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Philosophers

Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
Anaximander
G.E.M.Anscombe
Anselm
Louise Antony
Thomas Aquinas
Aristotle
David Armstrong
Harald Atmanspacher
Robert Audi
Augustine
J.L.Austin
A.J.Ayer
Alexander Bain
Mark Balaguer
Jeffrey Barrett
William Barrett
William Belsham
Henri Bergson
George Berkeley
Isaiah Berlin
Richard J. Bernstein
Bernard Berofsky
Robert Bishop
Max Black
Susanne Bobzien
Emil du Bois-Reymond
Hilary Bok
Laurence BonJour
George Boole
Émile Boutroux
Daniel Boyd
F.H.Bradley
C.D.Broad
Michael Burke
Lawrence Cahoone
C.A.Campbell
Joseph Keim Campbell
Rudolf Carnap
Carneades
Nancy Cartwright
Gregg Caruso
Ernst Cassirer
David Chalmers
Roderick Chisholm
Chrysippus
Cicero
Randolph Clarke
Samuel Clarke
Anthony Collins
Antonella Corradini
Diodorus Cronus
Jonathan Dancy
Donald Davidson
Mario De Caro
Democritus
Daniel Dennett
Jacques Derrida
René Descartes
Richard Double
Fred Dretske
John Dupré
John Earman
Laura Waddell Ekstrom
Epictetus
Epicurus
Austin Farrer
Herbert Feigl
Arthur Fine
John Martin Fischer
Frederic Fitch
Owen Flanagan
Luciano Floridi
Philippa Foot
Alfred Fouilleé
Harry Frankfurt
Richard L. Franklin
Bas van Fraassen
Michael Frede
Gottlob Frege
Peter Geach
Edmund Gettier
Carl Ginet
Alvin Goldman
Gorgias
Nicholas St. John Green
H.Paul Grice
Ian Hacking
Ishtiyaque Haji
Stuart Hampshire
W.F.R.Hardie
Sam Harris
William Hasker
R.M.Hare
Georg W.F. Hegel
Martin Heidegger
Heraclitus
R.E.Hobart
Thomas Hobbes
David Hodgson
Shadsworth Hodgson
Baron d'Holbach
Ted Honderich
Pamela Huby
David Hume
Ferenc Huoranszki
Frank Jackson
William James
Lord Kames
Robert Kane
Immanuel Kant
Tomis Kapitan
Walter Kaufmann
Jaegwon Kim
William King
Hilary Kornblith
Christine Korsgaard
Saul Kripke
Thomas Kuhn
Andrea Lavazza
Christoph Lehner
Keith Lehrer
Gottfried Leibniz
Jules Lequyer
Leucippus
Michael Levin
Joseph Levine
George Henry Lewes
C.I.Lewis
David Lewis
Peter Lipton
C. Lloyd Morgan
John Locke
Michael Lockwood
Arthur O. Lovejoy
E. Jonathan Lowe
John R. Lucas
Lucretius
Alasdair MacIntyre
Ruth Barcan Marcus
Tim Maudlin
James Martineau
Nicholas Maxwell
Storrs McCall
Hugh McCann
Colin McGinn
Michael McKenna
Brian McLaughlin
John McTaggart
Paul E. Meehl
Uwe Meixner
Alfred Mele
Trenton Merricks
John Stuart Mill
Dickinson Miller
G.E.Moore
Thomas Nagel
Otto Neurath
Friedrich Nietzsche
John Norton
P.H.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
Parmenides
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Plato
Karl Popper
Porphyry
Huw Price
H.A.Prichard
Protagoras
Hilary Putnam
Willard van Orman Quine
Frank Ramsey
Ayn Rand
Michael Rea
Thomas Reid
Charles Renouvier
Nicholas Rescher
C.W.Rietdijk
Richard Rorty
Josiah Royce
Bertrand Russell
Paul Russell
Gilbert Ryle
Jean-Paul Sartre
Kenneth Sayre
T.M.Scanlon
Moritz Schlick
Arthur Schopenhauer
John Searle
Wilfrid Sellars
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
J.J.C.Smart
Saul Smilansky
Michael Smith
Baruch Spinoza
L. Susan Stebbing
Isabelle Stengers
George F. Stout
Galen Strawson
Peter Strawson
Eleonore Stump
Francisco Suárez
Richard Taylor
Kevin Timpe
Mark Twain
Peter Unger
Peter van Inwagen
Manuel Vargas
John Venn
Kadri Vihvelin
Voltaire
G.H. von Wright
David Foster Wallace
R. Jay Wallace
W.G.Ward
Ted Warfield
Roy Weatherford
C.F. von Weizsäcker
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf

