PrintIn 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.
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.
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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.
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Click on the name of each season in the nimation above to see more information and read the corresponding season descriptions below.
SPRING: (Image of the tilt of the earth in the spring) In this configuration, the earth is not tilted with respect to the sun’s rays (The earth in this picture is actually tilted towards you as indicated by the fact that you can see the North Pole – green dot). Therefore, radiation strikes similar latitudes at the same angle in both hemispheres. The result is that the radiation per unity area is the same in both hemispheres. Since this situation occurs after winter in N. Hemisphere we call it spring, while in the S. Hemisphere it is autumn. This occurs on March 21.
SUMMER: (Image of the tilt of the earth in the summer) When the N. Hemisphere is tilted towards the sun, the sun’s rays strike the earth at a steeper angle compared to a similar latitude in the S. Hemisphere. As a result, the radiation is distributed over an area which is less in the N. Hemisphere than in the S. Hemisphere (as indicated by the red line). This means that there is more radiation per unity area to be absorbed. Thus, there is summer in the N. Hemisphere and winter in the S. Hemisphere. This situation reaches a maximum on June 21.
AUTUMN: (Image of the tilt of the earth in the autumn) In this configuration the earth is not tilted with respect to the sun’s rays (The earth in this picture is actually tilted towards you as indicated by the fact that you can see the North Pole – green dot). Therefore, radiation strikes similar latitudes at the same angle in both hemispheres. The result is that the radiation per unit area is the same in both hemispheres. Since this situation occurs after summer in the N. Hemisphere we call it autumn, while in the S. Hemisphere it is spring. This occurs on September 21.
WINTER: (Image of the tilt of the earth in the winter) When the N. Hemisphere is tilted away from the sun, the sun’s rays strike the earth at a shallower angle compared to a similar latitude in the S. Hemisphere. As a result, the radiation is distributed over an area which is greater in the N. Hemisphere than in the S. Hemisphere (as indicated by the red line). This means that there is less radiation per unit area to be absorbed. Thus, there is winter in the N. Hemisphere and summer in the S. Hemisphere. This situation reaches a maximum on December 21.
Self Check
Click on "Summer" in the above animation. When the northern hemisphere tilts toward the sun, the irradiation has a lower angle of incidence, meaning more photons strike a smaller area during the daytime. Answer the following questions for yourself.
- What happens to the southern hemisphere?
- What is the correlation between concentrated sunlight and the seasons?
- What happens beyond the Arctic Circle, which spans from about 66.5 degrees latitude to the North Pole?
Now, answer the same questions for autumn, spring, and winter.
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.
Self Check
You have seen these questions already in EME 810; you should be able to answer the following questions.
- What is the symbol for the day number?
- What is the declination, and what is the symbol for declination?
- What season is it in the Southern Hemisphere if the declination is a large positive number?
- How many hours of sunlight are in a day when the declination is zero?
- Does the sun always rise due East?