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PROFESSOR: And I think we're
about ready to get started.

00:00:29.060 --> 00:00:30.920
So welcome, folks,
for lecture number two

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of Fundamentals of Photovoltaics
focused on the solar resource.

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What I wanted to
do to get everybody

00:00:36.580 --> 00:00:38.220
in the mood of
thinking about the sun

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is pass around a few balls.

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So this is really a, to limber
you all up, but b-- whoop.

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[LAUGHTER]

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There we go.

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All right.

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Don't let it fall.

00:00:49.119 --> 00:00:49.660
There you go.

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I know Ashley's got solid hands.

00:00:51.230 --> 00:00:51.730
All right.

00:00:51.730 --> 00:00:52.460
Here's one.

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Pass that around as well.

00:00:53.870 --> 00:00:58.210
We'll get a few
more there, there,

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and lastly, right up the middle.

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There you go.

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OK.

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So today's lecture is really
about the solar resource.

00:01:06.400 --> 00:01:08.820
And as we go through,
it kind of helps

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to have a sphere in your
hands since oftentimes we

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perceive the world as being
flat-- no fault of our own.

00:01:16.760 --> 00:01:19.710
Locally, one can approximate
it as a flat body.

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That's certainly a
good possibility.

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You wouldn't mind passing these
out to your friends as well?

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AUDIENCE: Sure.

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PROFESSOR: Thanks.

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But in reality,
if we really want

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to understand the
solar resource,

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we really have to begin
understanding or thinking

00:01:30.710 --> 00:01:35.180
in terms of spheres and in terms
of circles or, in most cases,

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ellipses.

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And so we're going to dive
into the solar resource.

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Before we really dive in in
detail into the solar resource,

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I wanted to give you
feedback to your surveys.

00:01:43.710 --> 00:01:46.020
So you did a background
assessment survey, a census,

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if you will, and filled out a
number of questions last class

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about your backgrounds.

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And I wanted to provide
you the feedback,

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the consolidated information,
because it's really telling

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about who your colleagues are.

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This right here is a little
bit of a snapshot of expertise

00:02:00.810 --> 00:02:03.410
and current career trajectory.

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So the self-defined
expertise in the bottom left

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is really, I think, the
most telling parameter.

00:02:08.150 --> 00:02:10.229
For the undergrads here,
you may define yourself

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by your major today, but
when you graduate and go on

00:02:12.260 --> 00:02:14.790
to grad school, you might, say,
for example, do your undergrad

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in physics and then do
your graduate school

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in mechanical
engineering, but still

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consider yourself a
physicist at heart.

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And so that's why I asked
this question here--

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what is your self-defined
expertise-- because there

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are several graduate students
who have changed fields,

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if you will, from undergrad
to graduate school.

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Most people in the
audience, by and large,

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consider themselves engineers--
either material science

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engineers or
mechanical engineers.

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Chemistry is strong as well.

00:02:38.500 --> 00:02:42.280
And then we have about 10
different departments here

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represented.

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And that's really cool.

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It's going to manifest
itself in the class projects.

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And you'll see the diversity
of different inputs

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and perspectives
from your colleagues.

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The degree in progress--
undergrad/grad

00:02:55.580 --> 00:03:00.670
is about split 1/3 2/3
undergrad and grad.

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ASP is Advanced Studies
Program, so these

00:03:02.460 --> 00:03:04.460
are folks coming in from
industry who are actually here

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in the classroom.

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Some of your
colleagues in the class

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are folks who are in
industry and perhaps

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have real world PV experience.

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Several of the people
here in the class,

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as well, have
gained-- how do we say

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it-- have gained expertise
in solar with their hobbies,

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with their work.

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Some have installed
solar panels.

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Other ones have done research
or are doing research in solar.

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So it's a pretty diverse group.

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And some are, as well,
members of the solar car

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team, which is rolling out its
new model in a few days' time.

00:03:31.190 --> 00:03:33.450
In terms of learning
methods, it was pretty well

00:03:33.450 --> 00:03:36.020
split between hands-on
labs, field trips,

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and guest lectures.

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And I'll get back to
that in a few slides.

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In terms of class
project interest,

00:03:42.060 --> 00:03:44.260
there was a strong
interest in working

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with pre-established projects,
so we've listened to that.

00:03:47.340 --> 00:03:49.310
This is pretty consistent
with previous years.

00:03:49.310 --> 00:03:51.620
And so we have several
pre-prepared class projects

00:03:51.620 --> 00:03:52.960
ready for you.

00:03:52.960 --> 00:03:55.840
And a few of you had an interest
in the self-design project.

00:03:55.840 --> 00:03:57.090
I'd like to talk to you.

00:03:57.090 --> 00:03:59.500
I'd like to begin developing
those ideas as soon

00:03:59.500 --> 00:04:03.380
as possible so that when
we start assembling teams,

00:04:03.380 --> 00:04:05.625
if you do have a strong
idea for class project,

00:04:05.625 --> 00:04:08.000
we can begin crafting that
and molding that starting now.

00:04:08.000 --> 00:04:09.708
So please come up and
have a chat with me

00:04:09.708 --> 00:04:13.470
after class or during office
hours or during recitation.

00:04:13.470 --> 00:04:17.240
These are your learning
objectives defined by you.

00:04:17.240 --> 00:04:21.190
And they range-- I tried to
give it some continuum spectrum

00:04:21.190 --> 00:04:23.150
from natural sciences
to social sciences

00:04:23.150 --> 00:04:24.860
and engineering in the middle.

00:04:24.860 --> 00:04:29.620
And obviously, this is more
of a loop than a linear line,

00:04:29.620 --> 00:04:31.597
but bear with me.

00:04:31.597 --> 00:04:33.430
There was a strong
interest in fundamentals.

00:04:33.430 --> 00:04:35.810
And that certainly, I think,
what the core of the class

00:04:35.810 --> 00:04:38.550
is about or at least the
first third of the class.

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Going in terms of
size of the bubble,

00:04:40.350 --> 00:04:41.766
these are the
number of people who

00:04:41.766 --> 00:04:44.770
listed a particular topic as
of great interest to them.

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Economics and market, systems
and grid, current technologies,

00:04:48.385 --> 00:04:50.210
and emerging technologies.

00:04:50.210 --> 00:04:52.267
And so listening to
all of this, we have,

00:04:52.267 --> 00:04:54.600
or we are in the process of
preparing for you some guest

00:04:54.600 --> 00:04:57.640
lectures and field trips based
on this feedback right here.

00:04:57.640 --> 00:04:59.630
We have already
lined up a field trip

00:04:59.630 --> 00:05:02.830
to a local PV research
laboratory that

00:05:02.830 --> 00:05:06.150
produces modules like this
one right here only much, much

00:05:06.150 --> 00:05:09.350
bigger and has strong
collaboration with existing

00:05:09.350 --> 00:05:11.130
companies, startup
companies, in the area

00:05:11.130 --> 00:05:12.950
as well as more
established companies.

00:05:12.950 --> 00:05:15.034
So that'll be a lot of fun.

00:05:15.034 --> 00:05:16.450
And we're currently
in the process

00:05:16.450 --> 00:05:18.116
of arranging other
field trips and guest

00:05:18.116 --> 00:05:21.450
lectures to match this feedback
right here, so thank you.

00:05:21.450 --> 00:05:26.740
We'll mold the course, shape it,
craft it to fit your interests.

00:05:26.740 --> 00:05:28.830
So to hop into
the solar resource

00:05:28.830 --> 00:05:31.726
and without further ado,
the subject of today

00:05:31.726 --> 00:05:33.350
and the motivation
for wearing this tie

00:05:33.350 --> 00:05:36.074
is really the solar
resource, the sun.

00:05:36.074 --> 00:05:37.240
This is where it all starts.

00:05:37.240 --> 00:05:39.260
If we're to understand
PV, photovoltaics,

00:05:39.260 --> 00:05:41.100
the conversion of
sunlight into electricity,

00:05:41.100 --> 00:05:42.360
it starts from the sun.

00:05:42.360 --> 00:05:44.680
And so spending some good
time thinking about the sun

00:05:44.680 --> 00:05:46.510
is really, really important.

00:05:46.510 --> 00:05:49.050
And it will avoid the
embarrassing situation--

00:05:49.050 --> 00:05:52.070
how many of you have been at a
shopping center, walking along,

00:05:52.070 --> 00:05:54.820
and a little child is
asking his parent, Dad,

00:05:54.820 --> 00:05:56.420
why is the sky blue?

00:05:56.420 --> 00:05:57.850
Or why is the such and such?

00:05:57.850 --> 00:05:59.580
And the answers
you'll hear just make

00:05:59.580 --> 00:06:02.910
you want to tear your ears
out, say, my goodness.

00:06:02.910 --> 00:06:04.997
And so part of this is
just general knowledge.

00:06:04.997 --> 00:06:07.080
It's getting a feel for
the world and the universe

00:06:07.080 --> 00:06:09.663
and asking those questions again
that the little children will

00:06:09.663 --> 00:06:12.990
ask but we forget to ask as we
move on with our lives, right?

00:06:12.990 --> 00:06:13.490
OK.

00:06:13.490 --> 00:06:17.160
So moving forward, the
learning objectives for today

00:06:17.160 --> 00:06:18.510
are these right here.

00:06:18.510 --> 00:06:20.260
By the end of the
lecture-- and hopefully,

00:06:20.260 --> 00:06:22.330
you already have a good sense
of this based on your readings

00:06:22.330 --> 00:06:22.829
already.

00:06:22.829 --> 00:06:25.832
I'll quiz you on that
second-- verbally.

00:06:25.832 --> 00:06:28.290
We want to be able to quantify
the available solar resource

00:06:28.290 --> 00:06:31.880
relative to human energy
needs and other fuel sources.

00:06:31.880 --> 00:06:35.200
We want to recognize
and plot air mass zero

00:06:35.200 --> 00:06:38.220
and air mass 1.5 solar
spectra and describe

00:06:38.220 --> 00:06:39.950
the physical origins.

00:06:39.950 --> 00:06:42.910
We want to describe how
solar insulation maps--

00:06:42.910 --> 00:06:45.390
these are solar resource
maps, in other words, how

00:06:45.390 --> 00:06:47.270
much sunlight is available.

00:06:47.270 --> 00:06:51.080
And we want to be able to
estimate a solar resource

00:06:51.080 --> 00:06:54.870
amount locally at a
specific spot on the planet.

00:06:54.870 --> 00:06:57.710
We want to list the causes of
variation and intermittency

00:06:57.710 --> 00:07:00.270
of the solar resource
and quantify their time

00:07:00.270 --> 00:07:01.355
constant in magnitude.

00:07:01.355 --> 00:07:03.230
In other words, we want
to be able to discern

00:07:03.230 --> 00:07:05.354
what are the big effects
and what are the ones that

00:07:05.354 --> 00:07:06.216
don't really matter.

00:07:06.216 --> 00:07:08.340
We want to be able to
estimate the land area needed

00:07:08.340 --> 00:07:11.100
to provide sufficient solar
resource for a project,

00:07:11.100 --> 00:07:13.940
whether it's a house, a car,
a village, a country, a world.

00:07:13.940 --> 00:07:16.190
And a lot of this will be
on your homework assignment,

00:07:16.190 --> 00:07:18.480
so we'll give you the
tools here, but then ask

00:07:18.480 --> 00:07:20.290
you to address those questions.

00:07:20.290 --> 00:07:21.831
And for those of
you who have already

00:07:21.831 --> 00:07:24.630
picked up your p-set number one,
you'll see relevant questions.

00:07:24.630 --> 00:07:25.213
Where is this?

00:07:28.501 --> 00:07:33.250
Does anybody recognize
this right here?

00:07:33.250 --> 00:07:37.780
If I start rambling
off names, what city

00:07:37.780 --> 00:07:40.239
has Pennsylvania Avenue,
Independence Ave?

00:07:40.239 --> 00:07:41.280
AUDIENCE: Washington, DC.

00:07:41.280 --> 00:07:42.363
PROFESSOR: Washington, DC.

00:07:42.363 --> 00:07:45.140
This is right outside of the
National Air and Space Museum.

00:07:45.140 --> 00:07:49.160
What this little girl here
is pointing to is the sun.

00:07:49.160 --> 00:07:52.940
And then we have Mercury, Venus,
Earth, Mars, and so forth.

00:07:52.940 --> 00:07:55.100
So it's essentially a
solar system to scale.

00:07:55.100 --> 00:07:59.460
As you walk out of the
Air and Space Museum

00:07:59.460 --> 00:08:02.160
and walk down the street, you'll
be passing the different bodies

00:08:02.160 --> 00:08:03.610
in our solar system.

00:08:03.610 --> 00:08:05.560
And so just as a
quick little review

00:08:05.560 --> 00:08:08.220
to kind of get us situated
and to ask the questions

00:08:08.220 --> 00:08:10.240
that little kiddies
might ask us,

00:08:10.240 --> 00:08:14.434
how far is it from
the earth to the sun?

00:08:14.434 --> 00:08:15.790
AUDIENCE: 93 million miles.

00:08:15.790 --> 00:08:16.850
PROFESSOR: About
100 million miles.

00:08:16.850 --> 00:08:17.350
Yeah.

00:08:17.350 --> 00:08:19.420
93 million miles.

00:08:19.420 --> 00:08:22.580
Plus or minus somewhere in
the range of maybe a percent

00:08:22.580 --> 00:08:26.224
or so, a few percent
depending on what time of year

00:08:26.224 --> 00:08:28.640
we are since we're in a little
bit of an elliptical orbit.

00:08:28.640 --> 00:08:29.140
Good.

00:08:29.140 --> 00:08:32.140
So that's the
distance to the sun.

00:08:32.140 --> 00:08:34.960
It would be about 150
million kilometers.

00:08:34.960 --> 00:08:37.427
How long does it take light
to travel that distance?

00:08:37.427 --> 00:08:38.564
AUDIENCE: Eight minutes.

00:08:38.564 --> 00:08:40.980
PROFESSOR: About eight minutes,
eight and a third minutes,

00:08:40.980 --> 00:08:42.159
right?

00:08:42.159 --> 00:08:44.330
So it takes a little bit
for the light to reach us.

00:08:44.330 --> 00:08:45.300
Good.

00:08:45.300 --> 00:08:48.840
Some more questions-- how
far are the other planets

00:08:48.840 --> 00:08:52.980
in our solar system to the sun,
going in order from Mercury

00:08:52.980 --> 00:08:54.360
out?

00:08:54.360 --> 00:08:56.400
It's to get us situated here.

00:08:56.400 --> 00:08:57.830
If we are, at any
point, planning

00:08:57.830 --> 00:08:59.580
on throwing up satellites
and sending them

00:08:59.580 --> 00:09:01.246
with other planets,
this is a good thing

00:09:01.246 --> 00:09:03.500
to kind of keep in
the back of our minds.

00:09:03.500 --> 00:09:06.080
So if we define an
astronomical unit--

00:09:06.080 --> 00:09:07.580
not in terms of
our national debt,

00:09:07.580 --> 00:09:10.440
but in terms of the distance
from the earth to the sun--

00:09:10.440 --> 00:09:12.860
that's an astronomical unit.

00:09:12.860 --> 00:09:15.510
Mercury would be
somewhere around 0.4.

00:09:15.510 --> 00:09:16.640
Venus 0.7.

00:09:16.640 --> 00:09:18.060
Mars 1.5.

00:09:18.060 --> 00:09:20.160
So that's all kind of in
our neighborhood, right?

00:09:20.160 --> 00:09:22.201
And then from Mars to
Jupiter is a bit of a jump.

00:09:22.201 --> 00:09:23.615
It goes from 1.5 to 5.

00:09:23.615 --> 00:09:26.550
Then from Jupiter to
Saturn is 10-- well, sorry.

00:09:26.550 --> 00:09:28.620
10 is the distance
from Saturn to the Sun.

00:09:28.620 --> 00:09:31.580
And then 30 and then 40.

00:09:31.580 --> 00:09:33.080
Sorry, 10, 20, 30, 40.

00:09:33.080 --> 00:09:36.600
So it goes-- Jupiter's
5, Saturn 10.

00:09:36.600 --> 00:09:38.000
Uranus would be 20.

00:09:38.000 --> 00:09:38.920
Neptune 30.

00:09:38.920 --> 00:09:39.730
Pluto 40.

00:09:39.730 --> 00:09:42.010
Pluto, planet, sort of.

00:09:42.010 --> 00:09:44.705
So it's easy to remember those
numbers because it goes 5, 10,

00:09:44.705 --> 00:09:46.913
20-- that's just essentially
a sequence of doubling--

00:09:46.913 --> 00:09:48.894
and then 10, 20, 30, 40.

00:09:48.894 --> 00:09:50.560
I'm giving you
approximate numbers here,

00:09:50.560 --> 00:09:53.530
but that's something just
to keep in mind all in terms

00:09:53.530 --> 00:09:54.520
of astronomical units.

00:09:54.520 --> 00:09:56.436
So in case a little kid
comes up and asks you,

00:09:56.436 --> 00:09:59.780
you can spit out the answer.

00:09:59.780 --> 00:10:02.170
Let's talk about the sun.

00:10:02.170 --> 00:10:04.940
This is just a review of
our readings right here.

00:10:04.940 --> 00:10:07.090
This was a
representation of the sun

00:10:07.090 --> 00:10:08.800
and the Earth moving around.

00:10:08.800 --> 00:10:11.602
And what is solstice
and equinox?

00:10:11.602 --> 00:10:12.560
What do those refer to?

00:10:17.250 --> 00:10:20.574
What is the equinox?

00:10:20.574 --> 00:10:22.860
AUDIENCE: Equal amounts
of light and dark.

00:10:22.860 --> 00:10:24.860
PROFESSOR: Yeah, equal
amounts of light and dark

00:10:24.860 --> 00:10:26.610
throughout pretty
much all the world

00:10:26.610 --> 00:10:29.370
except if you're really
standing on the tippy top

00:10:29.370 --> 00:10:30.870
and the bottom.

00:10:30.870 --> 00:10:32.587
So equal amount
of light and dark

00:10:32.587 --> 00:10:34.420
throughout the world
on that particular day.

