. . Date: Fri, 10 Feb 2012 13:43:02 -0800 From: Richard Hake <rrhake@xxxxxxxxxxxxx> Reply-To: Net-Gold@xxxxxxxxxxxxxxx To: AERA-L@xxxxxxxxxxxxxxxxx Cc: Net-Gold@xxxxxxxxxxxxxxx Subject: [Net-Gold] Could the U.S. Significantly Reduce Its Yearly Emission of CO2 By Covering Its Rooftops With Photovoltaic Solar Panels? #2 . . YIKES! - The Subject Heading of my last post was ungrammatical :-(. Here's another try. . . 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. . ************************************************* . ABSTRACT: In a previous post "Concentration of Energy by PhotoVoltaic Solar Panels" [Hake (2012a) I posed the following "Fermi Problem": . "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?" . 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. . 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. . ************************************************* . In a previous post "Concentration of Energy by PhotoVoltaic Solar Panels" [Hake (2012)] I posed the following "Fermi Problem": . ****************************************** . 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) . ****************************************** . I gave four hints: . 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) . (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) . (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) . (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)]. . 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) . 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. . AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA . 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. . 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: . 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. . 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), . 2. 25% = 0.25 x 313 x 10^6 = 18 x 10^6 living singly: . 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) . 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) . BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB . 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 . 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) . 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 ;-). . DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD . 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 . 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." . 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. . . . 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> . . . " 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) . . . 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>. . . . CARMA. 2007a. CARbon Moniorinf for Action, "Center for Global Development"; data for U.S., online at <http://carma.org/region/detail/202>. . 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." . 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>. . 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>. . .