[net-gold] Could the U.S. Significantly Reduce It's Yearly Emission of CO2 By Covering Its Rooftops With Photovoltaic Panels?
- From: "David P. Dillard" <jwne@xxxxxxxxxx>
- To: Other Net-Gold Lists -- Educator Gold <Educator-Gold@xxxxxxxxxxxxxxx>, Educator Gold <Educator-Gold@xxxxxxxxxxxxxxxx>, net-gold@xxxxxxxxxxxxx, NetGold <netgold@xxxxxxxxxxxxxxx>, Net-Gold <net-gold@xxxxxxxxxxxxxxxx>, K-12ADMINLIFE <K12ADMIN@xxxxxxxxxxxxxxxxxxx>, K12AdminLIFE <K12AdminLIFE@xxxxxxxxxxxxxxx>, NetGold <netgold@xxxxxxxxxxxxxxxx>, Net-Platinum <net-platinum@xxxxxxxxxxxxxxx>, Net-Gold <NetGold_general@xxxxxxxxxxxxxxxxx>, Temple Gold Discussion Group <TEMPLE-GOLD@xxxxxxxxxxxxxxxxxxx>, Temple University Net-Gold Archive <net-gold@xxxxxxxxxxxxxxxxxxx>, Health Lists -- Health Diet Fitness Recreation Sports Tourism <healthrecsport@xxxxxxxxxxxxxxxx>, Health Diet Fitness Recreation Sports <healthrecsport@xxxxxxxxxxxxxxx>, HEALTH-RECREATION-SPORTS-TOURISM@xxxxxxxxxxxxxxxxxxx
- Date: Sat, 11 Feb 2012 06:52:16 -0500 (EST)
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Date: Fri, 10 Feb 2012 12:52:32 -0800
From: Richard Hake <rrhake@xxxxxxxxxxxxx>
Reply-To: Net-Gold@xxxxxxxxxxxxxxx
To: Net-Gold@xxxxxxxxxxxxxxx
Subject: [Net-Gold] Could the U.S. Significantly Reduce It's Yearly Emission of
CO2 By Covering Its Rooftops With Photovoltaic Panels?
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My previous post "Answer to Fermi Problem
Regarding Concentration of Energy by PhotoVoltaic
Solar Panels" of 9 Feb 2012 contained some
errors. Here's another try:
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If you reply to this long (18 kB) post please
don't hit the reply button unless you prune the
copy of this post that may appear in your reply
down to a few relevant lines, otherwise the
entire already archived post may be needlessly
resent to subscribers.
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*************************************************
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ABSTRACT: In a previous post "Concentration of
Energy by PhotoVoltaic Solar Panels" [Hake
(2012a) I posed the following "Fermi Problem":
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"What fraction 'f' of the yearly total U.S.
fossil-fueled electrical energy (and thus
fraction of yearly tons of CO2 emission from U.S.
fossil-fueled electrical energy production) could
be eliminated if all rooftops in the U.S. were
covered by photovoltaic solar panels?"
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In this post I estimate f = 1.1 - considerably
larger than the estimate f = 0.08 of MathEdCC's
Guy Brandenburg. Perhaps others would like to
consider this problem.
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In Hake (2012a) I warned (paraphrasing): "Before
recommending that all U.S. rooftops be covered
with PhotoVoltaic Solar Panels one should
consider the EMERGY associated with such a plan.
Odum wrote: "EMERGY measures both the work of
nature and that of humans in generating products
and services. . . . The photovoltaic power grid
at Austin, Tex., evaluated by King & Schmandt
(1991), is taking more EMERGY out of society than
it is generating."
.
So is the motto of Solar Forward
<http://solarforward.com/>: "SAVING THE PLANET,
ONE SOLAR SYSTEM AT A TIME" a deception? I THINK
NOT because the evaluation of King & Schmandt
(1991), failed to consider the devastating
decrease in EMERGY due to global warming if the
world's dependence on fossil fuels is not reduced.
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*************************************************
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In a previous post "Concentration of Energy by
PhotoVoltaic Solar Panels" [Hake (2012)] I posed
the following "Fermi Problem":
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******************************************
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What fraction "f" of the yearly total U.S.
fossil-fueled electrical energy (and thus
fraction of yearly tons of CO2 emission
from U.S. fossil-fueled electrical energy
production) could be eliminated if all
rooftops in the U.S. were covered by
photovoltaic solar panels? ............................
(Fermi Problem)
.
