Episode 6A New Hope…

ECE 371Sustainable Energy Systems

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AVG. DAILY SOLAR INTENSITY AT A TILT ANGLE

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SOLAR RESOURCE The total power from a radiant source falling on

a unit area is called irradiance with units of W/m2

Source of insolation is the sun

93 million miles away

1.4 million kilometers in diameter

Thermonuclear fusion furnace fusing hydrogen atoms into helium

3.8 x 1020 MW of electromagnetic energy radiates outward into space

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THE SOLAR SPECTRUM

The way to describe how much radiation an object emits is to compare it to a blackbody

Perfect emitter as well as perfect absorber

Perfect emitters radiate more energy per unit of surface area than any real object

Perfect absorbers absorb all radiation that impinges upon it

None reflected or transmitted through it4

THE SOLAR SPECTRUM Planck’s law describes the emitted power of a

blackbody for a given wavelength as a function of wavelength and temperature

Where,E = emissive power per unit area (W/m2/µm)T = absolute temperature (K)λ = wavelength in microns (µm)

]1[

1074.314400

5

8

−

×=

TeE

λ

λ

λ

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THE SOLAR SPECTRUM

The area under Planck’s curve between any two wavelengths is the power emitted by those wavelengths

The total area under the Planck’s curve is the total radiant power emitted, and it is expressed by Stefan-Boltzmann law of radiation

)/(1067.5

)(

428

4

KmWConstantBoltzmannStefan

WTAE

−×=−=

=

σ

σ

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THE SOLAR SPECTRUM

Modeling the earth as a blackbody at 15oCresults in the following emission spectrum

Figure 7.1

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THE SOLAR SPECTRUM

The interior of the sun is estimated to have a temperature of 15 million K

Radiation that emanates from the sun’s surface has a spectral distribution that closely matches that predicted by Planck’s law for a 5800 K blackbody

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THE SOLAR SPECTRUM

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THE SOLAR SPECTRUM

The total area under the blackbody curve has been scaled to 1.37 kW/m2

1.37 kW/m2 is the solar insolation just outside the earth’s atmosphere

Described as irradiation

Remember this number… 1 sun is 1000 W/m2

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EARTH’S ORBIT

Earth revolves around the sun in an elliptical orbit

One revolution in 365.25 days

Eccentricity of the ellipse is small

Orbit is nearly circular

Radius is about 150 million kilometers

Every 100,000 years the shape of orbit oscillates from elliptical to nearly circular

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Solar Video – Of Course

https://www.youtube.com/watch?v=taHTA7S_JGk

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What we LearnedTilt of earth 23.5 DegreesTropic of Cancer Latitude 23.5 Degrees (North)Tropic of Capricorn Latitide 23.5 Degrees (South)Equator 0 DegreesArtic Circle 66.5 Degrees North LatitudeAntarctic circle 66.5 Degrees South LatitudeSolar Noon Sun is directly overheadEquinox Sun directly over the equatorVernal Equinox 21-MarAutumnal Equinox 21-SepSummer Solstice 21-JunWinter Solstice 21-DecSolar Noon Sun is directly overhead

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What We Learned We need to face solar panels south in the

northern hemisphere. We need to face solar panels north in the

southern hemisphere. Solar panels are placed flat at the equator. Solar panels are tilted by an amount equal to the

latitude. The angle changes as the Earth rotates around

the sun.

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What We Learned Depending on where you are on the Earth, the

sun has to travel through different amounts of the atmosphere to reach you.

The more atmosphere the light goes through the less insolation reaches the ground.

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EARTH’S ORBIT

The following is the ecliptic plane

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ALTITUDE ANGLE OF SUN AT SOLAR NOON

The previous figure is a difficult diagram to use when trying to determine various solar angles as seen from the surface of the earth

An ancient way to show movement of earth with respect to sun is shown next

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ALTITUDE ANGLE OF SUN AT SOLAR NOON

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ALTITUDE ANGLE OF SUN AT SOLAR NOON

The angle δ formed between the plane of the equator and a line drawn from the center of the sun to center of the earth is called the solar declination

)]81(365360[sin45.23 −= nδ

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Cool MATLAB Plot

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ALTITUDE ANGLE OF SUN AT SOLAR NOON

The following figure defines the earth’s key latitudes

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ALTITUDE ANGLE OF SUN AT SOLAR NOON

The following figure shows a south-facing collector on the earth’s surface at an angle equal to the local latitude L

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Summary In the norther hemisphere, face panels South.