00:10:34.420 --> 00:10:39.380
So the day and the night have
the same amount of length.

00:10:39.380 --> 00:10:41.560
If you move over to
this region right here,

00:10:41.560 --> 00:10:44.350
this would be a region of our
northern hemisphere summer,

00:10:44.350 --> 00:10:45.750
southern hemisphere, winter.

00:10:45.750 --> 00:10:47.390
Over here, vice versa.

00:10:47.390 --> 00:10:49.855
And the solstice would be?

00:10:49.855 --> 00:10:51.764
AUDIENCE: The shortest
day of the year.

00:10:51.764 --> 00:10:52.430
PROFESSOR: Yeah.

00:10:52.430 --> 00:10:55.500
So the shortest or the
longest day of the year,

00:10:55.500 --> 00:10:57.810
depending on what
side you're on.

00:10:57.810 --> 00:11:01.010
So in the northern
hemisphere, the June solstice

00:11:01.010 --> 00:11:02.860
would be the summer solstice.

00:11:02.860 --> 00:11:04.692
For us, it would
be the longest day.

00:11:04.692 --> 00:11:06.400
And if you're in the
southern hemisphere,

00:11:06.400 --> 00:11:07.580
it would be the shortest day.

00:11:07.580 --> 00:11:09.163
Depending on what
time zone you're in,

00:11:09.163 --> 00:11:12.910
there might be a variation
of one day hither to.

00:11:12.910 --> 00:11:13.440
Good.

00:11:13.440 --> 00:11:14.130
OK.

00:11:14.130 --> 00:11:17.009
And what is this?

00:11:17.009 --> 00:11:18.300
What are the seasons caused by?

00:11:18.300 --> 00:11:20.550
What is this kind
of tilt right here?

00:11:20.550 --> 00:11:21.854
What is that called?

00:11:21.854 --> 00:11:23.020
AUDIENCE: Declination angle.

00:11:23.020 --> 00:11:24.228
PROFESSOR: Declination angle.

00:11:24.228 --> 00:11:26.026
And approximately
how much is that?

00:11:26.026 --> 00:11:26.900
AUDIENCE: 23 and 1/2.

00:11:26.900 --> 00:11:27.970
PROFESSOR: 23 and 1/2.

00:11:27.970 --> 00:11:28.520
23.45.

00:11:28.520 --> 00:11:29.970
Yeah, so 23 1/2 degrees.

00:11:29.970 --> 00:11:30.620
Good.

00:11:30.620 --> 00:11:31.120
OK.

00:11:31.120 --> 00:11:34.740
And we can visualize all
of this on the PV CD-ROM

00:11:34.740 --> 00:11:35.940
on the website.

00:11:35.940 --> 00:11:37.730
So this was part of
your assigned reading.

00:11:37.730 --> 00:11:41.070
And here's the earth
going around the sun

00:11:41.070 --> 00:11:42.592
in this representation.

00:11:42.592 --> 00:11:44.550
Likewise, if you want to
take one of your balls

00:11:44.550 --> 00:11:48.270
and just kind of imagine being
on one of those surfaces,

00:11:48.270 --> 00:11:49.860
you see the diurnal
rotation here.

00:11:49.860 --> 00:11:51.470
It's spinning around its axis.

00:11:51.470 --> 00:11:54.380
And as well, the
seasonal variation as it

00:11:54.380 --> 00:11:56.310
spins around the sun.

00:11:56.310 --> 00:11:58.900
That's important for a
number of reasons, right?

00:11:58.900 --> 00:12:02.020
That will determine how
much sunlight is normally

00:12:02.020 --> 00:12:04.080
incident on the planet.

00:12:04.080 --> 00:12:07.300
If you are normally incident,
if you're at this exact spot

00:12:07.300 --> 00:12:09.720
right here, you're receiving
the sunlight full on.

00:12:09.720 --> 00:12:13.180
But if you're up here
somewhere, your surface normal

00:12:13.180 --> 00:12:15.680
is some vector
pointing out like that.

00:12:15.680 --> 00:12:18.400
You're only going to be
receiving the cosine theta

00:12:18.400 --> 00:12:20.690
of that amount of sun.

00:12:20.690 --> 00:12:24.074
So if you're an extreme
example, if you're right here,

00:12:24.074 --> 00:12:25.240
you're not going to get any.

00:12:25.240 --> 00:12:26.823
But if you're in
this part right here,

00:12:26.823 --> 00:12:29.970
you're going to get cosine
of 0, which would be 1.

00:12:29.970 --> 00:12:31.500
So you get the
full amount of sun.

00:12:31.500 --> 00:12:33.900
And likewise, as you move
through the angles here.

00:12:33.900 --> 00:12:36.510
So it's important to understand
what the relative angle is

00:12:36.510 --> 00:12:40.710
between our surface normal and
the vector pointing at the sun.

00:12:40.710 --> 00:12:42.480
That varies as a
function of season.

00:12:42.480 --> 00:12:44.890
It varies as a function
of time of day.

00:12:44.890 --> 00:12:47.740
And obviously, over
the entire earth,

00:12:47.740 --> 00:12:51.147
you can define the
precise amount of sunlight

00:12:51.147 --> 00:12:52.730
coming in, the precise
solar resource,

00:12:52.730 --> 00:12:54.390
by a series of trig formula.

00:12:54.390 --> 00:12:55.587
It gets pretty complex.

00:12:55.587 --> 00:12:57.670
And this website will
actually walk you through it

00:12:57.670 --> 00:13:00.000
if you're so interested.

00:13:00.000 --> 00:13:02.250
Now this is all review
since folks have all done

00:13:02.250 --> 00:13:03.677
the background ready, right?

00:13:03.677 --> 00:13:05.010
All done the background reading.

00:13:05.010 --> 00:13:07.140
I expect you to before class.

00:13:07.140 --> 00:13:09.310
Let me ask you a few
trickier questions just

00:13:09.310 --> 00:13:11.650
to see if our creative
juices are really moving

00:13:11.650 --> 00:13:13.930
at this early time of day.

00:13:13.930 --> 00:13:17.060
When would be the
shortest day of the year?

00:13:17.060 --> 00:13:17.810
Let's start there.

00:13:17.810 --> 00:13:19.955
The shortest day of the year
is approximately December 22,

00:13:19.955 --> 00:13:20.510
right?

00:13:20.510 --> 00:13:21.860
In the solstice.

00:13:21.860 --> 00:13:29.215
When is the latest sunrise and
when is the earliest sunset?

00:13:32.566 --> 00:13:34.315
You might need to pick
up your little ball

00:13:34.315 --> 00:13:38.014
and rotate it around.

00:13:38.014 --> 00:13:40.590
Does anybody have
even just a gut sense?

00:13:40.590 --> 00:13:42.580
Would it be on the solstice?

00:13:42.580 --> 00:13:45.260
How many people think it's going
to be exactly on the solstice?

00:13:45.260 --> 00:13:45.760
Let's see.

00:13:45.760 --> 00:13:47.590
Earliest sunset--
how many people

00:13:47.590 --> 00:13:49.173
think that the
earliest sunset's going

00:13:49.173 --> 00:13:51.270
to be a little bit
before the solstice?

00:13:51.270 --> 00:13:53.520
How many people think a
little bit after the solstice?

00:13:53.520 --> 00:13:55.570
I know people don't really know.

00:13:55.570 --> 00:13:59.680
The reality is that the earliest
sunset would be a little bit

00:13:59.680 --> 00:14:04.070
before the solstice here,
and the latest sunrise

00:14:04.070 --> 00:14:06.790
would be a little bit
after the solstice.

00:14:06.790 --> 00:14:09.030
And it flips in summertime.

00:14:09.030 --> 00:14:15.510
It would be, let's see,
the earliest sunrise

00:14:15.510 --> 00:14:18.780
and the latest sunset before
and after the solstice

00:14:18.780 --> 00:14:20.380
respectively.

00:14:20.380 --> 00:14:20.880
OK.

00:14:20.880 --> 00:14:23.030
And you can think
about that in terms

00:14:23.030 --> 00:14:26.050
of what is the solar noon.

00:14:26.050 --> 00:14:29.830
The solar noon is when the
sun this is directly overhead

00:14:29.830 --> 00:14:32.200
relative to our
chronological noon, which

00:14:32.200 --> 00:14:36.350
is, I would say, less
dependent on the specific angle

00:14:36.350 --> 00:14:38.320
of the earth relative
to the sun as it

00:14:38.320 --> 00:14:41.126
moves around this trajectory.

00:14:41.126 --> 00:14:42.750
Let's get more into
that in recitation.

00:14:42.750 --> 00:14:44.750
I sense since there wasn't
much traction there I

00:14:44.750 --> 00:14:47.310
don't want to dwell.

00:14:47.310 --> 00:14:49.370
OK.

00:14:49.370 --> 00:14:51.230
Good, good, good.

00:14:51.230 --> 00:14:53.290
OK.

00:14:53.290 --> 00:14:55.230
Let's think a little
bit more in terms

00:14:55.230 --> 00:15:00.270
of the trajectory
of the sun later on

00:15:00.270 --> 00:15:02.920
as we move through some of
the introductory material.

00:15:02.920 --> 00:15:04.599
I don't want to dwell too much.

00:15:04.599 --> 00:15:06.140
I want to give a
little bit of review

00:15:06.140 --> 00:15:09.870
since I'm sensing that not
everybody did the readings.

00:15:09.870 --> 00:15:11.600
I expect you to do
the readings, folks.

00:15:11.600 --> 00:15:13.250
So let's keep with me here.

00:15:13.250 --> 00:15:16.440
So a touch of history,
since that was asked for.

00:15:16.440 --> 00:15:17.530
It was requested.

00:15:17.530 --> 00:15:20.560
I decided to launch a
little bit into a history

00:15:20.560 --> 00:15:22.660
of the study of the sun.

00:15:22.660 --> 00:15:27.500
Philosophers, going back to what
I suppose most would consider

00:15:27.500 --> 00:15:29.980
early India, studied the sun.

00:15:29.980 --> 00:15:34.910
There were some writings of
some of the earlier philosophers

00:15:34.910 --> 00:15:36.340
that were recorded.

00:15:36.340 --> 00:15:37.890
Some have interpreted
these writings

00:15:37.890 --> 00:15:41.570
as being indicative of,
perhaps, heliocentric models.

00:15:41.570 --> 00:15:43.900
These are poetry, folks.

00:15:43.900 --> 00:15:47.280
It's a very different
style of communication

00:15:47.280 --> 00:15:49.279
than what we have today
of technical writing,

00:15:49.279 --> 00:15:51.320
so it's difficult for us
to discern, or difficult

00:15:51.320 --> 00:15:54.820
for me, at least, to discern
when I read the lines verbatim

00:15:54.820 --> 00:15:58.490
if this is really
somebody thinking

00:15:58.490 --> 00:16:00.490
about the heliocentric
model or whether this

00:16:00.490 --> 00:16:02.594
is somebody just
describing the universe

00:16:02.594 --> 00:16:03.885
in the best of their abilities.

00:16:07.410 --> 00:16:10.850
I would say the real beginnings
of heliocentric models

00:16:10.850 --> 00:16:14.730
began in the third century
Before the Common Era

00:16:14.730 --> 00:16:17.750
and the notions of
interstellar distances

00:16:17.750 --> 00:16:20.030
estimated in a similar
manner to what we just

00:16:20.030 --> 00:16:21.280
walked through today, right?

00:16:21.280 --> 00:16:23.640
Estimating the distance
between the earth and the sun

00:16:23.640 --> 00:16:26.950
and then using that as a
measure or yardstick with which

00:16:26.950 --> 00:16:29.250
to measure the distances
to the other planets

00:16:29.250 --> 00:16:32.100
began somewhere
during that time.

00:16:32.100 --> 00:16:35.220
Likewise, these writings
of old made their way

00:16:35.220 --> 00:16:36.090
to the Middle East.

00:16:36.090 --> 00:16:38.690
And in the 10th
and 11th centuries

00:16:38.690 --> 00:16:41.190
of the Common Era,
the Middle East,

00:16:41.190 --> 00:16:46.450
the Arab world is really where
science and technology was at.

00:16:46.450 --> 00:16:49.080
And these days, I
mean, Europe was still

00:16:49.080 --> 00:16:51.780
largely mired in
the Middle Ages,

00:16:51.780 --> 00:16:53.620
starting to emerge
in a few places.

00:16:53.620 --> 00:16:57.330
But by and large, the
carriers of civilization

00:16:57.330 --> 00:17:00.750
in the Western world
were really centered

00:17:00.750 --> 00:17:03.020
and in some of the Arab
cities in the Middle East.

00:17:03.020 --> 00:17:07.420
And al-Biruni, in
particular, was very avid

00:17:07.420 --> 00:17:11.400
at applying methods of
astronomical observation,

00:17:11.400 --> 00:17:15.230
in particular to aid travel,
but in the process, discovering

00:17:15.230 --> 00:17:19.250
a thing or two about
our known universe.

00:17:19.250 --> 00:17:22.329
And of course, finally,
Johannes Kepler in Europe,

00:17:22.329 --> 00:17:25.410
once it starts to emerge
from the Middle Ages,

00:17:25.410 --> 00:17:30.680
with really taking observation
some other scientists, who

00:17:30.680 --> 00:17:32.990
very carefully plotted
out the position

00:17:32.990 --> 00:17:34.912
of the different
bodies, he came up

00:17:34.912 --> 00:17:36.620
with some of the
mathematical models that

00:17:36.620 --> 00:17:40.250
describe the motion of the
planets through the skies

00:17:40.250 --> 00:17:42.390
and is largely credited
with developing

00:17:42.390 --> 00:17:46.180
a series of laws that define
interplanetary motion.

00:17:46.180 --> 00:17:48.412
So a couple of
interesting things to note

00:17:48.412 --> 00:17:49.870
is that international
collaboration

00:17:49.870 --> 00:17:50.940
was really essential.

00:17:50.940 --> 00:17:53.520
These ideas didn't
develop in isolation.

00:17:53.520 --> 00:17:56.530
They were flowing
throughout the world.

00:17:56.530 --> 00:17:58.710
It's important to know
that many of the scientists

00:17:58.710 --> 00:18:00.430
were well-traveled
polyglots, meaning

00:18:00.430 --> 00:18:01.780
they spoke different languages.

00:18:01.780 --> 00:18:03.946
And that's how they were
able to interpret the texts

00:18:03.946 --> 00:18:05.970
and readings of other people.

00:18:05.970 --> 00:18:08.180
And it's also to note
that parallel astronomical

00:18:08.180 --> 00:18:11.570
developments were happening in
other regions of the world--

00:18:11.570 --> 00:18:14.490
the Far East, Mesoamerica,
and so forth, right?

00:18:14.490 --> 00:18:19.570
And so obviously, there may
have been some communication--

00:18:19.570 --> 00:18:22.770
I would say rather
sparse-- between especially

00:18:22.770 --> 00:18:23.820
with the Far East.

00:18:23.820 --> 00:18:26.230
But there was a fair
amount of communication

00:18:26.230 --> 00:18:28.860
between these regions here.

00:18:28.860 --> 00:18:31.660
And you can imagine writings
or ideas traveling from word

00:18:31.660 --> 00:18:34.450
of mouth along trade routes.

00:18:34.450 --> 00:18:36.922
So there was some communication.

00:18:36.922 --> 00:18:38.380
So back to our
learning objectives.

00:18:38.380 --> 00:18:41.040
Today, we're about to quantify
the available solar resource

00:18:41.040 --> 00:18:43.710
relative to human energies
and other fuel sources.

00:18:43.710 --> 00:18:44.440
So let's do that.

00:18:44.440 --> 00:18:46.065
We'll jump right into
one of the slides

00:18:46.065 --> 00:18:47.260
that I showed you last time.

00:18:47.260 --> 00:18:49.430
This is in terms
of terawatts av.

00:18:49.430 --> 00:18:52.780
Terawatts is a unit of
power, a very big one.

00:18:52.780 --> 00:18:55.240
"Tera" is 10 to the 12.

00:18:55.240 --> 00:18:57.610
And you can see
here the resource

00:18:57.610 --> 00:19:00.310
of the sun relative to the
wind energy resource base

00:19:00.310 --> 00:19:01.930
relative to human energy needs.

00:19:01.930 --> 00:19:05.470
If we just consider the resource
falling on the earth's surface,

00:19:05.470 --> 00:19:07.910
as opposed to that falling
on the outer atmosphere,

00:19:07.910 --> 00:19:09.368
there's a little
bit of a discount.

00:19:09.368 --> 00:19:12.660
But we're still very large
compared to human energy use.

00:19:12.660 --> 00:19:15.250
And if we redefine our
units from terawatts

00:19:15.250 --> 00:19:18.900
into HECs, which are Human
Energy Consumptions, defined

00:19:18.900 --> 00:19:23.220
in, say, 2050, where
one HEC is the average,

00:19:23.220 --> 00:19:28.880
let's say, energy
burn rate of 2050,

00:19:28.880 --> 00:19:30.460
you can see here
that these numbers

00:19:30.460 --> 00:19:33.060
are a few orders of
magnitude larger than what

00:19:33.060 --> 00:19:34.250
our human needs are.

00:19:34.250 --> 00:19:37.200
So if you were able
to capture only 1%

00:19:37.200 --> 00:19:40.500
of all of the solar resource
falling on the earth's crust,

00:19:40.500 --> 00:19:44.130
we would be actually
in pretty good shape.

00:19:44.130 --> 00:19:48.264
And 1% of the total land
area on the earth's crust--

00:19:48.264 --> 00:19:50.680
I believe somewhere between
1% and 2% of the United States

00:19:50.680 --> 00:19:53.530
is covered in asphalt
right now for roads.

00:19:53.530 --> 00:19:56.640
So this could be on houses,
on rooftops, on buildings,

00:19:56.640 --> 00:19:57.500
and so forth.

00:19:57.500 --> 00:20:01.530
We wouldn't necessarily
have to exclusively repave

00:20:01.530 --> 00:20:05.520
virgin farmland
with solar panels.

00:20:05.520 --> 00:20:09.020
So going back to quantifying the
solar power, we have our sun.

