Category Archives: Construction

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

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

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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 | 4 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

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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

Homemade Roof Pitch Protractor

As an amateur carpenter, I am always looking for simple and cheap construction tools. Recently, I have been working on improving my roof framing knowledge. During my reading on this topic, I saw this roof pitch protractor in a Journal of Light Construction (JLC) article . Notice how the template has a handle to make hauling it up a ladder easier. To get an accurate roof pitch, all you need to do is clamp a spirit level onto the template – simple, fast, accurate. Continue reading

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What R-Value Is Good Enough?

I plan on retiring at my lake home in Northern Minnesota. The first step in my retirement preparations is building a large garage on my retirement property that will allow me to work on my various projects – I have not mentioned it before, but I love doing auto body work. I am currently building a garage similar to that shown in Figure 1. Because northern Minnesota is quite cold in the winter, I needed to insulate and heat this structure. This post will review some observations that I made as to the value of insulation and of using modern ventilation systems with heat recovery capability. Continue reading

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Effective R Value of Common Wall Construction Methods

Because the winters are hard in this part of the country, I have become interested in the insulation value of different types of wall construction. My contractor has his preferred approach, and I am curious as to how it compares with other framing methods.

In this post, I will put together a simple model for computing the R-value of different types of wall construction. This analysis will provide me a quantitative basis for understanding which methods are the most economically sound. Continue reading

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Shimming and Trimming Stairs to Equalize the Risers

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

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