You do not need advanced math skills to follow and perform the arithmetic examples shown below. Anyone who can balance a checkbook or calculate the total square feet of floor space in his or her home, and understand why an area measuring 10 yards by 10 yards equals 100 square yards, can perform the following arithmetic examples and prove that American energy independence could be achieved with solar energy alone.
Science tells us that every square meter of the earth’s surface, when exposed to direct sunlight, receives about 1000 watts (1 kilowatt) of energy from the sun’s light. Depending on the angle of sunlight, which changes with the time of day, and the geographical location, the power of the sun’s light will be somewhat more or less than 1 kilowatt-hour per hour for every square meter of the earth’s surface exposed to the sun.
On average, and particularly in the Sunbelt regions of the Southwestern United States, every square meter area exposed to direct sunlight will receive about 1 kilowatt-hour per hour of solar energy. However, scientists estimate that sunlight will provide useful solar energy for only about 6 to 7 hours per day because, during the early hours and late hours of the day, the angle of the sun’s light is too low. So, for example, if the sun’s light provides 6 productive hours of solar energy per day, then a square meter of land in direct sunlight will receive about 6 kilowatt-hours of solar energy during the course of a day.
Scientists like to measure things using the metric system.
However, most Americans are unfamiliar with the metric system. (Europeans use the metric system.) It is easier for Americans to think in square feet and square yards because feet and yards are common lengths in the United States. So, for the sake of clarity and because this is written for an American audience, all measurements will be converted from meters to yards.
A meter is just a little longer than a yard (about 3 and ¼ feet to a meter, compared with 3 feet to a yard). There are 10.8 square feet in a square meter. There are 9 square feet in a square yard (3×3=9). A simple calculation can accomplish the conversion from square meters to square yards. A square yard is 83.33 percent of a square meter. Prove this by multiplying 10.8 (the number of square feet in a square meter) by 83.33%. The answer is nine (the number of square feet in a square yard). If you perform the calculation you will see that the answer is slightly less than the whole number 9 (but close enough for our purpose). Using this conversion, we can say that a square yard of land in direct sunlight receives 1000 x 83.33% = 833 watts of solar energy. This calculation can also be used in reverse to convert yards to meters, simply divide by .8333 (833 divided by .8333 = 1000 rounded).
Every square yard of land, if exposed to direct sunlight, receives about 833 watts of solar energy.
Therefore, a one square yard area exposed to continuous direct sunlight [in an optimal geographical location] for six hours will have received 6 hours x 833 watts = 4,998 watt-hours of solar energy during the course of a day. In round numbers, a one-square-yard area will receive about 5000 watt-hours (5 kilowatt-hours) per day of solar energy. Another way to obtain this result would be to take the 6 kilowatt-hours per meter (explained above in the third paragraph) and apply the conversion calculation (6 x 83.33% = 5 rounded).
Americans can assume, at least in the Sunbelt regions of the southwestern United States, that every square yard of land exposed to direct sunlight will receive about 5 kilowatt-hours per day of solar energy.
With the above information in mind, perform the following exercise: Measure an area ten yards long and ten yards wide. That would be thirty feet by thirty feet. Take a good look at its size of it. You are looking at an area covering 100 square yards. If that area were in direct sunlight all day it would receive about (5 x 100) 500 kilowatt-hours per day of solar energy. Now go look at your home electric bill. Your electric company calculates your home electric bill based on how many kilowatt-hours of electrical energy you use. Find the total amount of electricity that you have been billed for (given in kilowatt-hours). The amount of kilowatt-hours on your bill is for an entire month. If your home is a typical residential electric customer, you and your family consume between 500 and 1000 kilowatt-hours of electricity per month. Compare the quantity of electric energy your home consumed in one month with the quantity of energy the sun gives freely to a 100-square-yard area exposed to direct sunlight. One hundred square yards of sunshine provide as much energy in 1 to 2 days as an average family uses in an entire month!
It would be great if 100% of the sunshine became electricity, but solar energy and electricity are not the same. Technology accomplishes the conversion of solar energy to electricity. Several different technologies are used; perhaps the one that most people have heard of is the solar panel, made from photovoltaic cells called PV.
For a detailed explanation of photovoltaic cells, there is a very good article on the Internet located at:
www.howstuffworks.com/solar-cell.htm, it is well written and easy to read.
Conversion of one form of energy to another always causes a loss of energy.
In other words, the new form of energy will be less than the original. Efficiency is the word scientists use to describe the difference in power resulting from the conversion of one form of energy to another. The efficiency of commercially available solar panels (PV) is about 15%. This means that when a solar panel converts the sun’s light to electricity, only about 15 percent of the energy in the sunlight becomes electricity. The same thing is true of gasoline in your car. Your car’s engine can only convert about twenty-five percent of the energy in gasoline to mechanical energy that turns the wheels.
With an average efficiency of 15 percent, a square yard of solar photovoltaic cells (PV) would produce (5 kilowatt-hours of solar energy multiplied by 15% =) .75 kilowatt-hours of electric energy per day. Solar panels (PV) covering an area of ten yards by ten yards (100 square yards or 900 square feet) would produce 100 x .75 = 75 kilowatt-hours of electricity per day.
Seventy-five kilowatt-hours per day is a lot of electricity for a single-family home. If part of the electricity is stored in a home battery or is used to electrolyze water for producing hydrogen gas, and the gas is stored for use by a fuel cell when needed, then 100 square yards covered with solar panels would provide an average family with energy independence. Most detached family homes have more than 100 square yards (900 square feet) of roofs or that much space around their homes where solar panels could be installed.
In the Southwest, if you look at any commercial or industrial park, or any typical mall or supermarket you will see that most of the buildings have flat roofs. Those roofs require insulation to lower the cost of air conditioning on hot days. If those roofs were covered with solar panels the sun would provide electricity for the air conditioning and save businesses millions of dollars per month that would otherwise be paid to the utility companies.