Author Archives: mathscinotes

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 | 4 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

Lake Level Variation Over Time

My wife and I are building a vacation home on the shores of Eagle Lake in Itasca County, Minnesota. We also are active members of the local lake association, which is a group of homeowners who work on projects to keep our lake healthy. One task I perform on a yearly basis for the lake association is to draw a graph of how our lake level is varying over time (Figure 1). The lake level is important to homeowners because it affects the amount of beach that is exposed and the length of their docks. Continue reading

 
Posted in Cabin | Leave a comment

Sugar-to-Flour Mass Ratios in Cake Recipes

I have been working at becoming a better baker. Specifically, I have been trying to understand how recipes are developed. Many baker's begin developing their recipe's based on ratios of ingredients. The classic rule ratio of thumb for cake recipes is to use equal masses of flour, sugar, butter, and eggs – with the ingredient ratios expressed as 1:1:1:1. Continue reading

 
Posted in Baking | Leave a comment

Real-Life Equipment Optimization Problem

I recently was asked to provide a recommendation on how to schedule the operating time for three different machines that were producing three different products. This is not a made up problem, but reflects a real production situation. My solution uses Excel's Solver and its linear programming-based optimization routine to find an optimal machine scheduling plan. The solution I provided has proven to be useful to the folks who asked for it, and I thought it was worth sharing my solution here. Continue reading

 
Posted in General Mathematics | 3 Comments

Business Trip to Portugal

I just came back from a business trip to Aveiro, Portugal. What a beautiful place! It is a very vibrant university town that lies about 6 km from the ocean. It is known as the "Venice of Portugal" because of its system of canals, which is a legacy of the old days when Aveiro was a major source of sea salt for the region (Figure 1). The climate is warm, with a very substantial breeze that blows out toward the Atlantic ocean. I liked my visit so much that I plan on bringing my wife on a future trip. Continue reading

 
Posted in Personal | Leave a comment

Yet Another FPGA Differential Termination Example

An engineer asked me for assistance on determining the termination circuit for a Xilinx uG476 series 7 FPGA. The circuit works is slightly different manner than those termination circuits I have developed before (here and here) because there is not termination voltage, so I thought I should document my work in detail. I will be using Mathcad 15 to determining the optimal resistor values for (1) terminating the circuit in printed circuit board's characteristic impedance (Z0), and (2) ensuring that I preserve as much of the transmit signal level as possible without exceeding the input circuit's maximum voltage level. Continue reading

 
Posted in Electronics | 7 Comments