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Author Archives: mathscinotes
My wife and I are about half-way through the construction of a 2100 square foot home in northern Minnesota. This weekend, my neighbors and I were talking about the area of houses being built today, and no one in the conversation had any data. I grabbed my computer, jumped on the Internet, and very quickly found data from the Census Department that answered my question. Like most census information, the data is in the form of screwy tables that need to be parsed to get into a form that can easily be plotted. This exercise gave me another excellent example to use when I train staff on the use of Excel's Get and Transform tool. Figure 1 was the result of my search. For those who are interested, my workbook is here. Continue reading
Yesterday, a reader asked me how to compute the totality path width for the eclipse that will cross the US on 21 Aug 2017. I wrote a post on how to perform this calculation years ago. NASA has published a path width value of 114.7 km. This width will actually vary a bit as the shadow moves across the Earth because the distance change slightly between all the bodies involved. Also, the Earth and Moon are not perfectly round, which I assume. NASA has very detailed models that even include the variations due to mountains and valleys on the Moon. Continue reading
I am preparing to drive out to Idaho to experience totality during the August 21, 2017 eclipse. I am choosing to view the eclipse from Idaho because my granddaughter (and her parents) live in western Montana, and I can stop there for visit when I return to Minnesota. This will be a long drive through large states (Minnesota, North Dakota, Montana) that have a significant percentage of farm land. While planning my journey, I became curious as to the percentage of farmland in each of the fifty states. In this post, I compute the farm land percentage by taking the farm acreage in each state and dividing by the state's land area (water area removed). Continue reading
I have been reading about how low natural gas prices have been affecting the coal mining industry. Coal mining is affected because those coal-fired electrical generation plants that can switch fuels are converting to natural gas to achieve significant cost reductions. Also, natural gas can fuel peaking generators that are designed to provide peak load support. I had no idea what the price advantages were for natural gas so I surfed over the US Department of Energy's (DoE) web site and found two tables that provided a summary of the maintenance, fuel, and operating costs for different types of electrical generation. Continue reading
lon Musk gave a talk at the National Governors Association where he stated that a 100 mile square solar array built in place like Nevada could generate an amount of electrical power equal to that of the present electrical grid. This seems like an easy calculation to verify and I thought I do that analysis here. Continue reading
While answering a recent question about the tonnage sank by the top US submarine skippers during WW2, I realized that I had not made available my conversion of the JANAC data for vessels sunk by US submarines. The JANAC records are considered the official records because they were cross-checked with information from Japanese records. Continue reading
I was reading the Washington Post this weekend when I stumbled upon an 22-July-2017 article about concerns that ISIS in Mosul had access to an old medical radiation source. This source, which contains the radioactive isotope cobalt-60, is used in the treatment of cancer. However, cobalt-60 is extremely radioactive and could be used to build a dirty bomb. Fortunately, ISIS did not touch the source, but the concerns about a terrorist being able to use one of these radiation sources for a dirty bomb are real. Continue reading
I have had a number of discussions with coworkers about the different types of wall insulation – some of these discussions have been documented in previous blog posts (e.g. here , here, here). There exists wide cost and performance disparities between the different wall insulation technologies. With respect to cost, I view fiberglass batts as a low-cost insulation option and the spray foams (open and closed cell) as high-cost options. All the options have their advantages and disadvantages. Fine Homebuilding Magazine (August/September 2017) has an excellent article by Martin Holladay provides an excellent spreadsheet-like analysis that illustrates the trade-offs between open and closed-cell foam nicely. My goal in this post is to go through the computational details of his analysis and to discuss his approach to choosing the best insulation for your application. Continue reading
Putting a satellite into orbit requires that you impart a velocity of ~17,000 mph to the satellite. Because the Earth is rotating, its surface velocity gives you a head start on achieving orbital velocity when you launch toward the east – the direction of the Earth's rotation. The closer you move your launch site to the equator, the more velocity you get from the Earth's rotation. Continue reading
e nightly news reports have been filled with stories about the large iceberg that recently calved off of the Larsen C ice shelf. Reports of natural events always struggle with trying to convey the scale of events to the general public. In this case, the media has been reporting that the iceberg is (1) approximately the same area as the state of Delaware, (2) it contains a volume of water that is double that of Lake Erie, and (3) the mass of water it contains is about 1 trillion metric tons. Figure 1 shows a good graphic for area comparisons. Continue reading