Layout for Simple Japanese Hip Roof

Hello! Tonight we go further down the rabbit hole that is Japanese hip roof joinery. Where might it lead? To building of course! I’m not sitting here in my shop obsessively building joinery models as an attempt at some kind of mental masturbatory self indulgence. This is about a little corner of structure, a fundamental of human existence. It is then, as they say, an existential topic to speak of timber joinery.

I think most peoples experience with structure has been entirely sub-optimal. Except, maybe if you’ve lived on a boat. But for most of us we don’t even know what we’re missing. If you have the misfortune to live less than a comfortable first world existence then necessity becomes the drive that creates the idea of a better circumstance, and often a better structure.

Tonight I had the good fortune to speak with Mark Grable for a bit on the telephone, I found it galvanizing. You have to understand the potential out there for people that are willing to get shit done. How bad do you want it, how badly? Now go find out.

So, to get back to the topic at hand, I’m giving it another try with the simple Japanese hip roof model. This is walking step by step towards structure by understanding one small piece of it at a time.


We have our two keta beams joined together with a wedged mortise and tenon. By the way, my model is about half scale to what is listed in the book. My keta measure 60mm by 80mm. I feel awkward trying to explain this because my own understanding is so rudimentary, but here goes.

You can see that the layout starts quite simply with the hip centerline drawn on the top surface of the joined beams. Then the width of the hip rafter can be added in parallel to the centerline. Lucky for me this is a normal hip roof, symmetrical between the wall edges at 45 degrees.


Next I added the lines parallel to the top centerlines that represent  the top and bottom edge of the common rafter notches. Because there is a jack rafter projecting out from the end of the centerline of either beam the kogaeri line must extend into the layout for the hip rafter notch.  Then the cut lines for the rafter notches can fall in place. It does make things look a bit crowded in there.

I remember the first time I looked at these hip roof models and the layout for it. Mush! Unless your a genius its hard to work out what’s going on. Give things a name, order appears, and structure commences.


From there we can draw a series of lines perpendicular to the hip rafter, they all seem to have their own names too. You can see I’ve made a nice little series of squares by intersecting at the centerlines of the keta. There’s almost a hip rafter notch, but I’ll have to do a bit of layout on the hip rafter to find out where to place one of the cut lines on the keta.


I started the hip rafter layout with the middle honchu line. Where as the common pitch of the roof (rise/run) is 5/10, the hip rafter uses its own pitch, 5/14.14, based on the relationship of the normal hip rafter being the hypoteneuse of a right triangle whose two sides are equal.

With our hip rafter pitch we can mark both a level line and a plumb line. In this case I saved myself some time by grabbing the plumb line with my bevel gauge and referencing to the edge and not the centerline. In practice I wonder if that would be possible. This whole endeavor does seem to depend on quite carefully dimensioned and squared material. I wonder what acceptable tolerances are for beam cross section and squareness?


I made a mistake yesterday in the spacing of these lines, because I was measuring along the edge of the hip rafter and converting the distance between lines on the keta mathematically to the distance along the hip edge. I cut that out entirely this time, measuring equal distances along the level line of the hip rafter run.


I used the same method to transfer the distance to the back face of the keta beams. The distance between nyuchu line and the back face of the keta beam is equal to the distance between honchu line and the tip of the notch on the back. This ensures that we get a triangle that will be 45 degrees to plan when the hip rafter is at the proper slope. Remember how those three intersecting lines helped form a series of squares on the keta? Now they’re a bit stretched out on the bottom of the hip rafter.


Next I added the level baseline that intersects with the bottom rafter line and nyuchu. Because the baseline for this model is above the keta centerline 5mm I had to mark a line below the baseline that represents the top of the keta beams. This new line, “top of keta” extends to a new point where it hits the bottom of rafter line.


Last for the hip rafter was marking the front of the notch where it intersects with the side of the keta beam.


I’ve drawn some stars to help point out the new line derived from the hip rafter that is the start of the notch on the keta. All that was left from there was dropping the hip rafter notch lines down the side of the keta beam to the correct depth. I made a mistake there yesterday, hit the wrong numbers in the calculator or something. So I decided to get the numbers both mathematically and graphically.


This time apparently I did things okay. It wasn’t a perfect fit, but most of my marks lined up pretty well.


Pretty cool looking!


I did make one mistake, my jack rafters are not meeting the hip rafter in plane, but that was another simple mistake with how I marked the depth of the jack rafter line on the hip rafter, and I’m getting too tired to explain it properly. Sebastian and I will be cutting a slightly more complicated model next week some time, we’ll try to explain it together and I look forward to continue exploring this aspect of house joinery. Its quite challenging, but fun!

6 thoughts on “Layout for Simple Japanese Hip Roof”

  1. Save for explaining the half roof slope on the vertical side of the keta and how to cut the chamfer on the rafter you have done all the work for next week :p

    How you get the chamfer slope btw? In the book says 1/3 but i havent understood the why yet.

    Its funny what you say of the building, indeed a very existencia topic. Great work Gabe!

  2. And doubled….great work, you’re leaving the rest of us in the dust!

    God only knows what you guys will be up to by the time I can join in again, but there are plenty of really complex examples of joinery, taken from 16th century scrolls, that are in the Japanese house architecture book by Engel.

    Or I suppose that you will be actually constructing something……. a forge building, maybe?

    Thanks for the clear explanations in layout. This is exactly the type of information that I see being helpful to many others (like me!).


  3. Thanks guys! Truly, we are pulling each other along at times. Sebastian, I’ll need you to explain using the half roof slope, somehow I missed that? I found the chamfer on the hip rafter by measuring from the top edge along the level line of the hip rafter pitch half the width of the hip rafter. The depth of the chamfer is then the distance down from the edge to that point. Its directly from the chapter on hip rafter assemblies in “Japanese Joinery”, but I’m still confused as to why it works.

    I do hope to soon be putting this knowledge to the test, we’ll see.

  4. On your 9th photo you have the 10sqrt2 on top of the keta and 5 on the side. Since the angle is 45 the perpendicular to the to run is also 10sqrt2 tothe edge, so the distance on edge is 10×2. On the edge of the keta then you have a slope 5/20, ie half roof pitch. I made drawings but no computer atm

  5. Now that’s cool. Great job figuring the issues from last time. It definitely shows why joinery can require years of apprenticeship to master.

    To put all of this into practice will be amazing, constructing a structure entirely with joinery. I can’t wait to see it happen!

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