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a passive solar mini-tutorial
22 dec 1998
why bother?
in 1980, tom smith said:
after working on, literally, hundreds of passive designs... i am
convinced that energy efficiency will become considerably less exotic
in the future. it is my belief that if we just study closely what
is going on inside a house, we'll come up with some very simple, if
prosaic, solutions. if you have ever spent any time living in other
parts of the world you'd realize that a lot of our energy problems
stem from just plain doing it wrong. it's a snap to save energy in
this country. as soon as more people become involved in the basic
math of heat transfer and get a gut-level, as well as intellectual,
grasp on how a house works, solution after solution will appear.
why solar heating, vs photovoltaics?
because a typical us house needs several times more heat than electrical
energy, and that ratio is increasing with compact fluorescents and more
efficient appliances, and the us price per kwh of electrical energy is
falling under deregulation, and we don't have kwh wars in the middle east,
and solar house heating can be 100 times less expensive than pvs in dollars
per kwh per year, and sunspaces can have more than one use, which changes
their economics. (you can't read a newspaper inside a pv panel on a sunny
winter morning :-)
a rambling introduction
a sense of proportion is useful for solar house heating, especially for
houses that are close to 100% solar-heated (some people define "a solar
house" as "one with no other form of heat" and a very low electric bill,
which eliminates hand waving about "solar fractions" which might be only
20% or less. some "solar houses" are put up with solar glazing on the
shaded side :-) better ones have no backup systems, or inexpensive backup
systems with expensive fuel that is very rarely used, for instance 5 kw
electric air or water heaters...
i got some email from the relatives of a gentle older woman in lhasa, tibet
(a very cold place) who wanted to solar heat a future house. she was the
curator of a sacred public park near the city that did not allow any form
of fires, for some reason. she lived in an unheated house in the park and
had never lived in a house with any form of heat, and she was excited
about doing that :-)
she had finally gotten government permission to build a house in a certain
style that closely matched the exterior of the existing ancient buildings.
after a few weeks, with some language difficulties and faxes and so on,
it developed that she expected to heat her new house with something like
a single 4'x4' window. but that would not have been practical, because
the window size was inadequate, in unworkable proportion, like a child's
drawing of a cow with pencil-thin legs, or a 747 powered by a model
airplane motor.
passive solar heating concepts are fine, as far as they go, but we also
need "sanity checks," some numbers early in the design process, and some
proportional rules of thumb, like "make the south glass area about 25% of
the floor area," although those can be very misleading if misapplied.
for example, people often say that a direct gain house should not have more
than a certain ratio of glass/mass, because "the house will overheat," but
a simple cure for winter overheating is to open some windows on a sunny day.
that "wastes" solar energy, but solar energy is free. the real performance
problem is that direct gain houses lose lots of heat from their 24-hour
living spaces to the outdoors at night and on cloudy days, so above a
certain proportion, the glass loses more heat on cloudy days than it gains
on sunny days. on the other hand, not enough glass means not enough gain
on a sunny day. one might call this "the direct gain designer's dilemma."
one escape is to add an insulated wall between the living space and a
low-thermal-mass sunspace (low-thermal-mass so the sunspace quickly gets
close to the outdoor temperature at night, or on a cloudy day, and loses
and loses little heat through the sunspace glazing in unsunny times),
and use more sunspace glazing to raise the house heating fraction. the
more sunspace glazing the better, with no upper limit. no performance
is lost by adding that kind of glazing.
and it can be quite inexpensive. bayer's new clear dureflex urethane
greenhouse film costs about 35 cents per square foot, with a 10-year
guarantee. it comes in 100' (folded) rolls up to 30' wide, 100 times
less than a $35/ft^2 window, with less shading and a lot less framing.
see appendix b for further thoughts on sunspace construction.
cookbook approaches to solar house design (like "f-charts") may work well
for a few simple low-performance solar house configurations, but the design
options seem limited, and these approaches do not seem to give much insight
as to how to change a design to improve its performance.