00:20:09.020 --> 00:20:10.700
We're going to
start by quantifying

00:20:10.700 --> 00:20:13.970
the solar resource by assuming
that the sun is a black body.

00:20:13.970 --> 00:20:17.210
The same way that hot
objects emit light-- say,

00:20:17.210 --> 00:20:18.880
for example, when you
turn up your stove

00:20:18.880 --> 00:20:23.200
and you have a very warm
glow coming out of it--

00:20:23.200 --> 00:20:26.500
the sun is as well a hot
body, a black body, sorry.

00:20:26.500 --> 00:20:28.850
Very hot as well, somewhere
around 6,000 Kelvin.

00:20:28.850 --> 00:20:33.140
And the total radiated power is
given by Stefan Boltzmann's law

00:20:33.140 --> 00:20:35.940
here in the following way
where we have temperature

00:20:35.940 --> 00:20:38.135
to the fourth and
the temperature

00:20:38.135 --> 00:20:40.460
is somewhere around
6,000 Kelvin.

00:20:40.460 --> 00:20:42.980
And so we have this
power being radiated out

00:20:42.980 --> 00:20:44.280
at the surface of the sun.

00:20:44.280 --> 00:20:48.550
And then, as it travels outward,
it becomes, you could say,

00:20:48.550 --> 00:20:49.530
diluted in effect.

00:20:49.530 --> 00:20:53.700
Because the total surface area
of that sphere is increasing,

00:20:53.700 --> 00:20:55.060
obviously as r squared.

00:20:55.060 --> 00:20:57.530
And so by the time that that
light reaches the earth,

00:20:57.530 --> 00:20:59.660
it's only a very
small cross section,

00:20:59.660 --> 00:21:02.500
or very small solid
angle to be more precise,

00:21:02.500 --> 00:21:06.090
of the sun's surface that is
radiating directly at the earth

00:21:06.090 --> 00:21:08.947
right here because this, in the
absence of scattering centers

00:21:08.947 --> 00:21:10.780
in the universe that
might reflect or bounce

00:21:10.780 --> 00:21:12.774
the light back toward the earth.

00:21:12.774 --> 00:21:14.690
And you can calculate
the total power incident

00:21:14.690 --> 00:21:17.210
on the earth by that
simple formula right there.

00:21:17.210 --> 00:21:20.070
What is the radius of the earth?

00:21:20.070 --> 00:21:22.130
Again, one of these
simple numbers

00:21:22.130 --> 00:21:23.630
you should kind of
having your head.

00:21:23.630 --> 00:21:27.010
6,370 kilometers, somewhere
in that order, right?

00:21:27.010 --> 00:21:31.390
And so you can begin
estimating here the total power

00:21:31.390 --> 00:21:32.850
and the order of magnitude.

00:21:32.850 --> 00:21:35.250
It's going to be tiny
compared to the total power

00:21:35.250 --> 00:21:37.110
that the sun is
radiating thankfully,

00:21:37.110 --> 00:21:39.220
or else we'd be
pretty hot right now.

00:21:39.220 --> 00:21:43.910
So the average power
coming from the sun

00:21:43.910 --> 00:21:46.680
on the surface of
the outer atmosphere

00:21:46.680 --> 00:21:49.860
is around 1,366 watts
per square meter.

00:21:49.860 --> 00:21:51.525
Who's heard of 1,366 before?

00:21:51.525 --> 00:21:52.150
AUDIENCE: Yeah.

00:21:52.150 --> 00:21:52.310
PROFESSOR: Yeah?

00:21:52.310 --> 00:21:53.010
You've heard about it?

00:21:53.010 --> 00:21:53.509
All right.

00:21:53.509 --> 00:21:55.220
You know where the
number comes from now.

00:21:55.220 --> 00:21:56.880
It's pretty wonky.

00:21:56.880 --> 00:21:59.390
1366 is a startup
company, a spin-off

00:21:59.390 --> 00:22:02.251
of MIT focused on solar energy.

00:22:02.251 --> 00:22:02.750
OK.

00:22:02.750 --> 00:22:06.640
And so that's at the equinox,
which we just learned

00:22:06.640 --> 00:22:09.320
is occurring somewhere
around March 21,

00:22:09.320 --> 00:22:11.750
September 21-- coming up soon.

00:22:11.750 --> 00:22:13.440
Celebration.

00:22:13.440 --> 00:22:15.620
The ratio of the surface
areas of the spheres

00:22:15.620 --> 00:22:17.970
is really something to
keep in mind right there.

00:22:17.970 --> 00:22:18.980
OK.

00:22:18.980 --> 00:22:21.690
So we've quantified
the available resource

00:22:21.690 --> 00:22:23.300
relative to human energy needs.

00:22:23.300 --> 00:22:26.420
Now we have to come
up with some language

00:22:26.420 --> 00:22:28.340
that we use to
describe the sunlight

00:22:28.340 --> 00:22:30.460
moving through the
atmosphere of the earth

00:22:30.460 --> 00:22:32.700
and reaching the surface
of the earth, right?

00:22:32.700 --> 00:22:34.860
So we're going to use
what's called the air mass

00:22:34.860 --> 00:22:36.660
convention or AM convention.

00:22:36.660 --> 00:22:39.226
AM stands for Air Mass.

00:22:39.226 --> 00:22:41.600
Even without knowing much
about how the light is absorbed

00:22:41.600 --> 00:22:43.270
or how to quantify
it mathematically,

00:22:43.270 --> 00:22:46.980
we can assume that our
atmosphere contains molecules.

00:22:46.980 --> 00:22:48.490
It contains particulate matter.

00:22:48.490 --> 00:22:50.380
And that's going to interact
with the light in some ways.

00:22:50.380 --> 00:22:52.437
Probably either going
to absorb or scatter it.

00:22:52.437 --> 00:22:54.520
And so as the light passes
through our atmosphere,

00:22:54.520 --> 00:22:56.220
there's going to
be some absorption.

00:22:56.220 --> 00:22:58.792
And the greater the distance,
the greater the optical path

00:22:58.792 --> 00:23:01.250
length through the atmosphere,
the more absorption and more

00:23:01.250 --> 00:23:02.520
scattering there will be.

00:23:02.520 --> 00:23:05.070
And so we use air
mass, or AM convention,

00:23:05.070 --> 00:23:07.520
to define the path length
or the path distance

00:23:07.520 --> 00:23:08.570
through the atmosphere.

00:23:08.570 --> 00:23:11.160
AM0 would mean the
outer atmosphere.

00:23:11.160 --> 00:23:13.950
AM1 would be essentially
just going straight through,

00:23:13.950 --> 00:23:17.060
normal incidence so that the
direction of the trajectory

00:23:17.060 --> 00:23:19.970
of the light is parallel
to the surface normal

00:23:19.970 --> 00:23:21.580
of the earth at that location.

00:23:21.580 --> 00:23:23.200
And then air mass
1.5 and so forth

00:23:23.200 --> 00:23:26.039
is as we increase the
angle of the entry of light

00:23:26.039 --> 00:23:27.330
relative to the surface normal.

00:23:27.330 --> 00:23:28.967
So in other words,
as we go further

00:23:28.967 --> 00:23:30.550
from the equator to
northern latitudes

00:23:30.550 --> 00:23:32.770
that air mass number is
going to go up, up, up.

00:23:32.770 --> 00:23:33.270
OK.

00:23:33.270 --> 00:23:34.740
We'll explain it
with a few graphs

00:23:34.740 --> 00:23:36.710
and figures and a few slides.

00:23:36.710 --> 00:23:39.350
So we have our
atmospheric absorption.

00:23:39.350 --> 00:23:42.480
When we just glance at the earth
in these beautiful pictures

00:23:42.480 --> 00:23:46.290
taken from outer space, we can
see very obviously the clouds

00:23:46.290 --> 00:23:47.180
present.

00:23:47.180 --> 00:23:49.850
And more importantly,
if we were to zoom

00:23:49.850 --> 00:23:51.940
in on one of these
regions right here,

00:23:51.940 --> 00:23:56.980
we would see this
bluish hue coming

00:23:56.980 --> 00:24:00.460
from our atmosphere, which
is scattering preferentially

00:24:00.460 --> 00:24:02.410
the shorter
wavelengths of light.

00:24:02.410 --> 00:24:05.090
And more importantly,
this radius right here

00:24:05.090 --> 00:24:07.870
is somewhere on the order
of 6,370 kilometers.

00:24:07.870 --> 00:24:10.572
And this thin atmospheric
shell in on the order of 30.

00:24:10.572 --> 00:24:12.020
Right?

00:24:12.020 --> 00:24:14.200
So that's why you
don't really see

00:24:14.200 --> 00:24:18.340
too much of a ring around the
planet from this distance.

00:24:18.340 --> 00:24:20.910
So the atmospheric effects,
let's try to bend them

00:24:20.910 --> 00:24:22.880
into discrete buckets.

00:24:22.880 --> 00:24:25.120
This is a simplification,
but it helps us gain

00:24:25.120 --> 00:24:26.310
a foothold in understanding.

00:24:26.310 --> 00:24:28.520
And then from there, we
can make our understanding

00:24:28.520 --> 00:24:30.190
a bit more complex.

00:24:30.190 --> 00:24:33.180
So we have incoming solar
radiation coming from here.

00:24:33.180 --> 00:24:37.480
We have a number now that's
342 watts per square meter.

00:24:37.480 --> 00:24:40.584
Why is that number so
much lower than the 1,366

00:24:40.584 --> 00:24:42.480
that we were just talking about?

00:24:49.786 --> 00:24:51.619
AUDIENCE: Particles in
the air and pollution

00:24:51.619 --> 00:24:52.894
in the atmosphere.

00:24:52.894 --> 00:24:53.560
PROFESSOR: Yeah.

00:24:53.560 --> 00:24:56.070
So this is meant
to be an average

00:24:56.070 --> 00:24:59.160
over the entire day at one fixed
point along the ground, right?

00:24:59.160 --> 00:25:01.860
So as we're rotating around, we
have at least half of the day

00:25:01.860 --> 00:25:03.510
normally when we
don't have sunlight.

00:25:03.510 --> 00:25:06.950
And then there's, I would
say, the cosine theta angle

00:25:06.950 --> 00:25:09.160
is not 1 at all times.

00:25:09.160 --> 00:25:11.220
It's very rarely 1.

00:25:11.220 --> 00:25:13.980
And so this is a bit of a
discounted incoming solar

00:25:13.980 --> 00:25:16.460
radiation, essentially a
time-averaged solar radiation

00:25:16.460 --> 00:25:20.490
for a given patch of the
planet over a typical day.

00:25:20.490 --> 00:25:22.890
And so we have a variety
of processes here.

00:25:22.890 --> 00:25:25.140
We have reflection
off of clouds.

00:25:25.140 --> 00:25:26.840
That's pretty clear
to see from here.

00:25:26.840 --> 00:25:29.240
It looks nice and white.

00:25:29.240 --> 00:25:31.380
We have some absorbed
by the atmosphere,

00:25:31.380 --> 00:25:35.570
typically in a rotational or
vibrational modes of molecules

00:25:35.570 --> 00:25:38.100
up in the outer atmosphere,
sometimes by particulate matter

00:25:38.100 --> 00:25:39.370
as well.

00:25:39.370 --> 00:25:42.120
And then we have
the amount that's

00:25:42.120 --> 00:25:45.350
absorbed here by the surface,
of course, reflected as well.

00:25:45.350 --> 00:25:47.720
And so the amount that's
incident on the surface

00:25:47.720 --> 00:25:49.760
or coming down to us
is what we can actually

00:25:49.760 --> 00:25:51.980
use to make solar energy.

00:25:51.980 --> 00:25:53.350
And this is an average, right?

00:25:53.350 --> 00:25:55.890
Because sometimes the cloud
cover is a lot greater.

00:25:55.890 --> 00:25:58.090
And for that
particular day, we will

00:25:58.090 --> 00:26:00.460
have a lot less resource
striking the ground

00:26:00.460 --> 00:26:02.110
at a given time.

00:26:02.110 --> 00:26:05.740
This over here, this is
all mostly infrared, right?

00:26:05.740 --> 00:26:08.830
Where this is visible coming
in, once the light gets absorbed

00:26:08.830 --> 00:26:10.860
and then gets
re-emitted, it usually

00:26:10.860 --> 00:26:12.740
gets re-emitted in
the longer wavelength

00:26:12.740 --> 00:26:14.620
light or the infrared light.

00:26:14.620 --> 00:26:18.610
And this is the stuff that
gets blocked by or absorbed

00:26:18.610 --> 00:26:21.350
by greenhouse gases and then
re-emitted equiangularly.

00:26:21.350 --> 00:26:24.690
And some of it makes its way
back to the earth, right?

00:26:24.690 --> 00:26:25.190
OK.

00:26:25.190 --> 00:26:28.240
So air mass, let's
define that so

00:26:28.240 --> 00:26:30.070
that we have a common
language that we

00:26:30.070 --> 00:26:33.020
can use to describe the solar
resource from place to place.

00:26:33.020 --> 00:26:34.700
So again, this is the sun.

00:26:34.700 --> 00:26:37.310
This is the surface right here.

00:26:37.310 --> 00:26:41.760
And let's imagine that the angle
between the incident sunlight

00:26:41.760 --> 00:26:45.240
and the surface normal is 0
such that the cosine theta

00:26:45.240 --> 00:26:47.040
term is 1.

00:26:47.040 --> 00:26:49.470
Air mass here at this
point, at this point

00:26:49.470 --> 00:26:53.270
on the surface of the
earth, is going to be AM 1.

00:26:53.270 --> 00:26:56.640
So we call it air mass 1 if
the sun is literally directly

00:26:56.640 --> 00:26:59.570
overhead.

00:26:59.570 --> 00:27:02.100
What did we learn about the
declination angle of the earth?

00:27:02.100 --> 00:27:04.890
It's about 23 and
1/2 degrees, right?

00:27:04.890 --> 00:27:06.430
How far north are we?

00:27:06.430 --> 00:27:09.389
What is our latitude
here in Boston?

00:27:09.389 --> 00:27:09.930
AUDIENCE: 41.

00:27:09.930 --> 00:27:11.720
PROFESSOR: 41, 42ish, right?

00:27:11.720 --> 00:27:22.980
So let's for simplicity say that
here in Boston, our latitude

00:27:22.980 --> 00:27:28.320
of Boston Logan Airport is
approximately 41 degrees north.

00:27:28.320 --> 00:27:36.720
And let's say that the
declination of our planet

00:27:36.720 --> 00:27:41.150
is approximately
23 and 1/2 degrees.

00:27:41.150 --> 00:27:46.270
So what would be the angle
of the sun in the sky

00:27:46.270 --> 00:27:49.730
if you were to lie on your back
in the middle of the summer

00:27:49.730 --> 00:27:52.709
solstice and the middle
of the winter solstice

00:27:52.709 --> 00:27:54.750
and you're lying straight
on your back looking up

00:27:54.750 --> 00:27:57.970
at solar noon, what would the
angle of the sun in the sky

00:27:57.970 --> 00:28:01.070
be relative to the
surface normal?

00:28:01.070 --> 00:28:03.750
How far south would the sun be?

00:28:03.750 --> 00:28:07.200
Imagine that this is 0
degrees and that's 90, right?

00:28:07.200 --> 00:28:09.370
So relative to this
angle right here,

00:28:09.370 --> 00:28:11.620
where would the
sun be in the sky?

00:28:11.620 --> 00:28:15.090
Why don't you turn to your
neighbor right now and discuss?

00:28:15.090 --> 00:28:18.360
On the summer solstice,
the winter solstice,

00:28:18.360 --> 00:28:20.040
come up with some
set of angles there.

00:28:33.212 --> 00:28:33.920
All right, folks.

00:28:33.920 --> 00:28:36.050
What do we come up with?

00:28:36.050 --> 00:28:39.890
This is our little human
being, you, in Boston.

00:28:39.890 --> 00:28:42.260
This is south, and that's north.

00:28:42.260 --> 00:28:45.070
And we're at the solar
noon in the winter solstice

00:28:45.070 --> 00:28:46.300
in the summer solstice.

00:28:46.300 --> 00:28:48.130
So here's you.

00:28:48.130 --> 00:28:50.069
This is directly above.

00:28:50.069 --> 00:28:51.860
So I would say if you're
lying on your back

00:28:51.860 --> 00:28:53.651
and looking straight
up, that's the surface

00:28:53.651 --> 00:28:55.380
normal of the earth.

00:28:55.380 --> 00:28:57.730
In the summer, at
solar noon, the sun

00:28:57.730 --> 00:29:00.170
would be at what angle
relative to the surface

00:29:00.170 --> 00:29:01.206
normal of the earth?

00:29:01.206 --> 00:29:02.424
AUDIENCE: 17 and 1/2.

00:29:02.424 --> 00:29:04.560
PROFESSOR: 17 and 1/2,
somewhere around there.

00:29:04.560 --> 00:29:06.680
And how did you get that number?

00:29:06.680 --> 00:29:08.060
Subtract those two, right?

00:29:08.060 --> 00:29:09.930
So you get 41 minus 23 and 1/2.

00:29:09.930 --> 00:29:14.250
You're somewhere around 17,
18, somewhere around there.

00:29:14.250 --> 00:29:16.940
So we'll call it 18
degrees in summer,

00:29:16.940 --> 00:29:19.210
again, relative to
the surface normal.

00:29:19.210 --> 00:29:24.595
And in wintertime, what
does that work out to be?

00:29:24.595 --> 00:29:25.470
AUDIENCE: 64 and 1/2.

00:29:25.470 --> 00:29:26.480
PROFESSOR: 64 and 1/2.

00:29:26.480 --> 00:29:27.440
Similar logic, right?

00:29:27.440 --> 00:29:30.370
So we'll call it 65
degrees in winter.

00:29:30.370 --> 00:29:31.000
Good.

00:29:31.000 --> 00:29:34.340
So what does that work out
to be in terms of air mass

00:29:34.340 --> 00:29:36.040
for winter and summer?

00:29:38.460 --> 00:29:39.960
Quick engineering
approximation, I'm

00:29:39.960 --> 00:29:42.240
going to say that, in summer,
it's approximate air mass 1,

00:29:42.240 --> 00:29:43.500
but you can calculate
it real quick.