Tilt Angle = Latitude - δ In the southern hemisphere face panels nouth.

Tilt Angle = Latitude + δ

δ was our solar declination we calculated earlier.

If you don’t have a solar tracker, just set the tilt angle to the latitude.

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ALTITUDE ANGLE OF SUN AT SOLAR NOON

On the average, facing a collector toward the equator and tilting it up at an angle equal to the local latitude is a good rule-of-thumb for annual performance

For winter collection, the angle should be slightly higher

For summer collection the angle should be slightly lower

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Local Meridian The local meridian – (meridian: north south

longitudinal line) defines midday, as it signifies the highest point the Sun will reach in its daily arc across the sky.

This point is also called Solar Noon, and the sun is directly over the local meridian.

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SOLAR POSITION AT ANY TIME OF DAY

The difference between the local meridian and the sun’s meridian (suns present position) is the hour angle

Since earth rotates 360 degrees in 24 hours, or 15 degrees/hour, the hour angle is Hour angle: H = (15o/hour)(hours before solar noon)

The hour angle H at 11:00 A.M. solar time is H = +15o

The hour angle H at 2:00 P.M. solar time is H = - 30o 26

SOLAR POSITION AT ANY TIME OF DAY

Note: A negative hour means after solar noon. A negative hour angle means West. A positive hour mean before noon. A positive hour angle means East.

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οο φφδβ

δφ

δδβ

9090tantancos

cossincossin

sinsincoscoscossin

>≤≥

=

+=

ss

s

otherwisethenL

Hif

HLHL

Sunrise and Sunset

Since the Sun’s height is 0 degrees at sunrise and sunset, 𝛽𝛽 = 0, so

Solving for cos H

or

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0sinsincoscoscossin =+= δδβ LHL

δδδ tantan

coscossinsincos L

LLH −=−=

( )δtantancos 1 LH −= −

Sunrise and Sunset Note that when we talk about “solar noon,”

there are as many hours after solar noon as there are before noon.

So sunrise is at +H and sunset is at –H. To convert to an hour, remember that every 15

degrees is an hour, so

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑡𝑡𝑆𝑆𝑡𝑡𝑆𝑆 = 12: 00 − 𝐻𝐻⁄15° ℎ

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Sun Path Diagram

Sun path diagrams tell us where the sun is at any time

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Civil Time

All of this time stuff was screwed by by Ben Franklin, the Railroads, and the cosmos.

Franklin conceived daylight savings time. Railroads set up time zones…. The cosmos made the Earth’s orbit slightly

elliptical.

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Cool Stuff From the Book

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More Cool Stuff From the Book

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E = 9.87𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠𝑠 − 7.53𝑐𝑐𝑐𝑐𝑆𝑆𝑠𝑠 − 1.5𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠Where

B=360364

𝑆𝑆 − 81and n= day number

Solar Time = Clock Time + 4𝑚𝑚𝑚𝑚𝑚𝑚𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

(𝐿𝐿𝑐𝑐𝑐𝑐𝐿𝐿𝐿𝐿 𝑇𝑇𝑆𝑆𝑡𝑡𝑆𝑆 𝑀𝑀𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀𝑆𝑆𝐿𝐿𝑆𝑆 −

SUN PATH DIAGRAMS FOR SHADING ANALYSIS

Their application is in trying to predict shading patterns at a site, which is very important for photovoltaics that are very sensitive to shadows

What is needed is a sketch of the azimuth and altitude angles for trees, buildings, and other obstructions that can be drawn on top of a sun path diagram

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SUN PATH DIAGRAMS FOR SHADING ANALYSIS

Sections of the sun path diagram covered by obstruction indicates periods of time when the sun will be behind the obstruction and the site will be shaded

This can be done with Compass Plastic protractor Plumb bob

Screw this… use a cell phone….

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SUN PATH DIAGRAMS FOR SHADING ANALYSIS

This can be done with Compass Plastic protractor Plumb bob

The protractor and plumb bob provides the altitude angles of obstruction (doing a scan)

The azimuth angles of obstruction are measured using a compass (doing a scan) Note that compass points to magnetic north rather

than true north Correction is done by the magnetic declination 37

SUN PATH DIAGRAMS FOR SHADING ANALYSIS

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SUN PATH DIAGRAMS FOR SHADING ANALYSIS

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