a good simulation can do that by letting one change lots of parameters
and observe lots of aspects of the performance. but that may be expensive,
or require lots of overhead time for learning and leave some mysteries
about how the system interprets inputs or figures results, and it may be
tedious to use.
these canned approaches seem inadequate for high-performance houses that
store heat for multiple cloudy days in a row while they keep their room
temperatures constant. if a cookbook solar house design technique estimates
that your solar house will need an average of 1,000 gallons of oil per year
for heat in your location (only $500 or so, today :-), what do you change
to improve that? maybe you find out by trial and error, changing a few
things within limited options, with little physical insight as to what to
change or even in what direction, or insight as to the interactions between
changes. flying blind, as it were...
compare this to a simple math model prepared by someone who has taken the
time to learn some basic solar house heating physics and arithmetic. (this
took about 1 hour for one remarkable 11 year old girl whom i met at a tri-
state science fair, after i noticed that she was reading a college physics
book :-) one can use a few simple equations to estimate real temperatures
at various places in a house, change insulation values in various places,
and so on.
maybe some cookbook technique or computer package can be tortured into
being useful for a solar heating system for which it was not intended,
but that seems like asking a good cook to make cookies with one or more
prepackaged brownie mixes, vs some less expensive simple ingredients
and a predictable brownie recipe.
this new mini-tutorial ("the socratic method of solar house design" :-)
may help people acquire a more numerical sense of proportion about hybrid
solar house design, ie the design of houses that heat themselves almost
entirely with the sun, with large "solar fractions" and very little backup
fuel, and a large coefficient of performance (cop), the ratio of useful
solar heat power collected to electrical power required to run the system.
some solar houses with fans and no other form of heat have cops of 50:1.
an "active" solar house using some $50 honeywell damper motors consuming
2 watts when (rarely) moving and 0 watts when stopped might have a cop of
10,000, like a 34,000 btu per hour air conditioner or heat pump that uses
1 watt of electrical power, 3,000 times more efficient than a typical air
conditioner with a cop of 3.
(to operate a typical heat pump, we burn 3 btu of coal at a power plant
and send 2 btu of heat (and some water) up the cooling tower, in order to
deliver 1 btu of electrical energy to a house, which is consumed by the
heat pump to make 3 btu of heat. why not just burn the coal in the home
to make 3 btu of useful heat, or 2 btu of heat and 1 btu of electricity?)
someone technically trained might do the following tutorial very quickly.
i'm looking forward to meeting more gifted young people on may 2-8, 1999
while helping judge the 50th international science and engineering fair
in philadelphia.
this one is sponsored by intel, like last year's in fort worth, tx, where
1,122 participants from 35 countries competed for over 2 million dollars
in scholarships and awards. this year, about 1,500 "pre-college science
researchers" and their teachers and advisors and almost as many judges are
coming from nearly every state in the us and 50 foreign countries. some
competitive categories are physiological psychology, gerontological
physiology, molecular biology of diseases, nuclear and particle physics,
and mechanical, thermodynamic and solar engineering :-)
20 questions
this (frankly biased) tutorial begins with some problems based on
"ohm's law for heatflow" which any competent solar designer should be
able to solve in less than a half-hour (although they are beyond most
architects.) why not try to solve them before looking at the answers
at the end?
1. how many btu/hour of heat (p) flows through an 8'x8' r16 wall when
it's 70 f indoors and 30 f outdoors? (hint: p = (ti-to)a/r-value.)
2. what's p for an 8' r20 cube?
3. what's the temperature t inside that cube in the shade on a 30 f day?
4. how does using shadecloth improve sunspace collection efficiency?
5. if shadecloth blocks 80% of the incoming sun, and a house wall can
absorb 30% (it reflects 70%), what percent does the combination absorb?
6. does green absorb more sun than black?
7. if a house wall absorbs 30% of the sun, and green/black shadecloths
block 50/47%, what percentage of sun does the combination absorb?
8. what's p if t = 70 f, and we make the 8x8' south wall r2 glass?
