How to layout the Grizzly Flats dormer

Soon after posting the Grizzly Flats build a few months ago, a reader asked if I could post about the math for laying out the dormer roof. In his article, E. L. Moore gave a template for the dormer in HO-scale. Unfortunately, I made my N-scale bay window a little bigger than the plan, so I couldn't just shrink Mr. Moore's template down to N-scale and expect it to fit. I had to dust off a little of my high school geometry and draw a new one. It 's a bit boring, so I didn't post it then, but it can be useful for future scratchbuilt projects.

[Geometry of the basic roof shape.]

The thing to focus on is the basic shape of the roof and worry about the fancy cut-out later. Also, I haven't been in school for a long time, so my approach to the problem and its notation is probably old fashioned, so please bear with me. The key is to recognize where the right-angled triangles are, and then apply the Pythagorean theorem (that is, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides).

I should note that L (the width of the roof at the eaves) and h (the height to the peak from the eaves) can be measured from your building plans. W (the width of the dormer at the eaves) is something you prescribe. As I noted, because I didn't use the value of W that E. L. Moore noted in his plan, I had to recalculate x, y, and z.

That shaded triangle in the drawing is the one whose sides need to be calculated. It's a right-angled triangle, and so are the two triangles that make up the front face of the dormer. 

Once you've calculated the side lengths, x, y, and z, draw them on the material you're using to build the dormer and remember that x and y are perpendicular to each other. That'll give you a basic shape for the dormer roof panels. To accommodate the sloped, triangular cut-out in the dormer roof like the Grizzly Flats station has, just measure back along x and y from the 90-degree angle while you've got the panels on your drawing board.