Author Archives: mathscinotes

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

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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

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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

Naked and Afraid – Who Taps Out More? Men or Women

I have been receiving quite a few questions about my database of Naked and Afraid information. I only track the shows with 2-person teams – I am not a big fan of the XL episodes. There recently has been a number of shows where women have been particularly strong leaders and finishers, and some big, tough-looking men struggled right from the start and failed to complete the challenge. In response to some of the recent shows, a number of people have asked "Who taps out more – men or women?" So I have updated my Excel Workbook with the data from recent episodes and went to work. I have also updated Figure 1, which shows where the episodes were filmed. Continue reading

Posted in Naked and Afraid | 1 Comment

Royal Navy Losses in WW2

I have been doing quite a bit of reading lately on WW2 naval actions, and I have been putting together tables that show me ship losses by year. This information gives me a feel for the tempo of battle during the war. I first looked at US naval losses (link) and am now looking at the Royal Navy losses (Figure 1). Continue reading

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

A Little Beer Data

I gave a seminar last week on the use of Python with Pandas using Jupyter notebooks. When I give a seminar, I always have a worked example to illustrate the points that I am trying to make. This attendance at this seminar had a number of young men in it, so I decided to focus on a topic near and dear to their hearts – beer. I was amazed at the amount of beer knowledge showed by some individuals in the audience. Clearly, beer is a major part of their lives. I myself know NOTHING about beer, so I had to educate myself. The data provide interesting to analyze, and I will probably be augmenting my seminar with additional data over time. Continue reading

Posted in Python, software | Leave a comment

US Naval Losses in WW2

I have been putting together some information on US naval actions during WW2. Specifically, I wanted to look at US Naval losses by year during WW2 in order to get a feel for the change in battle tempo over time. The Wikipedia has an excellent page on all the US naval losses during WW2, so I simply downloaded this page, cleaned it, up and generated an Excel pivot table (Figure 1). The breakdown by combatant type is my own, everything else is from the Wikipedia. Continue reading

Posted in History Through Spreadsheets | 7 Comments