I'd put my money on the Sun and Solar Energy, what a source of Power! I hope we don't have to wait until oil and coal run out, before we tackle that.

— Thomas Edison, 1931.

I have no doubt that we will be successful in harnessing the sun's energy. If sunbeams were weapons of war, we would have had solar energy centuries ago.

— George Porter, Nobel Prize winner in Chemistry, 1967.

Figure 1.1: An artist's rendering of Archimedes' Death Ray, (c. 214-212 BC).

Source: Chris Devlin's Blog [1]

People have been leveraging solar thermal energy for millennia. The history of the use of solar energy for heating buildings (c. 4000 BC), creating fire (c. 1000 BC), and driving industrial processes (c. 1800 AD) has been well documented by archeologists and historians [2]. The sun comes up every day (with the exception of locations that are north of the Arctic Circle or south of the Polar Circle where the sun never rises above the horizon in the depths of winter). It is our most reliable source of energy and is the source of most other forms of energy on our planet. While often characterized as intermittent, with intermittence deriving from meteorology, atmospheric physics, and diurnal and seasonal patterns, barring any catastrophic event such as a meteor impact on Earth or the expiration of the sun, the sun is always shining somewhere, will shine again everywhere, and is the primary driver behind the thermal behavior of our environment.

Lesson Objectives

At the successful completion of Lesson 1, students should be able to:

• Identify solar temporal relationships;
• Describe solar geometric relationships;
• Recall key aspects impacting available solar radiation.

What is due for Lesson 1?

This lesson will take us one week to complete. Please refer to the Course Calendar in Canvas for specific time frames and due dates. Brief directions for the lesson assignments are given in the table below, and you can find more details on respective pages of this lesson.

Questions?

If you have any questions, please post them to our Questions and Answers discussion forum, located under the Modules tab in Canvas. I will check that discussion forum regularly will do my best to respond. While you are on the forum, please feel free to post your own responses if you are able to help out a classmate.

When you are courting a nice girl an hour seems like a second. When you sit on a red-hot cinder a second seems like an hour. That's relativity."

— Albert Einstein [4]

Einstein, in the special theory of relativity, proved that different observers, in different states of motion, see different realities."

— Leonard Susskind [5]

The location of the sun in the sky through time is relative to the location of the Earth with respect to the sun, the location of the observer on Earth, and the orientation of the collector at the observer’s location on Earth. The geometric relationships are defined by angles separated into three groups; 1) the relationship between the Earth and sun, as spheres, 2) the relationship between the sun and an observer (or point on the Earth), and 3) the relationship between a collector at some orientation and the sun. As the Earth rotates on its axis, the sun appears to traverse across Earth's sky. As the Earth orbits around the sun, the tilt of the axis moves the northern and southern hemispheres closer and further from the sun moving the sun's trajectory across Earth's sky higher and lower in the sky, creating seasons. The temporal and spatial relationships are inextricably linked.

Recall from EME 810 the following four tables showing the Angular Symbols for Standard Solar Relations. These angles are detailed in the D&B textbook in section 1.6. These angles are all critical to the calculation of solar energy on any given surface at some orientation. To calculate the energy balance across any time scale with respect to the incident solar radiation, you must know the geometric relationships that define the spherical realities of planetary motion relative to the sun for specific tilted surfaces on the planet. Each piece is defined relative to another piece. For example, a solar panel may have a tilt, beta, but that tilt is relative to the horizontal surface on the planet, not relative to the sun. Greek symbols, often with a subscript, are used to ensure clarity through unique identifiers for each angle. Additionally, the sign convention for each angle is critical, as an incorrect sign or origin can lead to drastically incorrect results. Be careful when performing calculations to ensure that each angle and sign is correct.

In EME 810, you learned and applied principles regarding the Earth's rotation, the cosine projection effect of light, and some insight into the driving force behind the seasons. These principles are critical for appropriate engineering of solar thermal solutions for utilities and industry. A comprehensive understanding of the solar resource and the physics behind the intermittent and cyclical behavior of solar energy enables the engineering of solar thermal systems that adequately meet a client's needs.

Figure 1.2 The axis of the Earth currently tilts approximately 23.5 degrees from the perpendicular (dashed line) to its orbital plane

Credit: David Babb.

Earth's Rotation

As we have seen in our reading, the Earth rotates with a roughly constant speed, so that every hour the direct beam (a ray pointing from the surface of the sun to a spot on Earth) will traverse across a single standard meridian (standard meridians are spaced $15^\circ$ apart). The implications are that the unit of one hour is equivalent to the rotation of Earth 15 degrees. When Earth rotates such that the beam of the sun shifts $+1^\circ$ of longitude from East to West: it takes 4 minutes of time.