******************************************
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I gave four hints:
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1. According to CARMA (2007a) the total electrical
energy production for 2007 in the U.S was
4.19 x 10^9 MWh/y[MWh = MegaWattHours]
of which 0.67 x 4.19 x 10^9 MWh/y
= 2.81 x 10^9 MWh/y =
2.8 x 10^12 kWh/y was fossil fueled...............................(H1)
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(2) According to the population clock at
<http://1.usa.gov/zaQynk>, the population
of the U.S. on 6 Feb 2012 = 313 x 10^6 ........................(H2)
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(3) According to
<http://en.wikipedia.org/wiki/Photovoltaic_system>:
"A typical '150 watt' solar panel is about a square
meter in size. Such a panel may be expected to
produce 1 kWh/day every day, on average,
after taking into account the weather and the
latitude"; thus . . . . . . . . . . . . 365 kWh/(yrm^2) .............(H3)
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(4) For Fermi Problem strategies see, e.g. :
a. <http://en.wikipedia.org/wiki/Fermi_problem>,
b. "Consider a Spherical Cow" [Harte (1988)],
c. "Consider a Cylindrical Cow" [Harte ( 2001)],
d. "Street-Fighting Mathematics [Mahajan (2010)].
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As far as I know (please correct me if I'm wrong)
as of 9 Feb 2012, the only discussion-list subscriber
to post a solution to the above Fermi problem,
was Guy Brandenburg (2012) of the MathEdCC list,
who estimated the total U.S. solar electrical energy
generation if all U.S. rooftops were covered by
solar panels as 2.2 x 10^11 kwhr/y,
thus f = (0.22 x 10^12) / (2.8x10^12), or f = 0.08 <----...(B)
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My own solution in 5 steps (A-E) below yields f = 1.1,
a factor 14 times higher than MathEdCC's
Guy Brandenburg's (2012) estimate f = 0.08.
Perhaps others would like to consider this problem.
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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A. Divide the total U.S. population of 313 x 10^6
from "H1" into two categories [(1) families and
(2) single persons], each with two subcategories
[(a), those in 1 or 2 story houses with roof area A,
and (b) those in buildings greater than two stories
with roof area 3A]. Here A = *average* roof area
of U.S. single-family houses in m^2.
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1. 75% = 0.75 x 313 x 10^6 = 235 x 10^6 living
in families averaging 4 persons each, for a total
of 235/4 x 10^6 = 59 x 10^6 families:
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a. 0.75 x 59 x 10^6 = 44 x 10^6 of whom live in
single-family houses of 1 or 2 stories, each with
roof area Am^2, hence
A(total single family houses) = 44A x 10^6 m^2.............(1),
where A = *average* roof area of U.S. single-family
houses in m^2.
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b. 0.25 x 59 x 10^6 = 15 x 10^6 of whom live in
buildings of more than 2 stories, each housing
25 families (100 people), and each with roof
area 3Am^2, hence 15/25 x 10^6 = 0.6 x 10^6
buildings with A(total buildings occupied by
families) = 1.8A x 10^6 m^2..............................................(2),
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2. 25% = 0.25 x 313 x 10^6 = 18 x 10^6 living singly:
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a. 0.25 x 18 x 10^6 = 4.5 x 10^6 of whom live in
houses of 1 or 2 stories, each with roof area A, hence
A (total single-person houses) = 4.5A x 10^6 m^2............. (3)
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b. 0.75 x 18 x 10^6 = 14 x 10^6 of whom live in
in buildings of more than 2 stories, each housing 100
people, and each with roof area 3Am^2, hence
14/100 x 10^6 = 0.14 x 10^6 buildings with
A(total single-person buildings) = 0.42A x 10^6 m^2..........(4)
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BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
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B. Adding Eq. (1, 2, 3, 4), yields a total U.S. roof area
A(total) = (44A + 1.8A + 4.5A + 0.42A) x 10^6 m^2
= . . . . . . . . . . . . . . . . . .. . . . . .
. . . . . .50A x 10^6 m^2...(5)
where A = *average* of roof area of U.S. single-family
houses in m^2.
.
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
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C. My own sub-middle-class-residence roof
has an area A = 170 m^2. Assuming that same
value for the *average* U.S. single-family house
A yields, from Eq. (5)
A(total) = 50 x 10^6 x 170 m^2 = 8.5 x 10^9 m^2..............(6)
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Note that according to Wikipedia <http://bit.ly/AA8dXS>,
A (total 50 states + DC land area) = 9.8 x 10^6 km^2 =
9.8 x 10^12 m^2, so the U.S. has plenty more land
for rooftops ;-).
