Category Archives: Construction

I regularly encounter interesting math, particularly geometry, in my woodworking and remodeling projects.

Cabin Is Complete

My cabin construction project is now complete. My wife and I are now beginning to furnish our new home, which will take some time. I continue to work on the garage construction myself, which will take until sometime in May to finish. Overall, our planning was good and there were no major surprises. The one area of difficulty that I did not fully appreciate is the remoteness of the site. Before you go to the site, you need to plan out every possible tool or part that you will need while there. Continue reading

Posted in Construction, Personal | 10 Comments

Electrical Conduit Math

As I have mentioned in other posts, I am building a large garage in northern Minnesota (Figure 1). I would show you some pictures of the interior, but I have promised my son that I will not post anything that could ruin his surprise when he sees it in April.  As part of this construction effort, I am using quite a bit of electrical conduit. Conduit consists of metal pipes (often called EMT) through which the wires pass and it must be bent to go around any barriers it encounters. Conduit is a very efficient way to wire a working area because it directly attaches to the wall and does requires opening holes in drywall and  repairing the damage. Conduit can also be updated and modified easily by running new/additional wires through it. Continue reading

Posted in Construction | 2 Comments

Dealing with Furnace Condensate At Low Temperatures

While working on my retirement home and workshop in northern Minnesota, I have noticed that my furnace is generating between five and seven gallons of condensate per day. The furnace is on quite often this time of year because the outside temperature is running about -30°F (-35°C). I currently pipe the condensate over to a floor drain, which is connected to my septic system. Continue reading

Posted in Construction, General Science | 10 Comments

Change in US House Square Footage Over Time

My wife and I are about half-way through the construction of a 2100 square foot home in northern Minnesota. This weekend, my neighbors and I were talking about the area of houses being built today, and no one in the conversation had any data. I grabbed my computer, jumped on the Internet, and very quickly found data from the Census Department that answered my question. Like most census information, the data is in the form of screwy tables that need to be parsed to get into a form that can easily be plotted. This exercise gave me another excellent example to use when I train staff on the use of Excel's Get and Transform tool. Figure 1 was the result of my search. For those who are interested, my workbook is here. Continue reading

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Insulation Opportunity Costs

I have had a number of discussions with coworkers about the different types of wall insulation – some of these discussions have been documented in previous blog posts (e.g. here , here, here). There exists wide cost and performance disparities between the different wall insulation technologies. With respect to cost, I view fiberglass batts as a low-cost insulation option and the spray foams (open and closed cell) as high-cost options. All the options have their advantages and disadvantages. Fine Homebuilding Magazine (August/September 2017) has an excellent article by Martin Holladay provides an excellent spreadsheet-like analysis that illustrates the trade-offs between open and closed-cell foam nicely. My goal in this post is to go through the computational details of his analysis and to discuss his approach to choosing the best insulation for your application. Continue reading

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CO2 Generation By Fuel Per Million BTUs of Heat

My year-round cabin in northern Minnesota needs a furnace, and a furnace needs fuel. My fuel options are fairly limited – fuel oil, liquid natural gas, or propane. I ended up choosing propane because the local propane gas supplier has a reputation for being reliable. While researching the fuels, I became curious about the amount of CO2 released into the atmosphere by the different fuel options for given amount of heat. Continue reading

Posted in Construction, General Science | 1 Comment

My New Cabin Construction

A number of folks have asked that I post pictures of my cabin construction project. The project actually consists of two separate activities: a large garage (started last fall) and a two-story cabin. I will start posting photos here as things progress. Continue reading

Posted in Construction, Personal | 9 Comments

Effect of Earth's Curvature on Suspension Bridge Dimensions

I have received a number of questions recently on how the curvature of the Earth affects building construction. In general, the effects of the Earth's curvature are ignorable because most man-made construction is on too small of a scale to notice the effects of the Earth's curvature. One well documented exception is the Verrazano-Narrows bridge, whose design took into account that the bridge towers are 1 5/8 inch farther apart at the top than at the bottom. In this post, I will show how to compute this value. Continue reading

Posted in Construction, General Science | 6 Comments

Using Excel's Solver and VBA For Repetitive Table Calculation

I will be providing some employee training on Excel in January, and I need an example of how to automate the use of Excel's Solver add-in – a powerful optimization tool that few engineers use effectively. When I give a training seminar, I make a serious effort to show how I use Excel on real problems. While I generally use Mathcad for most optimization applications, Mathcad does not support integer programming – an optimization method where some or all variables are restricted to be integers. Here is where Solver shines – it supports integer programming. Continue reading

Posted in Construction, Excel | 5 Comments

Radius Measurement Using Roller Gages

This post will demonstrate how to measure the radius of an arc using two roller gages. While I am a very amateur machinist, I have on occasion needed to measure the radius of an arc (i.e. partial circle) and have not been sure how to approach that measurement. It turns out to be simple given two equal diameter roller gages and a surface plate. You can determine by taking one measurement and knowing the roller gage diameter. Continue reading

Posted in Construction, Geometry, Metrology | 3 Comments