• $1\ h = +15^\circ\ \text{Earth rotation}$
• $4\ min = +1^\circ\ \text{Earth rotation}$

Wild fact: a time zone change of one hour is really just 15 degrees of separation between standard meridians.

The axis of rotation of the Earth is tilted at an angle of 23.5 degrees away from vertical, perpendicular to the plane of our planet's orbit around the sun.

The tilt of the Earth's axis is important, in that it governs the warming strength of the sun's energy. The tilt of the surface of the Earth causes light to be spread across a greater area of land, called the cosine projection effect.

Cosine Projection Effect

When you tilt a surface away from a beam of light, you spread the same density of light across a larger area. Recall that irradiance is in units of $W/m^2$, so a larger denominator means a smaller value of irradiance, right?

Explore the concept of the cosine projection effect in the following experiment.

Seasons and the Cosine Projection Effect

The sun is about 93 million miles away from the Earth (equivalent to ~150 million km). That is so far away that the photons from solar irradiation effectively travels in parallel rays. So, unlike the flashlight experiment, the tilt of the sun has no bearing on the intensity of the radiation reaching the Earth's surface. Instead, we find that the Earth's tilt controls the intensity of irradiation and the seasons.

Keep in mind that the Earth's axis points to the same position in space (toward the North Star, Polaris). As the Earth travels in a near spherical (a very small eccentricity into an ellipse) orbit around the sun, the northern hemisphere can be tilted toward or away from the sun, depending on its orbital position.

Figure 1.3 From late spring to late summer, the sun never sets at Barrow, Alaska (as this multiple exposure of the sun reveals)

Credit: Alaska Community Database, AK Division of Community and Regional Affairs.

Forecasters and meteorologists use different criteria to determine the "meteorological seasons." For example, meteorological winter in PA runs from December 1 to Feb 28/29, a period that statistically includes the three coldest months of the year. This is also centered on a time about 25 days after the Winter Solstice. 

Meteorological summer runs from June 1 to August 31, a period that includes the warmest three months of the year. Again, this is a period centered about 25 days from the Summer Solstice.

Please review the following NASA movie from 2000-2001, showing the rhythms of the most intense ultraviolet radiation coinciding with the most direct rays of the sun (around the summer solstices). Again, what may be a surprising observation is that the average air temperatures lag the sun's most direct days.

As one more example, review Pittsburgh's plot of annual average high temperatures. The maximum daily temperature occurs in late July, long after the summer solstice.

Figure 1.4 The annual variations of average, record-high, and record-low maximum temperatures at Pittsburgh, PA. Access the annual temperature stats at other cities [6]

Credit: Earth System Research Library

Recall from EME 810 that the time that we use in solar energy engineering is the apparent time and path of the sun relative to the aperture or collection device, called Solar Time. Because the Earth is a rotating sphere (360deg) that completes a rotation every 24 hours, 360 divided by 24 gives 15 degrees of rotation per hour, or one degree every 4 minutes. The chronological time that clocks use do not account for your geographic location beyond correcting for a time zone. Within a time zone, if you are geographically close to the next time zone, a larger time correction is necessary to convert to solar time. Additionally, the Earth does not rotate perfectly, rather, it wobbles on its axis creating what is known as an analemma. As such, an "equation of time" is necessary to convert between solar and standard time, as given in D&B equations 1.5.2 and 1.5.3.

Correcting with the Equation of Time: Accounting for Wobbles

Even in Greenwich, where no longitudinal correction is necessary, "noon" UTC will generally not be the time when the sun is directly overhead. We can see in the plot below that watch time and solar time are the same in Greenwich for only 4 days in the year.

• There are deviations of up to $\pm16$ minutes (regardless of your location on the planet).

As you will have read, our interpretation of watch time assumes an even progression for Earth's planetary rotation, with no weebles or wobbles or precession of the polar axis. However, you will now know that wobbling occurs, and there is great variability in the rotation of the Earth throughout the months of the year. This is why we add leap years and leap seconds to our calendars. So we create a "mean time" based on the length of an average day to keep things simple. Solar time has to correct for this mean time approximation.

Figure 1.5 Equation of time function represented over all the days of a year. Note how the minimum and maximum do not exceed 16 minutes.

