A Math Problem with a Model Roof

[LittleHaus]

I'm building a model of a German train station and I want to make a Jerkinhead roof ( clipped gable roof ) for it, but I feel like a jerk-in-the-head for not being able to figure out the math to make the measurements. Here is an example of the roof on a different N scale model:

https://pdf.grundschule-pretzschendo...um_Bahnhof.pdf

The height of the triangular portion of the roof depends on how much of an angle that clipped roof comes in. It seems like there is a simple mathematical way of doing these roofs, but I'm a rookie to building models and have not found the answer ( heck, I don't even know where to look ).

Simply put, I want to know how to figure out how high to make that triangular portion based on how deep it is cutting into the main roof.

Any help would be appreciated!

Connie

[Thumb Dog]

Hi All,

And hi, LittleHaus. My son has a degree in math from respected university, but he certainly didn’t get his aptitude from me. When confronted with a similar problem, I usually build a quick test model out of some blank card. Settle on the angle of your roof, draw and cut it out, and draw out, cut and glue a wall with its gable end that will fit under the cardstock roof. Don’t forget to leave enough overhanging eave. Make a good guess and snip out the triangle of your jerkinhead. Then, cut a separate paper triangle to fit. It won’t be perfect the first time, so do it again until you’re happy with the results. I found this process is a lot faster than fretting about the math. When done, write down your dimensions so you can use them on the other side of the building.

And the best part of all of this is you can now call yourself a scratch-building paper modeler.

Best of luck,

Score and fold,

Thumb Dog

[LittleHaus]

Thanks for your reply, Thumb Dog. I've been doing the trial and error method of making a test model with paper and then measuring the piece that ( eventually ) fitted, but I'm curious to know the math behind it, or at least a simple way to plot it directly without guessing.

If I was building a treehouse with a jerkinhead roof (not likely!) I wouldn't want to guess cut the wood until I got it right ( actually, in the case of cutting wood, it's easy to just mark it ).

Years ago, I did technical drawing, so I know there is a simple way to draw it - I just forgot what that way is!

[FRD]

If you want to know the mathematics involved, it's just a matter of looking at each triangle individually and using square root to determine the hypothesis of a right triangle, easier said than done.


I used to do it for fun when I was younger doing construction mathematics to calculate rafter framing but I'm old and grey now and forgot how to use square root to determine the hypothesis of a right triangle! (have fun!)

[sreinmann]

Okay, I'll take a stab. I think its best to use the Law of Sins.

Let's assume you know the pitch angle of your roof - that'll be angle B, probably acute. With that you'll also know the angles A and C. (also assuming that sides a and c are going to be equal).

Now, you need to determine your base and its a value you have to give and depends on how big a clip you want to get. That's side b.

Therefore SinB/b = SinA/a
You can cross multiply and remember that you know the values for b A and B and are looking to solve for a.
a * SinB = b * SinA
Google can calculate that if you plug it in and don't have a calculator btw.

Hope that helps.

[Vermin_King]

I do these things in Gimp. Set up a view for the roof edge, place the top and bottom connection points of the gable, and then place those onto the roof template. Then I make a line for the gable width and measure the lines. Create the template for each side of the gable roof from those measurements. I am assuming that 'clipped gable roof' is what we would call a hip roof around here. Again, it comes down to finding your connection points and measuring the lines, rotate the lines until they touch the corners. Scot suggests working from the angles, where I like rotating lines.

[LittleHaus]

Thanks all, for your replies. I'm going to try The Law of Sins tonight on a test model, sreimann. Vermin_King, yes, it's a hipped roof of sorts. Rotating lines on Gimp sounds like what I've been doing with pen and ruler on paper, but I don't understand how you can find the height of the side roof. It always seems to depend on how slanted the roof is. The more slanted, then the higher that side roof triangle needs to be. ( This is what comes from not paying attention to all those geometry lessons years ago ).

[Siwi]

Have a look at some videos by a railway modeller who makes the Youtube channel 'Chandwell Model Railway'. He has done some videos about precisely this sort of construction using Inkscape.

[Viator]

Originally Posted by LittleHaus

Thanks all, for your replies. I'm going to try The Law of Sins tonight on a test model, sreimann. Vermin_King, yes, it's a hipped roof of sorts. Rotating lines on Gimp sounds like what I've been doing with pen and ruler on paper, but I don't understand how you can find the height of the side roof. It always seems to depend on how slanted the roof is. The more slanted, then the higher that side roof triangle needs to be. ( This is what comes from not paying attention to all those geometry lessons years ago ).

If I understand you correctly, you are designing a model after the drawings or photographs of the real thing. So, if you have both the front view and the side view of the building with this roof in the orthographic projection, you can simply measure all the dimensions directly from the drawings.

[Vermin_King]

Originally Posted by Viator

If I understand you correctly, you are designing a model after the drawings or photographs of the real thing. So, if you have both the front view and the side view of the building with this roof in the orthographic projection, you can simply measure all the dimensions directly from the drawings.

Nice. I used to be a draftsman in college, back when they did drafting. This is what I translated to the Gimp method, as best I could