9. if a) the cube contains lots of (ie, "infinite") thermal mass, so t
changes very slowly over a week or so, and b) the window wall transmits
80% of 1,000 btu/ft^2 of sun that falls on it on an average december day
in phila, when the average outdoor temp is about 30 f, and c) over 24
hours, the solar energy that flows into the cube equals the heat energy
that flows out, what will the long-term interior temperature t be?
10. how does t change if a) we make the glass wall a shallow sunspace that
contains very little thermal mass, so it can heat up and cool down quickly,
in, say 5 minutes, when the sun comes out or disappears behind a cloud, and
b) that sunspace is warm (t) for 6 hours every day and cold (30 f) for 18
hours per day, and c) we add another r20 insulated wall between the living
space and the sunspace, and allow warm air to circulate between the living
space and the sunspace when the sun is shining (the air might circulate by
natural convection, with a couple of small holes at the top and bottom of
that r20 wall, equipped with one-way plastic film dampers to prevent
"reverse thermosyphoning" at night.)
11. how much air circulates between the house and the sunspace above,
if the holes are 2'x4' windows 12' apart, the sunspace is 90 f and
the house is 70 f (large hint: cfm = 16.6 av sqrt(hdt)).
12. how much heat does that airflow carry from the sunspace to the house?
(hint: 1 btu can heat about 60 cubic feet of air 1 degree f.)
those are basically static situations, "dc problems," in which the amount
of thermal mass is not numerically important, beyond "large" or "small."
in other situations, the amount of thermal mass matters:
13. how many btu (q) does it take to heat 8 oz. of water from 62 to 212 f
in order to make a cup of tea?
14. if the cube in question (9) contains 6 55 gallon containers of water
at t = 75 f, initially, how much heat (q) flows out of it during 12 hours
with no sun?
15. what's t for cube(9) after 12 hours with no sun? (hint: c pounds of
water cooling d degrees f provides cd btu of heat.)
16. how much heat flows out of cube(9) during the next 12 cloudy hours?
17. what's t for cube(9) after 24 hours with no sun?
18. if cube(10) contains 6 55 gallon containers of water at t = 75 f,
initially, how much heat (q) flows out of it during 12 hours with no sun?
19. what's t for cube(10) after 12 hours with no sun?
20. what's t for cube(10) after 24 cloudy hours?
spoiler!!! answers to questions follow...
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some possible answers :-)
1. how many btu/hour of heat (p) flows through an 8'x8' r16 wall when
it's 70 f indoors and 30 f outdoors? (hint: p = (ti-to)a/r-value.)
p = (70f-30f)8x8ft^2/r16 = 160 btu/hour. a/r-value is a "thermal
conductance," like an electrical conductance in mhos, ie 1/resistance.
individual conductances can be added up (like resistors in parallel)
to find the combined thermal conductance of a wall with some windows
or an entire house. an r-value/a is a "thermal resistance," analogous
to electrical resistance in ohms.
outside the us, p is a metric heatflow in watts, with temperatures in
degrees c, a in square meters and a metric r-value in degrees c-m^2/w.
2. what's p for an 8' r20 cube?
this cube has 6 faces, and each passes (70f-30f)8x8ft^2/r20 = 128 btu/h,
so p = 6x128 = 768 btu/h or 225 watts. alternatively, find the cube's
total thermal conductance, which i call u or "sar," ("sum of ai/r-valuei")
by adding up the thermal conductances of each face (as with resistors in
parallel), then use p = deltatxsar, where deltat (f) = tinside-toutside.
3. what's the temperature t inside that cube in the shade on a 30 f day?
a trick question :-) t = 30 f, if the cube has no other form of heat.
4. how does using shadecloth improve sunspace collection efficiency?
if can keep house return vs solar-heated air near the cool glazing,
increase solar absorptance, increase the absorbing surface area, which
lowers thermal loss to the outdoors, and decrease undesirable reradiation.
