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Author Archives: mathscinotes
The Cost of Minting Coins
I rarely think of the US government as producing any physical products, but there is one product that only it produces and that is extremely profitable – US money. The government sells money at its face value, which historically has had higher value than the cost of manufacturing it. In the year 2010, the US Mint generated $6.3 billion in profit from selling the money it manufactures. Continue reading
Posted in Financial
2 Comments
MTBF and Annualized Failure Rates
One of the more distasteful tasks I need to do is make estimates of annual product failure rates using MTBF predictions based on part count methods. I find this task distasteful because I have never seen any indication that MTBF predictions are correlated in any way with field failure rates. This is not solely my observation – the US Army has cancelled its use of part count method MTBF predictions (i.e. based on MIL-HDBK-217). However, the telecommunications industry has continued to use these predictions through their use of SR-332. If you want to see a simple example of an SR-332-based reliability prediction, see this very clear example from Avago. Continue reading
Posted in Statistics
8 Comments
Drag Coefficient From A Ballistic Drop Table
I thought it might be interesting show how you can approximate the drag coefficient for a bullet given a standard bullet velocity versus distance table. The folks at Barnes have put together a very nice discussion of how they go about characterizing a projectile using Doppler radar data. They also created an excellent infographic for a common hunting round showing the velocity versus distance table, actual drag coefficient, and G1/G7 reference drag coefficients (Figure 1). I thought I would take their table data and use that data to generate the drag coefficient chart. Since my data is limited, I do not expect a perfect reconstruction, but it should be close. Continue reading
Posted in Ballistics
1 Comment
Remakes Improving The "Robinson Crusoe on Mars" Theme
I just watched the movie The Martian with my oldest son, and I really enjoyed it (Figure 1). As I thought about the movie, it certainly was the best of the "man versus Mars" movies I have seen – and it was the first with a real sense of humor. Every so often, Hollywood rediscovers the escape from Mars theme and The Martian was the best of this genre yet. Continue reading
Posted in Personal
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Estimating The Lifetime of an Electrolytic Capacitor
Our optical products are powered by AC power converters (e.g. wall adapters, uninterruptible power sources) that we buy from outside sources. Over the last two weeks, I have been dealing with a number of aluminum electrolytic capacitor failures in these power products. Like all components, electrolytic capacitors eventually do wear-out (e.g. Figure 1). Unfortunately, their lives are relatively short (~15 years) compared to other components in the system. We have had some of these power sources in the field for nearly ten years, so we are starting to see some worn-out capacitors. Continue reading
Posted in Electronics
1 Comment
Mathcad Solution To XKCD Problem
XKCD is a great comic strip by Randall Munroe that takes a quirky look at the world of science. Randall recently posted a set of questions for a substitute teacher to pose to a math class that were interesting and attracted the attention of some problem-solving enthusiasts. Continue reading
Posted in General Mathematics
2 Comments
My Minnesota Accent
I am from a small town in Minnesota called Osseo. I had never traveled far from home until I finished my undergraduate work and moved to Ft. Collins, Colorado. When I arrived in Colorado, everyone that I met immediately knew I was from Minnesota – I had no idea that my accent was so strong. After living five years in Colorado, I also developed an ear for accents, and I also could pick out where people were from because everyone in Colorado was from somewhere else. Continue reading
Posted in Personal
2 Comments
Relative Sizes in Photographs Can Be Deceiving
I often see photographs that appear to show objects with different size relationships than we usually see. In Figure 1, for example, we see the Moon as nearly the same size as the sailboat. This happened because the sailboat is some distance from the camera and its angular extent is comparable to that of the Moon. Continue reading
Posted in optics
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Computing List Price from BOM Cost
All engineers must be familiar with the basics of product costing. In this post, I will cover a common product cost model (Figure 1) and provide two examples that illustrate how to calculate the list price of a product given the product's component costs plus some corporate parameters, like average discount rate and required gross margin. Continue reading
Posted in Financial
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