels have an r-value of about 20. this would be a poorly-insulated
house, by today's standards. each panel weighs about 20 pounds, and can be
easily lifted by one person.
the sun shines in through the glazing over the air heater, which is
attached to the front of the solar closet, and a plastic film backdraft
damper vc allows solar heated air to enter the closet and heat some 55
gallon drums full of water, when the passive air heater is warmer than
the drums. in our test box, vc will also have a fan to blow air into
the solar closet. we expect to omit this in the final design. 

the glazing is replex ((800) 726-5151) 20 mil flat, clear,
polycarbonate plastic, which comes in rolls 48" wide x 50' long,
and costs about $1.50/ft^2.

vr is a $12 leslie-locke afv-1b automatic foundation vent, available
from home depot, attached to a rectangular hole at the top of the closet,
with its bimetallic spring reversed and adjusted so the louvers are fully
closed when the house is above 60 f. this will allow warm air from the
solar closet to heat the house on a cloudy day. an open slot at the bottom
of the closet serves as the return air path. vc will have a fan, which
will only be used on very cold nights. 

vs is another foundation vent, adjusted so the louvers are fully closed
at 70 f (or lower.) when the house temperature is less than 70 f, vs will
open to allow sunspace air to warm the house. vs has another plastic
backdraft damper in front of it so that air can only flow through vs
from the sunspace into the house, not in the other direction. vs has a
fan in our test box. we expect to omit this in the final design.

steady-state performance

it is interesting to calculate two temperatures above: ts is the average
sunspace temperature when the sun is shining on an average day, and tw is
the steady-state solar closet temperature after a string of average days,
with some sun. the sunspace in this scheme overheats to act as a parasitic
or slave heater, helping the solar closet achieve a higher temperature,
while the losses from the hot glazing on the solar closet make the air
in the sunspace hotter. the sunspace air is used to heat the house on
an average day, with some sun. (this is similar to "khanh's radically
new approach to increasing the useful output of a flat-plate collector
panel..." as described on pages 118-125 of william shurcliff's 1979 book
_new inventions in low-cost solar heating_, published by brick house,
except that not all the "slave heat" is lost to the outside world.)

with these assumptions:

1. the average wintertime outdoor temperature is 30 f;
2. on an average winter day, the sunspace receives 1000 btu/ft^2 of sun
   over 6 hours;
3. the average house temperature is 70 f, with no air infiltration or
   internal heat generation;
4. the water and air in the solar closet and the passive air heater all
   have the same temperature (approaching this requires careful design);
5. each layer of glazing has an r-value and solar transmittance of 1,

on an average winter day, the 8' x 8' sunspace would receive

(1) eins =  4' x 8' x 1000 btu/ft^2 = 32k btu,

and this would be lost to the outside world through the sides and roof of
the structure as

(2) eouts =  6 hours (ts - 30) 32 ft^2/r1     sunspace, daytime
          + 18 hours (70 - 30) 16 ft^2/r20    west sunspace, nightime
          + 18 hours (tw - 30) 16 ft^2/r20    east sunspace, nightime
          + 24 hours (tw - 30) 36 ft^2/r20    solar closet, daily 
          + 24 hours (70 - 30) 36 ft^2/r20    house, daily 

	  = 192 ts             - 5760
	  +                       576
	  +          14.4 tw   -  432
	  +          43.2 tw   - 1296
	  +                    + 1728
          = 192 ts + 57.6 tw   - 5184.

on an average winter day, the solar closet would receive

(3) einc = 2' x 8' x 1000 btu/ft^2 = 16k btu,

and this would be lost through the outside world and the rest of the
house as approximately

(4) eoutc =  6 hours (tw - ts) 16 ft^2/r1     to the sunspace, daytime
          + 18 hours (tw - 30) 16 ft^2/r20    to the sunspace, nightime
          + 24 hours (tw - 30) 36 ft^2/r20    to the outside, daily
          + 24 hours (tw - 70) 16 ft^2/r20    to the house, daily.

	  = -96 ts  +  96   tw
	  +            14.4 tw    -  432
	  +            43.2 tw    - 1296
	  +            19.2 tw    -  576
          = -96 ts  + 172.8 tw    - 2304.

setting (1) = (2) and (3) = (4), and adding (4) to (2) twice,

64k = 403.2 tw - 9,792, so tw = (64k + 9,792)/403.2 = 183 degrees f.

substituting tw back into (1), 32k = 192 ts + 5,358, so ts = 138.8 f.

so after a string of average days with some sun, the closet will be about
40 degrees warmer than the peak daytime sunspace temperature, but it will
stay at that temperature 24 hours a day, "just coasting," vs. the low-
thermal mass sunspace, which will get icy cold every night. 

cloudy-day performance

on the first of several days with no sun, the structure will lose about 

(2) ens = 24 hours (70  - 30) 16 ft^2/r20     west sunspace
        + 24 hours (183 - 30) 16 ft^2/r20     east sunspace
        + 24 hours (183 - 30) 36 ft^2/r20     solar closet
        + 24 hours (70  - 30) 36 ft^2/r20     house
        = 12,043 btu.

if a 2' x 4' x 8' solar closet contains 2 55 gallon drums full of water,
along with some cement blocks and plastic soda bottles, it might have a
thermal mass of 1120 btu/f (see below) so on the first day with no sun,
the water temperature would decrease by about ens/c = 10.8 degrees f. if
the closet lost heat at this rate every day until it reached a minimum 
usable temperature of say, 80 f, (as the closet cools down, it actually
loses heat more slowly), it could provide useful heat for the "house"
for at least (183-80)/10.8 = 9.5 days in a row with no sun. taking account
of the fact that the closet cools more slowly as time goes on, it should
provide heat for about 14 days without sun: 

10 '2' x 4' x 8' solar closet house carryover
20 '        find steady-state closet temp
30 eins=32000!'sunspace solar gain (btu/day)
40 einc=16000'closet solar gain (btu/day)
50 cws=18*16/20+24*36/20'sunspace tw factor
60 cwc=6*16/1+18*16/20+24*36/20+24*16/20'closet tw factor
70 cs=6*30*32/1+18*30*16/20+24*30*36/20'sunspace constant
80 cs=cs-18*(70-30)*16/20-24*(70-30)*36/20'more sunspace constant
90 cc=18*30*16/20+24*30*36/20+24*70*16/20'closet constant
100 tw=(eins+2*einc+cs+2*cc)/(cws+2*cwc)'initial solar closet temperature
140 c=2*55*8+51*4.2+13*2.1'thermal mass of solar closet (btu/f)
150 closs=24*(70-30)*16/20'constant daily west sunspace heat loss (btu)
160 closs=closs+24*(70-30)*36/20'constant daily house heat loss (btu)
163 print"1000'          temp at"
165 print"1020' day      end of day"
170 for d=1 to 14 step 1'calc closet temp for 30 days without sun
180 tloss=24*(tw-30)*(16+36)/20'solar closet daily heat loss
190 heatloss = closs+tloss
200 tw=tw-heatloss/c'new solar closet temperature
210 print 1020+d;"'";d,int(tw+.5)
220 next d

thermal mass: 1122 btu/f

initial water temp: 187 f

      temp at
day   end of day

 1      176
 2      166
 3      156
 4      147
 5      138
 6      130
 7      122
 8      115
 9      108
 10     101
 11     95
 12     89
 13     84
 14     78

trying this out should be interesting :-)


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