Scientists

David Albert
Michael Arbib
Walter Baade
Bernard Baars
Jeffrey Bada
Leslie Ballentine
Marcello Barbieri
Gregory Bateson
John S. Bell
Mara Beller
Charles Bennett
Ludwig von Bertalanffy
Susan Blackmore
Margaret Boden
David Bohm
Niels Bohr
Ludwig Boltzmann
Emile Borel
Max Born
Satyendra Nath Bose
Walther Bothe
Jean Bricmont
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Melvin Calvin
Donald Campbell
Sadi Carnot
Anthony Cashmore
Eric Chaisson
Gregory Chaitin
Jean-Pierre Changeux
Rudolf Clausius
Arthur Holly Compton
John Conway
Jerry Coyne
John Cramer
Francis Crick
E. P. Culverwell
Antonio Damasio
Olivier Darrigol
Charles Darwin
Richard Dawkins
Terrence Deacon
Lüder Deecke
Richard Dedekind
Louis de Broglie
Stanislas Dehaene
Max Delbrück
Abraham de Moivre
Bernard d'Espagnat
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Gerald Edelman
Paul Ehrenfest
Manfred Eigen
Albert Einstein
George F. R. Ellis
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
David Foster
Joseph Fourier
Philipp Frank
Steven Frautschi
Edward Fredkin
Benjamin Gal-Or
Lila Gatlin
Michael Gazzaniga
Nicholas Georgescu-Roegen
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
A. O. Gomes
Brian Goodwin
Joshua Greene
Dirk ter Haar
Jacques Hadamard
Mark Hadley
Patrick Haggard
J. B. S. Haldane
Stuart Hameroff
Augustin Hamon
Sam Harris
Ralph Hartley
Hyman Hartman
John-Dylan Haynes
Donald Hebb
Martin Heisenberg
Werner Heisenberg
John Herschel
Basil Hiley
Art Hobson
Jesper Hoffmeyer
Don Howard
William Stanley Jevons
Roman Jakobson
E. T. Jaynes
Pascual Jordan
Ruth E. Kastner
Stuart Kauffman
Martin J. Klein
William R. Klemm
Christof Koch
Simon Kochen
Hans Kornhuber
Stephen Kosslyn
Daniel Koshland
Ladislav Kovàč
Leopold Kronecker
Rolf Landauer
Alfred Landé
Pierre-Simon Laplace
David Layzer
Joseph LeDoux
Gilbert Lewis
Benjamin Libet
David Lindley
Seth Lloyd
Hendrik Lorentz
Josef Loschmidt
Ernst Mach
Donald MacKay
Henry Margenau
Owen Maroney
Humberto Maturana
James Clerk Maxwell
Ernst Mayr
John McCarthy
Warren McCulloch
N. David Mermin
George Miller
Stanley Miller
Ulrich Mohrhoff
Jacques Monod
Emmy Noether
Alexander Oparin
Abraham Pais
Howard Pattee
Wolfgang Pauli
Massimo Pauri
Roger Penrose
Steven Pinker
Colin Pittendrigh
Max Planck
Susan Pockett
Henri Poincaré
Daniel Pollen
Ilya Prigogine
Hans Primas
Henry Quastler
Adolphe Quételet
Lord Rayleigh
Jürgen Renn
Emil Roduner
Juan Roederer
Jerome Rothstein
David Ruelle
Tilman Sauer
Jürgen Schmidhuber
Erwin Schrödinger
Aaron Schurger
Sebastian Seung
Thomas Sebeok
Franco Selleri
Claude Shannon
Charles Sherrington
David Shiang
Abner Shimony
Herbert Simon
Dean Keith Simonton
Edmund Sinnott
B. F. Skinner
Lee Smolin
Ray Solomonoff
Roger Sperry
John Stachel
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
Max Tegmark
Teilhard de Chardin
Libb Thims
William Thomson (Kelvin)
Richard Tolman
Giulio Tononi
Peter Tse
Francisco Varela
Vlatko Vedral
Mikhail Volkenstein
Heinz von Foerster
Richard von Mises
John von Neumann
Jakob von Uexküll
C. S. Unnikrishnan
C. H. Waddington
John B. Watson
Daniel Wegner
Steven Weinberg
Paul A. Weiss
Herman Weyl
John Wheeler
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
Günther Witzany
Stephen Wolfram
H. Dieter Zeh
Ernst Zermelo
Wojciech Zurek
Konrad Zuse
Fritz Zwicky

Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium
 
Solar Panel Study

There are many factors affecting the performance of photovoltaic (PV) panels converting solar energy to electricity. Very few of these are mentioned by the manufacturers of solar panels and those who install them. Some of them are simply beyond the control of the installers, who are generally following best industry practices and use popular software analysis tools to recommend the best system for a particular location.

Total Solar Irradiance (TSI)
Solar irradiance is the amount of solar energy in watts per square meter. At the Earth's distance from the Sun, 1360 watts pass through a square meter perpendicular to the sun's rays. The color temperature of this light is the same as the sun, approximately 6,000K. (K designates degrees Kelvin, measured from absolute zero.)