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DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
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D. Eq. (6) and H3 yield for the total U.S. solar
electrical energy generation if all rooftops
were covered by solar panels =
(8.5 x 10^9 m^2) x 365 kWh/(yr m^2)
= 3.1 x 10^3 x 10^9 = 3.1 x 10^12 kWh/y........................(7)
.
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
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E. Thus the fraction "f" of the yearly total U.S.
fossil-fueled electrical energy (and thus fraction
of yearly tons of CO^2 emission from U.S.
fossil-fueled electrical energy production)
that could be eliminated if ALL rooftops in the
U.S.were covered by photovoltaic solar panels is,
from Eq. (7) and H3
f = (3.1 x10^12 kWh/y) / (2.8 x 10^12 kWh/y)
or . . . . . . . . . . . . . . . . . . . . . . .
. . . f = 1.1 ..........(8) <-------
.
Note that in "Concentration of Energy by
PhotoVoltaic Solar Panels" [Hake (2012a)] I
warned:
.
"Before recommending, on the basis of one's
answer to the above Fermi problem, that all U.S.
rooftops be covered with photovoltaic solar
panels, one should consider the EMERGY associated
with such a plan - see "Environmental Accounting:
Emergy and Environmental Decision Making" [Odum
(1995)]. On page 1, Odum writes: "EMERGY, spelled
with an 'm,' measures both the work of nature and
that of humans in generating products and
services. By selecting choices that maximize
EMERGY production and use, policies and
judgements can favor those environmental that
maximize real wealth, the whole economy, and the
public benefit." On page 156-157 "Solar Voltaic
Power." Odum writes" "EMERGY evaluations of solar
voltaic arrays have yet to show any net EMERGY
yield. The power grid at Austin, Tex., evaluated
by King & Schmandt (1991), is taking more EMERGY
out of society than it is generating. . ."
.
On my blog entry "Concentration of Energy by
PhotoVoltaic Solar Panels" at
<http://bit.ly/Aimt1K> I advertise the motto of
"Solar Forward" <http://solarforward.com/>:
"SAVING THE PLANET, ONE SOLAR SYSTEM AT A TIME."
.
Considering the EMERGY evaluation by King &
Schmandt (1991), is the above motto a deception?
.
I THINK NOT because the evaluation of King &
Schmandt (1991), as set forth in Odum (1995),
failed to consider the devastating decrease in
EMERGY due to global warming if alternatives to
fossil fuel are not employed - see e.g. "Why
Carbon Matters" [CARMA (2007b)] and "Paleoclimate
Implications for Human-Made Climate Change"
[Hansen & Sato (2011)]. Hansen & Sato at
<http://1.usa.gov/AuzXMw> write:
.
"The paleoclimate record makes it clear that a
target to keep human made global warming less
than 2°C, as proposed in some international
discussions, is not sufficient - IT IS A
PRESCRIPTION FOR DISASTER. . . .[[my CAPS]]. . .
Assessment of the dangerous level of CO2, and the
dangerous level of warming, is made difficult by
the inertia of the climate system. The inertia,
especially of the ocean and ice sheets, allows us
to introduce powerful climate forcings such as
atmospheric CO2 with only moderate initial
response. But that inertia is not our friend - it
means that we are building in changes for future
generations that will be difficult, if not
impossible, to avoid."
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In addition, my estimate f ~ 1 [Eq. (8)]
suggests that covering U.S. rooftops with
photovoltaic solar panels would eliminate CO2
emissions due to fossil-fuel generated electrical
power in the U.S., thus also eliminating
[according to CARMA (2007a)] 2.8 x 10^9 tons of
CO2 emission per year. This is 8% of the total
worldwide emission of 33.5 x 10^9 tons of CO2 in
2010 - see <http://co2now.org/>, scroll to the
bottom of the page.
