Hip Roof Model Fail


From “Wood Joints in Classical  Japanese Architecture” we have this wonderful little hip roof model, of the intersection between the wall sill plates, or keta, and the hip rafter/adjoining jack rafters. The model has a pitch of 5/10. So, how the hell to go about building this thing? Its a murky depth to probe at first. There’s something really important about having the pieces in your hand as you mark for cuts, looking at the orientation. I’m also working (almost) entirely in metric, the time saved converting decimals to inches is appreciated. I still want a sashigane with square root scale, even if it means working in shaku.


Ahh, the good old compound miter for the jack rafter. Top face marked 45 degrees to plan, side faces marked with common rafter 5/10 pitch using the carpenters square. Bread and butter stuff if you’re cutting a stick framed roof.


The top edge of the hip rafter is beveled to stay in the plane of the roof, and the jack rafter has to meet that plane evenly. So how do you find the angle for beveling the top of the hip rafter? It gets more interesting than that, there’s a common “pivot point”, or toge that represents where the bottom face of the rafter meets the base line of the top of the sill plate. Usually it would seem toge is often an imaginary point a little above the center line of the keta beams. It matters because the joinery has to be cut on the hip rafter such that the top planes that form the roof slope lie in the same plane as the common rafters, there’s a relationship there that is not immediately clear how to apply in layout for the cutting of the joint.

For the purposes of my model I made toge 5mm above the centerline.


The sashigane is the most important tool in this awesome adventure. Can you say, hip rafter pitch?


Finding the bevel angle for the top of the hip rafter involved measuring along a  level line on the side face representing the 5/14.14 pitch for a distance half the width of the hip rafter.


The same use of the sashigane gives the plumb line as well, along which you can measure the distance to the bottom line of the jack rafters. I realized at this point that I made my hip rafter too deep, not sure about the proper proportioning yet.


On the keta, we have the center line above which is our imaginary pivot point. Based on the common rise/run of 5/10 I know that the bottom of the jack rafters will contact the top of the beam 10mm away from the center line. On the side face of the beam we have the all important kuchiwaki line, representing the bottom of the jack rafter notch.


“The Complete Japanese Joinery” was my main reference for understanding the process of layout. But I’ve already made a terminal error in my marking here, not to be found until I started cutting.


The downward slope of the jack rafter notching continues from the kuchiwaki line where it intersects the perpendicular keta beam. From there I measured up to find the slope cut on the nose of the beam. I couldn’t tell from the model if it was supposed to be flush with the top of the beam or slightly below.


At least I did a bang on job with the wedged tenon. This is the first time I’ve tried the technique of drilling small stress relief holes at the bottom of the saw kerfs on the tenon.


It should have been a simple matter to measure the notch depth, somehow it became way lower on the left side and I didn’t notice the twist until I started chiseling out the waste.


My second and more serious error was in the joinery for the hip rafter. The cuts on the side were properly marked at 5/14.14 pitch, but the spacing between marks for the bottom I multiplied from the keta beam using the square root of two, effectively marking for a 10/10 pitch roof…


At least I’ve reached an understanding of my mistakes, and know how to mark correctly for the next try. But that is for tomorrow, all this thinking of angles and hypotenuse makes for a night dreaming of triangles.

9 thoughts on “Hip Roof Model Fail”

  1. Lol that’s great.

    I don’t understand well what’s the problem, only he distance between the notches or the angle of the notches themselves..

    For the distance between the notches, I think we need to start marking the parallel line with different colors. One of the most difficult parts open my model, and what I made wrong, was the distance between the notches. I needed to cut it first to understand that they are parallel and the distance between the centers is diagonal of the timber width.
    For the angles of the notches, I don’t know if you cut them right and made the picture with the rafter horizontal but it got me thinking in how I marked mines. It took me a while, could not remember how I computed that slope. Well, I didn’t. With the proper slope marked on the sides of the rafter, you take the perpendicular to the side and transfer the start and the end if the notch to the base, with that distance projected again from the side to the center line will give you the proper angles for the notches. Then you can use your bevel gauge to mark the other ones.

    So, what I would propose to do, would be to cut the joint properly, then paint all the surfaces that meet on the horizontal, vertical or sloped plane of one color, say red green and blue, and all the edges that are horizontal, vertical, roof pitch, half roof pitch and the other with another colors. That way you could see in each piece where each plane will end up once everything is out together.

    Once this is clearly explained, cutting the next one is a piece of cake.

    Love this joints, they make me feel like homer saying “douh” all the time.

    1. You definitely have the right idea with color coding this stuff. I’m excited to see your next model now that I can actually tell what the hell is going on.

  2. That is some seriously complex joinery! To get all of those pieces to fit well is quite a task.

    It was certainly a noble effort. I’m looking forward to seeing your next attempt. I’m sure it will be a success.

    It’s fascinating to see how things were made so long ago. I wonder how these construction techniques would stand up to today’s buildings and codes. (I’m sure they’re not to code, but I’d be curious if they’re as good as what code requires.)

    1. Thanks! I’m having a lot of fun working out how to make the layout for this joinery. There’s some interesting video of different Japanese homes on seismic shake tables. It still leaves me a bit confused as to the best practice for structural integrity, but that often has quite little to do with why building code is written the way it is today.

  3. I’ve got the Shinwa sashigane model #10014. On the back side it’s got circle rule, square rule, and mortice depth gauge. I bought it from some random Amazon Prime affiliate, about $28. I looooooove it!

    I wonder if I should interpret that as some sort of a sign, haha?

  4. The tolerance for each piece is one half a layout line. Or, as they say in the machine tool trade, “dead nuts on”.

    Check sashigane for straight, parallel edges, and square.

    They didn’t use calculators, they used KoKouGen and sashigane to find some angles, marking on a board, and pitch runs marking on the sides of the Hips. Not that I know how exactly, but those are the clues I have to work with. Oh, and the sequence of lines, I’m betting that’s key.

    There’s a drawing of the KoKouGen used in making a hopper at the end of “5 Practical Handsaw Exercises.

    1. Thank you for clearing that up for me. I’ve gotten the idea that center line rule can allow for less than perfectly square or straight lumber, but its obvious that most of the joinery requires quite carefully prepared material. Would you believe I almost felt like I was cheating to use a calculator for some of the hip layout? The KoKouGen triangles are fascinating, I’m just starting to see how it all relates. Time to make a hopper!

  5. can somebody give me the link for the kokougen triangles? Have no idea what we are talking about here. Or is it just the drawings from Mark’s text, which by the way we should digitalise and republish.

    I didn’t need to compute anything btw, just the sqrt2 and that was it.

    What Mark says about the sequence… so true. I’ve found that when I understand a drawing is becuase I can follow the process to produce the lines, in a certain order. Otherwise I just see a mess of lines without sense.

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