It is of deep significance, however, that the energy density of the radiation is much lower, only 300K. If we capture the visible light energy (absorb it) and see what it emits, it is converted into invisible infrared heat radiation.

The Earth absorbs 6000K radiation during the day and emits it as 300K into the night sky. The day is a heat source, the night a heat sink. The Earth is a thermodynamic engine, extracting negative entropy (information) from the solar radiation, using it to power living things, as the great quantum physicist Erwin Schrödinger pointed out in his 1944 essay, "What Is Life?.

The Solar Electricity Handbook is a great resource for solar irradiance. Their web page offers a calculator that provides monthly values of average solar irradiance for many cities.

In our example for our Institute in Cambridge, we calculated irradiance for panels flat on the surface. It is clear that the production of power with panels flat in winter (1.8 kWh/m2) is greatly reduced from the rest of the year. In the summer it is 5.6 kWh/m2, over three times the power.

The calculator lets you set the panels tilt angle, even adjusting panels throughout the year to follow the sun's elevation angle in different seasons

We shall see below the reduction in winter is a combination of the spreading our of the sun's rays by the projection affect and the greater absorption of solar energy as the rays travel through the atmosphere at a low slanting angle when compared to the summer sun near overhead in the sky.

The Best Solar Panel Angle

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The question perhaps most often asked is what orientation to mount a panel, including its elevation angle and azimuth (compass direction). The best (and most expensive) answer is to mount the panel on a tracking device to follow the solar path across the sky. Next best is to point the panel due south, angled up to the local latitude, which aims the panel directly at the sun when it is highest in the sky (solar noon) at the spring and fall equinoxes.

But this is perfect for only two days at one moment of those days. At all other times the sun's direction varies widely. At sunrise and sunset, the sun is on the horizon (elevation angle 0°), and at solar noon it is high in the sky in summer, 23° above its equinox angle, and in winter low in the sky, 23° below the celestial equator.

At the equinoxes, the sun's elevation angle is equal to the local latitude. Most all research recommending an angle says point it due south (in the northern hemisphere) with elevation equal to the latitude. Twice a year for a single moment the panel is exactly perpendicular to the sun's rays.

Sadly, most residential installations have little choice of angle. Their angled roofs are in arbitrary directions and pitches. Flat roofs (typically commercial roofs are flat) can aim the panels in any direction, and usually choose an azimuth toward the earth's equator.

But the solar panel elevation angle on commercial roofs varies widely, from flat (0°) to latitude. Why is this?

The Major Factors
  • Absorption by the Atmosphere

    The solar energy at the top of the atmosphere is 1360 W/m2, but if the sun is in the zenith, directly overhead, only about 1050 W/m2 of direct solar rays reaches the earth surface. Another 70 W/m2 is scattered solar light from the blue sky and its ultraviolet light that causes sunburn even on cloudy days.

    At most times the solar radiation is slanting though the atmosphere at an angle. At an angle of 30°, the light passes through twice as much atmosphere. 1050/1360 = .77 passing through two atmospheres is .77 x .77 ≈ .6. At a 20° angle the sun passes through three times as much air so ≈ .45 or 45% gets through. At 15° only 35% reaches the earth surface.

  • The Projection Effect

    But this increasing loss of light energy is further exaggerated because light shining at an angle is spread out over a large area!

    At 30°, light energy in W/m2 is cut in half since the light falls on twice the area. At 20° it is one-third. At 15° one quarter.

    So the combination of absorption losses and projection losses is a reduction to 38% at 30°, 23% at 20°, and only 18% at 15°.

  • Temperature Effect

    PV panels produce more electricity at low temperatures, less at high temperatures. So when are panels are getting maximum solar irradiance in summer, we must degrade their performance from the nominal output at 25°C/77°F.

    Temperature 5°C/41°F 15°C/59°F 25°C/77°F 35°C/95°F
    Gain/Loss +10% +5% 0% -5%

  • So things are a bit worse in summer and better in winter

  • Direct Sun vs. Indirect Scattered Light

    We noted above that about 7% of the energy reaching the surface (70 W/m2) is scattered light. When the sun's elevation angle is below 10°, almost half the energy is coming from this scattered light.

  • First Surface Reflection

    But even these numbers are overoptimistic for low slant angles if the solar panel itself is flat on the surface. If it is tracking the sun at the 10°, angle, the panel would get 18% of the energy, plus some scattered light.

    If the panel lies flat, however, light can not enter the transparent glass surface as easily as it does when the light is perpendicular. The glass surface reflects more and more of the solar light at steep angles.

    We can probably ignore direct solar irradiance producing energy when the sun is less than 10 degrees above the horizon.

