Author Archives: mathscinotes

Calculating a Parameter's Worst-Case Range

Posted on 19-August-2016 by mathscinotes

Many electronic systems are required to generate an alarm when they detect their power failing – the alarm is referred to as a "dying gasp". These systems are required to generate a dying gasp alarm when their input voltage drops below a specified level. Continue reading →

Posted in Electronics | 3 Comments

The Tyranny of the Spreadsheet Cell

Posted on 15-August-2016 by mathscinotes

I had a conversation the other day with an engineer to whom I was expressing my frustrations with using Excel to process large data sets of complex numbers. She also has processed large data sets with Excel and commented that she found the processing painful. I told her about how I was using Excel to work with my data sets, but my techniques all seemed contrived and overly complex. While you can use Excel to work with these data sets, it is a bit like trying to use a Swiss Army knife as a screwdriver. Yes, it can turn a screw but there are much better ways! Continue reading →

Posted in software | 8 Comments

Asteroid Impact Damage Estimate

Posted on 12-August-2016 by mathscinotes

I have seen a number of articles in the popular scientific press about asteroid 1997 XF11 and the close approach it made to Earth back in June. The June approach was not that close – ~27 million kilometers. The closest approach is expected in 2028 and will be 980,000 km or 2.4 times the average Earth-Moon distance. Continue reading →

Posted in Astronomy | Comments Off on Asteroid Impact Damage Estimate

Planetary Atmosphere Leakage

Posted on 3-August-2016 by mathscinotes

I have always been interested in the fact that some planets have atmospheres and others do not. At the time of formation, planets have a primary atmosphere that consists largely of light elements (hydrogen and helium) – Earth has a secondary atmosphere formed outgassing from tectonic activity and comet impact residue. For small bodies, these low-molecular weight elements escape into space. I had never looked at how these gases escaped until I recently found a Wikipedia article about how gases escape from planetary atmospheres (e.g. Figure 1), and the math and physics involved were too enticing to pass up. Continue reading →

Posted in Astronomy | 3 Comments

Fiber Optic Cable and Lightning

Posted on 1-August-2016 by mathscinotes

Lightning is a tough problem. All of my personal electronic systems are well grounded and have the best surge protection I can buy. Yet I still suffer occasional losses due to lightning – for example, this weekend I replaced a surge-blown power adapter at my cabin in northern Minnesota. Intuitively, you would think that fiber optic systems should be better protected against lightning strikes than copper-based systems because glass fiber does not conduct electricity. This is not necessarily true. Continue reading →

Posted in Fiber Optics | 9 Comments

10,000 Boomers Turning 65 Everyday

Posted on 30-July-2016 by mathscinotes

The front-end of the baby boomers began to turn 65 in 2011 and they will continue to turn 65 until 2029. I started to wonder how many boomers are turning 65 every day? The Social Security Administration estimates that 10,000 Americans are turning 65 every day (source). As I thought about, I should be able to estimate the number of people that are turning 65 every day by examining graphs of the US population and birth rate (Figure 1). It is a nice Fermi problem and the subject of this post. Continue reading →

Posted in General Mathematics | 6 Comments

Airliner vs Car Fuel Usage

Posted on 26-July-2016 by mathscinotes

As I looked at the cost of airline tickets versus driving, I became curious as to how much fuel was used to fly me out to a Montana airport such as in Bozeman or Butte. I was surprised to learn that airliners can be quite fuel efficient compared to cars. This post contains my analysis. Continue reading →

Posted in General Science | 10 Comments

Shimming and Trimming Stairs to Equalize the Risers

Posted on 23-July-2016 by mathscinotes

In this post, I will show how to generalize my previous stair solution to handle these three cases. I also present some illustrations of what is involved in adjusting the stairs. The general solution used a Mathcad program to compute both the final riser height and the thickness of the shims or trim cuts required for each step. In general, you may need a combination of shims and trim cuts to resolve a riser height problem caused by changes in flooring height. Continue reading →

Posted in Construction | 2 Comments

Lateral Force Rating for Various Nails

Posted on 19-July-2016 by mathscinotes

I am an amateur carpenter, and I work hard to ensure that I always comply with the applicable building codes. The various codes include requirements for a properly nailed joint (examples). Since I like to understand where these requirements come from, I have been the reading some sections of the National Design Specification for Wood Construction (NDS) that address fastening. During my reading, I saw many interesting formulas associated with determining the NDS design ratings for nail withdrawal (covered here) and lateral force resistance – the subject of this post. Continue reading →

Posted in Construction | Comments Off on Lateral Force Rating for Various Nails

Layout Formula for a Balustrade

Posted on 16-July-2016 by mathscinotes

I am about to begin some construction on my cabin in northern Minnesota, and the design of the stairs has been on my mind. I consider well-designed stairs to be both beautiful and functional. A major factor in making a stairway beautiful is its balustrade – a railing with supporting spindles (aka balusters). The balustrade for a stairs is often referred to as a banister. Continue reading →

Posted in Construction | 3 Comments