00:29:43.500 --> 00:29:45.584
Somebody with a calculator
want to plug those in?

00:29:45.584 --> 00:29:47.280
AUDIENCE: And
roughly 2 in winter.

00:29:47.280 --> 00:29:48.738
PROFESSOR: And
roughly 2 in winter.

00:29:48.738 --> 00:29:51.250
All right?

00:29:51.250 --> 00:29:52.320
OK.

00:29:52.320 --> 00:29:54.850
We're going to get into
scattering of light

00:29:54.850 --> 00:29:56.920
in next lecture actually.

00:29:56.920 --> 00:29:59.375
And we'll see why that
matters in terms of especially

00:29:59.375 --> 00:30:01.400
of getting sunburned
since the shorter

00:30:01.400 --> 00:30:04.620
wavelengths, the ultraviolet,
are more sensitive to the path

00:30:04.620 --> 00:30:05.900
length.

00:30:05.900 --> 00:30:08.220
OK.

00:30:08.220 --> 00:30:08.790
Good.

00:30:08.790 --> 00:30:09.290
Very good.

00:30:09.290 --> 00:30:12.170
So we have pretty
much a gut sense

00:30:12.170 --> 00:30:14.310
now of where the
sun is in the sky.

00:30:14.310 --> 00:30:17.870
And as it moves from summer to
winter, from our perspective,

00:30:17.870 --> 00:30:19.846
it follows a little
bit of a, I would

00:30:19.846 --> 00:30:21.410
say, sinusoidal path, right?

00:30:21.410 --> 00:30:24.700
It stays in summer for a
long period of time up here.

00:30:24.700 --> 00:30:27.250
And then it moves pretty quickly
down here and stays here.

00:30:27.250 --> 00:30:30.555
So versus time, the angle
of the sun in the sky

00:30:30.555 --> 00:30:33.556
is following a sine curve,
or cosine curve if you will.

00:30:33.556 --> 00:30:34.250
Right?

00:30:34.250 --> 00:30:38.500
And so right now, the sun is
actually close to the middle.

00:30:38.500 --> 00:30:40.140
We're in September 13.

00:30:40.140 --> 00:30:42.930
The solstice is coming
up in a week's time.

00:30:42.930 --> 00:30:45.200
And so the slope
of that sine curve

00:30:45.200 --> 00:30:47.570
is at a maximum right about now.

00:30:47.570 --> 00:30:51.070
And so that the amount of
time that the day will change

00:30:51.070 --> 00:30:53.820
in length is changing
at its greatest point

00:30:53.820 --> 00:30:55.315
right now in the year.

00:30:55.315 --> 00:30:56.850
And so you really
begin to notice it

00:30:56.850 --> 00:30:58.610
if you start paying
attention or if you

00:30:58.610 --> 00:31:00.810
go to weather.com
and start looking up

00:31:00.810 --> 00:31:03.690
how long is today's
day going to last,

00:31:03.690 --> 00:31:05.337
when is the sunset tomorrow.

00:31:05.337 --> 00:31:07.420
I don't know about you
folks, but I like to cycle.

00:31:07.420 --> 00:31:09.790
And when I'm doing
my evening rides,

00:31:09.790 --> 00:31:12.220
I'm noticing it now
that I have to start

00:31:12.220 --> 00:31:14.849
earlier and earlier if I want
to put in, say, 30 or 40 miles.

00:31:14.849 --> 00:31:16.890
I'm not going to be able
to make it home in time.

00:31:16.890 --> 00:31:20.550
So that's the sun
and how it relates

00:31:20.550 --> 00:31:23.170
to you in your daily lives.

00:31:23.170 --> 00:31:25.145
We're going to get back
to this in a minute,

00:31:25.145 --> 00:31:26.020
so keep this in mind.

00:31:26.020 --> 00:31:28.550
Don't let it out of your RAM.

00:31:28.550 --> 00:31:31.900
Let's talk about the actual
solar spectrum for a minute.

00:31:31.900 --> 00:31:35.770
This is the sunlight intensity
in some very real units.

00:31:35.770 --> 00:31:37.020
We'll get to that in a minute.

00:31:37.020 --> 00:31:39.750
But think of this in terms
sort of like the total amount

00:31:39.750 --> 00:31:41.730
of power in a given bandwidth.

00:31:41.730 --> 00:31:44.732
So the wavelength right
here-- or the power density

00:31:44.732 --> 00:31:45.440
in the bandwidth.

00:31:45.440 --> 00:31:47.610
The wavelength is the
wavelength of light.

00:31:47.610 --> 00:31:50.140
Shown for your convenience
here is the visible spectrum.

00:31:50.140 --> 00:31:51.820
That's what our
eye-- mostly what

00:31:51.820 --> 00:31:54.530
our eye-- is able to
detect in this wavelength

00:31:54.530 --> 00:31:55.490
range right here.

00:31:55.490 --> 00:31:58.740
And the sun is emitting
over a much broader range

00:31:58.740 --> 00:31:59.540
of wavelengths.

00:31:59.540 --> 00:32:03.060
It's emitting following
a black body emission

00:32:03.060 --> 00:32:05.035
source at 6,000 Kelvin.

00:32:05.035 --> 00:32:06.410
And that's in this
very difficult

00:32:06.410 --> 00:32:08.790
to see green line right there.

00:32:08.790 --> 00:32:13.604
Air mass 0 spectrum looks like
this, this red line right here.

00:32:13.604 --> 00:32:15.520
And again, let me remind
you that the air mass

00:32:15.520 --> 00:32:18.410
0 is the light that's falling
on the outer atmosphere.

00:32:18.410 --> 00:32:21.390
There is no earth
atmospheric absorption yet.

00:32:21.390 --> 00:32:24.670
Why do we have these
little lines here?

00:32:24.670 --> 00:32:26.920
Do you see it's not
a perfect black body.

00:32:26.920 --> 00:32:30.480
We have some-- I'll give you
a hint-- absorption lines.

00:32:30.480 --> 00:32:32.340
Where is that light
being absorbed?

00:32:32.340 --> 00:32:35.620
Is it the ether between
the earth and the sun?

00:32:35.620 --> 00:32:36.120
No.

00:32:36.120 --> 00:32:37.120
There's no ether between
the earth and sun.

00:32:37.120 --> 00:32:38.578
Where is that light
being absorbed?

00:32:38.578 --> 00:32:40.130
AUDIENCE: Hydrogen
ions and stuff?

00:32:40.130 --> 00:32:41.850
PROFESSOR: In the
sun itself, right?

00:32:41.850 --> 00:32:44.100
So these are absorption
events occurring

00:32:44.100 --> 00:32:46.070
in the solar atmosphere.

00:32:46.070 --> 00:32:49.880
And now, if we do
air mass 1 or 1.5--

00:32:49.880 --> 00:32:53.180
let's push it up a little
bit from air mass 0--

00:32:53.180 --> 00:32:55.255
this is now passing
through an angle

00:32:55.255 --> 00:32:57.590
of somewhere around 60 degrees.

00:32:57.590 --> 00:32:59.420
Now what do we have?

00:32:59.420 --> 00:33:03.320
We have several absorption
lines occurring, right?

00:33:03.320 --> 00:33:05.920
And these correspond to
absorption events where?

00:33:05.920 --> 00:33:07.420
AUDIENCE: In the
earth's atmosphere.

00:33:07.420 --> 00:33:08.280
PROFESSOR: In the
earth's atmosphere.

00:33:08.280 --> 00:33:09.090
Exactly.

00:33:09.090 --> 00:33:11.722
And so we can attribute each of
these little absorption lines

00:33:11.722 --> 00:33:13.180
here to a particular--
usually it's

00:33:13.180 --> 00:33:16.120
a molecule in the
earth's atmosphere.

00:33:16.120 --> 00:33:18.890
Note the sensitivity of
the human in black right

00:33:18.890 --> 00:33:21.310
here and how well-matched
it is to the air mass

00:33:21.310 --> 00:33:23.500
1, air mass 1.5 spectrum.

00:33:23.500 --> 00:33:25.330
That's pretty cool.

00:33:25.330 --> 00:33:26.680
That's pretty cool.

00:33:26.680 --> 00:33:27.960
OK.

00:33:27.960 --> 00:33:30.050
So there you have the spectrum.

00:33:30.050 --> 00:33:34.460
Let's get to these units of
power density per bandwidth

00:33:34.460 --> 00:33:35.480
for a second.

00:33:35.480 --> 00:33:36.930
The way to think
about those units

00:33:36.930 --> 00:33:39.270
is as follows-- kilowatts
per meter squared.

00:33:39.270 --> 00:33:40.030
OK, I get that.

00:33:40.030 --> 00:33:43.340
It's the amount of power
falling on a unit area.

00:33:43.340 --> 00:33:46.220
Per micron, the reason
it's normalized per micron

00:33:46.220 --> 00:33:48.846
is because the wavelength
units right here is in microns.

00:33:48.846 --> 00:33:50.470
And if you take the
product of the two,

00:33:50.470 --> 00:33:52.460
it makes it pretty easy to
calculate the total power

00:33:52.460 --> 00:33:53.190
density, right?

00:33:53.190 --> 00:33:57.050
So if you want to calculate the
power density, the total watts

00:33:57.050 --> 00:33:59.440
per square meter,
falling on the earth,

00:33:59.440 --> 00:34:01.600
say, between 0.5
and 1 micron, you

00:34:01.600 --> 00:34:03.650
can calculate the
total amount of power

00:34:03.650 --> 00:34:05.204
by multiplying one
versus the other.

00:34:05.204 --> 00:34:07.370
So that's why they're in
this weird unit right here.

00:34:07.370 --> 00:34:09.212
It's to help you
perform calculations

00:34:09.212 --> 00:34:10.920
like the ones you'll
do in your homework,

00:34:10.920 --> 00:34:13.440
like the ones you'll do for
your class project and so forth.

00:34:13.440 --> 00:34:16.760
And it strikes a little bit odd
the first time you look at it,

00:34:16.760 --> 00:34:18.110
but it begins making sense.

00:34:18.110 --> 00:34:20.540
And you're appreciative
of it after a while.

00:34:20.540 --> 00:34:22.400
There are standard spectra.

00:34:22.400 --> 00:34:23.989
They're standard
reference spectra.

00:34:23.989 --> 00:34:26.880
Sure, you can go
outside and using

00:34:26.880 --> 00:34:28.230
some form of spectrophotometer.

00:34:28.230 --> 00:34:31.639
You can measure the incident
solar radiation and map

00:34:31.639 --> 00:34:35.739
out the spectral irradiance
as a function of wavelength.

00:34:35.739 --> 00:34:39.540
In terms of the planning
or communicating

00:34:39.540 --> 00:34:42.760
with other scientists, we
typically refer to standards.

00:34:42.760 --> 00:34:45.090
We use common yardsticks,
common metrics.

00:34:45.090 --> 00:34:46.830
And that facilitates
communication,

00:34:46.830 --> 00:34:49.550
avoids ambiguity,
avoids misunderstanding.

00:34:49.550 --> 00:34:52.860
And so these standards
right here, these ASTMs,

00:34:52.860 --> 00:34:55.370
refer to the
particular standards

00:34:55.370 --> 00:34:57.226
that are used for
those solar spectra.

00:34:57.226 --> 00:34:58.850
And in your supporting
online material,

00:34:58.850 --> 00:35:01.660
at the very end of the
lecture slides online,

00:35:01.660 --> 00:35:04.650
we go into some more
detail regarding that

00:35:04.650 --> 00:35:06.980
for those who are interested.

00:35:06.980 --> 00:35:09.130
So again, these little
absorption lines

00:35:09.130 --> 00:35:12.260
here correspond to specific
atmospheric events,

00:35:12.260 --> 00:35:15.100
interactions of that
particular wavelength of light

00:35:15.100 --> 00:35:19.650
with some molecule
usually in the atmosphere.

00:35:19.650 --> 00:35:22.400
We can, as well, have
generalized attenuation due

00:35:22.400 --> 00:35:24.140
to other scattering mechanisms.

00:35:24.140 --> 00:35:28.500
Notice right here in the short
wavelengths what's happening.

00:35:28.500 --> 00:35:31.300
From the red to the
blue, this light

00:35:31.300 --> 00:35:33.010
is particularly effective.

00:35:33.010 --> 00:35:35.520
We have a sharp drop in
the shorter wavelengths.

00:35:35.520 --> 00:35:39.450
And it grows sharper the
shorter in wavelength you go.

00:35:39.450 --> 00:35:43.500
So the attenuation due to
passing through the atmosphere

00:35:43.500 --> 00:35:47.310
grows or increases the
shorter in wavelength you go.

00:35:47.310 --> 00:35:52.420
And this is a process generally
called Rayleigh scattering.

00:35:52.420 --> 00:35:54.920
And there's a wavelength
to the fourth dependence.

00:35:54.920 --> 00:35:58.310
So as you go shorter and
shorter in wavelength,

00:35:58.310 --> 00:36:00.850
the likelihood or probability
of scattering will increase.

00:36:00.850 --> 00:36:02.380
Why is that pertinent to us?

00:36:02.380 --> 00:36:04.170
Well, now you can
answer that little child

00:36:04.170 --> 00:36:05.930
who walks up to you in the
shopping mall and says,

00:36:05.930 --> 00:36:06.890
why is the sky blue?

00:36:06.890 --> 00:36:11.130
You say, well, there is this
elastic scattering mechanism

00:36:11.130 --> 00:36:14.030
of electromagnetic
radiation whereby

00:36:14.030 --> 00:36:16.520
in a broad spectral event,
such as the sun, black body

00:36:16.520 --> 00:36:18.660
emission, we have the
shorter wavelengths that

00:36:18.660 --> 00:36:19.694
are scattered more.

00:36:19.694 --> 00:36:21.610
And that's why when we
look away from the sun,

00:36:21.610 --> 00:36:24.185
in the other direction, we see
those shorter wavelengths that

00:36:24.185 --> 00:36:25.770
are scattered back to us.

00:36:25.770 --> 00:36:27.270
That is pertinent
for two reasons.

00:36:27.270 --> 00:36:28.970
A, it makes the sky look blue.

00:36:28.970 --> 00:36:32.314
Secondly, it's not only the
short wavelengths in blue light

00:36:32.314 --> 00:36:34.855
that we're worried about, but
also the ultraviolet radiation.

00:36:34.855 --> 00:36:35.650
Right?

00:36:35.650 --> 00:36:40.750
So even on a cloudy day, if
there are a few open patches

00:36:40.750 --> 00:36:43.230
and you can get scattered
light coming in,

00:36:43.230 --> 00:36:44.790
you can still get sunburned.

00:36:44.790 --> 00:36:48.140
And secondly, there is
a very strong dependence

00:36:48.140 --> 00:36:51.400
on the path length, the optical
path length, the air mass,

00:36:51.400 --> 00:36:51.900
right?

00:36:51.900 --> 00:36:54.690
So if you go further north
in latitudes, where your air

00:36:54.690 --> 00:36:57.240
mass increases,
right-- because now,

00:36:57.240 --> 00:36:59.050
if you think about
the atmosphere

00:36:59.050 --> 00:37:00.137
as being kind of a flat.

00:37:00.137 --> 00:37:01.970
Just giving you an
approximation for minute.

00:37:01.970 --> 00:37:03.210
If you think of the
earth being flat

00:37:03.210 --> 00:37:04.585
and the atmosphere
of being flat,

00:37:04.585 --> 00:37:07.480
now the path length in
winter is much, much greater

00:37:07.480 --> 00:37:09.120
than the path length in summer.

00:37:09.120 --> 00:37:11.480
Same sun, just
different path length.

00:37:11.480 --> 00:37:14.880
You're much more likely to
get sunburned in the summer

00:37:14.880 --> 00:37:18.180
than you are in winter
because the path length is

00:37:18.180 --> 00:37:21.919
a lot shorter and the amount
of short wavelength ultraviolet

00:37:21.919 --> 00:37:23.460
radiation that will
be scattered away

00:37:23.460 --> 00:37:26.040
is going to be less in
the summer than in winter.

00:37:26.040 --> 00:37:28.460
That's also why if you go
south latitude, for example,

00:37:28.460 --> 00:37:31.160
from here to, say, Miami, your
incidence of getting sunburned

00:37:31.160 --> 00:37:35.085
is a lot greater, a lot
more than the total increase

00:37:35.085 --> 00:37:36.710
of the visible portion
of the spectrum.

00:37:36.710 --> 00:37:39.120
So the sun might not look
that different to you,

00:37:39.120 --> 00:37:42.850
but your incidence of sunburn
events goes up quite a bit.

00:37:42.850 --> 00:37:45.050
And that is due to
Rayleigh scattering.

00:37:45.050 --> 00:37:47.240
And now, by this
point, the little child

00:37:47.240 --> 00:37:49.310
has already run crying
back to the parent.

00:37:49.310 --> 00:37:51.530
But you have a full
satisfaction of knowing

00:37:51.530 --> 00:37:53.820
how the universe around
you is put together.

00:37:53.820 --> 00:37:56.620
And that actually was
a pretty deep problem.

00:37:56.620 --> 00:38:00.810
It took a long time for at
least European scientists

00:38:00.810 --> 00:38:04.810
to crack that nut and figure
out what was going on.

00:38:04.810 --> 00:38:07.430
Describe how solar
insulation maps are made

00:38:07.430 --> 00:38:10.230
and use them to estimate
the local solar resource.

00:38:10.230 --> 00:38:12.184
So we have metrology.

00:38:12.184 --> 00:38:13.600
We have techniques
that we can use

00:38:13.600 --> 00:38:16.380
to measure the amount of
sunlight that is out there.

00:38:16.380 --> 00:38:19.880
And now we want to apply those
in some systematic fashion

00:38:19.880 --> 00:38:23.680
to measure the average solar
resource around the planet,

00:38:23.680 --> 00:38:26.820
including the oceans, and
then use that information

00:38:26.820 --> 00:38:30.580
to estimate later on the
land area needed, or the size

00:38:30.580 --> 00:38:32.250
of the array, or
how many cells we're

00:38:32.250 --> 00:38:34.880
going to have to string together
based on the solar resource

00:38:34.880 --> 00:38:35.380
locally.