  • Bottom Surface Reflection

    Some manufacturers have noticed that radiation is not completely absorbed in the panel. They (e.g., Sunpower) have added a mirror at the back surface, so the photons get a second chance at absorption as they travel back to the front of the panel.

  • Environment Reflection

    Other manufacturers (e.g., LG) make the back surface transparent so radiation reflected from the environment, for example a white roof, can be absorbed. They argue that gains of as much as 30% can be achieved. LG and Sunpower have the two most efficient (and highest power) solar panels.

  • Shading

    Shading by trees, by nearby buildings, and by structures on the roof can be evaluated by the most popular analysis software (e.g., Aurora Solar and Helioscope). But when tilting panels up to be more perpendicular to the sun's rays, while optimal for a single panel or one row of panels, may produce the most shading - of panels that are behind other panels, especially when the sun is at low elevation angles and at azimuths away from due south.

    Shading just part of a panel may reduce the production of power much greater than the percentage shadowed. In his classic book Renewable and Efficient Electric Power Systems, Gilbert Masters showed PV module power losses from shading just a few cells.

    Since most PV panels are divided into three strings, each with a protective bypass diode to remove a string from power production if some of its cells are shaded, it is important to orient panels in landscape mode, so that any number of cells at the bottom are in the same string.

    Compare shading of the bottom cells in portrait mode which compromises all three of the panel strings.

  • Dirt or Snow on the Panel

    The higher the PV panel angle, the less likely that air pollution will collect and stay of the panel surface. A strong rain should clean it off. Panels lying flat on the roof are most likely to stay dirty and least likely to have snow slide off in winter.

    As we can see above, the 10% losses from dirt, in which all cells probably reduce power at the same rate, are less severe than even partial shading of a single cell.

Experimental Measurements

We can experimentally confirm the reduction in solar irradiance when the sun is at various angles with a white card and an inexpensive light meter.

We can confirm the power output of a PV panel at various angles to the sun with an inexpensive voltmeter and ammeter.

We can separate the production by direct sunlight from indirect scattered light with a board as large as the panel admitting only rays from the sun at a low elevation.

We can analyze shading by panels using 3D capabilities of the solar installers' software. We purchased both Aurora and Helioscope for this study.

We will ask solar panel manufacturers to loan us test panels, but will purchase leading solar panels if necessary.

Questions

Can solar panel software analysis tools tell us the power generated by an array of panels at different times of day? If they cannot, how can we believe their monthly averages?

Which of the major factors above reducing energy production are included in the algorithms of analysis software?

Sample Results

We began by modeling 47 panels (LG NeON 2 390W 72 Cell Mono 1500V SLV/WHT BiFacial Solar Panel, LG390N2T-A5) to the flat roof of our Information Philosophy Institute.

We oriented the panels due south and tilted them to four different angles - 47° (our latitude), 18°, 10°, and 0° (flat on the roof).

Helioscope software estimated the power output as 18.3 kW and generated the following monthly values for energy production.

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We can see that panels flat on the roof have no shading losses, where those tilted at latitude lose 18.6% .

We can use Aurora to visualize that shading at different times of day. The panels are separated enough to eliminate shading of a panel directly behind, but only at solar noon. At other times the shadow angles down to the sides, cutting off power from panels diagonally behind.

We again arranged 47 LG bifacial panels on the roof by using 1" panel spacing and 24" spacing between rows. Aurora also estimated power at 18.3 kW.

They are probably just multiplying 47 panels times 390W per panel! And the figure of 390W is when the LG bifacial is illuminated with 1000 W/m2, which is not achievable with panels in typical conditions.

When we look down from our latitude angle, we see that there is no panel shading. Aurora's camera view point is not very far above the roof. To show panel shading from the sun's POV it should be infinitely far away. So panels at the rear appear to be shading because of their perspective.

We can now rotate Aurora to see the panels from the east at the summer solstice, when the sun is 35° above the horizon and producing a bit under half the solar irradiance at its maximum for the day.

From the east, the panels are not facing the sun, but are edge on. The near perspective again diverges from the sun's perspective. The point is that instead of nearly half power, there is no power. It's not clear whether the Aurora irradiance (or "solar access value) gives us this reduction.

Shading in Aurora

On the flat unshaded part of the roof solar access is 100% and the irradiance is 1410 kWh/m2/yr.

When the cursor is on the unshaded portion of a panel tilted at 20° the solar access is 100% and the irradiance increases to 1610 kWh/m2/yr. A panel that was tilted to face the sun directly would have still higher irradiance. Aurora shows the monthly variation in irradiance.

Aurora shows the shading on a panel as the color changing from bright yellow to a dark purple. Above the cursor is on the shaded portion of a panel. Solar access averages only 75% and is way down in the winter months. Shading reduces irradiance to 1214 kWh/m2/yr.

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