Subject: Solar airships

From: [email-masked] (Nick Pine)
Date: 29 Sep 1995 05:06:37 -0400

Enough of this PV talk. Let's talk about a more practical form of solar
energy--solar heated balloons. A net.friend says:

>I'm also into airships, the kind that haven't been built since the   
>thirties. I'm fascinated by them. It's unfortunate that the lack of   
>readily available helium gas and the onset of a stupid war effectively  
>killed the age of the airship. My plan is this. Built an airship using   
>modern aluminium and fabrics. I'm thinking of a big ship, in the order of   
>four or five times the size of the Hinderburg.

Purdy big... Have you read John McPhee's book about modern airships?
It originally appeared in the New Yorker magazine, under the title
"The Deltoid Pumpkin Seed." He suggests building large thick delta-wing-
shaped airships. One might power an airship by somehow making it rise
and fall through the air, and turning the vertical motion into horizontal
motion by controlling the orientation: if it is falling and we tilt the
back end so it is above the forward end, it should move forward, no?
If it is rising, the forward end should be higher...

Bucky talked about large floating structures supported by solar hot air.

>The airship is black and the inside of the envelope is lined with highly
>reflective material. The idea is that any sunlight falling on the airship
>will heat up the envelope.

Sounds good so far. What's the reflective material for?

>Because of the foil or what ever you've got inside the envelope   
>gains heat slowly, providing the airship with increasingly more lifting   
>power. The longer you remain airborne the better the efficiency of the   
>system.

I would just make a transparent envelope outside a black one.

Or an envelope that is transparent on one half and black on the other,
if we can keep the transparent side aimed at the sun.

Or an envelope that has one transparent side and one aluminized mylar side,
with a small, high-thermal-mass (eg black water balloon) target in the center,
surrounded by a small insulating transparent envelope, with the outside
balloon oriented so that the sun passes through the transparent side and
gets reflected and concentrated by the shiny side onto the black target. 

>Excess helium can be tapped off and recompressed...

Helium? How about just solar heated air? This would work better with a
large airship. The volume, ie lifting force, increases with the cube of
the dimension, while the weight of the structure increases with the square,
as does the solar collecting area. If our airship material weighs, say,
1 pound/200 ft^2 (eg heat sealable Tedlar PVF film), and it has an R-value
of 1 ft^2-F/Btu, and it receives 1000 Btu/ft^2/day, and the outside temp
is, say, 62 F, what is the minimum size it has to be to hold itself up,
day and night? Air at 5000' and 62 F weighs 0.0625 lbs/ft^2...

In full sun, a r' radius sphere, say, for starters, containing some sort
of internal solar absorbing black cloud, surrounded by a transparent skin, 
would have a solar collecting area of pi r^2, and four times that area for
heat loss purposes, so if it absorbs 1000 pi r^2 Btu over 24 hours, and
it has an internal temperature Ts, in 62 F surrounding air, it will lose
24 hours x (Ts-62) x 4 pi r^2/R1 Btu in a day. So if the solar energy that
flows into the sphere during a day equals the heat energy that flows out
of the sphere during a day, the internal air temperature of the sphere
would be such that 

1000 x pi r^2 = 24 (Ts-62) 4 pi r^2, or equivalently

1000 = 24 (Ts-62) x 4, or Ts = 62 + 1000/96 = 62 + 10.4 = 72.4 F.

How much would this air weigh? As I recall,

Rho(83) = Rho(62) x (459+62)/(459+72) = 0.0625 x 521/531 = 0.0613 lbs/ft^3.

So the net lifting force is 0.0625 - 0.0613 = 0.0012 lb/ft^3.

The balloon would weigh 4 pi r^2/200 lbs, and it would have a volume
of 4/3 pi r^3, so it should be self-supporting when 

4 pi r^2/200 = 4/3 pi r^3 x 0.0012, or

r = 3/(200 x 0.0012) = 12'.

Hmmm. A 24' diameter balloon. Not very big... :-)

BTW, Charlie Overton's 1980 US Patent No. 4,237,868 "Solar Heating Balloon"
describes a tethered balloon being used as a solar thermal collector,
filled with a gas, lighter than air, with a pair of fluid conduits to
conduct a working fluid from the balloon to the ground and back...
As a working fluid, he suggests water containing a black dye or finely
divided carbon black, atomized into a very fine mist exposed to the sun.

>The airship is essentially a leisure vehicle, like a large yacht. It takes 3
>days to cross the Atlantic in a Hinderburg class ship with two 1938 vintage 
>diesels. Modern engines with modern propellors could easily do as well.

If we stored the heat in the thermal mass center, we could make the balloon
slowly rise and fall by opening and closing a vent in the transparent envelope
covering the center, perhaps with a fan, or we might vent some steam from the
thermal mass center to lighten the balloon and heat up the internal air, which
would make the balloon rise as the steam pushed it along. Then the vent to
the thermal mass would be closed and the balloon would fall as the inside air
lost heat through the skin. How long it would take to cross the Atlantic that
way? Not so fast as the Concorde, but consuming far less than the Concorde's
one TON of jet fuel per passenger crossing. 
 
>I can picture this in mind right now. An enormous graceful black airship   
>sailing across the New York or Paris landscapes. All it needs is some   
>modern technology.