00:38:35.380 --> 00:38:37.390
So how are these
insulation maps made,

00:38:37.390 --> 00:38:40.880
these maps that we'll use as
engineers to size our systems?

00:38:40.880 --> 00:38:43.150
First off, let me
define insolation.

00:38:43.150 --> 00:38:45.737
This is not insulation, as in
stuff you put around the house

00:38:45.737 --> 00:38:47.070
to keep the heat from going out.

00:38:47.070 --> 00:38:49.980
This is insolation with
an "o," a shorthand

00:38:49.980 --> 00:38:51.820
for incoming solar radiation.

00:38:51.820 --> 00:38:53.360
Insolation at the top there.

00:38:53.360 --> 00:38:56.130
It's typically given in units
of energy per unit area per unit

00:38:56.130 --> 00:38:59.650
time, so kilowatt
hours-- that's energy--

00:38:59.650 --> 00:39:01.376
per meter squared per day.

00:39:01.376 --> 00:39:04.000
And it's helpful when designing
or projecting these PV systems.

00:39:04.000 --> 00:39:06.290
And it's affected by a bunch
of stuff, which we'll get

00:39:06.290 --> 00:39:07.510
to over the next few slides.

00:39:07.510 --> 00:39:11.180
So we can measure
insolation from the ground.

00:39:11.180 --> 00:39:13.700
That's a surefire way to do it.

00:39:13.700 --> 00:39:16.930
This right here
is a pyranometer.

00:39:16.930 --> 00:39:20.130
Pyro, fire, sun.

00:39:20.130 --> 00:39:21.990
Ano, on top of.

00:39:21.990 --> 00:39:23.890
So anode/cathode.

00:39:23.890 --> 00:39:25.130
Cata, under.

00:39:25.130 --> 00:39:26.530
Ano, above.

00:39:26.530 --> 00:39:27.591
Catatonic, under.

00:39:27.591 --> 00:39:28.090
Right?

00:39:28.090 --> 00:39:28.890
OK.

00:39:28.890 --> 00:39:29.780
So pyranometer.

00:39:29.780 --> 00:39:32.600
So it's basically measuring
the sun above, right?

00:39:32.600 --> 00:39:34.120
Measuring the sunlight above.

00:39:34.120 --> 00:39:37.837
This is a full hemisphere
measuring the sunlight

00:39:37.837 --> 00:39:38.920
coming in from all angles.

00:39:38.920 --> 00:39:40.628
There's a small little
sensor right here.

00:39:40.628 --> 00:39:41.470
It's lying flat.

00:39:41.470 --> 00:39:43.510
And that glass is essentially
allowing the light

00:39:43.510 --> 00:39:46.270
from different angles
to get into the sensor.

00:39:46.270 --> 00:39:49.410
And this is a very narrow,
solid angle of the sky.

00:39:49.410 --> 00:39:51.420
It's probably just
looking at the sun,

00:39:51.420 --> 00:39:54.300
or in a particular direction
rather, plus or minus 2 and 1/2

00:39:54.300 --> 00:39:56.480
degrees in either direction.

00:39:56.480 --> 00:39:59.830
So it's a very limited
solid angle of the sky.

00:39:59.830 --> 00:40:02.130
This one over here would
be more appropriate, say,

00:40:02.130 --> 00:40:04.380
for a flat panel that's
receiving scattered light

00:40:04.380 --> 00:40:06.030
coming in at all angles.

00:40:06.030 --> 00:40:08.700
This one over here would be
more appropriate for a tracking

00:40:08.700 --> 00:40:11.460
system, especially a
concentrator system that

00:40:11.460 --> 00:40:13.850
has optics that only
accept light in from a very

00:40:13.850 --> 00:40:15.100
limited solid angle.

00:40:15.100 --> 00:40:17.830
So imagine you have a lens that
has to have like incident to it

00:40:17.830 --> 00:40:19.560
to focus it on the right spot.

00:40:19.560 --> 00:40:21.927
And if the sun moves in the
wrong spot or the-- put it

00:40:21.927 --> 00:40:24.010
another way-- if the lens
is in the wrong position

00:40:24.010 --> 00:40:26.270
relative to the incident
solar radiation,

00:40:26.270 --> 00:40:28.600
the light is being focused
off of the solar cell.

00:40:28.600 --> 00:40:30.260
And it doesn't
produce any power.

00:40:30.260 --> 00:40:35.110
So this is a system
that's used for measuring

00:40:35.110 --> 00:40:36.820
the direct solar
spectrum, which will

00:40:36.820 --> 00:40:39.920
be useful for calculating the
total output from concentrator

00:40:39.920 --> 00:40:40.940
systems.

00:40:40.940 --> 00:40:42.570
And this pyranometer
over here is

00:40:42.570 --> 00:40:46.870
useful for flat panel systems.

00:40:46.870 --> 00:40:49.587
And we can also measure
the total amount

00:40:49.587 --> 00:40:51.920
of incident solar radiation,
total amount of insolation,

00:40:51.920 --> 00:40:54.690
from the sky using
satellite imagery.

00:40:54.690 --> 00:40:57.640
This is an example
of a measurement.

00:40:57.640 --> 00:41:00.460
And this right here is
insolation, average insolation,

00:41:00.460 --> 00:41:04.520
from 0 to 550 watts
per square meter taken

00:41:04.520 --> 00:41:08.560
from a NASA satellite with
the NASA Earth Observatory.

00:41:08.560 --> 00:41:10.950
Very cool website, great
place to spend a Friday night

00:41:10.950 --> 00:41:12.390
if you don't have plans.

00:41:12.390 --> 00:41:15.740
Just log on here, and
bunches of maps from snow

00:41:15.740 --> 00:41:18.630
cover, to population density,
to CO2 being emitted,

00:41:18.630 --> 00:41:20.651
to wildfires around
the planet-- anything

00:41:20.651 --> 00:41:22.650
that a satellite can
measure, they're measuring.

00:41:22.650 --> 00:41:26.180
And the insolation
value is one of them.

00:41:26.180 --> 00:41:29.900
And so we have data
from various points.

00:41:29.900 --> 00:41:32.540
This is the
insolation in January.

00:41:32.540 --> 00:41:36.980
So in January, it's the
Southern Hemisphere's summer,

00:41:36.980 --> 00:41:38.710
the Northern
Hemisphere's winter.

00:41:38.710 --> 00:41:42.530
And as a result, we have
less insolation up north.

00:41:42.530 --> 00:41:44.050
We're in the blues.

00:41:44.050 --> 00:41:46.600
And the Southern Hemisphere
is more in the reds.

00:41:46.600 --> 00:41:49.170
And of course, the
tide turns in July.

00:41:49.170 --> 00:41:53.300
We have our summer and
the Southern Hemisphere

00:41:53.300 --> 00:41:54.400
has their winter.

00:41:54.400 --> 00:41:56.730
And the poor folks here in
Antarctica have nothing.

00:41:56.730 --> 00:41:59.610
So a couple of things
to note just already

00:41:59.610 --> 00:42:01.560
straight off the
bat, we're noticing

00:42:01.560 --> 00:42:05.050
that there's, in general,
higher insolation

00:42:05.050 --> 00:42:07.320
near the equator, the
equator passing right

00:42:07.320 --> 00:42:10.461
through here approximately.

00:42:10.461 --> 00:42:12.710
Fun fact-- small city up
there in the north of Brazil,

00:42:12.710 --> 00:42:14.709
there's a soccer field
that is half in the north

00:42:14.709 --> 00:42:16.101
and half in the south.

00:42:16.101 --> 00:42:17.350
That's neither here nor there.

00:42:17.350 --> 00:42:20.800
We have rainforests up here
in the north of Brazil,

00:42:20.800 --> 00:42:23.520
Central Africa, and
here in Southeast Asia.

00:42:23.520 --> 00:42:25.320
And even when the sun
is directly overhead,

00:42:25.320 --> 00:42:27.670
those clouds are preventing
some of the sunlight

00:42:27.670 --> 00:42:28.450
from getting in.

00:42:28.450 --> 00:42:31.040
And that's why right
at the equator itself,

00:42:31.040 --> 00:42:32.850
we typically have
less insolation

00:42:32.850 --> 00:42:34.860
than we do in the
tropics, say, Tropic

00:42:34.860 --> 00:42:36.960
of Capricorn, Tropic of Cancer.

00:42:36.960 --> 00:42:39.149
Tropic of Capricorn
running straight

00:42:39.149 --> 00:42:40.940
through Sao Paulo,
Brazil, Tropic of Cancer

00:42:40.940 --> 00:42:42.320
running through Key West.

00:42:42.320 --> 00:42:43.740
Just to situate yourselves.

00:42:43.740 --> 00:42:46.801
And the Tropics are how
far away from the equator?

00:42:46.801 --> 00:42:47.300
Right.

00:42:47.300 --> 00:42:47.799
OK.

00:42:47.799 --> 00:42:48.390
23 and 1/2.

00:42:48.390 --> 00:42:50.380
Good guess.

00:42:50.380 --> 00:42:51.130
Good.

00:42:51.130 --> 00:42:54.736
So what we're going
to do is now launch

00:42:54.736 --> 00:42:56.110
into our next
learning objective,

00:42:56.110 --> 00:43:00.210
which is to list the causes
of variation and intermittency

00:43:00.210 --> 00:43:02.250
of the solar resource
and quantify the time

00:43:02.250 --> 00:43:03.550
constants in magnitudes.

00:43:03.550 --> 00:43:06.897
This is really, really,
really, really important.

00:43:06.897 --> 00:43:08.980
The other stuff is very
useful from an engineering

00:43:08.980 --> 00:43:10.896
point of view from
answering certain questions

00:43:10.896 --> 00:43:12.580
in your homework.

00:43:12.580 --> 00:43:17.280
This right here is the singular
reason-- one of the singular

00:43:17.280 --> 00:43:19.080
reasons-- why solar
doesn't behave

00:43:19.080 --> 00:43:22.460
like a regular fossil fuel
source, why solar does not

00:43:22.460 --> 00:43:24.330
produce power all the time.

00:43:24.330 --> 00:43:26.510
It is variable in terms
of its power output.

00:43:26.510 --> 00:43:28.750
Variability generally
refers to the fact

00:43:28.750 --> 00:43:30.730
that we can predict it's coming.

00:43:30.730 --> 00:43:33.460
It's going to vary, but at least
we can predict it's coming.

00:43:33.460 --> 00:43:37.390
Intermittency, while
not a strict definition,

00:43:37.390 --> 00:43:40.220
the understanding when
somebody says "intermittency"

00:43:40.220 --> 00:43:43.340
or "intermittent power source,"
the impression that it gives

00:43:43.340 --> 00:43:45.980
is that it's
unpredictable in terms

00:43:45.980 --> 00:43:48.300
of its variability
and its variation.

00:43:48.300 --> 00:43:50.390
So we've talked a little
bit about the variation

00:43:50.390 --> 00:43:52.590
so far and about the
predictable nature of the sun.

00:43:52.590 --> 00:43:55.080
We've talked about how the
sunlight, the solar resource,

00:43:55.080 --> 00:43:57.170
varies from summer to winter.

00:43:57.170 --> 00:44:01.710
We've talked about how
the solar resource varies

00:44:01.710 --> 00:44:04.190
as a function of
latitude, right?

00:44:04.190 --> 00:44:07.780
But now, we're going to talk not
only in a little bit more depth

00:44:07.780 --> 00:44:10.870
about that and have a few
fun in-class exercises

00:44:10.870 --> 00:44:14.500
to get us really grasping
that concept in its entirety,

00:44:14.500 --> 00:44:18.660
but also talk about some
sources of intermittency, which

00:44:18.660 --> 00:44:21.230
if you have a large amount of
solar contributing to the grid

00:44:21.230 --> 00:44:23.480
and it is intermittent, and
you have no way of dealing

00:44:23.480 --> 00:44:26.860
with that, you're going to have
fluctuations of energy level

00:44:26.860 --> 00:44:30.810
on the grid or power levels
here as a function of time.

00:44:30.810 --> 00:44:33.250
And that's not going to be good.

00:44:33.250 --> 00:44:35.130
So in terms of the
seasonal variations,

00:44:35.130 --> 00:44:38.780
in terms of predicting
the amount coming

00:44:38.780 --> 00:44:40.350
from the sun at
a given point-- I

00:44:40.350 --> 00:44:44.100
told you it looks a little bit
like a sine, a cosine wave.

00:44:44.100 --> 00:44:45.190
And indeed, it does.

00:44:45.190 --> 00:44:47.990
You can calculate those values
based on this website right

00:44:47.990 --> 00:44:48.690
here.

00:44:48.690 --> 00:44:50.790
Just to show you how
nifty and cool it is,

00:44:50.790 --> 00:44:53.140
our friends at Arizona State
University, Stuart Bowden

00:44:53.140 --> 00:44:55.306
and Christiana Honsberg,
really put in a lot of time

00:44:55.306 --> 00:44:56.170
to make this.

00:44:56.170 --> 00:44:58.380
You can vary the time
or the day of year

00:44:58.380 --> 00:44:59.846
right here for instance.

00:44:59.846 --> 00:45:00.540
Right?

00:45:00.540 --> 00:45:03.520
And you can see how
the solar resource--

00:45:03.520 --> 00:45:07.690
this is the direct radiation,
kilowatts per meter squared.

00:45:07.690 --> 00:45:09.040
And this is the time.

00:45:09.040 --> 00:45:11.709
So if you take the integral
of the curve right here,

00:45:11.709 --> 00:45:12.750
you're going to get what?

00:45:12.750 --> 00:45:16.044
Units of--

00:45:16.044 --> 00:45:16.710
AUDIENCE: Power.

00:45:16.710 --> 00:45:17.418
PROFESSOR: Power.

00:45:17.418 --> 00:45:18.850
Power times time is?

00:45:18.850 --> 00:45:19.580
AUDIENCE: Energy.

00:45:19.580 --> 00:45:20.710
PROFESSOR: Energy.

00:45:20.710 --> 00:45:22.010
Energy per unit area, right?

00:45:22.010 --> 00:45:23.120
So you're going to
be able to calculate

00:45:23.120 --> 00:45:24.994
the total amount of
energy falling on a given

00:45:24.994 --> 00:45:28.360
area per day, let's say, right?

00:45:28.360 --> 00:45:32.730
So if we look at the size of
this little curve in winter,

00:45:32.730 --> 00:45:35.130
the total area under this
is going to be very small.

00:45:35.130 --> 00:45:37.370
And that's because the solar
resource is very small.

00:45:37.370 --> 00:45:42.000
And the sun rises late
and sets early in winter.

00:45:42.000 --> 00:45:45.770
And as we move towards
summer, obviously,

00:45:45.770 --> 00:45:48.470
the total amount of the
solar resource increases.

00:45:48.470 --> 00:45:51.200
Not only it increases
because of this

00:45:51.200 --> 00:45:53.550
that we have at solar noon.

00:45:53.550 --> 00:45:56.080
We have less of a path
through the atmosphere.

00:45:56.080 --> 00:45:58.190
We have more sunlight
reaching the earth.

00:45:58.190 --> 00:46:02.580
We have a total increase of
the amount reaching the earth.

00:46:02.580 --> 00:46:05.480
We also have that
cosine theta term here

00:46:05.480 --> 00:46:09.610
dictating the
cross-section incident

00:46:09.610 --> 00:46:12.110
to that sunlight
coming in increasing.

00:46:12.110 --> 00:46:13.990
And so that's driving
this going up.

00:46:13.990 --> 00:46:17.302
And we also have a
second fact that the time

00:46:17.302 --> 00:46:19.510
of the day, the total duration
of the day, increases,

00:46:19.510 --> 00:46:22.710
at least in northern
latitudes here at around 40,

00:46:22.710 --> 00:46:25.820
let's say, 41 degrees
north, here in Boston.

00:46:25.820 --> 00:46:30.830
And we have because these two
effects a much larger area

00:46:30.830 --> 00:46:33.170
underneath that curve.

00:46:33.170 --> 00:46:38.050
And so as we go through summer
and now finally to September 13

00:46:38.050 --> 00:46:40.690
and back to winter, our solar
resource goes back down again.

00:46:40.690 --> 00:46:41.689
So you can calculate it.

00:46:41.689 --> 00:46:42.940
You can visualize it.

00:46:42.940 --> 00:46:45.900
That's cool.

00:46:45.900 --> 00:46:49.660
And we can plot the
total amount of energy

00:46:49.660 --> 00:46:51.890
per unit area per day,
essentially the integral

00:46:51.890 --> 00:46:55.260
under that curve, as a function
of location around the US,

00:46:55.260 --> 00:46:58.520
around the world per
month let's say, right?

00:46:58.520 --> 00:46:59.769
So this is January.

00:46:59.769 --> 00:47:01.810
This is kilowatt hours
per meter squared per day.

00:47:01.810 --> 00:47:07.660
So it's just taking the
integral of the curves measured.

00:47:07.660 --> 00:47:10.290
So it's accounting for
cloudy days, which kind of

00:47:10.290 --> 00:47:11.321
has a depressive effect.

00:47:11.321 --> 00:47:13.070
This is an envelope
function, if you will,

00:47:13.070 --> 00:47:14.360
the maximum you could get.

00:47:14.360 --> 00:47:16.151
And then, of course,
local weather patterns

00:47:16.151 --> 00:47:17.590
will suppress that,
drive it down.

00:47:17.590 --> 00:47:21.230
So this is the real map
of the United States.

00:47:21.230 --> 00:47:24.630
And you can see in sunnier
areas that are less cloudy, over

00:47:24.630 --> 00:47:27.120
here, for example, in
Arizona and New Mexico,

00:47:27.120 --> 00:47:29.820
there's a large solar
resource even in January.

00:47:29.820 --> 00:47:33.410
Atlanta, which has half of the
number of sunny days per year

00:47:33.410 --> 00:47:37.160
as Phoenix does, even as
it's at the same latitude,

00:47:37.160 --> 00:47:39.324
is getting about half
the solar resource.

00:47:39.324 --> 00:47:40.740
They got a short
end of the stick.

00:47:40.740 --> 00:47:44.600
Again, this curve right here is
the envelope function, right?

