Author Archives: mathscinotes

My Personal PCB Design and Build Process

Posted on 13-July-2016 by mathscinotes

I have been designing circuits since I was a boy, and my passion for circuits has only grown over time. My home designs focus on sensor interfaces that I hook up to the Internet using Raspberry Pie and Arduino digital interfaces. These open-source HW interfaces make it possible to create incredibly powerful designs at home. Continue reading →

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Dealing with Climate Change Denial

Posted on 12-July-2016 by mathscinotes

I have lunch with all sorts of people. Occasionally, I end up sitting with a climate change denier, which happened today. Usually, I do not say anything because I really do not want an argument.

Today, I decided to mention Figure 1, which summarizes a set of measurements made since 1900 that show that sea level is rising. I then asked the climate change denier if they can explain the fact that sea level is rising –a fact has been confirmed by multiple measurements taken at multiple sites over more than 100 years. Continue reading →

Posted in General Science | 1 Comment

Withdrawal Force Rating for Various Nails

Posted on 11-July-2016 by mathscinotes

I have been reading some specifications on fastener requirements in carpentry. To ensure that I understand what I am reading, I decided to see if I could duplicate the design values for nailed connections. In this post, I will duplicate a table (Figure 1) for the withdrawal force ratings of various nails when used in a toe-nailed connection. In general, I try to avoid nails with a withdrawal load, but it is an allowed connection and it was easy to duplicate the results in a National Design Specification (NDS) document. I will be performing a similar computation for the lateral load rating in a later post. My Mathcad source and a PDF are stored here. Continue reading →

Posted in Construction | 3 Comments

Lightning-Induced Surge on Cable Wiring

Posted on 9-July-2016 by mathscinotes

Because I have had to deal with lightning in all sorts of contexts (e.g. military equipment, commercial hardware, consumer products), I have developed an enormous respect for the power of lightning (Figure 1). Because of this respect, I have worked to ensure that my own home has excellent lightning protection, including a sophisticated ground system. Even with all my precautions, last weekend lightning struck near my home and caused my garage door to open – letting rain into the garage, and my garage door opener to become unresponsive. Fortunately, I just had to cycle power again on the garage door opener and it started to work. Continue reading →

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Molarity, Molality, Mass Fraction Conversion Formula

Posted on 8-July-2016 by mathscinotes

I am doing some work with lead-acid batteries and their state of charge versus their H2SO4 electrolyte concentrations. While we normally use specific gravity to assess a battery's state of charge, some folks use molality (m), molarity (M), or mass fraction (w). These concentration metrics are all related by relatively simple formulas (Figure 1). Continue reading →

Posted in Batteries | 1 Comment

Volume Reduction in Ethanol-Water Mixtures

Posted on 2-July-2016 by mathscinotes

I recently toured a winery and, during the tour, I saw a number of charts related to various properties of ethanol and water mixtures. I was a bit puzzled when I saw Figure 1, which is a chart that I had never seen before. Figure 1 shows the amount of volume reduction experienced by an ethanol-water mixture compared to the separate volumes of the water and ethanol. I became curious about the chart and decided to see if I could derive these results on my own. Continue reading →

Posted in General Science | 3 Comments

Winery Tour – Domaine Carneros

Posted on 1-July-2016 by mathscinotes

I like to collect vineyard trivia while on these tours and this trip was no exception. Since I do not drink, my interests tend to focus on the farming aspects of the operations. I have discussed winery trivia before in this post. All photos in this post were taken by me. Continue reading →

Posted in Farming | 2 Comments

3D Plot Example Using PCB Trace Current vs Trace Area and Temperature Rise

Posted on 21-June-2016 by mathscinotes

I was asked this morning about how to create a 3D plot in Mathcad that shows a surface, two lines on the surface, and marks the point of intersection of the two lines (Figure 1). It just so happens that I have been looking at the amount of current that a PCB trace of a given area can carry for a given temperature rise above ambient. While the curve itself is a bit boring and viewing it in 3D does not add any value, this example does illustrate the procedure for generating this type of plot. Continue reading →

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A Little Analysis of a Visible Exoplanet

Posted on 20-June-2016 by mathscinotes

I saw an article in the popular science press about a real rarity – an exoplanet that can be seen (Figure 1). I dug around the web and found the journal article on which most of the press articles were based. Given their measurement data, I wanted to see if I could duplicate some of their computed exoplanet characteristics. In this post, I will be using some of the techniques learned about while listening to The Search for Exoplanets: What Astronomers Know. Continue reading →

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Extended Reach PoE Example

Posted on 16-June-2016 by mathscinotes

The popularity of Power Over Ethernet (PoE) has proven that customers find value in using a single cable for both data and power distribution. Unfortunately, copper-based Cat 5e/6 cable is limited to a 100 meters because of data transmission issues. To circumvent this limit, some equipment vendors are using composite fiber/copper cables – a single cable that contains fiber for data and large gauge copper wire for power distribution (Figure 1). Continue reading →

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