Author Archives: mathscinotes

Iceberg Size Analogies

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

Posted in General Science, News Fact Checking | Leave a comment

CO2 Generation By Fuel Per Million BTUs of Heat

My year-round cabin in northern Minnesota needs a furnace, and a furnace needs fuel. My fuel options are fairly limited – fuel oil, liquid natural gas, or propane. I ended up choosing propane because the local propane gas supplier has a reputation for being reliable. While researching the fuels, I became curious about the amount of CO2 released into the atmosphere by the different fuel options for given amount of heat. Continue reading

Posted in Construction, General Science | 1 Comment

Personnel Count of US Special Operations Forces

I have a son who lives in Butte, Montana – the home town of Robert O'Neill, a famous US Navy SEAL. We were discussing Mr. O'Neill's exploits one night and started to wonder about the size of the different US special operations forces. I quickly looked up some 2014 data from the Government Accountability Office (GAO) and put the data into a pivot table (Figure 1). I was a bit surprised at the numbers involved – it does not surprise me that the Army has the largest contingent, but the size of the Air Force's contingent was a surprise. Continue reading

Posted in Military History | 2 Comments

My New Cabin Construction

A number of folks have asked that I post pictures of my cabin construction project. The project actually consists of two separate activities: a large garage (started last fall) and a two-story cabin. I will start posting photos here as things progress. Continue reading

Posted in Construction, Personal | 4 Comments

Analysis of 555-Based PWM Circuit

I received a request for the design formulas that can be used to estimate the frequency (f) and duty cycle (DC) generated by the 555 timer-based Pulse Width Modulator (PWM)  circuit shown in Figure 1. The presence of diodes in the charge and discharge paths are the main cause of the confusion. Continue reading

Posted in Electronics | Leave a comment

Visualizing US vs IJN Aircraft Carrier Numbers During WW2

I watched an interesting lecture on American History TV this weekend called Japanese Perspective on the Battle of Midway by Anthony Tully. The most interesting part of the discussion occurred when Tully began showing how the US production of aircraft carriers eventually overwhelmed the Japanese ability to build carriers. He used some simple graphs to show the relative carrier strength of the US Navy versus the Imperial Japanese Navy (IJN) over time. In this post, I will come up with my own graphics to visualize this information. Continue reading

Posted in History Through Spreadsheets, Military History | Leave a comment

Coal Production By State

I have been listening to politicians discussing US energy policy the last few days. Very few facts were presented during these discussions, but one politician did casually mentioned that Wyoming produces more coal than the next six states combined. I did not know that Wyoming was such a dominating coal producer, and I began to look at how to fact check this statement. Fortunately, the US Energy Information Administration (EIA) has all the data readily available from this web page. Continue reading

Posted in Fact Checking | 6 Comments

Linear Temperature Coefficient Resistor Nonlinearity

Our products contain many analog circuits. These circuits often require temperature compensation in order to meet their requirements across the product's entire temperature range. To perform this compensation, we often use resistors with a specified Temperature Coefficients of Resistance (TCR). A vendor recently stopped manufacturing one of the resistors we use for temperature compensation, and we needed to find a substitute. While searching for a substitute resistor, I needed to understand just how linear the approved resistor's temperature variation is so I can find an appropriate substitute. Continue reading

Posted in Electronics | 1 Comment

An Intimidating Interview

I have been reading the book Building the H Bomb: A Personal History by Ken Ford. A major character in the book is Edward Teller, a very famous physicist who is best known as the father of the American H-bomb. I had to smile as I read about Edward Teller. When I worked at Hewlett-Packard, an electrical engineer named Russ Price talked about interviewing for a job at Lawrence Livermore National Laboratory, where he walked into a room and faced Edward Teller as his interviewer. He and Dr. Teller then proceeded to have a very technical interview. Continue reading

Posted in Management | 4 Comments

Recoil Calculation Example

I have been reading about the US Air Force's battle to retire the A-10 Warthog (Figure 1). The USAF has never cared for the A-10 and has made a number of attempts to replace it with either the F-16 or the F-35. During my reading, I saw the following statement about the recoil of it 30 mm Gatling gun, and the impact of this recoil on the A-10's speed. Continue reading

Posted in Ballistics, Military History | Leave a comment