00:47:44.600 --> 00:47:47.972
And off of that, you
can only go down.

00:47:47.972 --> 00:47:50.430
You can only decrease the amount
of solar resource actually

00:47:50.430 --> 00:47:53.310
arriving at our feet here.

00:47:53.310 --> 00:47:54.470
And so this is in January.

00:47:54.470 --> 00:47:56.560
And this is all in
the same color scale

00:47:56.560 --> 00:47:58.390
here as we move
through the months.

00:47:58.390 --> 00:48:03.620
So we'll move from January, to
February, to March, April, May,

00:48:03.620 --> 00:48:10.230
June, July, August, September,
October, November, December.

00:48:10.230 --> 00:48:12.460
So you can see across
the United States

00:48:12.460 --> 00:48:14.830
how the resource is
distributed geographically.

00:48:14.830 --> 00:48:17.590
The general trend that as
you go from south to north

00:48:17.590 --> 00:48:19.657
you have a decreasing
solar resource holds.

00:48:19.657 --> 00:48:21.990
You can also see the influence
of local weather patterns

00:48:21.990 --> 00:48:25.280
as well for the same latitude.

00:48:25.280 --> 00:48:26.450
So that's pretty nifty.

00:48:26.450 --> 00:48:29.570
And another nifty fact, if
you look at the year average

00:48:29.570 --> 00:48:32.330
value, annual-- this is the
annual average value-- here

00:48:32.330 --> 00:48:35.300
in Boston, we're averaging
around 4.5 kilowatt hours

00:48:35.300 --> 00:48:36.870
per meter squared per day.

00:48:36.870 --> 00:48:40.190
Phoenix, Arizona can be
upwards of 6 somewhere

00:48:40.190 --> 00:48:42.090
in the outskirts.

00:48:42.090 --> 00:48:43.840
It's not that bad.

00:48:43.840 --> 00:48:46.650
It's only a few
tenths of percent.

00:48:46.650 --> 00:48:48.680
It's not that bad,
I tell myself.

00:48:48.680 --> 00:48:50.830
I don't believe
it myself either,

00:48:50.830 --> 00:48:53.490
but I try to convince myself
of that during winter.

00:48:53.490 --> 00:48:53.990
All right.

00:48:53.990 --> 00:48:58.780
Let me show you the seasonal
and diurnal variations.

00:48:58.780 --> 00:49:00.620
We're increasing the
level of sophistication

00:49:00.620 --> 00:49:01.554
as we go along, right?

00:49:01.554 --> 00:49:03.220
We've assumed you've
done your readings.

00:49:03.220 --> 00:49:04.960
We've started with
some simple examples,

00:49:04.960 --> 00:49:07.320
and now we're really
taking it one step further,

00:49:07.320 --> 00:49:09.420
which is to introduce
the full 3D model.

00:49:09.420 --> 00:49:13.730
And I'm going to do that by use
of this really cool app that's

00:49:13.730 --> 00:49:16.960
available here.

00:49:16.960 --> 00:49:17.940
Right here.

00:49:17.940 --> 00:49:20.920
This is you standing
on the earth.

00:49:20.920 --> 00:49:22.900
And you can drag and
pull this around.

00:49:22.900 --> 00:49:25.130
You can see there's north,
south, east, and west.

00:49:25.130 --> 00:49:26.755
So I'm going to pull
it up a little bit

00:49:26.755 --> 00:49:28.890
just to give us a little
bit of perspective.

00:49:28.890 --> 00:49:30.480
Still, south is
facing toward us.

00:49:30.480 --> 00:49:31.620
North is away.

00:49:31.620 --> 00:49:34.310
The sun will rise in the
east and set in the west.

00:49:34.310 --> 00:49:41.490
Now, let's say I pull the
date back to September.

00:49:41.490 --> 00:49:45.340
So this little tool is so cool
because it recognizes your IP

00:49:45.340 --> 00:49:47.647
address and situates you
at the proper latitude,

00:49:47.647 --> 00:49:49.230
so we don't have to
touch that at all.

00:49:49.230 --> 00:49:50.360
It's approximately right.

00:49:50.360 --> 00:49:52.860
We're at 40, yeah,
about 41 degrees.

00:49:52.860 --> 00:49:54.490
We're right here in September.

00:49:54.490 --> 00:49:57.250
And in terms of time of
day, we can pretty much just

00:49:57.250 --> 00:50:00.080
cycle through the time
of day if we like.

00:50:00.080 --> 00:50:03.910
We could, for example,
start animation.

00:50:03.910 --> 00:50:06.780
Let's see, this is going
very fast right now.

00:50:06.780 --> 00:50:10.590
I'm going to slow it down so you
can see the time of day moving

00:50:10.590 --> 00:50:11.810
right over here.

00:50:11.810 --> 00:50:15.100
And you can see that
relative to our vantage

00:50:15.100 --> 00:50:16.960
point on the surface
of the earth,

00:50:16.960 --> 00:50:20.440
this little yellow dot here
and this yellow line is tracing

00:50:20.440 --> 00:50:24.780
through the path of the sun in
the sky from our perspective.

00:50:24.780 --> 00:50:26.691
And so as we go
through the seasons,

00:50:26.691 --> 00:50:28.440
I'm going to speed it
up just a little bit

00:50:28.440 --> 00:50:31.810
so that we pay more
attention to the position

00:50:31.810 --> 00:50:34.150
of this yellow line
and less attention

00:50:34.150 --> 00:50:35.240
to the diurnal variations.

00:50:35.240 --> 00:50:37.350
We're paying more attention
to the seasonal variations.

00:50:37.350 --> 00:50:39.183
I'm going to vary the
seasons by force here.

00:50:39.183 --> 00:50:43.470
I'm going to go back to
July or June if I may.

00:50:43.470 --> 00:50:44.329
Here we go.

00:50:44.329 --> 00:50:45.620
AUDIENCE: What's the blue line?

00:50:45.620 --> 00:50:46.090
So you can see it?

00:50:46.090 --> 00:50:46.756
PROFESSOR: Yeah.

00:50:46.756 --> 00:50:48.840
So there's a number of
other lines right here,

00:50:48.840 --> 00:50:51.190
and they're all
explained very carefully.

00:50:51.190 --> 00:50:54.700
There is the hour
of ascension, which

00:50:54.700 --> 00:50:59.560
would be prime hour circle.

00:50:59.560 --> 00:51:00.980
Yes.

00:51:00.980 --> 00:51:03.040
I'd have to go back and
double-check all of this,

00:51:03.040 --> 00:51:06.252
but I believe they relate
to would be the sunrise

00:51:06.252 --> 00:51:07.460
and sunset of that given day.

00:51:07.460 --> 00:51:09.140
Let's see if our
hypothesis is correct.

00:51:09.140 --> 00:51:11.730
No, it is not.

00:51:11.730 --> 00:51:14.540
That would have to be,
since it is varying

00:51:14.540 --> 00:51:18.400
in a systematic way from
January through the summer

00:51:18.400 --> 00:51:20.480
and then back to the
winter, I'm imagining

00:51:20.480 --> 00:51:23.711
this has something to do
with the direction of the sun

00:51:23.711 --> 00:51:25.460
relative to the earth,
right, as it traces

00:51:25.460 --> 00:51:27.567
that ellipse through the sky.

00:51:27.567 --> 00:51:29.900
So let's pay attention to
that yellow line for a minute.

00:51:29.900 --> 00:51:32.480
That's the one I want to attract
everybody's attention to.

00:51:32.480 --> 00:51:34.832
Now we're in June, so
in the height of summer.

00:51:34.832 --> 00:51:36.540
And relative to this
observer right here,

00:51:36.540 --> 00:51:38.970
the sun is further
up in the sky just

00:51:38.970 --> 00:51:40.800
like we traced out right there.

00:51:40.800 --> 00:51:43.460
And now, as we go
to winter, that line

00:51:43.460 --> 00:51:45.572
drops close to the horizon.

00:51:45.572 --> 00:51:46.780
So a couple of things happen.

00:51:46.780 --> 00:51:49.020
If we look like
this for instance,

00:51:49.020 --> 00:51:51.440
now we're looking straight
down on the observer.

00:51:51.440 --> 00:51:55.380
In wintertime, the sun
will rise in the southeast,

00:51:55.380 --> 00:51:57.810
and it will trace this
arc through the sky

00:51:57.810 --> 00:52:00.220
and set in the
southwest over here.

00:52:00.220 --> 00:52:05.930
In the summertime,
the sun will rise

00:52:05.930 --> 00:52:10.780
almost in the northeast,
slightly north of east, just

00:52:10.780 --> 00:52:12.130
slightly north of east.

00:52:12.130 --> 00:52:14.789
And that's why if you
have a north-facing window

00:52:14.789 --> 00:52:16.830
and you put your little
plant on the window sill,

00:52:16.830 --> 00:52:19.413
it'll get a little bit of direct
sunlight early in the morning

00:52:19.413 --> 00:52:20.370
and late at night.

00:52:20.370 --> 00:52:23.370
Because when the sun is tracing
this part or that part through,

00:52:23.370 --> 00:52:25.370
it's tracing the sky.

00:52:25.370 --> 00:52:28.270
So it's worth sitting down
with one of these plots,

00:52:28.270 --> 00:52:30.610
toying around with it,
getting accustomed to it,

00:52:30.610 --> 00:52:33.089
and understanding really
how the sun traces its arc

00:52:33.089 --> 00:52:35.130
throughout the sky relative
to our position right

00:52:35.130 --> 00:52:36.150
here on the earth.

00:52:36.150 --> 00:52:38.760
If we shift this
further up north,

00:52:38.760 --> 00:52:40.540
really interesting
things begin to happen.

00:52:40.540 --> 00:52:42.550
So for example, my
wife is in Sweden.

00:52:42.550 --> 00:52:45.970
If we go to her hometown right
here in the middle summertime

00:52:45.970 --> 00:52:48.940
at the solstice,
you can see the sun

00:52:48.940 --> 00:52:51.390
traces this awesome
route from north

00:52:51.390 --> 00:52:54.200
to north barely
leaving the horizon.

00:52:54.200 --> 00:52:56.880
If we look at, again,
from the perspective

00:52:56.880 --> 00:53:00.540
of the little creature
here, that yellow arc

00:53:00.540 --> 00:53:02.800
is really close to the horizon.

00:53:02.800 --> 00:53:04.710
Maybe it goes up
about that high,

00:53:04.710 --> 00:53:07.080
but it continues going
all the way to the north.

00:53:07.080 --> 00:53:09.130
And if you keep going
north, it will never

00:53:09.130 --> 00:53:11.220
set during the middle of summer.

00:53:11.220 --> 00:53:13.304
It'll just be
light all the time.

00:53:13.304 --> 00:53:15.470
And you can see here it
just traces that orbit right

00:53:15.470 --> 00:53:16.610
around there.

00:53:16.610 --> 00:53:17.860
It's all trig, folks.

00:53:17.860 --> 00:53:18.420
We can do it.

00:53:18.420 --> 00:53:21.920
We can sit down, and we can work
through the equations by hand.

00:53:21.920 --> 00:53:22.740
I did that once.

00:53:22.740 --> 00:53:23.698
It took me a long time.

00:53:23.698 --> 00:53:25.130
I didn't learn that much.

00:53:25.130 --> 00:53:29.410
I would instead advise you to
go to one of these simulations

00:53:29.410 --> 00:53:31.860
right here, but to understand
all the inputs into it,

00:53:31.860 --> 00:53:34.410
all the different
components, the fact

00:53:34.410 --> 00:53:37.110
that the earth is moving
around the sun as a declination

00:53:37.110 --> 00:53:40.380
angle, seasonal
variations, and so forth.

00:53:40.380 --> 00:53:41.370
Very useful tool.

00:53:41.370 --> 00:53:44.840
You have the website
link right here.

00:53:44.840 --> 00:53:45.340
And yeah.

00:53:48.000 --> 00:53:52.170
So from this tool-- actually,
one last tiny, tiny thing.

00:53:52.170 --> 00:53:57.290
From this tool right here, we
can understand why-- OK, this

00:53:57.290 --> 00:53:58.810
is a real stretch.

00:53:58.810 --> 00:54:02.500
And forgive me, social
scientists in the room,

00:54:02.500 --> 00:54:05.970
for doing this, but I have to
project a little bit of science

00:54:05.970 --> 00:54:08.320
onto human behavior.

00:54:08.320 --> 00:54:13.980
How far west is Madrid from GMT?

00:54:13.980 --> 00:54:15.730
Madrid, Spain?

00:54:15.730 --> 00:54:19.420
It's 3 degrees west
of the Great Meridian.

00:54:19.420 --> 00:54:21.960
So the line that divides the
East and the West Hemispheres

00:54:21.960 --> 00:54:23.830
is 3 degrees west.

00:54:23.830 --> 00:54:29.200
But it is one time zone
earlier than London,

00:54:29.200 --> 00:54:32.100
so it's in the same
time zone as Germany

00:54:32.100 --> 00:54:37.320
and all the other cities
that are east of London.

00:54:37.320 --> 00:54:39.265
And this is just for
convenience factor.

00:54:39.265 --> 00:54:41.640
If you're traveling from one
continental European country

00:54:41.640 --> 00:54:43.250
to the other, it
just makes sense

00:54:43.250 --> 00:54:44.690
to have everything be
on the same time zone.

00:54:44.690 --> 00:54:46.398
You get to work at
the same time sort of.

00:54:46.398 --> 00:54:48.160
Pick up the phone,
call somebody,

00:54:48.160 --> 00:54:49.510
you're doing business.

00:54:49.510 --> 00:54:53.570
Now relative to
everybody else in Europe,

00:54:53.570 --> 00:54:57.650
though, is the sun
setting later or earlier

00:54:57.650 --> 00:54:59.820
if you're that far
west in your time zone?

00:54:59.820 --> 00:55:00.680
AUDIENCE: Later.

00:55:00.680 --> 00:55:01.679
PROFESSOR: Later, right?

00:55:01.679 --> 00:55:04.080
So the sun is setting
later if you're there.

00:55:04.080 --> 00:55:06.790
So if you're eating according to
the sun, not according to what

00:55:06.790 --> 00:55:09.770
your watch is saying, but if
you're choosing to eat dinner

00:55:09.770 --> 00:55:12.100
when the sun is
setting, when will your

00:55:12.100 --> 00:55:14.940
watch say, oh my
goodness, it's really late

00:55:14.940 --> 00:55:16.899
when you're in Berlin or
when you're in Madrid?

00:55:16.899 --> 00:55:17.606
AUDIENCE: Madrid.

00:55:17.606 --> 00:55:19.280
PROFESSOR: When you're
in Madrid, right?

00:55:19.280 --> 00:55:21.890
So again, I'm not
saying that this

00:55:21.890 --> 00:55:25.007
is the sole reason for
social behavior being

00:55:25.007 --> 00:55:26.840
a little different on
the Iberian Peninsula,

00:55:26.840 --> 00:55:28.340
since Portugal
also eats very late

00:55:28.340 --> 00:55:30.173
and they're in the same
time zone as London,

00:55:30.173 --> 00:55:32.380
but it could be a
contributing factor.

00:55:32.380 --> 00:55:36.280
The sun is still up in the sky
when it's 5:00 PM in winter,

00:55:36.280 --> 00:55:40.350
let's say, where in Germany,
it's set a long time ago.

00:55:40.350 --> 00:55:42.640
So these are just little
things to keep in mind.

00:55:42.640 --> 00:55:46.550
An easy way to calculate,
when is the solar noon,

00:55:46.550 --> 00:55:48.090
you look at the
earth more or less

00:55:48.090 --> 00:55:49.740
like we're looking
at this right now.

00:55:49.740 --> 00:55:51.460
We have 360 degrees.

00:55:51.460 --> 00:55:54.940
We divide that
into 24 time zones.

00:55:54.940 --> 00:55:58.240
And then we say, OK,
about 15 degrees each.

00:55:58.240 --> 00:56:00.260
And then we can begin
counting from there.

00:56:00.260 --> 00:56:02.740
If in Boston, were
41 degrees north,

00:56:02.740 --> 00:56:05.720
but we're 71 degrees
west, we can say,

00:56:05.720 --> 00:56:08.010
OK we should be for GMT minus 5.

00:56:08.010 --> 00:56:10.550
We should be at
around 75 degrees.

00:56:10.550 --> 00:56:12.620
And so we're a little
earlier, so we do things

00:56:12.620 --> 00:56:15.119
a little earlier around here
than what the solar noon should

00:56:15.119 --> 00:56:17.510
be telling us to do things--
wake up a little earlier,

00:56:17.510 --> 00:56:18.350
go to bed a little earlier.

00:56:18.350 --> 00:56:19.974
And that's why students
are like, dang,

00:56:19.974 --> 00:56:21.540
there's no night
life around here.

00:56:21.540 --> 00:56:23.123
I'm not saying that's
the only reason,

00:56:23.123 --> 00:56:25.380
but it could be a
contributing factor.

00:56:25.380 --> 00:56:27.950
Whereas the opposite
happens when you're

00:56:27.950 --> 00:56:30.161
far west in your time zone.

00:56:30.161 --> 00:56:30.660
OK.

00:56:30.660 --> 00:56:32.760
So again, just trying
to wrap our heads

00:56:32.760 --> 00:56:36.079
around the solar resource and
around the world around us

00:56:36.079 --> 00:56:38.370
so that we can answer that
little child in the shopping

00:56:38.370 --> 00:56:40.080
mall when they come
with questions.

00:56:40.080 --> 00:56:42.004
What are these?

00:56:42.004 --> 00:56:43.662
AUDIENCE: [INAUDIBLE]

00:56:43.662 --> 00:56:45.370
PROFESSOR: Solar trash
compactors, right?

00:56:45.370 --> 00:56:46.180
AUDIENCE: At the Student Center.

00:56:46.180 --> 00:56:47.555
PROFESSOR: At the
Student Center.

00:56:47.555 --> 00:56:49.089
Anna's Taqueria is
right over there.

00:56:49.089 --> 00:56:50.380
Dunkin' Donuts is there, right?

00:56:50.380 --> 00:56:53.880
So these are solar panels
mounted on the tops of those.

