Author Archives: mathscinotes

My New Cabin Construction

Posted on 30-June-2017 by mathscinotes

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 | 10 Comments

Analysis of 555-Based PWM Circuit

Posted on 29-June-2017 by mathscinotes

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 | 1 Comment

Visualizing US vs IJN Aircraft Carrier Numbers During WW2

Posted on 26-June-2017 by mathscinotes

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 | Comments Off on Visualizing US vs IJN Aircraft Carrier Numbers During WW2

Coal Production By State

Posted on 5-June-2017 by mathscinotes

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

Posted on 25-May-2017 by mathscinotes

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

Posted on 23-May-2017 by mathscinotes

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

Posted on 21-May-2017 by mathscinotes

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 | 2 Comments

Lake Level Variation Over Time

Posted on 16-May-2017 by mathscinotes

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 | Comments Off on Lake Level Variation Over Time

Sugar-to-Flour Mass Ratios in Cake Recipes

Posted on 14-May-2017 by mathscinotes

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 | Comments Off on Sugar-to-Flour Mass Ratios in Cake Recipes

Real-Life Equipment Optimization Problem

Posted on 9-May-2017 by mathscinotes

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