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Richard Hake, Emeritus Professor of Physics, Indiana University
Honorary Member, Curmudgeon Lodge of Deventer, The Netherlands
President, PEdants for Definitive Academic References
which Recognize the Invention of the Internet (PEDARRII)
<rrhake@xxxxxxxxxxxxx>
Links to Articles: <http://bit.ly/a6M5y0>
Links to SDI Labs: <http://bit.ly/9nGd3M>
Blog: <http://bit.ly/9yGsXh>
Academia: <http://iub.academia.edu/RichardHake>
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" Over the past two centuries, mankind has
increased the concentration of CO2 in the
atmosphere from 280 to more than 380 parts per
million volume and it is growing faster every
day. . . .[[according to <http://co2now.org/> it
was 393.09 ppm for January 2012]]. . .. The
atmospheric concentration of CO2 has not been
this high for at least the past 650,000 years. As
the concentration of CO2 has risen, so has the
average temperature of the planet. Over the past
century, the average surface temperature of Earth
has increased by more than 1.3°F (0.74°C). If we
continue to emit carbon without restraint,
temperatures are expected to rise by an
additional 6°F (3.4°C) by the end of this
century. . . . . Despite mounting evidence of the
dangers posed by climate change, efforts to limit
carbon emissions remain insufficient,
ineffective, and, in most countries,
non-existent. If the world is to avert the worst
consequences of an altered climate, the status
quo must change quickly. Given current trends and
the best available scientific evidence, mankind
probably needs to reduce total CO2 emissions by
at least 80% by 2050. Yet each day emissions
continue to grow."
CARMA (2007b)
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REFERENCES [URL's shortened by <http://bit.ly/> and accessed on 10 Feb 2012.]
Brandenburg, G. 2012. "Re: Fermi Problems in Math
Education?" MathEdCC post of Feb 7, 2012 7:16 AM;
online on the OPEN! MathEdCC archives at
<http://bit.ly/wOxmrU>.
.
.
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CARMA. 2007a. CARbon Moniorinf for Action,
"Center for Global Development"; data for U.S.,
online at <http://carma.org/region/detail/202>.
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CARMA. 2007b. CARbon Moniorinf for Action,
"Center for Global Development"; "Why Carbon
Matters," online at <http://carma.org/blog/why/>.
CO2Now.org. 2012. Online at <http://co2now.org/>.
.
Hansen, J.E. & M. Sato. 2011. "Paleoclimate
Implications for Human-Made Climate Change," 20
July, online at
<http://arxiv.org/abs/1105.0968v2>; to appear in
Berger, Mesinger and Sijaci, eds., "Climate
Change at the Eve of the Second Decade of the
Century: Inferences from Paleoclimate and
Regional Aspects: Proceedings of Milutin
Milankovitch 130th Anniversary Symposium"
(Springer, in press), a popularization of this
paper is online as a 213 kB pdf at
<http://1.usa.gov/AuzXMw>.
.
Hake, R.R. 2012. "Concentration of Energy by
PhotoVoltaic Solar Panels" online on the OPEN!
AERA-L archives at <http://bit.ly/wdkAoL>.
[Transmitted to Math discussion lists as "Fermi
Problems in Math Education?"] Post of 6 Feb 2012
09:59:03-0800 to AERA-L and Net-Gold. The
abstract and link to the complete post were
transmitted to several discussion lists and are
also on my blog "Hake'sEdStuff" at
<http://bit.ly/Aimt1K> with a provision for
comments.
.
Harte, J. 1988. "Consider a Spherical Cow: A
Course in Environmental Problem Solving."
University Science Books. Amazon.com information
at <http://amzn.to/zRek6q>. Note the "Look
Inside" feature.
.
Harte, J. 2001. "Consider a Cylindrical Cow: More
Adventures in Environmental Problem Solving."
University Science Books. Amazon.com information
at <http://amzn.to/xecQhv>. Note the "Look
Inside" feature.
.
King, R.J. & J. Schmandt. 1991. "Ecological
Economics of Alternative Transportation Fuels,"
Report to Texas State Dept. of Energy,
Unpublished report, L.B.J. School of Public
Affairs, Univ. of Texas, Austin, 26 pp. A summary
of this report is given by Odum (1995) on pp.
156-157 in a section "Solar Voltaic Power."
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Mahajan, S. 2010. "Street-Fighting Mathematics:
The Art of Educated Guessing and Opportunistic
Problem Solving." MIT Press, publisher's
information at <http://bit.ly/ghF5XY> where the
book may be downloaded for FREE as a 770 kB pdf
by clicking on "Download This Book" in the
left-hand column. Author's information at
<http://streetfightingmath.com/>. Amazon.com
information at <http://amzn.to/xqOt3Q>.
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Odum, H.G.1995. "Environmental Accounting: Emergy
and Environmental Decision Making." Wiley,
publisher's information at
<http://bit.ly/wSeH9b>. Amazon.com information at
<http://amzn.to/ycGgJ2>, note the searchable
"Look Inside" feature." An expurgated Google
Preview is online at <http://bit.ly/w6aRIZ>.
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Other related posts:
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