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By Robert Rapier on Dec 29, 2008 with no responses

Final Comments on Solar Posts

I am going to be offline for a few more days, enjoying some time with the family. In the interim, Tom Standing has sent some detailed replies to some of the comments following his posts Arizona Solar Power Project and Ambitious Solar Plans in France.


Here is some additional material in response to a few of the comments that were submitted regarding my essays on the solar project in Arizona and the solar plan for France.

First is a general comment about my intent with the two essays. I am merely attempting to contribute some hard-edged reality to many solar proposals that do not seem to have been adequately appraised through the conceptual engineering process. The value and scale of proposals for renewable energy projects will be demonstrated through the laws of conservation of energy and thermodynamics. Rational calculations employing these laws are what I am basing my analysis on. We have at our disposal an immense database of solar insolation data on the NREL website, from which we can estimate how much energy a solar project is capable of delivering, and how the energy would be distributed with respect to time. I have also attempted to describe reasonable assumptions to fill in gaps of data or other information in order to complete the calculations. I fully realize that reasonable people will disagree with some of my assumptions, but I think that the differences will not significantly alter the conclusions.

Someone offered energy consumption by a range of vehicle size: one megajoule per mile at highway speeds for light vehicles, 2 MJ for heavier vehicles, and 10 MJ for 18-wheelers.

May I suggest we convert these numbers into units that we are familiar with, such as miles per gallon? A few key conversion factors can be used, as follows.

  • 1 joule/sec is the definition of 1 watt; therefore one kilowatt-hour is 3.6 million joules.
  • The heat equivalent of electrical energy is about 3,535 Btu per kWh (100% conversion).
  • Therefore, 1 Btu = 1,020 joules.
  • The heat value in 1 U.S. gallon of gasoline is 125,000 Btu.
  • The heat value in 1 U.S. gallon of diesel fuel is 138,000 Btu.

Working out the numbers, 1 MJ = ~ 1,000 Btu, which is 1/125 gallon of gasoline, which, according to the original comment, light vehicles could travel 125 miles/gal.

At 2 MJ/mile, SUVs would travel ~ 62 miles/gal.

The 10 MJ per mile for 18-wheelers burning diesel fuel calculates out to 13.8 miles/gal. Are these reasonable consumption rates? Most people would expect vehicular fuel consumption to be substantially higher.

The same commenter opined: “if a one square meter heterojunction panel can squeeze out 1.6 kWh = 5 MJ a day…”

Let’s estimate what the conversion of insolation to useful electricity would be for this panel, using NREL insolation data.

California’s Mojave Desert offers the highest annual average insolation of any of the 239 monitored stations in the U.S. – 6.6 kWh/ (m2-day) for unshaded fixed panels facing south, tilted at an angle = local latitude. If the panel yields 1.6 kWh of useful electricity in a day, then the conversion factor = 1.6/6.6 = 24.2%. If that same panel were exposed to insolation in St. Louis, MO where, with the same panel orientation, average annual insolation is 4.8 kWh/ (m2-day), and yields 1.6 kWh/day, the conversion factor = 1.6/4.8 = 33.3%. That would be a pretty good panel!


Here is my response to another comment about the French solar plan. The comment was by Bob Lynch, December 22 at 7:43 PM. He wrote: “The French though DO HAVE areas that bask (Basque?) in cloudless days, week after week. France has a strong infrastructure to deliver power far from where it is generated, so it does not have to be on millions of 17th century homes and hovels that dot the countryside.”

This, then, is my response:

If I interpret Mr. Lynch’s vision accurately, he believes that France could construct a major portion of their solar arrays in their sunniest regions, and then transmit the generated electricity to the populous regions where the climate is less favorable to collecting solar energy.

We can check the validity of such a proposal with the insolation data posted on the NREL website.

Click the link “In alphabetical order by state and city.” Then choose any city to obtain the data in spreadsheet format.

The insolation statistics I use here are for flat-plate collectors facing south at a fixed-tilt angle equal to the latitude of the site. This orientation gives the optimum solar exposure for fixed flat plates. Most installations will not match this ideal orientation. Collectors are tilted at varying angles, may not face due south, are not always clean, and may experience shading from nearby buildings or trees. Generally, solar installations generate about 15% less electricity than is calculated from insolation data and the manufacturer’s conversion factor.

Although the NREL data covers 239 stations in the United States, we can closely approximate insolation in France with comparable locations in the U.S. based on equivalent latitude and similarities in climate. The southern-most part of France, which provides the highest insolation, is in the range of latitude 43 to 44 degrees. A comparable location where the climate features “cloudless days, week after week,” is Boise, Idaho, latitude 43.57 degrees, with a semi-arid climate. The NREL data shows powerful insolation during the 6 months April through September of 5.8, 6.2, 6.5, 7.0, 6.8, and 6.5, respectively, in units of kWh/ (m2-day). The 30-year annual average is 5.1 (same units). I think we can say that there are scant areas in France where insolation would exceed that of Boise.

The insolation that I estimated as an average for France is 4.6, which, I think, is a fair representation of the regions where solar is most apt to be developed.

An important fact that we need to keep in mind is that average annual insolation does not vary greatly over wide reaches of the U.S. Similarly, variations in Europe would be narrow. For example, Sioux Falls, South Dakota is 850 miles due east of Boise (identical latitude), but with a humid continental climate. However, the 30-year average insolation is 4.8 (same units). It’s a good bet that across the southern quarter of France, insolation would be in the 4.8 to 5.1 range, hardly a bonanza for solar development.

Some 260 miles north-northwest of Boise is Spokane, Washington, latitude 47.63, the latitude that is about 80 miles south of Paris. Summer insolation in Spokane is generous, but noticeably below that of Boise: the 6 months April – September: 5.2, 5.6, 5.9, 6.5, 6.3, and 5.7, respectively. The 30-year annual average is 4.5. Spokane’s insolation is, therefore, likely to be near that of Paris and across the northern third of France. Thus, the 11 or 12% difference of insolation in France, between the sunniest south and the north, is probably not sufficient to justify transmission of large quantities of electricity. Solar-generated electricity would best be utilized near the source.