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Author Archives: mathscinotes
Steinhart-Hart Thermistor Calibration in Excel Using Matrix Formulas
I had a job this week that required that I use the Steinhart-Hart equation for modeling the thermistor resistance versus temperature relationship. The requirement was driven by the customer's need for high accuracy. Most thermistor applications do not demand high accuracy, but this application can tolerate no more than ±0.2 °C of error. This means that I cannot use the β-based thermistor model, which in this application would have an error of more than ±2 °C. This page will show how how to perform an efficient 3-point calibration using Excel and a bit of matrix math. As a side benefit, I am using this workbook as an example of matrix math in my Excel tutoring at a local library. Continue reading
Posted in Electronics
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Another Excel TEXTJOIN Example
I have been analyzing seemingly random fuse failures in different products. The failing fuse is similar to the unit shown in Figure 1. My analysis has shown that the fuses are failing because of damage they are sustaining during the manufacturing process. In my analysis report, I was asked to list each product that experienced a fuse failure and to list how many days each product was in service before the fuse failure occurred. Continue reading
Battleship Classes and Throw Weights
I just finished reading The Battle of Surigao Strait by Anthony Tully, a battle that saw the final clash of battleships. For a battleship aficionado, the climax of the fight was the contest between two Japanese battleships and six US battleships, where five of the six US battleships had been sunk or heavily damaged during the Pearl Harbor attack – only the USS Mississippi had escaped the carnage of Pearl Harbor. These were old battleships (Table 1) with two having been commissioned during WW1 and the rest shortly after the WW1 ended. Continue reading
Everest Climbers With No Supplemental Oxygen
I recently have seen pictures on the news of a line of people preparing to summit Mount Everest (Figure 1), which got me thinking about the difficulty of waiting in line under low-pressure conditions.The vast majority of the people who climb Everest use supplemental oxygen. The air pressure at the summit of Everest is about 0.3 atmosphere, which is not enough to support human life for an extended period of time. But a relatively small number of people have climbed Everest with No Supplemental Oxygen (NSO). In this post, I will look at this very select group of people. Continue reading
Posted in History Through Spreadsheets
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My Robot Lawn Mowers
I am working today in my garage office at my cabin in northern Minnesota. From the office window, I can see a Worx Landroid robot mowing the lawn (Figure 1). I installed two of these mowers (one for garage and one for cabin) because I am not regularly at the cabin and wanted to ensure the lawn was mowed even when I could not be there. Continue reading
Posted in Cabin
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US Dairy Industry Stats
Early in my life, I spent quite a bit of time around cows on small farms with about 160 to 200 acres of land, and 40 to 50 cows. I never saw a corporate farm. Three years ago, I spent quite a bit of time in Iowa working on a number of fiber optic deployments in rural areas populated with a large number of dairy operations. While performing fiber installation inspections, I noticed that many of the old farmhouses were occupied by renters and the land was being farmed by corporations. As I looked around both Iowa and Minnesota, I realized that the number of dairy farms is dropping fast (Figure 1). Continue reading
Using Excel to Convert a Number List to Dashed String of Ranges
While working on a test report for an aircraft manufacturer this week, I needed to convert a large number of number lists to strings of dashed ranges. For example, suppose you are given a list {1, 2, 3, 5, 6, 7, 8, 10}. Converting this list to a dashed set of ranges means generating the string "1-3, 5, 6-8, 10." Figure 1 shows another example with an optional prefix added to each number. Continue reading
US Iron and Aluminum Mining During WW2
My vacation/retirement cabin is in the iron mining region of Minnesota. The rock throughout the area shows the reddish hue of iron. I recently heard some old-timers talking about how the intensity of mining operations during WW2 took the last of the high-grade iron ore (hematite –Figure 1) and left only low-grade ore (taconite). This comment made me curious about mining during WW2. Continue reading
Posted in History Through Spreadsheets
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Estimating Exponential Time Constants
I have been presented with a large amount of experimental data from which I need to determine many exponential time constants. There are so many time constants to calculate that I need to automate the process. Continue reading
Posted in General Mathematics
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Determining RMS Acceleration for a Vibration Acceleration Spectral Density
I was asked last week to write a vibration test plan for a mobile electronic product. I am used to writing vibration test plans that follow canned procedures in standards like MIL-STD-810F or SAE J1455, but this case is different because the customer has specified a non‑standard random vibration acceleration profile, which is also called a Power Spectral Density (PSD). I need to determine the RMS g level for this profile. This post shows how I go about this calculation. I am not going to showing the customer's vibration PSD because it is proprietary. Instead, I will use a well‑known US Navy vibration PSD as a computation example (Figure 1). Continue reading
Posted in General Mathematics
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