5. if shadecloth blocks 80% of the incoming sun, and a house wall can
absorb 30% (it reflects 70%), what percent does the combination absorb?
it seems this way to me: taking as "100%" the sun that the glazing transmits,
the shadecloth blocks 80%, and transmits 20% on to the north. the house wall
absorbs 30% of that and reflects 70% of that, ie 14% of the original, which
is again 80% blocked by the back side of the shadecloth, which transmits
about 3% back towards the glazing. so the shadecloth and wall together absorb
97% of the sun.
painting the wall darker would raise that percentage, but not much. if the
wall were a mirror the shadecloth would still absorb 96%, ie 1-(1-0.8)^2.
this means a house wall need not be darkened when adding a sunspace.
6. does green absorb more sun than black?
some people say yes, because trees are so clever, but trees have other
goals in life than staying warm. ases passive solar pioneer norman
saunders, pe, says that we prefer to look at dark green vs flat black
solar collectors because our eyes are most sensitive to green, so a dark
green wall can absorb lots of sun and still look fairly bright and
aesthetically pleasing to our eyes.
7. if green and black shadecloths block 50 and 47% of the sun, and a
house wall can absorb 30%, what percent does the combination absorb?
about 95%. here's a picture with transmittances:
glazing green black house wall
100% 50% 53% 70%
| | | |
|--------100%-->-------50%-->-------27%-->|
| | | |
| | | |
|<--5%---------<--10%-------<--19%--------|
| | | |
8. what's p if t = 70 f, and we make the 8x8' south wall r2 glass?
deltat = 40 f, and sar = 5x64ft^2/r20 + 64ft^2/r2 = 48 btu/h-f, so
p = 40x48 = 1,920 btu/h, 2.5 times more than with an r20 south wall.
9. if a) the cube contains lots of (ie, "infinite") thermal mass, so t
changes very slowly over a week or so, and b) the window wall transmits
80% of 1,000 btu/ft^2 of sun that falls on it on an average december day
in phila, when the average outdoor temp is about 30 f, and c) over 24
hours, the solar energy that flows into the cube equals the heat energy
that flows out, what will the long-term interior temperature t be?
over 24 hours, 64ft^2x0.8x1000btu/ft^2 = 51.2k btu of solar energy flows
into the cube, which equals 24h(t-30f)48btu/h-f, so t = 30+51.2k/(24x48)
= 74.4 f, after a long string of average days.
this is a typical "direct-gain passive solar house," with lots of south
windows between the 24-hour living space and the outdoors. it works well
on sunny days, but loses lots of heat through the windows at night and
on cloudy days. it gets very cold inside after a few cloudy days in a row.
the only thing worse is a trombe wall (patented in 1881 by edw. morse of
salem, mass before its rediscovery by felix trombe in 1967 in france.
thermal shutters don't help much, since their r-value is much lower than
an r20 house wall, and if they operate automaticlly, they tend to leak air
around the edges.
10. how does t change if a) we make the glass wall a shallow sunspace that
contains very little thermal mass, so it can heat up and cool down quickly,
in, say 5 minutes when the sun comes out or disappears behind a cloud, and
b) that sunspace is warm (t) for 6 hours every day and cold (30 f) for 18
hours per day, and c) we add another r20 insulated wall between the living
space and the sunspace, and allow warm air to circulate between the living
space and the sunspace when the sun is shining...
52.2k = 6h(t-30)64ft^2/r2 for the south wall, during the day
+18h(t-30)64ft^2/r22 for the south wall, at night
+24h(t-30)5x64ft^/r20 for the other 5 walls, over one day.
= (t-30)(192+52.4+384)
= (t-30)628.4, so
t = 30+52.2k/628.4 = 113 f :-)
oops, too hot. what to do now? a) open a window to let in some colder fresh
air, since solar heat is free, or b) reduce the amount of insulation, which
makes the cube cheaper to build, or c) use less thermal mass (how much?),
and store the same amount of useful heat at a higher temperature, and build
another insulated wall between the 70 f living space and the 113 f mass, or
d) add an air conditioner
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