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  • Writer's pictureJim Martin

Pythagoras is my friend

We'll get to Pythagoras in a minute. First, I want to point out that the race is on! Once the first walls go up the whole structure becomes much more difficult to cover and protect from the rain. That's important because when plywood gets wet it can warp and de-laminate. That can be a real pain.

This means that we are essentially in an all-out sprint until the structure is "dried in"--meaning the exterior walls are covered with a vapor barrier (Tyvek), and the roof is covered with some kind of waterproof underlayment. It's going to be quite a journey to get there, but we have mapped it out and are going full-steam ahead.

Here are the basic bones of the front wall. It's shorter than the walls on either side because the sleeping loft will eventually sit on top of the wall and form the base of the two-foot overhang over the hitch. That large space in the middle will accommodate a 2' trapezoidal bump out that will hold the bathroom sink and a window in the upper portion, and some utilities underneath the sink. There's a bit of complexity to how that will attach to the trailer hitch, so framing that out is a project for another day.

Then the driver's side wall went in. It was a little tricky to get it laid out on the deck because the forward (loft) section of that final wall is so tall. But there was just enough room to assemble the wall lying down, and then stand it up in place. Here are the basic four walls of the structure!

The 2x4's sticking out toward us in this photo are the top plates for the cantilevered loft section. We'll get to finishing that framing as well as the trapezoidal bump out over the hitch soon.

Next we bolted the bottom plates to the trailer flange in ten places. These bolts went fast because they were short and there was no need to countersink them.

At this point it was time to check the basic framing to ensure that it was both square and plumb. This is the kind of stuff I geek out on a little bit. Some of you may know I began my professional career as a junior high math and science teacher. And every time a student complained about the seeming irrelevance of fractions, or right triangles, I would say, "Oh! if you are paying attention, this stuff comes up everywhere!"

Here are a couple of junior-high level real-world math applications.

How do you check a house (tiny or otherwise) to see if it's square? Here are just two simple but powerful methods:

  1. Measure the diagonals of the rectangle and compare the result. If they are equal, (or within a small fraction--say <3/16ths of an inch in this case), the structure is square.

  2. You can check three corners using the 3-4-5 method. This is based on the ancient geometric concept that any triangle will be a right triangle if it has legs measuring 3' and 4', and a hypotenuse measuring 5'. (Remember Pythagoras? He would say, "Of course! 3 squared plus four squared equals five squared. Easy.") It is also true, of course that multiples of three, four, and five will hold true as well. For example if one leg measures 6' and the other measures 8', the hypotenuse should measure 10'. And you only have to check three corners because if three are square, the fourth has to be also.

How do you check to see if a wall is plumb (straight up and down)? Of course a four foot level will work here, but there is also an ancient tool that can help you see if your corners are plumb in both directions at the same time. It's called a plumb bob. And it is, indeed, ancient. It shows up in Egypt over 4,000 years ago, and even gets a shout out from the Old Testament prophets Isaiah, Jeremiah, and Zechariah. It's a big deal--and elegant in its simplicity. All a plumb bob does is point straight down (well, straight toward the center of the earth, actually). If you need to find out if two points on a structure are vertically aligned, hang the plumb line from the top point, and the bob should point directly at the bottom point.

In my case, I made a mark four inches from the inside corner of the top wall plate and a corresponding mark on the bottom plate. I hung the plumb line from the top point and waited for it to stop swinging:

Not bad! Not bad at all. And what this means is that the corner is plumb in both directions. (Note: If the house had been out of square or plumb, I would have had to go through a process of loosening some of the screws holding the corners together and pushing/prying/banging with a small sledge until things were lined up. This is important because mistakes that this stage can become amplified as the building process continues.)

*climbs off soap box*

With the walls square and plumb, it was time to get some plywood on. The plywood serves as a structural underlayment for the eventual finished siding of the house. But more importantly at this stage, it stabilizes the structure and locks everything in place. With each sheet that goes on, the structure becomes more and more solid. It's so gratifying! Here's the first sheet of plywood attached! Here we used a combination of nail gun and 2.5 inch decking screws.

In this picture I'm almost finished framing out the section over the wheel well. There's a large "header" spanning the fender, then on top of the header the framing process continues: studs every 2' on center, and then the necessary framing for the picture window. There's also a header over the window as well. The purpose of these headers is to transfer the "load" of the structure down the wall without putting pressure on either the window or the fender--neither of which are designed to bear weight. The framing will be slightly different over the other fender only because the window on that side is of a different size and in a different position.

With that much done it was time to wrap up for the day. With rain in the forecast, we had to figure out how to protect the structure (or at least the plywood). Here's what it looked like at the end of the day (also note the second sheet of plywood on the right):

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