Credit: Jeffrey R. S. Brownson

For views of amazing solar analemma photography by Anthony Ayiomamitis, please visit his solar image gallery [7]. The gallery has a series of composite of images, taken at the same watch time every few days for an entire year to record the position of the sun. We call the shape an analemma. An analemma is a beautiful way to capture both the range of declination $\delta$ (along the length of the analemma) and the Equation of Time Et (the expansion or width of the analemma) in a graphical format. Notice how there is a big loop and a little loop, and compare the same big waves and little waves in the first image of the Equation of Time correction above. If you were to draw a line down the center, you would have removed the error from watch time, and you would be one step closer to solar time.

Figure 1.6: An analema

Extraterrestrial Variation

In addition to the geometric (space) and chronologic (time) relationships between collector surfaces on Earth and the sun, the intensity of the sun's irradiation changes based on the distance between the Earth and the sun because of the eliptical orbit of the Earth. While the average solar radiation flux is 1361 W/m², the annual fluctuation due to the Earth's eliptical orbit is greater than $\pm40$W/m², resulting in peak extraterrestrial radiation flux of about 1410 W/m² in January and lows of about 1320 W/m² in June. The following equations can be found in the D&B text section 1.4.

G_on = G_sc (1 + 0.033 cos(360n/365))

OR

G_on = G_sc (1.000110 + 0.034221 cos B + 0.001280 sin B
 +0.000719 cos 2B + 0.000077 sin 2B)

where G_on is the extraterrestrial radiation incident on the plane normal to the radiation on the n^th day of the year and B is given by

B = (n − 1) *360/365

Atmosphere

The Earth's atmosphere is the source of the greatest uncertainty in predicting solar radiation incident on a solar collector. Particulates, aerosols, clouds, moisture, etc. are the drivers behind the intermittency of incident solar energy due to atmospheric attenuation. Some meteorologists and atmospheric scientists have spent their entire careers focused on the problem of modeling the atmosphere to develop predictive tools for increased accuracy in energy models. The application of such atmospheric modeling tools is enabled with an accurate level of solar radiation known outside of the Earth's atmosphere (extraterrestrial).

Facts about Solar Thermal Energy

• Solar thermal energy has been used in various ways for millennia, ranging from simple fire starting with a pocket mirror to solar architecture to capture heat in buildings.
• 48% of the the sun's energy is in the infrared spectrum, invisible to the human eye, as heat.
• Solar thermal collectors can employ (absorb) nearly the entire solar spectrum
• The sun is the most abundant and reliable source of energy
• Financially, solar thermal energy conversion systems have reached grid-parity in many locations

Currently, we (humans) use an abundance of fossil fuels for much of our heat needs. While in the long run our society will switch to the source of all of those fossil fuels (the sun), the reality is that most of you have probably not experienced the direct impact of a solar thermal energy conversion system on your life. The truth is that we can do everything that we currently do in our society with solar energy. Much of the burden can be carried by solar thermal solutions. One terrific modern day example of a solar thermal energy system is the Drake Landing Solar Community in Alberta, Canada, where 95% of the the community's heating needs are supplied by on-site solar thermal collection and a connected seasonal thermal energy storage system. Our society uses a lot of heat. We need to keep working to make solar thermal energy solutions make sense and work well in more places whenever possible.

While solar thermal energy has been studied and leveraged for millennia, the technical difficulty and subsequent costs of appropriately meeting an energy need have hindered the wide adoption of solar thermal energy conversion systems, instead opting for other technologies and fuel sources. In light of your background and professional aspirations, write an essay that identifies your relationship with the course material.  The essays will serve two purposes: (1) sharing your perspective with the class and (2) second, thinking critically about the relevance of the course subject matter to your educational and career goals.

Solar thermal energy conversion systems at the utility scale have been developed for over a century using basic thermal principles, concentration systems, and mechanical engineering practices for heat and power. The article referenced below discusses some aspects for and some against the recent progress at the Ivanpah solar thermal electricity generation plant in the Mojave Desert, California, USA. While we are not seeing a mass conversion of our electricity generation infrastructure to solar thermal generation yet, the industry is experiencing significant growth.

Summary

This week, we’ve looked back at what we learned in EME 810 and refreshed our memories. We have taken this information and laid a foundation for applying our knowledge to the field of solar thermal energy for utilities and industry. Finally, we have introduced ourselves to each other and thought about what impact solar thermal energy has on each of us.

Reminder - Complete all of the Lesson 1 tasks!

You have reached the end of Lesson 1! Please double-check the to-do list on the Lesson 1 Introduction page [8] to make sure you have completed all of the activities listed there before you begin Lesson 2.