00:56:53.880 --> 00:56:57.704
And what the solar is doing
is charging a battery inside.

00:56:57.704 --> 00:56:59.370
Once the trash reaches
a critical lever,

00:56:59.370 --> 00:57:00.670
a sensor is triggered.

00:57:00.670 --> 00:57:05.010
It stops you from opening this
bin, and it compacts the trash

00:57:05.010 --> 00:57:08.179
and then releases and allows you
to open and put more stuff in.

00:57:08.179 --> 00:57:09.970
And what it does is it
minimizes the number

00:57:09.970 --> 00:57:11.890
of times between trash pickups.

00:57:11.890 --> 00:57:17.060
If labor is a large portion of
the cost of trash management,

00:57:17.060 --> 00:57:21.390
of refuse management, then it
eliminates some of the labor,

00:57:21.390 --> 00:57:23.610
transferring it instead
to the technology.

00:57:23.610 --> 00:57:27.110
And so installing these
at the Student Center,

00:57:27.110 --> 00:57:28.830
I had a little bit
of a pet peeve.

00:57:28.830 --> 00:57:31.120
[LAUGHTER]

00:57:31.120 --> 00:57:36.300
So you have angle
of the sun right

00:57:36.300 --> 00:57:39.030
here, which we just walked
through, 18 degrees in summer.

00:57:39.030 --> 00:57:42.760
And it just so happened
to work out that--

00:57:42.760 --> 00:57:44.224
and these numbers
were approximate.

00:57:44.224 --> 00:57:46.390
This was me going with my
kind of engineering sense.

00:57:46.390 --> 00:57:47.560
That's about 45 degrees.

00:57:47.560 --> 00:57:49.830
Count the number of paces.

00:57:49.830 --> 00:57:51.030
Equilateral triangle.

00:57:51.030 --> 00:57:52.640
Estimate the height of there.

00:57:52.640 --> 00:57:56.400
But in the middle of summertime,
when you are at the solstice,

00:57:56.400 --> 00:58:00.120
there is no so direct sunlight
hitting this trash can because

00:58:00.120 --> 00:58:01.950
of that overhang way up there.

00:58:01.950 --> 00:58:04.700
And it's not a problem for this
particular trash collector,

00:58:04.700 --> 00:58:06.214
since those panels
are way oversized

00:58:06.214 --> 00:58:08.630
for the amount of energy that
the trash collector actually

00:58:08.630 --> 00:58:09.860
needs.

00:58:09.860 --> 00:58:11.510
And there is a
fair amount of what

00:58:11.510 --> 00:58:13.590
we call diffuse sunlight,
meaning sunlight being

00:58:13.590 --> 00:58:14.840
scattered off of other things.

00:58:14.840 --> 00:58:17.324
That's why this portion
of the image looks white.

00:58:17.324 --> 00:58:19.615
It wouldn't look white if
there was no diffuse scatter.

00:58:19.615 --> 00:58:21.780
It'd look black, pitch
black, if there was nothing

00:58:21.780 --> 00:58:22.970
to scatter the light off.

00:58:22.970 --> 00:58:25.345
Like an outer space, there's
nothing to scatter this way.

00:58:25.345 --> 00:58:27.920
It looks like a black night.

00:58:27.920 --> 00:58:30.170
But instead, there's a large
amount of diffused light.

00:58:30.170 --> 00:58:31.628
There is some
sunlight reaching it.

00:58:31.628 --> 00:58:33.340
And since the panels
are way oversized

00:58:33.340 --> 00:58:35.540
and the system is
over-engineered,

00:58:35.540 --> 00:58:37.770
it still manages to
acquire enough energy

00:58:37.770 --> 00:58:38.710
to compact the trash.

00:58:38.710 --> 00:58:40.560
And it doesn't have
a catastrophic stop.

00:58:40.560 --> 00:58:42.700
But it was an
example of somebody

00:58:42.700 --> 00:58:46.810
not really thinking much about
the direction or the angle

00:58:46.810 --> 00:58:47.970
of the sun in the sky.

00:58:47.970 --> 00:58:50.040
They probably installed
it sometime around March

00:58:50.040 --> 00:58:52.490
when the snow started to melt
and the sun was right around

00:58:52.490 --> 00:58:54.090
here.

00:58:54.090 --> 00:58:57.660
And the angle was around
there, and it made it

00:58:57.660 --> 00:58:59.663
into the trash collectors.

00:58:59.663 --> 00:59:03.490
But as the summer came
along, it got shaded.

00:59:03.490 --> 00:59:05.730
So it's something
to keep in mind when

00:59:05.730 --> 00:59:07.010
doing a solar installation.

00:59:07.010 --> 00:59:09.370
It is important to
calculate these things.

00:59:09.370 --> 00:59:11.114
And I just pick out
once more example.

00:59:11.114 --> 00:59:12.530
I'd encourage you
to walk through.

00:59:12.530 --> 00:59:15.340
I was going to have that be a
small little in-class example,

00:59:15.340 --> 00:59:18.860
but since we're
running short on time,

00:59:18.860 --> 00:59:20.650
I'll just give it
to you like that.

00:59:20.650 --> 00:59:21.150
OK.

00:59:21.150 --> 00:59:23.190
Fixed versus tracking systems.

00:59:23.190 --> 00:59:27.230
So if the sun is moving
as a function of season

00:59:27.230 --> 00:59:30.570
and as a function of time
of day throughout the sky--

00:59:30.570 --> 00:59:32.960
and we can see that
very nicely, again,

00:59:32.960 --> 00:59:38.860
through our demo right here-- so
if the sun is actually moving,

00:59:38.860 --> 00:59:41.364
one embodiment would
say, OK, I know

00:59:41.364 --> 00:59:42.780
more or less what
the sun is going

00:59:42.780 --> 00:59:44.196
to do as a function of season.

00:59:44.196 --> 00:59:45.820
Forget the diurnal
variations, but just

00:59:45.820 --> 00:59:46.847
the seasonal variations.

00:59:46.847 --> 00:59:49.430
I know that the sun is going to
be on average somewhere around

00:59:49.430 --> 00:59:52.060
here, somewhere
around my latitude.

00:59:52.060 --> 00:59:56.910
So if I point my panel
at latitude tilt,

00:59:56.910 --> 01:00:01.410
since this angle was--
what was it-- 41 plus 23.

01:00:01.410 --> 01:00:03.510
This angle was 41
minus 23, so this would

01:00:03.510 --> 01:00:05.990
be right around 41 latitude.

01:00:05.990 --> 01:00:09.600
So if I aim my solar
panels at latitude tilt,

01:00:09.600 --> 01:00:12.540
then I'm going to get, on
average, some pretty decent

01:00:12.540 --> 01:00:14.320
power throughout the year.

01:00:14.320 --> 01:00:15.820
I'll have a little
lesson in winter,

01:00:15.820 --> 01:00:19.489
a little more in summer
because, well, just because

01:00:19.489 --> 01:00:21.280
of the amount of solar
resources available.

01:00:21.280 --> 01:00:24.320
But all in all,
I'll be all right.

01:00:24.320 --> 01:00:28.900
At most, I'll be off
by 23 and 1/2 degrees.

01:00:28.900 --> 01:00:29.750
You can do that.

01:00:29.750 --> 01:00:31.790
And that's called
fixed latitude tilt.

01:00:31.790 --> 01:00:34.680
And typically, you'll face the
panels south approximately.

01:00:34.680 --> 01:00:35.930
We'll get to that in a minute.

01:00:35.930 --> 01:00:37.500
It depends on local
weather patterns.

01:00:37.500 --> 01:00:38.730
If you have fog in the
morning, for instance,

01:00:38.730 --> 01:00:40.970
you want to face them
a little to the west.

01:00:40.970 --> 01:00:44.920
But we'll face them south
and at latitude tilt.

01:00:44.920 --> 01:00:47.130
Or we can decide,
no, let's actually

01:00:47.130 --> 01:00:49.955
track the sun throughout
the sky throughout the day.

01:00:49.955 --> 01:00:51.830
And so we'll start in
the east in the morning

01:00:51.830 --> 01:00:54.010
and have it rotating
through on one-axis tracker

01:00:54.010 --> 01:00:54.890
throughout the day.

01:00:54.890 --> 01:00:56.795
Or we can have a
two-axis tracker where

01:00:56.795 --> 01:00:59.590
it rotates to follow the sun
throughout the seasons as well,

01:00:59.590 --> 01:01:01.300
a kind of a north/south tilt.

01:01:01.300 --> 01:01:03.450
And that's what's
plotted right here.

01:01:03.450 --> 01:01:09.810
This is a quick approximation
of the fixed one-axis

01:01:09.810 --> 01:01:11.330
and two-axis
trackers for a given

01:01:11.330 --> 01:01:14.870
system in Boston using a
simulation tool called PVWatts.

01:01:14.870 --> 01:01:16.420
There's a link to that.

01:01:16.420 --> 01:01:18.920
It's based on the National
Renewable Energy Laboratory

01:01:18.920 --> 01:01:19.590
website.

01:01:19.590 --> 01:01:21.990
There's a link to that
at the end of the slides.

01:01:21.990 --> 01:01:23.850
But this shows you
the total system

01:01:23.850 --> 01:01:26.200
output in terms of
kilowatt hours in terms

01:01:26.200 --> 01:01:28.820
of hours per day.

01:01:28.820 --> 01:01:31.304
I think, yeah, it's a little
bit of an odd units there

01:01:31.304 --> 01:01:31.970
on the one-axis.

01:01:31.970 --> 01:01:35.082
But it shows you
the relative gain

01:01:35.082 --> 01:01:36.790
that you would get by
going to a one-axis

01:01:36.790 --> 01:01:38.570
and then, finally,
a two-axis tracker.

01:01:38.570 --> 01:01:40.250
So in many places,
it makes sense

01:01:40.250 --> 01:01:43.430
to go to one-axis tracker,
since especially you broaden out

01:01:43.430 --> 01:01:45.860
the peak near the
peak hours of the day.

01:01:45.860 --> 01:01:48.030
And that's really good.

01:01:48.030 --> 01:01:50.114
But not always does it
make sense financially

01:01:50.114 --> 01:01:51.280
to go to a two-axis tracker.

01:01:51.280 --> 01:01:53.113
You're adding another
motor onto that thing.

01:01:53.113 --> 01:01:55.390
It's really not
gaining you that much.

01:01:55.390 --> 01:01:57.630
Obviously, you have to
calculate it out yourself

01:01:57.630 --> 01:01:58.900
for that specific location.

01:01:58.900 --> 01:02:01.380
But by and large, a
generality, one-axis tracker

01:02:01.380 --> 01:02:03.320
makes sense for a flat panel.

01:02:03.320 --> 01:02:05.716
Now if you have a
concentrator lens in the front

01:02:05.716 --> 01:02:07.590
and it has to be looking
directly at the sun,

01:02:07.590 --> 01:02:10.680
then you're kind of forced
to go to two-axis tracker.

01:02:10.680 --> 01:02:11.180
OK.

01:02:11.180 --> 01:02:13.013
And there you have your
total system output,

01:02:13.013 --> 01:02:17.790
which is just the integral under
the curve over the entire year.

01:02:17.790 --> 01:02:19.890
So definitions-- I should
have done this before.

01:02:19.890 --> 01:02:22.190
But direct sunlight,
looking directly at the sun,

01:02:22.190 --> 01:02:24.810
and then diffuse sunlight or
scattered light coming off

01:02:24.810 --> 01:02:25.830
of other things.

01:02:25.830 --> 01:02:30.340
So diffuse sunlight would be
coming from the other angles

01:02:30.340 --> 01:02:32.199
in other directions in the sky.

01:02:32.199 --> 01:02:33.740
The direct sunlight
would pretty much

01:02:33.740 --> 01:02:37.325
be at the sun plus or
minus a few degrees.

01:02:37.325 --> 01:02:38.950
And we have different
ways of measuring

01:02:38.950 --> 01:02:42.492
the-- this would be flat plate.

01:02:42.492 --> 01:02:44.700
Up there on the upper left
it says, flat plate facing

01:02:44.700 --> 01:02:47.550
south latitude tilt. Just like
we said, it's facing south.

01:02:47.550 --> 01:02:49.520
In the United
States, that's good.

01:02:49.520 --> 01:02:51.710
Latitude tilt, meaning it's
tilted at our latitude.

01:02:51.710 --> 01:02:54.350
So if we go from the southern
tip of Florida and Texas

01:02:54.350 --> 01:02:56.490
up to the northern
tip of Minnesota,

01:02:56.490 --> 01:02:59.750
we'll be tilting
it more and more

01:02:59.750 --> 01:03:03.560
toward the south like this,
going from Texas to Minnesota.

01:03:03.560 --> 01:03:05.570
From Texas to Minnesota.

01:03:05.570 --> 01:03:09.880
And so latitude tilt
facing south flat plate.

01:03:09.880 --> 01:03:13.095
This is essentially accumulating
all of the sunlight, the direct

01:03:13.095 --> 01:03:15.470
and the scattered light,
because it's all being collected

01:03:15.470 --> 01:03:17.240
by the flat plate there.

01:03:17.240 --> 01:03:20.990
This map, on the other hand,
is for a two-axis tracker.

01:03:20.990 --> 01:03:24.400
And it's looking at the sun
plus or minus 2 and 1/2 degrees.

01:03:24.400 --> 01:03:27.120
And so it's really only
picking up this right

01:03:27.120 --> 01:03:28.760
here out of the sky.

01:03:28.760 --> 01:03:31.130
And when it's sunny all
the time, you're golden.

01:03:31.130 --> 01:03:32.130
You're tracking the sun.

01:03:32.130 --> 01:03:34.270
You're actually
getting more energy

01:03:34.270 --> 01:03:36.180
than you would if you
just at a flat plate

01:03:36.180 --> 01:03:38.721
because the cosine theta angle
is changing throughout the day

01:03:38.721 --> 01:03:39.820
if you have a flat plate.

01:03:39.820 --> 01:03:41.320
When the sun is in
the morning time,

01:03:41.320 --> 01:03:42.810
you have a flat plate like this.

01:03:42.810 --> 01:03:44.980
So if my sunlight is
coming in like this

01:03:44.980 --> 01:03:46.771
and I do cosine
theta of the angle,

01:03:46.771 --> 01:03:48.270
I'm only getting a
very small amount

01:03:48.270 --> 01:03:51.510
of the incident sunlight
projected onto this plate right

01:03:51.510 --> 01:03:52.010
here.

01:03:52.010 --> 01:03:54.960
If I was in the middle of the
day, now cosine theta is 1,

01:03:54.960 --> 01:03:57.010
I get the full sunlight.

01:03:57.010 --> 01:03:59.700
But if I have, for
instance, a tracker,

01:03:59.700 --> 01:04:02.579
I would be able to face
this panel due east

01:04:02.579 --> 01:04:04.120
and then track it
throughout the day.

01:04:04.120 --> 01:04:07.240
And that's where I'd get this
additional energy boost here

01:04:07.240 --> 01:04:11.760
in the mornings right there
from the tracking system.

01:04:11.760 --> 01:04:14.790
So if I have a tracker,
I get a big gain

01:04:14.790 --> 01:04:17.466
in the places that have
a lot of direct sun.

01:04:17.466 --> 01:04:19.590
And if I'm only looking at
a very small solid angle

01:04:19.590 --> 01:04:22.090
of the sky, if I'm only looking
at, say, this little portion

01:04:22.090 --> 01:04:25.010
the sun, on cloudy days,
most of the sunlight

01:04:25.010 --> 01:04:28.340
is coming off of the diffused
light, not from the sun.

01:04:28.340 --> 01:04:29.920
If I have a flat plate, I win.

01:04:29.920 --> 01:04:33.479
If I have a concentrator,
I lose on a cloudy day.

01:04:33.479 --> 01:04:35.770
And so that's why, in some
of the regions of the United

01:04:35.770 --> 01:04:39.030
States that are notoriously
cloudy-- I won't point

01:04:39.030 --> 01:04:42.290
to any one in
particular-- it's actually

01:04:42.290 --> 01:04:44.940
better for non-concentrating
solar in terms of total energy

01:04:44.940 --> 01:04:45.612
output.

01:04:45.612 --> 01:04:47.320
And in other regions
of the United States

01:04:47.320 --> 01:04:50.020
where we have a
lot of sunny days,

01:04:50.020 --> 01:04:52.667
you start having two-axis
trackers making sense.

01:04:52.667 --> 01:04:54.750
And it's just really the
ratio of these two maps--

01:04:54.750 --> 01:04:56.920
whoopsie-- this one,
which is flat plate,

01:04:56.920 --> 01:04:58.560
and that one, which
is concentrator.

01:04:58.560 --> 01:05:03.020
You see over here, we win if
we go for the concentrator.

01:05:03.020 --> 01:05:06.230
And over here, we
get more energy out--

01:05:06.230 --> 01:05:10.050
oopsie-- more energy out
if we use the flat plate.

01:05:10.050 --> 01:05:11.620
Now that's just energy.

01:05:11.620 --> 01:05:14.190
Obviously, cost and
economics factors

01:05:14.190 --> 01:05:17.890
what it takes to install it.

01:05:17.890 --> 01:05:19.370
OK.

01:05:19.370 --> 01:05:23.630
And weather patterns, I
promised I'd get back to this.

01:05:23.630 --> 01:05:26.330
Interesting to note that
for right near the equator,

01:05:26.330 --> 01:05:30.290
we have this drop
of the insolation.

01:05:30.290 --> 01:05:34.650
And there are these beautiful
maps put out by, again,

01:05:34.650 --> 01:05:37.660
NASA Earth Observatory that
show you the cloud fraction

01:05:37.660 --> 01:05:40.155
coverage of particular
spots around the planet.

01:05:40.155 --> 01:05:42.030
And you can see that
right near the equators,

01:05:42.030 --> 01:05:45.310
typically we have these
beautiful tropical forests.

01:05:48.320 --> 01:05:50.080
The high cloud cover
in those regions

01:05:50.080 --> 01:05:51.886
is blocking out some of the sun.

01:05:51.886 --> 01:05:53.510
And likewise, you
can see the dichotomy

01:05:53.510 --> 01:05:54.960
between Phoenix and Atlanta.

