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.