Yup :-)

Nick

---

From: [email-masked] (Nick Pine)
Date: 30 Sep 1995 08:55:11 -0400

Anthony Kalenak <[email-masked]> 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, with some fine
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 4' 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. 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.

Nick

Below is a test box, a 4' x 4' "house" attached to a solar closet.

                        8'
                               R14                      
         ---------------.---------------        30 F
        |               |               |
        |               |               |
        |      70 F    Vr      Tw       |
    4'  |               |               |
        |    "house"    |  solar closet |
        |               |               |
         ------Vs------- ------Vc-------
        |               |               | 9"
        |      Ts        ggggggggggggggg
        |           sunspace            | 7"
         ggggggggggggggggggggggggggggggg 

                     south

It could be built of 8 4' x 8' modular panels, each made from a 1 x 3
frame with a 4 x 8 sheet of Thermo-Ply attached to the inside face and
a 4 x 8 x 2" piece of Styrofoam cut to fit into the 1 x 3 frame.
Thermo-Ply is a 1/8" thick structural hardboard sheathing with one foil
and one white face, that costs about 20 cents a square foot. It is made
by Simplex Corp at PO Box 10, Adrien, Michigan 49221 (517) 263-8881.
Such panels would have an R-value of 14. This would be a poorly-insulated
house, by today's standards. Each panel weighs 31 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 could be 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);
   and 
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 =  8' x 8' x 1000 Btu/ft^2 = 64K 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) 64 ft^2/R1     Sunspace, daytime
          + 18 hours (70 - 30) 32 ft^2/R14    West sunspace, nightime
          + 18 hours (Tw - 30) 32 ft^2/R14    East sunspace, nightime
          + 24 hours (Tw - 30) 80 ft^2/R14    Solar closet, daily 
          + 24 hours (70 - 30) 80 ft^2/R14    House, daily 
          --------------------------------
          = 384 Ts + 178 Tw - 9736.

On an average winter day, the solar closet would receive

(3) Einc = 4' x 8' x 1000 Btu/ft^2 = 32K Btu,

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

(4) Eoutc =  6 hours (Tw - Ts) 32 ft^2/R1     To the sunspace, daytime
          + 18 hours (Tw - 30) 32 ft^2/R14    To the sunspace, nightime
          + 24 hours (Tw - 30) 80 ft^2/R14    To the outside, daily
          + 24 hours (Tw - 70) 32 ft^2/R14    To the house, daily.
          --------------------------------
          = -192 Ts + 425 Tw - 9188.

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

128K = 1,028 Tw - 28,112, so Tw = (128K + 28,112)/1,028 = 151.8 degrees F.

Substituting Tw back into (1), 64K = 384 Ts + 17,295, so Ts = 121.6 F.

So after a string of average days with some sun, the closet will be about
30 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) 32 ft^2/R14     West sunspace
        + 24 hours (152 - 30) 32 ft^2/R14     East sunspace
        + 24 hours (152 - 30) 80 ft^2/R14     Solar closet
        + 24 hours (70  - 30) 80 ft^2/R14     House
        ---------------------------------
        = 31,103 Btu.

If a 4' x 4' x 8' solar closet contains 8 55 gallon drums full of water,
along with some cement blocks and plastic soda bottles, it might have a
thermal mass of 4647 Btu/F (see below) so on the first day with no sun,
the water temperature would decrease by about Ens/C = 6.5 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 (152-80)/6.5 = 11 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. Adding an extra layer of
2" Styrofoam to make all sides of the closet to make it an R24 box,
should extend the time it takes to cool to 80 F, while keeping the
"house" warm, to about 26 days:

10 '4' x 8' solar closet carryover
20 '        find steady-state closet temp
30 EINS=64000!'sunspace solar gain (Btu/day)
40 EINC=32000'closet solar gain (Btu/day)
50 CWS=18*32/24+24*80/24'sunspace Tw factor
60 CWC=6*32/1+18*32/24+24*80/24+24*32/24'closet Tw factor
70 CS=6*30*64/1+18*30*32/24+24*30*80/24'sunspace constant
80 CS=CS-18*(70-30)*32/14-24*(70-30)*80/14'more sunspace constant
90 CC=18*30*32/24+24*30*80/24+24*70*32/24'closet constant
100 TW=(EINS+2*EINC+CS+2*CC)/(CWS+2*CWC)'initial solar closet temperature
140 C=4647'thermal mass of solar closet (Btu/F)
150 CLOSS=24*(70-30)*32/14'constant daily west sunspace heat loss (Btu)
160 CLOSS=CLOSS+24*(70-30)*80/14'constant daily house heat loss (Btu)
163 PRINT "         Temp at"
165 PRINT "Day      end of day"
170 FOR D=2 TO 30 STEP 2'calc closet temp for 30 days without sun
180 TLOSS=24*(TW-30)*(32+80)/24'solar closet daily heat loss
190 HEATLOSS = CLOSS+TLOSS
200 TW=TW-2*HEATLOSS/C'new solar closet temperature
210 PRINT D,INT(TW+.5)
220 NEXT D

RUN

        Temp (F) at
Day     end of day

 2      181
 4      171
 6      161
 8      151
 10     142
 12     133
 14     125
 16     117
 18     109
 20     102
 22     96
 24     89
 26     83
 28     77
 30     72

Trying this out should be interesting :-)

Nick