01:05:54.960 --> 01:05:58.200
Same latitude again, but Atlanta
having a higher cloud coverage

01:05:58.200 --> 01:06:01.450
than Phoenix and, hence, a
lower solar resource, a lower

01:06:01.450 --> 01:06:03.340
insolation.

01:06:03.340 --> 01:06:05.260
So you how all this
kind of ties together.

01:06:05.260 --> 01:06:07.180
That's all predictable
in a sense.

01:06:07.180 --> 01:06:11.820
This is unpredictable at a
local level for one system.

01:06:11.820 --> 01:06:14.500
If the sun is tracing its
route through the sky,

01:06:14.500 --> 01:06:16.002
and you have that
envelope function

01:06:16.002 --> 01:06:18.210
that you've just spent so
much effort calculating out

01:06:18.210 --> 01:06:20.543
with all your trig functions
in the computer simulation,

01:06:20.543 --> 01:06:22.720
the code that you've
just been given here.

01:06:22.720 --> 01:06:24.780
And now, a cloud comes
over, some random cloud

01:06:24.780 --> 01:06:26.110
that was very hard to predict.

01:06:26.110 --> 01:06:29.030
And you just have one panel,
one tiny little thing like this.

01:06:29.030 --> 01:06:30.200
And the cloud goes over it.

01:06:30.200 --> 01:06:31.741
Boom, all of a
sudden, you get a drop

01:06:31.741 --> 01:06:34.390
in your instantaneous
power output.

01:06:34.390 --> 01:06:35.330
Boom, drops again.

01:06:35.330 --> 01:06:36.800
Another cloud, drops again.

01:06:36.800 --> 01:06:39.830
And then a thunderstorm
in the afternoon.

01:06:39.830 --> 01:06:41.810
So a meteorologist
could have told you

01:06:41.810 --> 01:06:43.980
that this thunderstorm
was coming,

01:06:43.980 --> 01:06:45.760
but a meteorologist
would be hard pressed

01:06:45.760 --> 01:06:48.120
to be able to
predict the evolution

01:06:48.120 --> 01:06:50.730
of a tiny little cloud
over your system.

01:06:50.730 --> 01:06:54.810
And so the question is, to what
degree are these local weather

01:06:54.810 --> 01:06:56.610
patterns predictable
and unpredictable?

01:06:56.610 --> 01:06:59.850
And hopefully, some of
you, over this class,

01:06:59.850 --> 01:07:03.150
will be able to help answer
that question by analyzing data

01:07:03.150 --> 01:07:05.150
from tens of thousands
of systems that have been

01:07:05.150 --> 01:07:09.349
installed throughout California
in local geographical systems,

01:07:09.349 --> 01:07:11.890
for example, in the Los Angeles
region, San Francisco region,

01:07:11.890 --> 01:07:13.080
and so forth.

01:07:13.080 --> 01:07:15.700
If you start averaging
the curves, the energy

01:07:15.700 --> 01:07:18.580
outputs as a function of time,
from a variety of systems

01:07:18.580 --> 01:07:21.020
throughout a neighborhood,
you can probably average out

01:07:21.020 --> 01:07:22.370
the small tiny clouds.

01:07:22.370 --> 01:07:24.442
You probably can't average
out the thunderstorm.

01:07:24.442 --> 01:07:26.900
But you probably could have
predicted that the thunderstorm

01:07:26.900 --> 01:07:28.940
would've come along.

01:07:28.940 --> 01:07:32.290
And so this is a hot area of
solar research at the systems

01:07:32.290 --> 01:07:32.790
level.

01:07:32.790 --> 01:07:34.720
It's trying to
understand, to what degree

01:07:34.720 --> 01:07:36.680
are PV systems predictable?

01:07:36.680 --> 01:07:38.840
To what degree can
the power output

01:07:38.840 --> 01:07:42.070
of a PV system or an
ensemble of PV systems

01:07:42.070 --> 01:07:45.550
be predicted in advance so we
don't wind up in a situation

01:07:45.550 --> 01:07:48.300
where all of a sudden we
have this catastrophic drop

01:07:48.300 --> 01:07:51.979
of a cumulative PV system
output of, say, 30%

01:07:51.979 --> 01:07:53.520
and meanwhile, it's
a hot summer day,

01:07:53.520 --> 01:07:55.080
everybody's air
conditions are going,

01:07:55.080 --> 01:07:57.050
and we cause failure
of the power grid?

01:07:57.050 --> 01:08:00.000
Kind of worst case scenario.

01:08:00.000 --> 01:08:02.850
So this boils down to
intermittency with a short time

01:08:02.850 --> 01:08:05.760
constants tend to
be less predictable.

01:08:05.760 --> 01:08:06.650
Cloud cover.

01:08:06.650 --> 01:08:09.840
And it's relevant for predicting
power supply reliability.

01:08:09.840 --> 01:08:12.450
And the longer time constants
tend to be more predictable.

01:08:12.450 --> 01:08:15.100
The diurnal or seasonal
variations-- and these

01:08:15.100 --> 01:08:18.710
are relevant to calculating
total energy output annually.

01:08:18.710 --> 01:08:20.859
And oftentimes, when
we just work off

01:08:20.859 --> 01:08:23.380
of these long time constant
variability issues,

01:08:23.380 --> 01:08:26.920
we're assuming we have
access to easy storage.

01:08:26.920 --> 01:08:29.330
Right now, the solar
panels on top of my roof,

01:08:29.330 --> 01:08:30.789
they're producing
in excess of what

01:08:30.789 --> 01:08:33.038
we're consuming right now
because neither my wife or I

01:08:33.038 --> 01:08:33.550
are at home.

01:08:33.550 --> 01:08:35.100
And they're injecting
that power into the grid,

01:08:35.100 --> 01:08:37.120
and the grid is serving
as our big battery,

01:08:37.120 --> 01:08:39.319
as our storage unit.

01:08:39.319 --> 01:08:41.120
And I'm riding free.

01:08:41.120 --> 01:08:42.460
I'm a free rider right now.

01:08:42.460 --> 01:08:44.550
I don't pay for that
service necessarily.

01:08:44.550 --> 01:08:46.490
I do to NSTAR.

01:08:46.490 --> 01:08:52.135
But they're not charging
extra for the service of using

01:08:52.135 --> 01:08:53.260
the grid as my big battery.

01:08:55.770 --> 01:08:57.770
Another thing to keep
in mind is that we're

01:08:57.770 --> 01:09:01.710
calculating all this on
the basis of engineering

01:09:01.710 --> 01:09:03.010
and scientific principles.

01:09:03.010 --> 01:09:04.580
We're calculating
the solar resource,

01:09:04.580 --> 01:09:07.350
which is a good,
important first step.

01:09:07.350 --> 01:09:09.649
Now if we look at the
actual solar installations

01:09:09.649 --> 01:09:13.050
by year and by country--
this is a big table,

01:09:13.050 --> 01:09:16.520
but follow me on the two
underlined red lines here,

01:09:16.520 --> 01:09:21.260
DEU, that stands for
Deutschland, Germany, and USA.

01:09:21.260 --> 01:09:23.479
We'll see that Germany
has about seven times

01:09:23.479 --> 01:09:25.830
more solar installed
cumulatively

01:09:25.830 --> 01:09:27.710
than the United States does.

01:09:27.710 --> 01:09:31.000
And yet, if we look at the
solar resource in Germany

01:09:31.000 --> 01:09:34.830
relative to the US-- this is
average annual, same scale,

01:09:34.830 --> 01:09:38.920
going from 900 to 1,200 kilowatt
hours per kilowatt per year--

01:09:38.920 --> 01:09:41.439
we can see that there's a lot
more sun in the United States

01:09:41.439 --> 01:09:42.740
than there is in Germany.

01:09:42.740 --> 01:09:44.540
So there's something
else going on

01:09:44.540 --> 01:09:46.470
than just the solar resource.

01:09:46.470 --> 01:09:47.738
And that's economics.

01:09:47.738 --> 01:09:49.779
That's why we talk about
the policy and economics

01:09:49.779 --> 01:09:50.970
later on in class.

01:09:50.970 --> 01:09:53.399
That's why we dedicate
a sizable portion later

01:09:53.399 --> 01:09:55.230
on talking about that.

01:09:55.230 --> 01:09:57.580
Lastly, our final
learning objectives

01:09:57.580 --> 01:10:02.199
before we halt for questions
and for comments, we

01:10:02.199 --> 01:10:03.740
need to estimate
the land area needed

01:10:03.740 --> 01:10:06.131
to provide sufficient solar
resource for a project.

01:10:06.131 --> 01:10:08.130
And this is really where
your homework picks up,

01:10:08.130 --> 01:10:09.755
and we'll spend some
time in recitation

01:10:09.755 --> 01:10:11.470
walking through this.

01:10:11.470 --> 01:10:14.730
But it's important to
get your units right.

01:10:14.730 --> 01:10:18.480
And so I want to do a
quick quiz right now.

01:10:18.480 --> 01:10:23.320
Think in your minds
which of these properties

01:10:23.320 --> 01:10:25.720
corresponds to which units
or are described by which

01:10:25.720 --> 01:10:27.140
units over here on the right.

01:10:27.140 --> 01:10:29.752
So do a kind of a linkage
in your mind one to one,

01:10:29.752 --> 01:10:31.210
connect, connect,
connect, connect,

01:10:31.210 --> 01:10:34.670
without looking at your slides.

01:10:34.670 --> 01:10:40.720
And then we'll do it
in three, two, one.

01:10:40.720 --> 01:10:42.090
Those are your answers.

01:10:42.090 --> 01:10:44.530
So the ones that
usually get confused

01:10:44.530 --> 01:10:49.382
are power and energy,
kilowatts and kilowatt hours.

01:10:49.382 --> 01:10:51.590
I'm not saying it's easy,
but the way to remember it,

01:10:51.590 --> 01:10:53.131
the easiest way to
remember it, would

01:10:53.131 --> 01:10:55.210
be to remember
that the power time

01:10:55.210 --> 01:10:57.270
product is equal to energy.

01:10:57.270 --> 01:10:58.960
So if you have
power instantaneous

01:10:58.960 --> 01:11:01.337
energy burn rate versus
time, some plot that

01:11:01.337 --> 01:11:03.920
looks like this as you take the
integral of that curve, that's

01:11:03.920 --> 01:11:06.260
your total energy.

01:11:06.260 --> 01:11:11.220
So in terms of units, current
voltage power and energy,

01:11:11.220 --> 01:11:13.370
a hair dryer versus
a fridge, which

01:11:13.370 --> 01:11:15.310
is more likely to
blow a fuse and which

01:11:15.310 --> 01:11:17.906
is more likely to
blow your budget?

01:11:17.906 --> 01:11:20.120
AUDIENCE: A hair dryer is
more likely to blow a fuse.

01:11:20.120 --> 01:11:22.369
PROFESSOR: A hair dryer is
more likely to blow a fuse.

01:11:22.369 --> 01:11:23.252
Why is that?

01:11:23.252 --> 01:11:24.805
AUDIENCE: High voltage.

01:11:24.805 --> 01:11:26.055
PROFESSOR: Yeah, high voltage.

01:11:26.055 --> 01:11:27.180
Well, high current, really.

01:11:27.180 --> 01:11:28.570
Because everything's
running 120.

01:11:28.570 --> 01:11:29.610
It's a higher current.

01:11:29.610 --> 01:11:32.305
It's pushing the wattage
up to around 1.5,

01:11:32.305 --> 01:11:36.930
1.7, 1,500, 1,700 watts.

01:11:36.930 --> 01:11:40.490
And so it's running close
to the 15 amp limit.

01:11:40.490 --> 01:11:41.910
And the fridge,
on the other hand,

01:11:41.910 --> 01:11:44.336
is probably an order
of magnitude lower.

01:11:44.336 --> 01:11:45.960
But the fridge is
running all the time,

01:11:45.960 --> 01:11:48.790
and your hair dryer is only
running a few minutes a day.

01:11:48.790 --> 01:11:51.820
So in terms of blowing a fuse,
it uses a large amount of power

01:11:51.820 --> 01:11:53.610
for a very short amount of time.

01:11:53.610 --> 01:11:55.760
Whereas, the fridge uses
a small amount of power

01:11:55.760 --> 01:11:57.170
for a long amount of time.

01:11:57.170 --> 01:11:59.890
And the integral under that
curve winds up being more,

01:11:59.890 --> 01:12:01.970
typically, then your hair dryer.

01:12:01.970 --> 01:12:03.740
That's the total
amount of energy.

01:12:03.740 --> 01:12:05.070
And you pay by the energy.

01:12:05.070 --> 01:12:07.538
You pay by the kilowatt hour
to your utility company,

01:12:07.538 --> 01:12:09.246
and that's why it
would blow your budget.

01:12:09.246 --> 01:12:10.760
Yeah.

01:12:10.760 --> 01:12:11.260
Oopsie.

01:12:11.260 --> 01:12:13.135
So the numbers work out
to somewhere around 1

01:12:13.135 --> 01:12:15.270
kilowatt hour per day for
the fridge and about 1/2

01:12:15.270 --> 01:12:17.150
a kilowatt hour
for the hair dryer.

01:12:17.150 --> 01:12:19.780
A kilowatt hour is
how much in here?

01:12:19.780 --> 01:12:20.910
$0.18?

01:12:20.910 --> 01:12:23.070
Most people pay about
$0.18 per kilowatt hour.

01:12:23.070 --> 01:12:24.444
And so you can
calculate how much

01:12:24.444 --> 01:12:26.780
it costs to keep things
running in your house.

01:12:26.780 --> 01:12:30.057
Most of us don't usually
think about that.

01:12:30.057 --> 01:12:32.140
And last, last, last, last
point, in your homework

01:12:32.140 --> 01:12:34.960
assignments, you're going to
be asked to size out systems,

01:12:34.960 --> 01:12:37.530
PV systems, photovoltaic
systems, in different parts

01:12:37.530 --> 01:12:38.550
of the world.

01:12:38.550 --> 01:12:41.910
And the easiest way to do
that is if we take a panel

01:12:41.910 --> 01:12:43.510
and we say that this
panel right here

01:12:43.510 --> 01:12:46.910
is rated at a certain
amount of power,

01:12:46.910 --> 01:12:49.710
so under peak
illumination conditions.

01:12:49.710 --> 01:12:52.290
When the panel is seated
at incident sunlight,

01:12:52.290 --> 01:12:57.740
so the cosine theta term is 1,
and the incident solar resource

01:12:57.740 --> 01:13:02.320
is 1,000 watts per square meter,
so around AM 1.5 conditions,

01:13:02.320 --> 01:13:05.830
this panel right here would be
producing-- this one is tiny.

01:13:05.830 --> 01:13:07.400
It would be producing
6 watts peak.

01:13:07.400 --> 01:13:08.850
But most of these
panels over here

01:13:08.850 --> 01:13:12.820
are producing somewhere around
a few hundred watts peak.

01:13:12.820 --> 01:13:15.810
And so the panels are
rated in terms of watt peak

01:13:15.810 --> 01:13:17.860
because the panel manufacture
doesn't know where

01:13:17.860 --> 01:13:19.350
you're going to install them.

01:13:19.350 --> 01:13:20.550
You could decide that
you're going to install it

01:13:20.550 --> 01:13:22.910
in Alaska, in which case, it's
going to produce about half

01:13:22.910 --> 01:13:24.368
the energy than if
you installed it

01:13:24.368 --> 01:13:27.430
down south in the continental
US in, say, Arizona.

01:13:27.430 --> 01:13:29.750
Maybe a third of the energy.

01:13:29.750 --> 01:13:31.531
And so it doesn't
want to rate the panel

01:13:31.531 --> 01:13:32.780
in terms of the energy output.

01:13:32.780 --> 01:13:33.990
It's not going to
guarantee that you're

01:13:33.990 --> 01:13:36.421
going to get a certain energy
output off of the panel.

01:13:36.421 --> 01:13:37.920
But it will guarantee
that the panel

01:13:37.920 --> 01:13:40.320
was rated at maximum
power of such and such

01:13:40.320 --> 01:13:42.454
under standard
testing conditions.

01:13:42.454 --> 01:13:44.370
Now that's good because
you can generalize it,

01:13:44.370 --> 01:13:46.650
which you'll do
for your homework.

01:13:46.650 --> 01:13:49.830
But it also has a downside
because standard testing

01:13:49.830 --> 01:13:51.780
conditions aren't
real world conditions.

01:13:51.780 --> 01:13:54.900
The panel isn't always
operating at 25 degrees Celsius.

01:13:54.900 --> 01:13:57.400
The panel isn't operating
always at incident sunlight

01:13:57.400 --> 01:13:58.500
normal, right?

01:13:58.500 --> 01:14:02.480
And so the gap between
actually knowing

01:14:02.480 --> 01:14:04.540
how much the panel is
going to output in terms

01:14:04.540 --> 01:14:06.920
of its energy for
a specific location

01:14:06.920 --> 01:14:09.600
and what our calculations,
the back of the envelope

01:14:09.600 --> 01:14:14.640
calculations, will give us, that
gap is, from an economics point

01:14:14.640 --> 01:14:16.790
of view, there's a lot of
money to be made there.

01:14:16.790 --> 01:14:20.140
If you understand really well
how much of a given panel

01:14:20.140 --> 01:14:24.050
will output, you can then
predict to a much finer degree

01:14:24.050 --> 01:14:26.900
what you should be charging your
customer for installing panels

01:14:26.900 --> 01:14:29.145
in a particular location.

01:14:29.145 --> 01:14:31.270
So there's a lot of work
being done right now, more

01:14:31.270 --> 01:14:34.180
on the business side
of pulling the systems

01:14:34.180 --> 01:14:35.770
engineers along and
trying to increase

01:14:35.770 --> 01:14:37.530
the accuracy of predictions.

01:14:37.530 --> 01:14:41.750
And so with that, I will
leave off on this slide.

01:14:41.750 --> 01:14:44.200
We can get to it during
recitation tomorrow at 4:00.

01:14:44.200 --> 01:14:46.658
I welcome your questions here
at the front if you have any.

01:14:46.658 --> 01:14:48.860
Otherwise, I'll
see you tomorrow.