Category Archives: General Mathematics

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

 
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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

 
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Let's Grow Some Oats

I am going to grow and process some oats this year. This is a project that I have been interested in doing for a while because one of my sons is now in the oat business and he has shown some interest in working through the entire oat processing cycle. As a boy, I used to mill oats on the family farm, but I remember very little of that time. Continue reading

 
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Measuring Countersink Angle Using Gage Balls

This post will cover how to measure a countersink angle using gage balls. Figure 1 shows how a countersink is normally specified on an engineering drawing. I frequently use countersinks in my wood and metal working hobbies. In addition, using gage balls to measure the countersink angle provides a good example of how to apply basic geometry concepts to a practical problem.  I use this example in my role as a volunteer adult math tutor at our local library. Continue reading

 
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Evenly Spaced Points on Logarithmic Graphic Using Excel

I am doing some testing at an Electromagnetic Compatibility (EMC) facility this week. Part of the test specification requires that we inject audio frequency interference on the power supply lines at discrete frequencies that range from 10Hz to 100+KHz, with 30 frequencies selected from each decade of frequencies (e.g. 10 Hz to 100 Hz, 100 Hz to 1 kHz, etc.). Figure 1 shows a specification similar to the one I am performing. My test facility that has chosen the discrete frequencies to be evenly spaced on a logarithmic axis. I started to wonder how the frequencies were selected – let's work through it. Continue reading

 
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Air Conditioning Load of a Group of People

I was reading an article about HVAC (Heating, Ventilation, and Air Conditioning) calculations in the Journal of Light Construction that had a quote I found interesting. It said that

… 17 extra occupants added more than a half ton of cooling load. Continue reading

 
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One Drink Per Hour Can Get You Drunk

Back in 2011, I wrote a blog post that goes into the details on how the Blood Alcohol Content (BAC) versus drinks/time/gender are computed (Figure 1). These charts tell people how much they can drink and still stay under the BAC limits for driving under the influence. These charts are for a typical drinker and the actual BAC value will vary by person. Continue reading

 
Posted in General Mathematics, Health | 3 Comments

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

 
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Daily Tree Consumption for Toilet Paper

I was reading an article on National Geographic when I spotted an interesting factoid about the impact of Toilet Paper (TP) world-wide tree consumption.

Toilet paper wipes out 27,000 trees a day.

Like many factoids, I doubt there is a way to actually measure this number – it can only be estimated. Thus, it is a prime candidate for a Fermi solution. Continue reading

 
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Probability That An Old President Does Not Finish Their Term

Ronald Reagan (Figure 1) was our oldest president at the time of inauguration – 69 years 349 days old. The 2016 US presidential election is giving us a choice of two candidates that will be relatively old at inauguration: Donald Trump (70 years, 220 days), and Hilary Clinton (69 years, 86 days). Since US presidents often serve 2 terms, it is conceivable they we may have a 77- to 78-year old president in 2024. This fact makes me curious as to what is the likelihood that a 70 year-old's natural life will be long enough for them to serve one or two terms. Continue reading

 
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